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Structural Adhesive Joints

Scrivener Publishing 100 Cummings Center, Suite 541J Beverly, MA 01915-6106 Adhesion and Adhesives: Fundamental and Applied Aspects The topics to be covered include, but not limited to, basic and theoretical aspects of adhesion; modeling of adhesion phenomena; mechanisms of adhesion; surface and interfacial analysis and characterization; unraveling of events at interfaces; characterization of interphases; adhesion of thin films and coatings; adhesion aspects in reinforced composites; formation, characterization and durability of adhesive joints; surface preparation methods; polymer surface modification; biological adhesion; particle adhesion; adhesion of metallized plastics; adhesion of diamond-like films; adhesion promoters; contact angle, wettability and adhesion; superhydrophobicity and superhydrophilicity. With regards to adhesives, the Series will include, but not limited to, green adhesives; novel and high-performance adhesives; and medical adhesive applications. Series Editor: Dr. K.L. Mittal P.O. Box 1280, Hopewell Junction, NY 12533, USA Email: [email protected] Publishers at Scrivener Martin Scrivener ([email protected]) Phillip Carmical ([email protected])

Structural Adhesive Joints Design, Analysis and Testing

Edited by

K.L. Mittal and S. K. Panigrahi

This edition first published 2020 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA © 2020 Scrivener Publishing LLC For more information about Scrivener publications please visit www.scrivenerpublishing.com. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions. Wiley Global Headquarters 111 River Street, Hoboken, NJ 07030, USA For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com. Limit of Liability/Disclaimer of Warranty While the publisher and authors have used their best efforts in preparing this work, they make no rep­ resentations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchant-­ ability or fitness for a particular purpose. No warranty may be created or extended by sales representa­ tives, written sales materials, or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further informa­ tion does not mean that the publisher and authors endorse the information or services the organiza­ tion, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Library of Congress Cataloging-in-Publication Data ISBN 978-1-119-73643-1 Cover image: Pixabay.Com Cover design by Russell Richardson Set in size of 11pt and Minion Pro by Manila Typesetting Company, Makati, Philippines Printed in the USA 10 9 8 7 6 5 4 3 2 1

Contents Preface xiii

Part 1: General Topics

1

1 Surface Preparation for Structural Adhesive Joints Anushka Purabgola, Shivani Rastogi, Gaurav Sharma and Balasubramanian Kandasubramanian 1.1 Introduction 1.2 Theories of Adhesion 1.2.1 Mechanical Interlocking 1.2.2 Electrostatic (Electronic) Theory 1.2.3 Diffusion Theory 1.2.4 Wetting Theory 1.2.5 Chemical Bonding Theory 1.2.6 Weak Boundary Layer Theory 1.3 Surface Preparation Methods 1.3.1 Degreasing 1.3.1.1 Vapor Degreasing 1.3.1.2 Ultrasonic Vapor Degreasing 1.3.1.3 Other Degreasing Methods 1.3.2 Mechanical Abrasion 1.3.3 Chemical Treatment 1.3.3.1 Acid Etching 1.3.3.2 Anodization 1.3.4 Physical Methods 1.3.4.1 Corona Treatment 1.3.4.2 Flame Treatment 1.3.4.3 Plasma Treatment 1.4 Surface Preparation Evaluation Methods 1.4.1 Dyne Solutions 1.4.2 Water-Break Test

3 4 6 6 7 7 8 10 10 11 12 12 13 14 15 17 17 17 20 20 22 22 23 24 24 v

vi  Contents 1.4.3 Contact Angle Test 1.5 Applications of Structural Adhesives 1.5.1 Adhesives for Aerospace 1.5.2 Adhesives for Marine Applications 1.5.3 Adhesives for Medical and Dental Applications 1.5.4 Adhesives for Construction 1.5.5 Adhesives for Automotive Industry 1.5.6 Adhesives for Electronics 1.6 Summary Acknowledgment References

24 25 25 26 26 27 28 28 29 29 30

2 Improvement of the Performance of Structural Adhesive Joints with Nanoparticles and Numerical Prediction of Their Response 35 Farid Taheri 2.1 Introduction 36 2.1.1 Historical Perspective 36 2.1.2 Incorporation of Fillers in Adhesives 38 2.2 Use of Nanocarbon Nanoparticles for Improving the Response of Resins and Adhesives 41 2.3 Assessment of Performance of Adhesively Bonded Joints (ABJs) 54 2.3.1 Brief Introduction to the Procedures Used for Assessing Stresses in ABJs 54 2.3.2 Computational Approaches for Assessing Response of ABJs 56 2.4 Application of CZM for Simulating Crack Propagation in Adhesively Bonded Joints 60 2.4.1 Basis of the CZM 60 2.4.2 Applications of CZM to Bonded Joints 62 2.5 Application of xFEM for Simulating Crack Propagation in Adhesively Bonded Joints 66 2.6 Summary 69 Acknowledgement 70 References 70 3 Optimization of Structural Adhesive Joints P. K. Mallick 3.1 Introduction 3.2 Joint Configurations

79 79 80

Contents  vii 3.3 Joint Design Parameters 3.4 Substrate Stiffness and Strength 3.5 Adhesive Selection 3.6 Hybrid Joints 3.7 Summary References 4 Durability Aspects of Structural Adhesive Joints H. S. Panda, Rigved Samant, K. L. Mittal and S. K. Panigrahi Abbreviations Used 4.1 Introduction 4.2 Factors Affecting Durability 4.2.1 Materials 4.2.1.1 Adhesives 4.2.1.2 Adherends 4.2.2 Environment 4.2.2.1 Moisture 4.2.2.2 Coefficient of Thermal Expansion (CTE) 4.2.3 Stress 4.3 Methods to Improve Durability 4.4 Summary References 5 Debonding of Structural Adhesive Joints Mariana D. Banea 5.1 Introduction 5.2 Design of Structures with Debondable Adhesives (Design for Disassembly) 5.3 Techniques for Debonding of Structural Adhesive Joints 5.3.1 Electrically Induced Debonding of Adhesive Joints 5.3.2 Debonding on Demand of Adhesively Bonded Joints Using Reactive Fillers 5.3.2.1 Nanoparticles 5.3.2.2 Microparticles 5.4 Prospects 5.5 Summary Acknowledgements References

83 88 89 92 93 94 97 98 99 100 101 101 111 123 123 124 125 127 128 129 135 135 138 140 140 141 141 145 151 152 152 152

viii  Contents

Part 2: Analysis and Testing

159

6 Fracture Mechanics-Based Design and Analysis of Structural Adhesive Joints 161 Jinchen Ji and Quantian Luo Abbreviations and Nomenclature 161 6.1 Introduction 163 6.1.1 Analysis Methods of Adhesive Joints 164 6.1.2 Design Philosophy of Adhesive Joints and Fracture Mechanics Based Design 166 6.2 Stress Analysis and Fracture Modelling of Structural Adhesive Joints 167 6.2.1 Stress Analysis and Static Strength of Structural Adhesive Joints 168 6.2.1.1 Shear-Lag Model and Shear Stress 168 6.2.1.2 Beam-Adhesive Model, Shear and Peel Stresses 171 6.2.1.3 Load Update of a Single Lap Joint in Tension 177 6.2.2 Analytical Approaches of Linear Elastic Fracture Mechanics 180 6.2.2.1 An Approach Based on Adhesive Stresses for the Joint Under General Loading 180 6.2.2.2 Methods Based on a Beam Theory and a Singular Field 184 6.2.3 Fracture Prediction Using Cohesive Zone Model 185 6.2.3.1 Cohesive Zone Model 186 6.2.3.2 Cohesive Traction Law 186 6.2.3.3 Design Criteria Based on Cohesive Zone Model 187 6.3 Finite Element Modelling and Simulation 187 6.3.1 Finite Element Modelling for Stress Analysis of Adhesive Joints 188 6.3.2 Virtual Crack Closure Technique 188 6.3.3 Cohesive Zone Modelling and Progressive Failure 189 6.4 Experimental Approach and Material Characterization 190 6.4.1 Specimen and Test Standard 191 6.4.2 Data Reduction and Fracture Toughness, Mixed Mode Fracture 192 6.4.3 Measurement of Fracture Parameters and Progressive Failure Using DIC 192

Contents  ix 6.5 Prospects 193 6.5.1 Analytical Modelling and Formulation 193 6.5.2 Cohesive Zone Model and Progressive Fracture 193 6.5.3 Experimental Study on Fracture of Adhesive Joints 194 6.5.4 Optimal Design of Adhesive Joints and Use of Nanomaterials 194 6.6 Summary 195 References 195 7 Failure Analysis of Structural Adhesive Joints with Functionally Graded Tubular Adherends 205 Rashmi Ranjan Das 7.1 Introduction and Background Literature 206 7.2 Material Property Gradation in the Structural Adhesive Joint Region 210 7.3 Stress Analysis 212 7.4 Summary and Conclusions 216 References 217 8 Damage Behaviour in Functionally Graded Structural Adhesive Joints with Double Lap Joint Configuration S. V. Nimje and S. K. Panigrahi List of Symbols 8.1 Introduction 8.2 FE Analysis of Functionally Graded Double Lap Joint 8.2.1 Modelling of Double Lap Joint 8.2.2 Loading and Boundary Conditions 8.2.3 Modeling of Functionally Graded Adhesive Layer 8.2.4 Meshing Scheme of Double Lap Joint 8.2.5 Error and Convergence Study 8.3 Damage Onset in a Double Lap Joint 8.4 Adhesion/Interfacial Failure Propagation Analysis 8.4.1 Evaluation of SERR 8.5 Interfacial Damage Propagation Analysis 8.5.1 Onset of Adhesion/Interfacial Failure 8.5.2 Interfacial Failure Propagation in Double Lap Joint with Mono-Modulus Adhesive 8.5.3 Interfacial Damage Propagation in Functionally Graded Double Lap Joint 8.6 Conclusions References

221 222 222 227 227 229 229 231 231 233 234 235 237 237 238 240 242 243

x  Contents 9 Impact, Shock and Vibration Characteristics of Epoxy-Based Composites for Structural Adhesive Joints Bikash Chandra Chakraborty and Debdatta Ratna Descriptions of Abbreviations Symbols with Units 9.1 Introduction 9.2 Dynamic Viscoelasticity 9.2.1 Example 9.3 Toughened Epoxy Resins 9.3.1 Toughening Agents for Epoxy 9.4 Flexible Epoxy System 9.4.1 Vibration Response for Joined Beams 9.4.2 Experimental Evaluation 9.4.3 Flexible Epoxy-Clay Nanocomposite 9.5 Shock Response of Metallic Joints with Epoxy Adhesives 9.5.1 Shock Pulse: Fourier Transform 9.5.2 Shock Response 9.6 Summary References

247 248 249 250 252 255 257 258 263 265 268 270 274 275 277 283 284

10 Delamination Arrest Methods in Structural Adhesive Joints Used in Automobiles 289 P. Ramesh Babu 10.1 Introduction 290 10.2 Delamination Growth Studies in Laminated FRP Composite Bonded Joints 290 10.2.1 Analysis of Embedded Delaminations 291 10.3 Laminated Curved Composite Skin-Stiffener Joint Geometry and Material Properties 292 10.3.1 Configurations of the Models with Pre-Embedded Delamination 293 10.3.2 Loads and Boundary Conditions of the Joint for the Delamination Analysis 295 10.4 Finite Element Modelling with Embedded Delamination 295 10.5 Numerical Method for the Delamination Analysis 296 10.6 Computations of SERRs for Hybrid Laminated Curved Composite Skin-Stiffener Joint 298 10.7 Studies of Crack Growth Arrest with Fasteners in Bonded Joints 304 10.7.1 Modelling and Analysis of Skin-Stiffener Joint with Fasteners at Embedded Delamination 304

Contents  xi 10.8 Study of Crack Growth Arrest Mechanisms with Z-Fibre Pins in Composite Laminated Joints 307 10.9 Modelling and Analysis of Skin-Stiffener Joints with Z-Fiber Pins at Embedded Delamination 307 10.9.1 Estimation of Crack Growth Arrest (a) with Single Row of Z-Fiber Pins Reinforcement (b) with Multiple Rows of Z-Fiber Pins Reinforcement (c) Influence of Diameter and Space in between the Reinforced Pins on Fracture Toughness of the Composite Laminated Joint 308 10.10 Conclusions 312 10.11 Scope of Future Work 315 References 315

Index 319

Preface Among the myriad techniques available for mating/joining similar and dissimilar materials (metals, plastics, glass, ceramics and composites) the adhesive bonding technology is preferred and widely used because it offers many advantages vis-a-vis the other methods of joining, e.g., mechanical fastening, riveting, nailing, brazing and welding. Adhesive bonding is used for mundane (gluing of toys) to highly sophisticated applications. Most structures are comprised of a number of individual parts or components which have to be connected to form a system with integral load transmission path. The structural adhesive bonding represents one of the most enabling technologies to fabricate most complex structural configurations involving advanced materials (e.g., composites) for load-bearing applications. Even a cursory look at the literature will evince that there is a brisk activity in all relevant aspects to enhance the performance and durability of structural adhesive joints. Recently there has been activity in harnessing nanotechnology (use of nanomaterials) in ameliorating the existing or devising better performing structural adhesives. It should be emphasized that proper (adequate) surface preparation is sine qua non for high joint strength. Concomitantly, depending on the surfaces to be bonded, there is much interest in coming up with environmentally-benign (green) surface cleaning and modification techniques. Apropos, surface contaminants are a bête noire to an adhesive bond. Also, there is much interest in modeling and simulation of structural adhesive joints. The book comprising 10 chapters written by eminent researchers is divided into two parts: Part 1: General Topics and Part 2: Analysis and Testing. The topics covered include: surface preparation for structural adhesive joints; use of nanoparticles in enhancing performance of structural adhesive joints; optimization of structural adhesive joints; durability aspects of structural adhesive joints; debonding of structural adhesive joints; fracture mechanics of structural adhesive joints; failure analysis of structural adhesive joints; damage behavior in functionally graded xiii

xiv  Preface structural adhesive joints; impact shock and vibration characteristics of composites for structural adhesive joints; and delamination arrest methods in structural adhesive joints. It should be recorded here that all chapters were rigorously reviewed and all were suitably revised (some twice or thrice). So the material presented in this book is of archival value and meets the highest standard of publication. The book consolidates in an easily accessible volume the current state of structural adhesive joints and reflects the cumulative wisdom of a number of researchers actively engaged in the arena of structural adhesive joints. The book is profusely referenced and copiously illustrated. The book should be of immense interest to those involved in the mechanics of adhesive joints, adhesive bonding, and structural adhesive joints. Also the book should be of much use to adhesionists, materials scientists, polymer scientists and those working in construction, railway, automotive, aviation, bridge, and ship industries. As more advanced adhesives and adherend materials become available, the applications and use of structural adhesive joints will proliferate. Now it is our pleasant task to thank all those who were instrumental in making this book possible. Obviously, first and foremost our sincere and heartfelt thanks go to the authors for their keen interest, sustained enthusiasm, unwavering cooperation and sharing their valuable research experience in the form of written accounts without which this book would not have seen the light of day. We will be remiss if we fail to extend our thanks to Martin Scrivener (publisher) for his steadfast interest in and wholehearted support for this book endeavor. Kash Mittal P.O. Box 1280 Hopewell Jct., NY 12533 E-mail: [email protected] S. K. Panigrahi Defence Institute of Advanced Technology Pune, India

Part 1 GENERAL TOPICS

1 Surface Preparation for Structural Adhesive Joints Anushka Purabgola1, Shivani Rastogi1, Gaurav Sharma1 and Balasubramanian Kandasubramanian2* Nanomaterials Characterization Lab, Center for Converging Technologies, University of Rajasthan, JLN Marg, Jaipur, Rajasthan, India 2 Nano Surface Texturing Lab, Department of Metallurgical and Materials Engineering, Defence Institute of Advanced Technology (DU), Girinagar, Pune, Maharashtra, India

1

Abstract

Advanced structures require materials that can provide high tensile strength, modulus, along with good load bearing capacity. Several structural adhesives provide good strength to joints made of different materials. The applications of structural adhesives range from domestic appliances to ships and aircraft along with medical and dental fields. However, an efficient adhesion of the structural adhesives to adherends requires various surface treatment methods to be performed prior to the application of adhesives. These modification methods alter the surface free energy and impart distinct polar groups (-OH, -C=O) on the adherend which act as new receptive sites for adhesion. These surface treatment methods are basically divided into degreasing methods, mechanical abrasion methods (e.g., grit blasting), chemical modification methods (acid-etching, anodization, etc.), and physical treatment methods (corona treatment, flame treatment, plasma treatment, etc.). This chapter describes various surface preparation methods for the efficient application of structural adhesives along with theories of adhesion, surface treatment evaluation tests, applications, and future scope of structural adhesives. Keywords:  Tensile strength, surface treatment, degreasing, chemical modifications, physical treatment

*Corresponding author: [email protected] K.L. Mittal and S. K. Panigrahi (eds.) Structural Adhesive Joints: Design, Analysis and Testing, (3–34) © 2020 Scrivener Publishing LLC

3

4  Structural Adhesive Joints

1.1 Introduction Structural adhesives can be considered as high strength glues, used to hold two substrate surfaces with load-bearing permanent bonds [1]. The structural adhesives offer high modulus, high strength, and flexible bonds to produce lightweight materials [2] capable of maintaining structural integrity even under high stress. This cost-effective method of fabricating stress-bearing materials also provides the advantage of protection against corrosion [3]. The structural adhesives help in maintaining structural integrity of the materials by their ability of transmitting structural stress across the interface when subjected to high loads. The bonding of substrate surfaces using structural adhesives may result due to van der Waals forces, electrostatic attraction, or chemical bonding arising between the surfaces and adhesives (Figure 1.1). The structural adhesives are generally in liquid form during application between the surfaces, giving wettability to the surfaces followed by curing, thus resulting in rigid, high molecular weight and crosslinked attachment between adhesive and adherend. The structural adhesives are used in aircraft, ships, medical/dental, automotive, domestic appliances, electronics, and construction applications because they provide excellent loadbearing capability [4, 5]. The most widely used structural adhesives include silicones, epoxies, acrylics, urethanes, etc. [5]. The substrates that can be joined using structural adhesives include metals, composites, rubber, plastics, biomaterials (wood and honeycomb panels), etc. [6]. The binding and fabrication of materials using structural adhesives depends on a variety of factors including selection of suitable adhesive, surface preparation of adherend, quality control, proper joining design, etc. Out of all these requirements, surface preparation of the materials to be joined is an important aspect in the field of adhesive bonding. The surface preparation

Substrate 1 Substrates

Adhesion

Adhesion

Cohesion Adhesive Molecule

Adhesive

Figure 1.1  Interaction between adhesive and substrates.

Substrate 2

Surface Preparation for Structural Adhesive Joints  5 of materials prior to the application of structural adhesives is preferred because of the following reasons [6]: • To ensure the formation of strong layer on the surface; • To provide the maximum substrate surface for optimum molecular interaction between the adhesive and adherend; • To ensure achievement of significant joint strength for better stress transmittance across the interface; • To create specific voids/cavities/microstructures or to alter the chemical structure of surface in order to alter the surface free energy for proper adhesive bonding. The basic surface preparation methods employed prior to the application of structural adhesive include degreasing, mechanical abrasion, and chemical treatments. The degreasing of joint surfaces works by removing the traces of oil and grease contaminants and providing clean and contaminant-free surface to be joined. The degreasing of the joint surfaces can be done via multiple ways such as vapor degreasing, ultrasonic degreasing, and immersion/ spray/solvent wipe degreasing. Another surface preparation method with the advantages of simplicity and ease of performance is the mechanical abrasion. Mechanical abrasion methods (like grit blasting) remove most of the surface deposits (metal deposits such as tarnish, rust and mill scale) and provide joint materials with rough surfaces in order to enable the formation of strong bonds. The mechanical abrasion method is always followed by degreasing to remove the loose materials produced on the abraded material. The chemical treatment or electrolytic pretreatment is another surface preparation method which results in the joint surfaces with optimum strength, reproducibility and resistant to damage. Chemical treatment methods like acid etching work by altering the chemical morphology and composition of the joint surfaces which results in the elevation of the surface free energy, a favorable condition for the formation of high-strength bonds. Chemical treatment of joint surfaces also raises the probability of chemical bonds (van der Waals, covalent, hydrogen, polar, etc.) formation at the substrate – adhesive interface. The alternative surface preparation methods to the chemical treatment provide the same surface modifications but produce less harmful waste materials are corona, plasma and flame treatment methods. These surface treatment methods are always preferred and performed prior to the application of structural adhesives to obtain the optimum load-bearing and high strength bonds [6, 7]. The surface preparation method for the treatment of adherend surface is highly dependent on the nature of adhesive as well as adherend.

6  Structural Adhesive Joints The surface preparation methods used for the metals include degreasing, grit blasting, acid etching, anodization, etc. The surface preparation methods for the plastics are corona treatment, flame treatment, chemical etching, etc. and for the fluoroplastics, the chemical etching and grit blasting are generally performed. This chapter aims to describe distinct theories of adhesion (mechanical interlocking, electrostatic, diffusion, wetting, chemical bonding, and weak boundary layer), surface preparation methods that include degreasing (vapor degreasing, ultrasonic vapor degreasing, ultrasonication/ immersion/spray/wiping), chemical treatment (acid etching, anodization, etc.), mechanical abrasion (grit blasting), and other physical methods (flame treatment, corona treatment, plasma treatment). This is followed by various surface evaluation tests like dyne test, water-break test, contact angle test, etc. The chapter also covers a wide range of applications and future scope of structural adhesives.

1.2 Theories of Adhesion The phenomenon of adhesion has been described by various theories, explaining the mode of action by which adhesives bond adherends. These theories of adhesions include mechanical theory (mechanical interlocking), diffusion theory, electrostatic (electronic) theory, and adsorption/ surface reaction theory (wetting/chemical bond/acid - base interactions), etc. [8, 9]. These theories of adhesion are discussed as follows:

1.2.1 Mechanical Interlocking The mechanical interlocking theory postulates that the adhesion occurs due to the weaving of adhesive into the microstructures (pores, valleys, cavities, etc.) present on the surfaces of adherends. These irregularities arise by mechanical abrasion of joint surfaces which enhances the bond strength formed between two joint surfaces as shown in Figure 1.2.

Adhesive Substrate Mechanical Interlocking

Figure 1.2  Mechanical interlocking mechanism on an abraded surface.

Surface Preparation for Structural Adhesive Joints  7 The mechanical interlocking theory is supported by the fact that a better adhesion is achieved on the abraded/roughened surfaces as compared to adhesion between polished/smooth surfaces. This improved adhesive bonding after abrasion may also occur due to the increased contact area at the interface or formation of highly reactive surface after abrasion. But, this theory of adhesion fails because of the fact that good adhesion can also be achieved between smooth adherends. Also, the application of mechanical abrasion is not suitable on ductile material surfaces because it deteriorates the strong bond formation and makes material more susceptible to damage under unfavorable environmental conditions [10–13].

1.2.2 Electrostatic (Electronic) Theory The electrostatic theory of adhesion is based on the phenomenon of electron transfer between two materials (adhesive and adherend) with different electronic band structures [14–16]. This transfer of charges at the interface results in the formation of an electrical double layer, and the generated electrostatic forces provide the resistance to the separation of joint surfaces (Figure 1.3). This theory of adhesion also gets support from the observation of discharge when the adhesive is peeled off from the adherend surface [10]. However, the electrostatic interaction is relatively weak and not applicable to all substrates.

1.2.3 Diffusion Theory The diffusion theory of adhesion is generally applicable to polymeric adherends having sufficiently long polymeric chains with the ability of movement. The diffusion theory assumes that adhesives weaves into the adherend through interdiffusion mechanism. This can be perceived as entanglement of adhesive and adherend chains providing inseparable forces for the joint surfaces as shown in Figure 1.4.

–

–

–

–

–

–

–

–

–

+

+

+

+

+

+

+

+

+

Electrical Double Layer

Figure 1.3  Electrical double layer formation across adhesive/adherend interface.

8  Structural Adhesive Joints Adhesive Interdiffusion Substrate

Figure 1.4  Diffusion mechanism of adhesion.

The bond strength depends on the matching of solubility parameters between adhesives and adherends. The higher is the matching of solubility parameters between adhesives and adherends, the higher is the bond strength [10]. The cohesive energy density (CED) can interpret the diffusion bonding. The cohesive energy density (CED) and solubility parameter are given by equations (1.1) and (1.2).





Ecoh V

(1.1)

Ecoh V

(1.2)

CED =

δ = 

Where, Ecoh = Total energy required to separate molecules V = Molar Volume δ = Solubility Parameter The interdiffusion of adhesives into adherends as well as the bond strength increase at elevated temperature, e.g., the adhesion of polyethylene and polypropylene with butyl rubber increases rapidly above the melting temperatures of both polymers, i.e., 135 °C for polyethylene and 175 °C for polypropylene [17].

1.2.4 Wetting Theory The wetting theory postulates that a continuous molecular contact between two materials and the resultant forces at the interface provide good adhesive bond strength. An ideal adhesive should have good wetting property which requires lower surface tension of adhesive than the critical surface tension of the joint surfaces. A proper wetting is achieved when the applied adhesive flows into the irregularities like valleys and holes present on joint surfaces and in the case of poor wetting, the adhesive forms air bubbles,

Surface Preparation for Structural Adhesive Joints  9 and thus reduces the actual contact area between the adhesive and joint surfaces [8, 10, 18]. Figure 1.5 shows the concept of poor wetting and good wetting across the interface. The wetting between adhesive and adherend can be improved by some surface preparation techniques, such as application of a primer layer which is a solution of adhesive and organic solvent. Both surface topography and surface chemistry are responsible for the wetting behavior of adherend. There are distinct wetting regimes which describe wetting in different manners. These wetting regimes include Wenzel, Cassie-Baxter, and impregnated Cassie wetting regimes. As per the Wenzel regime, when a liquid drop contacts the adherend rough surface, the liquid completely infuses into the pores and only surface roughness is responsible for the increase in contact angle (for contact angle greater than 90° on a smooth surface). This is described by Wenzel’s equation for the contact angle on a rough surface given by

Cos θ = Rf Cos θY



(1.3)

Where, θ = Contact angle on the rough surface Rf = Roughness factor (Ratio of actual to projected area) θY = Young’s contact angle on smooth surface According to the Cassie-Baxter regime, when liquid does not infuse into the pores, air pockets are formed at the adhesive/adherend interface which further increase the contact angle on the surface given by the Cassie-Baxter equation:

Cos θC–B = Rf fSL Cos θY – 1 + fSL



(1.4)

Where, fSL= Fraction of projected area constituting solid-liquid interface. But, when the partial infusion of liquid in the pores occurs then a contact angle between Wenzel and Cassie-Baxter is formed and this is called

Adhesive

Adhesive

Adherend

Adherend Air Bubble

(a)

(b)

Figure 1.5  Wetting behavior of adhesives: (a) good wetting and (b) poor wetting.

10  Structural Adhesive Joints impregnating Cassie wetting regime. The contact angle in this case is given by [19–21];



Cos θ = 1 + fSL (Cos θY – 1)

(1.5)

The proper wetting is always preferred to impart good adhesion with permanent high strength bonds. This can also be achieved using suitable surface preparation methods.

1.2.5 Chemical Bonding Theory The chemical bonding theory is based on the formation of chemical bonds such as hydrogen bonds, covalent bonds, ionic bonds, van der Waals bonds, and acid-base interactions. Out of all these chemical bonds, covalent bond is the strongest and provides much better adhesion in comparison to the secondary forces/bonds [22]. The acid-base theory of adhesion is based on the polar interaction between Lewis acids (electron-deficient materials) and Lewis bases (electron-rich materials), e.g., interaction between BF3 and NH3 is an acid-base interaction. In BF3, the electronegative fluorine displaces the electrons far from boron, which imparts positive charge on boron and negative charge on fluorine. Similarly, NH3 is a Lewis base and nitrogen has negative charge. Therefore, positive boron and negative nitrogen can interact via acid-base interaction [23, 24].

1.2.6 Weak Boundary Layer Theory Weak boundary layer assumes that cohesive failure and weak boundary layers are the causes by which bond failure occurs [25]. The weak boundary layers can be formed in adherend as well as in adhesive and the contaminants present on the surfaces are responsible for their formation. There are some materials essentially having weak boundary layer problem, e.g., polyethylene and metal oxides. In polyethylene, the low molecular weight components are distributed in the polymer resulting in low-stress failure when PE is used either as adhesive or adherend. Similar problem is associated with the certain oxides (like aluminum oxide). The weak boundary layers can be formed in adhesive or adherend, and unfavorable bonding environment as well as improper wetting are the causes of their formation. In case of improper wetting at the interface, the air gets trapped in the adherend valley, reducing actual contact area, and thus decreasing the joint strength. The weak boundary layer problem can be overcome via various surface preparation methods [10, 23].

Surface Preparation for Structural Adhesive Joints  11

1.3 Surface Preparation Methods The proper adhesion of adhesive with the joint surfaces requires a variety of surface preparation techniques prior to the application of adhesive. These surface preparation methods remove the contaminants like dirt, oil, grease, paint coatings, rust, tarnish, etc., and thus allow the actual contact area of adherend to interact with the applied adhesive. If these surface preparation methods are not performed then the contaminants may remain attached to adherend surface, resulting in improper wetting, and hence, weak boundary formation may take place which may cause the bond failure during the prolonged service period of the material. As mentioned earlier, there Table 1.1  Various surface preparation methods for structural adhesives [10]. Surface preparation methods

Working principle

Degreasing

Vacuum degreasing

Using vapors of degreasing solvents which condense on materials, solubilize contaminants and then drip off

Ultrasonic vapor degreasing

Vapor degreasing followed by ultrasonication

Immersion/ wiping/spray

Immersing adherend in solvent, or wiping off contaminants by spraying solvent on adherend

Mechanical abrasion

Grit blasting

Impinging hard grits like Al2O3 on adherend’s surface

Chemical treatment

Acid etching

Immersing material in acids to obtain cavities and holes

Anodization

Formation of coatings using the application of voltage between anode and cathode

Corona treatment

Collision of the stream of charged particles driven by electric field with adherend surface

Flame treatment

Use of oxidizing flame to treat the surface

Plasma treatment

Collision of plasma obtained by ionizing the air/gas (by applying voltage at the electrode) with adherend

Physical methods

12  Structural Adhesive Joints are several surface preparation methods (Table 1.1) which are selected depending on the nature of adhesive as well as adherend. In addition to the adhesive-adherend nature, environmental factors as well as processing parameters play an important role in the selection [7]. This section describes different surface preparation methods in detail.

1.3.1 Degreasing Degreasing is the basic cleaning method applied to the joint surfaces before application of adhesives. There are distinct ways by which degreasing method removes the light as well as heavy contaminants from the adherend surfaces. The degreasing process is generally done before the physical and chemical modifications of the surfaces as this helps in the improvement of bond strength. The degreasing removes dust, grease, oil, paints, particulate matter, etc., and exposes the actual surface and adhesion receptive sites for the adhesive. The main degreasing methods include vapor degreasing, ultrasonic vapor degreasing, and other (immersion/spray/solvent wipe/ ultrasonication) degreasing methods [7, 26]. The SEM image of aluminum degreased with soap is shown in Figure 1.6. These degreasing methods are described as follows.

1.3.1.1 Vapor Degreasing Vapor degreasing method can be applied to both metallic as well as non-metallic adherends to remove the waxes, oil, grease, soil, etc. In vapor degreasing method, vapors of the cleaning solvent are directed towards the

Superficial contaminants

Rolling direction lines

5kV

X1,000

10µm

0001

12

40

SEI

Figure 1.6  SEM Image of degreased aluminum surface. Reprinted with the permission from [64]. Copyright 2018 Elsevier.

Surface Preparation for Structural Adhesive Joints  13 surface to be cleaned. The condensed drops of the solvents then solubilize the contaminants which then drip off with the condensed solvent drops (Figure 1.7). If there is a thick coating of contaminants on adherend surface which is hard to clean using vapor degreasing method then acetone scrubbing is performed first followed by the vapor degreasing method [10]. The vapor degreasing solvents are 1,1,1-trichloroethane (methyl chloroform), dichloromethane (methylene chloride), tetrachloroethylene (perchloroethylene), trichloroethylene, trichloro trifluoroethane, etc. Out of all these degreasing solvents, methyl chloroform and methylene chloride (DCM) are banned due to their high level of toxicity. Tetrachloroethylene and trichloroethylene are the most widely used solvents for the vapor degreasing process [27]. These solvents provide a wide range of boiling temperatures such as DCM has boiling point equivalent to 39°C and perchloroethylene has a boiling point equivalent to 121°C. Taking the toxicity levels of these chemicals into consideration, some ecofriendly degreasing solvents have been synthesized under the trade names of ventrel CMS/ SMT, EnSolv, HFE-7100, etc. [10]

1.3.1.2 Ultrasonic Vapor Degreasing The ultrasonic vapor degreasing method provides the benefits of vapor degreasing as well as ultrasonication. The surfaces to be joined are first subjected to vapor degreasing followed by submerging in a suitable solvent and Cooling System

Heating Fluid

Heating Jacket

Surface to be Treated

Vapors Agitator

Cleaning Solvents Heat

Figure 1.7  Vapor degreasing method.

14  Structural Adhesive Joints then ultrasonicating it. The ultrasonication transmits the high frequency sonic waves via solvent, thus agitating and causing cavitation (formation and collapse of bubbles in the solvent). This leads to the transmittance of energy to the contaminants present on the surface as shown in Figure 1.8. This method of degreasing is the most effective among all as it has the power of detaching contaminants even from cavities and holes. The frequency to be used for the ultrasonication generally ranges from 20,000 cycles/s to 50,000 cycles/s and the selection of particular frequency depends on various factors including adherend surface, contaminants on adherend as well as ultrasonication solvent [7, 10].

1.3.1.3 Other Degreasing Methods The other degreasing methods include immersion, solvent wiping, spray, and ultrasonication method. The ultrasonication method involves immersion of the material and then allows the transmittance of sonic waves that provides sufficient energy for the removal of contaminants. This method is less effective than other methods, but still it is suitable and sufficient for the removal of light contaminants. Solvent wiping is the simplest and straightforward among all the degreasing methods. Solvent wiping uses different chemicals which are poured just once (instead of complete immersion) on the tissue/ wipe followed by scrubbing the joint surfaces. This process is repeated a few Ultrasonicator Probe

Piezoelectric Probe Supplying Sound Energy

Figure 1.8  Ultrasonication surface preparation method.

Surface Preparation for Structural Adhesive Joints  15 times to obtain the optimum cleaning. However, solvent cleaning suffers from the risk of contaminating the joint surfaces. Immersion of joint surfaces in cleaning solvents for a certain period of time is also adequate for the removal of light contaminants, but fails in case of heavy contaminants. The solvent spraying involves the sprinkling of cleaning solvents at a high speed which results in flow and washing off the contaminants [10].

1.3.2 Mechanical Abrasion The mechanical abrasion methods like grit blasting imparts irregularities (like holes, cavities, etc.) at the joint surfaces which act as receptive sites for the adhesives. In the grit blasting process, grits having random shapes are impinged on the adherend surface using a pressurized gas or water as shown in Figure 1.9. This method for obtaining rough surfaces is generally used on fluoropolymer adherends. The grit blasting makes profiles on the adherend surfaces which can be measured using a profilometer. The profilometer consists in a diamond stylus which scans across the surface, and thus measuring the formed valleys and holes in micrometers, or sometimes in root mean square (RMS). Grit blasting generally forms profiles greater than 2.5 µm. There are distinct grits (Table 1.2) that can be used in this method and their selection depends on the various factors. Hardness of the grit is the most important factor as the grit which is to be used should always be harder than the adherend to make the surface rough enough. The grit size as well as density of grit are also among important parameters of grit blasting as they drastically affect the roughness of the surface.

Water Separator

Pressure Regulator

Pressure Gauge

Blast Abrasive Under Pressure

Pressurized Air

Nozzle

Mixing Valve Air and Abrasive Under Pressure

Figure 1.9  Grit blasting technique applied on a joint surface.

16  Structural Adhesive Joints Table 1.2  Grit blast materials and their density and hardness [7]. Grit blast material

Density (g/cm3)

Hardness (Mohs)

Walnut Shells

–

1-4

Silicon Carbide

3.2

9

Aluminum Oxide

3.8

9

Glass Bead

2.2

6

Plastic

1.45-1.52

3-4

Steel

7.87

6

Sand, Silica (Silicon Dioxide)

2.6

7

The density of grits also plays an important role in obtaining good quality of adhesion because denser materials impart more energy to the substrate as they have higher momentum. Therefore, the denser is the grit, the higher the extent of roughness is achieved, and better is the adhesion. But highly dense grits may also harm the substrate/adherend. The plastic grits, walnut shells, and sodium carbonate are the materials which can remove the paint as well as contaminants without severe damage to the substrate [7, 28]. The aluminum oxide grits are generally used on hard surfaces along with compressed air (80-100 psi) [29, 30]. Figure 1.10 shows the SEM image of Al2O3 grit-blasted surface of titanium.

0.4 µm

Figure 1.10  SEM image of Al2O3 Grit-blasted Titanium Surface. Reprinted with permission from [65]. Copyright 2002 Elsevier.

Surface Preparation for Structural Adhesive Joints  17

1.3.3 Chemical Treatment The chemical treatment uses chemical means to alter the surface nature and create receptive sites for improved adhesion. The cleaning/degreasing of the materials is always performed before the chemical modification of materials [31]. The chemical modification methods include acid etching process, and various forms of anodization, as described below.

1.3.3.1 Acid Etching The acid etching process involves the use of strong acids which make cavities and holes when these come in contact with the adherend surface. Initially the surfaces are cleaned with the solvents like acetone to remove the ink marks and initial contaminants [10]. For example, in FPL (Forest Products Laboratory) etch which is a sulfuric-chromic acid etch, the adherend is first cleaned using a vapor degreaser or immersing the adherend in an alkaline non-etching solution. This is followed by the immersion of adherend for the period of 12-15 minutes in the etching solution having sulfuric acid (10 parts by weight), sodium dichromate (1 part by weight), and DI water (30 parts by weight) [32]. The SEM image of FPL etched aluminum is shown in Figure 1.11.

1.3.3.2 Anodization The anodization of adherend surfaces is performed on materials such as aluminum to provide protection against corrosion, rust, tarnish, etc. The

0.4 µm

Figure 1.11  SEM Image of FPL (Sulfuric Acid and Dichromate) Etched Aluminum Surface. Reprinted with permission from [65]. Copyright 2002 Elsevier.

18  Structural Adhesive Joints different anodization methods involve chromic acid, sulfuric acid, phosphoric acid, and boric sulfuric acid, and thus are called chromic acid anodization (CAA), sulfuric acid anodization (SAA), phosphoric acid anodization (PAA), and boric sulfuric acid anodization (BSAA), respectively [33]. The simple anodization principle is shown in Figure 1.12. The anodization parameters of CAA, PAA, and BSAA are mentioned in Table 1.3. The anodization of metals like aluminum involves the electrolytic treatment by passing the current through an electrolyte. The metal acts as positive electrode (anode). The application of current leads to hydrogen release at the negative electrode (cathode) and oxygen at the metal surface, thus creating a layer of metal oxide on it. The metals like aluminum uses acid solution as electrolyte. Different electrolytic solutions require voltage in the range of 15-21 V. The chromic acid anodization (CAA) can be performed in three ways and the resulting anodization coatings are designated as type I A, type I B, and type I C. The type I A is the conventional chromic acid anodization coating formed using chromic acid bath (30-50 g/L) kept at the temperature of 37° C, and the voltage is slowly increased to 50 volts. The type I B coating is obtained by low voltage (~20 V) CAA. The deposition of type I B coating requires elevated temperature and electrolytes with high concentration. The type I C coating is formed by using an electrolyte which is Power Supply + – 1.6×10–19C

Electrostatic Membrane on Separator

dic Ano l i F m

Electrolyte

Anode

Figure 1.12  Anodization setup for surface preparation.

Cathode

Surface Preparation for Structural Adhesive Joints  19 Table 1.3  Anodization parameters of CAA, PAA, and BSAA [65]. Anodization parameters

CAA

PAA

BSAA

Electrolyte

CrO3

H3PO4

H2SO4 + H3BO3

Concentration (g/L)

40-50

100-120

30.5-52

Temperature (°C)

32-38

22-33

24.5-29

Applied Voltage (V/­min)

8-40

3-15

5-15

Process Time (min)

55

20-25

18-22

Rinsing Time (min)

1-5

5-15

3-15

Drying Method

Oven Dry (20°C)

Air Dry (< 43°C)

Air Dry

non-chromic. The coating thickness obtained by CAA ranges from 0.5 µm to 7.6 µm [31, 34]. The comparison of these CAA types along with the obtained coating weight is shown in Table 1.4. The sulfuric acid anodization (SAA) also gives two distinct coatings, type II and type III. The type II sulfuric acid anodization coating is obtained using sulfuric acid bath with the coating thickness in the range of 1.8 µm to 25.4 µm. The type III SAA has thickness more than 25 µm and is obtained from same sulfuric bath. The thickness of type III SAA coating generally ranges from 25 µm to 150 µm [31]. The Phosphoric Acid Anodization (PAA) involves immersion of material surface in phosphoric acid (9-12 %) solution maintained at the temperature of 19-25°C with an Table 1.4  Distinct CAA coating type, method used, and resulting coating weight [25]. CAA coating type

Method

Coating weight (mg/m2)

Type I A

Conventional chromic acid bath coating

18.58

Type I B

Low voltage / high temperature CAA coating

18.58

Type I C

Non-chromic acid electrolyte coating

18.58-65.03

20  Structural Adhesive Joints applied voltage of 9-16 V for the duration of 20-25 minutes. The coating formed by phosphoric acid anodization offers the best resistance to hydration along with the advantage of better durability than any other anodization method [35]. The Boric Sulfuric Acid Anodization (BSAA) is adopted after observing toxic impact of chromium [36]. The BSAA involves the immersion of material surface in the 30.5-50 g/L solution of H2SO4 and H3BO3 (5.2-10.7 g/L) maintained at the temperature of 24.5-29°C with the applied voltage of 5 V-15 V and holding time of 18-22 minutes. BSAA provides coating thickness and durability close to that of CAA. Although, the morphology exhibited by BSAA is intermediate between CAA and PAA.

1.3.4 Physical Methods The other physical methods providing surface treatment equivalent to surface modifications with less hazardous waste include corona treatment, flame treatment, plasma treatment, etc. which are described as follows.

1.3.4.1 Corona Treatment The corona treatment of materials uses charged particles like ions and electrons driven by an electric field at a low temperature which alters the property and nature of surface. A corona is generated when a high voltage is applied at the electrode followed by the air space. This results in the generation of charged particles stream having high velocity, colliding with the surface of adherend which is neutral. This collision at the surface produces free radicals which, in turn, react with the atmospheric oxygen to generate peroxide groups which when decomposed give different polar groups [37]. The generated distinct polar groups such as carbonyl (-C=O), hydroxyl (-OH), carboxylic acid (O=C-OH), etc., act as new receptive sites for adhesion. The atomic oxygen (O) is an important charged species which is generated in the presence of UV light (equation 1.6):

2O2 → O + O3

(1.6)

The generated atomic oxygen then impinges on surfaces in the form of continuous stream and generates carbonyl (-C=O) and hydroxyl (-OH) polar groups by reacting with the carbon and hydrogen, respectively, which then form hydrogen bonds with the applied adhesives. The corona treatment method is generally applied to the plastics. The corona treatment is always described by corona dosage which gives the amount of energy

Surface Preparation for Structural Adhesive Joints  21 applied to the 1 m2 of the treated surface. The corona dosage is given by equation (1.7):

D=



P We × V

(1.7)

Where, D = Corona Dosage (J/mm2); P = Power (W); = Electrode width (mm); V = Web Speed The corona treatment setup has an electrode, a dielectric (electrical insulator), and ground (return path). Three configurations of corona treatment setup are available. In the conventional configuration, the roll which is subjected to corona is covered with the dielectric material (silicone rubber). An air gap of approximately 1.5-2.5 mm is maintained between the electrode and the roll. The application of high voltage across the gap produces the corona discharge directed towards the treating surface. This configuration is only applicable for nonconductive materials. In the second configuration of corona treatment, the bare roll is manufactured from anodized aluminum and the dielectric is present on the electrode. The first and second configurations of corona treatment are shown in Figure 1.13. The third configuration is known as double dielectric in which both electrode as well as roll are covered with dielectric [7]. The SEM image of 1s corona-treated LLDPE is shown in Figure 1.14. The corona treatment of materials is a successful method as it facilitates the formation of polar sites for efficient adhesion along with less harm to the material surface than chemical treatments.

Bare Aluminum

Covered Electrode

(a)

(b) Air Gap (Corona)

Moving Roll

Air Gap (Corona) Material Silicone Covering Dielectric

Bare Roll (Aluminum) Ceramic Covering

Material

Figure 1.13  Corona treatment method (a) first configuration and (b) second configuration.

22  Structural Adhesive Joints

Figure 1.14  SEM image of 1s corona-treated LLDPE. Reprinted with the permission from [66]. Copyright 2017 Elsevier.

1.3.4.2 Flame Treatment In the flame treatment method of surface preparation, an oxidizing flame (mixture of propane and air) is used for the surface treatment of polymers. The generated flame contains species like atomic oxygen (O), OH, NO, etc. These species generate polar functional groups on the treated surface which act as new receptive sites for applied adhesives. One of the important key factors in the flame treatment is the correct flame control. The flame treatment system contains gas and air control valves to inhibit pressure fluctuations, assuring that the oxidizing mixture is always maintained at its optimum. The flame treatment setup is shown in Figure 1.15. The flame treatment method of surface preparation suffers from the risk of over-flaming as it can damage the material integrity [7, 38, 39].

1.3.4.3 Plasma Treatment The plasma treatment also uses high voltage applied at the tip of electrode to ionize the air/gas and create charged plasma directed towards the material to be treated. Although, the plasma treatment has comparatively lesser width area than corona treatment, but it can elevate the surface free energy considerably. The corona treatment, on the other hand, has the benefit of covering large area at a time. Plasma is referred as the fourth state of matter

Surface Preparation for Structural Adhesive Joints  23 Gas Valve

Gas

Zero Pressure Regulator

Gas Adjustment Valve Air and Gas Heater Exhaust Fan

High Velocity Burner Venturi Mixer Air Adjustment Valve Centrifugal Air Pressure Blower

Figure 1.15  Flame treatment setup for surface preparation.

consisting of both negatively and positively charged particles along with the neutral atoms and molecules which gives them conducting as well as neutral nature. There are several gases like argon, helium, nitrogen, CO2, oxygen, tetrafluoromethane (CF4), sulphur tetrafluoride (SF4), fluorine, etc., which are used to produce plasma. The plasma treatment modifies the surface by forming unsaturated bonds, stable free radicals, and polar groups acting as new receptive sites. In the plasma treatment, the surface to be treated is first placed inside the chamber. The low pressure is then created inside the chamber by vacuum followed by the release of the gas in the chamber. The gas inside the chamber is then ionized by voltage application across the electrode. The synthesized ionized gas is then allowed to interact with the surface which imparts free radicals and polar functional groups to improve the adhesion. The plasma treatment is also efficient in eliminating the weak boundary layers by allowing crosslinking of the low molecular weight species present on the surface [40–42].

1.4 Surface Preparation Evaluation Methods The success of surface preparation implementation on a joint surface is generally determined by various methods which are selected depending on the material as well as adopted preparation method. The bond strength and mode of failure are also important factors which are determined after

24  Structural Adhesive Joints adhesion testing. This section covers some methods for the evaluation of the effectiveness of surface preparation methods [43].

1.4.1 Dyne Solutions Dyne solutions have surface tension between 30-70 dynes/cm and are made up by mixing two distinct chemicals. The dyne solution test involves positioning the drops of different dyne solutions onto the treated surface and then observing the spreading of the droplets for a fixed time (2 seconds). If the dyne solution drops form a liquid film on the treated surface then the surface is supposed to be contaminants free and if the drops are observed to be retaining their shape then contaminants are still present on the surface and the surface needs to be treated again. This method is generally used after degreasing of joint surfaces and is successful with the plastic adherends [44].

1.4.2 Water-Break Test The water-break test is based on the fact that a contaminant-free surface is able to hold a continuous water film without any breaks. On the other hand, the contaminated surface will have isolated water droplets instead of a continuous film. This condition of retaining a continuous film of water on chemically-active and polar surfaces is called water-break free condition. The distilled water is used in this test with the water drainage time of approximately 30 seconds. The water break on the surfaces requires repetition of cleaning and surface treatment on the surface until the test is passed. In case the failure is repeated even after few treatment cycles, then there is need of investigating the surface treatment method itself [7, 45].

1.4.3 Contact Angle Test The contact angle test is based on determining the wettability in the form of contact angle between the treated surface and the liquid taken as reference such as distilled water. The small contact angle indicates an effective wetting between liquid and surface, while the large contact angle reflects poor wetting behavior. All the surfaces to be treated have a definite critical surface tension, designated as γc. The liquids having surface tensions lower than γc will completely wet the surface with zero contact angle, while the liquids with surface tensions greater than γc will show poor wetting with a

Surface Preparation for Structural Adhesive Joints  25 definite contact angle. The critical surface tension, γc, of the surface is measured at 20°C in dyne/cm (now mN/m). The contact angle between the liquid and adherend surface decreases with the increase in surface treatment cycles. The contact angle is more reliable and quantitative approach when compared with dyne test and water-break test as it is based on a particular property i.e. wettability [7, 46].

1.5 Applications of Structural Adhesives Recently, a variety of adhesives have been proposed to transfer the load from one adherend to another to which these have been applied. Structural adhesives are used in a variety of fields including aerospace, marine, medical and dentistry, electronics and construction. This section highlights the scope of these adhesives in commercial as well as at industrial level.

1.5.1 Adhesives for Aerospace Aerospace structural adhesives are effectively used in a variety of aeronautical components including rotatory wing aircraft, spacecraft and missiles [47–49]. • Aircraft: Due to the stiffness, strength and lightweight requirements, honeycomb constructions are widely used in aircraft. Furthermore, honeycomb panels can be used as aerofoils and flooring. For instance, Boeing aircraft 747 can withstand 300 kg payload when carbon fiber reinforced skin along with honeycomb core is used as flooring [50]. • Helicopters and helicopter blades: The high-performance adhesives like epoxy film adhesives find a variety of applications in aerospace industry mainly in component assembling such as helicopter rotor blades. The rotor blades mainly consist of aluminum-, titaniumand glass fiber reinforced plastic skins which are bonded to a metal rib in the front section, and to a honeycomb core to form trailing edges. For instance, the blades of Westland Lynx helicopter are designed to transmit stress by bonding steel with nylon-modified epoxy. Moreover, the reinforcing edges

26  Structural Adhesive Joints and window cut-offs are designed with a Nomex honeycomb core and carbon reinforced plastics [49, 50].

1.5.2 Adhesives for Marine Applications Structural adhesives have a wide range of applications in watercraft as well. The use of direct adhesive junctions has replaced the overlap joint structural junctions, conventionally used between shell and the bulkhead of a sailing boat [51]. These structural adhesives have been successfully tested on 3 boat prototypes. For instance, vinyl-ester based adhesives were used between the shell (made of polyester/glass stratified composite) and the bulkhead (made of plywood) of the sailing boat, due to their superior long-term behavior. Moreover, these adhesives were further used in between the bulkhead and the hull in order to test their load-carrying potential in motorboats [51]. Glass-reinforced plastics (GRPs) are used efficiently in the construction of warships. Even though GRP is considered to be expensive than steel plate, its non-magnetic and lightweight properties make it a good candidate in ship building industry. In 1981, Bowditch and Stannard discussed the use of toughened acrylics for adhesive bonding which resulted in the formation of smooth surfaces [52]. Due to their simplicity and efficiency, adhesive joints are actively used in the ship industry to join different materials including, portholes, sea chest, windshields, cabin panels etc. [53]. Silyl Modified Polymer based sealants and adhesives, for instance, are used to join various components which offers flexibility, high peel strength and high impact resistance. In addition to these adhesives, adhesives for glass–GFRP joints have also drawn attention in the ship manufacturing industry [53]. Moreover, adhesives are used to laminate wood for keel, stern, ribs, bilge strings and gunwale in the yachts [50]. Resorcinol-formaldehyde wood adhesive is a material suitably used to bond planks to the ribs.

1.5.3 Adhesives for Medical and Dental Applications The use of adhesives in medical [54] and dental areas has been made since the last few decades. Structural adhesives are being used in various medical areas including infant immunization, heart bypass, urological surgery, flu shots etc. Furthermore, these adhesives may also be used to assemble medical devices [55]. • Medical applications:

Surface Preparation for Structural Adhesive Joints  27 Pressure-sensitive adhesives based on natural rubber were prepared initially for self-adhesive bandages which were then replaced by poly(acrylic acid), and ethers [55]. Cyanoacrylate adhesives [56] are actively used for curing the skin wound and are considered for closing the wound quickly. Furthermore, adhesives like acrylic, acrylic-rubber hybrid etc. are used for transdermal patches which helps to control the flow rate of drug into the body. Cyanoacrylate adhesives (CAs) provide strong thermosetting bonds between various materials without an additional catalyst. They are considered to be the rapid curing adhesives possessing a lap-shear strength of 13.7 MPa. The main advantages of using CAs include fast bond formation, no solvent evaporation during bond formation and high bond-strength with thin glue-line. CAs along with other tissue adhesives can be effectively applied in wound closure and fistula repair. The tissue adhesives used in gastrointestinal (GI) endoscopy typically include fibrin glue, thrombin and CAs. They can be used for curing bleeding sites including gastric variceal, esophageal variceal, peptic ulcer, etc. [55]. • Dental applications: Adhesives in dentistry are used to support composite fillings or composite cement. Adhesives used in this field are designed in such a way that they not only withstand mechanical forces but also prevent leakages along the restoration margins. Moreover, the capability of these adhesives depends on 2 factors including the enamel-dentin adhesive bonding and the adhesive must adhere to the lining composite [55].

1.5.4 Adhesives for Construction In 1973, University of Dundee demonstrated the development of new roadway deck for bridges which were expected to be lighter in weight as compared to the conventional reinforced concrete. The idea paved way for various satisfactory long-term durable bridge decks. They used epoxyresin adhesive for bonding which was either applied to concrete core or to a steel soffit plate. Structural adhesives used in building constructions [57] mainly consist of poly(vinyl acetate) (PVAc), synthetic resin, epoxy resin, urea-formaldehyde, resorcinol-formaldehyde and phenol-formaldehyde. These adhesives mainly intend to provide strong water-resistant glues. The common sites where these

28  Structural Adhesive Joints structural adhesives are applied include ceramic tiles, roofing and flooring, wall coverings, pre-fabricated panels, timber bonding, and other electronic household connections of wires and cables. Epoxy adhesives are suitably used in bridge constructions including anchors for arch bridges, footbridges etc. Structural adhesives used in this field provide simple and cost-effective alternative to the materials currently being used. These adhesives are so versatile that they can be efficiently used to bond timber, concrete and steel membranes [50].

1.5.5 Adhesives for Automotive Industry The future of automobiles is based on bonding which serves as an essential feature in the construction of vehicles [58]. For instance, one-component epoxy adhesive and one-component polyurethane adhesive are effectively used for spot-weld bonding and glass fiber reinforced polyester resin body part bonding. Moreover, side windows and windshields are also sealed using one-component polyurethane. Accordingly, a comparison was carried out regarding the lap-shear strength in joints for polymeric composites including Resin Transfer Molding (RTM) and Sheet Molding Compound (SMC), galvanized steel and acrylonitrile butadiene styrene (ABS) thermoplastics, which eventually resulted in good adhesion between the substrate and the adhesive. These adhesives are proven to be successful in terms of increased strength and stiffness along with reduced weight. For instance, the lightweight concept leads to the introduction of new functions in car body designs. Adhesive bonding in cars is characterized by homogeneous stress distribution along with no heat effects on the substrate structure.

1.5.6 Adhesives for Electronics In addition to aerospace, automotive, marine, medical and dental applications, structural adhesives are also used in electronics due to their compatibility with certain substrates. For instance, aliphatic polymers, such as poly (methyl methacrylate) (PMMA), are mainly used for molding, casting and coating, which form materials with excellent optical clarity. These adhesives are used in electronics mainly due to their low glass transition temperature (Tg) as well as high thermal stability [59]. The structural adhesives are also used to fix the power devices because of their conductive nature and also provide thermal protection to protect the structural integrity of the devices [47, 60, 61]. Plastic packages and printed circuit boards (PCBs) are certain areas where high-purity epoxy resins are being used effectively.

