Chapter 8: Mechanical FailureISSUES TO ADDRESS... How do cracks that lead to failure form? How is fracture resistance quantified? How do the fracture

resistances of the different material classes compare? How do we estimate the stress to fracture? How do we estimate the stress to fracture? How do loading rate, loading history, and temperature

affect the failure behavior of materials?

Ship-cyclic loadingfrom waves

Computer chip-cyclicthermal loading

Hip implant-cyclicloading from walking

Chapter 8 - 1

from waves. thermal loading. loading from walking.Adapted from Fig. 22.30(b), Callister 7e.(Fig. 22.30(b) is courtesy of National Semiconductor Corporation.)

Adapted from Fig. 22.26(b), Callister 7e.

Adapted from chapter-opening photograph, Chapter 8, Callister & Rethwisch 8e. (by Neil Boenzi, The New York Times.)

Fracture mechanisms Ductile fracture

Accompanied by significant plasticAccompanied by significant plastic deformation

Brittle fracture Little or no plastic deformation CatastrophicCatastrophic

Chapter 8 - 2

Ductile vs Brittle FailureVery

DuctileModerately

Ductile BrittleFracturebehavior:

Classification:

Adapted from Fig. 8.1, Callister & Rethwisch 8e.

Large Moderate%AR or %EL SmallLarge Moderate%AR or %EL Small Ductile fracture is usually more desirable than brittle fracture!

Ductile:Warning before

fracture

Brittle:No

warning

Chapter 8 - 3

than brittle fracture! fracture warning

Example: Pipe Failures

Ductile failure:-- one piece-- one piece-- large deformation

Brittle failure:-- many pieces-- small deformations

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

Chapter 8 - 4

permission.

Moderately Ductile Failure Failure Stages:

necking

void nucleation

void growthand coalescence

shearing at surface fracture

Resulting 50 mm50 mm Resultingfracturesurfaces

50 mm50 mm

(steel)

particlesserve as void

From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd

100 mmFracture surface of tire cord wire loaded in tension Courtesy of F

Chapter 8 - 5

serve as voidnucleationsites.

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.)

loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

Moderately Ductile vs. Brittle Failure

cup-and-cone fracture brittle fracture

Adapted from Fig. 8.3, Callister & Rethwisch 8e.

Chapter 8 - 6

Brittle FailureArrows indicate point at which failure originated

Chapter 8 - 7Adapted from Fig. 8.5(a), Callister & Rethwisch 8e.

Brittle Fracture Surfaces Intergranular(between grains) 304 S. Steel

(metal)

Transgranular(through grains)

316 S. Steel ( )Reprinted w/permission from "Metals Handbook", 9th ed, Fig. 633, p. 650. Copyright 1985, ASM International, Materials P k OH (Mi h b

(metal)Reprinted w/ permission

from "Metals Handbook", 9th ed, Fig. 650, p. 357.

Copyright 1985, ASM Park, OH. (Micrograph by J.R. Keiser and A.R. Olsen, Oak Ridge National Lab.)4mm

International, Materials Park, OH. (Micrograph by

D.R. Diercks, Argonne National Lab.)

160mm

Polypropylene(polymer)Reprinted w/ permission from R.W. Hertzberg, "D f ti d

Al Oxide(ceramic)

Reprinted w/ permission from "Failure Analysis of B ittl M t i l " 78"Defor-mation and

Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.35(d), p. 303, John Wiley and Sons Inc 1996

Brittle Materials", p. 78. Copyright 1990, The

American Ceramic Society, Westerville, OH.

(Micrograph by R.M. Gruver and H Kirchner )

Chapter 8 - 8

Sons, Inc., 1996. Gruver and H. Kirchner.) 3mm1mm

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

Ideal vs Real Materials Stress-strain behavior (Room T):

TS TS

TS

Flaws are Stress Concentrators!

Griffith CrackGriffith Crack

K

2/12 a ot

tom K

2

where t = radius of curvature = applied stress

t

o = applied stressm = stress at crack tip

Chapter 8 - 10

Adapted from Fig. 8.8(a), Callister & Rethwisch 8e.

Concentration of Stress at Crack Tip

Adapted from Fig 8 8(b)Adapted from Fig. 8.8(b), Callister & Rethwisch 8e.

Chapter 8 - 11

Engineering Fracture Design

Stress Conc Factor K t

Avoid sharp corners! max

2.5

Stress Conc. Factor, K t =wmax

0

increasing w/h2.0r ,

filletradius

h

1.5Adapted from Fig. 8.2W(c), Callister 6e.(Fi 8 2W( ) i f G H

radius

r/h

h fill t di0 0.5 1.0

1.0(Fig. 8.2W(c) is from G.H. Neugebauer, Prod. Eng.(NY), Vol. 14, pp. 82-87 1943.)

