• Author / Uploaded
• Belen Tapia

• Categories
• Fatiga (material)
• Materiales
• Ingeniería de Edificación
• Ciencia de los Materiales
• Mecánica de sólidos

Citation preview

5/7/2012

8. Falla Mecánica • Como se inician las fallas? • Como se estiman esfuerzos de fractura?

Chip de computadora sometido a cargas ciclicas termica. Sometido a fuerzas cíclicas de olas.. Adapted from chapter-opening photograph, Chapter 8, Callister 7e. (by Neil Boenzi, The New York Times.)

Adapted from Fig. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.) Chapter 8 - 1

Mecanismos de Fractura • Fractura dúctil – Ocurre con deformación plástica • Fractura Frágil – Poco o nada de deformación plástica – Catastrófico

Chapter 8 - 2

1

5/7/2012

Falla Ductil vs Fragil Modo, comportam.. de fractura

Muy ductil

Moderadam. ductil

Fragil

Adapted from Fig. 8.1, Callister 7e.

%AR o %EL  Grande Moderado • Ductil deseable generalmente.

Ductil: avisa inminente fractura

pequeño Fragil: Sin aviso warning Chapter 8 - 3

Ejemplos de fallas • Falla Ductil: -- una pieza -- Deformacion grande

• Falla Frágil: -- muchas pedazos -- pequeña deformación Figures from V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.1(a) and (b), p. 66 John Wiley and Sons, Inc., 1987. Used with permission.

Chapter 8 - 4

2

5/7/2012

Falla Ductil Moderado • Evolution a falla: necking

s

•Superficie fracturada

void nucleation

void growth and linkage

shearing at surface

fracture

50 50mm mm

(acero) partículas son sitios de nucleación de cavidades

100 mm From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 11.28, p. 294, John Wiley and Sons, Inc., 1987. (Orig. source: P. Thornton, J. Mater. Sci., Vol. 6, 1971, pp. 347-56.)

Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission. Chapter 8 - 5

Falla Ductil vs. Fragil

Fractura copa-y- conoe

Fractura Fragil

Adapted from Fig. 8.3, Callister 7e.

Chapter 8 - 6

3

5/7/2012

Falla Fragil Flechas indican los puntos de origen de la falla

Adapted from Fig. 8.5(a), Callister 7e.

Chapter 8 - 7

Superficies de fractura frágil • Intergranular (entre granos)

4 mm

304 S. Steel (metal)

• Intragranular (dentro de granos 316 S. Steel

Reprinted w/permission (metal) from "Metals Handbook", Reprinted w/ permission 9th ed, Fig. 633, p. 650. from "Metals Handbook", Copyright 1985, ASM 9th ed, Fig. 650, p. 357. International, Materials Copyright 1985, ASM Park, OH. (Micrograph by International, Materials J.R. Keiser and A.R. Park, OH. (Micrograph by Olsen, Oak Ridge D.R. Diercks, Argonne National Lab.) National Lab.)

Polypropylene (polymer) Reprinted w/ permission from R.W. Hertzberg, "Defor-mation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.35(d), p. 303, John Wiley and Sons, Inc., 1996.

160 mm

Al Oxide (ceramic) Reprinted w/ permission from "Failure Analysis of Brittle Materials", p. 78. Copyright 1990, The American Ceramic Society, Westerville, OH. (Micrograph by R.M. Gruver and H. Kirchner.)

3 mm

1 mm (Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p. 1119.)

Chapter 8 - 8

4

5/7/2012

Materiales Ideales vs Reales • Comport. Stress-strain ( T amb): E/10

s Material perfecto

sin defectos

Fibra de vidrio, prod cond esp

E/100

Ceramico tipico 0.1

TSmateriales sc or

Kt > Kc

1/ 2

 2E s  sc     a 

donde – – – –

E = modulo de elasticidad s = energía superficial especifica a = ½ de longitud interna de grieta Kc = sc/s (fracture toughness)

Para ductil => remplace s por s + p donde p es energia de deformacion plastica Chapter 8 - 14

7

5/7/2012

Fracture toughness (Resistencia a Fractura) Metals/ Alloys

Graphite/ Ceramics/ Semicond

Polymers

100

K Ic (MPa · m0.5 )

70 60 50 40 30

Composites/ fibers C-C (|| fibers) 1

Steels Ti alloys Al alloys Mg alloys

Based on data in Table B5, Callister 7e.