Surface Preparation for Structural Adhesive Joints  29 Furthermore, polyfunctional epoxies produced by epoxidation of cresol novolac and phenol novolac are actively used for electronic applications. The structural adhesives are also used to block the sound caused by electromagnetic interference in electronic devices [62, 63]. Flexible epoxies, as structural adhesives, are used to design stress-relief vibrating devices in electronics, such as bubble memory devices and LEDs. Conductive adhesives are also used in electronic applications as curing agents between broken circuits and wires. Polyamide adhesives are mainly used in flexible circuits and MCBs (Miniature Circuit Breakers), however, these adhesives are amongst those materials which have only a very small share in the global market [59].

1.6 Summary This chapter has covered various conventional as well as recent surface preparation methods used for structural adhesives for advanced applications in different fields ranging from aerospace to domestic appliances. The chapter has discussed basic surface preparation methods such as degreasing, grit blasting, acid etching, and anodization and various advanced surface preparation methods such as corona treatment, flame treatment, plasma treatment, etc. to enhance the adhesion ability of joint surfaces. The surface preparation evaluation tests like dyne solution, water-break free test, and contact angle test have also been mentioned. This chapter has also covered numerous applications of structural adhesives in different fields including aerospace, marine, construction, automotive, electronics, dental, and medical applications. The chapter concludes that surface preparation of joint surfaces prior to the application of adhesives provides additional receptive sites for an efficient adhesion with less probability of bond failure in distinct load-bearing situations.

Acknowledgment The authors would like to thank Dr. C. P. Ramanarayanan, ViceChancellor of DIAT (DU), Pune for support and motivation. The authors are thankful to Mr. Swaroop Gharde and Mr. Prakash M. Gore for their continuous efforts in manuscript refinement and technical support. The authors are thankful to the Editor and the reviewers for improving the quality of the manuscript by their valuable comments and suggestions.

30  Structural Adhesive Joints

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Surface Preparation for Structural Adhesive Joints  31 18. S. Ebnesajjad, Introduction and adhesion theories, in: Handbook of Adhesives and Surface Preparation, S. Ebnesajjad (Ed.), pp. 3–13, Elsevier (2011). 19. S. Padhi, S. Gosavi, R. Yadav, and B. Kandasubramanian, Quantitative evolution of wetting phenomena for super hydrophobic surfaces, Mater. Focus. 7, 305–315 (2018). 20. P. Gupta and B. Kandasubramanian, Directional fluid gating by Janus membranes with heterogeneous wetting properties for selective oil-water separation, ACS Appl. Mater. Interfaces 9, 19102–19113 (2017). 21. B.N. Sahoo, B. Kandasubramanian, and B. Sabarish, Controlled anisotropic wetting behaviour of multi-scale slippery surface structure of non fluoro polymer composite, Express Polym. Lett. 7, 900–909 (2013). 22. D.E. Packham, Theories of fundamental adhesion, in: Handbook of Adhesion Technology, L. Silva, A. Oechsner, and R, Adams (Eds.), Second Edition, pp. 11–41, Springer International Publishing (2018). 23. E.M. Petrie, Theories of adhesion, in: Handbook of Adhesives and Sealants, E.M. Petrie (Ed.), pp. 39–58, Elsevier (2007). 24. M.M. Chehimi, A. Azioune, and E. Cabet-Deliry, Acid-base interactions: Relevance to adhesion and adhesive bonding, in: Handbook of Adhesive Technology, A. Pizzi and K.L. Mittal (Eds.), Second Edition, pp. 95–144, CRC Press, Boca Raton, FL (2003). 25. J.J. Bikerman, Causes of poor adhesion: weak boundary layers, Ind. Eng. Chem. 59, 40–44 (1967). 26. A. Oldewurtel, Surface treatment methods., in: Mold-Making Handbook for the Plastic Engineering, K. Stoechkhert (Ed.), pp. 351–372, Elsevier (2019). 27. M.J. Troughton, Adhesive bonding, in: Handbook of Plastics Joining, M.J. Troughton (Ed.), Second Edition, pp. 145–173, Elsevier (2009). 28. D.J. Varacalle, D.P. Guillen, D.M. Deason, W. Rhodaberger, and E. Sampson, Effect of grit-blasting on substrate roughness and coating adhesion, J. Thermal Spray Technol. 15, 348–355 (2006). 29. L.W. McKeen, Substrates and substrate preparation, in: Fluorinated Coatings Finish and Finishes Handbook, S. Ebnesajjad (Ed.), pp. 99–107, Elsevier (2006). 30. S. Bose, Coatings repair, in: High Temperature Coatings, S. Bose (Ed.), pp. 247–251, Elsevier (2007). 31. S. Ebnesajjad, Surface preparation of metals, in: Handbook of Adhesives and Surface Preparation, S. Ebnesajjad (Ed.), pp. 83–106, Elsevier (2011). 32. R.S. Shane, Preparation of metal surfaces for adhesive bonding, in: Proc. Symposium on Shear and Torsion Testing, pp.10-72, ASTM International (2009). 33. A. Bjorgum, F. Lapique, J. Walmsley, and K. Redford, Anodising as pre treatment for structural bonding, Int. J. Adhesion Adhesives 23, 401–412 (2003). 34. M.G.S. Ferreira, M.L. Zheludkevich, J. Tedim, and K.A. Yasakau, Self-healing nanocoatings for corrosion control, in: Corrosion Protection and Control Using Nanomaterials, V.S. Saji and R. Cook (Eds.), pp. 213–263, Elsevier (2012).

32  Structural Adhesive Joints 35. Standard recommended practice for preparation of aluminum surfaces for structural adhesives bonding (Phosphoric Acid Anodizing), ASTM D3933-98,. 36. D. Arnott, A. Rider, and J. Mazza, Surface treatment and repair bonding, in: Advances in the Bonded Composites Repair of Metallic Aircraft Structures, A.A. Baker, L.R.F. Rose, and R. Jones (Eds.), pp. 41–86, Elsevier (2002). 37. J. Izdebska, Corona treatment, in: Printing on Polymers, J. Izdebska and S. Thomas, (Eds) pp. 123–142, Elsevier (2016). 38. P. Fabbri and M. Messori, Surface modification of polymers: chemical, physical, and biological routes, in: Modification of Polymer Properties, C.F.J. Gastinel and J.M. Kenny (Eds.), pp. 109–130, Elsevier (2016). 39. A.H.C. Poulsson, D. Eglin, R. Geoff Richards, Surface modification techniques of PEEK including plasma surface treatment, in: PEEK Biomaterials Handbook, S. Kurtz (Ed.), pp. 179–201, Elsevier (2019). 40. M. Niaounakis, Surface treatment, in: Biopolymers: Processing and Production, M. Niaounakis (Ed.), pp. 303–326, Elsevier (2015). 41. L. Zhu, W. Xu, M. Ma, and H. Zhou, Effect of plasma treatment of silk fibroin powder on the properties of silk fibroin powder/polyurethane blend film, Polym. Eng. Sci. 50, 1705–1712 (2010). 42. M. Thomas and K.L. Mittal (Eds.), Atmospheric Pressure Plasma Treatment of Polymers, Wiley-Scrivever, Beverly, MA (2013). 43. D.L. Williams and K.L. Mittal, Wettability techniques to monitor the cleanliness of surfaces, in: Developments in Surface Contamination and Cleaning: Fundamentals and Applied Aspects, Second Edition, R. Kohli and K.L. Mittal (Eds.), pp. 445–476, Elsevier (2016). 44. J.G. Drobny, Processing methods applicable to thermoplastic elastomers, in: Handbook of Thermoplastics and Elastomers, J.G. Drobny (Ed.), pp. 29–160, Elsevier (2007). 45. R. Kohli, Methods for monitoring and measuring cleanliness of surfaces, in: Developments in Surface Contamination and Cleaning:Characterization and Analysis of Contaminants, R. Kohli and K.L. Mittal (Eds.), pp. 107–178, Elsevier (2017). 46. M.S. Islam, L. Tong, and P.J. Falzon, Influence of metal surface preparation on its surface profile, contact angle, surface energy and adhesion with glass fibre prepreg, Int. J. Adhesion Adhesives 51, 32–41 (2014). 47. P. Sanoj and B. Kandasubramanian, Hybrid carbon-carbon ablative composites for thermal protection in aerospace, J. Composites, 1–15 (2014). 48. Y. Badhe and K. Balasubramanian, Eco-friendly redemption of butyl rubber in cost efficient ablative composites for aerospace applications, Energy Environ. Focus. 4, 40–46 (2015). 49. D. Driver, Adhesive bonding for aerospace applications, in: High Performance Materials in Aerospace, H.M. Flower (Ed.), pp. 318–339, Springer, Dordrecht (1995).

Surface Preparation for Structural Adhesive Joints  33 50. R.D. Adams and W.C. Wake, Structural Adhesive Joints in Engineering, Second Edition, Springer (1997). 51. A. Roy, Y. Nadot, and P. Casari, Adhesive bonding for structural marine applications, Proc. RINA - Int. Conf. - Innovations in High Performance Sailing Yachts, 133–138 (2008). 52. M.R. Bowditch, J.D. Clarke, and K.J. Stannard, The strength and durability of adhesive joints made underwater, in: Adhesion 11, K.W. Allen (Ed.), pp. 1–16, Springer (1987). 53. G. Di Bella, G. Galtieri, E. Pollicino, and C. Borsellino, Mechanical characterization of adhesive joints with dissimilar substrates for marine applications, Int. J. Adhesion Adhesives 41, 33–40 (2013). 54. G.K. Schalau II, A. Bobenrieth, R.O. Huber, L.S. Nartker, and X. Thomas, Silicone adhesives in medical applications, in: Applied Adhesive Bonding in Science and Technology, InTech (2018). 55. S. Ebnesajjad, Adhesives for medical and dental applications, in: Handbook of Adhesives and Surface Preparation, S. Ebnesajjad (Ed.), pp. 345-368, Elsevier (2011). 56. J.M. Korde and B. Kandasubramanian, Biocompatible alkyl cyanoacrylates and their derivatives as bio-adhesives, Biomater. Sci. 6, 1691–1711 (2018). 57. R.H. Gillespie, Elastomeric adhesives in building construction, Build Res (Washington D.C.) 9, 11–23 (1972). 58. J.G. Quini and G. Marinucci, Analysis of structural adhesives for automotive, in: Proceedings of the 7th International Conference on Mechanics and Materials in Design, 1353–1354 (2017). 59. G. Rabilloud, Adhesives for electronics, in: Handbook of Adhesives and Sealants, P. Cognard (Ed.), pp. 349-483, Elsevier (2005). 60. Y. Badhe and K. Balasubramanian, Reticulated three-dimensional network ablative composites for heat shields in thermal protection systems, RSC Adv. 4, 43708–43719 (2014). 61. N. Katiyar and K. Balasubramanian, Thermal modelling of hybrid composites of nano cenosphere and polycarbonate for a thermal protection system, RSC Adv. 4, 47529–47535 (2014). 62. R.P. Magisetty, A. Shukla, and B. Kandasubramanian, Terpolymer (ABS) cermet (Ni-NiFe2O4) hybrid nanocomposite engineered 3d-carbon fabric mat as a x-band electromagnetic interference shielding material, Mater. Lett. 238, 214–217 (2019). 63. A. Joshi, A. Bajaj, R. Singh, P.S. Alegaonkar, K. Balasubramanian, and S. Datar, Graphene nanoribbon-PVA composite as EMI shielding material in the x band, Nanotechnology 24, ID:455705 (2013). 64. N.G. Gonzalez-Canche, E.A. Flores-Johnson, P. Cortes, and J.G. Carrillo, Evaluation of surface treatments on 5052-H32 aluminum alloy for enhancing the interfacial adhesion of thermoplastic-based fiber metal laminates, Int. J. Adhesion Adhesives 82, 90–99 (2018).

34  Structural Adhesive Joints 65. G.D. Davis and J.D. Venables, Surface treatments of metal adherends, in: Adhesion Science and Engineering, A.V. Pocius and D.A. Dillard (Eds.), pp. 947–1008, Elsevier (2002). 66. A. Popelka, I. Novák, M.A.S.A. Al-Maadeed, M. Ouederni, and I. Krupa, Effect of corona treatment on adhesion enhancement of LLDPE, Surf. Coatings Technol. 335, 118–125 (2018).

2 Improvement of the Performance of Structural Adhesive Joints with Nanoparticles and Numerical Prediction of Their Response Farid Taheri

*

Department of Mechanical Engineering, Dalhousie University Halifax, Nova Scotia, Canada

Abstract

The use of nanoparticles as an effective means for improving the performance of adhesives and resins has attracted considerable attention immediately after the helical microtubules of graphitic carbon were introduced. Since then, several researchers have harnessed the outstanding mechanical properties of nanoparticles (NPs) to improve performances of adhesives and resins. As a result, the number of scholarly articles on this topic has also increased exponentially since the early 90s, with no plateau in the rate of scholarly publications in sight. Overall, a large majority of the available articles concerning the incorporation of NPs for improving the performance of adhesives and resins are experimentally oriented compared to a relatively much lower number of articles that examine the characterization of the performance of such composite materials both theoretically and/ or numerically. This chapter, therefore, aims at providing a summary of the recent advances concerning the use of nanoparticles for improving the performance of adhesively bonded joints (ABJs). The emphasis is placed on the articles that have explored the influences of environmental parameters that affect the performance of NP-reinforced ABJs. A review of the relevant numerical studies with a particular emphasis on the extended finite element method is also presented.

Email: [email protected] K.L. Mittal and S. K. Panigrahi (eds.) Structural Adhesive Joints: Design, Analysis and Testing, (35–78) © 2020 Scrivener Publishing LLC

35

36  Structural Adhesive Joints Keywords:  Nanoparticles, nanocomposites, adhesives, bonded joints, mechanical properties, processing parameters, cohesive zone method, extended finite element method

2.1 Introduction 2.1.1 Historical Perspective The historical perspective on the first use of a material for joining structural components is rather sketchy. While structures with stones date back to 4850 BC, the first instance when a specific material was used to join structural elements perhaps goes back to 2700 BC, when Egyptians built a large mud-brick temple for holding deceased kings who were worshiped [1]. Notwithstanding, Mazza et al. [2] report that the earliest known adhesive was discovered in central Italy. According to Mazza et al., over 200,000 years ago, two stone flakes were strapped together by birch bark that was immersed in a tar-like material, thereby forming an axe. The use of an adhesive is also attributed to Egyptians, when approximately 2000 years ago they used some adhesive material to form wooden caskets. From the perspective of the actual structural uses of adhesives in the context of engineering, one could cite the first use of protein-based adhesives during the 1st World War for laminating wood (or as currently referred to as “plywood”) [3]. These laminated structural materials were primarily used in components with a curvature (e.g., propeller), where the incorporation of solid wood would have been difficult and costly. Moreover, various animal-based glues were used to fabricate various light-weight aircraft structural components, as the engine technology had not advanced to the stage to enable flying of relatively heavier components made of solid wood. For instance, solid wooden spars were replaced by considerably lighter, hollow box spars, which were constructed by bonding successive strips of spruce. As the aircraft industry progressed and larger planes were needed, synthetic adhesives had to be developed. One of the most significant developments in adhesive technology was the development of Urea-Formaldehyde resin, which was discovered by Holzer in 1884, first patented in 1918 [4]. However, the actual commercialization of this important adhesive material was done by BASF in Germany in 1937. The importance of this resin was its good resistance to moisture and cold environment; however, it would suffer when it came in contact with an acidic environment. The other issue with this adhesive was its low viscosity, which would prevent its use in

Improvement of the Performance of Structural Adhesive Joints  37 many practical applications. As a result, chemical remedies were developed and utilized. It should also be stated that around the same time frame, two other types of adhesives: Phenol-Formaldehyde and ResorcinolFormaldehyde adhesives were also discovered. These materials provided enhanced properties, including accelerated curing amongst many others. The research and development in resin and adhesive technology progressed further, primarily due to the commencement of the Second World War. The synthesis of resins and adhesives enabled formation of fiberreinforced composites, honeycombs and other composite sandwich structural configurations. As the years went by, the adhesive technology further evolved and various adhesive types were developed and marketed. Nowadays adhesives are available in three distinct forms: (i) solvent-based liquids, (ii) pastes and (iii) films. The first type of adhesives are available in the single-component format, while the second type of adhesives are available in both single- or dual-component systems. The last category adhesives are available in a film format with different thicknesses and widths; they can also be of the type that would require curing in order to form a strong bond. Soon after their discovery in the 1950s, film adhesives became the favourite adhesive format in the aerospace industry. The prime example is the use of Redux Film 775 (a phenol–formaldehyde adhesive) by de Havilland (now British Aerospace) and SAAB in their aircraft in the early 60s. It should be noted that today the aerospace sector uses primarily epoxy-based adhesives. Today, many of the civilian and military aircraft’ primary and secondary structural components, including the subframe structures, are joined together with adhesives. Perhaps the most recent example would be Airbus A380. Several structural components in this aircraft (e.g., the vertical tailplane, spoilers and ailerons, nacelles, centre wing box landing, gear hatches and radome) have been assembled using adhesive films and pastes [5]. Moreover, today’s adhesive vendors can provide adhesives for almost any situations (i.e., hot, wet, and other environmental and load resisting conditions). The technology has evolved to the stage where one can even apply certain resins and adhesives in wet and submerged environments [6]. It is worth noting that soon after the development of strong and versatile resins and adhesives, engineers realized the limitations imposed to the adhesives by adherend surfaces. It was soon realized that appropriate adherend surface preparation was critical to the integrity of bonded joints. Inadequate surface preparation can prevent adhesives from bonding properly to substrates, thereby limiting the strength that an adhesive could provide to the assembly. In other words, such joints could fail at loads well below the design loads (i.e., the load that a properly surface

38  Structural Adhesive Joints prepared bonded joint could sustain cohesively). Interfacial failures could also occur over time in service in joints that are exposed to harsh environments, including elevated temperature and sustained humidity. Therefore, there exists a significant body of research with its primary focus on surface preparation techniques by which the maximum strength of adhesives could be effectively used. It should, however, be noted that even once an effective surface preparation is used to prepare the optimal bonding surfaces, delays in bonding the surface prepared substrates could develop other issues that would affect the bond strength, which could, in turn, result in degradation of the bond capacity. As a result, research into the development of appropriate and effective primers that protect the prepared surfaces of adherends was initiated. The outcomes of such research and development motivated the creation of essentially two distinct types of primers: (i) those used for protecting adherends surfaces, and (ii) those that inhibit corrosion of the surfaces [7]. The surface type primers are usually solvent-based and can be applied to abraded and prepared surfaces by spraying or using brushes or rollers. The corrosion inhibitors essentially perform a similar function as the surface treatment primers but also provide additional corrosion protection to prepared surfaces. It should be mentioned that while polymer adhesives have been widely used in aerospace and automotive industries, but as it has been reported by Rubin [8], they also made their way into infrastructure applications since the early 60s. Robin reported the use of thermosetting, elastomeric, and thermoplastic adhesives with the purpose of gap-filling reinforcement to replace weldments in structural steel joints with the added advantages of increasing joint flexibility and economy, as well as facilitating ease of fabrication.

2.1.2 Incorporation of Fillers in Adhesives In order to improve adhesives’ performance, especially to enhance their toughness, researchers started to incorporate fillers in adhesives. Besides improving the toughness and stiffness of adhesives, incorporation of fillers produced many other benefits to adhesives. For instance, fillers could enhance an adhesive’s rheological and electrical properties, heat resistance, and control of the coefficient of thermal expansion and thermal shrinkage of adhesives, as well as mitigating their creep. One of the earliest works that examined the influence of fillers in the adhesive is the work conducted by Nielsen [9]. He identified that much work was needed to further characterize dispersion and agglomeration of particles in adhesives, as well as examining the influences of particle shape and particle orientation on the

Improvement of the Performance of Structural Adhesive Joints  39 mechanical properties of the filler-reinforced adhesives. He also identified the lack of effective theoretical methods for evaluating the effects of the above-mentioned parameters. The research works that focused on investigating the improvement of adhesion property of adhesives by the addition of particulates continued its pace until the 90s, followed by a noticeable increase in the rate of studies conducted on the topic ever since. For instance, Mitsui et al. [10] investigated polystyrene system reinforced with rigid particulates and obtained improved impact strength. They also observed a threshold for the inclusion amount of the particulates, which was suggested to be 1 wt%. They observed degradation of the strength when lower and higher weight-­ percent contents of the particulates were used to reinforce the resin. They also observed that particulates with an average diameter of approximately 2  μm produced the most optimal improvement in the strength. Kinloch et al. [11] demonstrated improvement in epoxy resin properties by the addition of nano-SiO2. They observed a 5 oC enhancement in the glass-transition temperature (Tg) of the resin when 8 wt% of the nanoparticle was added to the resin. However, the more significant enhancement was observed in the resin fracture energy, Gc, which was enhanced by 92% upon the addition of 4 wt% of nano-SiO2 particles. Moreover, several researchers (see for example, [12–16]) investigated the influence of a second micro-phase of dispersed rubber particles into the epoxy polymer with the aim to improve the toughness of the polymer without significantly impairing the other desirable engineering properties. Typically, the rubber particles used had a diameter of approximately 1 to 5 µm in diameter with a volume fraction of about 10 to 20%. While some researchers investigated the improvement in the mechanical properties of resins gained by the addition of rubber particulates in resins, others [17] on the other hand, incorporated inorganic particles such as silica, alumina and talc to improve both toughness and modulus. However, it has become evident that the toughness increase gained by inorganic particles is usually lower than that which could be achieved through the use of rubber particles [12, 18]. As stated earlier, while carbon nanotubes (CNTs) were introduced by Iijima [19] in 1991, nevertheless, the applications of nanocarbon started attracting a significant attention in the early 2000s. This said, however, the use of nanoclay as reinforcement in elastomeric media is traced back to a patent filed in 1947 [20]. However, most of the studies conducted prior to 2000 had primarily focused on evaluating and characterizing the properties of nanoparticles (see for instance [21–24]). Interestingly, while it has been shown by several investigators that inclusion of nanocarbon

40  Structural Adhesive Joints particles in resins could cause severe agglomeration at above 2 wt% (see for instance, [25]), nanoclays have been incorporated in resins in much greater quantities (optimally between 7%-10% [26]). In a notable study, Ngo et al. [27] examined the influence of nanoclay inclusion on EPON 828 epoxy resin, which was subsequently cured with three different types of hardeners. They managed to obtain significant gains of 377% in the critical stress intensity factor (KIC) and 838% in the critical strain energy release rate (GIC) when the resin was reinforced with 6 wt% Cloisite 30B nanoclay and cured with Jeffamine D2000 hardener. They also observed that the nanoparticle size significantly affected the gain in fracture toughness for all the nanoclay contents considered by them, and that the optimal wt% of nanoclay would change based on the hardener type used. In other words, when the resin was cured using the Jeffamine D230 hardener, the optimal nanoclay content was 2 wt%, however, as stated, when Jeffamine D2000 hardener was used, 6 wt% of nanoclay proved to be the optimal content. Other nanoparticle types have also been incorporated in various resins with the aim to improve the mechanical, thermal and other properties of polymeric resins. For a detail review of the studies using various nanoparticle types, the reader is referred to [28]. In 2003, Gilbert et al. [29] used nanoalumina particles to develop an epoxy-based film adhesive with 5 wt% and 10 wt% contents of the nano­ particles. The films were subsequently bonded to aluminum substrates and the specimens were tested under single lap joint and climbing drum peel configurations. Moreover, double-cantilever beam (DCB) specimens and end notch flexure (ENF) specimens prepared with substrates made of a high-performance woven carbon fiber-epoxy prepreg were also used to evaluate mode I and mode II interlaminar fracture toughness values of the film. The test results revealed a cohesive failure in all specimens, indicating an effective adhesion had been achieved. The increase in nanoparticles content also enhanced the peel and shear strengths of the adhesive systems. In another notable study, Zhai et al. [30] demonstrated a significant gain of five folds in the pull-off adhesion strength of their bonded joints when a two-part epoxy adhesive was reinforced with 2wt% nano-Al2O3 which was mechanically dispersed in the resin. Other wt% contents (1%, 1.5%, 3% 4% and 5%) of the alumina nanoparticles were also tried. While interfacial crack usually occurred in joints that were prepared with the neat epoxy, a mixed failure mode was observed when the epoxy was reinforced with Al2O3 nanoparticles. They in fact observed that the cohesive strength of the joint increased as a function of increasing nanoparticle (NP) content. In the following sections, we explore the most recent efforts expended on improving the mechanical response of adhesives by incorporation of

Improvement of the Performance of Structural Adhesive Joints  41 nanoparticles, as well as the gain in performance of the bonded joints prepared by such reinforced adhesives. The focus will be on the use of various forms of nanocarbon particles. In addition, the methodologies developed for estimating the mechanical properties of such nanoparticle-reinforced composites will be briefly presented. The chapter will be completed by reviewing some of the most recent numerical methodologies and techniques used for simulating the response of adhesively bonded joints.

2.2 Use of Nanocarbon Nanoparticles for Improving the Response of Resins and Adhesives As briefly stated earlier, several researchers have examined the influence of nanoparticles on enhancing various aspects of resins and adhesive that affect their performance under various loadings and environments. Such studies have investigated the enhancement in the mechanical [26, 31, 32], electrical [33], thermal [34, 35] and other properties [36] of resins/adhesives. A concise summary of such works can be found in [28, 37–39]. Here the notable studies that have directly examined the effect of nanocarbon particles on the performance of adhesively bonded joints are reviewed. One of the earliest works that investigated the influence of nanocarbon particles in ABJs is the work of Sun et al. [40] and Meguid and Sun [41]. They considered both alumina nanopowder and CNTs as reinforcements with contents ranging between 0.2 wt% to 15 wt%. Their joints were made with dissimilar substrates made of 6061-T6 aluminum and unidirectional carbon epoxy. They obtained an increase of approximately 18% and 38% in the ultimate tensile strength and 15% and 33% in the ultimate shear strength corresponding to the resins reinforced with alumina nanopowder and CNT, respectively (see Figure 2.1). It should be noted that while the authors stated that their epoxy’s strength properties degraded at weight percentages above 10%, however, the graphs included in their articles clearly show a significant rate of degradation of the properties at 5 wt% nanoparticle contents. Moreover, while several researchers since then have basically consented that the optimum nanocarbon content for enhancing the load-bearing properties of polymers hovers between 0.5 wt% to 3 wt%, it is not clear how Meguid and Sun [41] managed to obtain workable adhesives with CNT nanoparticle contents above 5 wt%. Aronsson et al. [42] were one of the earliest group of researchers that developed nanofiber-reinforced adhesive with enhanced properties for

1.60

1.6

Normalised ultimate shear strength (MPa)

Normalised ultimate tensile strength (MPa)

42  Structural Adhesive Joints

1.4 1.2 1 0.8 0.6 0.4

EANT

EANP

0.2 0 0

5

10

15

1.40 1.20 1.00 0.80 0.60 0.40 0.20

EANT

EANP

0.00

Weight Percentage of Nanoparticles

10 0 5 Weight Percentage of Nanoparticles

(a)

(b)

15

Figure 2.1  Effect of weight percentage of nanoparticles on the (a) ultimate tensile strength and (b) ultimate shear strength of Dexter Hysol EA 9330 [40] (EANT=CNTreinforced; EANP = Alumina nanoparticle-reinforced).

bonding electronic chips. They conducted shear test on adhesively bonded joints in a rather crude and nonstandard fashion. Moreover, unfortunately, their experimental results were poorly presented, in that one cannot discern the differences among their specimens and the associated results as presented in their manuscript. Nevertheless, this investigation is one of the pioneering works using nanofibers in adhesives. Shortly after the above study, Saeed and Zhan [43] investigated the influence of the addition of multiwall carbon nanotube (MWCNT) (between 0.1  wt% to 1.5 wt% concentration) to two types of thermoplastic polyimides. The influence of the MWCNT on the adhesive was evaluated via single-lap shear and wedge specimens tested under quasi-static loading condition. The results of this study can be summarized as follows. Firstly, the MWCNT caused a shift in the viscoelastic response of the adhesive at its glass-­transition temperature (i.e., from liquid to solid-like). They also observed a continuous increase in the tensile modulus and breaking strength of the adhesive up to 1.5 wt% MWCNT content. The lap shear strength was also enhanced for MWCNT contents of 0.5-1 wt%. This trend was also observed when the joint’s endurance characteristic was being evaluated using the standard wedge test method. Finally, the inclusion of nanoparticles improved the lap shear strength at elevated temperatures up to 200 oC. In another study, Yu et al. [44] also investigated the influence of CNT on improving the adhesion properties of Epikote 240 epoxy resin in joints made with 2024-T3 aluminum alloy substrates. CNTs with contents of 0, 0.5, 1, 2, 3.5 and 5 wt% were added to the resin. The optimum CNT

Improvement of the Performance of Structural Adhesive Joints  43 content was observed to be 1 wt%. While the enhancing influence of CNTs after 1 wt% content diminished somewhat linearly as a function of wt% of CNTs, the degradation rate increased significantly once the CNT content was increased above 3.5 wt%. Significant CNT agglomeration was also observed in the adhesive with 5 wt% CNT content. In an interesting and somewhat of a fundamental study, Kim and Choi [45] investigated the influence of dispersion method of CNTs in the adhesive on the strength of adhesively bonded joints with aluminum substrates. They also used the impedance method to detect defects in their nano­ composite specimens and monitored the influence of dispersion quality on their defect detection results. They used only one concentration of CNTs (i.e., 1 wt%); however, two types of CNTs were used (i) non-surface treated CNTs, and (ii) surface treated CNTs, The surface treated CNTs were processed by dispersing them in a bath of nitric acid with a concentration of 7 mol and sonicating them. The mixture was then stirred in a boiling water bath using a magnetic stirrer at 90 oC for 120 minutes. The nanoparticles were then washed and neutralized, and subsequently placed in an oven at 80 oC for 600 minutes to dry. They discovered that the inclusion of CNTs actually degraded the shear strength of their bonded joints that were bonded with adhesive in which CNTs were dispersed using the threeroll-mill process. In contrast, when CNTs were dispersed using the sonication method, the joints shear strength increased by 12.8% in joints with untreated surface and 10.8% in joints with treated surface. In another notable study, Park and Lee [46] investigated the influence of inclusion of carbon black in an epoxy resin under cryogenic environment using the double lap joints formed by unidirectional glass-epoxy composite substrates. The carbon contents of 0.1, 0.1, 1.5, 2 and 3 wt% were considered in the study. The maximum increase in tensile strength of 22% was obtained at 1.5 wt% carbon black content when the joint was tested at room temperature, while the maximum improvement in the lap shear strength of 27% was obtained at 1 wt% carbon content when the joint was tested at the cryogenic temperature of −150 oC (Figure 2.2). Nonetheless, the trend in variation of the shear strength as a function of carbon black content tested at both temperatures is very similar. Interestingly, the standard deviation in their results also increased at CNT fractions above the optimum level of 1.5 wt%. Their test results conducted at a subfreezing temperature of -150 oC were also very interesting. Firstly, they attained the maximum shear strength at weight-fraction of 1 %, as opposed to 1.5%, which was observed for the room-temperature test results. Secondly, the standard deviations in the strength results were observed to be significantly less than those observed in the test results obtained at room temperature.

40 35 30 25 20 15 10 5 0

0

0.5

1.5 2.5 1 2 Carbon black content (wt%) (a)

3

3.5

Lap shear strength (MPa)

Lap shear strength (MPa)

44  Structural Adhesive Joints 20 15 10 5 0

0

0.5 1 1.5 2 2.5 3 Carbon black content (wt%) (b)

3.5

Figure 2.2  Lap shear strength of adhesively bonded double lap joints with respect to the carbon black content at (a) 25°C and (b) −150°C [46].

In a subsequent study, Park and Lee [47] investigated the influence of surface treatment on carbon black reinforced XB5013 epoxy used to prepare double lap joints with glass-epoxy substrates. During the curing process of their prepreg glass-epoxy substrates, they embedded carbon black on the surfaces of glass/epoxy substrates by dispersing them in methyl ethyl ketone (MEK) and spraying the mixture on the surface of the uncured substrates to enhance the adhesion characteristics of the substrates. They examined the surface morphology of the substrates with SEM. They also established the minimum amount of MEK required to treat the surfaces for obtaining an optimal bond strength. The amount of MEK that led to the optimum surface roughness was determined to be 0.89 g/cm2. This concentration of MEK improved the lap shear strength by 3.5-fold compared to the strength of the joints that were prepared without incorporating the mentioned surface treatment of the adherends. Moreover, they compared the lap shear strength of the specimens whose bonding surfaces were prepared by the aforementioned technique, and those prepared by the conventional grit blasting and abrasive sanding. The average shear strengths of the especially surface treated specimens were approximately 32% and 26% higher than those of the joints that were prepared by sandblasting and abrasive sanding, respectively. There are also a couple of other important studies that were conducted in 2009, which examined the influence of nanocarbon particles for strengthening epoxy adhesive. Prolongo et al. [48] used carbon nanofibers (CNFs) to reinforce the adhesive used to fabricate single-lap bonded joints with unidirectional carbon-epoxy substrates. A significant part of the study was devoted to examining the influence of surface treatments using the conventional grit blasting, peel-ply imprint on the bond surface and the atmospheric plasma treatment on the bond strength of their joints. They demonstrated the significant influence of the surface treatment on the

Improvement of the Performance of Structural Adhesive Joints  45

Average lap shear strength (MPa)

failure mode and the fracture mechanism. The joints prepared by atmospheric plasma surface treatment produced the highest strength when 0.5 wt% CNFs were used to reinforce the adhesive. The results as illustrated in Figure 2.3 are quite interesting. The specimens prepared with peel-ply imprint bond surface treatment technique produced the lowest values regardless of the CNF content (though the results were slightly better when the adhesive was reinforced with 0.5 wt% CNF content). The feasibility of improving the mechanical performance of epoxy adhesives by inclusion of CNFs and CNTs in the epoxy used to join carbon fiber-epoxy laminates was also investigated by Gude et al. [49]. The main objective of this study was to verify whether addition of the nanoparticles in the resin could enhance the fracture toughness of the joints. Figure 2.4 illustrates the influence of the nanoparticles on the fracture toughness of their double-cantilever beam (DCB) specimens evaluated by the corrected beam theory. The values seen in the figure indicate that the addition of the carbon nanoparticles to the adhesive increased the fracture toughness of the DCB joints, although large standard deviations in the results were reported by the authors. The cause of the high standard deviation in their results was the fact that only 20% of the CNT-reinforced epoxy specimens failed in a cohesive mode, while 80% of the CNT-reinforced specimens and all of the specimens prepared by the neat epoxy and the CNF-reinforced epoxy failed in an interfacial mode. Khashaba et al. [50] attempted to improve the mechanical performance of an Epocast epoxy adhesive, which is an adhesive primarily used in aerospace applications, by different types of nanoparticles. They used three

16 14 Plasma 12 Grit-blasting

10

Peel ply 8 0.00

0.25

0.50 % CNF

0.75

1.00

Figure 2.3  Average lap shear strength of the bonded joints prepared by different surface preparation techniques by Prolongo et al. [48].

46  Structural Adhesive Joints Epoxy Epoxy/CNF Epoxy/CNT

120 110 GIC (J/m2)

100 90 80 70 60

 

20

30

40

60 70 50 Crack length (mm)

80

90

Figure 2.4  Influence of CNF and CNT on the fracture toughness (G1c) of DCB specimens [49].

different NPs, namely MWCNTs, SiC and Al2O3 with various weight contents. The selection of the nanoparticle types was based on the nanoparticles’ aspect ratio. In total, four different types of nanoparticles were used to reinforce epoxy resin. The NPs, SiC and Al2O3 were used in 0.5%, 1.0%, 1.5%, 2.0% weight contents while MWCNTs were used at 0.25%, 0.50%, 0.75% and1.00 %. weight contents They used the standard ASTM tensile and Iosipescu shear test methods to assess the performances of their different types of nanocomposites. It was observed that spherical Al2O3 and SiC nanoparticles, that had relatively lower aspect ratios compared to MWCNT NPs, could be dispersed in their resin relatively significantly easier. They noted that MWCNTs entangled in rope-like networks, thus causing difficulty to disperse. The highest tensile strengths produced by the various nanocomposites were associated with nanocomposites containing 0.5wt% MWCNT, 1.5 wt% SiC, and 1.5wt% Al2O3 nanoparticles. These nanocomposites generated improvements of 7.5%, 4.0%, and 0.5% in tensile strength, and 18.2%, 19.7% and 7.1% in tensile modulus, respectively, compared to the pristine epoxy. The improvements in the shear properties by the abovementioned nanocomposites were 5.5%, 4.9% and 6.3% for the shear strength, and 10.3%, 16.0%, and 8.1% for the shear modulus, respectively. As can be seen, the maximum enhancement in properties was attained when a lower weight content of MWCNTs was incorporated; whereas, on the contrary, the higher weight contents of SiC and Al2O3 produced the maximum enhancements. In another study, Mansourian-Tabaei and Jafari [51] investigated the influence of different nanoparticles (i.e., MWCNT, Al2O3, SiO2 and talc) as well as their hybrids (combinations) on the performance of bonded joints

Improvement of the Performance of Structural Adhesive Joints  47 with 2024-T3 aluminum substrates. They considered six weight fractions of the nanoparticles (i.e., from 0 to 3 wt%) in an epoxy resin, and the comparison was made against the performance of joints made with the neat epoxy. The study investigated the lap shear strength, thermal stability and elongation-at-break of the bonded joints. Also investigated was the influence of a new process they used for dispersing the hybrid nanoparticles into the resin on the mechanical performance of the joints. The process used for dispersing the NPs started by sonicating the mixtures of resin and nanoparticles in an ultrasonic bath, followed by mechanically stirring the mixtures at room temperature. The mixtures were then sonicated again, followed by degassing them in a vacuum chamber. The resulting joints fabricated by the NP reinforced-epoxy exhibited significant improvements compared to the joints fabricated using the neat resin. A maximum gain of approximately 70% in the lap shear strength of joints prepared with 1.5 wt% content of alumina nanoparticles was obtained, while the joint strength decreased at the higher NP contents; nevertheless, the changes in the strength at the higher NP contents were all positive when compared to the strength of unreinforced joints. The gain in the lap shear strength for joints fabricated with MWCNT-reinforced resin was reported as approximately 50% corresponding to 3 wt% content of the NPs. Ironically, no strength-related results were reported for the SiO2- and talc-reinforced adhesives. Moreover, no appreciable changes in resins’ ductility (i.e., elongation at failure) were observed. Furthermore, amongst the joints made by these differently reinforced resins, the MWCNT reinforced epoxy exhibited the highest thermal stability at high temperatures compared to the other NP-reinforced resins; the worst performance was exhibited by the SiO2- and talc-reinforced adhesives. In another study conducted by Razavi et al. [52] investigated the influence of the inclusion of combined SiO2 and MWCNT nanoparticles (with an equal weight ratio of 1:1) in an epoxy resin. SiO2-reinforced epoxy and MWCNT-reinforced epoxy were also prepared for comparison purposes. The study included 0.2, 0.5 and 0.8 wt% of the singular and combined nanoparticles in their resin. The neat and reinforced resins were used to fabricate single-lap bonded joints with 7075-T6 aluminum substrates. A summary of the results obtained by the investigators is shown in Figure 2.5. By considering the results illustrated in Figure 2.5(a), when the shear strengths of the nanoparticle-reinforced joints are compared to those of the joints prepared by the neat adhesive, one can see a degradation in strength of the joints fabricated using the resin reinforced with 0.2 wt% SiO2 and 0.8 wt% MWCNT. However, the other selected weight-fractions of the nanoparticles produced some improvements in the shear strength

48  Structural Adhesive Joints

Shear strength (MPa)

16 14 12 10 8 6 4 2 0

0.2 wt%

0.5 wt% SNPs

0.8 wt%

MWCNTs

Pure adhesive

Hybrid

Pure adhesive

(a)

Elongation at failure (mm)

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

0.2 wt%

0.5 wt% SNPs

0.8 wt%

MWCNTs

Hybrid

Pure adhesive

Pure adhesive

(b)

Figure 2.5  Comparison between the (a) shear strength (b) elongation at failure for the single-lap joints reinforced with single and mixed nanoparticles (i.e., silica nanoparticles (SNPs) and multi-walled carbon nanotubes (MWCNTs)) investigated by Razavi et al. [52].

of the joints. Moreover, no degradation in the strength was observed in the joints made with an adhesive containing the hybrid nanoparticles. In fact, in comparison to the shear strength of joints made with the neat resin, the highest gain of 19.5% in the strength was observed for the joints with adhesive containing 0.8 wt% hybrid NPs. As for the joints ductility, as can be discerned from the elongation at failure results shown in Figure 2.5(b), the joint fabricated by the hybrid NP-reinforced adhesive produced the greatest ductility in comparison to the joints prepared by both the neat and single-type NP-reinforced adhesives. Therefore, one can conclude that, in

Improvement of the Performance of Structural Adhesive Joints  49 general, the hybrid NPs produced more positive effects than those gained by the inclusion of single-type NPs. The number of works in regard to the use of nanocarbon particles to reinforce resins and adhesives has increased noticeably in the last decades. While most of the articles published in this area in the last decade and the beginning of this decade have primarily examined the influence of CNTs, since then several researchers have examined the influence of different types of nanocarbon particles in resins and adhesives. One of the earliest works that used graphene nanoplatelets in adhesively bonded joints is a series of works by Taheri and his co-workers [53–55]. They reinforced West System epoxy with different fillers and nanoparticles (i.e., Q-cell, CNFs, CNTs and GNPs) with weight-percentages of 0.25, 0.5 and 1. They used the reinforced adhesives to prepare tensile test specimens of the neat and reinforced resins, as well as single lap bonded joints made of glassepoxy and carbon-epoxy substrates. They subjected the specimens to various tensile loading rates (1.5, 15, 150, 1500 mm/min) and shear loading at 1.5, 3 and 2.04E5 mm/min. They observed that the Q-cell reinforced adhesive did not perform satisfactorily, and that Q-cell created workabilityrelated issues (unworkable low viscosity). However, the addition of CNTs, CNFs and GNPs to the resin enhanced the mechanical properties of the resin. Moreover, their single lap shear test results revealed that the 1 wt% GNP reinforcement produced the highest gain in the lap shear strength. In another study, Ahmadi-Moghadam and Taheri [56] reinforced Araldite LY1564 (Bisphenol-A) epoxy resin (with Aradur 2954 (cyclo­ aliphatic polyamine) hardener) with GNPs and CNTs. Four different contents (0.5, 1, 2 and 3 wt%) were used to reinforce the resin. They observed a linear increase in mode I fracture toughness in their GNP-reinforced resin. They obtained up to 90% enhancement in the fracture toughness for the resin that was reinforced with 3 wt% GNPs (see Figure 2.6) against 75% increase when a mixture of GNPs and CNTs was included in the resin (1.7 wt% and 0.3 wt%, respectively). However, the gain was at the expense of 11% degradation in mode II fracture toughness of the resin. They also observed that the presence of nanoparticles enhanced the plastic deformation at the crack tip, creating more shear-bands in the vicinity of crack front under mode-I fracture. They identified the crack deflection being the main factor responsible for the improved toughening mechanism. In a follow-up study [57], the authors functionalized their GNPs by three different means (i.e., silane-functionalized graphene oxide GNPs and amino-­functionalized GNPs (referred to as G-NH2 hereafter). They gained a further 82% improvement in the fracture toughness of their epoxy resin with the addition of only 0.5 wt% of amino-functionalized GNP.

50  Structural Adhesive Joints 2

KI (GNP-reinforced resin) KI (CNT+GNP-reinforced resin) KII (GNP-reinforced resin) KII (CNT+GNP-reinforced resin)

Knanocomposite/Kneat epoxy

1.5

1

0.5

0.5 wt%

1 wt% 2 wt% Nanofiller content

3 wt%

Figure 2.6  Normalized fracture toughness versus wt% content of nanoparticles [56].

It should be noted that the significant improvement in the response of the functionalized GNP-reinforced resin had also been reported by other investigators over a decade ago. For instance, in 2005 Gojny et al. [58] reported 11% gain in the Young’s modulus of an epoxy that was reinforced by 0.3 wt% amino-functionalized double-walled-CNT. The improvement they obtained in the fracture toughness of the resin was much more significant, as high as 43% at 0.5 wt% content of amino-functionalized double-walled-CNT. In an interesting study conducted by Ma et al. [59], the enhancement of tensile and lap-shear strengths of Araldite GY251 Epoxy and HY956 Hardener by various carbon NPs was investigated. They added 1 wt% coiled multi-walled carbon nanotubes (CMWCNTs) and conventional MWCNTs to an epoxy resin. The prepared specimens were tested both at room and cryogenic temperature of -196 oC. They observed CMWCNT-reinforced resin produced 4.46% and 36.9% improvements in the tensile strengths of the specimens that were tested at room and cryogenic temperatures, respectively. In comparison to the aforementioned results, MWCNT-reinforced resin yielded 6.82% and 28.7% improvements, respectively. However, interestingly, the inclusion of MWCNTs in the resin caused minor degradation of resin shear strength when tested at room temperature, but indeed enhanced its strength by 9.68% when the reinforced resin was tested at the cryogenic temperature. In contrast, MWCNT reinforced resin strength was not degraded at room temperature, but the gain in strength at cryogenic temperature was only 1.47%.

Improvement of the Performance of Structural Adhesive Joints  51 The influence of inclusion of carboxyl functionalized MWCNTs on fracture behavior of the adhesively bonded joints was also examined by Gheibi et al. [60]. Bonded joints specimens were fabricated in the DCB and end-notched flexure (ENF) configurations using Araldite 2015 adhesive. They observed that reinforcing the adhesive with up to 0.3 wt% MWCNTs content led to the improvement of both mode I and mode II critical strain energy release rates (SERR). However, additional MWCNT content in excess of 0.5 wt% was observed to have adverse effect caused by the agglomeration phenomenon. In another investigation, Khan et al. [61] prepared a GNP-reinforced poly(vinyl acetate) (PVAc) adhesive. They used solution processing technique to prepare composites of PVAc and solvent exfoliated GNPs. They conducted tensile and lap shear tests on the adhesive and demonstrated that the strength and toughness of the GNP-reinforced PVAc increased 4 and 7 times, respectively, when the resin included 0.7 wt% GNPs. In an experimental investigation conducted by Asaee et al. [62] the feasibility of improving the bonded interface between fiber-reinforced plastic (FRP) composite and AZ31B-H24 magnesium (Mg) alloy by incorporation of GNPs in the West System room-cured two-part epoxy was studied. They incorporated amino-functionalized GNPs (NH2-GNPs) with 0, 0.05, 1 and 2 wt% concentrations in the resin. Square shaped 100 x 100 mm2 specimens were fabricated. Each specimen was rigidly held at its four edges and impacted at its center with a semi-spherical impactor. Their experimental results revealed that the specimens whose interfaces were reinforced with the functionalized GNPs could endure the impact energy more effectively. In particular, the addition of 0.5 wt% and 1 wt% of the GNPs was observed to have improved the ductility and resiliency of their 3D fiber-metal laminate specimens. As a result, these specimens could sustain a larger local deformation in comparison to the baseline specimens (i.e., the specimens whose FRP/Mg interface resin did not include any GNP). Quite recently, An et al. [63] examined the influence of CNTs on the response of a bonded joint with aluminum substrates. They prepared single-lap bonded joints with a two-part epoxy resin with two different adherend thicknesses (i.e., thin (0.2 mm) and thick (0.7 mm)) and evaluated the influence of CNTs on the static strength and failure modes of the joints. A total of seven concentrations of CNTs were considered (i.e., 0, 0.05 0.1 0.3, 0.5, 0.7, 1 wt%). Impedance method was also used to detect defects in their bonded joints. They actually observed significant reductions in the lap shear strength of their thin joints; the reduction was as much as 47% for the joints prepared with the adhesive that contained 1 %wt CNTs. However, in the thicker joints, the strength was marginally improved (by

52  Structural Adhesive Joints only 10.77% when 1 %wt CNTs were used in the adhesive). They attributed the degrading outcomes in the thinner joint to the incorporation of the CNTs which caused the reduction in the adhesive effective contact area with the substrates, thus causing interfacial failure mode. In contrast, cohesive failure mode prevailed in their thicker bonded joints. The author of this chapter does not agree entirely with the reason provided by An et al. Indeed, compared to a relatively thick joint, a thin joint would undergo greater local deformation in its overlap region, which would result in comparatively significantly higher bending moment in the region. This greater bending moment will give rise to greater magnitude of the peel stress in comparison to the shear stress, while the latter would be more dominant in the thicker joint. Consequently, peel stress would have more detrimental effect on the bonded joint, and as a result, the thin joint would fail at much lower applied load. Finally, one of the most recent studies that investigated the influence of the inclusion of nanoparticles on the response of bonded joints is that by De Cicco and Taheri [64]. The study considered the in-plane compression and impact-buckling responses of a novel 3D fiber-metal laminate (3D-FML), whose metal/FRP interfaces were reinforced with NH2-functionalized GNPs. In this study, a particular emphasis was placed on investigating the influence of GNP reinforcement on a bonded interface that included an initial delamination. The responses of their reinforced interfaces were compared with those formed by the neat resin. Another interesting aspect of the study was the investigation of the response of GNP-reinforced joints at sub-freezing temperature of -50 °C. Similarly to the work of Asaee et al. [62], 0, 0.5, 1 and 2 wt% GNPs were incorporated in West System’s roomcured epoxy resin. The resin was then used to bond magnesium sheets to a 3D FRP core. The authors observed an unexpectedly low level of improvement in impact energy absorption which was anticipated. The maximum gain in the energy absorption was reported at 12.5% when the resin was reinforced with 0.5 wt% GNP content. They attributed the low margin of improvement to the chemical incompatibility of the magnesium alloy with the epoxy resin, which caused premature interfacial failure, thereby not allowing the GNPs to exhibit their beneficial attributes (i.e. in bridging cracks and resisting crack advancement). Moreover, GNPs inclusion in the resin caused an adverse effect on the performance of the interfaces when the specimens were tested at the sub-freezing temperature. In effect, the inclusion of the GNPs led to an increase in delamination propagation compared to the non-GNP reinforced specimens. This could be attributed to the mismatch of the coefficients of thermal expansion and Poisson’s ratios of the GNPs and their surrounding resin. It should be noted that, in

Improvement of the Performance of Structural Adhesive Joints  53 a different work, the same authors [65] investigated the effect of different surface preparation techniques on the interface bond strength of the aforementioned materials combination. They demonstrated that none of the commonly practised surface preparation techniques, including an elaborate technique that had been developed specifically for treating magnesium alloy substrates, could not generate adequate interface bond strength between magnesium and epoxy. The authors, therefore, developed and proposed a relatively simple technique to improve the interface bonding strength of magnesium-to-epoxy resins. As seen above, most of the studies that examined the use of nanocarbon particles for reinforcing adhesives have been conducted using thermoset adhesives. One of the very few works that investigated the use of carbon nanoparticles in a thermoplastic resin is the work of Littlefield et al. [66]. They incorporated various types of graphenes in poly(ether ether ketone) (PEEK)  with the main objective of creating an adhesive for use in high-temperature applications. They reinforced the resin with 1, 2, 5, 10 and 35 wt% GNP contents. They exposed the reinforced resin to microwave and observed their 2, 5 and 10 wt% reinforced resins beginning to exhibit bulk melting and bubbling within 4:15 , 3:30 and 2:56, minutes, respectively. Their lap shear test results indicated that inclusion of 2 wt% GNPs improved the strength of the PEEK by 72%; however, the gain in the strength significantly decreased once the GNP content was above 5 wt%. Unfortunately, the lap shear tests were done at room temperature; therefore, the strength of the adhesive at higher temperatures remained unexplored. In another work, Stitt [67] examined the influence of incorporation of GNPs in a high-impact polystyrene (HIPS) co-polymer containing butadiene as a toughness modifier. Lap shear specimens were fabricated using the aforementioned GNP-reinforced thermoplastic adhesive as per ASTM D1002 in a “sandwich” configuration. Joints were made with carbon-epoxy substrates as well as with aluminum substrates. In addition, plasma treatment was used to treat the bonding surfaces. Adhesive thickness was kept constant in all their specimens by placing two 0.5 mm wires on the surface of one of the adherends. The reinforced adhesive was turned into a thin film on one of the adherends and the joint was processed in a convection oven at 225 oC and in an industrial microwave oven. Their results revealed that the plasma treatment had a significant effect when applied on the aluminum substrates, leading to doubling the load-bearing capacity of their joints; however, the influence of plasma treatment on the carbon-epoxy substrates was not as significant (i.e., it led to a marginal gain of 11%). Moreover, the bonded joints that were fabricated with the GNP-reinforced

54  Structural Adhesive Joints resin and were processed in a convection oven exhibited slightly lower lap shear strength compared to the specimens prepared by using neat resin in the same oven. In contrast, the lap shear strength of GNP-reinforced joints processed in microwave oven increased by 135% for the plasma-treated joints in comparison to the untreated joints. One of the issues that is often neglected in the research works that have considered performance gain by inclusion of various types of nanocarbon particles in resins and adhesives has been the issue of galvanic corrosion that is promoted by such particles. The issue of galvanic corrosion was identified by the aerospace industry in the 90s, when it was noted that aircraft alloys (more specifically, the two most commonly used aluminum alloys: 2024-T3 and 7075-T6) were susceptible to local galvanic corrosion [68, 69]. Specific to ABJs, Gkikas et al. [70] demonstrated that while the addition of 0.5 wt% CNTs to an epoxy adhesive improved the performance of their ABJs by almost 50%, the addition of CNTs increased the galvanic corrosion of the joints with aluminum 2024-T3 adherends by a small amount. However, the rate of galvanic corrosion increased significantly when the CNT content was increased from 0.5 wt% to 1 wt%.

2.3 Assessment of Performance of Adhesively Bonded Joints (ABJs) 2.3.1 Brief Introduction to the Procedures Used for Assessing Stresses in ABJs Adhesively bonded joints offer certain advantages over mechanically fastened joints, especially when joining fiber-reinforced polymer composite (FRP) materials. The main disadvantage of mechanically fastened joints is their low structural efficiency, which is a direct result of the anisotropic and brittle nature of most FRP adherends. As a result, higher stress concentrations are often developed when FRP substrates are joined with mechanical fasteners; such stress concentrations could vary significantly from one composite to the next, mainly depending on the fiber alignment and lay-up sequence of the FRP, while the stress concentration around holes in isotropic materials would be somewhat consistent from one isotropic material to another. Comparatively, under an applied far-field stress, the stress concentration around a hole in an isotropic material would be hovering at approximately three times the far-field applied stress. However, in finerreinforced laminate composites, the stress concentration can be less than a factor of three, or it can exceed by more than six times the far-field stress

Improvement of the Performance of Structural Adhesive Joints  55 magnitude [71]. Moreover, the typical structural efficiency of a mechanically fastened joint mating FRP components as a rule of thumb would be generally about 30% when joining unidirectional laminates and 50% for quasi-isotropic laminates ([72, 73]). The structural efficiency in this context refers to the strength of the joint over the strength of the substrate laminate. In contrast, adhesively bonded joints offer higher structural efficiency, at approximately 80% of the strength of the weakest adherend [72]. Along with high structural efficiency, adhesive joints are generally lighter (sleeker) than their mechanically fastened counterparts, thus, are often a more economical alternative. Despite the mentioned efficiency of bonded joints, the joint will inevitably be subjected to significant stress concentrations, which are developed at the ends of the overlap region. Theoretical assessment of adhesively bonded joints, specifically lap joints, started with the solution proposed by Volkersen [74], who provided an equation by which the stress in the overlap region could be assessed. In 1944, Goland and Reissner [75] improved Volkersen’s solution, enabling the calculation of the peel stress in the overlap region. However, Goland and Reissner did not account for the presence of the adhesive layer in the model on which their solution was developed; in other words, they approximated the flexural stiffnesses of the joint’s constituents, assuming the flexural stiffness of the overlap region being eight times that of the adherend. Later in 1973, Hart-Smith [76] addressed the shortcoming of Goland and Reissner’s solution. Goland and Reissner’s had assumed a single section to model the overlap segment of the joint (in other words, they had lumped the stiffnesses of the two substrate sections in the overlap section as one equivalent section). Hart-Smith improved joint deformation model by removing the lumping of the overlap section, accounting for the rigidity of each constituent in the region. This was achieved by idealizing the region using a layered beam so as to better represent the deformations in the two adherends. Since the work of Hart-Smith, several researchers have expended significant efforts to improve the above-mentioned solutions. For instance, Oplinger [77] proposed bending moment eccentricity factor using a layered beam model, so as to evaluate the deformations of a balanced single-lap joint under tension more effectively. In essence, Oplinger decoupled the deformations of the two adherends in the overlap section and related them to the through-thickness shear deformations of the adhesive layer. Tsai and Morton [78] concluded that Hart-Smith’s solution provided accurate results when applied to bonded joints with short overlaps, while Oplinger’s model would provide more accurate results when joints with relatively long overlap lengths are considered. Since then, several researchers have

56  Structural Adhesive Joints expended efforts to develop a solution that could evaluate the stresses in bonded joints, especially in asymmetric FRP bonded joints in a more effective and accurate manner (see for instance: [79–81].)