Chapter 8 - 12

sharper fillet radius

Crack PropagationCracks having sharp tips propagate easier than cracks

having blunt tips A plastic material deforms at a crack tip, which

blunts the crack.deformeddeformed region

brittle ductile

Energy balance on the crack Elastic strain energy-

energy stored in material as it is elastically deformed this energy is released when the crack propagates creation of new surfaces requires energy

Chapter 8 - 13

q gy

Criterion for Crack PropagationCrack propagates if crack-tip stress (m)

exceeds a critical stress (c)( c)2/12

sc Ei.e., m > c

whereE = modulus of elasticity

acm c

E = modulus of elasticity s = specific surface energy a = one half length of internal crack

For ductile materials => replace s with s + pwhere p is plastic deformation energy

Chapter 8 - 14

p p gy

Fracture Toughness RangesGraphite/Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

SteelsC-C(|| fibers) 1

70

100

Based on data in Table B.5,C lli t & R th i h 8

)

Mg alloysAl alloys

Ti alloys

3040506070

Callister & Rethwisch 8e.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

m

0

.

5

10

20

C/C( fibers) 1

Al/Al oxide(sf) 2

Al oxid/SiC(w) 3

Y2O3/ZrO 2(p)4

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.

5

c

(

M

P

a

Si carbide

43

Diamond

PP

PET67

Al oxideSi nitride

Al oxid/SiC(w)

Al oxid/ZrO 2(p)4Si nitr/SiC(w) 5

Glass/SiC(w) 6

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

K

I

c

PC2

3 PVC

Chapter 8 - 15

Proc., Vol. 7 (1986) pp. 978-82.1Si crystalGlass -sodaConcrete

Glass 6

0.5

0.7

Polyester

PS

0.6

Design Against Crack Growth Crack growth condition:

K Kc = aY Largest, most highly stressed cracks grow first!

--Scenario 1: Max flaw --Scenario 2: Design stressScenario 1: Max. flaw size dictates design stress.

Kcd i

Scenario 2: Design stressdictates max. flaw size.

21

cKa

maxa

Ydesign

max

designY

a

amax

no fracture

no fracture

Chapter 8 - 16

amaxfracture fracture

Design Example: Aircraft Wing

Two designs to consider... Material has KIc = 26 MPa-m0.5

Design A--largest flaw is 9 mm--failure stress = 112 MPa

Design B--use same material--largest flaw is 4 mm

f il t ?--failure stress = ? Use...

maxa

YKIc

c

Key point: Y and KIc are the same for both designs.

= a = YKIc constant

BmaxAmax aa cc 9 mm112 MPa 4 mm

--Result:

Chapter 8 - 17Answer: MPa 168)( B c B maxAmax cc

Impact Testing Impact loading:

-- severe testing casek t i l b ittl

(Charpy)

-- makes material more brittle-- decreases toughness

Adapted from Fig 8 12(b)Adapted from Fig. 8.12(b), Callister & Rethwisch 8e. (Fig. 8.12(b) is adapted from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, p , ,Mechanical Behavior, John Wiley and Sons, Inc. (1965) p. 13.)

fi l h i ht i iti l h i ht

Chapter 8 - 18

final height initial height

Influence of Temperature on Impact EnergyImpact Energy

Ductile-to-Brittle Transition Temperature (DBTT)...( )

FCC metals (e.g., Cu, Ni)

BCC metals (e.g., iron at T < 914C)

c

t

E

n

e

r

g

y

polymers

More DuctileBrittle

I

m

p

a

c

High strength materials (y > E/150)o e uct ett e

Adapted from Fig. 8.15, Callister & Rethwisch 8e.

TemperatureDuctile-to-brittle

transition temperature

Chapter 8 - 19

p

Design Strategy:Stay Above The DBTT!

Pre-WWII: The Titanic WWII: Liberty ships

Stay Above The DBTT!

y

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

Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley andMaterials , (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.)

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.)

Chapter 8 - 20

Problem: Steels were used having DBTTs just below room temperature.

Fatigue

Adapted from Fig. 8.18,

Fatigue = failure under applied cyclic stress.

compression on topspecimen p g ,Callister & Rethwisch 8e. (Fig. 8.18 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper S ddl Ri NJ )t i b tt

countermotor

flex coupling

bearing bearing

Saddle River, NJ.)

Stress varies with time.-- key parameters are S m and max

tension on bottom

key parameters are S, m, and cycling frequency

min timem S

Key points: Fatigue...--can cause part failure, even though max < y.

ibl f 90% f h i l i i f il

Chapter 8 - 21

--responsible for ~ 90% of mechanical engineering failures.

Types of Fatigue Behavior Fatigue limit, Sfat:

--no fatigue if S < Sfatcase for steel (typ.)unsafe

m

p

l

i

t

u

d

e

Adapted from Fig. 8.19(a), Callister & Rethwisch 8e

Sfat

safe

S

=

s

t

r

e

s

s

a

Rethwisch 8e.

N = Cycles to failure103 105 107 109

S

For some materials, there is no fatigue

case for Al (typ.)unsafe

a

m

p

l

i

t

u

d

e

limit!Adapted from Fig. 8.19(b), Callister & R th i h 8

safe

S

=

s

t

r

e

s

s

a

Chapter 8 - 22

Rethwisch 8e.

