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Cast Iron Advanced Material Modelling Lecture Series

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© 2016 ANSYS, Inc.

April 28, 2016

Overview

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Classification of Cast Iron

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Background on Grey Cast Iron

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Cast Iron plasticity model: assumptions

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Cast Iron plasticity model: yield criterion

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Defining the Cast Iron plasticity model

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Element support for the Cast Iron plasticity model

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Post-processing considerations

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Summary

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ANSYS documentation on the Cast Iron plasticity model

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Suggested reading

© 2016 ANSYS, Inc.

April 28, 2016

Classification of Cast Iron Cast Iron includes a wide range of iron alloys: • Contains appreciable amount of carbon and silicon in alloy (silicon for softening affect), which affect mechanical behavior;

• Cooling rate also affects properties; • Cast iron has many advantages, including low cost, ability to cast into complex shapes, good damping capabilities, etc.; • Cast iron includes gray cast iron, nodular (ductile) cast iron, white cast iron, malleable cast iron, etc. Each has specific characteristics and microstructure. Subsequent discussion will focus on gray cast iron, on which this MAPDL material model is based. 3

© 2016 ANSYS, Inc.

April 28, 2016

Background on Grey Cast Iron Gray Cast Iron is comprised of graphite flakes in a pearlite/ferrite matrix. • Unlike steels, which usually have < 1% carbon, gray cast iron contains > 2% carbon. The excess carbon precipitate forms graphite flakes in the steel matrix during solidification. • In compression, graphite flakes do not have a significant effect on material behavior, and inelastic response is dominated by ductile steel. • In tension, these graphite flakes act as stress raisers which cause localized plastic flow at low stresses (1/3 1/5 of compressive strength) and can eventually initiate fracture (i.e., low strength in tension). The cracks also result in inelastic volume change.

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© 2016 ANSYS, Inc.

April 28, 2016

Background on Grey Cast Iron The microstructure of gray cast iron can be looked at as a twophase material with graphite flakes embedded in a steel matrix. This microstructure leads to a substantial different behavior in tension and compression. In tension, the material is more brittle with low strength and cracks form due to the graphite flakes. In compression, no cracks form and the graphite flakes behave as incompressible media that transmit stress and the steel matrix governs the overall behavior.

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© 2016 ANSYS, Inc.

April 28, 2016

Cast Iron plasticity model: assumptions • The model is used to simulate grey cast iron; • The elastic behavior is assumed to be isotropic; • The elastic behavior is assumed to be the same in tension and compression; • The model is for plastic, not brittle response. It does not simulate fracture or failure; • The model allows to differentiate yield strength values and hardening behaviors in tension and compression; • The plastic behavior is assumed to harden isotropically and that restricts the model to monotonic loading only.

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© 2016 ANSYS, Inc.

April 28, 2016

Cast Iron plasticity model: assumptions

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Inelastic strains are assumed to be incompressible in compression (npl = 0.5);

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Inelastic volume change in tension is governed by a userinput plastic Poisson’s ratio. Although this value may vary with stress, MAPDL assumes that the plastic Poisson’s ratio only varies with temperature;

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The model cannot be combined with any other material model.

© 2016 ANSYS, Inc.

April 28, 2016

Cast Iron plasticity model: assumptions

Idealized response of Grey Cast Iron in tension and compression Source: ANSYS Documentation, Theory Reference, section 4.2.19.

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© 2016 ANSYS, Inc.

April 28, 2016

Cast Iron plasticity model: yield criterion A composite yield surface is used to describe the different behavior in tension and compression. The tension behavior is pressure-dependent and the Rankine maximum stress criterion is used. This criterion can be represented as a box in the 3D principal stress space (rectangle in 2D). The compression behavior is pressure-independent and the von Mises yield criterion is used. This criterion can be represented as a cylinder in the 3D principal stress space (an ellipse in 2D). In the principal stress space, the yield surface is a cylinder with a tension cutoff (cap).

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© 2016 ANSYS, Inc.

April 28, 2016

Cast Iron plasticity model: yield criterion s2

s1 3D Principal Stress Space

2D Principal Stress Space

p s3 s1

s2

Cross section of yield surface: 2D view

Cross section of the yield surface: 3D view

Cast Iron is assumed to have von Mises yield criterion in compression and Rankine yield criterion in tension. This forms a composite yield surface. The tensile flow potential gives a nonassociated flow model and results in an unsymmetric material stiffness tensor. As such, the option NROPT,UNSYM is recommended if convergence difficulties arise. 10

© 2016 ANSYS, Inc.

April 28, 2016

Cast Iron plasticity model: yield criterion

p q=60

Cross section of yield surface: 3D view

Cast Iron yield surface Source: ANSYS Documentation, Material Reference, section 4.4.7.

Figure on the left shows that going from the tip of the composite yield surface along the outside (parallel to the axis of the cylinder), the two yellow lines will differ. Figure on the right shows the yield surfaces plotted in the meridional plane in which the ordinate and abscissa are von Mises equivalent stress and pressure, respectively. 11

© 2016 ANSYS, Inc.