2.3.2 Computational Approaches for Assessing Response of ABJs The other approach for assessing the performance of adhesively bonded joints is the fracture mechanics approach. Development of a crack creates local stress concentration that, theoretically speaking, is considered as an infinite value. Therefore, a special parameter is used to study crack intensity, the so-called stress intensity factor, K [82]. The stress intensity factor is also used to describe the singular stress and displacement fields around the crack-tip. There is another parameter in fracture mechanics that is often used in the analysis of linear-elastic cracked members, referred to as the strain energy release rate, G. The strain energy release rate represents the change in the member’s strain energy with respect to crack growth. The total strain energy release rate is the sum of strain energy release rates in all fracture modes. (i.e., modes I, II and III). Another more generalized parameter is the path independent J-integral proposed by Rice [83], which under certain conditions can take into account non-linear material behaviour. In linear elastic materials, the J-integral is equivalent to the total strain energy release rate. There are numerous studies that have used these approaches, either analytically or numerically (e.g., using the finite element method). In modelling adhesively bonded joints using the finite element approach, one must take account of certain important considerations. Firstly, one ought to use much finer mesh when discretizing the regions near the overlap’s ends, as the peak peel and shear stresses in the adhesive are known to occur in these regions. Secondly, the model must take into account the possibility of large deformations and geometric nonlinearities. Several techniques have been incorporated in various commercial FE codes for evaluating the stress intensity factors and strain energy release rates, most notable ones being the crack-tip opening displacement (CTOD), modified crack closure integral (MCCI) and the J-integral methods [84]. However, more effective numerical approaches and techniques have been developed in the recent years with the specific aim of modelling crack initiation and propagation accurately. In the recent years, the main techniques used to simulate fracture initiation and propagation with the aid of the finite element method are the (i) element erosion approach, (ii) cohesive zone modelling (CZM), and (iii) extended finite element method (xFEM). It should

Improvement of the Performance of Structural Adhesive Joints  57 be noted that other techniques, like the virtual crack closure technique (VCCT), may also be coupled with other algorithms to simulate crack propagation in a body; however, only the techniques that could individually simulate crack propagation are briefly discussed in this chapter. In addition to the aforementioned approaches, three exist three main approaches in the modern computational mechanics for simulating fracture initiation and propagation in a body; they are: (i) the element erosion approach, (ii) the cohesive zone modelling (CZM), and (iii) the extended finite element method (xFEM). As one may deduce from its title, in the element erosion approach, the elements located on a potential crack path are deleted based on certain appropriate stress or strain criterion, therefore, creating a crack path. While this approach is the simplest amongst the three noted approaches; however, the resulting crack path is extremely mesh-dependent. Therefore, the accuracy of the results could vary significantly [85]. CZM’s fundamentals are often attributed to the early works by Dugdale [86] and Barenblatt [87], who presented their pioneering works in the early 60s. Dugdale developed a methodology by linking fracture and strength criteria. He stated that stresses in a notched material are limited by the yield strength of the material (or fracture strength, depending on the material’s intrinsic response), in turn causing a thin plastic zone ahead of the notch. Barenblatt subsequently used the cohesive forces in the body with the crack to solve the problem of equilibrium. These two researchers were the first to recognize the fact that a yielded zone at the tip of a crack in a material would result in a reduction in the stress singularity. The first incorporation of Dugdale and Barenblatt theoretical works in a numerical context can be referred to the work of Hillerborg and his coworkers [88, 89]. Since then, CZM algorithm has been included in most mainstream commercially available finite element codes such as ABAQUS, ANSYS and LS-Dyna to name a few, and has been extensively used to treat various crack and delamination problems in various materials. There has also been an extensive body of work utilizing computational CZM to simulate crack propagation in adhesively bonded joints under various loading conditions (see for instance: [90–96]). Moreover, CZM has been widely used to simulate delamination propagation in fiber-reinforced composites. One of the earliest such analyses is the study that was conducted by Espinosa et al. [97] in 2000, who employed CZM combined with a viscoelastic model to study the delamination of a glass fiber-reinforced composite. The xFEM approach involves the use of special elements that are “enriched” in such a way that their formulation could account for the presence of a discontinuity, without the need for creating an actual discontinuity

58  Structural Adhesive Joints between the elements. As a result, one can simulate the development of a crack in a stressed body, as well as propagation of that crack, which may travel in multiple directions [98–101]. The fundamentals of xFEM approach are briefly explained here. xFEM accounts for the presence of the discontinuity by using an enrichment function for the elements that are traversed by the crack (for more information on this phenomenon please refer to [99]). Let Ӏ be the set of all the nodes in the domain Ω and J be the set of all the nodes belonging to the enriched elements, excluding the one containing the crack tip, which is assigned to set K. The nodal variable (e.g., displacement) can, therefore, be represented by [85]:

( )

u x =



∑ N ( x )u + ∑N ( x )u + ∑N ( x )u i

 i∈I \ J 

∪

∗ i

i

∗∗ i

∗ i

i∈J

 K 

i∈K

∗∗ i



(2.1)

In the above equation, ui, ui∗ and ui∗∗ are the regular and enriched nodal variables, while Ni, N i∗ and N i∗∗ are the regular and enriched shape functions (with asterisks), respectively. The following equation represents the enriched shape functions:



( ( )) ( ( ))

N i∗ = N i  H f x + H f xi  ,

(2.2)

and 4

∗∗ i

N = Ni

∑ β ( x ) − β ( x ) , k

k

i

(2.3)

k =1

In the above equations, H denotes the Heaviside function. Variable can be represented by:



 θ θ θ θ β ( r ,θ ) =  r cos , r sin , r sinθ sin , r sinθ cos  (2.4) 2 2 2 2 

where r and θ are graphically illustrated in Figure 2.7.

Improvement of the Performance of Structural Adhesive Joints  59 Nodes є K Nodes є J Enriched elements n

x r θ

Crack surface ∂Ω

0

f (x_ )


0

Domain Ω

f (x) _ =0

Figure 2.7  Graphical illustration of the extended finite element method (xFEM) approach [102].

Note that in order to apply xFEM effectively, the previously described CZM can be used to obtain the crack opening displacement, after which the maximum principal stress criterion or the maximum shear stress criterion could be used to establish the onset of crack propagation and its direction (this issue will be elaborated further in the forthcoming discussion). Subsequently, once the selected criterion is satisfied in the element containing the crack tip, the element is considered as failed and the crack tip is advanced by one element. Comparing the two approaches, one can conclude that CZM would be a relatively easier method to implement [87]; however, it requires a priori knowledge of the crack path. Comparatively, xFEM would be more effective, especially in situations where the crack path is unknown, or in cases where a crack may kink or bifurcate. Moreover, xFEM’s formulation is significantly more complex than that of the conventional finite element [103, 104]. Therefore, the use and implementation of xFEM requires special skill to generate accurate results. For this reason, and the fact that its algorithm is currently not available in most commercial finite element softwares, its use has been limited to relatively a few studies. These studies have essentially simulated crack initiation and/or propagation in various materials (e.g., chopped strand mat-reinforced composite [105], orthotropic media [106], aluminum-ceramic bi-layered material [107]). In comparison, even fewer works are available in which xFEM has been used to treat crack in adhesively bonded joints or for simulating delamination propagation. Some of such notable works are as follows: Wang and Waisman [108], who simulated plies delamination and cracking of their laminate composite by xFEM and showed the mesh independency of their results. It should be

60  Structural Adhesive Joints noted that while several researchers have demonstrated the outstanding capability of xFEM in treating complex crack problems, nonetheless, the nature of the selected xFEM formulation and its implementation algorithm have been shown to have strong effects on the generated results. At this juncture, it is also worth mentioning that other techniques, such as the Virtual Crack Closure Technique (VCCT), may also be coupled with other algorithms to simulate crack propagation in a body; however, in this chapter, we limit the discussion to the techniques that could individually simulate crack propagation.

2.4 Application of CZM for Simulating Crack Propagation in Adhesively Bonded Joints 2.4.1 Basis of the CZM In this section, a few studies that have investigated the crack initiation and growth in bonded joints are briefly reviewed, followed by the studies that have incorporated xFEM to conduct similar simulations. The implementation of CZM will be first described briefly. This would include the implementation of the actual material’s physical traction-separation response. There are various CZM models that have been developed to describe the pre- and post-fracture states of materials. These models are distinguished essentially based on the basic functions used to define the traction-separation response of the material (e.g., bilinear, multilinear, polynomial, trigonometric, and exponential). One of the first studies that incorporated CZM for analyzing ABJs was that by Alfano [109]. In this work, the influence of the shape of the most commonly used interface traction-separation models was investigated by analyzing an interface crack in pure Mode I and Mode II. The numerical performance and accuracy of the predicted results were also discussed. Alfano found that the trapezoidal model gave the worst results both in terms of numerical stability and convergence of the FE solution when compared to the results obtained using the analytical solution. In contrast, the exponential model was found to produce the most accurate results. Interestingly, the bilinear model was shown to produce the most optimal solution based on a compromise between CPU time and accuracy. The schematic representation of the bilinear traction-separation model which is also the most widely used traction-separation model, is shown in Figure 2.8.

Traction σ

Traction σ

Improvement of the Performance of Structural Adhesive Joints  61

Gc

Gc

(a)

Separation δ

(b)

Separation δ

Figure 2.8  Comparison of the (a) actual physical and (b) numerical representations of a material’s traction-separation response [94].

The bilinear cohesive model is typically represented by the following mathematical relationship:



 σ  n σ =  σs  σ  t

  K nn    =  K ns   K nt  

K ns K ss K st

K nt   δn  K st   δ s K tt   δt

   = K δ (2.5)  

where σ represents the traction, and subscripts n, s and t refer to the normal (out-of-plane) and first and second in-plane shear directions, respectively, Kij terms represent the respective stiffness values of the cohesive layer, and δs are the corresponding separation displacements of the cohesive model. Subsequently, a suitable damage criterion which establishes the onset of damage is incorporated. Often the maximum stress criterion or maximum strain criterion or the quadratic nominal stress or strain criterion is used for the purpose. This step is followed by the implementation of an evolution failure criterion, which evaluates the failure of the material. The failure criteria that are widely used are the power-law and the Benzeggagh and Kenane criteria. It should be noted that one could trace the damage in a mixed-mode cracking situation by combining the damage resulting due to each mode by the so-called “mode-mixity” ratio (for more details see [110]). However, one of the most useful articles with respect to how to conduct a practical CZM analysis, specifically how to select the various parameters involved in such analysis, is the article prepared by Song et al. [111].

62  Structural Adhesive Joints Therefore, the reader is highly encouraged to review this practical and useful article if deciding to conduct a cohesive zone modelling analysis.

2.4.2 Applications of CZM to Bonded Joints An interesting application of CZM in modelling response of adhesively bonded joint under a loading condition which is different from the conventionally used static tensile load has been presented by Mohamed and Taheri [110], who investigated the applicability of CZM in predicting the response of bonded joints subject to both mechanical and cyclic thermal loadings. In this study, the response of DCB specimens that were subjected to varying thermal cycles (from 1 to 1000 cycles) in the temperature range of -35 oC to + 45 oC and subsequently subjected to the conventional DCB static loading was studied. The joints response under thermal loading and the subsequent mechanical loading was monitored using the CZM facility of ABAQUS FE software. The bilinear traction-separation law was used along with the maximum principal stress and the Benzeggagh and Kenane failure criterion. The details of the multi-step analysis in ABAQUS platform are provided in this article. A close comparison of the experimental and CZM generated results is illustrated in Figure 2.9(a). They also demonstrated that CZM FE analysis could successfully predict the degradation of DCB specimens strength which was caused as a result of the applied thermal cycles (see Figure 2.9(b)). The authors also simulated the response of an end-notch flexural bonded specimen using the same approach. The results of the simulation also showed a closed agreement with the experimentally obtained results. 250

0.9 0.8 0.7

150 100 0 Cycles 1000 cycles FE Baseline FE 1000 Cycles

50 0

0

10

20 Displacement (mm) (a)

30

40

Damage Index

Load (N)

200

0.6 0.5 0.4 0.3 0.2 0.1 0

0

200

400 600 800 1000 Number of applied thermal Cycles (b)

1200

Figure 2.9  (a) Comparison of the experimental and the CZM FE simulation results for the baseline (not thermally cycled) and thermally cycled specimens (b) variation of the damage index as a function of the applied thermal cycles showing degradation of the joint strength due to the applied thermal cycles [110].

Improvement of the Performance of Structural Adhesive Joints  63 The influence of the nature of two cohesive laws on the response of bonded pipe joints was investigated by Ouyang and Li [112]. The objective of the investigation was to examine the effect of the two traction-­separation models, namely the equivalent linear CZM and the widely used bilinear CZM, on predicting the torsional capacity of the bonded pipes which would be affected by the predicted magnitude of the interface fracture energy in the bond region. Their equivalent linear CZM does not include the separation segment of the conventional bilinear traction-separation model; however, it has identical shear strength and fracture energy as in the bilinear CZM. The traction-separation models were shown to influence significantly the magnitude and distribution of the interface shear stresses on pipes mated with different bond lengths as seen in Figure 2.10. However, interestingly, as illustrated in Figure 2.11, the influence of the CZM model on the torsional capacity of the bonded pipes was shown to be quite insignificant. In another study, Barbosa et al. [113] conducted an experimental and numerical study to predict the tensile response of tubular joints with 6061T6 aluminum adherends bonded with three different adhesives. They also used the commonly incorporated bilinear traction-separation CZM. The three adhesives used were a relatively brittle epoxy (Araldite AV138), a more ductile epoxy (Araldite 2015) and a highly ductile polyurethane (Sikaforce 7752). They investigated the Influence of the effective overlap length for the joints made by these three adhesives. They obtained an accurate prediction of the responses of the joints formed by the two epoxy adhesives, while the results obtained for the polyurethane joint under­predicted the load capacity of the joint. They attributed the discrepancies of their results to the bilinear nature of the traction-separation model which could

20

15 10

5

Linear Bilinear

0 0 10 20 30 40 50 60 70 80 Distance measured from the left end of main pipe (mm) (a)

Interface shear stress (MPa)

Interface shear stress (MPa)

20

15 10

Linear Bilinear

5

0

0 80 120 160 200 240 280 320 40 Distance measured from the left end of main pipe (mm) (b)

Figure 2.10  Influence of the CZM traction-separation model on the interface shear stress distribution for bonded pipes with a bond length of (a) 80 mm and (b) 320 mm [112].

64  Structural Adhesive Joints 150

Tmax (kN-m)

120 Equivalent Linear Bilinear_K = 1 Bilinear_K = 8

90 60 30 0 0

40

80

120 160 200 240 Bond legth L (mm)

280

320

Figure 2.11  Relationship between the torsion load capacity and bond length for the linear and bilinear cohesive zone models [112].

not accurately capture material fracture response. They hypothesized that the high ductility of the adhesive enabled the adhesive to endure higher peak shear and peel stresses that could not be accurately simulated by the bilinear CZM. Shadlou and Taheri [114] also utilized CZM through ABAQUS FE software to study the sensitivity of the interface of FRP layers used to wrap the damaged (gouged) section of a steel pipe subjected to various types of combined loading conditions. The FRP wrap is used to restore the damaged pipe’s strength. The purpose of the investigation was to illustrate (a) the influence of axial load on such rehabilitated pipes, which is often overlooked when specifying the thickness of such FRP wraps used to restore the strength of damaged pipes, and (b) to explore the influence of disbond between the FRP wrap and pipe, which could occur in practical cases due to significant temperature changes and/or thermal shocks, which is also ignored in the design of rehabilitated pipes. The pipe considered had a diameter of 152 mm with a rectangular shaped gouge with dimensions of 75 mm x 12 mm located at the center span of the pipe, with its large dimension oriented axially on the pipe. Each pipe was first subjected to a specific value of internal pressure and was subsequently subjected to a specific magnitude of axial load (both compressive and tensile) or bending moment, which could cause failure of the pipe as determined through the FE analysis. The FE calculated ultimate strength values were then compared with the values obtained through the ASME standard’s equation. In addition, the effects of FRP thickness, length and state of the pipe on the

Improvement of the Performance of Structural Adhesive Joints  65 effectiveness of the FRP repair system were systematically investigated. The traction-separation of the material was incorporated using the bilinear model. They demonstrated a good comparison between their computation simulation results and those obtained using the ASME standard. Using the CZM FE analysis, they showed important observations that due to space limitation cannot all be presented here. As an example, they showed the effect of FRP wrap disbond on the normalized axial load-bearing capacity of the bonded pipes. It was shown that when the pipe had no internal pressure, its capacity would be virtually unchanged whether being subjected to compressive or tensile axial load. Moreover, the axial load capacity would decrease by approximately 20% if the FRP wrap bond region was fully disbonded. However, the application of internal pressure changes the response significantly, in that the effectiveness of the FRP wrap becomes strongly dependent on the nature of the axial load (i.e., whether it is compressive or tensile). Fairly recently, De Cicco and Taheri [115] also investigated the influence of disbond at the interface of a DCB specimen and in the adhesive interface layer between metal and FRP of a complex three-dimensional fiber-laminate(3D-FML) hybrid composite system, which could be developed due to an axial impact. They used both xFEM and CZM analyses individually, as well as a hybrid analysis combining CZM and xFEM in the framework of LS-Dyna finite element software. While as stated previously, CZM could predict disbond along a pre-determined path (i.e., in this case, assumed to have propagated only within the adhesive layer at the interface), they were successful in tracking the kinked path of the advancing disbond by using the hybrid CZM and xFEM analyses (see Figure 2.12). As can be seen in the figure, the disbond that initially developed within the adhesive started moving towards the adhesive/metal interface, and subsequently propagating along the interface (i.e., through the cohesive elements).

2.39 mm

Initial crack tip position

(a)

18.13 mm

(b)

Figure 2.12  Coupled xFEM/CZM prediction of crack propagation (a) in a DCB test specimen and (b) as a result of the existence of initial disbond between metallic and FRP constituents of a hybrid fiber-metal laminate composite [115].

66  Structural Adhesive Joints

2.5 Application of xFEM for Simulating Crack Propagation in Adhesively Bonded Joints As stated above, compared to CZM, applications of xFEM in adhesively bonded joints are relatively scarce. As demonstrated by De Cicco and Taheri [115], while xFEM as an individual method has been effectively used to detect cracks and their propagation in various solid materials, including fiber-reinforced composites [116], its effectiveness increases significantly when combined with CZM when crack propagation in bonded joints is to be simulated. The effectiveness of combined xFEM/CZM was also recently demonstrated by Bouhala et al. [117]. They predicted the critical strain energy release rate in mode I of a DCB specimen joining unidirectional carbon epoxy experimentally and with the use of xFEM/CZM. The bilinear traction-separation CZM was used in this study as well. In another study, Stuparu et al. [118] also used xFEM/CZM to simulate the response of a single lap joint using ABAQUS finite element code. They were successful in capturing the crack initiation and its propagation leading to a complete failure of the joint. The simulation was initiated by tracking the crack that was advancing from the adhesive to the interface region by XFEM. The subsequent failure of the interface region was simulated by the use of cohesive elements inserted in the interface region. They also captured the phenomenon of the crack propagation diverting from the middle of the adhesive layer to the interface and propagating at this location until failure, without diverting its path back into the adhesive layer (and potentially into the adherend). It should be noted that while the crack initiation and its propagation and kink were simulated by xFEM, but once the crack diverted into the interfacial region, the subsequent crack advancement was captured through a series of zero-thickness CZM elements up to the failure stage. A follow-up study was also conducted by Stuparu et al. [119] by which they simulated crack propagation in a 20 mm long overlap region of three single lap joints, each having different adhesive layer thickness (i.e., 1, 3, and 5 mm). Each overlap region had an initial crack length of 5 mm, located at one end of the adhesive layer. Similarly to their previous analysis, the adhesive/adherend interfaces were modelled with zero-thickness CZM elements. The observed similar crack propagation profile as they did in their previous study (noted in the earlier paragraph), in that the crack traveled along the adhesive for a while and then it diverted into the interface and advanced along the interface.

Improvement of the Performance of Structural Adhesive Joints  67 Campilho [120] conducted a study to evaluate the integrity of CZM/ xFEM modelling facility of ABAQUS for simulating the response of adhesively bonded single and double-lap joints with aluminum adherends, bonded with a brittle adhesive (Araldite AV138). They examined a series of joints with different overlap lengths (between 5 to 20 mm) and compared the outcome of their simulations with some experimental data. First, they compared the results obtained by the use of CZM, which compared favourably with the experimental results since in these cases, the propagation path was known a priori. As for the predicted results by xFEM, which enables tracking a crack travelling along arbitrary paths in a solid continuum element, the authors stated that xFEM methodology was not suitable for predicting damage propagation in the bonded joints. The reason was the fact that in ABAQUS the crack is propagated orthogonally to the maximum principal stresses/strains calculated at the crack tip. Invariably, as a consequence, the crack would be growing towards the adherend in such bonded joints, after which it will travel along the adherend-adhesive interface. Mubashar et al. [121] also conducted elastic xFEM/CZM analysis of a single lap joint with aluminum 2024-T3 adherends and FM73-M epoxy adhesive in ABAQUS finite element. The study basically mimicked the other xFEM/CZM investigations noted earlier with one interesting difference, in that they also modeled the fillets located at the ends of the adhesive layer (i.e., at the ends of the overlap region). As in most analyses cited in this chapter, they also used the bilinear traction-separation model in the CZM portion of the analysis. Moreover, the value of the critical shear stress was determined using the penalty based cohesive zone finite element approach, as suggested by Diehl [122]. As expected, and illustrated pictorially in Figure 2.13, the initial failure of the adhesive occurred in the overlap end region, near the lower adherend corner, where the stress singularity exists. The crack propagation path predicted by xFEM is also illustrated in the figure which upon encountering the layer of cohesive elements, crack propagation simulation is taken over by the cohesive elements. Note that at the same time, the crack also continues to propagate within the xFEM portion of the model toward the free surface of the fillet, while the crack propagation in the CZM element layer continues until the entire adhesive layer is cracked (hence, failed). Mubashar et al. [121] further highlighted the limitation of the algorithms as implemented in ABAQUS as follows. They stated that the crack in ABAQUS is always initiated in the middle of the adhesive element and that the cohesive layer experiences damage before the material actually experiences failing load.

68  Structural Adhesive Joints Upper adherend

Lower adherend Crack initiation

(a)

Crack propagation

Crack propagation in cohesive layer

(b)

(c)

Figure 2.13  Crack initiation and development in the adhesive layer predicted by CZM and xFEM elements; (a) location of crack initiation, (b) crack extending towards the upper adherend, and (c) crack advancing within the CZM elements [121].

They stated: “Since one complete cohesive element has to fail, the XFEM and cohesive element cracks are not connected at their ends and the cohesive zone crack extends the XFEM crack by the element length. However, since the element length is small, this does not induce a major effect on the overall load-bearing capacity of the joint.” They also concurred with the explanation provided earlier by Campilho [120] (i.e., crack propagation in xFEM develops orthogonally to the maximum principal stress/strain). This issue obviously impacts the damage initiation to be element size-dependent. Moreover, if xFEM was to be used instead of using the cohesive layer of elements positioned at the mid-thickness of the adhesive layer, as explained earlier, due to the aforementioned issue, the crack would have propagated towards the adherend. Therefore, in the opinion of the writer, the arbitrary positioning of the CZM in the mid-thickness level within adhesive causes

Improvement of the Performance of Structural Adhesive Joints  69 yet a different bias with respect to crack propagation, which would not be necessarily take place in actual situations. Finally, a somewhat different study is mentioned here, which was conducted by Ezzine et al. [123]. In this study a hybrid riveted/adhesively bonded joint was analyzed by xFEM/CZM approach using ABAQUS FE software. As in all such studies noted here, they also used the bilinear CZM, with the quadratic stress criterion for damage initiation and a power-law criterion for guiding damage propagation. Again, these authors also presumed the expected crack growth direction by placing CZM element along a path within the adhesive layer, thus forcing a cohesive failure of the joint.

2.6 Summary This chapter provided a rather concise summary of some of the notable studies that have used nanoparticles to reinforce resins/adhesives used to fabricate adhesively bonded joints. While some studies have reported the adverse effect of nanoparticles on the load-bearing capacity of reinforced bonded joints; nevertheless, in general, nanoparticles inclusion at an appropriate weight fraction in resins/adhesives could enhance the performance of bonded joints significantly. As for the use of various nanocarbon particles, it has been demonstrated that the potential benefits gained by the use of such nanoparticles in reinforcing adhesives could be significantly enhanced with an appropriate functionalization applied to the nano­particles. However, one of the major parameters that has been overlooked in most such studies is the issue of their cost. Some studies have mentioned that certain nanoparticles would have advantage over other nanoparticles due to their cost; nonetheless, most such claims have overlooked considerations such as the cost associated with the efforts required for mixing and preparing the reinforced adhesives, as well as the limitation imposed by the curing time of the reinforced adhesive for bonding real-life large structural components. Another issue that needs considerable attention is the performance (especially, the long-term) of such reinforced adhesives, especially in harsh environments (e.g., hot, cold and cyclic thermal loads). Some of the works reviewed in this chapter have provided contradictory results when nonreinforced adhesively bonded joints have been tested under cold, hot and varying temperature conditions. This chapter also reviewed some of the articles that have considered the simulation of damage initiation and propagation in bonded joints using the most recently developed numerical methodologies and algorithms (i.e.,

70  Structural Adhesive Joints cohesive zone method (CZM) and the extended finite element method (xFEM)). It was concluded that the combination of xFEM and CZM provided an effective and fairly accurate means for predicting the performance of adhesively bonded joints. However, the current implementation of the algorithms in commercial finite element codes has created limitations in simulating the actual crack advancement in bonded joints, especially those mating fiber-reinforced composite adherends. In such practical situations, a crack may be diverted from within the adhesive to the interface and subsequently may penetrate into the laminate adherend; to the best of author’s knowledge, at this time, such simulation has not been successfully carried out. In all, therefore, more investigations are needed to address the aforementioned issues.

Acknowledgement The author is gratefully indebted to the Natural Sciences and Engineering Research Council of Canada (NSERC), which provided funding in support of most of the author’s works cited in this chapter.

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76  Structural Adhesive Joints 90. H. Khoramishad, A. D. Crocombe, K. B. Katnam and I. A. Ashcroft, Predicting fatigue damage in adhesively bonded joints using a cohesive zone model. Intl. J. Fatigue. 32, 1146–1158 (2010). 91. M. Iranpour and F. Taheri, Analytical and computational investigation into the influence of the compressive stress cycles on crack growth under variable amplitude loading using CTOD. Fatigue Fracture Eng. Mater. Structures. 37, 645–658 (2014). 92. C. D. M. Liljedahl, A. D. Crocombe, M. A. Wahab and I. A. Ashcroft, Modelling the environmental degradation of adhesively bonded aluminium and composite joints using a CZM approach. Intl. J. Adhesion Adhesives. 27, 505–518 (2007). 93. P. Hu, X. Han, L. F. M. Da Silva and W. D. Li, Strength prediction of adhesively bonded joints under cyclic thermal loading using a cohesive zone model. Intl. J. Adhesion Adhesives. 41, 6–15 (2013). 94. A. Turon, C. G. Dávila, P. P. Camanho and J. Costa, An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models. Eng. Fracture Mech. 74, 1665–1682 (2007). 95. S. Sugiman, A. D. Crocombe and I. A. Aschroft, Experimental and numerical investigation of the static response of environmentally aged adhesively bonded joints. Intl. J. Adhesion Adhesives. 40, 224–237 (2013). 96. M. Mohamed and F. Taheri, Fracture response of double cantilever beam subject to thermal fatigue. J. Strain Analysis Eng. Design. 53, 504–516 (2018). 97. H. D. Espinosa, S. Dwivedi and H.-C. Lu, Modeling impact induced delamination of woven fiber reinforced composites with contact/cohesive laws. Computer  Methods in Applied Mechanics and Engineering. 183, 259–290 (2000). 98. N. Moës, J. Dolbow and T. Belytschko, A finite element method for crack growth without remeshing. Intl. J. Numerical Methods in Engineering. 46, 131–150 (1999). 99. T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing. Intl. J. for Numerical Methods in Engineering. 45, 601–620 (1999). 100. R. Krueger, Virtual crack closure technique: History, approach, and applications. Appl. Mech. Reviews 57, 109–143 (2004). 101. V. K. Goyal, E. R. Johnson and C. G. Dávila, Irreversible constitutive law for modeling the delamination process using interfacial surface discontinuities. Composite Structures. 65, 289–305 (2004). 102. D. De Cicco, In-depth understanding of the stability response of a novel 3d fiber-metal laminate under axial impact loading. Doctoral thesis, Department of Mechanical Engineeirng, Dalhousie University, Halifax, NS, Canada (2019). 103. Y. Wang, C. Cerigato, H. Waisman and E. Benvenuti, XFEM with high-­order ­material-dependent enrichment functions for stress intensity factors

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3 Optimization of Structural Adhesive Joints P. K. Mallick

*

Department of Mechanical Engineering, University of Michigan-Dearborn, Dearborn, MI, USA

Abstract

This chapter provides information on various aspects for optimum design and improved performance of adhesively bonded joints in structural applications. They include joint configurations, joint design parameters, substrate properties and adhesive selection. Methods to improve joint performance by adhesive layer modification, substrate shaping and hybrid joining are presented. Keywords:  Lap joints, joint strength, joint design parameters, optimum design, adhesive selection, hybrid joints

3.1 Introduction This chapter considers the design of adhesive joints that are finding increasing applications in many load-bearing structures in aerospace, automotive and other industries. Adhesive joints are made by using an adhesive layer between two substrates (adherends) that may be similar or dissimilar in material characteristics and/or properties. The adhesive is usually a thermosetting polymer, such an epoxy or a polyurethane, which has a much lower modulus than the substrates. It is applied in the joining areas of the substrates in an uncured or partially cured condition. Depending on the adhesive type, curing can take place either at room temperature or at an elevated temperature, often in the presence of an applied pressure normal to the adhesive layer. As the curing reaction transforms the adhesive from its liquid or semi-liquid state to a solid state, bonding is developed between Email: [email protected] K. L. Mittal and S. K. Panigrahi (eds.) Structural Adhesive Joints: Design, Analysis and Testing, (79–96) © 2020 Scrivener Publishing LLC

79

80  Structural Adhesive Joints the substrate surfaces and the adhesive. In recent years, many new adhesive grades have been developed that provide high strength, fracture toughness and crash energy absorption. Along with the improvement in adhesive materials technology, there is also a better understanding of their mechanical behavior that are important considerations in the design of adhesive joints. The primary purpose of a joint, including an adhesive joint, is to transfer loads from one member to another member in a structure. Depending on the joint configuration and load application, load transfer via an adhesive joint can take takes place by shear, tension or combination of shear and tension. Since joints are often the weakest areas in a structure, and service failure of many load-bearing structures often initiates at the joints, it is important to consider the joint configuration and joint design at the early design stages of the structure. Adhesive selection and joint quality also play significant roles in the joint performance. The purpose of this chapter is review literature on these topics and present the findings in light of optimum performance of adhesive joints. It should be noted that vast majority of studies on stresses in adhesive joints and their strengths involve single lap joints under tensile loading. This includes various analytical approaches, finite element analysis and the experimental determination of joint strength using standardized tensile shear tests [1]. The strength of the adhesive joint determined in these standardized tests is called the “lap shear strength”, which is simply the tensile load at which the single lap joint has failed divided by the overlap area. Design considerations for adhesive joints discussed in this chapter are based on the published studies on single lap adhesive joints.

3.2 Joint Configurations The simplest and most common adhesive joint between two or more flat substrates is a single-lap joint (Figure 3.1a) in which load transfer between the substrates takes place through a distribution of shear stresses in the adhesive. However, since the tensile loads applied at the substrate ends are not along the same line of action, a bending moment is generated at the adhesive joint. The bending action sets up a distribution of peel stresses that are directed normal to the substrate-adhesive interfaces. In addition, there is also an axial stress distribution in the adhesive layer. All three stress distributions exhibit peak values very close to the lap ends of the adhesive layer and relatively low values over much of the lap length (Figure 3.2). The double lap joint, shown in Figure 3.1b eliminates much of the bending

Optimization of Structural Adhesive Joints  81

(a)

(b)

(c)

(d)

(e)

(f)

Figure 3.1  Basic bonded joint designs: (a) single lap joint, (b) double lap joint, (c) single strap joint, (d) double strap joint, (e) stepped lap joint, and (f) scarf joint.

5.622 Peel Stress

4.922 4.221

Stress (MPa)

3.521 Axial Stress

2.821 2.121 1.420

Shear Stress

0.720 0.020 –0.679 –1.380

0

0.976

1.953

2.930

3.907

4.884

5.861

6.838

7.815

8.792

9.769

11.723 12.7 10.746

Distance along Overlap Length (mm)

Figure 3.2  Distribution of shear, peel and axial stresses at the adhesive mid-thickness in a single lap adhesive joint between two flat SMC-R composite substrates (Adhesive thickness = 0.762 mm, Substrate thickness = 2.54 mm).

82  Structural Adhesive Joints action and the resulting peel stresses present in the single lap joint. Since the average shear stress in the adhesive layer is also reduced by nearly onehalf, a double lap joint shows a higher joint strength than a single-lap joint. However, it is not completely free of bending moments. Even though the middle substrate does not experience any bending, load transfer from the top and bottom substrates to the middle substrate involves bending action [1]. Thus, peel stresses also exist in the adhesive layers of a double lap joint. The use of a bonded strap either on one side (Figure 3.1c) or on both sides of the substrates (Figure 3.1d) also improves the joint strength compared to single lap joints. Stepped lap (Figure 3.1e) and scarf joints (Figure 3.1f) can potentially produce very high joint strengths; however, in practice, the difficulty of machining the steps or steep scarf angles often overshadows their advantages. If a stepped lap joint is used in a laminated composite structure, it may be easier and less expensive to lay up the steps prior to curing the laminate instead of machining. Depending on the part design and complexity, other joint designs are possible. Some examples are shown in Figure 3.3. Bonded lap joints are used in tubular structures; however, they are much more difficult to make compared to lap joints between flat substrates. If the gap between the inner tube and the outer tube is very small, the adhesive may be pushed out Lap Joints

Stiffener Joints

Simple Lap Tapered Single Lap

T- Section

Hat Section

Joggle Lap Corrugated Backing Double Butt Lap

Butt joint

Double Scarf Lap

Tubular joint

T-joints without reinforcement (left) and with reinforcement (middle and right)

Figure 3.3  Examples of several different types of adhesive joint designs.

Optimization of Structural Adhesive Joints  83 during the assembly process. Under axial tensile loading, the adhesive in tubular joints experiences a combination of shear stress and radial tensile stress, both showing their peak values near the joint ends. Butt joints in which the two substrates are in line with each other and T-joints in which they are normal to each other are also used. Inclined T-joints in which the angle between the two substrates is less than 90o are also used. In general, adhesive joints are weaker in tension than in shear, and therefore, reinforcements may be necessary to obtain high structural performance from butt and T-joints.

3.3 Joint Design Parameters The key stresses in a single lap adhesive joint that control the joint strength are the peak shear stress and peak peel stress in the adhesive layer as well as at the adhesive-substrate interfaces. The primary effort in improving joint strength is focused on reducing these peak stresses and/or making the stress distribution uniform across the overlap length. The joint strength depends not only on the adhesive strength, but also on the joint design parameters, substrate stiffness and adhesive modulus, all of which influence the stress distributions and peak stresses in an adhesive joint [2]. However, there may be other considerations that must be taken into account in the overall design of the structure. For example, in a single lap joint, increasing the substrate stiffness by increasing its thickness reduces the bending action, and, therefore, reduces the maximum peel stress. The maximum shear stress is also reduced. However, while reductions in maximum stresses help in improving the joint strength, the substrate weight is increased due to increased thickness, and this may not be desirable in weight-sensitive structures. The joint design parameters for single lap adhesive joints are the adhesive thickness (t), overlap length (L), overlap width, and substrate end design (Figure 3.4). In order to achieve good bonding and high joint strength, a minimum adhesive thickness is required. Typically, the optimum adhesive thickness is between 0.1 to 0.2 mm [3]. As the adhesive thickness is Substrate Thickness (h)

Overlap Length (L) Adhesive thickness (t)

Spew (Fillet)

Adhesive Layer

Figure 3.4  Joint design parameters in a single lap adhesive joint.

84  Structural Adhesive Joints increased, the joint strength becomes lower [4, 5]. This is shown in Figure 3.5 in which the adhesive thickness was varied between 0.1 to 3 mm in a steel-steel adhesive joint. At high adhesive thickness, the possibility of creating internal defects, such as voids and microcracks, increases, and they often lead to early failure and lower joint strength. Increase in bending moment due to increasing adhesive thickness (which increases the distance between the off-centered load lines) may also contribute to the thickness effect. Increasing the overlap width increases the joint strength proportionately. Increasing the overlap length also results in higher joint strength; however, not proportionately. At high overlap lengths, increase in joint strength is relatively small (Figure 3.6). The reason for the initial increase in joint strength is the large reduction in peak peel stress with increasing overlap length; but as it becomes large, the reduction in peak peel stress becomes small [6]. The ratio of lap length L to substrate thickness h improves the joint strength significantly at small L/h ratios. At high L/h ratios, the improvement is much smaller. In many instances, when a pressure is applied during bonding, small amounts of adhesive are squeezed out of the overlap area and form a spew at each substrate end. Many studies [7–11] have shown that spews tend to reduce stress concentrations at the joint ends and improve the joint strength. Most of the studies involved finite element analysis of single lap joints with triangular spew at the ends of the overlap (Figure 3.7). Crocombe and Adams [8] 7 6

45° spew fillet

Failure load (kN)

5 4 3 2 Square-ended

1 0

0

0.5

1

1.5

2

2.5

3

3.5

Bondline thickness (mm)

Figure 3.5  Failure load as a function of adhesive (bondline) thickness in a steel-steel adhesive joint with square ends and 45° spew fillet [4].

Optimization of Structural Adhesive Joints  85

Joint Strength (MPa)

28

Fiberglas-Fiberglas

21

Fiberglas-Aluminum

14

7

0

Adhesive: Epoxy Substrate Thickness: Fiberglas (1 mm) Aluminum (1.6 mm) 0

25 Overlap Length (mm)

50

Figure 3.6  Effect of overlap length on joint strength.

(a)

(b)

Figure 3.7  Two different adhesive spew shapes at the overlap ends of single lap adhesive joints. (a) Triangular adhesive spew and (b) oval-shaped adhesive spew.

have shown that with a 45o triangular spew, the principal stress decreased by 40% compared to a joint without a fillet. Adams and Harris [10] tested single lap joints made of aluminum substrates and an epoxy adhesive, and observed a 28% increase in joint strength when a 45o triangular spew was included. An example of higher joint strength with a 45o spew can also be observed in Figure 3.5. At 0.1 mm adhesive thickness, there is very little difference between the joints with square ends and 45o spews; but at 3 mm adhesive thickness, the joint failure load with 45o spew is more than twice that for the square-ended joint.

86  Structural Adhesive Joints The effect of adhesive spew shape on the peak shear and peel stresses has been studied by Lang and Mallick [11] using finite element analysis. These shapes include full and half-triangular, full and half round, full rounded with fillet, oval and arc. As the summary of their results in Table 3.1 shows, spew shape has a significant effect on the stress concentrations, with the arc-shaped spew providing the maximum benefit out of all the spew shapes considered. Tapering the substrate ends (Figure 3.8) reduces the high peel stresses at these locations and improves the joint strength [7, 8, 11]. Tapering, which can be either internal or external, reduces the local stiffness of the joint at the overlap ends and distributes the stresses more uniformly. Another method developed to increase the joint strength is to modify the corner geometry of the substrates on the adhesive side of the joint to a round shape [11, 12]. Rounding the substrate corner (Figure 3.9) reduces the stress concentration at the overlap ends, creates a more uniform stress distribution, and moves the location of the maximum stresses from the overlap end. Compared to a square-ended joint, a 54% higher joint strength Table 3.1  Effect of spew shape on the reduction of maximum shear, peel and axial stresses at the substrate-adhesive interface relative to a square-ended joint [11]. Percent reduction in peak stress relative to a square-ended joint Spew geometry

Shear stress (τxy)

Peel stress (σyy)

Axial stress (σxx)

Half triangular (θ = 45o)

45

71

28

Full triangular (θ = 45o)

50

73

31

Half rounded

29

33

15

Full rounded

37

42

20

Full rounded with a fillet

54

82

36

Oval

49

65

32

Square

37

40

19

Arc (radius = 6 mm)

60

87

35

Optimization of Structural Adhesive Joints  87

(a)

(b)

(c)

(d)

Figure 3.8  Tapering of substrate ends to improve joint strength. (a) Joint with square ends; (b) Joint with outside taper in the top substrate; (c) Joint with inside taper in the top substrate; (d) Joint with inside taper in the top substrate and a triangular adhesive spew. r

Top substrate with sharp corner

Top substrate with rounded corner

Figure 3.9  Corner rounding of substrates to improve joint strength.

was observed when a 3.2 mm corner radius was included in the aluminum substrates in addition to a 45o triangular spew [11]. In another study [12], it was shown that increasing the corner radius increased joint strength appreciably when a brittle adhesive was used, but did not change the joint strength much when a flexible adhesive was used. Several studies have been conducted to combine substrate tapering with adhesive spew to reduce stress concentrations at the overlap ends [13–15]. One of these studies is due to Hildebrand [13] in which different shapes of adhesive spew, internal substrate tapering and rounded corners were

88  Structural Adhesive Joints considered to determine their effects on the strength of joints between a fiber-reinforced plastic and a metal substrate. His results showed that depending on the joint configuration, the joint strength increased by 90 to 150%. Rispler et al. [16] applied an evolutionary optimization technique to determine the adhesive spew shape with the objective of minimizing the maximum principal stresses in the adhesive. The substrate materials were a carbon fiber reinforced epoxy (CFRE) and a titanium alloy. Their study shows that as the adhesive modulus is increased, the optimum spew angle decreases and its shape becomes more curved. Ojalvo [17] developed an analytical optimization method to determine the optimum substrate profile that will produce a uniform shear stress distribution in double lap joints. In the optimum design, the outer substrate ends have a curved profile instead of a uniform taper over part of the overlap region. This profile also produces peel stresses that are much lower than the shear stresses in the joint. Groth and Nordlund [18] used finite element method and a structural shape optimization program to develop substrate profiles in single lap, double lap and double strap joints that will minimize the weight or minimize the maximum shear stress. They observed that the optimum substrate profiles in the overlap region are non-uniform in thickness and do not follow a smooth curvature. While these profiles produce significant reductions in weight and/or maximum shear stress, they are difficult to fabricate.

3.4 Substrate Stiffness and Strength Substrate stiffness has a large effect on the stress distributions and the magnitudes of the peak stresses near the ends of the adhesive joint [19–21]. In many applications, the thickness of the substrates on two sides of the joint may be different or the substrate materials may have different modulus values. Equal axial stiffness for the substrates is highly desirable for achieving the maximum joint strength. Since axial stiffness is a product of modulus E and thickness h, it is important to select the proper thickness of each substrate so that E1h1 E2h2. If the two substrates are of the same material, their thicknesses must be equal. Since in a single lap joint, the substrates experience bending in the joined area, their bending stiffness determines the amount of rotation that can take place due to bending. The bending stiffness is proportional to Eh3, where E is the modulus of the substrate material and h is its thickness. Thus, the substrate with a lower stiffness will tend to bend more compared

Optimization of Structural Adhesive Joints  89 to the substrate with a higher stiffness. Increase in stiffness of the substrates reduces the amount of rotation and produces more uniform stress distributions in the adhesive layer. Experiments show that joint strength increases with increasing substrate stiffness, which can be achieved by either increasing the substrate thickness or increasing the substrate modulus. When substrates of unequal bending stiffness values are combined, it is observed that the peak shear and peel stresses near the edges of the interface of the substrate with lower modulus and/or lower thickness are higher than those near the edge of the interface of the substrate with higher modulus and higher thickness. If the substrate thickness on both sides of the joint is the same, the peak shear stress and the peak peel stress are increased as the difference in the moduli of the upper substrate material and the lower substrate material increases. With the same substrate material on both sides of the joint, the peak shear stress and the peak peel stress are increased as the difference in thickness between the upper substrate and the lower substrate increases. Another substrate property that influences the joint strength is the yield strength of the substrate material. In the case of a ductile substrate, yielding of the substrate at the ends of the overlap creates a plastic hinge in the substrate and allows it to undergo large plastic deformation. This causes the adhesive strains to increase considerably and leads to joint failure if the adhesive has a low strain-to-failure. According to Adams et al. [1], a conservative estimate of the tensile load at which yielding will occur in the substrate is proportional to the yield strength of the substrate material. Thus, the joint strength will be expected to be higher if the substrates have a higher yield strength.

3.5 Adhesive Selection Adhesive selection depends on a number of factors, such as the substrates to be bonded, adhesive application method, surface preparation requirement, adhesive bonding time, operating environment (temperature, humidity, chemicals, etc.), stress levels and cost. Adhesive bonding time depends on the adhesive type, curing mechanism and curing condition. In applications requiring a very rapid cure, a fast curing two-part toughened acrylic may be preferred over an epoxy that usually takes longer time to cure. However, a slower curing adhesive may be selected if the bond area is large, since in such a case, the rapid curing system may need a very fast mixing and dispensing system; otherwise, the adhesive mix will start to gel and increase in viscosity before it is properly spread over the entire

90  Structural Adhesive Joints joining surface. Film adhesives are selected over liquid or paste adhesives for applications requiring precise control of adhesive thickness and positioning. Since they will not start to cure until the appropriate pressure and temperature are applied, they can be disassembled and repositioned if any adjustments are needed during the joining process. Adhesive properties and their variation due to moisture absorption, temperature, etc. are also important considerations in adhesive selection. A list of the adhesive properties that influence the joint strength is given below. 1. Shear and tensile properties (strength, modulus and strainto-failure) and their variations with environment, such as temperature and humidity 2. Fracture toughness, which measures the resistance to crack propagation from an existing defect in the adhesive layer or a crack developed during load application 3. Coefficient of thermal expansion relative to the coefficients of thermal expansion of the substrates, since it is one of the factors that controls the thermal residual stresses in the cured adhesive 4. Resistance to creep (which depends on both time and temperature), particularly for long-term applications under sustained loads 5. Chemical resistance and relative humidity, if the adhesive is exposed to chemicals or humid conditions that can alter its properties. The important characteristics of a good adhesive are high shear and tensile strengths but low shear and tensile moduli. Flexible adhesives with low modulus make the stress distributions in the adhesive more uniform and reduce the maximum stresses that occur at the overlap ends. High ductility and fracture toughness of the adhesive are important properties to consider if the substrates have dissimilar stiffness values or if the joint is subjected to impact loads. An efficient way of increasing the joint strength is to use a low-­modulus, flexible adhesive only near the ends of the overlap and a higher modulus, stiffer adhesive in the central region (Figure 3.10). The low modulus adhesive at the ends helps to reduce peak shear and peel stresses and the high modulus adhesive carries a larger share of the load. A study on the use of mixed adhesives in steel-steel single lap joints showed significant joint strength improvements over single adhesive alone [22]. In this study,

Optimization of Structural Adhesive Joints  91 Low-modulus (flexible) adhesive at the overlap ends

High-modulus adhesive in the middle

Figure 3.10  Adhesives with two different modulus values in the overlap region.

when a very flexible adhesive was used in the mixed-adhesive joint, the joint strength improved by 52% compared to a joint with the stiff adhesive alone and 121% compared to a joint with the very flexible adhesive alone. Sancaktar and Kumar [23] reported that a single lap joint between two steel substrates with a rubber-toughened epoxy adhesive with a modulus of 1.87 GPa was nearly 2.5 times stronger than a comparable joint with an epoxy adhesive with a modulus of 3.1 GPa. The joint strength with rubber-toughened epoxy at the ends of the overlap and epoxy in the middle was similar to the one obtained with rubber-toughened epoxy over the entire overlap. Raphael [24] proposed that for optimum joint performance, an adhesive layer with variable shear modulus and shear strength along its length will be ideal. In a different approach, Lang and Mallick [25] used recessing in the middle section of the adhesive layer and noted that there was no significant increase in peak stresses at the overlap ends. Olia and Rossettos [26] reported similar results for adhesive joints with gaps subjected to bending. Because of this, joints with multiple recesses may be a viable alternative to continuous adhesive joints in structural applications where weight and cost savings are desirable. However, they should be considered with caution in critical applications, since if cracks appear in the adhesive in the overlap ends, there will be no material to prevent or reduce their growth. The quality, strength and failure mode of adhesive joints depend on the number and types of defects in the adhesive layer. These defects are generated during the bonding operation, and they may include voids (due to entrapped air bubbles), unbonded areas, weak bonds, and fine cracks in the adhesive layer. High adhesive viscosity at the time of its application on the substrates, inadequate pressure application, presence of contaminants on the substrate surfaces and uneven temperature distribution during curing are some of the reasons for the development of these defects. Another important factor in good bonding is wettability of the substrate surface by the adhesive. For good wettability, the surface tension of the adhesive should be lower than the surface free energy of the substrate. In a review article on the role of interface in adhesion phenomenon, Mittal [27]

92  Structural Adhesive Joints concluded that the interfacial tension between the liquid adhesive and the substrate is the most important criterion for wettability and adhesion. The lower its value, the higher the joint strength. Some of these defects in the adhesive layer are often difficult to detect even with non-destructive inspection, such as ultrasonic C-scan, and cannot be remedied without destroying the substrates. This is one of the reasons for adding mechanical fasteners to adhesive joints in many primary aircraft structures so that the combined hybrid joint will be more reliable. The hybrid joints that combine adhesive with threaded fasteners, rivets and welds are described in the next section.

3.6 Hybrid Joints A hybrid joint is created by combining two or more types of joining methods in the same joint to improve its performance. One of these hybrid joints is when mechanical fasteners, such as rivets and bolts, are combined with an adhesive layer (Figure 3.11). The mechanical fastener shares the load with the bonded joint and act as the secondary load path after the bonded joint has either weakened or failed. As a result, not only is the joint strength improved, but also the joint failure may take place in a progressive manner.

(a) Spot weld

(b)

(c)

Figure 3.11  Hybrid joints. (a) Bolted-bonded joint, (b) weld-bonded joint, and (c) rivetbonded joint.

Optimization of Structural Adhesive Joints  93 Kelly [28] studied the load sharing between the fastener and the adhesive in a bonded/bolted hybrid joints and observed that the benefit of adding a bolt to an adhesive joint is greater if the joint is flexible, either due to adhesive flexibility or due to joint design. The load shared by the bolt increases with increasing substrate thickness and adhesive thickness, but decreases with increasing overlap length, adhesive modulus and distance between the bolts. The role of the adhesive modulus in load sharing by the bolt has also been noted in other publications on bonded/bolted joints [29, 30]. Fu and Mallick [31] noted that bonded/bolted joint has a higher static strength and a longer fatigue life than the bonded joint. The performance of the hybrid joint depends on the washer size, since it affects the distribution of clamping pressure in the substrate and the adhesive layer. Other forms of hybrid joints are weld bonding and rivet bonding. Weld-bonding is of interest in the automotive industry where resistance spot welding is commonly used for joining steel with steel and adhesive bonding is being considered for joining mixed materials, such as steel with aluminum. Weld-bonding combines resistance spot welding and adhesive joining in the same joint. The adhesive carries the main structural load and the spot weld helps reduce the peel stresses and improve the crashworthiness by carrying the out-of-plane loads. In making weld-bonded joints, the adhesive (usually a one-part heat-curable epoxy) is applied first and spot welds are made afterward. Rivet-bonding (or simply riv-­bonding) in the automotive industry is a combination of self-piercing riveting and adhesive bonding. Self-piercing rivets are commonly used for joining aluminum with aluminum. In the rivet-bonding process, the two sheets to be joined are first coated on one side each with an adhesive, typically a onepart heat-curable epoxy, and then they are joined using self-piercing rivets. The adhesive is cured later at an elevated temperature. Depending on the adhesive type and the joint design, the strengths of both weld-bonded and rivet-bonded joints are in general higher than the respective spot welded or riveted joint. The fatigue strength is also higher with both weld-bonded and rivet-bonded joints.

3.7 Summary This chapter has presented the important design and material parameters that influence the stress distributions in a single lap joint and affect the joint strength under static tensile loading condition. Their contributions to the joint strength were examined by da Silva et al. [32] using a “Design of Experiments” approach, more specifically by Taguchi method. They

94  Structural Adhesive Joints observed that lap shear strength increases with increases in substrate yield strength (with 19.7% contribution), substrate thickness (with 20.3% contributions), overlap length (with 20% contribution) and adhesive toughness (with 10.4% contribution). It also increases as the adhesive thickness is decreased (with 8.8% contribution). The surface treatment has a negligible effect. Many of the other factors that contribute to adhesive joint strength increase are described in this chapter. However, a comprehensive adhesive design optimization study that takes into account all the joint design parameters is still lacking. As the use of adhesive joints in structural applications increases, it is expected that there will be many different types of joint designs and the loading may include fatigue, impact and other dynamic conditions. More design optimization studies are needed in these areas as well. The potential for hybrid joints for long-term applications should also be explored further for critical structural applications.

References 1. R. D. Adams, J. Comyn and W. C. Wake, Structural Adhesive Joints in Engineering, 2nd Edition, Chapman and Hall, London, UK (1997). 2. I. U. Ojalvo and H. L. Eidinoff, Bond thickness effects upon stresses in singlelap adhesive joints, AIAA J. 16, 204-211 (1978). 3. L. F. M. da Silva, E. A. S. Marques and R. D. S. G. Campilho, Design rules and methods to improve joint strength, in: Handbook of Adhesion Technology, 2nd Edition, L. F. M. Da Silva, A. Öchsner and R. D. Adams (Eds.) pp 773-810, Springer, Heidelberg (2018). 4. L. D. R. Grants, R. D. Adams and L. F. M. da Silva, Experimental and numerical analysis of single-lap joints for the automotive industry, Int. J. Adhesion Adhesives, 29, 405-413 (2009). 5. J. M. Arenas, J. J. Narbon and C. Alia, Optimum adhesive thickness in structural adhesive joints using statistical techniques based on Weibull distribution, Int. J. Adhesion Adhesives, 30, 160-165 (2010). 6. L. J. Hart-Smith, Designing to minimize peel stresses in adhesive-bonded joints, in: Delamination and Debonding of Materials, ASTM STP 876, W. S. Johnson (Ed.), pp. 238-266, ASTM, Philadelphia (1985). 7. L. F. M. da Silva and R. D. Adams, Techniques to reduce peel stresses in adhesive joints with composites, Int. J. Adhesion Adhesives, 27, 227-235 (2007). 8. A. D. Crocombe and R. D. Adams, Influence of the spew fillet and other parameters on the stress distribution in the single-lap joint, J. Adhesion, 13, 141-155 (1981).