N = Cycles to failure103 105 107 109

S

Rate of Fatigue Crack Growth Crack grows incrementally

typ. 1 to 6 mKd a a~

increase in crack length per loading cycle

mKdN

increase in crack length per loading cycle

Failed rotating shaft-- crack grew even though

crack origin

crack grew even thoughKmax < Kc

-- crack grows faster as increases Ad t d f increases crack gets longer loading freq. increases.

Adapted fromFig. 8.21, Callister & Rethwisch 8e. (Fig. 8.21 is from D.J. Wulpi, Understanding How Components Fail

Chapter 8 - 23

How Components Fail, American Society for Metals, Materials Park, OH, 1985.)

Improving Fatigue Life

Adapted fromFig. 8.24, Callister & Rethwisch 8e

1. Impose compressivesurface stresses

a

m

p

l

i

t

u

d

e

Rethwisch 8e. (to suppress surfacecracks from growing)

N = Cycles to failure

moderate tensile mLarger tensile m

S

=

s

t

r

e

s

s

a

near zero or compressive m

N = Cycles to failure

--Method 1: shot peening

tshot

--Method 2: carburizing

C-rich gasput surface

into compression

C rich gas

2. Remove stressconcentrators. Adapted from

bad better

Chapter 8 - 24

Adapted fromFig. 8.25, Callister & Rethwisch 8e. bad better

CreepSample deformation at a constant stress () vs. time

0 t

Primary Creep: slope (creep rate) decreases with time

Adapted from

decreases with time.

Secondary Creep: steady-statei.e., constant slope /t)

Chapter 8 - 25

Adapted fromFig. 8.28, Callister & Rethwisch 8e. Tertiary Creep: slope (creep rate)

increases with time, i.e. acceleration of rate.

Creep: Temperature Dependence Occurs at elevated temperature, T > 0.4 Tm (in K)

tertiary

primarysecondary

elastic

Chapter 8 - 26

Adapted from Fig. 8.29, Callister & Rethwisch 8e.

Secondary Creep Strain rate is constant at a given T,

-- strain hardening is balanced by recoverystress exponent (material parameter)

activation energy for creep( t i l t )

RTQK cns exp2

strain rate (material parameter)applied stressmaterial const.

S 200Adapted from

RT

Strain rateincreaseswith increasing 40

100200

s

(

M

P

a

) 427C

538C

Adapted fromFig. 8.31, Callister 7e. (Fig. 8.31 is from Metals Handbook: Properties and Selection: Stainless Steels, Tool g

T, 102040

S

t

r

e

s

s

649C

Materials, and Special Purpose Metals, Vol. 3, 9th ed., D. Benjamin (Senior Ed.), American Society for Metals, 1980 p 131 )

Chapter 8 - 27

10-2 10-1 1Steady state creep rate (%/1000hr)s

1980, p. 131.)

Creep Failure

Failure: along grain boundaries.

applied

g.b. cavities

appliedstress

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

Chapter 8 -

Wiley and Sons, Inc., 1987. (Orig. source: Pergamon Press, Inc.)

28

Prediction of Creep Rupture Lifetime Estimate rupture time

S-590 Iron, T = 800C, = 20,000 psiTi t t t

LtT r )log20(Time to rupture, tr

p

s

i

)

100

time to failure (rupture)

function ofapplied stress

temperature

r

e

s

s

(

1

0

3

10

20

3

S

t

r

data for S-590 Iron

310x24)log20)(K 1073( rt103 L (K-h)

112 20 24 2816 24

Chapter 8 -

Ans: tr = 233 hrAdapted from Fig. 8.32, Callister & Rethwisch 8e. (Fig. 8.32 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).)

29

Estimate the rupture time forS-590 Iron, T = 750C, = 20,000 psiS 590 o , 50 C, 0,000 ps

Solution:

p

s

i

)

100

LtT r )log20(Time to rupture, tr

e

s

s

(

1

0

3

p

10

20

time to fail re (r pt re)

function ofapplied stress

temperature

LtT r )log20(

S

t

r

e

data for S-590 Iron310x24)log20)(K 1023( rt

time to failure (rupture)

103 L (K-h)

112 20 24 2816 24

)g)(( r

Ans: tr = 2890 hr

Chapter 8 - 3030

Adapted from Fig. 8.32, Callister & Rethwisch 8e. (Fig. 8.32 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).)

Ans: tr 2890 hr

SUMMARY Engineering materials not as strong as predicted by theory Flaws act as stress concentrators that cause failure at

Sharp corners produce large stress concentrationsd t f il

Flaws act as stress concentrators that cause failure at stresses lower than theoretical values.

and premature failure. Failure type depends on T and :

-For simple fracture (noncyclic and T < 0.4Tm), failure stressFor simple fracture (noncyclic and T 0.4Tm), failure stress decreases with:- increased maximum flaw size,- decreased T,,- increased rate of loading.

- For fatigue (cyclic :- cycles to fail decreases as increases.

Chapter 8 - 31

y- For creep (T > 0.4Tm):

- time to rupture decreases as or T increases.

ANNOUNCEMENTSReading:

Core Problems:

Self help Problems:Self-help Problems:

Chapter 8 - 32