20

Al/Al oxide(sf) 2 Y2 O 3 /ZrO 2 (p) 4 C/C( fibers) 1 Al oxid/SiC(w) 3 Si nitr/SiC(w) 5 Al oxid/ZrO 2 (p) 4 Glass/SiC(w) 6

10 Diamond

7 6 5 4

Si carbide Al oxide Si nitride

PET PP

3

PVC

2

PC

1

Si crystal

Glass -soda Concrete

0.7 0.6 0.5

Composite reinforcement geometry is: f = fibers; sf = short fibers; w = whiskers; p = particles. Addition data as noted (vol. fraction of reinforcement): 1. (55vol%) ASM Handbook, Vol. 21, ASM Int., Materials Park, OH (2001) p. 606. 2. (55 vol%) Courtesy J. Cornie, MMC, Inc., Waltham, MA. 3. (30 vol%) P.F. Becher et al., Fracture Mechanics of Ceramics, Vol. 7, Plenum Press (1986). pp. 61-73. 4. Courtesy CoorsTek, Golden, CO. 5. (30 vol%) S.T. Buljan et al., "Development of Ceramic Matrix Composites for Application in Technology for Advanced Engines Program", ORNL/Sub/85-22011/2, ORNL, 1992. 6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc., Vol. 7 (1986) pp. 978-82.

Glass 6

PS Polyester

Chapter 8 - 15

Diseño usando mecánica de fracturas • Condición para crecimiento de grieta:

K ≥ Kc = Ys a

• la grieta más grande, más estresada crece primero! -- 1: El tamaño max de defecto determina el esfuerzo de diseño

sdesign 

--2: Esfuerzo de diseño determina el tamaño max de defecto.

Kc Y amax

amax

1  K c      Ysdesign 

2

amax

s

fractura

fractura

no fractura

no fractura

amax

s

Chapter 8 - 16

8

5/7/2012

Ej. Diseño: ala de avión • Material tiene Kc = 26 MPa-m0.5 • dos casos a considerar... Diseño B Diseño A --Defecto más grande es 9 mm --esfuerzo de falla = 112 MPa

sc 

• Use...

Kc Y amax

--mismo material --defecto más grande es 4 mm -- Esfuerzo de falla = ?

• punto clave: Y and Kc son lo mismo en ambos diseños --Resultado: 112 MPa

(sc

9 mm

amax

A  (sc

4 mm

amax

B

Answer: (sc )B  168 MPa

•comentario!



Chapter 8 - 17

Test de impacto • Impact loading:

(Charpy)

-- severe testing case -- makes material more brittle -- decreases toughness Adapted from Fig. 8.12(b), Callister 7e. (Fig. 8.12(b) is adapted from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, John Wiley and Sons, Inc. (1965) p. 13.)

final height

initial height

Chapter 8 - 18

9

5/7/2012

Temperatura • Aumento en temperatura... --aumenta %EL y Kc

• Temperatura de Transicion Ductil- a - Fragil (DBTT)... Energia de Impacto

FCC metales (ej., Cu, Ni) BCC metales (ej., Fe a T < 914°C) polimeros Fragil

Mas Ductil mater altamente resist. s y > E/150) Adapted from Fig. 8.15, Callister 7e.

Temperatura Temp.Trans.Ductil-a-fragil Chapter 8 - 19

Estrategia de diseño: estar sobre DBTT!

• Pre-WWII: The Titanic

Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard, The Discovery of the Titanic.)

• WWII: Liberty ships

Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Earl R. Parker, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.)

Problema: Se uso un tipo de acero con un DBTT ~ T ambiente Chapter 8 - 20

10

5/7/2012

Fatiga • Fatiga = falla bajo esfuerzo ciclico. specimen compression on top bearing

motor

bearing

counter

flex coupling tension on bottom

• Esfuerzo varia con tiempo.