Optimization of Structural Adhesive Joints  95 9. M. Y. Tsai and J. Morton, The effect of spew fillet on adhesive stress distributions in laminated composite single-lap joints, Composite Structures, 32, 123-131 (1995). 10. R. D. Adams and J. A. Harris, The influence of local geometry on the strength of adhesive joints, Int. J. Adhesion Adhesives, 7, 69-80 (1987). 11. T. P. Lang and P. K. Mallick, Effect of spew geometry on stresses in single lap adhesive joints, Int. J. Adhesion Adhesives, 18, 167-177 (1998). 12. X. Zhao, R.D. Adams and L. F. M. da Silva, Single lap joints with rounded adherend corners: experimental results and strength prediction, J. Adhesion Sci. Technol, 25, 837-856 (2011). 13. M. Hildebrand, Non-linear analysis and optimization of adhesively bonded single lap joints between fiber reinforced plastics and metals, Int. J. Adhesion Adhesives, 14, 261-267 (1994). 14. G. Belingardi, L. Goglio and A. Tarditi, Investigating the effect of spew and chamfer size on the stresses in metal/plastics adhesive joints, Int. J. Adhesion Adhesives, 22, 273-282 (2002). 15. E. M. Moya-Sanz, I. Ivanez and S. K. Garcia-Castillo, Effect of geometry on the strength of single-lap adhesive joints of composite laminates under uniaxial tensile load, Int. J. Adhesion Adhesives, 72, 23-29 (2017). 16. A. R. Rispler, L. Tong, G. P. Steven and M. R. Winsom, Shape optimization of adhesive fillet, Int. J. Adhesion Adhesives, 20, 221-231 (2000). 17. I. U. Ojalvo, Optimization of bonded joints, AIAA J., 23, 1578-1582 (1985). 18. H. L. Groth and P. Nordlund, Shape optimization of bonded joints, Int. J. Adhesion Adhesives, 11, 204-212 (1991). 19. S. Cheng, D. Chen and Y. Shi, Analysis of adhesive-bonded joints with non-identical adherends, J. Eng. Mech., 117, 605-623 (1991). 20. L. Dorn and W. Liu, The stress state and failure properties of adhesive-bonded plastic/metal joints, Int. J. Adhesion Adhesives, 22, 273-282 (2002). 21. P. N. B. Reis, J. A. M. Ferreira and F. Antunes, Effect of rigidity on the shear strength of single lap adhesive joints, Int. J. Adhesion Adhesives, 31, 193-201 (2011). 22. L.F.M. da Silva and M. J. C. Q. Lopes, Joint strength optimization by the mixed-adhesive technique, Int. J. Adhesion Adhesives, 29, 509-514 (2009). 23. E. Sancaktar and S. Kumar, Selective use of rubber toughening to optimize lap-joint strength, J. Adhesion Sci. Technol., 14, 1265-1296 (2000). 24. C. Raphael, Variable-adhesive bonded joints, Appl. Polym. Symposia, 3, 99-108 (1966). 25. T. P. Lang and P. K. Mallick, The effect of recessing on the stresses in adhesively bonded single- lap joints, Int. J. Adhesion Adhesives, 19, 257-259 (1999). 26. M. Olia and J. N. Rossettos, Analysis of adhesively bonded joints with gaps subjected to bending, Int. J. Solids Structures, 33, 2681-2691 (1996). 27. K. L. Mittal, The role of the interface in adhesion phenomena, Polym. Eng. Sci., 17, 467-473 (1977)

96  Structural Adhesive Joints 28. G. Kelly, Load transfer in hybrid (bonded/bolted) composite single lap joints, Composite Structures, 69, 35-43 (2005). 29. C.-T. Hoang-Ngoc and E. Paroissien, Simulation of single lap bonded and hybrid (bolted/bonded) joints with flexible adhesive, Int. J. Adhesion Adhesives, 30, 117-129 (2010). 30. K. Bodjona, K. Raju, G.-H. Lim and L. Lessard, Load sharing in single-lap bonded/bolted composite joints. Part I: model development and validation, Composite Structures, 129, 268-275 (2015). 31. M. Fu and P. K. Mallick, Fatigue of hybrid (adhesive/bolted) joints in SRIM composites, Int. J. Adhesion Adhesives, 21, 145-159 (2001). 32. L. F. M. da Silva, G. W. Critchlow and M. A. V. Figueiredo, Parametric study of adhesively bonded single lap joints by the Taguchi method, J. Adhesion Sci. Technol., 22, 1477-1494 (2008).

4 Durability Aspects of Structural Adhesive Joints H. S. Panda1, Rigved Samant1, K. L. Mittal2 and S. K. Panigrahi3* Department of Metallurgical and Materials Engineering, Defence Institute of Advanced Technology, Pune, India 2 P.O. Box 1280, Hopewell Jct., NY, USA 3 Department of Mechanical Engineering, Defence Institute of Advanced Technology, Pune, India

1

Abstract

Structural adhesives have been used for bonding in various structural applications for more than seven decades. The incorporation of a structural adhesive primarily eliminates stress concentrations in a joint generated by mechanical fasteners. It improves the working-life of materials involved in the joint. A structural system is comprised of adhesive joints, structural members and materials from different families. Therefore, an adhesive joint must survive longer than the estimated working life of the entire structural system. This chapter reviews the factors which affect the durability of an adhesive joint and also the approaches to improve durability of a joint. The main culprit in the durability of an adhesive joint is the moisture present in the environment. This chapter discusses in detail the ways to eliminate the moisture-related durability issues and various other factors assisting it. Also, this chapter briefly addresses the accelerated test techniques which are used for faster accumulation of scientific data related to the durability aspects of an adhesive joint. Keywords:  Durability, structural adhesive, epoxy, structural joints, moisture, stress, nanofillers, nanoparticles

*Corresponding author: [email protected] K.L. Mittal and S. K. Panigrahi (eds.) Structural Adhesive Joints: Design, Analysis and Testing, (97–134) © 2020 Scrivener Publishing LLC

97

98  Structural Adhesive Joints

Abbreviations Used AEP Al CAA CCC CPCC CTE Cu D DDS DGEBA DPTZ E-N E-P ε max ′ FPL FRP IMID IPD mPDA ME170 ME170g ME120k ME120w N-P NST PA PAA PAM Pip RT SACO SEM SWT TETA Tg TGDDM V-P Zr

1-(2-Aminoethyl)piperazine Aluminium Chromic Acid Anodization Chromate Conversion Coating Chromate-Phosphate Conversion Coating Coefficient of Thermal Expansion Copper Diffusion coefficient Diaminodiphenylsulfone Diglycidyl ether of bisphenol A 3,6-di-2-pyridyl-1,2,4,5-tetrazine Epoxy-novolac Epoxy-polyamide Maximum relative dielectric permittivity Forest Products Laboratory Fiber-reinforced polymer imidazole Isophorone diamine Metaphenylene diamine Modified epoxy with unsupported film Modified epoxy with glass beads Modified epoxy with knitted nylon carrier Modified epoxy with woven nylon carrier Nitrile-phenolic Neutral Spray Test Poly(acrylic acid) Phosphoric Acid Anodization Polyacrylamide Piperidine Room temperature Sandblast Coating Scanning Electron Microscopy Saturated Water Test Triethylenetetramine Glass transition temperature Tetraglycidyl-4,4’-diaminodiphenylmethane Vinyl-phenolic Hexafluorozirconic acid

Durability Aspects of Structural Adhesive Joints  99

4.1 Introduction The purpose of a structural adhesive joint is to transfer and support the design loads for an estimated lifetime and specified service conditions [1]. The joint must have the ability to withstand aggressive environmental conditions and maintain satisfactory long-lasting performance [2]. Therefore, it is of concern as well as of interest to study the performance of such adhesive joints to persist in the face of worst weather conditions. Previously, only the aircraft, automobile, and electronic industries used the adhesive joints. However, development of new composite materials and their induction in civil engineering applications has extensively increased their uses [3, 4]. The criticality of an adhesively bonded joint varies depending on theoperating conditions and environment [5]. The non-critical cases involve those that are subjected to low stresses and are protected from ruthless environmental conditions such as the joints in the door of a refrigerator. Whereas, adhesive joints in military and civilian aircraft, internal building panels, direct glazing of an automobile are exposed to complex stresses as well as erratic weather conditions. These are considered as consequential or critical applications of adhesively bonded joints [6]. Moreover, sustaining the excellent joint durability in extreme conditions is a tough task compared to obtaining the requisite joint strength in the beginning. Increased durability demands higher initial costs via exclusive structural materials or unique processing methods. The structural systems are comprised of adhesive joints, structural members and materials from various families. The structural systems are generally designed to survive for a lifespan of more than 50 years. Therefore, it is a pre-requisite for an adhesive bond to have a longer life span than the structural system. Indeed, most of the literature published in the last 40 years on adhesive bonding has dealt with various aspects of the durability of structural adhesive joints. However, most of the literature has focused on the durability of structural adhesive joints in aerospace applications. This chapter encompasses relevant applications in aerospace, automobile, electronic and civil sectors [7]. The durability of a bonded joint depends on numerous factors, ranging from its surrounding environment to the interface between adhesive and adherend. All these factors are discussed first to obtain a better understanding of intricacies and difficulties faced by engineers while deploying them in structural design. The assessment of adhesives for durability in structural applications is a time-consuming practice. Hence, scientists around the globe have formulated accelerated

100  Structural Adhesive Joints tests for assessing durability [8]. The detailed explanation of these tests is also provided in this chapter. In the end, various means to improve the durability are discussed.

4.2 Factors Affecting Durability The durability of a material can be defined as “Probability that material will have a relatively long continuous useful life, without requiring an inordinate degree of maintenance.” Hence durability is a function of the rate of adhesive bond degradation [1]. The rate of bond degradation is influenced by various factors, which can be classified into three main categories, namely material, environment and stress [9]. The material category is comprehensive and includes the adhesive, the adherend and the interface between them [10]. The environment is mainly governed by temperature and moisture. Other miscellaneous factors also contribute, such as the omnipresence of other liquids, extreme pH, but their contribution is less than that of moisture and temperature. The adhesive bonds generally show considerable strength against shear stresses due to the even distribution of stress over a wide area. However, in a practical scenario, stresses can be introduced in the bonded joints from various directions via push, pull or shear and this gives rise to complex stresses in the joint [11]. These complex stresses are conducive to affect the lifetime or residual strength of the bonded joint. Moreover, adhesively bonded joints are particularly susceptible to cleavage, peel and tensile stresses (Figure 4.1).

(c) Shear (a) Compression

(b) Tension

(d) Peel

(e) Cleavage

Figure 4.1  Types of stresses experienced by an adhesive joint [11].

Durability Aspects of Structural Adhesive Joints  101

4.2.1 Materials This section discusses the factors related to adhesives, adherends, and the interface between them.

4.2.1.1 Adhesives The most prominent driving factors for degradation of an adhesive joint are the effects of water and temperature [12]. Water is regarded as the God’s cruelest liquid when it comes to adhesion and soapy water is even worse. A mundane example showing what water can do is that even a child can peel a hot potato, try to peel a cold potato. When monsoon season starts (it rains cats and dogs) quite often adhesively bonded joints start failing. The Holy Grail in the field of adhesion is how to make water-resistant bonds. Making of adhesive bonds which can withstand the onslaught of water has eluded the adhesion community. Only barnacle knows how to make true water-resistant bonds. Barnacle sticks to the ship hull in ocean water, which is not Holy water and contains electrolytes, corrosives and other undesirable chemicals. So, barnacle really is the ultimate adhesionist. Someone many years ago wrote an interesting, instructive and inspiring article with the title “The Erudite Scientists Can Learn a Lot from Lowly Barnacle.” Apropos, there is currently much research activity in deciphering the mechanism of barnacle adhesion and how to replicate it. In the presence of moisture, an adhesive material degrades by physical, mechanical or chemical processes. The resulting damage can lead to deterioration of adhesive properties of the bonded joint [13]. Diamant et al. [14] studied the impact of network structure on the moisture accumulation inside the epoxies. They altered the network by crosslinking the epoxies with distinct proportions of mono/diamine and this resulted indecrease in density and increase in free volume. Additionally, the reduction in coefficients of diffusion is observed for the compositions with greater molecular weights between crosslink points (Figure 4.2). Also, newly formed micro-cracks facilitate moisture absorption via penetration due to the presence of severe swelling circumstances (such as a water-boil procedure). Hence, it is concluded that the coefficient of moisture diffusion into epoxy resin depends on four primary variables: (i) the structure of the polymer network, (ii) the polymer polarity, (iii) the polymer’s physical morphology, and (iv) microdamage under high humidity circumstances. The water permeability in an adhesive largely depends on the stoichiometric ratio of epoxy to amine [15]. Grave et al. cured epoxy-diglycidyl ether of bisphenol A (DGEBA), with various stoichiometric ratios of

102  Structural Adhesive Joints –18 + –19

In D

+ –20 + –21

–22

+

2.9

3.0

3.1

3.2 I (10–3°K–1) T

3.3

3.4

3.5

Figure 4.2  Arrhenius plot for diffusion coefficient (D): ▫ - Low molecular weight between crosslinks and ⚪– High molecular weight between crosslinks [14].

triethylenetetramine (TETA) [16]. Study on the stoichiometric ratios of epoxy and amine ranging between 3:1 to 1:3 elucidatesan increase in equilibrium water uptake (Figure 4.3). It is evident that sample with stoichiometric ratio 1:3 rapidly absorbs a large amount of water and detaches from the electrode. Hence no measurement for stoichiometric ratio 1:3 could be obtained (Figure 4.4).

log Weight Uptake (%)

10

1

0.1 0

2000

4000

6000 8000 10000 12000 14000 (Time)1/2/d (s1/2mm–1)

Figure 4.3  Water uptake plots of adhesives with respect to different epoxy to amine stoichiometric ratios: ▪3:1, ▴1.5:1, ▾1:1, ♦1:2, +1:3 [16].

Durability Aspects of Structural Adhesive Joints  103 1.2

Dielectric Permittivity

1.0 0.8 0.6 Ratio 3:1 Ratio 2:1 Ratio 1.5:1

0.4

Ratio 1:1 Ratio 1:2

0.2 0.0 0

2000

4000

6000

8000

(Time)1/2/d (s1/2mm–1)

Figure 4.4  Dielectric permittivity plots at 10 Hz for a range of epoxy to amine stoichiometric ratios [16].

Further examination of the moisture absorption features of an adhesive with different stoichiometric ratios indicates the existence of water in the matrix, and the polar dielectric property of water helps to characterize it.The variations in the dielectric loss and permittivity over time in the frequency range 103 to 1010 Hz identify the nature of water present in the epoxy matrix [17]. The water present in the system exists in two forms: (i) bound water - dispersed molecularly across the epoxy matrix and (ii) free water - probably residing in the matrix or adsorbed on the surface of the cavities [18]. From Fick’s second law, the dielectric increment as a result of diffusion is given by



ε ′ − ε 0′ 4 = 1− ε max π ′ − ε 0′

∞

∑ n=0

(−1)n [ ×e 2n + 1

D ( 2n+1)2 π 2t h2

]



(4.1)

Where, ε max ′ = maximum dielectric permittivity value of water after diffusion into polymer matrix, h = thickness of the sample, n = series expansion number. In this case, by considering only the first term in Eq. (4.1) the diffusion coefficient (D) can be estimated (i.e. n = 0) and using the

104  Structural Adhesive Joints half time (t = t 1 ) corresponding to [

D ( 2n+1 )2 π 2t

h e Thus,

2

]

2

ε′ − ε′0 1 = , with the condition that ε′max − ε′0 2

< 1.



D=

− h2 π ln π 2t 1 8 2

(4.2)



Furthermore, Eq. (4.2) can be rewritten in the approximate form,



D = 0.0947

h2 t1 2

(4.3)



The changes in the stoichiometric ratio do not really affect the diffusion coefficient of the DGEBA/TETA system. Table 4.1 summarizes the results of the same. Also, Figure 4.4 represents normalized dielectric permittivity graphs at a frequency of 10 Hz. The dielectric permittivity variation at a lowfrequency (10Hz) clarifies that the water molecules originally flow through the matrix and only form ‘free’ water when a water molecule encounters a micro-void. Table 4.2 presents values of ‘free’ and ‘bound’ water obtained in the matrix from variation in dielectric permittivity [18–20]. Once epoxy ′ ) and diffusion Table 4.1  Maximum relative permittivity (ε max coefficients (D) with respect to different epoxy to amine stoichiometric ratios obtained from dielectric measurements [16]. Stoichiometric ratio

ε max ′ (relative)

D (cm2/s)

3:1

0.36

1.91 × 10-8

2:1

0.37

0.83 × 10-8

1.5 : 1

0.39

1.18 × 10-8

1:1

0.53

1.43 × 10-8

1:2

>1.3

0.95 × 10-8

1:3

>100

–

Durability Aspects of Structural Adhesive Joints  105 Table 4.2  Calculated values of bound and free water with respect to different epoxy to amine stoichiometric ratios obtained from dielectric measurements [16]. Stoichiometric ratio

% Bound water

% Free water

3:1

70.3

29.7

2:1

66.7

33.3

1.5 : 1

47

53

1:1

46

54

1:2

18.1

81.9

1:3

10

90

absorbs moisture, it can alter adhesive properties through plasticization (reversible), hydrolysis, and cracking or crazing (irreversible) [21]. The free water molecules have low interaction with the polymer network; hence they possess higher mobility. The higher mobility is useful in the characterization of free water. On the other hand, the bound water has to overcome a high energy barrier; hence, these water molecules are immobilized [10, 22] and are responsible for plasticization [23–26], the single hydrogen bond in the bound water-primarily attributes to the plasticization. According to Zhou and Lucas [27] there exist two types of bound water, Type I and Type II: Type I–single hydrogen bond and Type II–more than one hydrogen bond. The Type-II bound water manifests a pseudo-crosslink using a second bridge between the chain segments, hence possesses relatively lesser mobilization. Therefore, bound water with more than one hydrogen-bond markedly contributes to plasticization [23, 28]. The study on hygrothermal effects (combination of heat and moisture) on epoxy resin indicates that hydrogen bonding facilitates an interlocking of water molecules in the matrix of epoxy resin. Zhou and Lucas reported that the water present in the system is mainly the “bound water” [27]. The main difference between Type I (Figure 4.5) and Type II (Figure 4.6) bound water is the extent of thermal activation energy and the nature of hydrogen bond. The Type I bound water has a thermal activation energy of 9.5 kcal/mol whereas type II possesses activation energy of 15.1 kcal/mol. Therefore, it is comparatively easier to remove the water from the resin by desorption in the case of Type I bound water due to lower activation energy. Moreover, Type I bound water forms a single hydrogen bond, while Type II bound water forms multiple hydrogen bonds with the resin network. This renders the Type I bound water to act as a plasticizer, whilst Type II bound water results

106  Structural Adhesive Joints main chain structure

H

H

O :

H OH : O

H

H

O H :

H

N

Figure 4.5  Bound water of Type I – Single hydrogen bond [27]. secondary crosslinking

OH

H H OH

O :H

H :

H

O

:

O H

:

:

O

:

H

O

H

H

H

H

:

:

OH

N

Figure 4.6  Bound water of Type II – More than one hydrogen bond [27].

in secondary crosslinks with the structural segments. The temperature and time are the two main factors to influence the Type II bound water uptake. A comparative study of three different epoxy systems (DGEBA + mPDA, TGDDM + DDS, and Fiberite 934) exposed to different temperatures concludes that the higher exposure temperature assists the residual water retention inside the matrix (Figure 4.7). Moreover, the amount of residual water in the matrix rises rapidly withincrease in exposure time for a particular absorption exposure temperature (Figure 4.8). Hence, the amount of Type II bound water exponentially increases with prolonged exposure time and higher exposure temperature [29], i.e. high-temperature circumstances tend to deteriorate the joint more quickly. The study of Bowditch from the Defence Research Agency, UK shows a progressive loss of strength of epoxy adhesive joint with submersion in the water [30]. The ageing at 50 °C in water, reduces the failure stress on epoxy adhesive. A comparative study of epoxy adhesive with two different types of fillers (aluminium and calcium carbonate) shows loss of strength (Figures 4.9 and 4.10). However, the mechanisms for loss of strength inthese two cases are different. For epoxy with calcium carbonate fillers, immersion

Durability Aspects of Structural Adhesive Joints  107 0.5 0.45

Water Retained (w%)

0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 TGDDM + DDS

DGEBA + mPDA

Fiberite934

Bathed at 45°C then desorbed at 60°C for 1450hr Bathed at 60°C then desorbed at 60°C for 1450hr Bathed at 75°C then desorbed at 60°C for 1450hr Bathed at 90°C then desorbed at 60°C for 1450hr

Water Retained (w%)

Figure 4.7  Water retention results for three different water-saturated epoxy systems [27]. 0.5 0.4 0.3 0.2 0.1 0

0

500

1000

1500

2000

Water Immersion Time (hr)

Figure 4.8  Water retention at 90 °C of epoxy Fiberite 934 [27].

in water separates the filler particles from the matrix and exposes them to the environment. This, in turn, gives rise to a locally weaker region in the matrix. The locally weaker region in the adhesive is situated near the interface; and the failure primarily starts from here. Whereas, in the case of aluminium-filled epoxy-based adhesive, filler particles in the matrix separate at the interface. The filler particles facilitate the formation of an oxide layer due to hydration and cause a reduction in strength. The glass transition temperature (Tg) is the temperature window where polymer transitions from hard or brittle or glassy state to a soft or flexible

108  Structural Adhesive Joints 30

Failure stress (MPa)

20

10

0 0

1000 1500 2000 500 Ageing in water at 50°C (h)

Figure 4.9  Variation in failure stress of bulk adhesive with CaCO3 filler particles after aging in water [30].

rubbery (viscoelastic) material [31]. The cure schedule vastly influences the final Tg [32]. The low-temperature cures such as room temperature (RT) cures result in the lowest possible Tg of all. Very high Tg values are unachievable by room temperature curing; higher Tg requires curing at elevated temperature. As an example, Tg of an adhesive could be between 80 °C and 160 °C, based on the cure schedule. Gonzalez Garcia et al. formulated various adhesives with a single epoxy and different aliphatic amine networks. The diglycidyl ether of bisphenol-A (DGEBA) was used as an epoxy network [33]. The following amines Triethylenetetramine (TETA), Piperidine (Pip), 1-(2-Aminoethyl)piperazine (AEP) and Isophorone diamine (IPD) were used as curing agents to develop various adhesive formulations. The AEP and Pip have relatively lower value of Tg. The curing of Pip system involves homopolymerization [34]. It allows lower crosslink density and results in a lower value of Tg [35–37]. On the other hand, the TETA and IPD systems demonstrate higher Tg values (Table 4.3).

Durability Aspects of Structural Adhesive Joints  109 60

50

Failure stress (MPa)

40

30

20

10

0

0

1000 1500 2000 500 Ageing in water at 50°C (h)

2500

Figure 4.10  Variation in failure stress of bulk adhesive with Al filler particles after aging in water [30].

4.2.1.1.1

Effects of Tg

Elastic Modulus: The fundamental relationship between elastic modulus and Tg of adhesive is:the greater the Tg, the higher the cross-linked density and the higher the elastic modulus (Table 4.3) [38]. The storage modulus falls as the epoxy temperature rises above the Tg. This indicates the change from rigid to compliant state. An adhesive stressed at ambient temperature Table 4.3  Thermal, mechanical and adhesive properties of different adhesives [33]. Adhesive

Tg (°C)

Elastic modulus (MPa)

Adhesive strength (MPa)

DGEBA/IPD

155

3.77

17.5

DGEBA/TETA

124

3.1

16.6

DGEBA/AEP

115

2.87

19.9

DGEBA/Pip

80

2.62

21

110  Structural Adhesive Joints shows a low percent elongation and poor energy dissipation if the adhesive has high Tg along with high storage modulus [39]. Lap-shear Strength: Table 4.3 indicates that the lap shear adhesive strength of epoxy will increase as the Tg value falls. Interestingly, the above behaviour is attributed to the adhesive strength of cured adhesive. Cohesive failure becomes more prevalent as the epoxy becomes compliant [40], and it facilitates the detachment of the two substrates. The adhesive DGEBA/Pip has a low value of Tg. Also, the network structure of adhesive DGEBA/Pip exhibits negligible hydroxyl concentration. Hence, DGEBA/Pip shows relatively lesser percentage of cohesive failure due to its low tendency to absorb water. The moist environment decreases the ability of adhesive to resist failure. Comparatively, the reduction in the adhesive strength of the DGEBA/ Pip system is less at both ambient temperature and 80°C (Figures 4.11, 4.12). As discussed earlier, the curing of Pip system involves homopolymerization. The homopolymerization reduces the hydroxyl concentration in thePip network. The water uptake ability of an adhesive depends heavily on the existence of hydroxyl groups [41]. Therefore, low water uptake ability of the DGEBA/Pip network makes it more durable than others. The above result concludes that there is direct relationship between the Tg and durability of the adhesive. The proper curing method yields a low value of Tg. The lowest possible Tg produces adhesive with lowest crosslinking and the lowest number of hydroxyl groups. It consequently makes adhesive stouter and more durable.

Adhesive strength (MPa)

20

15

10 0 day 15 day 45 day 90 day 150 day

5

0

TETA

IPD

AEP

Pip

Figure 4.11  Adhesive strengths of different epoxy adhesives in water environment for different durations at ambient temperature [33].

Durability Aspects of Structural Adhesive Joints  111 0 day 7 day 15 day 30 day

Adhesive strength (MPa)

20

15

10

5

0

TETA

IPD

AEP

Pip

Figure 4.12  Adhesive strengths of different epoxy adhesives in water environment for different durations at 80 °C [33].

4.2.1.2 Adherends The adherends are the structural members of a joint and are joined together by an adhesive. An adhesive establishes a bond in two manners: physical bond (mechanical interlocking) and chemical bond [42]. Topography and surface morphology dictate the extent to which the adhesive is mechanically interlocked. Furthermore, its chemistry regulates degree and type of chemical bonding. The adhesive bond always requires good contact between the adhesive and adherend, with appropriate surface free energy [43] and efficient wettability [44]. The roughness of the adherend surface determines the ultimate durability. Aluminium, Steel, and Titanium are the most widely used metals for structural applications.

4.2.1.2.1 Aluminum

The aluminium surface is prone to oxidation easily [45]. The aircraft industry uses Al-Cu(2024-T3) or Al-Zn(7075-T6) for manufacturing structural components [46]. Studies on the durability of epoxy/2024-T3Al adhesively bonded systems using Scanning Electron Microscopy (SEM) conclude that the degree of mechanical interlocking between the oxide and adhesive, and the resistance of the oxide to hydration determine the performance of the adhesive bond. The surface is pretreated in order to enhance the capability of an adhesive to interlock with the adherend surface. The microroughness generated by shallow pores and protrusions of oxide layer of Al furnish

112  Structural Adhesive Joints a physical bond between adhesive and oxide surface. Forest Products Laboratory (FPL) etching and Phosphoric Acid Anodization (PAA) are two main pretreatments which have been traditionally used over the years to improve the interlocking ability of aluminium surface. Between these, PAA gives more durable bonds as compared to FPL etching. The Chromic Acid Anodization (CAA) process is also used but to a lesser extent. The surface formed by the FPL process is further anodised with H3PO4 and CrO3 to perform PAA and CAA processes, respectively. Venables studied the microstructures of a differently pretreated surface using Scanning Electron Microscopy [47]. Aluminium is very prone to oxidation, and surface pretreatment forms an oxide layer of Al2O3. The PAA process delivers noticeably thicker oxide layer. The SEM study concludes that the surface treated with PAA process has longer protrusions with hexagonal cell structure. The whisker-like protrusions manifest better physical bond to a polymer and, therefore, PAA exhibits a more robust bond than the FPL surface treatment (Figures 4.13 and 4.14). However, the final morphology after CAA process largely depends on the prior history of the surface. The fresh oxide layer develops below the aged oxide layer and the aged layer’s surface morphology helps to interlock. Therefore, the bondability of a CAA surface relies extensively on the earlier structure of surface oxide. The moisture hampers the interlocking ability of the surface [48]. The moisture intrusion at the bondline causes oxide to transform into hydroxide with radical changes in the morphology. The hydration studies carried out on the surfaces of Phosphoric Acid Anodization (PAA) and Forest Products Laboratory (FPL) etching indicatethat Al2O3 transforms into oxyhydroxide ~5 nm ~40 nm ~40 nm

Oxide film

~5 nm

Al

Figure 4.13  Isometric drawing of oxide morphology on a FPL-treated Al surface [46].

Durability Aspects of Structural Adhesive Joints  113 ~10 nm

~400 nm

~100 nm

~40 nm

Oxide Al

Figure 4.14  Isometric drawing of oxide morphology on a PAA-treated Al surface [46].

AlOOH (boehmite), and further hydration transforms it to trihydroxide Al(OH)3 (bayerite). This transformation is referred to as oxide-to-hydroxide conversion. Also, the aluminium hydroxide (boehmite) adheres poorly to the aluminium underneath. However, once the conversion is accomplished, hydroxide detaches from the adherend and failure occurs. Figure 4.15 depicts the failure model in case of hydroxide conversion.

Aluminum hydroxide formed during wedge test

Crack extension Aluminum hydroxide formed after crack propagation

Alum

inum

Adh es

ive

Original FPL Oxide

Aluminum

Figure 4.15  Schematic representation of hydration leading to the failure in a wedge test specimen [46].

114  Structural Adhesive Joints The FPL and PAA processes require different times to complete the processes. The PAA process forms phosphate particles. Moreover, it acts as a hydration inhibitor. The hydration inhibition is essential to have better resistance against the oxide-to-hydroxide conversion. Davis et al. studied the hydration behaviour of PAA anodised surface using surface behaviour diagram [46]. The PAA anodised aluminium surface under continual exposure to 100 % r. h. at 50 °C produces surface behaviour diagram (Figure 4.16). It is concluded that hydration develops in three stages: (i) reversible adsorption of H2O at the surface of AlPO4 layer, (ii) slow dissolution of hydrated phosphate along with hydration of freshly exposed Al2O3 to AlOOH, and (iii) nucleation and growth of bayerite, i.e. AlOOH to Al(OH)3. Also, Figure 4.16 explains the role of slow dissolution rate of phosphate by slowing down the oxide-to-hydroxide conversion. The dotted line in the diagram depicts the reaction path of rapid dissolution rate of phosphate along with slow oxide hydration. The region under the triangle at the right bottom depicts the reaction path when both dissolution rate of phosphate and oxide hydration rate are slow. The dots along with numbers denote experimental points. The number depicts the reaction time in hours. Moreover, experimental points are very close to the bottom right corner. This indicates very slow dissolution of hydrated phosphate because

AlPO4

AlPO4 2H2O

AlPO4, H2O

9 ×

H2O

192 Al(OH)3

22 96

24

72 AlOOH

4

2

1 Al2O3

Figure 4.16  The ternary surface behaviour diagram of A1PO4-A12O3-H2O PAA aluminum oxide surface. The numbers indicate the time of exposure in hr. 100 % r.h. at 50-60 °C [46].

Durability Aspects of Structural Adhesive Joints  115 of accelerated oxide hydration. In summary the dissolution rate of phosphate controls the oxide-to-hydroxide conversion up until bayerite phase starts to nucleate [49]. The chemical and electrical industries use wrought aluminium alloy due to its high electrical conductivity, workability and corrosion resistance. The 1050 aluminium alloy is the most prominent in this category. Niknahad et al. demonstrated various pretreatments on 1050 Al alloy [50]. Chromatephosphate conversion coating (CPCC) is a traditional and old way of coating the surface. Newer blends such as hexafluorozirconic acid (Zr), poly(acrylicacid) (PA) and polyacrylamide (PAM) show better adhesion strength as well as corrosion resistance. PA/PAM/Zr pretreatment improves the corrosion resistance markedly. However, adhesion strengths in both dry and wet conditions are comparatively high for CPCC. Consolidated data are represented in Figure 4.17. Aluminium alloy AA6060 (Al-Mg-Si) is another important class of Al alloy. Extruded bars, rods, and wire are manufactured using this alloy. The anodising pretreatment is expensive and elaborate. Hence, extruded bars

Dry Adhesion Strength (kg/cm2) Wet Adhesion Strength (kg/cm2) Adhesive Remaining (%)

100

160

80

120

60

80

40

40

20 0

0 No. 1

No. 4

No. 10 No. 13 Treatment

No. 16

CPCC

Figure 4.17  Adhesion strengths of differently pretreated aluminium samples and percentage of adhesive remaining after humidity test, different pretreatment numbers have different combinations (in wt%) of PAA-PAM-Zr No .1 – PAA=0, PAM= 0, Zr = 0 No. 2 - PAA=0, PAM=2, Zr=0.2 No. 10 – PAA=1, PAM=0.5, Zr=0.2 No. 13 - PAA=2, PAM=0, Zr=0.2 No. 16 – PAA=2, PAM=2, Zr=0 [50]

Adhesive Remaining (%)

Adhesion Strength (kg/cm2)

200

116  Structural Adhesive Joints and rods do not undergo anodising pretreatment. Moreover, the use of simpler pretreatments such as alkaline (NaOH) etch followed by deoxidation, and chromate conversion coating (CCC) is preferred. The CCCs are inert, hydrophobic and stable over a wide range of pH. Also, these are corrosion resistant and provide self-healing. However, the conversion process generates massive quantities of environmentally hazardous hexavalent chromium and heavy-metal waste. Therefore, the scientific community recommends environmentally benign Ti-Zr-based conversion coating. The experiments performed by Lunder et al. concluded that Ti-Zr-based pretreatment is inferior to CCC in terms of durability; however, it is superior compared to alkaline etch [51]. The wedge test reveals that the CCC is the best pretreatment in terms of crack growth. Wedge test exposes a specimen to a relative humidity of 96% at 40 °C. Initially, the crack grows due to cohesive failure of the adhesive, although to some extent also depends on surface pretreatment. Ti-Zr-based (high pH) pretreatment and alkaline etch pretreatment exhibit shortest initial crack and most prolonged initial crack, respectively (Figure 4.18a). However, after an initial exposure time of 10 h, a specimen with CCC pretreatment shows constant and slow crack growth (Figure 4.18b). The crack development usually decreases over time owing to the reduction in stress intensity at the crack tip with an enhancement in crack length. Ti-Zr-based (high pH) pretreatment manifests most extended crack length after 1340 hr, even after exhibiting shortest initial crack. CCC pretreatment exhibits a significantly short crack length after 1340 hr. Ti-Zrbased (low pH) pretreatment shows comparatively shorter crack length after long term exposure. The high pH pretreatment (pH=4) is one with more volume of conversion coating and low pH pretreatment (pH=2) has less volume of conversion coating. The more the volume, thicker the coating. The defects in a thicker coating facilitate rapid interfacial diffusion of water. The rapid diffusion of water along the edges of the wedge specimen coupled with prolonged exposure time influences the entire joint ahead of the crack tip. This induces a reduction in adhesive strength. Therefore, conversion coating volume must not become excessive in order to achieve more durable adhesive bonds with Ti-Zr-based pretreatment. Hence the final ranking of pretreatments based on durability is as follows: CCC(best) >>Ti-Zr (low pH) >Ti-Zr (High pH) ≈ Alkaline etch and deoxidation. The sol-gel process is nothing but Ti-Zr-based process as it uses titanium or zirconium alkoxide as a precursor [52]. Meyer et al. studied the durability of sol-gel process on AA6016 (used in automobiles) and AA7075 (used in aircraft) [53]. The sol-gel coating production is environment-friendly and non-toxic. A slightest modification in precursor mixture results in variation in the properties of an adhesive. The coatings show an increase

Durability Aspects of Structural Adhesive Joints  117 90

Total crack length (mm)

85 80 75 70 65 60

0

1

(a)

2

3 4 5 6 7 Exposure time (hours)

8

9

10

Total crack length (mm)

110 100 90 80 70 60 (b)

0

200

400 600 800 1000 Exposure time (hours)

1200

1400

Figure 4.18  Crack length vs time for AA6060 wedge test specimen on exposure to 96% r.h. and 40°C: (a) initial stage (10h) of environmental crack growth, (b) crack growth on eight weeks of exposure for different surface pretreatments: ◊- NaOH with deoxidation, □- Ti-Zr pH 2.9 for 90 sec, ▴- Ti-Zr pH 4.0 for 90 sec, ▵- CCC pretreatment [51].

in lap shear strength in the salt spray test, even though simultaneous crack formation occurs (Figure 4.19). Therefore, the sol-gel coating is an interesting and environmentally safe alternative to other (PAA, CAA) pretreatments [54].

4.2.1.2.2 Steel

Steel adherends are susceptible to corrosion in a moist environment. A designer often uses steel in a structure to minimise the production cost. Therefore, designers never employ expensive pretreatments such as anodising or etching on steel adherends [55]. Also, the same chemical treatment shows tendency to react with different steel samples differently. i.e.

118  Structural Adhesive Joints 40

Lap shear strength (MPa)

35 30

as-prepared NST 500 NST 750 NST 1000 SWT 500

25 20 15 10 5 0

6016

7075

Figure 4.19  Variation in lap shear strength after exposure for different time periods, 6016- Al alloy of 6000 series, 7075- Al alloy of 7000 series, NST- Neutral Spray Test, SWTSaturated Water Test (Number after NST and SWT is the test period in hours) [53].

a pretreatment that would give one steel alloy a durable adhesive strength would yield a poor outcome for another steel alloy. The designer therefore utilises steel without any surface pretreatments. However, grit or shot blasting and alternative mechanical abrasion pretreatments clean the surface and provide more oxide layer for mechanical interlocking with the adhesive [56]. These are not as exotic as PAA or etching, but improve performance and reduce the cost of surface preparation. Nevertheless, civil and marine industries use steel extensively for structural applications. As we know, the durability of the adhesive bond primarily depends on mechanical interlocking with the surface. Also, the change in surface roughness value alters the ability of an adhesive to undergo mechanical interlocking. Therefore, surface roughness value plays a vital role to achieve desirable durability of adhesives [57]. The increase in air pressure and blasting time increases the roughness of the substrate (Figures 4.20 and 4.21). However, above particular limits of pressure and time the residual grit starts to entrap inside a highly roughened surface. The entrapment results in the reduction in adhesive bond strength. The adhesive bond strength increases with an increase in hardness of a material. The heat treatment of the material gives a variety of hardness values. The main parameter is blasting angle. Table 4.4 shows that for the same heat treated (quenched) substrates, blasting angle of 90° gives higher surface roughness than 45°; however, the latter shows higher adhesive strength. The 90° blast angle produces a huge quantity of residual grit, therefore blast angle of around 45° is preferred.

Durability Aspects of Structural Adhesive Joints  119 12 10

Ra (µm)

8

0.3 N/mm2 0.4 N/mm2 0.5 N/mm2 0.6 N/mm2 0.7 N/mm2

6 4 2 0

25 cm

30 cm

40 cm

Grit Blasting Distance

Figure 4.20  Variation in the surface roughness for different blasting pressures. The annealed AISI 4130 steel was grit blasted for 3 seconds [57].

12

0.3 N/mm2

0.4 N/mm2

0.6 N/mm2

0.7 N/mm2

0.5 N/mm2

Ra (µm)

10 8 6 4 2 0

 

3 sec

6 sec

10 sec

Grit Blasting Time

Figure 4.21  Variation in the surface roughness for different blasting pressures. The annealed AISI 4130 steel was grit blasted from a distance of 40 cm [57].

The civil engineers are shifting towards the use of fibre reinforced polymers (FRPs) to strengthen and repair existing civil engineering structures [58]. The steel/FRP joints in such structures use adhesive for bonding [59]. Dawood and Rizkalla [60] investigated the effect of moisture exposure on steel/FRP lap shear joint for a duration of 6 months. They prepared two specimens, one with only grit blasting and other with grit blasting followed by silane pretreatment. Also, Linghoff and Naumes [59] studied the effect of moisture on steel/FRP lap shear joint with specimen treated with sandblast

Hardness (Vickers)

185

185

185

415

415

Surface treatment

Annealing

Annealing

Annealing

Quenching

Quenching

40

40

25

25

25

Working distance (cm)

6

6

10

6

3

Blasting time (s)

0.6

0.6

0.4

0.4

0.4

Blasting pressure (MPa)

45

90

90

90

90

Blasting angle (°)

7.93

8.65

4.81

5.13

4.62a

Ra (μm)

55.1

53.2

42.3

44.2

41.7

Adhesive bond strength (MPa)

Table 4.4  Effect of various surface treatments and surface roughness of steel substrate on the adhesive bond strength [57].

120  Structural Adhesive Joints

Durability Aspects of Structural Adhesive Joints  121 coated (SACO) surface preparation. The exposure to silane pretreatment along with grit blasting exhibits lesser degradation in adhesive strength compared to grit blasting without silane pretreatment (Figure 4.22). The silane pretreatment is comprised of grit blasting followed by application of a silane primer. The primary function of the primer is to wet the adherend and penetrate into every small part of the material to form both physical and chemical bonds uniformly. A homogeneous distribution of chemical coating on the bondline provides higher stability to the steel/adhesive interface.

4.2.1.2.3 Titanium

The marine, aircraft and aerospace industries use Ti-6Al-4V titanium alloy predominantly for structural applications [61]. Titanium is mostly incorporated in high-temperature applications because of its stability in hot and humid conditions. The oxide layer formed in the case of CAA treatment for titanium adherend is characteristically amorphous. However, moisture dependent changes in the morphology of the substrate are relatively slow compared to aluminium. At moderate temperature conditions, the crack propagation is primarily in the adhesive due to cohesive failure. Meanwhile, mechanical interlocks provided by the protruded oxide layer remain intact [62].

1.7

Normalized Adhesive Strength

1.5 1.3 1.1 0.9 0.7 0.5 0.3

0

30

60

90

120

150

180

Exposure Time (Day)

Figure 4.22  Variation in adhesive strength of CFRP/steel joints for different surface treatments over prolonged moisture exposure ▵- Grit blasting only [60], ▴- Grit blasting with silane treatment [60], ●-Grit blasting only [59], ⚪- Blast coating SACO. The strength values are normalized with respect to the strength of grit-blasted-only specimens [59].

122  Structural Adhesive Joints The high temperature (above 200 °C) application preferably uses titanium as a material of choice owing to its lightweight and high melting point. Similarly, the designer uses an adhesive with a high curing temperature to avoid plasticization [63]. Moreover, the durability of titanium adhesive bonds in a hot andhumid environment decreases as a result of oxide instability at elevated temperatures. The solubility of oxygen in titanium increases with a rise in temperature [64]. The oxygen involved in CAA or other anodising process dissolves or diffuses in titanium, leaving gaps at the metal-oxide interface (Figure 4.23). Clearfield et al. studied thehigh-temperature bond durability of titanium alloy processed with various surface treatments [64]. It showed that in the case of a CAA process, stresses concentrate over small areas at the interface causing joint failure. The adherends kept at 600 °C for 1 h and 300 °C for 710 h show the same mode of failure. The formation of a thick oxide layer in the CAA process leads to failure during the high-temperature application. Therefore, the industry uses other high-temperature compatible surface treatments like plasma-spray [65] and sol-gel [66]. The plasma-spray method provides a fractal-like microrough coating. It forms a thin layer of native oxide, unable to cause failure mode like as discussed above. Plasma-sprayed adherend kept at 450 °C for 165 h in a tensile test, and 230 °C for 1000 h in a wedge test shows failure in the adhesive. However, cohesive failure occurs within coating in case of the wedge test specimen. The eco-friendlier sol-gel process retains 50-60% of initial adhesive strength after 10,000 h at a temperature of 177  °C. However, the long duration of current test methods and inadequacy of more accelerated test methods to give reliable results hinder the improvement of a sol-gel process. Laser texturing of a substrate using pulsed lasers is also a viable option considering the eco-friendly nature of the process. However, little to no research has been done regarding adhesive bond strength and durability of pulsed laser textured substrate. Ti Oxide

Diffusion Zone

Micro-pores

Ti-6Al-4V

Figure 4.23  Schematic diagram of oxygen diffusion from the oxide into titanium alloy at high temperature.

Durability Aspects of Structural Adhesive Joints  123

4.2.2 Environment The factors related to the environment totally depend on the nature of the surrounding. As already discussed, moisture and temperature variations are the most critical parameters [67]. Moreover, the thermal expansion coefficient plays an important role where materials from various families are being bonded together.

4.2.2.1 Moisture An adhesive bond exposed to the external environment always comes in contact with water in the form of moisture. Water readily diffuses through the adhesive or adherend, if it is porous. It travels along the adhesive/ adherend interface and migrates through cracks and crazes via capillary action. Moisture attacks the bond by (i) plasticization, (ii) disruption of secondary bonds at the interface, (iii) swelling of adhesive with the induction of concomitant stresses, (iv) hydrolysis/cracks/craze, and (v) corrosion of adherend surface. Gledhill et al. [68] suggest that for a short bond degradation, i.e., for a dry joint, the bond can regain some of its lost strength. If bond degradation has not proceeded too far, then the first three processes mentioned above are reversible to some extent. It is concluded that weakening of a joint does not occur below critical water concentration, or even if weakening occurs, it is reversible [69]. The locus of the failure varies from cohesive within the adhesive to that at the interface after moisture penetration [67]. Moreover, due to the polar nature of metal oxides, water molecules disrupt any dispersion (van der Waals) bonds at the interface [70]. The work of adhesion WA in an inert medium is represented as,



WA = γa + γs – γas

(4.4)

Where, γa and γs - Surface free energies of adhesive and substrate, respectively γas - Adhesive-substrate interfacial free energy Work of adhesion in the presence of liquids such as water WAl is represented as,



WAl = γal + γsl – γas

(4.5)

Where, γal and γsl - Interfacial free energies of adhesive/liquid and substrate/liquid interfaces, respectively.

124  Structural Adhesive Joints Table 4.5  Work of adhesion for different interfaces [70]. Work of adhesion (mJ/m2) Interface

In inert medium

In water

Interfacial degradation of the bond after immersion in water

Epoxy/Steel

291

-255

Yes

Epoxy/Al

232

-137

Yes

Epoxy/Silica

172

-57

Yes

Epoxy/CFRP

88–99

22–24

No

In an inert medium, positive WA is associated with a stable interface and negative work of adhesion is associated with an unstable interface which is prone to degradation. Table 4.5 shows data for the WA for different interfaces. It depicts that moisture displaces epoxy adhesive from steel, aluminium, and silica substrates and promotes degradation of the adhesive bond. However, moisture softens the bond between epoxy and carbon fibre, and it remains thermodynamically stable [71].

4.2.2.2

Coefficient of Thermal Expansion (CTE)

Every material expands or contracts under variation in temperature. It is known that each and every material has its own coefficient of thermal expansion (CTE) [72]. Hence, the stresses are induced in a joint comprised of dissimilar materials, under the influence of variation in temperature [73]. The CTE comes into picture when an adhesive bond is made of different classes of materials. Figure 4.24 shows CTE values for commonly used materials in structural applications. The CTE of a polymer is usually 10-100 times higher than other materials. The stresses start to develop along the ­adhesive/ adherend interface. The adhesive does not allow interfacial stresses to induce stress within the adhesive as long as the temperature is above the Tg of the adhesive. However, once the temperature goes below the Tg, the adhesive becomes less compliant and the stresses start to induce [73]. Thus, CTE differences between the substrate(s) and adhesive and the degree of cooling below the Tg influence thermal stresses induced in the joint [9]. There are two approaches to minimize the thermal stresses caused: one is to mix low and high CTE polymers to match the CTE of the substrate and the other is to add mineral fillers to the adhesive to reduce the CTE. In the case of an adhesive joint made of mismatched adherends, e.g. composite to steel, an engineer uses a near-room temperature curing adhesive.

Durability Aspects of Structural Adhesive Joints  125 CTE (10–6/K) Wood (across grain) Wood (along grain) Titanium Steel Aluminium Epoxy (below Tg) Epoxy (above Tg) 0

20

40

60

80

100

120

140

160

180

200

Figure 4.24  Coefficients of thermal expansion for different materials [10].

4.2.3 Stress The environmental exposure induces stresses in the joint that, in turn, influence the durability of an adhesive joint [42, 68]. The cyclic stresses tend to degrade joint more rapidly than the constant stresses. The degradation of joint causes a decrease in the lifetime or a decrease in the residual strength of the joint. The stresses on a joint make primary and secondary chemical bonds, both within the polymer itself and across the polymer–oxide interface, more susceptible to environmental attack by lowering the activation energy for bond breaking [69, 71]. The stresses boost the rate of moisture transport in the adhesive through craze or micro-crack formation [69]. The high-speed military aircraft experiences cyclic stresses on the body, which makes it vulnerable to ageing as discussed above. The bonded composite system withstands one to four thermal “spikes” or cycling per day [74]. This shows that water enters the microcracks during each thermal cycle (0 °C – 150 °C – 0 °C). Moreover, hydrolysis study of adhesives on water exposure at 80 °C indicates that a stressed sample undergoes hydrolysis within a few weeks, whereas unstressed sample remains unaffected for over three months. The wedge test provides a better evaluation of relative durability compared to the lap shear strength test. The wedge test evaluates durability at the crack tip. The crack tip is exposed to the influence of water passing

126  Structural Adhesive Joints through the edge of the specimen. Hence, stresses induced at the crack tip make the specimen prone to failure. The testimony for wedge test being superior is the fact that Boeing has correlated results of wedge test on actual components of aircraft with their in-service durability [9, 75]. Briskham and Smith studied the effect of cyclic stresses on the durability of the aluminium-epoxide joints using different surface treatments [76]. The joint was submerged in a tank filled with water. The tank was maintained at a temperature of 55 °C and was subjected to cyclic stress between 0.15 to 1.2 MPa. It performs best in case of PAA treatment, whereas aminosilane coupling agent shows worst results. PAA pretreated joints experience cohesive failure within the adhesive, whereas other treatments encounter failure at or near the interface. Ashcroft et al. [77] exposed stressed joints made with various adhesives to the natural ageing for 6 years. The stressed joints with epoxy-polyamide (E-P) and the one with modified epoxy (ME120k) lost their adhesive strength completely while others retained a significant amount of their strength (Figure 4.25).

Residual strength

1.2 1

0%

0.8

5% 10%

0.6

20%

0.4 0.2

ME120k

ME120w

ME170g

N-P

ME170

E-N

V-P

E-P

0

Figure 4.25  Effect of different loads (5%, 10% and 20%) on the residual strength of double lap joints prepared with different adhesives exposed to hot/wet conditions for six years, E-P: Epoxy-polyamide, V-P: Vinyl-phenolic, E-N: Epoxy-novolac, ME170: Modified epoxy with unsupported film, ME170g: Modified epoxy with glass beads, N-P: Nitrilephenolic, ME120w: Modified epoxy with woven nylon carrier, ME120k: Modified epoxy with knitted nylon carrier [77].

Durability Aspects of Structural Adhesive Joints  127

4.3 Methods to Improve Durability The degradation of an adhesive joint is an inevitable phenomenon; however, various methods can be employed to slow down the process and achieve considerable control over it. Various ways to improve durability can be assigned to materials, environment and design. The most feasible option to improve durability is either by selecting a suitable material or altering the surface treatment. The awareness and use of nanotechnology have increased in the scientific community in the last two decades. Ahmad et al. [78] incorporated nano-fillers and microparticles in a room temperature cured epoxy. Nano-filler addition enhances environmental stability, and the addition of microparticles provides a better moisture resistance [79–81]. Also, the substitution of titanium for aluminium resolves most of the moisture-related problems, though it is not an economically feasible solution. Zhai et al. studied variation in the pull-off strength of an epoxy adhesive after incorporation of nanoparticles as additives [82]. The nanoparticles of Al2O3, CaCO3 and SiO2 were incorporated inan epoxy adhesive. The incorporation of nanoparticles in an epoxy adhesive significantly boosts the adhesive strength of the epoxy adhesive compared to the pure epoxy adhesive. The Al2O3 nanoparticles have average size of 80 nm in diameter, nano-CaCO3 40∼80 nm, and nano-SiO2 10∼20 nm. Figure 4.26 shows nanoparticles with maximum diameter size (Al2O3) give the best pull-off adhesion strength. Moreover, azole and tetrazine based hydration inhibitors on anodised aluminium adherends provide corrosion resistance and improved durability [83]. Whelan et al. [83] synthesized corrosion inhibitors based on imidazole (IMID) and 3,6-di-2-pyridyl1,2,4,5-­tetrazine (DPTZ). The chelating property of DPTZ inhibits Cl-ions. It provides hydrothermal sealing against electrolytic attack. The most effective but absurd way to improve durability is to change the environment of the adhesive joint. The adhesive joints do not degrade at moderate temperatures and in low moisture conditions. A proper design of joint maximises the durability of the joint. An excellent design slows down the process of moisture reaching the bondline. The design incorporates a drain hole to prevent the accumulation of water and promotes runoff. The proper application of a sealant helps in the prevention of water ingress [84]. The overdesigning of a joint makes it more resistant to sudden impacts, and it experiences only a small fraction of stress. This enables joint to withstand load even after moisture degrades a small portion of the joint. However, this approach is infeasible, considering the cost and weight of the joint.

128  Structural Adhesive Joints Pure epoxy adhesive With nano-Al2O3 With nano-CaCO3

Pull-off adhesion strength (MPa)

18 16

With nano-SiO2

14 12 10 8 6 4 2 0

Figure 4.26  Variation in pull-off adhesion strength of epoxy from low carbon steel substrate for different nanoparticle additives [82].

4.4 Summary The aggressive environment makes it difficult to achieve long-term durability of adhesively bonded joints. The moisture present in the environment is the main culprit in the degradation of the joint. The moisture attacks the secondary bonds (van der Waals) that adhesive makes with the adherend surface. Therefore, it has to rely on the primary bond (covalent or ionic) or a physical bond (mechanical interlocking). The more adverse environmental condition degrades the joint faster, and, as a result,an early failure of the joint occurs. The designers provide special arrangements in the design of the adhesive joint in order to improve the durability of the adhesive joint. The primary or physical bonds become less prone to environmental degradation with the use of hydration-resistant surface treatment. A reactive surface treatment, such as sol-gel, stabilizes the chemical bonds at the interface and slows down bond degradation. However, the long test duration required for assessment of durability is still the main reason behind little to no improvement in understanding the durability aspects of an adhesive joint. The available methods consume years in evaluating the durability of a particular adhesive or surface pretreatment. Therefore, a more reliable and accelerated assessment method is needed in the near future.

Durability Aspects of Structural Adhesive Joints  129

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132  Structural Adhesive Joints 47. J.D. Venables, Adhesion and durability of metal-polymer bonds J. Mater. Sci. 19, 2431–2453 (1984). 48. S. Ogata and Y. Takahashi, Moisture-induced reduction of adhesion strength between surface oxidized Al and epoxy resin: Dynamics simulation with electronic structure calculation J. Phys. Chem. C 120, 13630–13637 (2016). 49. W. Vedder and D.A. Vermilyea, Aluminum + water reaction Trans. Faraday Soc. 65, 561–584 (1969). 50. M. Niknahad, S. Moradian, and S.M. Mirabedini, The adhesion properties and corrosion performance of differently pretreated epoxy coatings on an aluminium alloy Corrosion Sci. 52, 1948–1957 (2010). 51. O. Lunder, F. Lapique, B. Johnsen, and K. Nisancioglu, Effect of pretreatment on the durability of epoxy-bonded AA6060 aluminium joints Int. J. Adhesion Adhesives 24, 107–117 (2004). 52. J.H. Osborne, Observations on chromate conversion coatings from a sol-gel perspective Prog. Organic Coatings 41, 280–286 (2001). 53. S. Meyer, U. Schubert, M. De Bardi, R. Wiesinger, M. Schreiner, and T. Grohmann, Adhesion pretreatment of aluminum by sol-gel processing Int. J. Adhesion Adhesives 51, 103–110 (2014). 54. T.L. Metroke, R.L. Parkhill, and E.T. Knobbe, Passivation of metal alloys using sol-gel-derived materials - A review Prog. Org. Coatings 41, 233–238 (2001). 55. H.M. Clearfield, D.K. McNamara, and G.D. Davis, Adherend surface preparation for structural adhesive bonding, in : Adhesive Bonding, L.H. Lee (Ed.), pp. 203–237, Springer US (1991). 56. L. Kozma and I. Olefjord, Surface treatment of steel for structural adhesive bonding Mater. Sci. Technol. (United Kingdom) 3, 954–962 (1987). 57. S.K. Asl and M.H. Sohi, Effect of grit-blasting parameters on the surface roughness and adhesion strength of sprayed coating Surf. Interface Anal. 42, 551–554 (2010). 58. M. Dawood, Durability of steel components strengthened with fiber-reinforced polymer (FRP) composites, in : Rehabilitation of Metallic Civil Infrastructure Using Fiber Reinforced Polymer (FRP) Composites: Types Properties and Testing Methods, V.M. Karbhari (Ed.), pp. 96–114, Elsevier (2014). 59. M. Heshmati, R. Haghani, and M. Al-Emrani, Environmental durability of adhesively bonded FRP/steel joints in civil engineering applications: State of the art, Composites Part B 81, 259-275 (2015). 60. M. Dawood and S. Rizkalla, Environmental durability of a CFRP system for strengthening steel structures Constr. Build. Mater. 24, 1682–1689 (2010). 61. M. Natan and J.D. Venables, The stability of anodized titanium surfaces in hot water J. Adhesion 15, 125–136 (1983). 62. P. Molitor, V. Barron, and T. Young, Surface treatment of titanium for adhesive bonding to polymer composites: A review Int. J. Adhesion Adhesives 21, 129–136 (2001).