April 28, 2016

Defining the Cast Iron plasticity model The Cast Iron plasticity model is available in MAPDL via the TB,CAST command or via the MAPDL GUI. It can be introduced into Workbench Mechanical by means of a command object. Below is the step-by-step procedure to follow for its definition:

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Input elastic material properties in Engineering Data

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Define the Cast Iron plasticity model via TB,CAST

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Input the plastic Poisson’s ratio via TBDATA

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Define uniaxial stress-strain curves in tension and compression via TB,UNIAXIAL

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Use TBTEMP if constants are temperature-dependent (with a maximum of 10 temperature sets)

© 2016 ANSYS, Inc.

April 28, 2016

Defining the Cast Iron plasticity model Example of APDL syntax to use in a command object to define the Cast Iron plasticity model e = 100000 nupl = 0.03

! Young's modulus ! Plastic Poisson's ratio

epsy_t = 0.055E-2 epsy_c = 0.203E-2

! Strain value at yielding in tension ! Strain value at yielding in compression

sigy_t = e*epsy_t sigy_c = e*epsy_c

! Stress value at yielding in tension ! Stress value at yielding in compression

tb,cast,matid,,,isotropic tbdata,1,nupl tb,uniaxial,matid,1,5,tension tbpt,,epsy_t,sigy_t tbpt,,0.10E-02,90 tbpt,,0.25E-02,166 tbpt,,0.35E-02,199 tbpt,,0.45E-02,222

tb,uniaxial,matid,1,5,compression tbpt,,epsy_c,sigy_c tbpt,,0.50E-02,345 tbpt,,0.80E-02,401 tbpt,,1.10E-02,453 tbpt,,1.40E-02,483

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© 2016 ANSYS, Inc.

April 28, 2016

Defining the Cast Iron plasticity model Such a constitutive equation is also available in the MAPDL Graphical User Interface as shown below:

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© 2016 ANSYS, Inc.

April 28, 2016

Defining the Cast Iron plasticity model Material parameters description: NUPL in tension User-defined plastic Poisson’s ratio in tension. This value determines the amount of volumetric expansion during tensile plastic deformation. Although it may vary with stress, ANSYS assumes it only varies with temperature. Uniaxial Compression Curve and Uniaxial Tension Curve Define uniaxial stress-strain curve in compression and tension respectively. The maximum number of pairs of stressstrain data is 20. Material parameters can be temperature-dependent and up to 10 temperature sets can be defined.

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© 2016 ANSYS, Inc.

April 28, 2016

Defining the Cast Iron plasticity model If not specified beforehand, there will be a reminder regarding the definition of the elastic properties of the material:

Next, linear elastic properties should be defined:

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© 2016 ANSYS, Inc.

April 28, 2016

Defining the Cast Iron plasticity model It should be noted that the first stress/strain pair defined in the uniaxial tension/compression curve needs to be consistent with the specified Young’s modulus otherwise an error is encountered. For example, the following material properties will generate such an error:

In fact 54 / 0.55e-3 = 98181.8182 does not match 100000 as specified. 17

© 2016 ANSYS, Inc.

April 28, 2016

Element support for the Cast Iron plasticity model Supported elements for the Cast Iron plasticity model are the following: PLANE182 (not applicable for plane stress) PLANE183 (not applicable for plane stress) SOLID185, SOLID186, SOLID187, SOLSH190, CPT212, CPT213, CPT215, CPT216, CPT217, PLANE223, SOLID226, SOLID227, SOLID272, SOLID273, SOLID285, PIPE288, PIPE289

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© 2016 ANSYS, Inc.

April 28, 2016

Post-processing considerations Computation of equivalent plastic strains When viewing equivalent plastic strains, notice that ANSYS assumes a Poisson’s ratio of 0.5 (i.e. plastic strains are incompressible), therefore: • In compression, due to the fact that the Cast Iron plasticity models assumes incompressible plastic strains, this is consistent; • In tension, due to the fact that the Cast Iron plasticity model simulates compressible plastic strains (i.e. the plastic Poisson’s ratio is an input requirement), this requires users to consider another way (e.g. an APDL macro) to post-process these quantities.

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© 2016 ANSYS, Inc.

April 28, 2016

Summary

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The Cast Iron plasticity model is used to model grey cast iron

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Elastic properties in tension and compression are the same

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Yield strength and hardening can be different in tension and compression

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The model requires the plastic Poisson’s ratio in tension and the uniaxial stress-strain curve in tension and compression

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The hardening behavior is isotropic

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Up to 10 temperature-dependent sets can be inputted

© 2016 ANSYS, Inc.

April 28, 2016

ANSYS documentation on the Cast Iron plasticity model The Cast Iron plasticity model is documented in the online manual: ANSYS Documentation > Mechanical APDL > Material Reference > 4. Nonlinear Material Properties > 4.4. Rate-Independent Plasticity > 4.4.7 Cast Iron ANSYS Documentation > Mechanical APDL > Theory Reference > 4. Structures with Material Nonlinearities > 4.2. Rate-Independent Plasticity > 4.2.19 Cast Iron Material Model

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© 2016 ANSYS, Inc.

April 28, 2016

Suggested Reading • Hjelm, H. E. Yield Surface for Gray Cast iron under Biaxial Stress. Journal of Engineering Materials and Technology. 116.2 (1994): 148-154. • Chen, W. F., D. J. Han. Plasticity for Structural Engineers. New York: SpringerVerlag, 1988.

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© 2016 ANSYS, Inc.

April 28, 2016