-- parametros clave son S, sm, y frecuencia

Adapted from Fig. 8.18, Callister 7e. (Fig. 8.18 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.)

s

smax sm

S

smin

time

• Puntos clave: Fatiga...

-- puede producir falla parcial, aun con smax < sc. -- causa ~ 90% de las fallas mechanicas. Chapter 8 - 21

Parámetros de diseño de Fatiga • Límite de Fatiga, Sfat:

S = stress amplitude

no-fatiga si S < Sfat

inseguro

caso para acero (tip.)

Sfat seguro 10 3

• Algunas veces, el límite de fatiga es cero!

10 5 10 7 10 9 N = Cycles to failure

S = stress amplitude inseguro

seguro 10 3

Adapted from Fig. 8.19(a), Callister 7e.

Caso para Al (tip.)

Adapted from Fig. 8.19(b), Callister 7e.

10 5 10 7 10 9 N = Cycles to failure Chapter 8 - 22

11

5/7/2012

Mecanismo de fatiga • Grieta crece incrementalmente tip. 1 to 6

da m  (K  dN

~ (s a

Increm. longitud de grieta por ciclo de carga crack origin

• Failed rotating shaft --crack grew even though Kmax < Kc --crack grows faster as • s increases • crack gets longer • loading freq. increases.

Adapted from Fig. 8.21, Callister 7e. (Fig. 8.21 is from D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.) Chapter 8 - 23

Creep Deformation (a altaT) a un esfuerzo constante (s) vs. times s,e

0

t

Creep primario: slope (creep rate) decreases with time. Creep secundario: steady-state i.e., constant slope. Creep terciario: slope (creep rate) increases with time, i.e. acceleration of rate.

Adapted from Fig. 8.28, Callister 7e. Chapter 8 - 24

12

5/7/2012

Creep • Ocurre a temperaturas elevadas, T > 0.4 Tm

tertiary primary

secondary

elastic

Adapted from Figs. 8.29, Callister 7e. Chapter 8 - 25

Creep secundario • Veloc. de deformación es constante T,y s dados -- Endurecimiento por deformación se balancea con recuperación. stress exponent (material parameter)

 Q  e s  K 2sn exp  c   RT 

strain rate material const.

• Strain rate aumenta a valores altos de T, s

activation energy for creep (material parameter)

applied stress 2 00 10 0

Stress (MPa)

Adapted from Fig. 8.31, Callister 7e. (Fig. 8.31 is from Metals Handbook: Properties 538 °C and Selection: Stainless Steels, Tool Materials, and Special Purpose Metals, Vol. 3, ed., D. Benjamin 649 °C 9th (Senior Ed.), American Society for Metals, 1980, p. 131.)

427°C

40 20 10 10 -2 10 -1 Steady state creep rate

1

es (%/1000hr)

Chapter 8 - 26

13

5/7/2012

Creep: Falla • Falla: a lo largo de limites de grano

• Estimate rupture time S-590 Iron, T = 800°C, s = 20 ksi

g.b. cavities 100 20 10 From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.32, p. 87, John Wiley and Sons, Inc., 1987. (Orig. source: Pergamon Press, Inc.)

• Time to rupture, tr

T ( 20  logt r )  L

data for S-590 Iron 1 12 16 20 24 28 3 L(10 K-log hr)

24x103 K-log hr

T ( 20  logt r )  L

function of applied stress time to failure (rupture)

temperatura

Adapted from Fig. 8.32, Callister 7e. (Fig. 8.32 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).)

Stress, ksi

applied stress

1073K

Ans: tr = 233 hr Chapter 8 - 27

Resumen • Materiales de ingeniería no alcanzan resistencias teóricas. • Defectos producen concentraciones de esfuerzos que causan falla prematura. • esquinas agudas producen concentraciones grandes de esfuerzos y causan falla prematura. • Tipo de falla depende de T y esfuerzo:

Chapter 8 - 28

14