Durability Aspects of Structural Adhesive Joints  133 63. P. Peyser and W.D. Bascom, The anomalous lowering of the glass transition of an epoxy resin by plasticization with water J. Mater. Sci. 16, 75–83 (1981). 64. H.M. Clearfield, D.K. Shaffer, S.L. Vandoren, and J.S. Ahearn, Surface preparation of Ti-6Al-4V for high-temperature adhesive bonding J. Adhesion 29, 81–102 (1989). 65. P. Maressa, L. Anodio, A. Bernasconi, A.G. Demir, and B. Previtali, Effect of surface texture on the adhesion performance of laser treated Ti-6Al-4V alloy J. Adhesion 91, 518–537 (2014). 66. C. Park, S.E. Lowther, J.G. Smith, J.W. Connell, P.M. Hergenrother, and T.L. St Clair, Polyimide-silica hybrids containing novel phenylethynyl imide silanes as coupling agents for surface-treated titanium alloy Int. J. Adhesion Adhesives 20, 457–465 (2000). 67. J. Comyn, Durability of adhesives in wet conditions, in : Adhesives in Marine Engineering, J. Weitzenböck (Ed.), pp. 187–207, Elsevier (2012). 68. R.A. Gledhill, A.J. Kinloch, and S.J. Shaw, A model for predicting joint durability J. Adhesion. 11, 3–15 (1980). 69. G.D. Davis and J.D. Venables, Surface and interfacial analysis, in : Durability of Structural Adhesives, A.J. Kinloch (Ed.), pp. 43–84, Applied Science Publishers (1983). 70. R.A. Gledhill and A.J. Kinloch, Environmental failure of structural adhesive joints J. Adhesion 6, 315–330 (1974). 71. A.J. Kinloch, The service life of adhesive joints, in : Adhesion and Adhesives, A.J. Kinloch (Ed.), pp. 339–404, Springer(1987). 72. PDL Staff, Mechanical fastening, in : Handbook of Plastics Joining, M.J. Troughton (Ed.), pp. 105–136, Elsevier (1997). 73. M.L. Williams, R.F. Landel, and J.D. Ferry, The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids J. Am. Chem. Soc. 77, 3701–3707 (1955). 74. C.E. Browning, The mechanisms of elevated temperature property losses in high performance structural epoxy resin matrix materials after exposures to high humidity environments Polym. Eng. Sci. 18, 16–24 (1978). 75. A.A. Baker and J. Wang, Adhesively bonded repair/reinforcement of metallic airframe components: materials, processes, design and proposed throughlife management, in : Aircraft Sustainment and Repair, R.B. Jones, A.A. Matthews and V. k. Neil Champagne (Eds.), pp. 191–252, Elsevier (2017). 76. P. Briskham and G. Smith, Cyclic stress durability testing of lap shear joints exposed to hot-wet conditions Int. J. Adhesion Adhesives 20, 33–38 (2000). 77. I.A. Ashcroft, R.P. Digby, and S.J. Shaw, A comparison of laboratoryconditioned and naturally-weathered bonded joints J. Adhesion 75, 175– 201 (2001). 78. Z. Ahmad, M.P. Ansell, and D. Smedley, Epoxy adhesives modified with nano- and microparticles for in situ timber bonding: Effect of environment on mechanical properties and moisture uptake J. Eng. Mater. Technol. Trans. ASME 132, 0310161–0310168 (2010).

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5 Debonding of Structural Adhesive Joints Mariana D. Banea

*

Federal Center of Technological Education of Rio de Janeiro, Rio de Janeiro, Brazil

Abstract

Adhesive bonding is a viable technique for joining a wide range of materials (e.g. metals, polymers, ceramics, etc., and combinations of any of these materials). However, one disadvantage of adhesive bonding is the permanent character of the joint. In many situations (e.g. repair and disassembly processes), it is desirable that the joint can be separated easily, without damaging the substrates so that the materials can be reused. Thus, as a result of the significant pressure on reducing costs and increasing demand for material recyclability, the development of new techniques and processes for easy recycle and repair of bonded structures is becoming of great interest for the industry. This chapter presents the recent developments in the use of debonding technologies and summarizes the different strategies and approaches used for debonding of structural adhesive joints. The use of fillers in the adhesive which can be triggered by an external stimulus (e.g. heat: thermal and induction, electrical or magnetic flux) to induce mechanical separation of the substrates is discussed. It is concluded that there is no universally accepted debonding method due to the wide variety of adhesive bonded joint systems and applications. The selection of the appropriate debonding technique will depend on the particular application needs and constraints. Keywords:  Adhesive joints, debonding, recycling, thermally expandable particles (TEPs), nanoparticles, additives

5.1 Introduction Adhesive bonding has found applications in various areas from high technology industries such as aeronautics, aerospace, electronics, and Email: [email protected] K.L. Mittal and S. K. Panigrahi (eds.) Structural Adhesive Joints: Design, Analysis and Testing, (135–158) © 2020 Scrivener Publishing LLC

135

136  Structural Adhesive Joints automotive to traditional industries such as construction, sports and packaging [1–3]. Adhesives can be used to join metals, polymers, ceramics, cork, rubber, and combinations of any of these materials [4]. Moreover, nowadays, new products consist more and more of a combination of new advanced materials, which need to be joined according to their specific characteristics [5, 6]. These materials (e.g. ceramics, carbon fibre reinforced polymers (CFRPs), etc.) are usually expensive which creates an increasing demand for recyclability, driven by economic as well as environmental reasons. Thus, the development of new techniques and processes for easy recycle and repair of bonded structures is becoming of great interest for the industry [7]. If bonds can be broken without damage of the components, recycling is easier. Also for an environmentally-friendly disassembly of bonded structures, it is necessary to separate the joint between the bonded components so that the different materials can be reused. During the last years, the concept of the ‘circular economy’ has received growing attention in order to achieve a more sustainable society [8]. To reduce the negative impact on the environment, manufacturers need to design more sustainable products and to implement cleaner production systems for 3R operations (3R–Reuse/Remanufacture/Recycle) (see Figure  5.1). As more severe legislation requirements on manufacturer

Materials

Bonding

Recycle

Reuse or Repair

Structures (Final products)

Debonding

Figure 5.1  Scheme of the concept of 3R in industry: reuse, repair (remanufacture) or recycle of materials at end of life.

Debonding of Structural Adhesive Joints  137 responsibility are implemented in many parts of the world, the use of recycled materials is increasingly important [9]. Apart from recycling, there are other end-of-life options including reuse and remanufacturing. These three R’s can be categorised as recovery strategies. To enable these three end-of-life options of a product, a certain level of disassembly is required [9]. In this context, adhesives can have a significant part in how easily structures (products) can be recycled in the near future. Dismountable bonded structures are required for: repair, recycling or reuse of critical materials. This requirement is generally important with products that have a very high degree of complexity or cost (e.g. integrated electronic components, aerospace structures, automotive structures, or wind turbine blade components). With adhesives that can be easily debonded, repairs can be made easily and parts can be upgradable. For example, the automotive industry has legislative drivers which promote recycling of materials and, therefore, necessitating ease of dismantling in a simple and cost-effective manner. In fact, recent mandatory targets state that all vehicles must be 95% recyclable [10]. In addition, debondable adhesives will facilitate the use of composites or new advanced materials in mixed-material vehicle structures because they can provide adhesively bonded joints with the durability and the reversibility of mechanically fastened joints but with reduced weight. Consequently, there is a growing need to develop adhesives that debond on demand for easy disassembly of the bonded structures and to separate parts for reuse or recycling. Currently, debonding of structural adhesive joints is mainly based on mechanical destruction (thermal degradation of the adhesive, cutting of the adhesive or a combination of these methods), which can damage or even destroy the substrates [7]. Acids and solvents may also be used, but health and safety concerns arise. For example, in the case of disassembly of windscreens and frames in the automotive industry, electric knives are used. This produces significant residue, wastage, and breakage and also raises serious safety issues. Several adhesive suppliers give basic advice on adhesive debonding [11]. There are many patents that have been issued about methods of separating bonded joints in the last years [12–17]. However, only a small number of debonding adhesives are commercially available at the moment [18–20]. A large number of innovative techniques in the field of debondable adhesives have been developed recently. This chapter overviews the progress and results of ongoing research and development efforts in order to achieve dismountable structural adhesive joints. A comprehensive discussion of debonding techniques of structural adhesively bonded joints using fillers (nano and micro) is presented.

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5.2 Design of Structures with Debondable Adhesives (Design for Disassembly) Nowadays, design for disassembly has become an important issue in several industries, where the possibility of recovering the materials at the end of life of the products is considered. The industry has made significant progress in recycling technology. However, the use of lightweight materials such as polymers and fibre reinforced composites makes the recycling process more challenging. It is well known that the main joining technique for polymers and composites is adhesive bonding as it generally outperforms traditional joining technologies when joining dissimilar materials and non-metal materials. Nevertheless, it encounters more problems during the recycling process of end-of-life products. For example, the recycling and recovering process of composite materials is quite complicated, due to their physical and chemical characteristics [21]. Thus, using debondable adhesives might become a basic requisite in the design approach of structures. A debondable adhesive is an adhesive system that maintains certain adhesion strength during its period of service, but can be easily dismantled upon the application of an external stimulus (see Figure 5.2). One of requirements of debondable adhesives is related to the external stimulus employed as a trigger to turn-off the adhesion of the bonded

ON

OFF

Bonded structure in service (External stimulus OFF) External stimulus (e.g. heat, potential, etc.)

End of life, repair or maintenance of the structure (External stimulus ON) Interfacial failure

Figure 5.2  Schematic of debondable adhesive systems.

Cohesive failure

Debonding of Structural Adhesive Joints  139 structure. The external stimulus should be different enough from the in-service conditions in order to avoid unwanted debonding (accidental triggering). Another aspect is the failure mode of the joint after debonding, which can be interfacial, cohesive or mixed mode failure. From a practical point of view, the ideal case would be to obtain interfacial failure after debonding, in order to be able to avoid as much as possible the labour-intensive reconditioning of the materials used. Most of the debondable adhesives are irreversible systems. However, there are some reversible debondable systems reported in the literature, usually adhesives with low cross-link densities or low glass transition temperatures, which are considered non-structural adhesives and are not considered in this chapter [7]. There are several other aspects to be taken into account in order to design a structure with a debondable adhesive. For example, the type of adhesive used must be considered. While low strength adhesives are relatively easy to debond, high strength structural adhesives can be quite challenging to debond. The maximum service temperature of the adhesive is important as the bonded parts need to be heated above this temperature for easy debonding. For example, polyurethanes, acrylic and 2-part epoxy adhesives degrade permanently at temperatures around 200°C, while one-part epoxy adhesives need higher temperatures to degrade. The type and nature of the materials bonded (metallic, plastic, etc.) should also be taken into account. Similarly to adhesives, the maximum temperature that the substrates can be submitted to needs to be taken into account. For instance, plastics and composites can be damaged by heat or solvents, while for some debonding techniques the substrates must be electrically conductive. Another aspect that should be considered is the size of the area that needs to be bonded/debonded and the configuration of the joint. If the adhesion area is not accessible, some techniques will not be applicable (e.g. the case of light induced debonding technique). Finally, sensitivity of other components close to the bonded area (e.g. sensitive electronics or weak plastics which could be damaged by heat or chemicals) must be considered. The selection of the right debonding technique will depend on the application needs and constraints. Incorporating recovery principles into the product design stage is important nowadays due to the increased pressure on costs and increasing demand for material recyclability. Controlled debonding may become a basic requirement for disassembly and recycling of materials in the future. Consequently, debondable adhesives can play an important role in how easily a structure can be recycled.

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5.3 Techniques for Debonding of Structural Adhesive Joints There are several techniques for debonding of structural adhesive joints proposed in the literature such as use of electrically debondable adhesives, and methodologies based on the incorporation of fillers in the adhesive which are externally triggered to induce damage within the adhesive. This section presents the principal techniques developed so far for debonding of structural adhesive joints.

5.3.1 Electrically Induced Debonding of Adhesive Joints Electrically induced debonding of adhesives is a new technology developed for disassembly of bonded structures [18, 22–24]. The technology called ElectRelease™ was developed by EIC Laboratories Inc. (Norwood, MA, USA) and is a technique in which adhesives can be released on demand with the help of an applied potential. The technology is based on a chemical reaction at the interface between the adhesive layer and the anodic adherend connected to the positive electrode of a DC power supply. Depending on the applied potential (10-50 V recommended) to the adhesive joint, the substrates can be debonded in seconds. The joint surfaces must be electrically conductive and kissing bonds must be avoided in order to prevent any short circuit between the substrates. However, this technology can also be applied to non-conductive or coated substrates using a foil patch prebonded with ElectRelease™. This patch consists of two sheets of aluminium foil laminated with a thin layer of pre-cured ElectRelease™. The patches are cut to shape, and any commercial adhesive can be applied to each surface. The non-metallic parts are then bonded with the adhesive-coated patch. The parts are debonded by applying a voltage between the two metal foils. The bond separates at the interface between the ElectRelease™ and the positive foil. A number of electrically debonding adhesive formulations have been patented [25, 26]. Two of these, epoxy-based, are on the market, as E4 and M4 (EIC Laboratories Inc., Norwood, MA, USA) [18]. Leijonmarck and co-workers [23, 24] investigated the ElectRelease technology and provided further understanding of the debonding mechanism. They observed a delamination process at the interface between the aluminium anode and the adhesive layer, detected the changes in polymer chemistry using Raman spectroscopy and also analysed the emission of volatile species using mass spectrometry. The reactions during polarization of the laminates consisted

Debonding of Structural Adhesive Joints  141 of two steps, with aluminum oxide/hydroxide formation as the first and the build-up of a sulphur-rich organic film as the second. On the other hand, the dominating cathodic reaction was hydrogen gas evolution. The amount of hydrogen gas released from the samples was within a factor 2 of the charges passed before the tearing of the laminates. The hydrogen gas created bubbles, visible in a light microscope, for charge densities over 50 mC/cm2. Shiote et al. [27] investigated the effect of applied voltage on the residual strength of joints bonded with the electrically dismantlable adhesive ElectRelease™ (E4). The influences of the adhesion area and the material type of adherend (i.e. steel, aluminum alloy, and copper alloy) were also investigated. They found that the residual strength does not depend on the adhesion area but only on the charge density. The type of adherend material has an impact on the residual strength of the joint. The initial strengths of steel and aluminum alloy specimens are high, and the strengths decrease quickly by electrical conduction, while copper alloy has a lower initial strength and exhibits interfacial failure without any electrical treatment. More recently, Jeong [28] reviewed the electrically debonding adhesives presenting various research results. Several important mechanisms of electrically debonding adhesives: faradaic reaction, phase separation and anode detachment, cathodic debonding, gas emission mechanism, and mechanical stresses were discussed.

5.3.2 Debonding on Demand of Adhesively Bonded Joints Using Reactive Fillers One of the methodologies for achieving a controllable adhesive debonding mechanism is by activating functional fillers located either in the matrix of the adhesively bonded joint or in the primer. These additives can be nanoparticles or microcapsules which can be activated by an external stimulus (energy sources such as: heat (thermal and induction), electric potential, electromagnetic energy, etc.).

5.3.2.1 Nanoparticles The principle of using nanoparticles for controlled debonding is based on the fact that the bonded joint has an adhesive or a primer layer which contains nano-scale particles which have ferromagnetic, ferrimagnetic, superparamagnetic or piezoelectric properties. As a result of the alternating electromagnetic fields, large amounts of localised heat are produced

142  Structural Adhesive Joints in the primer layer of the bonded joint. This localised heat input causes in the case of adjacent thermoplastic adhesive layers softening of the thermoplastic binder [29]. If thermoset adhesives are adjacent to the boundary layer of the primer, then the cross-linked structure in the binder matrix is broken up due to the high degree of localised heating. In both cases, quasi-adhesive-substrate separation with a low energy input is enabled as a result of the highly localised heating of the boundary layer. A similar system has been presented by Kolbe et al. [30] and generally follows the principle of an alternating magnetic field inducing heat to the adhesive. However, this approach can be used for any application where at least one non-metallic substrate is bonded. Preferably, both substrates should be non-metallic as metal by itself is strongly heated in the magnetic field and shield the field. Recently, Ciardiello and co-workers [31–36] used metallic (iron oxide) nanoparticles, embedded in a hot-melt adhesive (HMA) coupled with an electromagnetic induction system to debond adhesively bonded plastic joints. The material used in these works as substrate is a polypropylene used by automotive industries to adhesively bond plastic bumpers, low tailgates, air ducts, and dashboards while the adhesive is a polyolefin hotmelt adhesive. The electromagnetic field generated by the inductor is able to increase the temperature of the embedded iron oxide nanoparticles that can melt the thermoplastic adhesive [33]. The authors state that the traditional techniques used to dismantle plastic adhesive joints can damage the components or substrates. The most used traditional techniques for separating plastic joints are: warming the adhesive up to its melting temperature, the use of a chemical solvent, or the mechanical cut of the adhesive layer. However, the heating and chemical technique can damage also the substrates because they can have similar melting points and because chemical solvents can be aggressive also for the substrates. On the other hand, mechanical cut cannot be used when there is a non-uniform shape of the bondline or in the case where the bondline is not on the edge but well integrated into the structures [35]. The works related to the mechanical properties [33, 35] showed that the nanoparticles embedded in the adhesive led to an increase of the maximum bearing load compared to the neat adhesive. The authors showed that this increase was related to the presence of small particle aggregates that had a toughening effect on the bondline that led to an increase of the maximum load compared to the neat adhesive. Their works [33, 35] showed that the adhesive joints could be separated with all the three adhesive compositions used, which were the hot-melt adhesives prepared with three different weight percent, namely 3%, 5%, and 10%. Of course, the separation time is lower when the weight percentage of the particles is higher. They reported quickest separation times of 13 s, 55 s

Debonding of Structural Adhesive Joints  143 and 109 s for adhesives prepared with the investigated particle concentrations by weight of 10%, 5%, and 3%. The authors also investigated [33] the parameters of the electromagnetic field (power, current, and frequency) in order to minimise the separation time. The authors found that the most influencing parameter is the frequency of the electromagnetic field. Ciardiello and co-workers [32, 34] also investigated the mechanical properties of the adhesive joints subjected to different environmental aging cycles at different temperature and humidity environments. Three different ageing cycles have been adopted. The first one consists of the exposure at 90°C without the control of the Relative Humidity (RH) for 500 h. The second one consists of the exposure at 40°C with RH set at 98% for 500 h. The third one is a shorter cycle (72 h) made of three different cycles: exposure at 80°C without RH for 24 hours, exposure at 40°C with RH set at 98% for 24 hours and exposure at −40°C for 24 hours. The most aggressive environmental ageing cycle for all the analysed adhesives (neat and modified) is the one at 90°C that leads to a reduction of the maximum load sustained by the adhesive joints by 50% compared to the unaged specimen. However, this reduction was reported for the adhesive joints prepared with both the neat and the nanomodified adhesives. On the other hand, the other two adopted ageings did not lead to a reduction of the mechanical load. Further, the authors found that the separation time between the unaged and aged joints did not change for all the considered adhesive compositions [32]. The authors studied also the mechanical response of this adhesive under dynamic loads since it is used for bonding plastic bumpers [36, 37]. Even in this case, the presence of the particles led to slightly higher bearing loads for the adhesive joints prepared with the nanomodified adhesive. Along the same line, the American Chemistry Council’s Plastics Division (ACC-PD) and Michigan State University (MSU) through its Composite Vehicle Research Center used iron oxide nanoparticles at loadings of 4-20% in a variety of thermoplastic adhesives to develop reversible adhesive joints that can be debonded and re-bonded multiple times, using electromagnetic energy [38]. Lee et al. [39] used evaporable polymeric nanocapsules in an adhesive thin film to form gas bubbles through thermal stimulus and showed a debonding effect (see Figure 5.3). They showed, through various analyses, that the adhesive film containing evaporable nanocapsules maintained the initial properties of the adhesive film and through thermal treatment, vaporization of the core material forms bubble gaps at the film interface and successfully reduces the adhesive strength (see Figure 5.4). An evaporable film with a nanocapsule loading of 1.0 wt % resulted in high transmittance, with the highest adhesive strength reduction after 5-min thermal

144  Structural Adhesive Joints (a)

Shell: PEI Core: PMMA

Initiator PEI

After thermal treatment MCH

MCH/PMMA/PEI

MMA (b) Adhesive thin film

Polymeric nanocapsules

Bubble gaps of evaporated MCH

Thermal treatment

Figure 5.3  Debonding technique using polymeric nanocapsules with an adhesive thin film which form gas bubbles through thermal stimulus (a) Concept of a polymeric nanocapsule containing internal evaporable material. (b) Schematic representation of debonding mechanism through the formation of bubble gaps at the interface of a thin film adhesive containing evaporable nanocapsules (hydrophobic methylcyclohexane (MCH)/ poly(methyl methacrylate (PMMA) core/polyethyleneimine (PEI)) [39].

Adhesive strength (kgf/cm2)

12 10

9.87 6.69

8

6.27

6

5.73

4 2 0

Ref.

100 130 Temperature (°C)

150

Figure 5.4  Adhesive strengths of untreated (Ref.) and heat-treated adhesive thin films modified with polymeric nanocapsules, after thermal treatment for 5 min at 100, 130, and 150 °C [39].

Debonding of Structural Adhesive Joints  145 treatment. The authors state that this technique using the polymeric nanocapsules is expected to be applicable to advanced adhesive thin films used in the display and semiconductor industries, owing to its capability of controlling the adhesive strength while maintaining initial film properties. Recently, Son et al. [40] also used vaporizable shell-crosslinked nanocapsules with a transparent adhesive thin film. The shell-crosslinked nanocapsules consisted of an outer shell of polyacrylonitrile (PAN)/poly(methyl methacrylate) (PMMA) copolymer, and an inner core of a thermally evaporable methylcyclohexane. Upon heating at 100 °C in the attached state, the methylcyclohexane (MCH) in the core of the cross-linked nanocapsules vaporized and the debonding occurred at the interface between the upper and lower substrates. Rescoll Technological Center (France) developed and patented a debonding technology called INDAR Inside® [19, 41]. The Rescoll process involves formulating new adhesives or reformulating commercial adhesives (polyurethane and epoxy structural adhesives are possible). This technology is based on the incorporation, in a formulated adhesive or primer, of a specific additive called INDAR. Upon heating at a specified temperature, the additive starts to decompose and release gases which migrate by diffusion from the bulk adhesive to interfaces generating local stresses leading to debonding of the joint. Depending on the type of additive several debonding temperatures are available. This technology has been implemented for ground proof tests on the structure of the Global Astrometric Interferometer for Astrophysics (GAIA) spacecraft and dismantling of plastic tailgates [42]. One of the advantages of this technology is that the parts are easy to clean due to interfacial failure. On the other hand, a difference between the maximal service temperature and debonding temperature (at least 50°C) must be guaranteed in order to avoid premature activation of the additives.

5.3.2.2 Microparticles Another technique developed for adhesive debonding involves imbedding microparticles (microcapsules) in the adhesive layer [4, 7, 43–46]. These microparticles might be thermally expandable particles (TEPs) or blowing agents, which can be activated at a certain temperature to induce mechanical separation of the substrates. The principle of debonding using TEPs is depicted in Figure 5.5. Thermally expandable microparticles were developed by Dow Chemical Co in the early 1970s [17] and are particles made up of a thermoplastic shell filled with liquid hydrocarbon. Heating them, two transformations

146  Structural Adhesive Joints Adhesive + TEPs

Expanded TEPs Adherend

Adherend Heating Adherend

Adherend

Figure 5.5  Scheme of principle of debondable adhesives with TEPs particles (upon heating TEPs expand above the curing and service temperature of the adhesive and thus destroy or weaken the cohesion of the bonded joint making possible the separation of the adherends with a low mechanical force).

will occur (see Figure 5.6a). One is the softening of the shell material and the other is the gasification of the hydrocarbon liquid inside it. As a consequence, the shell will expand as the gas inside it will push the softened shell from inside out causing it to grow in size. When fully expanded, the growth in volume of the particle can be from 50 to 100 times. When heat is removed, the shell stiffens and the particle remains in its expanded form. TEPs were mainly synthesized using suspension polymerization to make use of polymer barrier properties for effective expansion [47–53]. The physical properties of the TEPs depend on the constituent polymers [47, 54–56]. For example, polyacrylonitrile and poly(methacrylonitrile) can effectively prevent gas release and are frequently used as capsule shell components. Expansion temperatures of TEPs range from 70°C to 285°C depending on particle and grade. They are commercialized worldwide by several companies such as: Expancel Nobel Industries (Sweden) [57], and Matsumoto Yushi Seiyaku (Japan) [58], among others. TEPs are used by the industry in a wide variety of applications [59–65]. However, the use of this technique applied to adhesives started in Japan by Sakurai [65] to bond plywood boards. Later, Ishikawa et al. [66] modified and improved the technique for bonding wallpaper on plywood or plasterboards in construction fields. This innovative idea has been extended to structural adhesives for recycling purposes by Nishiyama and co-workers [45, 46]. The simple heating of the joint over 100°C leads to an easy separation of the bonded materials. Bain and Manfre [16] patented a method and apparatus for bonding and debonding adhesive surfaces using TEPs and thermal energy to debond interfaces in an adhesive system. The external stimulus that can be used to activate the microspheres can be a source of electromagnetic waves such as IR or UV radiation, or from a convection oven or from electrical

Debonding of Structural Adhesive Joints  147 Core: liquid hydrocarbon Tension of shell

Heating

Internal pressure

Shell: co-polymers 10–50µm The diameter increases by 3–5 times and volume by 50–100 times (a)

Expansion Ratio

10 µm

Tmax

Tstart

RT

60 µm

Unexpanded

Start of expansion Shrinking Balloon formation

Degradation and/or explosion of the TEPs!!! 10 µm

(b)

30 µm

Figure 5.6  (a) Model of TEPs expansion mechanism, (b) SEM images of TEPs before heat activation and after the TEPs were submitted to temperatures above the Tg of the TEPs shell which shows the degradation and/or explosion of the TEPs.

means such as a battery or a laser or from an ultrasonic source or from gas or air or from white light. Depending on the microsphere used, the debonding temperature can be adjusted from 80°C to 220°C. The authors state that the formulations investigated were suitable especially for the automotive industry. Kim and co-workers [67, 68] used TEPs with a polyurethane adhesive and found that the debonding of the joint was possible with microwave treatment for 4 min. McCurdy et al. [69] used TEPs with three structural adhesives for the automotive industry in order to achieve joint dismantling. They found that matching a high performance TEP with a high performance adhesive is not sufficient to obtain an efficient joint

148  Structural Adhesive Joints dismantling as there are important implications for joint performance (i.e. joint durability). Nevertheless, the success of the concept of using TEPs with adhesives depends on the combination of the TEP and the adhesive system. Recently, Banea and co-workers [43, 44] investigated debonding of similar and multi-material adhesive joints bonded with two commercial structural adhesive systems used in the automotive industry (one polyurethane and the other epoxy). Single lap joints (SLJs) were fabricated and tested to assess the influence of TEP content on the lap-shear strength of adhesive joints. Further, the ability of the TEPs-modified joints to support temperature controlled debonding was evaluated. The evaluation of debonding was performed by exposing the SLJs’ adhesive layer to an electromagnetic field (the SLJs specimens were locally heated by an electromagnetic induction method as can be seen in Figure 5.7). This setup directly allowed determining the temperatures the TEPs-modified adhesives are subjected to using an infrared (IR) camera. When the power supply is switched on, the timer is started in order to measure the time to failure for each joint tested. The procedure followed for debonding evaluation is summarized in the scheme presented in Figure 5.8. If the joint did “fail” then the debonding parameters (i.e. temperature and time to failure) were measured. If the joint did “not fail”, the residual strength was measured. A comprehensive test programme was designed to identify suitable combinations of materials for an efficient joint dismantling [70–76]. It was found that the mechanical properties of the TEPs-modified adhesives depended on the TEP content, decreasing with increasing TEP content. Further, it was shown that debonding of adhesive joints bonded with heating station

fixture IR camera

SLJ specimen

weight

induction coil

Figure 5.7  Schematic of the test setup for debonding evaluation of TEPs-modified adhesives.

Debonding of Structural Adhesive Joints  149

Induction heating + TEPs

FAIL

NO FAIL

Measure temperature and time to fail

Measure residual strength

Figure 5.8  Scheme of debonding evaluation procedure.

commercially adhesive systems used in the automotive industry was possible [43, 44]. The weight fraction of TEPs used and the temperature were found to be the major factors in determining the debondability of the joints. The temperature response as a function of time is shown in Figure 5.9. For unmodified SLJs, debonding of the adhesive joints is possible only by induction heating at 230°C for SikaForce®7888 adhesive and 250°C for Betamate™2098 adhesive. This difference in the debonding temperatures can be related to the difference in the glass transition temperatures (Tg) of the adhesives. If only the induction heating method is used for debonding, the debonding temperature is the temperature at which the thermal decomposition of the adhesive occurs. However, the joint debonding requires high temperatures which can overheat the joint components and even damage or destroy them. Besides, toxic and irritant emission gases are produced due to chemical decomposition. Furthermore, by addition of TEPs the debonding temperature can be lowered by as much as 52% for the Betamate™2098 adhesive, and by approximately 40% for SikaForce®7888. Another important observation is that the less rigid adhesive (i.e Betamate™2098 with a Young’s modulus of 0.93 GPa) is easier to debond (lower debonding temperature and time) than the structural polyurethane adhesive (Young’s modulus of 2.5 GPa). This may be explained by the fact that TEPs are allowed to expand more within the cured Betamate™2098 epoxy adhesive than within the cured stiffer polyurethane adhesive as stiffer materials have a higher cross-link density and, consequently, lower free volume and reduced molecular mobility [43]. Relatively similar debonding temperatures were found for multimaterial/dissimilar joints debonding as for similar joints, but higher induction

150  Structural Adhesive Joints

Temperature [°C]

260

0% 5% 10%

230 200 170

15%

140

25% 20%

110 80

60

80

100

120 Time [s] (a)

140

160

Temperature [°C]

260

180

0%

230 200 170

10% 15% 20% 25%

140 110 80

30

60

90

5%

120 Time [s] (b)

150

180

210

Figure 5.9  Debonding evaluation tests showing the temperature response of TEPsmodified joints with different TEPs concentrations by weight percentage (0%, 5%, 10%, 15%, 20% and 25% wt. TEPs) as a function of time for SikaForce®7888 adhesive (a) and Betamate™2098 (b) [43].

heating power is generally necessary to disassemble multi-material adhesive joints [44]. Kishi and co-workers [77, 78] proposed the use of expandable graphite as an additive to provide higher-temperature bonded joint performance. Expandable graphite is a graphite intercalation compound. After purification of the graphite flakes, an acid, mostly sulfuric, nitric or acetic acid is intercalated into the crystal layers of the graphite. The mechanism of exfoliation of expandable graphite is complex. The temperature at which the graphite expands depends on the size of the particle (or flake) and the type of intercalated compound. Larger particles expand at lower temperatures. They used expandable graphite which begins to expand at 200°C with an epoxy adhesive to study debonding of CFRP and steel plates adhesive joints and found a good dismantlability at 250°C. In a different study, Pausan et al. [79] used an epoxy and a polyurethane adhesive, containing different amounts of expandable graphite to

Debonding of Structural Adhesive Joints  151 investigate the debondable property. The short- and long-term mechanical properties of lap shear and wedge cleavage joints were evaluated. They found that the addition of just a few percent of graphite was sufficient to provide a reliable debonding mechanism. Moreover, the usual adverse side effects on joint performance, associated with incorporating functional additives, were far more limited. One advantage of the debonding technologies presented here is that they are feasible with thermosetting high strength adhesives. However, the main disadvantage of this approach is that the additives may interfere with the initial adhesion, resulting in weak joints. There are also some concerns about accidental triggering and also about the filler types and gases involved.

5.4 Prospects Structural debondable adhesives through application of an external stimulus are highly relevant for various industries (e.g. automotive, aerospace, construction, packaging, sportswear, and semiconductor) for economical as well as environmental reasons as they can significantly contribute to the sustainable use of materials (repairing, reuse and recycling). There is a technological need for effective solutions that provide safe adhesion when the bonded structure are in service, while also permitting a simple and clean separation of bonded parts “on demand” without the need for additional complex process steps. Easily debondable adhesive joints would allow for flexible assembly, easier and cheaper repair, easy upgrading as new technology becomes available for simplified dismantlement and recycling. However, there are several challenges that need to be overcome for a more general use of this technology. The first one is to be able to incorporate debonding characteristics into an adhesive system without meaningfully altering its physical and mechanical characteristics, as it is important to ensure that the mechanical properties and adhesive strength after the incorporation of any type of debonding mechanism are not compromised. Second, there are some concerns about accidental or premature debonding. Finally, the durability of the adhesive joint up to the time of debonding should also be assured. Some of the techniques presented in this chapter are commercially available. However, there is a great amount of developing innovative technology that still needs to prove its efficiency. The selection of the right debonding technique will depend on the application needs and constraints. Further developments might lead to more general use of this technology in the industry.

152  Structural Adhesive Joints Incorporating recovery principles into the product design stage is important nowadays due to the increased pressure on costs and increasing demand for material recyclability. Controlled debonding may become a basic requirment for disassembly and recycling of materials in the future. Consequently, debondable adhesives can play an important role in how easily a structure can be recycled.

5.5 Summary This chapter has presented the recent developments in the use of debonding techniques for structural adhesive joints. The main techniques for debonding of structural joints currently being studied are based on electrically debondable adhesives, and on the incorporation of fillers in the adhesive. The preferred technique should be easy to apply, environmentally friendly, cost effective and should not leave any adhesive residue on the substrate. However, none of these techniques has been widely adopted because of the wide variety of adhesively bonded joint systems that exist. Also, there is a variety of applications, adhesives, substrate materials, and overall performance requirements. Moreover, newly developed debonding techniques and the focus of industry on new adhesive products that can debond on demand open up new exciting opportunities for development in this field and offer a promising potential in the future.

Acknowledgements M. D. Banea would like to acknowledge the support of the Brazilian Research Agencies CNPq and FAPERJ.

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156  Structural Adhesive Joints 49. M. Jonsson, O. Nordin, A. L. Kron, and E. Malmström, Thermally expandable microspheres with excellent expansion characteristics at high temperature, J. Appl. Polym. Sci. 117, 384-392 (2010). 50. M. Jonsson, O. Nordin, E. Malmström, and C. Hammer, Suspension polymerization of thermally expandable core/shell particles, Polymer 47, 3315-3324 (2006). 51. J. G. Kim, J. U. Ha, S. K. Jeoung, K. Lee, S. H. Baeck, and S. E. Shim, Halloysite nanotubes as a stabilizer: fabrication of thermally expandable microcapsules via Pickering suspension polymerization, Colloid Polym. Sci. 293, 3595-3602 (2015). 52. N. V. Lebedeva, S. N. Sanders, M. Ina, A. P. Zhushma, S. D. Olson, M. Rubinstein, and S. S. Sheiko, Multicore expandable microbubbles: Controlling density and expansion temperature, Polymer (United Kingdom) 90, 45-52 (2016). 53. M. J. Rheem, H. Jung, J. U. Ha, S. H. Baeck, and S. E. Shim, Suspension polymerization of thermally expandable microspheres using low-temperature initiators, Colloid Polym. Sci. 295, 171-180 (2017). 54. J. H. Bu, Y. Kim, J. U. Ha, and S. E. Shim, Suspension polymerization of thermally expandable microcapsules with core-shell structure using the SPG emulsification technique: Influence of crosslinking agents and stabilizers, Polymer (Korea) 39, 78-87 (2015). 55. Z. S. Hou and C. Y. Kan, Preparation and properties of thermoexpandable polymeric microspheres, Chinese Chemical Letters 25, 1279-1281 (2014). 56. Y. Kawaguchi, Y. Itamura, K. Onimura, and T. Oishi, Effects of the chemical structure on the heat resistance of thermoplastic expandable microspheres, J. Appl. Polym. Sci. 96, 1306-1312 (2005). 57. Expancel Home page. Available: http://www.akzonobel.com/expancel/, (2019). 58. L. Matsumoto Yushi-Seiyaku Co. Available: http://www.mtmtys.co.jp (2019). 59. C. Sato, Recycling and environmental aspects, in: Handbook of Adhesion Technology: Second Edition. L.F.M. da Silva, A. Öchsner and R.D. Adams (Eds.), Vol. 2, pp. 1751-1774, Springer International Publishing (2018). 60. T. Naganuma and Y. Kagawa, Effect of particle size on the optically transparent nano meter-order glass particle-dispersed epoxy matrix composites, Composites Sci. Technol. 62, 1187-1189 (2002). 61. M. Tomalino and G. Bianchini, Heat-expandable microspheres for car protection production, Prog. Organic Coatings 32, 17-24 (1997). 62. L. Andersson and L. Bergström, Gas-filled microspheres as an expandable sacrificial template for direct casting of complex-shaped macroporous ceramics, J. European Ceramic Soc. 28, 2815-2821 (2008). 63. M. Cao, Z. Sun, G. Bin, Q. Xia, L. Li, J. Li, and H. Li, Preparation of low temperature expandable microspheres and its application in foaming ink, Lecture Notes in Electrical Engineering 477, 697-707 (2018).

Debonding of Structural Adhesive Joints  157 64. S. Y. Chen, Z. C. Sun, L. H. Li, Y. H. Xiao, and Y. M. Yu, Preparation and characterization of conducting polymer-coated thermally expandable microspheres, Chinese Chemical Letters 28, 658-662 (2017). 65. H. Sakurai, Evaluation of adhesive properties of elastomeric adhesive. The development and utilization of the removable adhesive, Bulletin Shizuoka Industrial Technology Research Center 43, 11-16 (1998). 66. H. Ishikawa, K. Seto, S. Shimotuma, N. Kishi, and C. Sato, Bond strength and disbonding behavior of elastomer and emulsion-type dismantlable adhesives used for building materials, Intl J. Adhesion Adhesives 25, 193-199 (2005). 67. D. Kim, I. Chung, and G. Kim, Dismantlement studies of dismantlable polyurethane adhesive by controlling thermal property, J. Adhesion Sci. Technol 26, 2571-2589 (2012). 68. D. Kim, G. Kim, G. Song, and I. Chung, Dismantlment adhesion properties of dismantlable polyurethane-silica hybrid adhesive, Polymer (Korea) 40, 216-224 (2016). 69. R. H. McCurdy, A. R. Hutchinson, and P. H. Winfield, The mechanical performance of adhesive joints containing active disbonding agents, Intl J. Adhesion Adhesives 46, 100-113 (2013). 70. M. D. Banea, L. F. M. Da Silva, and R. D. S. G. Campilho, A study on microstructure characteristics of TEPs-modified adhesives, Microscopy Microanalysis 21, 7-8 (2015). 71. M. D. Banea, L. F. M. da Silva, R. J. C. Carbas, A. Q. Barbosa, S. de Barros, and G. Viana, Effect of water on the behaviour of adhesives modified with thermally expandable particles, Intl J. Adhesion Adhesives 84, 250-256 (2018). 72. M. D. Banea, L. F. M. da Silva, R. J. C. Carbas, and R. D. S. G. Campilho, Mechanical and thermal characterization of a structural polyurethane adhesive modified with thermally expandable particles, Intl J. Adhesion Adhesives 54, 191-199 (2014). 73. M. D. Banea, L. F. M. Da Silva, R. J. C. Carbas, and R. D. S. G. Campilho, Structural adhesives modified with thermally expandable particles, J. Adhesion 91, 823-840 (2015). 74. J. Bonaldo, M. D. Banea, R. J. C. Carbas, L. F. M. Da Silva, and S. De Barros, Functionally graded adhesive joints by using thermally expandable particles, J. Adhesion 95, 995-1014 (2019). 75. M. D. Banea, L. F. M. Da Silva, R. Carbas, and S. D. E. Barros, Effect of temperature and moisture on the tensile properties of a TEPS-modified adhesive, Materiale Plastice 55, 478-481 (2018). 76. M. D. Banea, L. F. M. Da Silva, R. J. C. Carbas, D. K. K. Cavalcanti, and L. F.  G. De Souza, The effect of environment and fatigue loading on the behaviour of TEPs-modified adhesives, J. Adhesion 96, 423-436, 2020.. 77. H. Kishi, J. Imade, Y. Inada, C. Sato, S. Matsuda, and A. Murakami, Dismantlable epoxy adhesives for recycling of structural materials, in Proceeding of ICCM International Conferences on Composite Materials, Kyoto, Japan (2007).

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Part 2 ANALYSIS AND TESTING

6 Fracture Mechanics-Based Design and Analysis of Structural Adhesive Joints Jinchen Ji and Quantian Luo* School of Mechanical and Mechatronic Engineering, University of Technology Sydney, Australia

Abstract

This chapter presents fracture mechanics based analysis and design of adhesively bonded structures. Common configurations and stress analysis characteristics of structural adhesive joints are introduced. Stress analysis and energy release rate based on a shear-lag model are firstly presented to show the importance of using fracture mechanics based design for structural adhesive joints. Modelling of adhesive joints and analytical stress analysis formulations are then derived to calculate energy release rates based on adhesive stresses; approaches to determine energy release rates based on the singular stress field and the beam theory are discussed. Finite element analysis based virtual crack closure technique and cohesive zone models to simulate progressive failure in adhesive joints are reviewed. Measurement of fracture toughness is discussed and determination of fracture parameters using state-of-the-art digital image correlation is presented. Keywords:  Adhesive joint, fracture mechanics, failure criteria, static stress strength, crack initiation and growth, digital image correlation

Abbreviations and Nomenclature Term Definition CLS Cracked lap shear CNT Carbon nanotube CZM Cohesive zone model DCB Double cantilever beam *Corresponding author: [email protected] K.L. Mittal and S. K. Panigrahi (eds.) Structural Adhesive Joints: Design, Analysis and Testing, (161–204) © 2020 Scrivener Publishing LLC

161

162  Structural Adhesive Joints DIC ENF ERR FBD FEA LEFM MMB SIF SLJ VCCT XFEM Ad c D E F G Gi Gic Gk GT k kσ kτ M Mk N Q V Vk t ta ti u w φ ϕ v σ τ ε

Digital image correlation End notched flexure Energy release rate Free-body diagram Finite element analysis Linear elastic fracture mechanics Mixed mode bending Stress intensity factor Single lap joint Virtual crack closure technique Extended finite element method Axial stiffness Half of the overlap length Bending stiffness Young’s modulus Tensile force Shear modulus Energy release rate for mode i (i = I, II, III) Critical energy release rate for mode i (i = I, II, III) Transverse shear stiffness Total energy release rate Edge moment factor Peel stiffness Shear stiffness Bending moment Edge moment Axial force Transverse shear force Shear force Edge shear force Cohesive traction stress Thickness of the adhesive Thickness of adherends i (i = 1, 2) Axial displacement Deflection Phase angle Rotational angle Poisson’s ratio Peel stress Shear stress Peel strain

Fracture Mechanics-Based Design  163 γ i, j, k, l

Shear strain Dummy subscripts

6.1 Introduction Adhesive joints have found wide applications in industry such as aerospace, electrical, automotive, marine, oil and construction industries [1–4]. There has been an increasing use of adhesive bonding technology in industry due to its superiority over conventional joining technologies in many aspects such as high specific strength, flexibility, damage tolerance and fatigue resistance. This technology can effectively join machine and structural parts with similar or dissimilar materials. Figure 6.1 shows common configurations of adhesive joints. Adhesive bonding technology is an ideal technique in many applications as it is easy to use and has high bonding strength, e.g., composite patch repairs for aircraft structures and rehabilitation of oil and gas pipelines [5–10]. To enhance or retrofit concrete beams widely used in civil Outer Adherend Overlap Adhesive Adherends (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

Figure 6.1  Configurations of adhesive joints (a) single lap joint, (b) double lap joint, (c) tapered single lap joint, (d) tapered double lap joint, (e) butt joint, (f) scarf joint, (g) stepped single lap joint, (h) double stepped double lap joint, (i) T-joint, (j) L-joint.

164  Structural Adhesive Joints engineering, fiber reinforced polymer plates are often adhesively bonded on concrete beams [11–13]. In intelligent structures and energy harvesting systems, functional materials such as piezoelectric ceramics are adhesively embedded or bonded to host structures [14–17]. These applications are indicated in Figure 6.2.

6.1.1 Analysis Methods of Adhesive Joints As illustrated in Figure 6.1 and Figure 6.2, a lap joint represents a typical configuration of adhesive joints and thus its analysis plays an important role in adhesively bonded structures. When adhesive joints are used as load bearing structures, in general, an adhesive layer has thickness of a fraction of millimeter, e.g., 0.1~0.3 mm for aircraft, automotive and civil structures, and elastic moduli are much less than those of adherends, e.g., Young’s moduli are 4.44 GPa and 3.05 GPa for adhesive materials Redux 326 and AV 119, respectively [1–4]. In practical applications, adhesive joints can be subjected to static, impact and cyclic loadings. Structural failure can occur in the adhesive and adherends or at interface. Fracture propagation path may be in the adhesive, along the interface or vary in the adhesive and interface. Therefore, structural analysis and design for adhesive joints are very complicated. As shown in Figure 6.1, a single lap joint (SLJ) is the simplest joint in geometry. It can easily join two components with different materials to efficiently transfer load from one component to the other. This simple joint configuration has been widely used in practice and is used as a standard specimen to calibrate mechanical properties of adhesive joints in test

(b)

(a) Concrete beam

FRP plate (c)

PZT

(d)

Figure 6.2  Typical applications of adhesive bonding technology (a) single side repairs or strap joint, (b) double side repairs or strap joint, (c) FRP plated concrete beam, (d) piezoelectric (PZT) smart plate.

Fracture Mechanics-Based Design  165 standards ASTM D1002 ASTM D3163, ASTM D5868 [3]. As an SLJ is an important joint configuration, study on its stress state, fracture behavior and impact performance has attracted extensive interest in research community and industry. Great efforts have been made to obtain simple closed-form solutions for the SLJ as they offer fundamental features for structural adhesive joints and are quite useful in preliminary design stages [18–37]. As shown in Figure 6.2, stress analysis of structural adhesive joints is normally a three-dimensional (3D) problem and thus analytical solutions can be hardly derived. In practice, the adhesive layer is very thin as compared to adherends and its Young’s modulus is much less than that of adherends. In this case, one-dimensional (1D) or two-dimensional (2D) mechanics model can be approximately established and theoretical analysis can be conducted [18–24, 26, 29, 30, 33–37]. Volkersen [18] modelled adherends as rods and the adhesive as a continuous shear spring. In this shear-lag model, there is shear stress only in the adhesive and the shear stress is constant through the adhesive thickness. Goland and Reissner [19] modelled adherends as beams and the adhesive as a continuous normal and shear spring. In this beam-­adhesive model, shear and peel (normal) stresses are constants through the thickness. When the adhesive is relatively thick, 1D models for stress variations through the adhesive and 2D elastic medium models [21, 22, 25, 27, 28, 32] have been proposed to enhance the beam-adhesive model. The beam-adhesive model has been widely adopted for analysis and design of structural adhesive joints and it is also used to find energy release rates in fracture mechanics based analysis and design. A distinctive feature of analysis for the SLJ in tension is its eccentric loading path resulting in geometric nonlinearity, which poses a great challenge to derive analytical solutions [8–10, 19, 20, 29, 30, 33, 34, 38–41]. Geometric nonlinearity for a balanced SLJ was considered in [19] but the overlap was treated as a homogeneous beam with neglecting adhesive deformations for load update. Hart-Smith [20] considered individual beams of the overlap for balanced and unbalanced SLJs but the geometric nonlinearity of the overlap was ignored. Oplinger [38] modified Hart-Smith’s formulation by considering large deflection effects of the overlap but neglected peel effects on load update. Luo and Tong [36, 42] presented ­geometricallynonlinear analysis for composite SLJs. In this geometrically-nonlinear model, effects of geometric nonlinearities of the overlap and outer adherends, shear and peel deformations of the adhesive and transverse shear stiffness of adherends were taken into account and the analytical solutions were approximately derived. Yousefsani and Tahani [34] further modelled

166  Structural Adhesive Joints composite adherends as layerwise beams in geometrically-nonlinear analysis of SLJs and Jiang et al. [35, 41] considered unbalanced SLJs with geometric nonlinearity. Since stress analysis, fracture and impact behaviors of adhesive joints are quite complicated, analytical solutions are only available for simple joint configurations and simplified mechanics models. Numerical approaches, particularly finite element analysis (FEA), have been widely used in analysis and design of structural adhesive joints. In practice, analytical and numerical results on adhesive joints must be verified by experiment. Material properties of the adhesive such as elastic constants, yielding and ultimate stresses, critical energy release rates (ERR), finite life and fatigue strengths can be determined only by experiment. As the adhesive layer is very thin, it is difficult to directly measure adhesive stress, stress concentration, energy release rates and dynamic responses in conventional mechanical testing. With the advance of testing technology such as digital image correlation (DIC), experimental study on structural adhesive joints using DIC has recently attracted much attention as detailed displacement and strain fields of the adhesive can be measured using this technique.

6.1.2 Design Philosophy of Adhesive Joints and Fracture Mechanics Based Design Depending on loading types and service environments, design philosophy of structural adhesive joints can be classified as designs based on static strength, fracture mechanics, finite life, fatigue strength, impact and residual strength. Failure of structural adhesive joints may occur in adherends, adhesive or at interface. For the composite adherend, its failure may be matrix cracking, fiber debonding from matrix, fiber breaking, and adhesive debonding from adherends. In general, most of joint failures occur in the adhesive and thus this chapter will be focused on the adhesive failure and interface debonding or adhesive debonding from adherends; also fracture mechanics based analysis and design for the structural adhesive joints under static loading are mainly discussed in this chapter. This chapter is organized as follows. In Section 6.2, analytical stress analysis, energy release rate formulation, and cohesive damage zone models for structural adhesive joints under static loading are presented. Section 6.3 reviews finite element analysis approaches for energy release rate computations and simulation of progressive failure. In Section 6.4, experimental approaches to determine fracture toughness of adhesive joints are

Fracture Mechanics-Based Design  167 elaborated and experimental investigation into structural adhesive joints using DIC is discussed. Further work is discussed in Section 6.5 and summary is in Section 6.6.

6.2 Stress Analysis and Fracture Modelling of Structural Adhesive Joints In fracture mechanics based design of structural adhesive joints, energy release rates and their critical values or fracture toughness must be determined. Fracture toughness of adhesive joints can be determined by experiment only. Energy release rates may be found by theoretical analysis, numerical computation such as finite element analysis (FEA) and experimental study. In this section, analytical modelling and formulation are presented. Design criterion based on linear elastic fracture mechanics (LEFM) may be written as:



GI GII GIII + + ≤1 GIc GIIc GIIIc

(6.1a)

where Gi and Gic (i = I, II and III) are the energy release rate (ERR) and the critical ERR for mode i. The LEFM criterion has been widely applied for design of adhesive joints. Since many lap joints can be treated as the 2D problems, design criteria of structural adhesive joints with mixed mode I and II fracture can be expressed as [1–3, 43–45]:





GI GII + ≤1 GIc GIIc GT ≤ Gc at ϕ = arctan

(6.1b)

GII GI

(6.1c)

where GT is the total ERR; Gc is the critical ERR at phase angle φ; GT = GI + GII. As crack initiation normally occurs at the adhesive edge, the total ERR and the phase angle may be calculated based on the adhesive stresses:

168  Structural Adhesive Joints



∆a   G = lim 1 σ(t d ε) = tδ σ a edge  I ∆a→0 ∆a 2 Ea  0  ∆a  1 t τ(ta d γ ) = δ τ edge  GII = ∆lim a→0 ∆a 2Ga  0

∫

(

)

∫

(

)

2

2

=

1 σ edge 2kσ

(

1 = τ edge 2kτ

(

)

)

2

2

(6.2)

where ∆a is the virtual crack length; ta is the adhesive thickness; σ and ε are peel stress and strain; τ and γ are shear stress and strain; Ea and Ga are Young’s and shear moduli of the adhesive material, kσ and kτ denote peel and shear stiffnesses; σedge and τedge denote δ peel and shear stresses at the edge.

6.2.1 Stress Analysis and Static Strength of Structural Adhesive Joints Eq. (6.2) reveals important relationships between stresses and energy release rates of the adhesive joints. When Eq. (6.2) is used to obtain energy release rates, shear and peel stresses must be found first.

6.2.1.1 Shear-Lag Model and Shear Stress Volkersen [18] proposed a shear-lag model for an adhesive joint as in Figure 6.3. The equilibrium equations for free-body diagrams (FBDs) in Figure 6.3(a) are:



dN1 dN 2 + τ = 0; −τ = 0 dx dx

(6.3)

where Ni (i=1, 2) are the axial forces of adherends 1 and 2. Constitutive equations for the adhesive and adherends are:





τ=

Ga (u2 − u1 ) ta

N i = Adi

(6.4)

dui i = 1, 2 dx

(

)

(6.5)

Fracture Mechanics-Based Design  169 c

c

Adherend 1 F

x F

Adhesive z

20

Adherend 2 (a)

15

N1+dN1 τn

N1 τ

10

0.1 mm

0.2 mm

5

τ N2

0

N2+dN2

–1

–0.5

dx

0 ξ (c)

0.5

1

(b)

Figure 6.3  Shear-lag model (a) single lap joint in tension, (b) free-body diagrams of the shear-lag model, (c) adhesive shear stress distribution along the overlap.

in which ui (i=1, 2) denote the axial displacements of adherends 1 and 2. Substituting Eqs. (6.4) and (6.5) into Eq. (6.3) yields the governing differential equation for the adhesive shear stress and the solution is given by [3]:

 β F   cosh βv x (1 − ψ )sinh βv x  τ = v  −   2   sinh βv c (1 + ψ ) cosh h βv c 

where

βv =

(1 + ψ )G

a

ta Ad1

and ψ =

Ad1 Ad 2



(6.6)

where Adi (i = 1, 2) are the extension stiffnesses of adherends 1 and 2; F is the applied tensile force per unit width and (2c) is the joint length. A unit width and plane stress state have been assumed in the above formulations and will be used subsequently. Shear stress in Eq. (6.6) can be written in a non-dimensional form as:



τn =

τ τ avg

 cosh(βv c )ξ (1 − ψ )sinh(βv c )ξ  = (βv c )  −   sinh(βv c ) (1+ ψ )cosh(βv c ) 

(6.7)

170  Structural Adhesive Joints where τavg = F/(2c) is the average shear stress and = x/c. Non-dimensional shear stresses are plotted in Figure 6.3(b) for the lap joint with the following material constants and geometrical sizes: E1 = E2 = 70 GPa, Ea = 3 GPa, νa = 0.36, c = 30 mm, t2 = 2t1 = 4 mm, ta = 0.1 and 0.2 mm. Figure 6.3(c) shows that (1) peak shear stress occurs at the adhesive edge; (2) the peak stress is much larger than the average one; and (3) the peak shear stress for the thinner adhesive (0.1 mm) is significantly larger than that for the thicker adhesive (0.2 mm). The numerical results in Figure 6.3(c) correlate fairly well with FEA results [46, 47]. If shear stress criterion τmax ≤[τ] is used to design adhesive joints, the thicker the adhesive, the smaller the shear stress and the larger the failure load. However, experimental results show that failure load decreases with an increase of the adhesive thickness for the relatively thick adhesive [20, 22, 37, 48–51]. For a relatively long overlap, the maximum shear stress can be approximately written as:



 ψβ F  2cψβv   F   τ max = v =  1 + ψ  1 + ψ   2c     τ = βv F =  2cβv   F   max 1 + ψ  1 + ψ   2c  

ψ ≥1

(6.8a)

ψ ≤1

The non-dimensional maximum shear stress and ERR for mode II can be derived as:





 τ 2cψβv  τ n max = max = τ avg 1 + ψ   τ max 2cβv  τ = n max =  τ avg 1 + ψ  2     G = Ga G =  ta   2cψβv   II    2  II 0  τ avg  2c   1 + ψ  c  2  Ga    ta   2cβv   GII 0 =  2  GII =  2c   1 + ψ   τ avg c  

ψ ≥1

(6.8b)

ψ ≤1

ψ ≥1 (6.8c) ψ ≤1

Fracture Mechanics-Based Design  171 When ta = 0.1 and 0.2 mm and the data from Figure 6.3(c) are used, τnmax = 19.45, 13.75, and GII0 = 0.63, 0.63, respectively. It can be seen that τnmax decreases with an increase of the adhesive thickness; GII0 is approximately equal for ta = 0.1 and 0.2 mm, which agrees with test results for the thin adhesive [20, 22, 37, 48–51]. This indicates the importance of fracture mechanics based design for structural adhesive joints. In general, structural adhesive joints exhibit mixed fracture modes as there exist both shear and peel stresses in the adhesive.

6.2.1.2 Beam-Adhesive Model, Shear and Peel Stresses Due to transverse displacement of SLJs, there exists peel stress in the adhesive. Goland and Reissner [19] proposed a beam-adhesive model to account for shear and peel stresses in the adhesive. In this model, the adhesive and adherends are described by using a continuous spring with shear and peel stiffnesses and the Euler beam.

6.2.1.2.1 Shear and Peel Stresses in the Linear Overlap

In stress analysis for the overlap in [19], geometrical nonlinearity was not considered as shown in Figure 6.4(a). The equilibrium equations for the FBDs of Figure 6.4(a) are:



 dN dQ dM1 t1 1 + τ = 0; 1 + σ = 0; + τ − Q1 = 0   dx dx dx 2   dN 2 − τ = 0; dQ2 + σ = 0; dM 2 + t1 τ − Q = 0 2  dx dx dx 2



(6.9)

where the balanced lap joint is considered; t1 is the thickness of adherends 1 and 2; σ is the peel stress. The constitutive equations for the adhesive and adherends are [19]:

τ=



Ga  t1  dw1 dw 2   Ea w 2 − w1 (6.10) +  u2 − u1 +  ; σ =  2  dx ta  dx   ta

(

)

N i = Ad1

(

dui dw ; Mi = − Di i  (i =1, 2) dx dx

)

(6.11)

172  Structural Adhesive Joints N1

Q1+dQ1

Q1

Q1 Q1+dQ1 N1+dN1

N1+dN1

M1

M1+dM1

N1 M1

M1+dM1

τ

τ

σ

σ

τ

τ τ σ

σ

N2

τ

Q2

Q2+dQ2 N2+dN2 M2+dM2

M2

Q2

τ Q2+dQ2

N2 N2+dN2 M2+dM2

M2

dx

dx (a)

(b)

Figure 6.4  Stress analysis of the beam-adhesive model (a) free-body diagrams in linear analysis, (b) free-body diagrams in geometrically-nonlinear analysis.

where w denotes the beam deflection; D is the bending stiffness and D2 = D1 for the balanced lap joint. By substituting Eqs. (6.10) and (6.11) into Eq. (6.9), governing equations in terms of shear and peel stresses can be derived as:

d 3τ d 4σ 2 dτ − β = 0 ; + 4βσ4 σ = 0 c dx dx 3 dx 4



(6.12)

in which



βc2 = α a βτ2 ; βτ =

8Ga 2 2 Ea 1 4A t2 ; βσ = ×4 ; α a = 1 + α k ; α k = d1 1 Ad1ta 2 D1ta 4 D1

(

)



(6.13)

where αa and αk reflect the influences of composite lay-ups on the adhesive stresses; αa = 1 and αk = 3 for the isotropic adherends. Eq. (6.13) is an extension of the formulation in [19] for the adherends of symmetric lay-up laminates.

Fracture Mechanics-Based Design  173 Analytical solutions of Eq. (6.12) are:

(

)

(

)

 β Ft + 2α k M k cosh βc x α k Ft1 − 2 M k  τ= c 1 + 8α at1 sinh βc c 8α at1c     σ = βσ 1 sinh βσ x sin βσ x + Bσ 4 cosh βσ x cos βσ x 



(6.14)

in which

(

)

(

)

    B = 2βσ  M k βσ sinh βσ c cos βσ c + cosh βσ c sin βσ c + Vk sinh βσ c sin βσ c  σ 1  sinh 2βσ c + sin 2βσ c  2βσ  M k βσ sinh βσ cos βσ c − cosh βσ c sin βσ c + Vk cosh βσ c cos βσ c    Bσ 4 = sinh 2βσ c + sin 2βσ c 



(6.15)

where Mk and Vk are the edge moment and shear force as shown in Figure 6.5(b); F is the tensile force of the SLJ. The peak stresses occur at the overlap ends x = c:



τ max =

(

)

(

);σ

Ft1 βc c + α k + 2α k M k βc c − 1 8α at1c

max

 V  = βσ2  M k + k  βσ   (6.16)

By substituting Eq. (6.16) into (6.2), energy release rates are obtained as listed in Table 6.1.

6.2.1.2.2 Shear and Peel Stresses for the Geometrically-Nonlinear Overlap

Luo and Tong [29, 36] considered the geometric nonlinearity of the overlap for SLJs as in Figure 6.4(b). The equilibrium equations for FBDs of the balanced SLJ shown in Figure 6.4(b) are:

174  Structural Adhesive Joints l

c

c Left outer adherend F

Overlap I

O1

z (a)

O

O2 Right outer adherend Tk

Vk

x3

Mk

Mk

F

F

II

l

z3

x

B

A

Vk

Tk

x

z (b)

I

F

II (c)

Figure 6.5  Beam-adhesive model for single lap joint in tension (a) simply supported SLJ, (b) deformation of the simply supported SLJ, (c) clamped-clamped SLJ.

 dN dQ dM1 t1 1 + τ = 0; 1 + σ + τφ1 = 0; + τ − Q1 = − N1φ1   dx dx dx 2   dN 2 − τ = 0; dQ2 − σ − τφ = 0; dM 2 + t1 τ − Q = − N φ 2 2 2 2  dx dx dx 2

(6.17)

where ϕ is the rotational angle. Constitutive equations for composite adherends based on the 1st order shear deformation theory are:

 2    N = A  dui + 1  dui  + 1 φ 2  − B dφi i di i i    dx  dx 2  dx  2     du 1  du  2 1   dφ Mi = Bi  i +   + φi2  − Di i dx   dx 2  dx  2     dwi   Qi = Gki  dx − φi  

(i = 1, 2)

(6.18)

Adhesive-beam (Nonlinear overlap)   β+ + β+    M k +  s1 2 s 2  Vk   2βσ   

2

2

 Vk   M k + β  (Euler beam) σ  

(Timoshenko beam Δ > 0)

βσ4 2kσ

βσ4 2kσ

–

Shear-lag

Adhesive-beam (Linear overlap)

GI

Model

2

 [2α k M k + Ft1 (1 − rk )]βa1c coth βa1c    8α at1c 1    2kτ  α k ( Ft1 − 2 M k )βa 2c coth βa 2c +  8α at1c  

1  Ft1 (βcc + α k ) + 2α k M k (βcc − 1)   2kτ  8α at1c 

F2 4 Ad1

GII

Table 6.1  Energy release rates of the balanced SLJs calculated using edge stresses.

2

Fracture Mechanics-Based Design  175

176  Structural Adhesive Joints where Gk is the transverse shear stiffness; B is the extension-bending coupling stiffness and B = 0 for the symmetric lay-up laminate. By substituting Eqs. (6.10) and (6.18) into Eq. (6.17), considering the symmetric lay-ups and neglecting some nonlinear terms with less influence on stress, the governing equations in terms of displacements can be approximately derived as [29, 36]:



 d 3u β 2  du t d 2w  a a  − τ a+ 1 =0 3 4  dx 2 dx 2   dx  4 2 2 2 2  d wa − α k βτ  dua + t1 d wa  − β k d wa = 0  dx 4 2t1  dx 2 dx 2  2 dx 2 

2 d 2us d 4w s 2 d ws = 0 ; − 4 β + 4 βn4σ w s = 0 ng 2 4 2 dx dx dx



(6.19)

(6.20)

where

 2 β k2  4  4 β k2 β g2  1 2 Ea β =  β g +  ; βnσ =  βσ + (6.21)  ; βg = × 8 2  2 Gk1ta   2 ng





 2u = u + u ; s 2 1  2ua = u2 − u1 ;

2w s = w 2 − w1 ;

2φs = φ2 − φ1

2wa = w 2 + w1 ;

2φa = φ2 + φ1

(6.22)

The closed-form solutions of Eqs. (6.19) and (6.20) can be derived in terms of ua, wa, us and ws and then shear and peel stresses are obtained by Eq. (6.10). The peak stresses can be approximately expressed as [36]:

(

)

(

)

 2α k M k + Ft1 1 − rk  βa1c coth βa1c α k Ft1 − 2 M k βa 2c coth βa 2c  + τ max =  (6.23) 8 α t c 8α at1c a 1

Fracture Mechanics-Based Design  177



   −   βσ2  M k + β s1 Vk  < 0  β 2    σ  σ max =   β s+1 + β s+2    2  βσ  M k +  2β 2  Vk  > 0   σ 

(6.24)

where  −  β = β σ +β   +  β = β + β −β σ    β  = β  

β− = β σ − β




β − β −β σ



β =

= β − β σ

(6.25)

Generally, 0 for the composite adherends or for the very thin adhesive. When ta → 0, shear and peel stresses approach infinity, leading to stress singularity. The ERRs should be used to study this interface fracture problem. The ERRs for this nonlinear overlap of SLJs can be approximately derived by substituting Eqs. (6.23) and (6.24) into Eq. (6.2), as shown in Table 6.1.

6.2.1.3 Load Update of a Single Lap Joint in Tension It is worth noting that edge moment Mk and shear force Vk vary with tensile load of SLJs. They should be determined by considering large deflection of the SLJ and updated with the load increase, as shown in Figure 6.5(b). Goland and Reissner [19] considered stress analysis of the overlap and load update separately. In load update, the overlap was treated as an entire beam. The bending moment and the shear force of the simply supported SLJ shown in Figure 6.5(a) can be expressed as [19]:



Mk = k

(t + t ) F ; V a

1

2

k

=

( )

dM 3 l dx

3

(6.26)

178  Structural Adhesive Joints in which



k=

1 1 or k = when cothβkl ≈1 1 + βk / βo tanh βoc coth βkl 1 + βk / βo tanh βoc

(

)

(

)







(6.27)

where k is referred to as the bending moment factor or edge moment factor; βo = F / Do in which F is the tensile force and Do is the bending stiffness of the overlap. It should be noted that the adhesive thickness was ignored in [19] but it was given in Eq. (6.26) for consistence with other formulations. Hart-Smith [20] noticed inconsistency in the load update derived in [19] and then presented coupled formulations for stress analysis and load update. In load update, he modelled adherends of the overlap as individual beams and derived the edge moment factor for the SLJ in Figure 6.5(a) as [20]: k=



1

( )

2

1 + βkc coth βkl + βkc / 6

or k =

1

( )

2

1 + βkc + βkc / 6

when coth βkl ≈1

(6.28)





In Eq. (6.28), the overlap large deflection was neglected. Oplinger [38] considered the large defection of the overlap and conducted coupled formulations for load update but peel effects were neglected. Luo and Tong [29, 36, 52] considered the geometric nonlinearity of the overlap as in Figure 6.4(b) and derived coupled formulations for SLJs and extended to taking into account composite adherends and clampedclamped SLJs. The edge moment factors for two boundary conditions in Figure 6.5(a) and 6.5(c) were respectively derived as:

( )

1 + βkc k=

2

βa1cf ( βa 2c ) − 1

(

) cf ( β c ) + α

8α a βa1c 1 + ta / t1

 βa1 a2 1 + β k c co oth β k l + β k c α sM + 8α a βa1c 

( )

( )

2

k

 (6.29)  

Fracture Mechanics-Based Design  179

1+ k=

2 βa1cf ( βa 2c ) − 1 βkc + ( βkc ) sinh β k l 8α a βa1c (1 + ta / t1 )

(

)

 βa1cf βa 2c + α k  1 + β k c coth β k l + β k c α sM +  8α a βa1c  

( )

( )

2

(6.30)

where

(

)

f β a 2c =





βa 2c coth βa 2c − 1

(β c) a2

2

;α sM =

βs−1 βs+1 + βs+2  < 0 or α = > 0 sM 2 βn2σ c 4βn2σ c

(

)

(

)

(6.31)



The geometrically-nonlinear FEA showed that the edge moment factors calculated by Eqs. (6.29) and (6.30) correlated very well with those predicted by the geometrically nonlinear FEA [29, 36, 41, 52–54]. In the fully-coupled formulations considering geometric nonlinearity in [29, 36, 52], the balanced SLJ was considered. Jiang and coworker [35, 41] extended the formulations in [29, 36] to the unbalanced SLJ and the results also correlated well with those computed by the geometrically-nonlinear FEA. When the edge moment factor is determined, the edge moment can be updated and then shear and peel stresses are found. When the maximum shear and peel stresses are used in design of structural adhesive joints, design criteria can be defined as [55, 56]:



Maximum stress criterion:  σmax ≤ [σ] and τmax ≤ [τ] (6.32a)



Von Mises criterion:  (σvon)max ≤ [σ]



σ  τ  Tsai-Wu criterion:   max  +  max  ≤ 1  [σ]   [τ] 

2

(6.32b)

2

(6.32c)

where [σ] and [τ] are the allowable peel and shear stresses. Section 6.2.1.1 indicated that the shear stress criterion was in conflict with many experimental results. When Eq. (6.32a), (6.32b) or (6.32c) is employed, the same

180  Structural Adhesive Joints issue is raised, i.e, the thicker adhesive offers lower edge stresses leading to higher strength, which is also not supported by the experimental data [50, 51, 57–59]. Therefore, design criteria of structural adhesive joints need to be further investigated and fracture mechanics based design has attracted increasingly interest.

6.2.2 Analytical Approaches of Linear Elastic Fracture Mechanics In fracture mechanics based design criterion stated in Eq. (6.1), energy release rates (EERs) of the adhesive joint may be found by analytical, numerical or experimental approaches and the critical energy release rate or fracture toughness can be determined by experiment combined with analytical and/or numerical analysis. Therefore, calculation of ERRs plays a critical role in fracture mechanics based design. In this section, analytical approaches to determine ERRs are discussed and numerical methods will be presented in Section 6.3.

6.2.2.1 An Approach Based on Adhesive Stresses for the Joint Under General Loading Table 6.1 lists some ERR formulas of the SLJ subjected to tensile load. In this subsection, ERRs of adhesive joints under general loading are presented on the basis of adhesive stresses.

6.2.2.1.1 ERRs of the Joint with Symmetric Adherends Under General Loading

An adhesive joint subjected to general loading is shown in Figure 6.6. By referring to the FBDs in Figure 6.4(a), the equilibrium equations for the joint with identical adherends, referred to as a symmetric joint, have been derived in Eq. (6.9). It is noted that the linear overlap is considered here as adhesive stresses evaluated by the linear overlap and the geometrically-nonlinear overlap are almost the same for the prescribed edge forces of the overlap. Substituting the constitutive equations for the adhesive and adherends given in Eqs. (6.10) and (6.18) into Eq. (6.9) yields [60]:



d 3τ dτ − βc2 =0 3 dx dx

(6.33)

Fracture Mechanics-Based Design  181 2

M1 N1 Q1 M2

1

Adherend 1 Mo

x Adhesive 1 Failure initiation edge

1

No

N2

Qo Q2

2

Adherend 2 2

z

Figure 6.6  J-integral of structural adhesive joints, route 1: along the adhesive boundary, route 2: along the beam boundary.



2 d 4σ 2d σ − 4 β + 4 βσ2 σ = 0 g 4 2 dx dx

(6.34)

Solution to Eq. (6.33) can be expressed as:



τ = A1e βc x + A2e − βc x + A3

(6.35)

where Ai (i = 1, 2, 3) are the integration constants. The solution of Eq. (6.34) depends on:



(

)

= β g4 − βσ4 = 1 − Csta β g4 where,Cs =

2Gk21 Ea D1

(6.36)

When the adhesive is sufficiently thin leading to (1 – Csta) > 0, >0; in this case, solution to Eq. (6.34) is:



+

+

+

+

σ = B1e βs1x + B2e − βs1x + B3e βs 2 x + B4e − βs 2 x

(6.37)

β s+1 = 2 β g2 + β g4 − βσ4 ; β s+2 = 2 β g2 − β g4 − βσ4

(6.38)

where



182  Structural Adhesive Joints in which βi (i = 1, 2, 3, 4) are the integration constants to be determined by the boundary conditions. The boundary conditions of the adhesive joint shown in Figure 6.6 are:

x →∞: τ = 0; σ = 0





x = 0:

dτ d 2σ d 3σ dσ = Hn ; 2 − 4 β g2σ = Hm ; 3 − 4 β g2 = Hq dx dx dx dx

(6.39)

(6.40)

where,

  1  t  Hn = kτ  ( N 2 − N1 ) − 1 ( M 2 + M1 ) 2D1   Ad1   k  Hm = − σ ( M 2 − M1 ) D1   kσ  H q = − (Q2 − Q1 ) D1 



(6.41)

In Eq. (6.41), Ni, Qi and Mi (i = 1, 2) are the force components of the cross section at the crack-tip as shown in Figure 6.6. By substituting Eqs. (6.35) and (6.37) into Eqs. (6.39) and (6.40), the integration constants can be determined. The shear and peel stresses are derived as: Hm β s+2 + H q Hm βs+1 + H q + H n − βc x − βs+1x e ;σ = + e + e − βs 2 x + +2 2 + + +2 2 βc (βs1 − βs 2 )(βs 2 − 4 β g ) (βs 2 − βs1 )(βs1 − 4 β g )



τ =−

(6.42) The maximum shear and peel stresses occur at x = 0:

 H  τ max = τ (0) = − n βc   Hm β s+2 + H q Hm β s+1 + H q  σ = σ (0) = +  max (β s+2 − β s+1 )(β s+12 − 4 β g2 ) (β s+1 − β s+2 )(β s+22 − 4 β g2 ) 

(6.43)

Fracture Mechanics-Based Design  183 By substituting Eq. (6.43) into Eq. (6.2). The ERRs are obtained as: 2   D1 1 2 1    GI = 2kσ σ max = 4D1 ( M 2 − M1 ) + Gk1 ks (Q2 − Q1 )   (6.44)  2   1 2 1  2 τ max = ( N 2 − N1 ) − α k ( M 2 + M1 )  GII =  2kτ 16 Ad1  t1  

where

ks =



2 1 + 1 − Cst a + 1 − 1 − Cst a   2 

(6.45)

Eq. (6.44) can be applied to interface fracture and parameter ks reflects interface flexibility:

 k =1  s   ks = 2

When ta

ta → 0 ta → 1/ Cs



(6.46)

0, it becomes an interface fracture problem.

6.2.2.1.2 ERRs of the Adhesive Joint with Asymmetric Adherends

When adherends 1 and 2 are not identical, referring to as an asymmetric joint, shear and peel stresses of the adhesive joint under general loading can be derived [45]. The ERRs for interface fracture are [60, 61]:  k1d  GI = ×  2 k1d k4 d − k22d  2     k5d  k22d   Q2 Q1    k2d  N 2 N1  1  t 2 M 2 t1 M1    M 2 M1  − − + − 1− − − −           D1    D2 D1  k4 d  k1d k4 d   D2 D1    k1d  Ad 2 Ad1  2  D2    2     G = 1  N 2 − N1  − 1  t 2 M 2 + t1 M1    II 2k1d  Ad 2 Ad1  2  D2 D1    

(

)

(6.47)

184  Structural Adhesive Joints where

4α 4α t t 1 1 1 1 k1d = a1 + a 2 ; k2d = 1 − 2 ; k4 d = + ; k5d = + 2D1 2D2 D1 D2 G k1 G k 2 Ad1 Ad 2 (6.48)

Numerical results predicted by Eq. (6.47) agree well with those predicted by the formulations in [62–68].

6.2.2.2 Methods Based on a Beam Theory and a Singular Field As shown in Eq. (6.1a) or (6.1b), both the total ERR and the phase angle or mode mixity are required to determine crack initiation in the adhesive joint based on the LEFM criterion. They can be found using the adhesive stresses as discussed in Subsection 6.2.2.1. In addition, other analytical approaches can also be used to find the total ERR and the phase angle for interface fracture such as: (a) the global method based on the beam theory [63, 65, 67, 69], (b) the local method based on the stress singular field [70–73], and (c) the global-local method [67, 74, 75]. These methods are developed for interface fracture and may also be used for structural adhesive joints when the adhesive is very thin [62–65]. The total ERR and the phase angle for a symmetric joint predicted by these methods are almost the same. For the double cantilever beam with initial crack length a subjected to transverse force P, some results are listed in Table 6.2 for comparison. In Table 6.2, the formulations given in [76, 77] are derived on the basis of the local method considering shear force effects; the formulation in [66] is based on the global method; by using the global-local method, the same formulation as that in Eq. (6.43) for ks = 1 can be obtained. For the asymmetric joint, the total ERRs predicted by different methods are almost the same but the phase angles have discrepancies. As compared with virtual crack closure technique (VCCT) using the FEA, the mode mixity predicted by the local method correlates better with that by FEA, particularly for isotropic materials. However, experimental results show that the global method agrees well with the test data in many cases [78–80]. It has been an open issue as to which mode partition approach is most suitable for interface crack in adhesive joints [80, 81]. Furthermore, experimental results also show that the mode mixity of adhesive joints is fracture toughness dependent [80–82].

Fracture Mechanics-Based Design  185 Table 6.2  Normalized energy release rate GIo of a symmetrical double cantilever beam. Literature

Bao et al. [76]

Li et al. [77]

Szekrenyes and Uj [66]

Luo and Tong [60] for ks = 1

Luo and Tong [60] for ks = 2

 GD  GIo  GIo = I2 21   Pa    t1   1 + 0.697     a 

2

  t1   1 + 0.674     a 

2

2  t   t  1 + 1.066  1  + 0.57  1    a   a  

  t1   1 + 0.535     a 

2

  t1   1 + 0.757     a 

2

2

6.2.3 Fracture Prediction Using Cohesive Zone Model The LEFM is suitable for brittle materials and it may not be applicable to ductile adhesive materials due to their plastic deformation. Crocombe [49] proposed global yielding as a failure criterion for adhesive joints to take into account adhesive plastic deformation. Clark and McGregor [83] considered ultimate tensile stress over a zone as a failure criterion. Sheppard et al. [84] developed a damage zone model for failure analysis of adhesive joints. Weißgraeber and Becker [53] studied failure of adhesive joints based on finite fracture mechanics. Liljedahl et al. [85] used a cohesive zone model in conjunction with both elastic and elasto-plastic continuum behaviors to predict the mixed mode failure of the lap shear joints, which showed excellent correlation with the experimental results. A cohesive zone model (CZM) is applicable to both brittle and ductile materials. It can be used to predict failure of the adhesive joints with plastic deformation and to simulate damage growth.

186  Structural Adhesive Joints

6.2.3.1 Cohesive Zone Model The CZM was originally proposed in 1960s to study fracture behaviors near a crack-tip [86, 87]. In the CZM, fracture is assumed to be gradually developed behind the crack-tip in a finite zone resisted by cohesive force. As shown in Figure 6.7(a), when traction stress t reaches the maximum value tmax, the crack is initiated and the relative displacement of two opposing points at the crack-tip is equal to δc. The crack will propagate once t decreases to zero at δ = δmax. The CZM has been widely applied for predicting strength of adhesive joints [88–96]. De Moura et al. [89] discussed cohesive and continuum mixed-mode damage models to predict failure of the adhesive joints based on testing the double cantilever beam and the end-notched flexure specimens. Campilho et al. [91] experimentally and numerically studied problems on using a cohesive damage model to predict the tensile behavior of CFRP single-strap repairs, which indicated that the cohesive mixed-mode damage model was adequate for ductile adhesives. Neto et al. [92] parametrically studied composite joints using the CZM for both brittle and ductile adhesives. Campilho et al. [90] studied the effects of cohesive law shapes on the CZM for adhesive joints. To simulate failure process using the CZM, a traction-separation relation, referred to as a cohesive traction law, plays a key role.

6.2.3.2 Cohesive Traction Law The cohesive traction law reflects the constitutive behavior of the cohesive zone. A number of cohesive tractions laws have been proposed, of which bilinear in Figure 6.7(a), trapezium in Figure 6.7(b) and exponential laws are most commonly used. In general, bilinear and trapezium laws are

t

t

Gc

tmax

0

Gc

tmax

δc

δmax δ (a)

0

δc1

δc2 (b)

Figure 6.7  Cohesive traction law (a) bilinear law, (b) trapezium law.

δmax δ

Fracture Mechanics-Based Design  187 applicable for brittle and ductile materials, respectively, and the exponential law predicts accurate results for structures with simple configurations. Selecting and acquiring the cohesive law are important to predict the joint strength and determining the mixed mode cohesive law is challenging [93, 94, 97]. Carvalho and Campilho [93, 94] used the DCB and endnotched flexure (ENF) specimens to obtain tensile and shear cohesive laws of the adhesive and then studied mixed mode fracture of SLJs. Nurprasetio et al. [95] used the CZM to evaluate bonding strength and fracture criterion for aluminum alloy–woven composite adhesive joints. Nunes and Campilho [96] tested failure of the asymmetric tapered DCB and developed the mixed mode cohesive traction law to estimate the mixed-mode fracture strength.

6.2.3.3 Design Criteria Based on Cohesive Zone Model For pure mode I, II or III, ERR Gi and its critical value Gic (i = I, II, III) can be expressed as: δk

δi max

∫

Gi = ti dδ i ; Gic =

0

∫ t dδ (i = I , II , III ) i

(6.49)

i

0

The CZM based design criteria can be stated as [98]: n

p

q



 t I   t II   t III   t  +  t  +  t  ≤ 1 crack initiation (6.50a) Im ax  II m ax  II Im ax 



 GI   GII   GIII   G  +  G  +  G  ≤1 crrack propagation (6.50b) Ic IIc IIIc

n

p

q

(

)

(

)

where n, p and q are the factors ( 1).

6.3 Finite Element Modelling and Simulation Analytical approaches discussed in Section 6.2 for stress analysis and fracture prediction of adhesive joints are available only for simple geometry. Structural performance of adhesive joints depends on geometry, material,

188  Structural Adhesive Joints boundary and loading conditions. In practice, stress analysis for complex joint geometry is a 3D problem in nature. Geometric and material nonlinearities need to be considered for most of joining structures. Therefore, analytical solutions are quite complicated and even impractical in most cases. Experimental methods are time-consuming and cost-expensive. Numerical approaches, especially FEA, are widely used for stress analysis, fracture prediction and progressive damage simulation of adhesive joints.

6.3.1 Finite Element Modelling for Stress Analysis of Adhesive Joints As indicated in Section 6.1, (a) the adhesive layer is much thinner than adherends; (b) its Young’s modulus is considerably lower than that of the main structure; and (c) failure often occurs in the adhesive or debonding from adherends; and (d) there exists stress singularity near the adhesive edges. These features must be carefully treated in FEA modelling for adhesive joints. The simplest FEA model is based on the beam-adhesive model where special elements are derived for the adhesive layer and beam or plate/ shell elements are used to describe adherends. This simple FEA model cannot describe the free shear stress boundary conditions and complex stress states near edges and interfaces [23, 99, 100]. Hence, 2D and 3D FEA models are widely used [83, 101–108]. Extended finite element modelling has been shown to be effective in predicting progressive failure of adhesive joints [82, 109–113]. Clark and McGregor [83] developed 2D FEA models to calculate the detailed adhesive stresses and concluded that failure occurred at the maximum principal stress exceeding the ultimate tensile stress of the adhesive material over a finite zone. Gonçalves et al. [112] developed the 3D FEA model for adhesive joints where geometric and material nonlinearities were considered and solid brick elements as well as specially interface elements were derived. Panigrahi and Pradhan presented [106] 3D failure analysis and damage propagation behavior of adhesively bonded composite SLJs, in which the full 3D FEA was developed to compute adhesive stresses in detail and damage propagation was simulated by the strain ERR approach using virtual crack closure technique (VCCT).

6.3.2 Virtual Crack Closure Technique In the FEA for the LEFM, the VCCT is an effective method for calculating ERRs. As shown in Figure 6.8, ERRs for mixed modes I and II in one-step approach VCCT using a 4-node element can be expressed as [114]:

Fracture Mechanics-Based Design  189 z Zw a

∆a

∆a

wl ul

l l’

wl’

Zi i

xXu

Xi

ul’

Figure 6.8  Schematic of virtual crack closure technique for a 4-node isoparametric element.





1 1 Zi w l − w l ′ ≈ Zi w l − w l ′ ∆a→0 2∆a 2∆a

)

(6.51a)

1 1 Xi ul − ul ′ ≈ Xi ul − ul ′ ∆a→0 2∆a 2∆a

(6.51b)

GI = lim

GII = lim

(

)

(

)

(

(

)

where a is the virtual crack length, wl, wl', ul and ul' denote the displacements; Zi and Xi are the force components. In FEA simulation, when the ERR reaches its critical value, crack will propagate. Guild et al. [115] used 2D FEA to simulate progressive failure of composite adhesive joints. Yang and Thouless [116] investigated mixedmode fracture analyses of plastically-deforming adhesive joints and developed the mode-dependent CZM model to predict crack initiation and propagation. To simulate progressive failure, the CZM is an efficient tool in the FEA simulation.

6.3.3 Cohesive Zone Modelling and Progressive Failure Definition and connectivity of cohesive elements are similar to those of continuum mechanics based discrete elements but stress-strain relationships are defined by the cohesive traction law. It is better to image a cohesive element as two separate faces in thickness direction. Cohesive elements can also be modelled with zero thickness when relative displacements of the two surfaces along thickness direction are used as freedoms at element nodes. Therefore, they can be used to model adhesive and interface fractures.

190  Structural Adhesive Joints As illustrated in Figure 6.7, cohesive elements are useful to study crack initiation (t = tmax, δ = δc) and propagation (t = 0, δ = δmax). Campilho et al. [109] used the standard FEA and the extended finite element method (XFEM) to predict strengths of single-lap and double-lap joints. The XFEM allows the growth of discontinuities within bulk solids along an arbitrary path. By enriching degrees of freedom with special displacement functions, the XFEM could overcome the main restriction of the cohesive elements. Fernandes et al. [111] considered adhesive selection for SLJs in which the experiment was carried out in combination with the XFEM and the CZM. Liu et al. [117] presented parametric study of size, curvature and free edge effects on the predicted strength of bonded composite joints by using the FEA in conjunction with the CZM to predict the strength of selected joint features.

6.4 Experimental Approach and Material Characterization In addition to analytical and numerical approaches, ERRs may also be measured by experiment and the critical ERR can be determined only by experiment combining with analytical or numerical analysis. Johnson and Mall [102, 118, 119] experimentally studied fracture strengths of the DCB and cracked lap shear (CLS) specimens bonded with adhesives EC-3445 and FM-300 by combining analytical and FEA approaches. Groth [120] studied stress singularity at corners of SLJs in which the stress intensity factor (SIF) determined by FEA was used to predict failure of the SLJ and compared with the test. Fernlund et al. [121] presented a fracture envelope to predict failure of the adhesive joints based on the LEFM approach. In this envelope, ERRs were calculated by using the J-integral for large deformations together with mode partition. The fracture envelope was applied to the CLS, SLJ and double strap joint specimens. Yang and Thouless [116] experimentally studied mixed mode fracture of the plastically-deforming adhesive joints. Potter and coworkers [115, 122] studied crack propagation and control of the composite joint by experiment and FEA. Fernlund and Spelt [43] designed a jig rig to test GIc and GIIc of adhesive joints, which allowed to measure over an entire range from mode I to mode II. Choupani [123] studied interfacial mixed-mode fracture characterization of adhesively bonded joints by means of the FEA. Dillard et al. [124] observed that fracture energy for mixed mode fracture of adhesive joints was lower than the pure mode fracture energy and indicated importance of developing fracture envelopes over a wide range of mode mixities.

Fracture Mechanics-Based Design  191 Chaves et al. [125] reviewed fracture mechanics tests for adhesively bonded joints, in which specimens, apparatus and data reduction techniques in light of analytical formulations were discussed. Pure mode I and mode II tests and sophisticated apparatuses to test mixed mode fracture were also discussed.

6.4.1 Specimen and Test Standard Fracture toughness can be tested for pure modes I, II and III, and then the fracture criterion of Eq. (6.1) or (6.2) is used for the mixed mode fracture. The mixed mode failure can also be studied by developing fracture envelopes as in [43, 44, 124]. Figure 6.9 illustrates specimens and apparatuses commonly used to test fracture behaviors such as fracture toughness and cohesive traction law [88, 125–127]. In an experimental study, test standards listed below should be used: ASTM D3433-99(2012): Standard Test Method for Fracture Strength in Cleavage of Adhesives in Bonded Metal Joints ISO 25217:2009: Adhesives-Determination of the mode I adhesive fracture energy of structural adhesive joints using P

a

L a

L P

P (b)

(a) P

c

P

a

c

P

a P (c)

(d)

Figure 6.9  Specimens to determine fracture toughness (a) symmetric double cantilever beam, (b) end notched flexure, (c) asymmetric double cantilever beam, (d) mixed mode bending specimen.

192  Structural Adhesive Joints double cantilever beam and tapered double cantilever beam specimens ASTM D6671 / D6671M-19: Standard Test Method for Mixed Mode I-Mode II Interlaminar Fracture Toughness of Unidirectional Fiber Reinforced Polymer Matrix Composites

6.4.2 Data Reduction and Fracture Toughness, Mixed Mode Fracture There are many data reduction schemes and an accurate and suitable one is important to test fracture toughness. In general, LEFM based data reduction schemes can be applied to brittle fracture, otherwise the CZM based data reduction should be used. In this subsection, the LEFM based closedform formulations are discussed for pure mode I using the DCB and pure mode II using the ENF specimen. The ERR of the DCB specimen given in Table 6.2 can be used to obtain fracture toughness for mode I approximately. De Moura et al. [88] developed an accurate data reduction scheme to measure the fracture energy of adhesive joints under pure mode I loading where the root rotation, stress concentration and fracture process zone effects were considered. When DCB and ENF specimens in Figure 6.9(a) and Figure 6.9(b) are used to determine fracture toughness, critical energy release rates can be expressed as [88, 89, 125]:

GIc =



6 Put2  2ae2 1  +  2  2 B h  E f h 5G13 

(6.52)

9 Put2 ae2 16 BE f h 2

(6.53)

GIIc =

where Ef is the equivalent flexure modulus; B and 2h are the specimen width and height; ae denotes the equivalent crack length; G13 is the transverse shear modulus and Put is the ultimate applied load.

6.4.3 Measurement of Fracture Parameters and Progressive Failure Using DIC Although ERRs of adhesive joints may be determined by experiment, accurate measurements of displacement and strain fields are quite challenging

Fracture Mechanics-Based Design  193 owing to very thin adhesive and stress singularity near the edge. Tracy et al. [128] experimentally studied fracture toughness of ceramic matrix composites using the J-integral with the digital image correlation (DIC) technique. This study showed that conventional methods to measure fracture parameters of ceramic matrix composites were quite difficult owing to damage complexity and the DIC technique would be effective. With the advent of high speed and high resolution cameras, the DIC technique is highly developed. The DIC can measure displacement and strain fields in micro- and nano-scales and thus can be used to test fracture parameters such as ERRs, cohesive laws and progressive failure of adhesive joints. Svensson et al. [129] tested cohesive laws for interlaminar failure of carbon fiber reiforced polymer laminates. Becker et al. [130] developed an approach to calculate the J-integral by using the DIC full-field displacement data. Felipe-Sese and Díaz [131] discussed damage methodology approaches via combining the fringe projection and DIC. Samadian et al. [132] measured the crack-tip opening displacement by means of DIC. These studies show that DIC has a great potential in testing fracture behaviours and progresssive failure of adhesive joints.

6.5 Prospects 6.5.1 Analytical Modelling and Formulation In fracture mechanics based analysis of adhesive joints, it is important to develop an effective fracture envelope with mode mixity to predict crack initiation and to numerically simulate failure progression. As indicated in [59, 80, 81, 92, 133, 134], mode mixity could be fracture toughness dependent. Adhesive thickness, adherend materials and their thicknesses can also affect mode mixity considerably. These pose a great challenge to develop simple models, to derive analytical solutions and to determine fracture toughness. Further study including these issues would be very helpful to predict failure of structural adhesive joints.

6.5.2 Cohesive Zone Model and Progressive Fracture The strength prediction and progressive failure simulation highly rely on the CZM traction law and relevant parameters. Constante et al. [135] presented tensile fracture characterization of adhesive joints by standard and optical techniques in 2015, where the J-integral was used to obtain the tensile cohesive traction law; Lelias et al. [97] discussed characterization

194  Structural Adhesive Joints of cohesive zone models for the joints with thin adhesive layers in 2019, which indicated that testing cohesive parameters for mixed mode fracture needs to be further investigated. FEA simulation for progressive failure relies on choosing suitable CZM laws and failure criteria. In computation, numerical issues may also be encountered owing to highly nonlinear analysis. Efficient FEA modelling and computation would offer cost-effective approaches to design structural adhesive joints.

6.5.3 Experimental Study On Fracture of Adhesive Joints It is well accepted that fracture toughness for a specific fracture mode is material property for isotropic materials. However, it is not only dependent on the adhesive but also is related to adherend materials for adhesive joints [136]. It is believed that the adherend material dependence is because the cured adhesive in the different joints possesses different values of glass transition temperature [133]. When adhesive is used to join dissimilar materials or composite laminates, the problem is more complicated. As adhesive joints involve 3D stress state, fracture can be mixed modes I, II and III. Chen et al. [137] measured fracture toughness in mode I using a three-point bending specimen and that in mode III using a circular specimen with a notch under torsion. Loh and Marzi [138] conducted the outof-plane DCB test to determine the critical energy release rate in mode III of adhesive joints and then [139] used the mixed mode controlled DCB specimen to test failure of adhesive joints in mixed I and III mode. As compared to study on fracture toughness of modes I and II, experimental study on mode III fracture is quite limited. Therefore, testing mixed mode fracture toughness, particularly for the mixed modes I, II and III, needs to be further studied. Measurements of ERRs and characterization of cohesive traction law using DIC have recently attracted considerable attention [97, 127–132]. It is expected that this technique will be intensively studied in experimental investigation into adhesive joints under static, impact and cyclic loadings.

6.5.4 Optimal Design of Adhesive Joints and Use of Nanomaterials To enhance fracture strength of structural adhesive joints, optimal design of configurations such as spew-fillet joints and hybrid joints with stitch and bolts [140–142] would be useful. Jeevi et al. [142] recently reviewed scientific work on adhesively bonded composites. This review indicated

Fracture Mechanics-Based Design  195 that surface treatment and joint configuration would significantly affect mechanical properties of adhesive joints and the hybrid joint could greatly improve structural strength. Nanomaterials have been extensively studied and also have been used in adhesive joints to enhance bonding strength [143–147]. Razavi et al. [145] incorperated polyacrylonitrile nanofibers in an epoxy-adhesive layer and exhibited improvement of 127% in the mode I fracture energy. Jojibabu et al. [143] used carbon nano-fillers such as carbon nanotubes (CNTs) and graphene nanoplatelets in the adhesive and showed that rheological property, thermal stability and strength of the lap shear joints were significantly improved. De Cicco et al. [144] presented a review on the use of nanoparticles for enhancing the interlaminar properties of composite laminates and adhesively bonded joints. These investigations indicate that difficulties in using nanomaterials in adhesive joints are control of dispersion of nanoparticles and a lack of understanding of micro-mechanisms.

6.6 Summary In this chapter, distinctive features of stress analysis and fracture behaviours of structural adhesive joints were discussed. Literature review and discussion were presented for the topics: (1) analytical modelling and formulations of stress analysis, (2) calculation of energy release rates based on adhesive stress and other approaches, (3) cohesive zone model and traction law, (4) geometrically-nonlinear FEA for stress analysis, computation of energy release rates using the VCCT and simulation for progressive failure of adhesive joints using the CZM, (5) determination of fracture toughness by experiment incorporating analytical data reduction and fracture measurement using DIC.

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7 Failure Analysis of Structural Adhesive Joints with Functionally Graded Tubular Adherends Rashmi Ranjan Das

*

Department of Mining Machinery Engineering Indian Institute of Technology (Indian School of Mines), Dhanbad, India

Abstract

The present research has focused on exploring the use of functionally graded adherends in place of laminated FRP composite tubular adherends in a bonded Tubular Single Lap Joint (TSLJ) subjected to uniaxial tensile loading with the sole objective of reducing stress concentration in the joint region. Elastic properties (E, υ) of tubular adherends of a structural adhesive joint have been varied as per the Power-law function based gradation. Suitable ANSYS Parametric Design Language (APDL) codes have been developed for modeling and analysis of a functionally graded structural adhesive joint and have also been validated with results from analytical models proposed in literature. The developed APDL codes are capable of suitably grading the material properties (E, υ) along axial direction of tubular adherends. Structural SOLID 185 elements of ANSYS 18.0 have been used for discretizing the structural adhesive joint region. Effect of variation of layer number (M) has been studied for an optimum number of axial divisions for smooth variation of properties without compromising the minimum possible CPU time and computational accuracy. Finally, stress and failure analyses of the adhesive joint region have been carried out for optimum layer number and a specific value of the compositional gradient exponent (n = 0.1). Keywords:  Bonded joint, FEM, FGM, FRP, tubular joint

Email: [email protected] K.L. Mittal and S. K. Panigrahi (eds.) Structural Adhesive Joints: Design, Analysis and Testing, (205–220) © 2020 Scrivener Publishing LLC

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206  Structural Adhesive Joints

7.1 Introduction and Background Literature Although structural adhesive joints with laminated FRP composite adherends have better tailored mechanical properties, the mismatch of their material properties across the interface introduces large interlaminar stresses that can cause severe delamination. The insidious nature of the delamination damages and their detrimental effects are common issues encountered with FRP composite made bonded pipe joints and have been reported extensively in literature. These adverse effects can be overcome by replacing the laminated FRP composite adherends in the bonded Tubular Single Lap Joint (TSLJ) by Functionally Graded Materials (FGMs). FGMs are a special class of materials usually made from ceramics and metals in appropriately graded proportions of the constituent materials to suit requirements. The ceramic in an FGM offers thermal barrier effect and protects the metal from corrosion and oxidation and the metallic constituent contributes strength and fracture toughness to the FGMs. The compositions and the volume fractions of the constituents in an FGM are varied gradually, thus giving a non-uniform micro-structure in the material with continuously graded micro-properties that are the most distinctive features of FGMs. Through variation of elastic modulus (and Poisson’s ratio) of the adherends along the axial direction as per Power-law distribution will not only improve resistance of the structural adhesive joint against adhesion failure but also will make the bonded TSLJ completely devoid of delamination damages. The present document deals with stress analysis of bonded TSLJ made with functionally graded adherends, whose elastic properties can be suitably tailored through Power-law function based variations to improve fracture resistance of the structural joint against adhesion failure. Functionally Graded Materials (FGMs) were first introduced as a concept by a group of scientists in Sendai, Japan in 1984 [1] and then developed by other scientists [2, 3]. There are a significant number of research articles available on this ever-growing subject since the past two decades. Most of the articles deal with the new applications of these materials in diversified fields of utmost engineering importance. The main applications of FGMs have been in high temperature environments, most of the research on FGMs has been restricted to thermal stress analysis, thermal buckling, fracture mechanics and optimization. This has been inspired by some naturally occurring material systems such as bamboo, bone, sea shells, teeth, etc. FGMs are heterogeneous materials featuring a smooth material composition gradation for achieving a specific function. Most commonly, metal-ceramic FGMs are used to make the transition from a metal part, which is strong but cannot operate at high temperatures, and a

Failure Analysis of Structural Adhesive Joints  207 ceramic part, which is efficient in shielding against high temperatures but has low tensile strength. Tremendous progress has been made in the field of FGMs in recent days. Approximately 1200 papers were published in the last ten years which dealt with theory or applications of FGMs. In analyzing the problems associated with FGMs, most of the authors suggested to consider their thermal response. An excellent introduction to this topic can be found in the work of Tanaka and co-workers [4, 5]. Regarding the optimality of gradation to reduce thermal stresses, the authors have developed a scheme to reduce thermal stresses by means of finite element analysis. Aboudi et al. [6] worked out thermoelastic theory for the response of FGMs with bi-directional material gradation. Wetherhold et al. [7] introduced the use of FGMs to eliminate or control thermal deformation. They concluded that by creating FGMs in the form of a symmetric composite whose fibre volume fraction varies throughthe-thickness one can control the deformation. Stresses in FGMs under thermal loading have been analyzed extensively by various authors [8–10] with regards to the elastic-plastic material behaviour. Cheng and Batra [11] analyzed thermo-mechanical deformations of a linear elastic functionally graded elliptic plate with rigidly clamped edges. Cho and Oden [12] analysed thermal stress characteristics of FGMs. They investigated the effects of the material variation through-the-thickness and the size of the FGM layer inserted between metal and ceramic layers using the finite element method. They used the asymptotic expansion method for the analysis and found that the gradients in material properties significantly affected the response of functionally graded plates under thermal loads. Cheng and Batra [11] studied 3D thermo-mechanical deformations of a simply supported functionally graded rectangular plate using an asymptotic method. They found that the assumption of a constant through-the-thickness deflection made for the 2D plate theories was invalid for the case of thermal load. Cho and Ha [13] investigated the optimum volume fraction distribution that minimizes steady-state thermal stresses in FGMs with 1D volume fraction variation using both penalty-function and golden section methods. Vel and Batra [14] obtained an exact solution for 3D deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads. They also presented an analytical solution for 3D thermo-mechanical deformations of a simply supported functionally graded rectangular plate subjected to time-dependent thermal loads. Nemat-Alla [15] introduced two-dimensional FGMs (2D-FGMs) to withstand super-high temperatures along with reduction in thermal stresses. They also showed that 2D-FGMs have high capabilities to reduce thermal and residual stresses than conventional FGMs. Shen [16] presented a

208  Structural Adhesive Joints non-linear bending response of FGM plates subjected to transverse loads and in thermal environments. In his paper non-linear bending behaviour of functionally graded rectangular plates subjected to a transverse uniform or sinusoidal load and thermal environments was studied using a mixed Galerkin perturbation technique to determine the load-deflection and load-bending moment curves. Kieback et al. [17] have nicely described the recent trends for the fabrication of functionally graded materials. In this paper the authors mainly concentrated on the powder metallurgical and electrodeposition techniques. Kashtalyan [18] derived three-dimensional elasticity solutions for the bending of FGM beams. Apalak and Gunes [19] investigated 3D thermal residual stresses occurring in functionally graded plates subjected to various thermal fields and showed that a 3D model is necessary in order to understand the stress state of the functionally graded plates subjected to different temperature fields. Wang and Qin [20] have extended the stress analysis of FGMs to fracture analysis. In the same paper they found that the mixed boundary value problem is reduced to a singular integral equation with the crack contact length as an additional unknown variable. The transient thermal analysis for a generalized thermoelastic solid was done by Mallik and Kanoria [21]. They concluded that the Laplace-Fourier double transform method can be effectively applied to solve a generalized thermoelastic problem of an isotropic functionally graded material with a periodically varying heat source. Kang and Li [22] analyzed the simple cantilever beam subjected to end load which was made with FGMs, and concluded that neutral axis location is dependent on the volume fraction gradation and a gamma function based formula cited in their research report. Bobaru [23] explained the designing of optimal volume fractions for FGMs with temperature-dependent material properties in a comprehensive manner. He solved the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions. Bahtui and Eslami [24] developed the coupled thermo-elasticity theory of functionally graded shells. They examined the coupled thermo-elastic response of a functionally graded circular cylindrical shell. Abrate [25] raised an astonishing issue that the FGM plates behave like homogeneous plates. He verified his conclusions through analytical studies by using the classical plate theory and higher-order three-dimensional elasticity-based plate theories. The variations in material properties through-the-thickness of the plate introduce a coupling between the in-plane and bending deformations which complicates the analysis. This can be overcome by a proper choice of the reference surface, thus coupling can be eliminated so that the bending of the plate is governed by the same equation of motion as that for homogeneous plates.

Failure Analysis of Structural Adhesive Joints  209 Delale and Erdogan [26] analytically studied the crack problem in an infinite plate where the elastic properties varied exponentially in the direction of the crack. They showed that the asymptotic crack tip stress is similar to that of homogeneous materials in terms of square root singularity. They also showed that the influence of the Poisson’s ratio on the stress intensity factors is not very significant. Eischen [27] obtained a theoretical solution for the elastic stress and displacement fields near a crack tip in a two-dimensional non-homogeneous cracked body utilizing an extension of the William’s eigenfunction expansion technique. An important study on FGM plates was published by Erdogan and Wu [28] dealing with the analyses of a plane elasticity problem for a non-homogeneous layer containing an internal crack, by assuming Young’s modulus of the medium to vary continuously (exponentially) in the thickness direction with a constant value of Poisson’s ratio. Anlas et al. [29] employed the finite element method for the study of cracked and uncracked plates made with FGMs. The material property variation was discretized by assigning different homogeneous elastic properties to each element. Finite Element results were compared to existing analytical results and the effect of mesh size was discussed. Stress intensity factors were calculated for an edge-cracked plate using both the strain energy release rate and the J-contour integral. Anlas et al. [30] solved edge crack problem for the plate made of FGMs in mode-I. In the finite element model, the change in material property was modelled discretely, by assigning each of the elements the value of elastic modulus at the centroid of the element calculated by an exponential relation. They evaluated ‘J-contour integrals’ using ANSYS. Ravichandran and Barsoum [31] have provided a generalized method to determine the Stress Intensity Factor (SIF) equations for cracks in finite-width specimens made with FGMs based on force balance in regions ahead of the crack tip. The method uses the Westergaard’s stress distribution ahead of the crack in an infinite plate and is based on the requirement of isostrain deformation of layers of varying moduli ahead of the crack tip. Rao and Rahman [32] have presented a ‘continuum shape sensitivity method’ to calculate mixed mode SIFs for a stationary crack in two-dimensional, linear elastic, isotropic FGM plates. Studies related to stress and failure analyses of adhesive bonded functionally graded pipe joints are very much limited in literature. However, recently 3D thermal residual stress analysis of an adhesive bonded functionally graded TSLJ has been carried out for a uniform temperature field throughout the joint and two edge conditions by Apalak et al. [33]. A detailed review on functionally graded adhesive bonded joints has been presented by Apalak [34]. The present analysis is a sequel to the analysis carried out by Das and Pradhan [35]. Specimen geometry, loading and boundary conditions of the

210  Structural Adhesive Joints Purely ceramic zone

Purely metallic zone l

a

t

Clamped end: u = v =w = 0

Purely metallic zone

r,u

h

Radially constrained: u = 0

z,w

r1

θ,v

2c

F

Inner adherend made with FGM Outer adherend made with FGM Epoxy adhesive Simulated adhesion failure of length ‘a’

Figure 7.1  Sectional view of the adhesive bonded functionally graded TSLJ specimen with simulated adhesion failure of length ‘a’ at the interface of inner adherend and adhesive.

bonded TSLJ specimen considered here have been kept exactly the same as by Das and Pradhan [35]. Effective overlap length (2c = 22 mm), concluded in their analysis, has also been kept the same. As per their conclusions, adhesion (interfacial) failure is presumed to initiate and propagate from the free edge of the inner adherend-adhesive interface of the overlap length nearer to the clamped end of the bonded TSLJ. In order to decrease the rate of growth of adhesion failure, the two adherends are considered to be made of functionally graded materials composed of ceramic (Al2O3) and metal (Ni) phases, as shown in Figure 7.1.

7.2 Material Property Gradation in the Structural Adhesive Joint Region In order to decrease the rate of growth of adhesion failure, the two adherends are considered to be made of functionally graded materials composed of ceramic (Al2O3) and metal (Ni) phases. These graded FGM tubular adherends would reduce and redistribute the stress concentrations at the bondline interfaces occurring mostly due to the presence and interaction of geometric and material discontinuities through the joint thickness leading to adhesion failure. An actual FGM consists of ceramic and metal particles with arbitrary shapes mixed in random dispersion structures. Theromomechanical properties of the FGMs are functions of the shape and orientation of the ceramic and metal particles, the dispersion structure, as well as the volume fraction. The mechanical properties of the ceramic and metal phases have been adopted from the work of Apalak et al. [33].

Failure Analysis of Structural Adhesive Joints  211 The adhesion failure has been shown to propagate in a self-similar manner in the joint along the axial (z) direction of the structure, and hence the mechanical properties of both adherends have been graded uni-directionally along the axial direction as per the Power-law variation (as per this law, material properties in the functionally graded material based structural adhesive joint have been varied along a longitudinal direction as per Equation (7.1)) [3, 22]. The material property gradation schemes adopted for the adherends are discussed in detail in the following Sections. A portion of the outer adherend lying outside the overlap region has been considered to be purely metallic (Em, υm). Whereas, the mechanical properties of the outer adherend lying within the overlap region of the bonded TSLJ have been varied continuously from purely ceramic (Al2O3) phase near the free edge of the outer adherend to purely metallic (Ni) phase towards the other end of the overlap portion. Such material gradation has been achieved through variation of material properties as per the Powerlaw variation mentioned below:









()

(

E z = E cm + E c – E cm

()

(

)

()

(

()

(

υ z = υcm + υ m – υcm

(7.1)

n

)

z  c 

)

 z  c 

)

 z  c 

υ z = υcm + υc – υcm

E z = E cm + E m – E cm

n

 z  c 

(7.2)

n

(7.3)

n

(7.4)

where, Em, Ec and υm, υc are the Young’s moduli of elasticity and Poisson’s ratios for purely metallic (m) and purely ceramic (c) phases, ‘z’ is the axial position within the overlap region from the center of the overlap length (–c ≤ z ≤ c), and ‘n’ is the compositional gradient exponent (n = 0.1, 0.2, 0.5, 1.0, 2.0, 5.0, and 10.0). Ecm and υcm are calculated using the following expressions.

212  Structural Adhesive Joints (a)

(b)

3.6×105

3.0×10–1

n = 0.1 n = 0.2

3.2×105 2.8×105 2.4×105

n = 0.5

n = 1.0

n = 2.0

n = 5.0

n = 10.0

2.0×105 –1.0

–0.5

0.0 z/c

0.5

n = 0.5

2.8×10–1 2.7×10–1

n = 5.0 n = 1.0

n = 0.2

2.6×10–1 n = 0.1

2.5×10–1 1.0

n = 10.0

n = 2.0

2.9×10–1 Poisson’s raio (ν)

Modulus of Elasticity (E) MPa

4.0×105

–1.0

–0.5

0.0 z/c

0.5

1.0

Figure 7.2  Through-the-overlap length variation of material properties: (a) Young’s modulus of elasticity ‘E’ and (b) Poisson’s ratio ‘ν’ of the bonded TSLJ made with FGM.



(

E cm = E c + E m – E c

)

n

 1  2 

(7.5)

n



 1 υcm = υc + (υ m – υc )    2

(7.6)

The modulus of elasticity (E) and Poisson’s ratio (υ) variations in the functionally graded overlap regions of the FGM adherends along with the variation of the compositional gradient exponent (n = 0.1, 0.2, 0.5, 1.0, 2.0, 5.0, and 10.0) are shown in Figures 7.2 (a) and (b).

7.3 Stress Analysis FEM based stress analysis of a bonded TSLJ made with FGM has been carried out using ANSYS 10.0 FE programme on a high speed IBM platform. The adherends and adhesive layer of the bonded TSLJ have been modelled using three-dimensional brick elements. These 3-D brick element models are more accurate, especially in separating the total Strain Energy Release Rate (SERR) into individual components, GI, GII, and GIII. Suitable APDL codes have been developed to assign the power-law variations of the mechanical properties of the adherends. As the adhesion failure propagates in the bonded TSLJ made with FGM, a smooth variation of the material properties of the FGM adherends in the joint is a

Failure Analysis of Structural Adhesive Joints  213 critical issue for the FE modelling. The number of finite elements used in the functionally graded region (overlap region) of the adherends is increased in order to have a smooth variation of the material properties from purely ceramic to purely metallic phase as shown in Figure 7.3. Each finite element of the FGM adherends within the functionally graded zone can be treated as an isotropic and homogeneous layer. Hence, the number of finite elements used to mesh the functionally graded zone (overlap region) of the adherends of the bonded TSLJ has been referred to as ‘layer number’ denoted by ‘M’ [33]. For this purpose, the number of layers (M) has been considered to be M = 11, 22, 33, 44, 110, and 154 (Figure 7.3). As the number of finite elements (M) used for discretizing the structural bonded joint region/overlap length is increased, it requires more CPU time due to larger number of nodes. However we arrive at a converged solution for stress values in the structural joint region for number of layers, M ≥ 110. Hence, 110 finite elements have been used for each of the adherends within the functionally graded zone for smooth variation of material properties. In other words, it can be said that the transition of the mechanical properties from ceramic-rich to metal-rich zone has been carried out using a minimum of 110 isotropic and homogeneous layers (finite elements) in between the purely ceramic to purely metallic zone of the functionally graded overlap region.

No. of finite elements used in the overlap region = M

–.725049 FGM-TSLJ

M = 11

.767815

M = 22

2.261

3.754

5.246

6.739

M = 44

8.232

9.725

11.218

12.711

M = 110

M = 154

Figure 7.3  Number of finite elements (M) used in the overlap region of the functionally graded structural adhesive joint.

214  Structural Adhesive Joints Adhesive peel stresses along the inner adherend-adhesive interface and adhesive-mid layer within the overlap region evaluated through finite element mesh patterns adopted based on the above philosophy are seen to have magnitude in close proximity with the available literature for the case of thermal residual stress analysis of a bonded TSLJ made with FGM (Ni/Al2O3) adherends, as given by Apalak et al. [33]. These are shown in Figures 7.4 (a) and (b). The bondline interfaces (i.e., inner adherend-adhesive interface, outer adherend-adhesive interface, and adhesive-mid layer) within the joint have been considered to investigate the effects of increases in the number of layers (M) and compositional gradient exponent (n) on stress distributions at these critical interfaces. The peel (σr) and radial-­circumferential shear (τrθ) stresses at all the critical bondline interfaces are seen to be

(a)

(b)

2

3

Analytical solution [33] Present FE solution

Peel stress (σr), MPa

Peel stress (σr), MPa

3

1 0

–1

1 0

–1

–2 –1.0

2

Analytical solution [33] Present FE solution

–2 –0.5 0.0 0.5 Overlap length (z/c)

1.0

–1.0

–0.5 0.0 0.5 Overlap length (z/c)

Adherend-adhesive interface

t ta Mid-surface of adhesive Adherend-adhesive interface

Figure 7.4  Peel stress distributions along the (a) adherend-adhesive interface and (b) mid-surface of adhesive within coupling/overlap region of the structural adhesive joint made with FGM.

1.0

Failure Analysis of Structural Adhesive Joints  215 concentrated towards the metal-and ceramic-rich zones of the overlap region with almost negligible values in rest of the portions of the bondline interfaces for n = 0.1 (Figures 7.5 (a), (b), and (c)). Magnitudes of peel (σr) and radial-axial shear (τrz) stress concentrations at all the critical bondline interfaces are seen to be maximum towards the ceramic-rich zone of the bonded joint made with FGM. The radial-circumferential shear stresses (τrθ), although are seen to be comparatively small in magnitude, have concentrated towards the metal-rich edge for n = 0.1. The von Mises (σeqv) stress magnitudes are seen (Figure 7.6) to be maximum towards the ceramic-rich edge of the joint for the inner adhrend-adhesive interface and the mid-surface of the adhesive. However, for the outer adherend-adhesive interface, these stresses are seen to be concentrated towards the metal-rich edge of the overlap length of the bonded TSLJ.

0.30 0.15

2.0×10–7

M = 11 M = 22 M = 44 M = 110 M = 154

M = 11 M = 22 M = 44 M = 110 M = 154

1.6×10–7

Shear stress (τrθ), MPa

Peel stress (σr), MPa

0.45

1.2×10–7 8.0×10–8

0.00

4.0×10–8

–0.15 –0.30

–0.20 –0.25 –0.30 –0.35 –0.40 –0.45 –0.50 –0.55 –0.60 –0.65 –1.0

Shear stress (τrz), MPa

(a)

0.0

–4.0×10–8

0.45

0.15 0.00 0.0 z/c

0.5

1.0

0.6

Peel stress (σr), MPa

0.0 z/c

0.5

0.2 0.0

–0.2 M = 11 M = 22 M = 44 M = 110 M = 154

–0.4 –0.6 –0.5

0.0 z/c

0.5

1.0

1.0 M = 11 M = 22 M = 44 M = 110 M = 154

2.5×10–8 2.0×10–8

0.5

1.0

0.0 z/c

0.5

1.0

0.0 z/c

0.5

1.0

–0.35 –0.40 –0.45

–0.60

1.0×10

–0.65

–9

5.0×10

–0.70 –0.5

0.0 z/c

0.5

–0.75 –1.0

1.0 M = 11 M = 22 M = 44 M = 110 M = 154

1.5×10–7

M = 11 M = 22 M = 44 M = 110 M = 154

–0.5

–0.20 –0.25 –0.30 –0.35

1.0×10–7

–0.40

5.0×10–8

–0.45 –0.50

0.0 –1.0

0.0 z/c

–0.55

–8

0.0 –1.0

–0.5

–0.50

1.5×10–8

2.0×10–7

0.4

–0.8 –1.0

–0.5

3.0×10

M = 11 M = 22 M = 44 M = 110 M = 154

–0.5

–1.0 –8

0.30

–0.15 –1.0

(c)

1.0

Shear stress (τrθ), MPa

Peel stress (σr), MPa

0.60

0.5

Shear stress (τrz), MPa

(b)

0.0 z/c

Shear stress (τrz), MPa

–0.5

Shear stress (τrθ), MPa

–1.0

M = 11 M = 22 M = 44 M = 110 M = 154

–0.5

0.0 z/c

0.5

1.0

–1.0

M = 11 M = 22 M = 44 M = 110 M = 154

–0.5

Figure 7.5  Effect of number of layers (M = 11, 22, 44, 110, 154) on peel and shear stress distributions along: (a) inner adherend-adhesive interface, (b) mid-surface of the adhesive layer, and (c) outer adherend-adhesive interface of the bonded TSLJ made with FGM for n = 0.1.

216  Structural Adhesive Joints (b)

6 5 4 3 2 1 –1.0

–0.5

(c) 1.6

M = 11 M = 22 M = 44 M = 110 M = 154

0.0 z/c

0.5

1.0

1.4 1.2

M = 11 M = 22 M = 44 M = 110 M = 154

von Mises stress (σeqv), MPa

7

von Mises stress (σeqv), MPa

von Mises stress (σeqv), MPa

(a)

1.0 0.8 0.6 –1.0

–0.5

0.0 z/c

0.5

1.0

8

M = 11 M = 22 M = 44 M = 110 M = 154

7 6 5 4 3 2 1 –1.0

–0.5

0.0 z/c

0.5

1.0

Figure 7.6  Effect of number of layers (M = 11, 22, 44, 110, 154) on the von Mises stress distributions along: (a) inner adherend-adhesive interface, (b) mid-surface of the adhesive layer, and (c) outer adherend-adhesive interface of the bonded TSLJ made with FGM for n = 0.1.

7.4 Summary and Conclusions Adhesion failure analysis of the bonded TSLJs made with FGM adherends has been performed. The adherends of the bonded TSLJ have been functionally graded within the overlap region by a power-law variation of the material properties from purely metallic (Ni) to purely ceramic (Al2O3) phase. Suitable APDL codes have been developed to describe the material properties of the functionally graded materials used as adherends. Stress magnitudes corresponding to the critical regions of the structural adhesive joint (shown in Figure 7.4) have been compared with the results available in literature and are found to be in good agreement. Some of the salient conclusions are as follows: • A layer number (M) of 110 has been found to be the optimum one ensuring smooth variation of adherend properties without compromising the computational accuracy and minimum computational time. • Peel (σr) and radial-circumferential shear (τrθ) stresses at all the critical bondline interfaces are seen to be concentrated towards the metal-and ceramic-rich zones of the overlap region with almost negligible values in the rest of the portions of the bondline interfaces for n = 0.1. • The power-law variation description of the material properties should be done for a lower value of the compositional gradient exponent (n) as higher values of ‘n’ make the bonded joint more prone to adhesion failures. • By varying the material compositional gradient exponents from metal-rich to ceramic-rich compositions, the

Failure Analysis of Structural Adhesive Joints  217 magnitudes of the stress values corresponding to the portions of the critical bondline interfaces localized to purely metallic and purely ceramic edges and the propagating adhesion failure front are seen to be increased.

References 1. N. Konda and F. Erdoga, The mixed mode crack problem in a nonhomogeneous elastic plane, Eng. Fracture Mech., 47, 533-545 (1994). 2. N. Noda, Thermal stresses in functionally graded materials, J. Thermal Stresses, 22, 477-512 (1999). 3. J.N. Reddy, Analysis of functionally graded plates, Intl. J. Numerical Methods in Engineering, 47, 663–684 (2000). 4. K. Tanaka, Y. Tanaka, and K. Enomoto, Design of thermoelastic materials using direct sensitivity and optimization methods. Reduction of thermal stresses in functionally gradient materials, Computer Methods in Applied Mechanics and Engineering, 106, 271-284 (1993). 5. K. Tanaka, Y. Tanaka, and H. Watanabe, An improved solution to thermo elastic material design in functionally gradient materials: Scheme to reduce thermal stresses, Computer Methods in Applied Mechanics and Engineering, 109, 377-389 (1993). 6. J. Aboudi, M.J. Pindera, and S.M. Arnold, Thermoelastic theory for the response of materials functionally graded in two directions, Intl. J. Solids Structures, 33, 931-966 (1996). 7. R.C Wetherhold, S. Seelman, and J. Wang, The use of functionally graded material to eliminate or control thermal deformation, Composites Sci. Technol., 56, 1099-1104 (1996). 8. S. Ueda and M. Gasik, Thermal-elasto-plastic analysis of W-Cu functionally graded materials subjected to a uniform heat flow by micromechanical model, J. Thermal Stresses, 23, 395–409 (2000). 9. Y.M. Shabana and N. Noda, Thermo-elasto-plastic stresses in functionally graded materials subjected to thermal loading taking residual stresses of the fabrication process into consideration, Composites: Part B, 32, 111–121 (2001). 10. K.M. Liew, S. Kitipornchai, X.Z. Zhang, and C.W. Lim, Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders, Intl. J. Solids Structures, 40, 2355-2380 (2003). 11. Z.Q Cheng and R.C. Batra, Three-dimensional thermoelastic deformations of a functionally graded elliptic plate, Composites: Part B, 31, 97–106 (2000). 12. J.R. Cho and J.T. Oden, Functionally graded material: a parametric study on thermal-stress characteristics using the Clark–Nicholson–Galerkin scheme, Computational Methods Applied to Mechanical Engineering, 188, 17–38 (2000).

218  Structural Adhesive Joints 13. J.R Cho and D.Y Ha, Volume fraction optimization for minimizing thermal stress in Ni-Al2O3 functionally graded materials, Mater. Sci. Eng. A, 334, 147155 (2002). 14. S.S. Vel and R.C Batra, Exact solution for thermoelastic deformations of functionally graded thick rectangular plates, AIAA J., 40, 1421-1433 (2002). 15. M. Nemat-Alla, Reduction of thermal stresses by developing two dimensional functionally graded materials, Intl. J. Solids Structures, 40, 7339-7356 (2003). 16. H.S Shen, Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments, Intl. J. Mech. Sci., 42, 561-584 (2002). 17. B. Kieback, A. Neubrand, and H. Riedel, Processing techniques for functionally graded materials, Mater. Sci. Eng., A, 362, 81–105 (2003). 18. M. Kashtalyan, Three dimensional elasticity solution for bending of functionally graded rectangular plates, European J. Mech. A/Solids, 23, 853-864 (2004). 19. M.K. Apalak and R. Gunes, Thermal residual stress analysis of Ni–Al2O3, Ni–TiO2 and Ti–SiC functionally graded composite plates subjected to various thermal fields, J. Thermoplastic Composite Mater., 18, 119-152 (2005). 20. H. Wang and Q.H. Qin, Meshless approach for thermo-mechanical analysis of functionally graded materials, Journal of Engineering Analysis with Boundary Elements, 32, 704-712 (2008). 21. S.H. Mallik and M. Kanoria, Generalized thermoelastic functionally graded solid with a periodically varying heat source, Intl. J. Solids Structures, 44, 7633-7645 (2007). 22. Y.A. Kang and X.F. Li, Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force, Intl J. Non-Linear Mech, 44, 696-703 (2009). 23. F. Bobaru, Designing optimal volume fractions for functionally graded materials with temperature dependent material properties, ASME Trans.: J. Appl. Mech., 74, 861-874 (2007). 24. A. Bahtui and M.R. Eslami, Coupled thermoelasticity of functionally graded shells, Mech. Res. Commun., 34, 1-18 (2007). 25. S. Abrate, Functionally graded plates behave like homogeneous plates, Composites: Part B, 39, 151-158 (2008). 26. F. Delale and F. Erdogan, The crack problem for a nonhomogeneous plane, J. Appl. Mech., 50, 609-614 (1983). 27. J.W. Eischen, Fracture of nonhomogeneous materials, Intl. J. Fracture, 34, 3-22 (1987). 28. F. Erdogan and B.H. Wu, The surface crack problem for a plate with functionally graded properties, J. Appl. Mech., 64, 449-456 (1997). 29. G. Anlas, M.H. Santare, and J. Lambros, Numerical calculation of stress intensity factors in functionally graded materials, Intl. J. Fracture, 104, 131143 (2000).

Failure Analysis of Structural Adhesive Joints  219 30. G.Anlas, J. Lambros and M.H. Santare, Dominance of asymptotic crack-tip fields in elastic functionally graded materials, Intl. J. Fracture, 115, 193-204 (2002). 31. K.S. Ravichandran and I. Barsoum, Determination of stress intensity factor solutions for cracks in finite-width functionally graded materials, Intl. J. Fracture, 121, 183-203 (2003). 32. B.N Rao and S. Rahman, Mesh-free analysis of cracks in isotropic functionally graded materials, Eng. Fracture Mech., 70, 1-27 (2003). 33. M. K. Apalak, R. Gunes, and S. Eroglu, Thermal residual stresses in an adhesively bonded functionally graded tubular single lap joint, Intl. J. Adhesion Adhesives, 27, 26-48 (2007). 34. M. K. Apalak, Functionally graded adhesive bonded joints, Rev. Adhesion Adhesives, 2, 56-84 (2014). 35. R.R. Das and B. Pradhan, Adhesion failure analysis of bonded tubular single lap joints in laminated fibre reinforced plastic composites, Intl. J. Adhesion Adhesives, 30, 425-428 (2010).

8 Damage Behaviour in Functionally Graded Structural Adhesive Joints with Double Lap Joint Configuration S. V. Nimje and S. K. Panigrahi* Department of Mechanical Engineering, Defence Institute of Advanced Technology (Deemed University) Girinagar, Pune, India

Abstract

Damage analysis of functionally graded adhesively bonded double lap joints (DLJs) made of laminated FRP composites has been carried out using three-dimensional finite element (FE) analysis. Tsai-Wu coupled stress failure criterion has been utilized to detect onset of interfacial damage in the double lap joint structures under longitudinal loading. Subsequently, damage growth rates have been computed along the damage front pre-existing at the critical location in the double lap joint structure. Modified crack closure integral (MCCI) based on the concept of fracture mechanics has been used to evaluate individual and total strain energy release rate (SERR) along the damage front. Based on evaluation of failure indices, it is shown that the interfacial damage in the joint structure initiates at the interface of main adherend and adhesive layer towards loaded end of adhesive bondline. Magnitudes of SERR indicate that the interfacial failure propagates under mixed mode condition. Therefore, total SERR (GT) is considered as the governing and characterizing parameter for damage propagation. In the present work, novelty of functionally graded adhesive along the bondline is explored in order to enhance damage growth resistance of double lap joint structures. Further detailed study has been made for functionally graded double lap joints with different damage lengths. The results showed that a functionally graded adhesive offers significant reduction in damage growth driving forces for shorter interfacial damage lengths.

*Corresponding author: [email protected] K.L. Mittal and S. K. Panigrahi (eds.) Structural Adhesive Joints: Design, Analysis and Testing, (221–246) © 2020 Scrivener Publishing LLC

221

222  Structural Adhesive Joints In view of the above, recommendations can be made for use of functionally graded adhesives in the double lap joint structures to achieve improved structural integrity and service life. Keywords:  Double lap joint, functionally graded adhesive, interfacial failure, MCCI, SERR

List of Symbols a E ν E(x) R Ex, Ey, Ez νxy, νyz, νzx σ x, σ y, σ z τxy, τyz, τzx Fx, Fy, Fz GT

Z S

Y T YC

Δa

Damage length Young’s modulus of the epoxy adhesive Poisson’s ratio of the epoxy adhesive Material gradation function for Functionally Graded Adhesive Modulus ratio Young’s moduli referred to geometric axes (x, y, z) Poisson’s ratios referred to orthogonal axes Normal stresses in orthogonal Cartesian coordinates Shear stresses in orthogonal Cartesian coordinates Nodal forces at the crack tip Total Strain Energy Release Rate (SERR)

Out-of-plane normal (Transverse) strength Out-of-plane shear strength Yield strength of adhesive in tension Yield strength of adhesive in compression Virtual crack extension

8.1 Introduction Adhesively bonded joints of Fiber Reinforced Polymer (FRP) composites have been one of the most important and evolving technologies for many structural applications in a wide variety of industries. Compared to other joining methods like mechanical fastening, welding, brazing and soldering, adhesive bonding offers improved performance and substantial economic advantages. The ability to join dissimilar materials (like laminated composites), joining of thin sheets and joining of materials with complex geometrical configurations has made the adhesive bonding more attractive over the other methods of joining. A smoother load transfer between the connecting members helps in lowering the localized stress concentrations as compared to mechanical fasteners. It offers the potential for a reduced

Functionally Graded Structural Adhesive Joints  223 weight and cost, and it has found widespread acceptance in many engineering fields. Interlaminar stresses are induced in the vicinity of the singular regions in case of bonded joints made of FRP composites. These stresses can cause damages such as adhesion failure (interfacial failure), cohesive failure and delamination damages or combination of these. The adhesion failure initiates from the stress singularity regions and propagates along the bondline interfaces due to peeling or shearing. These failures occur on a macroscale when surface preparation or material qualities are poor and, consequently, this mode of failure cannot be ignored. Though all joints are assumed to be fabricated to specifications, but due to the above-mentioned reasons, adhesion failures are expected to initiate from the edges of the stress singularity points. Kelly [1] showed numerically and experimentally that the failure of bonded joints occurs with the fracture initiating from the toe of the adhesive fillet and propagating along the adherend–adhesive interface in case of a single lap joint (SLJ). An interesting experimental study on the crack growth behaviour for an SLJ with adhesive fillets has been carried out by Potter et al. [2]. An FEA for adhesively bonded SLJs using elasticity and elasto-plastic theories was reported by Liu [3]. Stress distributions and concentrations in the adhesive layer for different joining parameters (geometry, material properties and loading) were studied and compared. The existence of stress gradients through-the-thickness of the adhesive layer, close to the joint edges, was observed by Adams and Peppiatt [4]. They performed a linear elastic FEA on an SLJ, employing more than one element through-the-thickness of the adhesive layer, and also studied the adhesive yielding, using an iterative elasto-plastic FE program. Pickett and Hollaway [5] presented both classical and finite element solutions for elastic-plastic adhesives stress distributions in bonded SLJs. The results showed how the development of adhesive yielding occurred when the joints were loaded to failure. A two-dimensional finite element method based on the updated Lagrangian formulation of elastic solids was presented by Reddy and Roy [6]. Their results were in good agreement with those reported in literature. The effects of boundary conditions and mesh size on stress distributions in a lap joint were also investigated. Sage [7] conducted experimental work for double strap bonded joints made of unidirectional carbon fibre reinforced plastics. Results showed that the direct stress concentrations arising at sharp changes can lead to tensile instead of shear failure. This could be avoided by providing fillets using pure epoxy based adhesive. Another joint configuration that has received considerable attention is the Double Lap Joint (DLJ). Hart-Smith [8] studied adhesively bonded DLJs using elastic-plastic analytical techniques. Explicit

224  Structural Adhesive Joints solutions obtained include sufficiently simple formulas for predicting the shear bond strength and the plastic zone length. It was shown that with a particular geometric configuration and specified material properties, the maximum bond shear strength was achievable between specified adherends in case of a DLJ. Tong [9] used an arbitrary shear stress-strain model as a basis for developing the expression for the bond shear strength. In this case, closed-form solutions for the shear strain and stress distributions were mathematically intractable. However, the bond shear strength could be determined without completely solving the governing equation. It was shown that bond shear strengths could be characterized by the maximum strain energy density in shear for the adhesive. The expression for the bond shear strength was also presented to include the thermal mismatch effect between the thermal expansion coefficients of the two adherends. Adams et al. [10] indicated that an internal bending moment was established in a DLJ, which Volkersen [11] had accounted for in his work, so that normal stresses arise, acting normal to the adhesive layer. The maximum values of these normal stresses occur in the adhesive layer and the inner adherend at the end of the overlap. These normal stresses, called peel stresses, influenced significantly the failure of the joint. This arises for two reasons: firstly, the strain capability of structural adhesives is very limited in tension, as compared with in shear,and, secondly, the transverse tensile strength of a fibrous composite is much lower than the strength parallel to the fibers. Most of the predictions assumed the failure of the adhesive and did not address the problem of interlaminar adherend failure. Adams and Wake [12] presented theoretical studies to draw upon both established analytical and original FEA to describe the shear and tensile stress distributions in the FRP composite to metal DLJ, taking into account the above factors. Tong et al. [13] showed the effect of the end mismatch on mechanical behaviour of an adhesively bonded DLJ. Parametric results showed that the end mismatch had a noticeable effect on the adhesive shear and peel stresses and a significant effect on the normal displacement. Also, they included the effect of end mismatch in the peel stress expression developed by Tong et al. [14] in their further research. Finally, the surface normal displacement and the peel stress in the adhesive layer were validated by comparing them with the experimental results obtained using holographic interferometry technique. Altus [15] made a profound study on the three-dimensional aspects of DLJs including all three modes of fracture simultaneously, to find out how far the fracture mechanics approach could be used as a designing tool for further use of DLJs and to follow the influence of different materials on

Functionally Graded Structural Adhesive Joints  225 the three-dimensional behaviour to check the accuracy, using numerical technique. It is highlighted that the singular regions for common adhesive-adherend are so small that regular continuum mechanics tools may be limited in failure predictions and the two-dimensional solutions would show higher critical load for the same problem. Panigrahi and Pradhan [16] have carried out three-dimensional finite element analysis for understanding the onset and subsequent growth of damages due to the adhesion failure and the delamination induced damage in laminated FRP composite DLJs. Locations of damage initiation are identified by strength criterion proposed by Tsai and Wu [17] and individual components of SERR are computed using MCCI to study the damage propagation. In order to relieve high stress concentrations at the free edges of the overlap region and to have more uniform stress distributions, an adhesive layer with variable modulus has been proposed. This requires at least the use of two adhesives with different mechanical and thermal properties as the adhesive layer. Pires et al. [18] have used a stiff adhesive in the middle part of bondline, while a low modulus adhesive towards the edges prone to stress concentrations. It was observed from experimental and numerical analyses that there was a significant increase in the strength of bi-adhesive bonded joints compared with that of monomodulus adhesive. Fitton and Broughton [19] have investigated the behavior of a variable modulus adhesive layer using numerical and experimental techniques. Authors noticed significant changes in the mode of failure and improvement in the joint strength when a variable modulus adhesive was used to bond unidirectional carbon fibre reinforced plastics. Testing demonstrated that joint optimization was crucial for bonding materials that are particularly sensitive to peel stresses. Temiz [20] investigated the application of two adhesives possessing different stiffnesses along the overlap length in a double strap joint subjected to bending moment and the possible gains in joint strength through the use of bondline with graded stiffness. A hard adhesive was applied in the middle portion of the overlap, while a softer adhesive was applied towards the edges prone to stress concentrations. The same author carried out non-linear FE analysis to predict failure loads by which effective ratios of properties can be identified for maximum joint strength. Ozer and Oz [21] have carried out 3D FE analysis of bi-adhesive double lap joints considering various bond length ratios and determined the influence of hybrid-adhesive bondline on peel and shear stress distributions. They have recommended appropriate bond-length ratios for improved joint strength based on FE analysis.

226  Structural Adhesive Joints The bi-adhesive or mixed joint concepts constituted the early stages of functionally graded adhesives. The concept of a functionally graded adhesive implies, in fact, that one or more material properties such as elastic modulus, Poisson’s ratio, or coefficient of thermal expansion and thermal conduction, are altered along one or more coordinate directions based on a distribution law: power or exponential. Kumar [22] presented an axisymmetric elastic stress analysis of adhesively bonded tubular lap joints based on variational principle. Functionally modulus graded bondline (FMGB) was used to join similar or dissimilar adherends of tubular joint structure. The bondline was graded by suitable smooth and continuous functions. Results showed significant reductions in peel and shear stress peaks in FMGB compared to those in mono-modulus bondline adhesive joints. Parametric study was conducted in order to see the influence of material and geometric properties of joints on stress distribution along the bond length. Kumar and Scanlan [23] also provided an analytical framework for stress analysis of a shaft-tube bonded joint using the variational technique. Functionally modulus graded bondline (FMGB) adhesives were employed in order to reduce peak peel and shear stress levels. These investigators found that there were significant decreases in peak peel and shear stress levels in FMGB joints compared to those of mono-modulus adhesive materials. Stapleton et al. [24] used enhanced joint finite element analysis where analytical formulation was used to obtain exact shape functions for modelling of joint. In their research, grading of adhesive was achieved by strategically placing glass beads with varied densities within the adhesive layer. They have addressed practical concerns regarding the use of functionally graded adhesives (FGAs) which include manufacturing complications, alterations to grading due to adhesive flow during manufacturing and impact of loading conditions on effectiveness of grading. These practical concerns were addressed by the same researchers through analytical study. Carbas et al. [25] developed a technological process to functionally modify the adhesive along the bondline in order to vary mechanical properties, allowing a more uniform stress distribution. In their research work, grading of adhesive was achieved by induction heating, giving a graded cure of adhesive along the bondline. The findings of their research work indicated higher joint strength of the graded joint compared to the cases where the adhesive was cured uniformly at low temperature or at high temperature. The same authors carried out analytical analysis in order to predict the failure load of the joints with graded cure and isothermal cure. Nimje and Panigrahi [26] have performed damage analyses of functionally graded adhesively

Functionally Graded Structural Adhesive Joints  227 bonded tubular lap joints of laminated FRP composites under varied loadings. They have used SERR as the characterizing and governing parameter for assessing damages emanating from the critical locations. Outcome of their research indicated that the material gradient profile of the adhesive layer offered significant reduction in SERR. The same authors [27] have studied failure propagation characteristics using SERR along failure fronts in functionally graded adhesively bonded tubular socket joints of laminated FRP composites. In the present work, damage evolution in functionally graded adhesively bonded double lap joints of laminated FRP composites and fracture behaviour of embedded damages have been discussed with respect to the variation of the individual modes of strain energy release rate as the characterising parameters along the damage front. The novelty of a functionally graded adhesive is introduced with appropriate function profile for enhanced damage growth resistance of the considered joint structure. Several numerical simulations have been made to show the influence of a graded adhesive with varied modulus ratios on damage onset and its propagation in a double lap joint structure.

8.2 FE Analysis of Functionally Graded Double Lap Joint The present research deals with three-dimensional FE analysis for a functionally graded adhesively bonded double lap joints made of laminated FRP composites. The out of plane stress components have been evaluated along the interfacial surfaces of bondline which are utilized to predict the location of onset of failures in the joint. A series of numerical simulations have been performed in order to visualize the effect of a functionally graded adhesive on damage growth.

8.2.1 Modelling of Double Lap Joint The geometry and configuration of the double lap joint specimen considered in the present research work is shown in Figure 8.1. The top, main and bottom adhereds are made of graphite/epoxy composite laminates with ply schemes [0]8, [0]16, and [0]8, respectively. The mechanical properties of the adherends and the isotropic adhesive layer used are given in Tables 8.1 and 8.2, respectively. The main dimensions of adherends and adhesive were taken as in [16, 28]: the length of

228  Structural Adhesive Joints Top [0]8 adherend

Functionally graded adhesive Main [0]16 adherend

z w

h1 y

ta

x

h1

10 kN

h2

2c L

Bottom [0]8 adherend

Figure 8.1  Geometry and configuration of a functionally graded double lap joint.

the joint L = 230 mm, thickness of top and bottom adherends h1 = 2 mm, thickness of main adherend h2 = 4 mm, width of the joint w = 20 mm, length along the overlap region 2c = 50 mm, thickness of adhesive layer ta = 0.5 mm. Two types of adhesives are used in the present analysis, isotropic adhesive layer and functionally graded adhesive layer with smooth and continuous Table 8.1  Layerwise orthotropic material properties of Gr/E (T300/934) composite plates [12, 30]. Elastic properties Ex

127.50 (GPa)

Ey

9.00 (GPa)

Ez

4.80 (GPa)

Gxy = Gxz

4.80 (GPa)

Gyz

2.55 (GPa)

υxy = υxz

0.28

υyz

0.41

Strengths Z (Out-of-plane normal (Transverse) strength)

49 (MPa)

S (Out-of-plane shear strength)

2.55 (MPa)

Functionally Graded Structural Adhesive Joints  229 Table 8.2  Elastic properties of epoxy adhesive [12, 30]. E

2.8 (GPa)

υ

0.4

Strengths YT

65 (MPa)

YC

84.5 (MPa)

variations of gradation profiles. The details of functionally graded adhesive layer are given in the next section.

8.2.2 Loading and Boundary Conditions A static force of 10 kN is applied to the right side of the main adherend. The displacement boundary conditions are given as: (i) u = v = w = 0, for all nodes at x = 0, (ii) w = 0, for all nodes at z = 2.5 and 4.5 mm within the region 0 ≤ x ≤ 25 mm and at z = 2 mm within the region 205 mm ≤ x ≤ 230 mm Boundary condition at (ii) has been taken into account to prevent any rotation of the adherends at x = 0 and 230 mm.

8.2.3 Modeling of Functionally Graded Adhesive Layer In the present investigation, continuous variation of elastic modulus of adhesive along the bondline has been considered. The smooth variations of bondline modulus have been implemented by applying adhesives of different moduli in the bondline which is expressed by the following linear function profile [26, 29]:





( )

(

)

x c

(90 ≤ x ≤ 115)

(8.1)

( )

(

)

x c

(115 ≤ x ≤ 140)

(8.2)

E x = E2 + E1 − E2 ×

E x = E2 − E1 − E2 ×

230  Structural Adhesive Joints Material non-homogeneity of graded bondline has been evaluated in terms of modulus ratio (R) which is expressed as follows

R=



E2 E1

(8.3)

The detailed distribution of graded properties with varied modulus ratios along the bondline of the double lap joint structure is shown in Figure 8.2. Based on stress distributions [22, 31], a flexible adhesive having low value of elastic modulus (E1) is used at both overlap end zones (x = L/2 ± c). Whereas stiffest adhesive having the highest value of elastic modulus (E2) is used in the central portion of the double lap joint structure (x = L/2). The upper bound modulus E2 is taken as 2.8 GPa and the lower bound modulus E1 is varied according to modulus ratio ‘R’ as expressed in Equations (8.1–8.2). A stiffer adhesive following linear function profile as shown in Figure 8.2 has been used in the remaining portion of bondline. For modelling of a double lap joint with FGA, the region of adhesive is assumed to have a Young’s modulus varying continuously and smoothly along the x-axis using Equations (8.1) and (8.2). In the FE model, the changes of material property have been modelled discretely by assigning the value of E(x) at the middle for each of the elements within the adhesive layer [32].

Young’s Modulus (E), MPa

3000 2500 2000 R=1 R=2 R=5 R=8

1500 1000 500 0

0

10 20 30 40 50 Distance along the bond length, mm

Figure 8.2  Elastic modulus gradation for different modulus ratios (R) along the bond length.

Functionally Graded Structural Adhesive Joints  231

8.2.4 Meshing Scheme of Double Lap Joint In the present research three-dimensional brick elements are used to model the specimen. Layered version of SOLID 186, which is twenty node element, is used in modelling the laminated composite adherends. One element is used in the thickness directions of the top and main adherends. The adhesive layers are modelled using SOLID 186 structural solid element. In the present FE analysis element size of 0.25 mm is maintained in the regions where stress concentrations are expected. Two elements are used along the thickness direction in meshing the adhesive layers. The elements defined above are accurate, expedient or appropriate for modelling joints made of laminated FRP composites. To increase the computational efficiency, a graded mesh is created. Fine mesh is implemented in the regions where high stress gradients are expected. The graded mesh adopted for the present analysis is shown in Figure 8.3.

8.2.5 Error and Convergence Study Convergence and error determination is important in finite element analysis. This has been carried out extensively to achieve the optimized stress values. A series of numerical simulations for the validated FE model with different element numbers in the adhesive layer have been carried out to determine the out-of-plane stress component ‘σz’. The convergence of the double lap joint model was achieved by increasing the mesh density, with

(a)

(b)

Figure 8.3  Meshed model of a DLJ (a) full model, and (b) zoomed view.

232  Structural Adhesive Joints error in stress value being kept to less than 1.2%. The out-of-plane stress values for different element numbers ‘n’ are given in Table 8.3. In the present numerical analysis, the validation of the model has been done by comparing the results with the existing literature [33]. The values of shear stress (τxz) within the adhesive layer has been evaluated and compared with the available literature [33]. Referring to Figure 8.4 shear stress distribution within the adhesive layer shows good agreement with the available results.

Table 8.3  Out-of-plane normal stress (σzz) values with different numbers of elements (0.4n, 0.51n, 0.58n, n). σzz (MPa)

Distance along bond length (mm)

0.4n

0.51n

0.58n

n

% Error

0

–2.34

–2.27

–2.21

–2.19

1.15

3

–1.64

–1.65

–1.65

–1.65

0.00

6

0.36

0.35

0.35

0.35

0.16

9

0.70

0.70

0.70

0.70

0.03

12

0.58

0.58

0.58

0.58

0.01

15

0.41

0.41

0.40

0.41

0.02

18

0.26

0.26

0.26

0.26

0.02

21

0.14

0.14

0.14

0.14

0.00

24

0.04

0.04

0.04

0.04

0.00

27

–0.05

–0.05

–0.05

–0.05

0.00

30

–0.15

–0.15

–0.15

–0.15

0.00

33

–0.28

–0.28

–0.28

–0.28

0.00

41

–0.73

–0.72

–0.73

–0.72

0.01

44

–0.62

–0.62

–0.62

–0.62

0.09

50

0.51

0.52

0.51

0.51

0.00

Functionally Graded Structural Adhesive Joints  233 18 16

L.F.M. Da Silva and R.D. Adams [33] Present numerical solution

14 τxz, MPa

12 10 8 6 4 2 0 0

10 20 30 40 Distance along overlap length, mm

50

Figure 8.4  Distribution of shear stresses along the adhesive layer.

8.3 Damage Onset in a Double Lap Joint One of the major concerns in laminated FRP composite double lap joints is the prediction of location of damage initiation due to the prevailing tri-axial states of stresses which have been accurately evaluated by three-dimensional FEA. An adhesively bonded double lap joint experiences two important modes of mechanical failure: (i) interfacial failure also known as adhesion failure which occurs at the interface of adhesive and adherend, (ii) cohesive failure is within adhesive layer. The interfacial failure initiates from the stress singularity points of adhesively bonded double lap joint structures. The onset of failure at the bondline interfacial surfaces has been predicted by Tsai and Wu [17] from coupled failure criterion through computation of failure indices ‘e’. Accordingly a failure surface in the stress space can be represented in the following form:

f (σk) = Fiσi + Fij σi σj = 1

(8.4)

Where, i, j, k = 1, 2, ……6. Fi and Fij are strength tensors. In the double lap joint structure, the interlaminar or out-of-plane stresses are responsible for the initiation of interfacial failure. Hence, only these stress components have been used in Eq. (8.4) to determine the failure index values ‘e’ and are given by

234  Structural Adhesive Joints (i) Interfacial failure in tension, for σz > 0; 2



2

2  τ yz   τ xz   σz  2  Z  +  S  +  S  = e  yz  T xz

 e ≥ 1, faailure (8.5)  e ≤ failure 1, no 

(ii) Interfacial failure in compression, for σz < 0; 2



2

2

 τ yz   σz   τ xz  2 + +  S  =e  Z   S   yz  C xz

 e ≥ 1, faailure (8.6)  e ≤ failure 1, no 

Similarly the failure index of adhesive layer is formulated by assuming cohesive failure. As reported by Adams [34], parabolic yield criterion is expressed as

(σ1 – σ2)2 + (σ2 – σ3)2 + (σ3 – σ1)2 + 2 (|YC|– YT)(σ1 + σ2 + σ3) = 2|YC|YT (8.7) Using Eqs. (8.5), (8.6) and (8.7) failure indices are evaluated for three surfaces viz. two interfacial surfaces and mid-surface of adhesive layer. YT and YC measure the yield strengths in tension and compression, respectively. Based on the magnitudes of ‘e’, the critical locations for onset of damage in a double lap joint structure have been identified. Subsequently, the damage propagation behaviour of a double lap joint has been studied using strain energy release rates (GI, GII, GIII).

8.4 Adhesion/Interfacial Failure Propagation Analysis The damage propagation behaviors due to interfacial/adhesion failures emanating from the critical locations have been modelled and their propagations are governed by the individual modes of SERR along the interfacial failure front for the considered laminated FRP composite double lap joint. In the laminated FRP composite plates of double lap joint, due to their inherent complexities as a result of geometrical, loading and material properties, exact closed-form expressions for SERR are not possible. The singularity of crack-tip stress field in an orthotropic medium is quite different

Functionally Graded Structural Adhesive Joints  235 from that of the conventional square root singularity at the crack-tip in a homogeneous isotropic material system. This leads to the evaluation of interlaminar fracture energy released due to the propagation of the existing interfacial failure by a very small amount [16]. Strain energy release rate procedure is suitable for assessing damage propagation behaviour due to the reason that it is based on a sound energy balance principle implying its robustness, and also mode separation of SERR is possible. Irwin’s theory of crack closure has been followed for evaluating individual modes of strain energy release rates. This aspect is very important, as in most of the cases the fracture mechanism is a mixed mode phenomenon in multi-directional laminated FRP composites.

8.4.1 Evaluation of SERR Based on the magnitudes of failure indices, interfacial failure is expected to trigger at the interface of main adherend and adhesive layer towards the loaded ends of bondline as shown in Figure 8.5. Accordingly, the configuration for evaluation of MCCI applied to adhesively bonded double lap joint for computation of SERR along the embedded interfacial failure length ‘a’ existing at the interface of main adherend and adhesive layer is shown in Figure 8.6. Except in the interfacial failure region, multipoint constraints are imposed on the nodes along the interfacial failure front. Furthermore, it has been assumed that the interfacial failure plane is the weakest and interfacial failure will propagate parallel to x-y plane. Thus the possibility of out-of-plane propagation is ignored. The three components of the strain energy release rate viz. GI, GII, and GIII have been evaluated using the Modified Crack Closure Integral (MCCI) method and have been used as parameters for assessing the damage propagation characteristics [16]. Main adherend

Top adherend F/2

F

F/2 a Bottom adherend

Initiation of adhesion failure from the stress singularity points at the edges of the DLJ

Figure 8.5  Pre-embedded adhesion failure existing at the interface of main adherend and adhesive.

236  Structural Adhesive Joints Propagated damage front Damage surface of adhesive

B A

Main adherend damage surface z, w y, v

∆a

x, u

∆a

∆a

∆a Pre-embedded delamination length a

Figure 8.6  MCCI applied to the double lap joint for computation of SERR along the adhesion failure front.

Evaluation of interlaminar stresses σz, τxz and τyz along the interfacial failure front and the displacement fields around it is the central point of focus of any strain energy release rate analysis. Then the strain energy release rates along the interfacial failure front can be calculated from these stresses and displacement fields using Irwin’s theory of crack closure. The strain energy released by the propagation of interfacial failure of length a to a + ∆a is given by



1 W= 2

a + a

a / 2

∫ ∫ a

σ (x, y) × δ ( x −a, y ) dxdy

− a / 2

(8.8)

where, δ(x−∆a, y) is the crack opening displacement between the top and bottom interfacial failure surfaces and σ(x,y) is the stress at any point on the interfacial failure front required to close the delaminated area. Then, the strain energy release rate (G) is obtained as



G = lim

a→0

W A

(8.9)

where, ∆A represents the interfacial failure propagated area and equals one element area in x-y plane i.e. ∆a×∆a for the present case. The MCCI method has the advantage of mode separation of strain energy release rate, which will help for a qualitative analysis of damage propagation behaviour.

Functionally Graded Structural Adhesive Joints  237 Accordingly, the three components of strain energy release rate GI, GII and GIII for Modes I, II, and III can be expressed as follows:

1 GI = lim ∆a→0 2∆A

a+∆a

∆a/ 2

a

− ∆a/ 2

T

a+∆a

∆a/ 2

∫ ∫τ a

a+∆a

xz

( x , y ) × [uT ( x − ∆a, y )

(8.11)

− ∆a/ 2



∆a/ 2

∫ ∫τ a

(8.10)



− uB ( x − ∆a, y )] dxdy 1 GIII = lim ∆a→0 2∆A



z

− w B ( x − ∆a, y )] dxdy 1 GII = lim ∆a→0 2∆A



∫ ∫ σ (x , y ) ×[w (x − ∆a, y )

yz

( x , y ) × [vT ( x − ∆a, y )

(8.12)

− ∆a/ 2

− v B ( x − ∆a, y )] dxdy



8.5 Interfacial Damage Propagation Analysis The three-dimensional nature of the stress field on different interfacial surfaces i.e. (i) top/bottom adherend and adhesive layer, (ii) middle of adhesive layer, (iii) main adherend and adhesive layer of the joint have been used for finding out the region for initiation of failures in the joint. The failure indices ‘e’ have been computed using Tsai-Wu’s coupled stress failure criterion given in (Eqs. (8.5–8.7)).

8.5.1 Onset of Adhesion/Interfacial Failure The variations of ‘e’ have been shown in Figure 8.7. It is observed that ‘e’ values are the highest at stress singularity points i.e. at the interface of main adherend and adhesive layer. Referring to Figure 8.7, it is clearly observed that the interfacial failure onset is triggered at the interface of main adherend and adhesive layer from the loaded end of bond length.

238  Structural Adhesive Joints (a)

(b)

6

0.25 0.20

4

Failure index, e

Failure index, e

5

3 2 1

0.15 0.10 0.05 0.00

20

0 0 Dist

anc10 20 e al ong 30 bon 0 d le 40 ngt h, m 50 m

(c)

5

20

–0.05

15 10 mm , dth Wi

0 Dist 10 anc e al 20 ong 30 bon 0 d le 40 ngt 50 h, m m

10

5

h,

dt Wi

15 mm

6

Failure index, e

5 4 3 2 1 0 0 Dist anc 10 e al 20 ong bon 30 d le 40 ngt h, m

10 5

m

50

0

h,

dt Wi

15 mm

20

Figure 8.7  Distributions of failure index ‘e’ in double lap joint on different interfaces between: (a) top adherend and adhesive layer, (b) the mid-surface of adhesive layer, and (c) main adherend and adhesive layer.

Failure initiation location predicted in the present research work is in qualitative agreement with experimental and numerical evidences available in published literature [16].

8.5.2 Interfacial Failure Propagation in Double Lap Joint with Mono-Modulus Adhesive The failure analyses indicate the critical locations for the onset of interfacial failure. The vulnerability of joint can be ascertained by pre-embedding the damages at the critical locations of DLJ (Figure 8.5) and, allowing these to propagate. Individual modes of SERR, GI, GII and GIII considered as fracture parameters governing the propagation of damages, have been computed

Functionally Graded Structural Adhesive Joints  239

45

45

40

40

35

35

30

GII, J/m2

GI, J/m2

using Eqs (8.10–8.12) along the interfacial damage fronts. Figures 8.8 (a-c) exhibit the variations of GI, GII and GIII with varied interfacial damage lengths ‘a’. Referring to Figures 8.8(a-c), it is observed that interfacial damage front will propagate at almost constant rate except at the edges. Near the free edges GI, GII values are significantly less compared to those values in the centre of interfacial failure front. Away from the boundary region mode III SERR (GIII) values are significantly lower. But in middle portion, damage propagation is not due to individual modes. However, it will be propagated under mixed mode. SERR values go on increasing, which indicates that structural integrity of the double lap joint will go on decreasing as the interfacial damage propagates. On comparing the individual modes of SERR, GIII is insignificant except at free edges. For increased damage length, magnitudes of GII are higher compared to GI. The contributions of GI and GII are significant for all values of interfacial damage length. Hence,

(a, mm) a=3 a=6 a=9 a = 12 a = 15 a = 18 a = 21 a = 24

25 20 15 10 5 0

30

(a, mm) a=3 a=6 a=9 a = 12 a = 15 a = 18 a = 21 a = 24

25 20 15 10 5

5 10 15 Interfacial damage front, mm (a) 9

20

0

0

5 10 15 Interfacial damage front, mm (b)

20

8 (a in mm) a=3 a=6 a=9 a = 12 a = 15 a = 18 a = 21 a = 24

GIII, J/m2

7 6 5 4 3 2 1 0

0

5 10 15 Interfacial damage front, mm (c)

20

Figure 8.8  Variation of individual modes of SERR along the interfacial damage front for varied pre-embedded damage lengths ‘a’ at the interface of main adherend and adhesive: (a) GI , (b) GII, and (c) GIII.

240  Structural Adhesive Joints it can be said that interfacial damage propagates under mixed mode condition. Therefore, total SERR, GT is considered as the governing parameter for interfacial damage propagation. The desirable intention of the double lap joint designer is to retard interfacial damage propagation rate in order to enhance the structural integrity of the joint. As a result, the strength and lifetime of the joint structure can be significantly improved. In the present research, efforts were made to retard interfacial damage propagation rate by employing a functionally graded adhesive along the bondline. The effects of graded bondline on propagation rate are extensively discussed in the next section.

8.5.3 Interfacial Damage Propagation in Functionally Graded Double Lap Joint In the present work, modulus of adhesive is continuously and smoothly varied along the bondline using appropriate linear function profile (Eqs. 8.1 & 8.2). As reported earlier in section 8.5.1, it is expected that failure initiation will take place at the interface of main adherend and adhesive layer from the loaded ends of bond length. Figures 8.9(a-d) exhibit the total SERR (GT) variations with modulus ratios R = 1, 2, 5, 8 for varied interfacial failure lengths a = 3 to 24 mm. It is observed that interfacial failure propagation rate (GT) is curving towards the free edges of failure front. This behaviour with graded adhesive is found to be similar to mono-modulus adhesive (R = 1). Referring to Figures 8.9(a) – (d), it can be noted that the total SERR (GT) values for smaller damage length are continuously decreasing for varied graded material properties of the adhesive. On the other hand, it is also observed that damage growth driving forces for higher damage length are continuously increasing with respect to modulus ratio. This behaviour is in qualitative agreement with the results observed by Ravi Chandran and Barsoum [29] for crack growth analysis of graded plates. Exact reductions in the magnitudes of SERR at the middle of interfacial damage front due to use of graded adhesive with varied modulus ratios are clearly indicated in Figure 8.10. Here total SERR (GT) is normalized by GT,homo. GT,homo stands for total G with homogeneous adhesive material. This normalized value is plotted against the material non-homogeneity parameter i.e. modulus ratio (R). value at the middle of interfacial damage front with non-homogeneously graded adhesive material is smaller than that of the homogeneous adhesive material. As the material non-homogeneity increases, the difference between GT and GT, homo increases. For a specific value of modulus ratio R, the effect of material gradation of adhesive on

120

120

110

110

100

100

90

90

80

80

70 60

a=3 a=6 a=9 a = 12 a = 15 a = 18 a = 21 a = 24

50 40 30 20 10

0

70 60

30 20 10

20

0

5 10 15 Interfacial damage front, mm

(a)

20

(b) 120

110

110

100

100

90

90

80

80 GT, J/m2

70 60 50 40 20 0

70 60 50 40

(a in mm) a = 15 a=3 a = 18 a=6 a = 21 a=9 a = 24 a = 12

30 10

a=3 a=6 a=9 a = 12 a = 15 a = 18 a = 21 a = 24

50 40

5 10 15 Interfacial damage front, mm

120

GT, J/m2

GT, J/m2

GT, J/m2

Functionally Graded Structural Adhesive Joints  241

a=3 a=6 a=9 a = 12

30 20 10

5 10 15 Interfacial damage front, mm

20

0

a = 15 a = 18 a = 21 a = 24

5 10 15 Interfacial damage front, mm

(c)

20

(d)

Figure 8.9  Total SERR, GT along the interfacial damage front for varied pre-embedded interfacial damage lengths ‘a’ in a functionally graded adhesively bonded double lap joint with various modulus ratios R: (a) R = 1, (b) R = 2, (c) R = 5, (d) R = 8. 1.6

GT/GT, homogeneous

1.4 1.2 1.0 0.8

a = 3mm a = 6mm a = 9mm a = 12mm a = 15mm a = 18mm a = 21mm a = 24mm

0.6 0.4 0.2

1

2

3

4 5 Modulus ratio, R

6

7

8

Figure 8.10  Effect of adhesive gradation on SERR(GT/GT,homogeneous) at the middle of preembedded interfacial failure front in a double lap joint for different damage lengths.

242  Structural Adhesive Joints GT is more intense for shorter interfacial damage lengths. This linear material gradient profile indicates very significant SERR reductions for shorter interfacial failure lengths, which are necessary design characteristics of functionally graded adhesives to arrest the damage growth. This behaviour of graded structure is in qualitative agreement with many researchers [35] who showed that material property gradation could cause a decrease in the magnitude of mode-I stress intensity factor under both mechanical and thermal loadings. The other researcher [36] applied strain energy density criterion to crack problem in graded materials. The effect of property gradation on critical conditions for onset of crack growth is discussed and it is shown that a graded material can offer higher resistance to crack growth and suppress crack growth in some situations. Overall, the above discussion indicates that potential use of a functionally graded adhesive can be explored widely for enhanced damage growth resistance in adhesively bonded double lap joint structure.

8.6 Conclusions Damage analysis of a functionally graded composite double lap joint structure has been carried out in order to detect the critical locations for damage onset. Subsequently, damage growth rates have been computed for varied interfacial damage lengths using MCCI method. The novelty of a functionally graded adhesive is explored in the DLJ for enhanced damage growth resistance. The following specific conclusions are drawn based on results and observations made for the damage in the double lap joint structure: • The interfaces of main adherend and adhesive layer from the loaded ends of horizontal bondline are found to be critical locations for damage onset in the double lap joint. • Interfacial damage propagates under mixed mode condition. The SERRs variation along the interfacial damage front is constant along the width of the joint except at the free edges. The rate of interfacial damage growth propagation in the central portion of the double lap joint is higher than that at the free edge. • A functionally graded adhesively bonded double lap joint reveals significant reduction in damage growth driving forces (SERRs) compared to that for mono-modulus adhesive.

Functionally Graded Structural Adhesive Joints  243 • For a specific value of modulus ratio R, the effect of functionally graded adhesive on total SERR is more intense for shorter interfacial damage lengths. Material gradient profile of adhesive indicates significant SERR reduction for shorter interfacial damage lengths, which is a necessary design characteristic for a functionally graded adhesive to delay the damage growth. • A functionally graded double lap joint offers significant damage growth resistance. Hence a double lap joint with a functionally graded adhesive is recommended to the joint designer to prolong service life of structure.

References 1. G. Kelly, Quasi-static strength and failure life of hybrid (bonded/bolted) composite single-lap joints, Composite Structures 72, 119–129 (2006). 2. K.D Potter, F.J. Guild, H.J. Harvey, M.R. Wisnom and R.D. Adams, Understanding and control of adhesive crack propagation in bonded joints between carbon fiber composite adherends, Intl. J. Adhesion Adhesives 21, 435–443 (2001). 3. A.T. Liu, Linear elastic and elasto-plastic stress analysis for adhesive lap joints, TAM Report no. 410 University of Illinois at Urbana-Champaign (1976). 4. R.D. Adams and N.A. Peppiatt, Stress analysis of adhesively bonded lap joints, J. Strain Anal. 9, 185–196 (1974). 5. A.K. Pickett and L. Hollaway, The analysis of elastic adhesive stresses in bonded lap joints in FRP structures, Composite Structures 3, 55–79 (1985). 6. J.N. Reddy and S. Roy, Non-linear analysis of adhesively bonded joints. Intl. J. Non-Linear Mech. 23, 97–112 (1988). 7. G.N. Sage, Some aspects of bonded joint design in CFRP, J. Composite Mater. 7, 256–260 (1976). 8. L.J. Hart-Smith, Adhesive-Bonded Double Lap Joints. NASA-CR-112235 (1973). 9. L. Tong, Bond shear strength for adhesive bonded double-lap joints. Intl. J. Solids Structures 31, 2919–2931 (1994). 10. R.D. Adams, R.W. Atkins, J.A. Harris and A.J. Kinloch, Stress analysis and failure properties of carbon fiber reinforced plastics/steel double lap joints, J. Adhesion 20, 29–53 (1986). 11. O. Volkersen, Die niektraftverteiling in zugbeanspruchten mit konstanten Laschenquerscritten, Luftfahrtforschung 15, 41–47 (1938). 12. R.D. Adams and W.C. Wake, Structural Adhesive Joints in Engineering, Elsevier Science Publishing Company, United Kingdom (1984).

244  Structural Adhesive Joints 13. L. Tong, A. Sheppard and D. Kelly, The effect of adherend alignment on the behaviour of adhesively bonded double lap joints. Intl. J. Adhesion Adhesives 16, 241–247 (1996). 14. L. Tong, A. Sheppard and D. Kelly, Relationship between surface displacement and adhesive peel stress in bonded double lap joints, Intl. J. Adhesion Adhesives 15, 43–48 (1995). 15. E. Altus, Three-dimensional singularities in double lap joints, Eng. Fracture Mech. 21, 1098-1112 (1985). 16. S.K. Panigrahi and B. Pradhan, Onset and growth of adhesion failure and delamination induced damages in double lap joint of laminated FRP composites, Composite Structures 85, 326–336 (2008). 17. S.W. Tsai, and E.M. Wu, A general theory of strength for anisotropic materials, J. Composite Mater. 5, 58–80 (1971). 18. I. Pires, L. Quintino, J.F. Durodola and A. Beevers, Performance of biadhesive bonded aluminum lap joints, Intl. J. Adhesion Adhesives 23, 215– 223 (2003). 19. M.D. Fitton and J.G. Broughton, Variable modulus adhesives: an approach to optimized joint performance, Intl. J. Adhesion Adhesives 25, 329–336 (2005). 20. S. Temiz, Application of bi-adhesive in double-strap joints subjected to bending moment, J. Adhesion Sci. Technol 20, 1547–1560 (2006). 21. H. Ozer and O. Oz, Three dimensional finite element analysis of biadhesively bonded double lap joint, Intl. J. Adhesion Adhesives 37, 50–55 (2012). 22. S. Kumar, Analysis of tubular adhesive joints with a functionally modulus graded bondline subjected to axial loads, Intl. J. Adhesion Adhesives 29, 785–795 (2009). 23. S. Kumar and J.P. Scanlan, Stress analysis of shaft-tube bonded joints using a variational method, J. Adhesion 86, 369–394 (2010). 24. S.E. Stapleton, W.M. Waas and S.M. Arnold, Functionally graded adhesives for composite joints, Intl. J. Adhesion Adhesives 35, 36–49 (2012). 25. R.J.C. Carbas, L.F.M. da Silva and G.W. Critchlow, Adhesively bonded functionally graded joints by induction heating, Intl. J. Adhesion Adhesives 48, 110–118 (2014). 26. S.V. Nimje and S.K. Panigrahi, Strain energy release rate based damage analysis of functionally graded adhesively bonded tubular lap joint of laminated FRP composites, J. Adhesion 93, 389–411 (2017). 27. S.V. Nimje and S.K. Panigrahi, Effects of functionally graded adhesive on failures of socket joint of laminated FRP composite tubes, Intl. J. Damage Mech. 26, 1170–1189 (2016). 28. L.F.M. Da Silva and R.D. Adams, Joint strength predictions for adhesive joints to be used over a wide temperature range. Intl. J. Adhesion Adhesives 27, 362–379 (2007).

Functionally Graded Structural Adhesive Joints  245 29. K.S. Ravi Chandran and I. Barsoum, Determination of stress intensity factor solutions for cracks in finite-width functionally graded materials. Intl. J. Fracture 121, 183–203 (2003). 30. L. Tong and G.P. Steven, Analysis and Design of Structural Bonded Joints. Kluwer Academic Publishers (1999). 31. S.V. Nimje and S.K. Panigrahi, Numerical simulation for stress and failure functionally graded adhesively bonded tee joint of laminated FRP composite plates, Intl. J. Adhesion Adhesives 48, 139–149 (2014). 32. G. Analas, J. Lambros and M.H. Santare, Dominance of a asymptotic cracktip fields in elastic functionally graded materials, Intl. J. Fracture 115, 193– 204 (2002). 33. L.F.M. Da Silva and R.D. Adams, Joint strength predictions for adhesive joints to be used over a wide temperature range, Intl. J. Adhesion Adhesives 27, 362–379 (2007). 34. R.D. Adams, Strength predictions for lap joints, especially with composite adherends: A review. J. Adhesion 30, 219–242 (1989). 35. B. Yildirim, S. Dag and F. Erdogan, Three dimensional fracture analysis of FGM coatings under thermo-mechanical loading. Intl. J. Fracture 132, 369– 395 (2005). 36. N. Jain, C.E. Rousseau and A. Shukla, Crack-tip stress fields in functionally graded materials with linearly varying properties. Theo. Appl. Fracture Mech. 42, 155–170 (2004).

9 Impact, Shock and Vibration Characteristics of Epoxy-Based Composites for Structural Adhesive Joints Bikash Chandra Chakraborty1* and Debdatta Ratna2 1

Formerly Scientist, Naval Materials Research Laboratory, Defence Research & Development Organisation, India 2 Naval Materials Research Laboratory, Defence Research & Development Organisation Shil-Badlapur Road, P.O. Anand Nagar, Additional Ambernath, India

Abstract

In order to qualify an epoxy-based composition as a structural adhesive which can withstand shock, impact or vibration, it is essential to tailor the cross-linked matrix appropriately. Toughness with adequate strength is desired to qualify an adhesive for structural application. In this chapter, different types of flexible cured epoxy compositions and nanoclay composites of some flexible epoxies are discussed in relation to their dynamic mechanical properties and have correlated these properties to vibration, impact and shock sensitivity. Improvement of toughness and flexibility of epoxy resin by physical or chemical addition of liquid rubbers, or using long chain epoxy and/or long chain amine and also the effect of incorporation of nanoparticle are discussed with examples. Impact energy of a few flexible epoxy compositions is discussed. A brief discussion on dynamic mechanical properties with relevant mathematical expressions is included with numerical and graphical representations. Subsequently, mathematical models for vibration sensitivity of adhesive joints are discussed. The damping study is restricted here only to sandwich construction of simple rigid beams. A method of testing the vibration sensitivity for a sandwich beam is included. Mathematical expressions for shock response of beams bonded with some flexible epoxy-based adhesives are discussed with the numerical and graphical representations. For simplicity, only half sine

*Corresponding author: [email protected] K.L. Mittal and S. K. Panigrahi (eds.) Structural Adhesive Joints: Design, Analysis and Testing, (247–288) © 2020 Scrivener Publishing LLC

247

248  Structural Adhesive Joints wave is considered as a shock pulse. The Shock Response Spectra for an undamped and adhesive bonded damped system are also shown as a frequency domain plot. Keywords:  Flexible epoxy, adhesive, nanocomposite, dynamic mechanical property, vibration, shock, impact, damping

Descriptions of Abbreviations Abbreviation

Description

ATBN

Amine terminated poly(butadiene acrylonitrile)

CL

Constraining layer

CLD

Constrained layer damping

CTBN

Carboxyl terminated poly(butadiene acrylonitrile)

CTPEGA

Carboxyl terminated poly(ethylene glycol) adipate

CTPEHA

Carboxyl terminated poly(ethyl hexyl acrylate)

dB

Decibel (a unit to define power ratio)

DGEBA

Diglycidyl ether of bisphenol-A

DMA

Dynamic mechanical analysis/analyser

DSA

Dynamic signal analyser

FFT

Fast Fourier Transform

FRP

Fibre reinforced plastic

GPa

Giga Pascal

GRP

Glass reinforced plastic

HTPB

Hydroxyl terminated polybutadiene

KV

Kelvin -Voigt

MMT

Montmorillonite (clay)

MPa

Mega Pascal

MS

Mild steel

OMMT

Organically modified montmorillonite

Pa

Pascal (N/m2)

Characteristics of Epoxy-Based Composites  249 phr

Parts per hundred parts of resin (by weight)

SRS

Shock Response Spectra

WLF

Williams, Landel & Ferry

Symbols with Units Symbol Description A A constant in Duhamel integral for shock response aT Shift factor b Width of a beam C1 Constant in WLF equation for shift factor C2 Constant in WLF equation for shift factor E Young’s modulus Ea Activation energy of relaxation Dynamic or Storage modulus Eʹ Loss modulus Eʺ E0 Dynamic modulus in rubbery region Dynamic modulus in glassy region E

dimensionless m dimensionless K N/m2 J/mol N/m2 N/m2 N/m2 N/m2

fn ∆f G* g Hij h I L KIC kn

Hz Hz N/m2 m/s2 dimensionless m m4 m MPa.m0.5 dimensionless

Mn

m

Natural frequency -3 dB bandwidth Complex shear modulus Acceleration due to gravity Thickness ratio i=1,2, j=3 Thickness of beam or adhesive layer Moment of inertia Length of beam Critical stress intensity factor A constant in the equation for natural frequency Number average molecular weight of polymers mass

Unit dimensionless

g/mol kg

250  Structural Adhesive Joints R T Tg Tref t tc u u u

V1, V2 w α α1,3 δ η0 ηs ψ23

0

ω ωd ωn ξ

Universal gas constant Temperature Glass transition temperature Reference temperature (1) Thickness of vibrating beam (2) time Thickness of constraining layer Displacement Velocity Acceleration Intensity of vibration (e.g. acceleration) Mass per unit length Response (displacement) of an element under shock Ratio of Young’s modulus of constraining layer and that of the vibrating beam Phase angle Viscoelastic loss factor of adhesive System loss factor Shear parameter (1) Relaxation time (2) duration of shock pulse A constant in Arrhenius expression for ­relaxation time Angular frequency Damped natural frequency Undamped natural frequency Damping factor

J/mol.K ºC, K ºC, K ºC, K (1) m (2) s m m m/s m/s2 Volts kg/m m dimensionless rad dimensionless dimensionless dimensionless (1) s (2) s s rad/s rad/s rad/s dimensionless

9.1 Introduction Epoxy resins have been known as structural adhesives since the 1950s [1, 2]. The overwhelming choice of this resin is due to its easy curing process, high polar forces of adhesion, sufficient mechanical strength, capability

Characteristics of Epoxy-Based Composites  251 to retain its integrity in various hostile environments [3–8] and excellent applicability in any contour of a structure. This resin is useful as adhesive for a large variety of structural substrates [9–14]. However, most structures, under service, experience either shock, impact force, and/or continuous vibration. The shock or impact load may result in catastrophic failure of a structural adhesive joint and a steady state vibration may result in fatigue failure of the joint. Therefore, the adhesive joint has to be sufficiently tough so that it can absorb sufficient impact energy. In continuous vibration, it should have sufficient hysteresis loss in wide frequency and temperature ranges as required for the service conditions. Cured epoxy resins are quite strong in mechanical deformation but suffer from brittleness depending on the cross-link density which is determined by the molecular size and functionalities of the reacting species, viz. epoxy and amine hardener. The brittleness also results in low peel strength of the adhesive layer. Typically, a liquid epoxy precursor based on diglycidyl ether of bisphenol-A (DGEBA) having molecular weight of 470 and functionality of 2, and a diamine of molecular weight 145 and functionality of 4 are used to make a strong cured thermoset resin. The resulting thermoset is, however, hard and brittle. Therefore, various methods are used to impart toughness to the epoxy resin with an optimum balance of mechanical strength and viscoelastic loss property. The toughening of epoxy resin has been reported since the 1970s [15–21]. A very detailed review of the literature on toughening processes is written by Hodgkin et al. [22]. Further developments in this area are abundantly available in literature and need not be mentioned here in detail. However, hyperbranched polymers, organically modified nanoclays, carbon nanotubes, reactive oligomers, high molecular weight epoxy resin and polyetheramine etc. are being used to develop strong and tough epoxy matrix [23–28]. The use of an oligomer as a flexibiliser or use of a longchain molecule generally reduces the inherent strength. However, recent advancements in polymer-clay nanocomposites and nanocarbons, derivatives of graphene and other nanoparticles have been found to be effective in augmenting the strength without much compromise in toughness. In order to qualify an adhesive which can withstand low or high cycle fatigue, shock/impact force or transient vibration, it is essential to design the cross-linked matrix appropriately, analyse the thermophysical and dynamic thermomechanical properties in wide frequency and temperature ranges. The basic requirement of a matrix to be tough is that the glass transition temperature (Tg) must not be very far from the service temperature. For example, if an adhesive is used at 35°C, the Tg must be around this temperature. This is because near the Tg, the polymer segments can move and a part of the applied force is dissipated due to the internal friction of the segments

252  Structural Adhesive Joints as they try to move past each other. The damping is considered as the energy lost due to the time-dependent strain and internal friction, when a dynamic force is applied. The ability to absorb the strain energy is directly dependent on the chemical structure and thermodynamic state of the molecule. In addition, the time period of the applied dynamic force plays an important role in the extent of damping depending on whether the time of relaxation is comparable to it or not. Coinciding the relaxation time with the time period of oscillation of the dynamic force results in maximum possible damping. In general, a high frequency vibration requires a soft material with very fast relaxation process (low relaxation time) and a low frequency vibration needs harder material with slow relaxation process (higher relaxation time). Therefore, for the shock pulse of very small duration, the damping material should have nearly the same relaxation time (fast process) as the shock pulse. On the other hand, steady state vibration is a continuous process, and may cover a wide range of frequency. The relaxation in transient and continuous vibration is adjusted according to the frequency range. However, the energy required to withstand a dynamic force as shock or impact depends much on the dynamic elastic modulus and also on the viscoelastic loss factor. The damping is determined by three main parameters of the adhesive layer – dynamic modulus in any mode of deformation, the loss factor, and the thickness of the layer. The damping in an adhesive layer in between two rigid substrates is caused by shear deformation as a result of conversion from transverse to lateral strain. This is termed as constrained layer damping (CLD). All adhesive joints essentially behave as a CLD system. In this chapter, the dynamic viscoelastic behavior of polymers is discussed with special reference to the epoxy based toughened adhesives which are promising materials as structural adhesives. Few mathematical expressions on the quantitative damping are discussed with examples of some epoxy-based compositions to demonstrate the extent of shock/­ vibration mitigation by the adhesive layer.

9.2 Dynamic Viscoelasticity Polymers are neither perfectly elastic solids nor viscous liquids, but behave as combination of these two, and are termed as “viscoelastic”. Under an external force, a polymer experiences an instant strain as the elastic response and a time-dependent strain as the viscous response. The elastic strain is directly proportional to the stress and the viscous strain rate (time derivative of strain) is directly proportional to the stress. Hence, a physical

Characteristics of Epoxy-Based Composites  253 interpretation of a polymer can be either a summation of two strains or summation of two stresses as described by Maxwell’s model and by KelvinVoigt (KV) model, respectively. In these basic models, the elastic part is represented by a spring, having a spring constant independent of time, and a dashpot where the strain increases with time at a constant stress, so that the strain rate is directly proportional to the stress. In Maxwell’s model, the spring and the dashpot are arranged in series, so that the Maxwell body behaves as a viscoelastic liquid and in KV model, the spring and dashpot are arranged in parallel, so that the KV body behaves as a viscoelastic solid. The basic Maxwell model describes the stress relaxation and defines relaxation time of a polymer, while the basic KV model describes the creep phenomenon and defines retardation time of a polymer. Stress relaxation arises from the tendency of the segments to minimize the instantaneous stress at a constant strain through the segmental motion. Retardation arises from the tendency of the molecule to deform continuously under a constant stress as the segments can move. Obviously, these phenomena can only be exhibited by a polymer above its glass transition temperature, since in the glassy state, the segmental mobility is frozen. However, neither of these two models truly represents a real polymer. There are many models developed with spring and dashpot in different combinations to predict the behaviour of a real polymer. Three-parameter Zenner model and four-parameter Berger model are among the mostly used ones. There are, in addition, semi-empirical models too for describing nearly accurately the viscoelastic behavior of polymers. Considering dynamic loading on a polymer, such models yield some useful expressions for dynamic modulus, loss modulus and loss factor with respect to frequency. Considering Zenner model of a typical viscoelastic solid body, these are expressed as:

E0 + ω 2τ 2 E∞ Dynamic or Storage Modulus:  E ′ = (9.1) 1 + ω 2τ 2

ωτ ( E∞ − E0 )



Loss Modulus:  E ′′ =



and Loss Factor:  tan δ =

1 + ω 2τ 2

(E

∞

)



− E0 ωτ

E0 + E∞ω 2τ 2

(9.2)



(9.3)

254  Structural Adhesive Joints where, E0 = Elastic modulus in rubbery region (ω→0)   E∞ = Elastic modulus in glassy region (ω→ )    ω = angular frequency     τ = relaxation time The relaxation time is defined as the time required for a molecule to reduce the stress to (1/e) of the original (instantaneous) stress at a constant strain. The dynamic properties are dependent on temperature as the relaxation time follows an Arrhenius type relationship with temperature (T) as:

 E  τ = τ 0 exp  a   RT 



(9.4)

where, τ0 is a constant, Ea is the activation energy of relaxation process, R is universal gas constant and T is the temperature in K. On substituting Eq. 9.4 in Eqs. 9.1, 9.2 and 9.3, temperature dependence of the dynamic properties can be obtained at any constant frequency. The effect of temperature is exactly opposite to the effect of frequency on the dynamic properties. The dynamic or storage modulus grows with increasing frequency at a constant temperature but diminishes with increasing temperature at constant frequency. The temperature and frequency (inverse of time) are related mathematically by Eq. 9.4 as well as by an expression by Williams, Landel & Ferry (WLF) [29]. The expression defines a shift factor, which is used to relate a set of frequency and temperature to another set for the same values of the dynamic viscoelastic properties. The expression assumes that the free volume of a polymer is constant below the glass transition temperature and increases linearly above this temperature, so that the volume expansion coefficient is constant until any melting or flow takes place. Therefore, the WLF equation is valid for temperature above the glass transition. The equation is expressed as:



( (

) )

 τ  −C1 T − Tref log aT = log  =  τ ref  C2 + T − Tref

( )

(9.5)

Where τ denotes relaxation time and C1, C2 are constants. The values of these constants are: C1 = 17.44 and C2 = 51.6 when the reference temperature Tref = Tg and C1 = 8.86 and C2 = 101.6 at Tref = Tg + 50

Characteristics of Epoxy-Based Composites  255 The Arrhenius equation (Eq. 9.4) can also be used to calculate the shift factor as follows:



 τ log aT = log   τ ref

( )

 Ea  1 1  = R T −T   ref

  

(9.6)

The above Eq. 9.4 and Eq. 9.6 are also valid when the polymer is in random motion, which is possible above the glass transition.

9.2.1 Example An epoxy resin cured with a diamine has the following parameters. E0 = 2x108 N/m2 E∞ = 4x109 N/m2 R = 8.314 J/mol.K Ea = 240 kJ/mol. τ = 600 s at 30°C a. Construct the Eʹ, Eʺ and tanδ vs. frequency curves for 30°C fixed temperature. b. Construct the Eʹ, Eʺ and tanδ vs. temperature curves for 1 Hz fixed frequency. Solution: a. For calculating Eʹ, Eʺ and tanδ at various frequencies, Eq. 9.1 to Eq. 9.3 were used with T = 303 K (i.e. 30°C). Hence τ is taken as 600 s. Frequencies from 10-5 Hz are taken to show the dependence of Eʹ on frequency. The values obtained for the dynamic properties are plotted in Figure 9.1. The Eʹ assumes the value of E∞ at 10-3 Hz. The loss factor peak appears at a lower frequency compared to the loss modulus peak, which is also observed for real polymers. It can be noted that the peak loss factor (and loss modulus) frequency is very low, of the order of 7x10-5 Hz (about 3x10-3 Hz for loss modulus peak). The dynamic modulus Eʹ assumes the maximum value E∞ in the glassy region above 10-3 Hz. b. For calculating Eʹ, Eʺ and tanδ at various temperatures, the τ0 as per Eq. 9.4 is used andτ at 30°C is taken as 600 s. Substituting Eq. 9.4 in Eqs. 9.1 to 9.3, we obtain the dynamic

256  Structural Adhesive Joints properties at various temperatures from 290 K to 400 K and are plotted in Figure 9.2. Eʹ assumes the value of E0 at a temperature of about 345 K (72°C). The loss factor peak appears at a higher temperature than the loss modulus peak.

2.50 3.0E+09 2.00

E"

3.0E+08

Loss factor 3.0E+07

1.50

1.00

3.0E+06

Loss factor

E', E" (N/m2)

E'

0.50

3.0E+05 1.0E-05

1.0E-03

1.0E-01 Frequency, Hz

1.0E+01

0.00

Figure 9.1  Frequency dependence of dynamic mechanical properties: Storage Modulus (Eʹ); Loss Modulus (Eʺ) and Loss factor at 30ºC fixed temperature: theoretical (Example 9.2.1, Section 9.2). 2.50 E'

3.0E+09

2.00

Loss factor

3.0E+08

1.50

3.0E+07

1.00

3.0E+06

3.0E+05 290

0.50

310

330

350 370 Temperature, K

390

0.00 410

Figure 9.2  Temperature dependence of dynamic mechanical properties: Storage Modulus (Eʹ); Loss Modulus (Eʺ) and Loss factor at 1 Hz fixed frequency: theoretical (Example 9.2.1, Section 9.2).

Loss factor

E', E" (N/m2)

E"

Characteristics of Epoxy-Based Composites  257 4.0E+09

0.7 E'

0.6

E" 0.5 0.4 4.0E+08 0.3

Loss factor

E', E" (N/m2)

Loss factor

0.2 0.1 4.0E+07

30

50

70

90

110 130 Temperature, ºC

150

170

0 190

Figure 9.3  Temperature dependence of dynamic mechanical properties at 1 Hz fixed frequency for a typical cured epoxy resin.

From Figures 9.1 and 9.2, it can be observed that the nature of the dynamic properties is approximately similar as in experimental results with real cross-linked epoxy resin. However, an epoxy sample having similar glassy modulus is shown in Figure 9.3 for comparison. The measurement was done with varying temperature at a fixed frequency of 1 Hz.

9.3 Toughened Epoxy Resins A variety of flexible adhesives are made from conventional epoxy resin, either physically mixed or chemically reacted with a liquid rubber such as polyamide, hydroxyl terminated polybutadiene, carboxyl terminated, or amine terminated nitrile rubber (oligomer), etc. The advantage of such products is that there can be very distinct microscale phase separation, and the soft segments enhance the impact energy and toughness. This is observed for both physically mixed or chemically reacted liquid rubbers. A large variety of commercial flexible epoxy adhesives are available for bonding wood, glass, metals, plastics, etc. Mostly these are combinations of long chain epoxy resin and long chain amines. For example, a conventional epoxy resin has an epoxy equivalent weight of 185-200. For a long chain epoxy resin, the molecular weight can be even 2000 or more but those with molecular weight of about 6000 are solid and need a solvent for curing reaction to take place with amines. For the amines, a particular type of polyetheramine, commercially available as ‘Jeffamine’, is available in a wide

258  Structural Adhesive Joints range of number average molecular weights 300 to 900, which can be used as hardeners to yield hard to very soft and flexible cured epoxy products even with conventional epoxy resin of low molecular weight. In addition, recent developments in nanoscale materials are being used for improvement in toughness and strength simultaneously. Nanoclays such as montmorillonites, fumed silica, nanocarbons, graphene are mostly used. The nanoclays are intercalated and, to some extent, exfoliated when the epoxy oligomers enter the gallery of the layers of the clay and upon curing with hardener, the morphology is fixed as a well distributed polymer segments in the clay structure. This enhances shock/vibration damping and strength simultaneously. However, for a densely cross-linked thermoset, the effect is not pronounced. In case of platelet nanomaterials and nanofibres, the external dynamic stress, beyond a critical value, enables the polymer chains to slip past the fibre-polymer interface reversibly to enhance the strain related energy consumption, which means that both damping and impact energy are enhanced. The examples of such epoxy modifications and flexible epoxy adhesives are described below.

9.3.1 Toughening Agents for Epoxy The most common toughening process for epoxy resin is to add a low molecular weight rubber-like flexibiliser, which may or may not take part in cross-linking reaction with the epoxy or the amine hardener. Non-reactive species are less preferred due to their complete phase separation after curing. However, these additives are also reported to be effective in improving fracture toughness and impact energy. The incorporation of bitumen is found to enhance flexibility of epoxy resin as reported by Zavareh and Vahdat [27]. The authors have shown that only 2% bitumen addition improved the impact energy and fracture toughness by 3 times, while the mechanical strength, elongation and elastic modulus remained unchanged. Inclusion of polyetherimide in epoxy resin shows a two-phase system as seen by two distinct peaks in DMA loss factor (tan and also increased fracture toughness (KIC value) 2.5 to 3 times [17]. Reactive species also undergo phase separation after curing, but in a microscale. Rubbery modifiers with reactive functional groups such as carboxyl-terminated copolymer of butadiene and acrylonitrile (CTBN) or amine terminated copolymer of butadiene and acrylonitrile (ATBN) are generally used in the liquid form to ensure easy miscibility with epoxy resin. Liquid nitrile rubber with various functional groups has been investigated and maximum improvement in bond strength was observed for carboxyl groups due to

Characteristics of Epoxy-Based Composites  259 formation of epoxy-ester groups which contribute to polar interaction [30]. Such two-phase morphology drastically enhances both the fracture toughness and impact energy. Similarly, carboxyl terminated poly(2-ethyl hexyl acrylate) (CTPEHA) oligomer of average molecular weight 3600-9500 is also reported for use as a reactive flexibiliser in epoxy resin [31]. The glass transition temperature measured by DSC was seen to be 95°C with 30 phr CTPEHA ( Mn = 3600) as compared to 115°C for original epoxy resin. A typical DMA curve of the loss factors of the neat and CTPEHA modified epoxies is shown in Figure 9.4. The loss factor improved with CTPEHA content and is highest for 20 phr CTPEHA. However, the temperature of loss peak is somewhat reduced from 139°C to about 131.4°C and for 30 phr CTPEHA, it is about 124°C, which are quite high for ambient temperature use of the toughened adhesive. The damping is expected to be higher for such modified epoxy adhesives compared to the neat epoxy resin. The authors have shown that the impact energy for 10 phr CTPEHA is highest and the improvement over unmodified epoxy matrix was about 80%. The impact energy of the unmodified epoxy was lowest. 1 0 phr CTPEHA

0.9

10 phr CTPEHA 20 phr CTPEHA

0.8

30 phr CTPEHA

Loss factor

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

50

70

90

110 Temperature, °C

130

150

170

Figure 9.4  Dependence of dynamic viscoelastic loss factor of epoxy modified with varying contents of carboxyl terminated poly(ethyl hexyl acrylate) (CTPEHA). Reproduced from [31]. D. Ratna, A.K. Banthia and P.C. Deb, Acrylate-based liquid rubber as impact modifier for epoxy resin, J. Appl. Polym. Sci. 80, 1792–1801 (2001). With permission from Publisher- John Wiley & Sons.

260  Structural Adhesive Joints The impact energy is directly proportional to the loss modulus (product of dynamic modulus and loss factor) of a polymer at ambient temperature, since loss modulus represents the strain energy absorbed by the polymer under dynamic loading [32]. The dynamic modulus near ambient temperature (35°C) for 10 phr CTPEHA modified epoxy was about 20 to 30 percent higher than other compositions, while the loss factors were almost identical (about 0.03). It seems that the correlation with loss modulus is not accurate. There are reports where the impact energy is correlated to various dynamic mechanical properties such as relative difference in dynamic modulus at glassy and rubbery states [33], area under the loss factor peak [34], the quantitative values of the loss factor (damping) peak and temperature or frequency of the peak [35]. Similarly, a reactive liquid rubber carboxyl terminated poly(ethylene glycol) adipate (CTPEGA) was introduced into the epoxy resin at different contents and the dynamic loss factor showed increasingly higher loss factor peak value and peak area along with reduction in the temperature of peak loss factor. Figure 9.5 shows the DMA curves of neat and CTPEGA modified epoxy containing 10, 20 and 30 phr CTPEGA. The effect of CTPEGA modifier on impact energy of epoxy resin (LY556) is shown in Figure 9.6. It is seen that the impact energy is highest for 20 phr CTPEGA. 0.8 0.7

0 phr CTPEGA 10 phr CTPEGA 20 phr CTPEGA 30 phr CTPEGA

0.6

Loss factor

0.5 0.4 0.3 0.2 0.1 0

40

60

80

100 Temperature, °C

120

140

160

Figure 9.5  Dependence of dynamic viscoelastic loss factor of modified epoxy on varying contents of carboxyl terminated poly(ethylene glycol) adipate (CTPEGA). Reproduced from: D. Ratna, B.C. Chakraborty and P.C. Deb, Carboxyl terminated poly(ethylene glycol) adipate modified epoxy network 1. Synthesis and thermal characterisation, J Polym Mater, 14(2) 189 (1997).

Characteristics of Epoxy-Based Composites  261 35 33

Impact energy (J/m)

31 29 27 25 23 21 19 17 15 0

10

20

30

40

50

CTPEGA Content (phr)

Figure 9.6  Effect of carboxyl terminated poly(ethylene glycol) adipate (CTPEGA) modifier on the impact energy of cured epoxy resin. Reproduced from [21]. D. Ratna, A.B. Samui and B.C. Chakraborty, Flexibility improvement of epoxy resin by chemical modification, Polym. Int. 53, 1882–1887 (2004). With permission from the publisher John Wiley & Sons.

The effect of the molecular weight of the modifier is also important in flexibilising epoxy resin. As usual, lower molecular weight is more effective, but the associated reduction of strength and lowering of glass transition are of concern for structural adhesives. The effect of CTPEGA molecular weight on flexibilising of epoxy is studied by Ratna and coworkers [36]. The intermediate molecular weight of about 4000 is seen to be most effective. Figure 9.7 shows the effect of three CTPEGA modified epoxy cured resins CR-1, CR-3 and CR-5 where CTPEGA molecular weights ( Mn) were 2312, 4840 and 6775, respectively. The broadness of the loss factor peak on modification indicates a higher damping effectiveness over a wide temperature and hence over a wide frequency range. Lowering of loss factor peak temperature is higher for lower molecular weight CTPEGA. The most broadened loss peak is for the intermediate molecular weight CTPEGA (Mn = 4841) although the numerical value of the peak is much lower (0.4) compared to neat epoxy and other modified matrices. The adhesive developed by Ratna and coworkers [37] using CTPEGA modified epoxy (eq. wt.195±5) and hardener (eq.wt. 278±5) showed considerable improvement in lap shear joint strength for aluminum to aluminum (alloy B51 SWP) and T-peel strength for nitrile rubber vulcanisate to mild steel strips as can

262  Structural Adhesive Joints 0.7 Neat LY556 0.6

CR-1 CR-3

Loss factor

0.5

CR-5

0.4 0.3 0.2 0.1 0

50

70

90

110 130 Temperature, ºC

150

170

190

Figure 9.7  Effect of molecular weight on loss factor of neat cured epoxy and CTPEGA modified cured epoxy compositions. Neat LY556 mol. wt. 390; CR-1: Modified epoxy mol. wt. 4000; CR-3 : Modified epoxy mol. wt. 6200; CR-5 : Modified epoxy mol. wt. 8500. Reproduced from [36]. M. Murali, D. Ratna, A.B. Samui and B.C. Chakraborty, Synthesis, characterization, and evaluation of carboxyl-terminated poly(ethylene glycol) adipatemodified epoxy networks: effect of molecular weight, J Appl Polym Sci 103, 1723–1730 (2007). With permission from the publisher - John Wiley & Sons.

be seen from Table 9.1. Here also, the adhesion strengths of aluminium to aluminium (lap shear) and nitrile rubber to mild steel (T-peel) are highest for the 20 phr containing flexible epoxy matrix. For 40 phr CTPEGA containing epoxy, the adhesion strength is found to be lower than that of neat epoxy matrix, due to inherent low strength of the composition. Addition of isocyanate capped hydroxyl terminated polybutadiene (HTPB, Mn = 2700) as a reactive flexibiliser was used for epoxy resin (equivalent weight 204) and the impact strength was found to improve about 1.5 times compared to neat epoxy as reported by Soares et al. [38]. One of the most effective ways for improvement in toughness and strength of flexible epoxy adhesives is incorporation of nanoparticles [22–26, 39]. Extensive studies have been carried out in this area by many researchers, and the epoxy-nanoparticle interactions and properties of adhesives are discussed in detail by Taheri [40] and by Kenig et al. [41]. Organically modified montmorillonite (OMMT) clays are extensively used with low molecular weight oligomers for intercalation and exfoliation of the clay, thereby enhancing barrier properties, dynamic elastic

Characteristics of Epoxy-Based Composites  263 Table 9.1  Adhesion strength of a typical toughened epoxy.

CTPEGA content (phr)

Lap Shear Strength (Al-Al lap joint) MPa

T-Peel Strength (Nitrile rubber-Mild steel joint) kJ/m2

0 (neat epoxy)

9.70 (±1)

5.50 (±1)

10

11.10 (±1.2)

8.25 (±1.2)

20

13.50 (±1.5)

11.75 (±1.2)

30

9.30 (±1)

7.85 (±1)

40

5.95 (±1)

4.60 (±1)

Data reproduced from: D. Ratna, B.C. Chakraborty and P.C. Deb, A novel adhesive based on flexibilized epoxy resin, Paper presented in Third International Symposium on Adhesive Joints held at Providence, RI, USA on June 26-28 2002.

modulus and impact energy of the cured product. The glass transition temperature and the -relaxation frequency (in vibration) for such cured epoxy-clay nanocomposites are not much compromised compared to the virgin cured epoxy. Inclusion of carbon nanoparticles such as multiwalled and ­single-walled carbon nanotubes, carbon nanofibers, graphene and graphene derivatives greatly reinforce the cured flexible epoxy resin, thereby improving the toughness and strength. Among such nanoparticles, graphene derivatives are new addition. The epoxy matrix-graphene oxide interaction is much higher compared to graphite since graphene is a single layer laminate type particle, having much larger surface area in identical volume fraction. Yi et al. [42] used HTPB ( Mn = 2300-3500) and montmorillonite (MMT) clay to improve the impact energy of an epoxy resin (eq.wt.184189). The mechanical strength was somewhat enhanced by the addition of MMT in particular, the impact strength improved up to two-fold on using 3% HTPB and also to the same extent for a ternary composition of 10% HTPB with 1% MMT. The dynamic mechanical properties show considerable increase in loss factor broadening, and it would reflect in the frequency scale as well.

9.4 Flexible Epoxy System Flexibility can be in-built in an epoxy resin if a high molecular weight epoxy resin or the hardener is used instead of low molecular weight species, so

264  Structural Adhesive Joints

Storage Modulus, N/m2

1.0E+10 1.0E+9 1.0E+8 SD-1 SD-2 SD-3

1.0E+7 1.0E+6 1.0E+5

1

10

100 1000 Frequency, Hz (a)

10000

100000

2 SD-1 SD-2 SD-3

1.8 1.6 Loss factor

1.4 1.2 1 0.8 0.6 0.4 0.2 0 1.0E+00

1.0E+01

1.0E+02

1.0E+03 1.0E+04 Frequency, Hz (b)

1.0E+05

1.0E+06

Figure 9.8  (a) Frequency dependence of storage modulus of flexible epoxy compositions at a reference temperature of 25°C. SD-1 (LY556+Polyetheramine mol. wt. 300); SD-2 (LY556 + Polyetheramine mol. wt. 500) and SD-3 (LY556+Polyetheramine mol. wt. 800) (b) Frequency dependence of loss factor of flexible epoxy compositions at a reference temperature of 25°C. SD-1 (LY556+Polyetheramine mol. wt. 300); SD-2 (LY556 + Polyetheramine mol. wt. 500) and SD-3 (LY556+Polyetheramine mol. wt. 800). Reproduced from [45]. D. Ratna, N.R. Manoj, L. Chandrasekhar and B.C. Chakraborty, Novel epoxy compositions for vibration damping applications, Polym. Adv. Technol. 15, 583-586 (2004). Reproduced with permission from the Publisher - John Wiley & Sons.

Characteristics of Epoxy-Based Composites  265 that the cross-link density is reduced. A sprayable damping coating has been described by Sophiea et al. where mixtures of rigid and flexible epoxy resins are used [43]. The curing agents are long chain amines/dianhydrides and dicyandiamide and their derivatives. The composite loss factor is maximum 0.16 for damping of steel substrate. Hirakouchi et al. have invented a damping material based on polyester and/or epoxy/phenoxy resins having glass transition temperature varying from -60 to 0°C [44]. These compositions are suitable as adhesives with vibration damping characteristics in sandwich constructions such as constrained layer damping (CLD). Ratna et al. [45] reported a flexible epoxy containing low molecular weight epoxy (LY556) cured with polyether diamine (Jeffamine) hardener of various molecular weights. The flexibility can be tailored to enable the cured resin to absorb shock and vibration in a wide frequency range. The DMA traces of Storage modulus and Loss factor for 10-105 Hz at a reference temperature of 25°C for three such diamines having molecular weights of the polyether chain as 300, 500 and 800 taken to cure an epoxy of equivalent weight of 195±5 are shown in Figure 9.8(a) and Figure 9.8(b). The compositions are designated as SD-1, SD-2 and SD-3 having Jeffamine 300, 500 and 800, respectively. The glass transitions (denoted by loss factor peaks) are drastically different as can be seen from the figure. The loss factor of SD-1 in this frequency range was quite low (0.18 to 0.018) and the peak loss factor might be at a frequency below 1 Hz. The loss factors of SD-2 and SD-3 were found to be reasonably high in the frequency range of 10-1000Hz, SD-2 having very broad peak. The dynamic modulus values suggest that SD-1 is the highest among all and those of SD-3 and SD-2 are very strongly dependent on frequency in the vibration rage of 10 Hz to 10000 Hz.

9.4.1 Vibration Response for Joined Beams The joining of beams in several engineering structures is very common. One way of joining is to use an adhesive, strong enough to withstand the loads and tough enough to withstand prolonged vibration as well as transients such as shock. In the field of acoustic silencing and design of quiet machines, the foundation frames are often joined beams (typically I-sections and T-sections) with damping type adhesives. The vibration by the machine or the base excitations are damped at the foundation frames to some extent depending on the properties of the adhesive and other parameters. Typical split I-section and split T-section are shown in Figure 9.9. The joined beams by an adhesive are typically treated as a constrained layer damping arrangement, since the adhesive would undergo shear

266  Structural Adhesive Joints

Adhesive

I-Section

T-section

Figure 9.9  Typical structural joints used in machine foundation frames.

deformation in between the two structural hard substrates. In order to assess the attenuation of vibration by a joined beam with an adhesive, some mathematical models can be used with the basic material properties such as Young’s modulus, shear modulus, loss factors, density, dimensions, and dynamic force. Prediction of vibration response of a few flexible epoxybased adhesives and one experimental evaluation are discussed here. Storage modulus and loss factor data of SD-1 (Epoxy-Jeffamine 300), SD-2 (epoxy-Jeffamine 500) and SD-3 (epoxy-Jeffamine 800) at a reference temperature of 25ºC are used to calculate their damping capability as an adhesive for aluminium to FRP and aluminium to aluminum joints. The substrates were typical rectangular beams of length 180 mm, width 10 mm and thicknesses 6 mm and 1.5 mm. The adhesive layer was 0.50 mm thick in each case. Figure 9.10 and Figure 9.11 show the performance of the adhesives in typical damping of these joined beams. The damping is theoretically calculated as a system loss factor according to the simple equation by Nakra [46] and the system loss factor is given by:

ηs =

Hη0

3 13

(



(9.7)

) (1 + η )

(9.8)

)

(1 + α13 H ) M 2 + η02 + HM

The terms H and M are defined as:



H=

3ψ 23 1 + H13 + 2H 23 H 23

(

2

2 0

Characteristics of Epoxy-Based Composites  267

M = 1+



(

)

 ψ 23  1 + 1 1 + η02  H 23  α13 H13 

(9.9)

0.12

System loss factor

0.1 0.08 0.06 SD-1 SD-2 SD-3

0.04 0.02 0

0

500

1000

1500

2000

2500

Frequency, Hz

Figure 9.10  System loss factor in vibration of the aluminium and GRP beams bonded with flexible epoxy-based adhesives: SD-1 (LY556+Polyetheramine mol. wt. 300); SD-2 (LY556 + Polyetheramine mol. wt. 500) and SD-3 (LY556+Polyetheramine mol. wt. 800): Theoretical prediction.

0.25

SD-1 SD-2 SD-3

System loss factor

0.2 0.15 0.1 0.05 0

0

500

1000 1500 Frequency, Hz

2000

2500

Figure 9.11  System loss factor in vibration of the two aluminium beams bonded with flexible epoxy based adhesives: SD-1 (LY556+Polyetheramine mol. wt. 300); SD-2 (LY556+Polyetheramine mol. wt. 500) and SD-3 (LY556+Polyetheramine mol. wt. 800): Theoretical prediction.

268  Structural Adhesive Joints Shear parameter

23

is defined as

ψ 23 =

G∗  nπ  E3h    L



2

(9.10)

2



where, n = Mode number, L= Length of sandwich beam, G*, η0 = Complex shear modulus & loss factor of the adhesive, α13 = E1/E3, H13 = tc/h, H23 = t/h and Ei = Young’s modulus of ith layer. From theoretical predictions, it is seen that the adhesives, so designed, have system loss factors exceeding 0.1 for SD-2 and SD-3. Higher damping ability at a very low frequency is very important for large structural elements, since the natural frequencies and dominant harmonics of vibration of large, heavy structures are generally very low, within 25 Hz. However, a relatively lower damping adhesive SD-1 has an advantage of very high Young’s modulus, which is required in static structural element joints, especially where the load bearing ability is more important than any vibrational force.

9.4.2 Experimental Evaluation The aluminum-Glass reinforced plastic (GRP) joint using the same dimensions as above was experimentally evaluated for damping by a 0.5 mm thick flexible epoxy layer which was based on SD-2. Figure 9.12 shows the experimental setup for such vibration study in the laboratory. The aluminium beam is clamped as a single cantilever on a rigid stand. The beam is excited by either an instrumented hammer or an electrodynamic shaker and the vibration is picked up by an accelerometer fixed on the Accelerometer Dynamic Signal Analyser Base

Adhesive Constraining layer Force: F(t)

Figure 9.12  Experimental setup for vibration study of an adhesively bonded beam.

Characteristics of Epoxy-Based Composites  269 beam. The instrumented hammer has a force transducer and is connected to the Dynamic Signal Analyser (DSA) and a computer for data processing. The acceleration is normalized by the striking force of the hammer and expressed as g/N, where g is the acceleration due to gravity and N is the force in Newton. The vibration spectrum is obtained in time domain. Therefore, this spectrum is transformed to frequency domain by Fast Fourier Transform (FFT). The FFT output gives frequency vs. vibration intensity in g/N. After the hammer strike, the beam is under free vibration, and a vibration spectrum is obtained in time domain. The FFT is used to transform the vibration spectrum from time domain to frequency domain. The frequency domain spectrum shows several intensity peaks and the corresponding frequencies are various modes of natural frequencies (modals), e.g. f1, f2, f3 etc. Vibration damping is determined by the ‘system loss factor’ and is calculated by the following simple equation:



ηS =

∆f fn

(9.11)

where, fn = natural frequency of mode n, ∆f = frequency difference at a value of the intensity 0.707 times the peak intensity or -3 dB bandwidth when the vibration response is expressed in power ratio as shown in Eq. 9.12 below. Vibration response was measured for a frequency band of 100-5000 Hz. The response is Power ratio in dB scale which is defined as:



V  Power ratio, dB = 20 log  1   V2 

(9.12)

Where V2 is the response acceleration of the beam (in voltage) recorded. The V1 is a reference acceleration of 1cm/s2. If the beam is excited by an electrodynamic shaker, the vibration is forced vibration. The shaker sweeps the frequency from 10 Hz onwards and the vibration input to the beam and output from the beam are compared to record the intensity ratio and hence the power ratio as explained above. In this case, the difference in dB for every frequency can be taken as actual vibration attenuation. Figure 9.13 shows the vibration response of the adhesive in power ratio (dB) against frequency sweep using an electrodynamic shaker. The responses of both the bare aluminum beam and the joined beam system are plotted to find out the difference in vibration power level. There is

270  Structural Adhesive Joints 100 90 Vibration power ratio, dB

80 70 60 50 40 30 Aluminium : 6 mm

20

Al+Adhesive +GRP

10 0 –10 100

1000 Frequency, Hz

10000

Figure 9.13  Experimental vibration sensitivity of aluminium and GRP beam bonded by a flexible epoxy adhesive. Thicknesses: Aluminium: 6 mm; GRP: 1.5 mm; Adhesive: 0.5 mm.

no direct correlation between the system loss factor and dB loss, but an approximate estimate can be made from theoretical damping calculation (Figure 9.10) and dB loss by experiment (Figure 9.13). In the present case, 0.1 system loss factor corresponds to about 15dB power loss. The damping is about 10 dB to 15 dB by experiment (Figure 9.13) and correspondingly the system loss factor (Figure 9.10) is 0.06 to 0.1 for 200-5000 Hz.

9.4.3 Flexible Epoxy-Clay Nanocomposite One concern with both SD-1 and SD-2 is the low Young’s modulus, which is not desirable for large or critical applications where external force is quite dominant compared to self-weight, for example in bending and flexural vibrations of a joined beam structure. Augmentation with nanomaterials can be one solution to overcome this drawback without significant compromise in damping effectiveness. The incorporation of nanoclay in epoxy resin enhances toughness in case of flexible epoxies. A typical flexible epoxy SD-2 made with a diglycidyl ether of bisphenol A cured with a polyetheramine of molecular weight 500 was used for making epoxy-clay nanocomposite. Varying contents (1%, 5% and 7.5%) of organically modified nanoclay (amine modified Cloisite Na+ clay) was used in the epoxy and the frequency-dependent dynamic mechanical analysis at 25°C reference temperature was carried out to study the effect

Characteristics of Epoxy-Based Composites  271 of nanoclay incorporation. Figure 9.14(a) and Figure 9.14(b) show storage modulus and loss factor vs frequency. The enhancement of Young’s modulus (storage modulus at low frequency) is quite significant for 1%, 5% and 7.5% (10-37MPa) nanoclay-epoxy compared to the pure flexible epoxy SD-2 and

Storage Modulus (E'), MPa

10000

1000

1% Nanoclay

100

5% Nanoclay 7.5% Nanoclay 10

1

0

1000

2000 3000 Frequency, Hz (a)

4000

5000

1.4 1% Nanoclay

1.2

5% Nanoclay

Loss factor

1

7.5% Nanoclay

0.8 0.6 0.4 0.2 0

0

1000

2000 3000 Frequency, Hz (b)

4000

5000

Figure 9.14  (a) Frequency dependence of storage modulus of flexible epoxy compositions with varying contents of nanoclay at a reference temperature of 25°C. (b) Frequency dependence of loss factor of flexible epoxy compositions with varying contents of nanoclay at a reference temperature of 25°C.

272  Structural Adhesive Joints SD-3 (0.5-1.0MPa). The loss factor peaks are somewhat shifted to lower frequency (300-900 Hz) for 5% and 7.5% nanoclay containing compositions. The dynamic modulus and loss factor data of these nanoclay composites are used to calculate the vibration damping (system loss factor) using Eqs. 9.7 to 9.10 for 6 mm thick mild steel substrates joined to 1.5 mm thick mild steel by these 0.50 mm thick nanocomposites as adhesives. For comparison, SD-2 properties are also used to calculate the damping for this substrate joint. Figure 9.15 shows the system loss factors by these epoxy-based nanocomposites for the first five natural frequencies of the steel beam held in single cantilever mode. Similarly, two steel beams of 6 mm thickness each joined by the same adhesives are also evaluated for theoretical system loss factor using Eqs. 9.7, 9.8 and 9.9. The results are shown in Figure 9.16. The natural frequencies are calculated using the following expression [47, 48]:

fn =



kn 2π

EIg wL4

(9.13)

where, E = Young’s modulus of mild steel (207GPa). I = moment of inertia = bh3/12, w (kg/m), L, b and h are the weight per length, length, width and thickness of the beam respectively. g = acceleration due to gravity (9.81 m/s2). MS (6 mm) - MS (1.5 mm) Adhesive : 0.5 mm 0.3 5% Nanoclay

System loss factor

0.25

7.5% Nanoclay SD-2

0.2 0.15 0.1 0.05 0 100

1000 Frequency, Hz

10000

Figure 9.15  System loss factor in vibration of a 6 mm thick mild steel (MS) beam bonded to 1.5 mm thick mild steel (MS) beam by flexible epoxy SD-2 (LY556+Polyetheramine mol. wt. 500) and nanoclay composites.

Characteristics of Epoxy-Based Composites  273 MS (6 mm) - MS (6 mm) Adhesive : 0.5 mm 0.35 5% Nanoclay

System loss factor

0.3

7.5% Nanoclay

0.25

SD-2

0.2 0.15 0.1 0.05 0 100

1000 Frequency, Hz

10000

Figure 9.16  System loss factor in vibration of a 6 mm thick mild steel (MS) beam bonded to 6 mm thick mild steel (MS) beam by flexible epoxy SD-2 (LY556+Polyetheramine mol. wt. 500) and nanoclay composites.

kn is a constant, having values depending on modes (n) and is 3.52 for mode-1, 22 for mode-2, 61.7 for mode-3, 121 for mode-4, and 200 for mode-5. Accordingly, the natural frequencies are f1 = 152 Hz, f2 = 957 Hz, f3 = 2657 and f4 = 5211 Hz. The first four natural frequencies of a rigidly joined beams of 6 mm and 1.5 mm thickness are 189 Hz, 1184 Hz, 3321 Hz and 6513 Hz, respectively. For rigidly bonded beams of 6 mm + 6 mm thickness, these frequencies are 303 Hz, 1894 Hz, 5314 Hz and 10422 Hz, respectively. The corresponding adhesive bonded beams will have slightly lower natural frequencies due to the damping nature of the adhesive layer. It can be seen that the epoxy-clay nanocomposite with 5% nanoclay gives good damping, especially at lower frequency ( τ  π  u (t ) =



(9.16)

276  Structural Adhesive Joints

 πt  u0τ 2  π t  − sin for 0 < t < τ τ  π 2  τ   2 u0τ  2t   u(t ) = 2  − 1 for t > τ   π τ  u(t ) =



(9.17)

Fourier Transform of the half sine pulse as in Eq. 9.15 is given by:

Acceleration, a(t), m/s2

30 25 20 15 10 5 0

0

0.002

0.004

Acceleration amplitude, m/s2

60

0.006 0.008 Time, s (a)

0.01

0.012

50 40 30 20 10 0

0

200

400

600 Frequency, Hz (b)

800

1000

Figure 9.17  (a)  A half sine wave in time domain representing a shock pulse with acceleration amplitude of 27 m/s2 for a duration of 10 ms calculated using Eq. 9.15. (b)  Frequency domain representation of the acceleration amplitudes for the half sine shock pulse of Figure 9.17(a) calculated using Fourier Transform (Eq. 9.18).

Characteristics of Epoxy-Based Composites  277

X( f ) =

Af0 cos(π f / 2 f0 ) π f02 − f 2

(

(9.18)

)

And the acceleration in frequency domain (for acceleration pulse input) is given by:

F(f) = 2π f0X(f)



(9.19)

where f0 is the frequency of the pulse and f is the frequency of the sine waves and can be taken theoretically from 0 to . A typical example is shown in Figure 9.17(a) for a shock force pulse of peak intensity 1 N acting on an aluminum beam of mass 0.03645 kg for 10 ms duration and hence the acceleration amplitude is 27 m/s2. The frequency domain intensities by Fourier Transform are calculated using Eqs. 9.18 and 9.19 and are shown in Figure 9.17(b). It is seen that the dominant frequency range is 0 to 200 Hz. The maximum shock intensity components are up to 10 Hz. Beyond 200 Hz, the intensity is reduced to less than 2.7 m/s2 which is one tenth of the half sine shock amplitude of 27 m/s2.

9.5.2 Shock Response The shock response is best given mathematically by convolution integral or Duhamel Integral. The expression for damped response is a modified undamped response by multiplication with exp[-ξωd(t-τ)]. The expressions are:

1 (a) Undamped system: X (t ) = mω n

t

∫ A(τ )sinω (t − τ ) dτ (9.20) n

0

(b) Damped system:



1 X d (t ) = mω d

t

∫ A(τ)exp −ξω (t − τ) sin ω (t − τ) dτ (9.21) d

d

0

where ωn is the n-th mode natural frequency of the system under shock.

278  Structural Adhesive Joints The A(τ) is the amplitude at a time τ and the calculation of X(t) is done for a period at least 3 times the pulse duration τ. The above expressions can be solved for X(t) by numerical method taking a small interval of time, e.g. ∆τ .02τ, where τ is the pulse duration. In the case of damped object, resonance frequency of the object under shock is given by:

ωd = ωn 1 − ξ2

(9.22)

where ξ is the damping factor which is half of the loss factor η. Damped shock responses of various epoxy adhesives are calculated using the above expressions and some of the examples are given below. Example -A The epoxy adhesive composition SD-2 is a soft material and has on average CLD loss factor 0.125 as shown in Figure 9.11. when used in the Aluminium-Aluminium joined beam. However, for calculation of damped response, the system loss factor of the joined beam with adhesive will be taken as 0.12 for SD-2 as the first natural frequency of total metal thickness of 7.5 mm is 134 Hz. The natural frequency is calculated using Eq. 9.13 applicable for a single cantilever beam clamped at one end. The damping factor is taken as half of the CLD loss factor, i.e., 0.06. Incidentally, the pulse frequency is 1/2τ = 50 Hz since pulse duration is 0.01 seconds. The response was calculated using Eqs. 9.20, 9.21 and 9.22. Numerical method of calculation was used taking small differential time ∆τ as s and summation of the terms under the integral is taken as approximately the same as the integrated value. The response in terms of displacement is calculated up to 0.03 s, since after that instant, the intensity of the post-shock peak vibration fell below 20% of peak value. The response is expressed in displacement (deflection) of the object. Figure 9.18 shows the shock response by a joined beam of aluminum 6 mm thick and aluminum 1.5 mm thick with SD-2 adhesive. The shock is taken as a half sine pulse of 10N force for a duration of 0.01 s and the beam dimensions and natural frequency as described above. It is seen that the damping of the shock wave to about 25% of the highest amplitude is observed compared to undamped beam without SD-2 adhesive. The characteristics of the rigidly bonded and flexible epoxy adhesive bonded beams are similar, showing maximum deflection after the pulse duration and at an instant of approximately 0.005 s, which is about half

Characteristics of Epoxy-Based Composites  279 Al-Al beam Shock response 0.0007 Response (displacement), m

0.0006

AL(6 mm) +Al (1.5mm)

0.0005

Adhesive (SD-2) bonded

0.0004 0.0003 0.0002 0.0001 0 –0.0001 –0.0002 0

0.005

0.01

0.015

0.02

0.025

0.03

Respose time, s

Figure 9.18  Shock response of an aluminium beam of 7.5 mm thickness without adhesive and for 6 mm and 1.5 mm thick aluminium beams boned with SD-2 adhesive (LY556+Polyetheramine mol. wt. 500).

the pulse duration (0.01 s). This is due to the higher natural frequency of the beam (134 Hz) compared to the frequency of the pulse (50 Hz). The time required for substantial decay in response is decided by the natural frequency of the object (joined beam in the present case) and the damping factor of the CLD (beam-adhesive-beam), which is 0.06 in the present case. A significant decay (by about 80%) is observed after 0.03 s, which is 3 times the pulse duration. Example -B The shock response of steel beams bonded by the two adhesives, namely flexible epoxy SD-2 and its 5% nanoclay composite, are calculated using the same Eqs. 9.20 to 9.22. Two cases are shown here. Case B-1 The base beam is Mild Steel (MS), having dimensions 180 mm x 10 mm and 6 mm thickness. The second beam is MS, having the same lateral dimensions but 1.5mm thick. Firstly, it is assumed that the beams are joined rigidly without flexible adhesive. Hence it becomes a 7.5 mm MS beam. The first resonance frequency of the 7.5 mm beam is 132 Hz, almost the same as aluminum beam of Example-A. This is because the E/w ratios of MS and aluminum are approximately equal. The adhesive is 5% nanocomposite of SD-2. The thickness of the adhesive is 0.5 mm. With these parameters, it is seen that the CLD

280  Structural Adhesive Joints loss factor of this system at 132 Hz is 0.12 for SD-2 and 0.185 for SD-2 with 5% nanoclay. Therefore, we take the damping ratio ( ) = 0.06 for SD-2 and 0.0925 for SD-2 with 5% nanoclay for shock response calculation. The shock characteristics are the same as in Example-A. For comparison, the shock response with SD-2 adhesive is also taken here. Figure 9.19 shows the shock responses of two beams rigidly bonded with SD-2 and 5% nanoclay composite of SD-2 adhesives. The first observation is that there is hardly any difference in the shock response by SD-2 and the nanocomposite. Secondly, the shock response is almost similar to that as in the case of aluminum beam joint in Example-A. The displacement as such is very small as the mass of the MS beam is much more than that of aluminum. The undamped amplitude is only about 0.22 mm and that for adhesive bonded beam is about 0.16 mm. The reduction in peak intensity is only about 27%. The significant shock reduction (89%) is only at the instant of 0.03 s, about 3 times the pulse duration. Here also, the peak shock intensity is at 0.005 s, which is half the pulse duration. Case B-2 Two mild steel (MS) beams of 6 mm thickness each with similar lateral dimensions as in Case B-1 are taken to calculate the effect of flexible adhesive joining these two beams. Firstly, it is assumed that the beams are joined rigidly without 0.00025 Without adhesive With adhesive SD-2 With adhesive SD-2+5% nanoclay

Response (displacement), m

0.0002 0.00015 0.0001 0.00005 0

–0.00005 –0.0001

0

0.005

0.01

0.015 0.02 Response time, s

0.025

0.03

Figure 9.19  Shock response of a mild steel (MS) beam of 7.5 mm thickness without adhesive and two mild steel (MS) beams 6 mm and 1.5 mm thick bonded with adhesives SD-2 (LY556 + Polyetheramine mol. wt. 500) and SD-2 with 5% nanoclay.

Characteristics of Epoxy-Based Composites  281 the adhesive as in Case B-1 and the first natural frequency of 12 mm thick beam is found to be 212 Hz as calculated for a cantilever beam using Eq. 9.13. The shock is taken as a half sine pulse of 100N force for a duration of 0.01 s. Then the shock response is calculated assuming no damping. Subsequently, the damping coefficients of SD-2 and SD-2 with 5% nanoclay were taken and shock responses were calculated. The results are shown in Figure 9.20. Here again, like Case B-1, there is no significant difference in the shock reduction by SD-2 and the nanocomposite adhesives. The shock response reduction in case of SD-2 is 25% for maximum displacement at 0.004 s and 30% for the nanocomposite. The peak value of the undamped rigid beam of 12 mm thickness is about 0.40 mm. It is seen that there are two successive peaks of displacement within the pulse duration, one at 0.004 s and the other at 0.0076 s. This ‘ringing’ during pulse occurs when the first peak response (displacement) occurs within half the pulse duration (here 0.005 s). The heavy objects have low natural frequency and the lighter objects have higher natural frequency. The peak intensities of the shock depend on the natural frequency. The ratio of response amplitude to the input amplitude for a definite natural frequency (of an object which is experiencing the shock) is given by:

α  (T / τ )cos(πτ / T )  τ = sin ω n (t − )  2 2 ψ p  (T / 4τ ) − 1  2



(9.23)

0.0005 without adhesive Responce (displacement), m

0.0004

with SD-2 with SD-2 + 5% nanoclay

0.0003 0.0002 0.0001 0 –0.0001 –0.0002 0

0.005

0.01

0.015

0.02

0.025

0.03

Response time, sec

Figure 9.20  Shock response of a mild steel (MS) beam of 12 mm thickness without adhesive and two beams each 6 mm thick bonded with adhesives SD-2 (LY556+Polyetheramine mol. wt. 500) and SD-2 with 5% nanoclay.

282  Structural Adhesive Joints where T = time period of natural oscillation of the object under shock and is related to its natural frequency ωn as:

T=



2π ωn

(9.24)

Figure 9.21 shows the Shock Response Spectra (SRS) in terms of intensity ratio (α/φp) drawn by taking peak response at various assumed natural frequencies. A half sine pulse shock is of 0.01 s duration is used here for the calculation. The curve is also referred as Maximax Response curve. The significance of these spectra here is that for objects of low natural frequency (to about 20 Hz), the shock output is lower than the input intensity (α/ψp