Chapter 8-

ISSUES TO ADDRESS...• How do flaws in a material initiate failure?• How is fracture resistance quantified; how do different material classes compare?• How do we estimate the stress to fracture?

1

• How do loading rate, loading history, and temperature affect the failure stress?

Ship-cyclic loadingfrom waves.

Computer chip-cyclicthermal loading.

Hip implant-cyclicloading from walking.

Adapted from Fig. 8.0, Callister 6e. (Fig. 8.0 is by Neil Boenzi, The New York Times.)

Adapted from Fig. 18.11W(b), Callister 6e. (Fig. 18.11W(b) is courtesy of National Semiconductor Corporation.)

Adapted from Fig. 17.19(b), Callister 6e.

CHAPTER 8:MECHANICAL FAILURE

Chapter 8-

Mechanical Failure

• The usual causes for failure are:– Improper materials selection and processing– Inadequate design– Misuse

• Cost of failure– 1000 Billions of $ or YTL annually– Loss of human life !

Chapter 8 -

Fracture mechanisms

• Ductile fracture– Occurs with plastic deformation

• Brittle fracture– Little or no plastic deformation– Catastrophic

Chapter 8 -

Ductile vs. Brittle Failure

Adapted from Fig. 8.3, Callister 7e.

cup-and-cone fracture brittle fracture

Chapter 8-

Heverill Fire Department aerial ladder failure from: http://www.engr.sjsu.edu/WofMatE/FailureAnaly.htm

From http://plane-truth.com/comet.htm

Chapter 8-

Mechanical Failure:How do materials break ?

• Fracture: crack growth to rupture at a critical load– Ductile vs Brittle fracture

– Principles of Fracture Mechanics• Stress Concentration

– Impact Fracture Testing

• Fatigue: crack growth due to cycling loads– Cyclic stresses, the S-N curve

– Crack initiation and propagation

– Factors that effect fatigue behavior

• Creep: high temperature plastic deformation– Stress and temperature effects

– Alloys for hi-temperature usage

Chapter 8-

Very Ductile

Moderately Ductile BrittleFracture

behavior:

Large Moderate%AR or %EL: Small

2

• Ductile fracture is desirable!

• Classification:

Ductile: warning before

fracture

Brittle: No warning

Failure is catastrophic

Adapted from Fig. 8.1, Callister 6e.

DUCTILE VS BRITTLE FAILURE

Substantial plastic deformationAbsorb high amounts of energy before fractureWhat is the reduction in x-sectional area ?

Chapter 8-

Fracture, in detail

• Two steps involved in fracture:– Crack formation– Crack growth

• Two fracture modes can be defined– Ductile (preferred, most metals and some polymers)

• extensive plastic deformation in the vicinity of a crack• Extension of crack length requires an increase in the applied load,

hence crack is stable unless stress is increased. Crack propagation is therefore slow

– Brittle (undesired, ceramics, metals at low temperatures)• Takes place w/o appreciable plastic deformation• Crack is unstable, will propagate with high speed once formed

and w/o increase in applied stress

Chapter 8-

Ductile vs Brittle

Q1:What is ductility ?

Q2: What is toughness?

Chapter 8 -

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

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.

Example: Failure of a Pipe

• Brittle failure: --many pieces --small deformation

Observe the variation in the amount of plastic deformation

Chapter 8 -

• Evolution to failure:

• Resulting fracture surfaces (steel)

50 mm

particlesserve as voidnucleationsites.

50 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.)

100 mmFracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

Moderately Ductile Failure

necking

void nucleation

void growth and linkage

shearing at surface fracture

Chapter 8-

Ductile Fracture

Cup and cone fracture in Aluminum

SEM of the fracture surface:Fractographic studies

Dimples, micro-cavities that initiate crack formation, on the surface will be observed during high resolution investigation of the cup and cone type fracture surfaces.

Cup Cone

Dimple

Micro-void

Chapter 8 -

• Intergranular(between grains)

• Intragranular (within grains)

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.)

316 S. Steel (metal)

Reprinted w/ permission from "Metals Handbook", 9th ed, Fig. 650, p. 357.

Copyright 1985, ASM International, Materials

Park, OH. (Micrograph by D.R. Diercks, Argonne

National Lab.)

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

3 mm

4 mm160 mm

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

Brittle Fracture Surfaces

Chapter 8-5

• INTERgranular (between grains)

• TRANSgranular (within grains)

Al Oxide(ceramic)

316 S. Steel (metal)

304 S. Steel (metal)

Polypropylene(polymer)

3m

4 mm160m

1 mm

BRITTLE FRACTURE SURFACES

1. No appreciable plastic deformation2. Fast moving crack3. Propagation direction is nearly 90º to

applied stress4. Crack often propagates by cleavage,

breaking of bonds along specific crystallographic planes, aka cleavage planes

Transgranular fracture: Cracks move in and through grains. Fracture surface have faceted texture because of different orientation of cleavage planes .

Intergranular fracture: Crack propagation isalong grain boundaries (grain boundaries are weak or embrittle due to impurity segregation, etc.)

Chapter 8 -

• Stress-strain behavior (Room T):

Ideal vs Real Materials

TS << TSengineeringmaterials

perfectmaterials

E/10

E/100

0.1

perfect mat’l-no flaws

carefully produced glass fiber

typical ceramic typical strengthened metaltypical polymer

• DaVinci (500 yrs ago!) observed... -- the longer the wire, the smaller the load for failure.• Reasons: -- flaws cause premature failure. -- Larger samples contain more flaws!

Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.4. John Wiley and Sons, Inc., 1996.

Chapter 8-

Flaws ; Stress concentrators

• Fracture strength of a brittle solid is related to the cohesive forces between atoms, bond strength. It can be estimated that the theoretical cohesive strength of a brittle material should be around ~ E/10. But experimental fracture strength is normally E/100 - E/10,000.

• Much lower fracture strength is explained by the effect of stress concentration at microscopic flaws. The applied stress is amplified at the tips of micro-cracks, voids, notches, surface scratches, corners, etc. that are called stress concentrators raisers.

• The magnitude of this amplification depends on micro-crack orientations, geometry and dimensions.

TABLES 6.1 and 6.2In chapter 6

Chapter 8-7

• Elliptical hole in a plate:

• Stress distrib. in front of a hole:

• Stress concentration factor:

BAD! Kt>>3

o

2a

Kt max /o

• Large Kt promotes failure:

FLAWS ARE STRESS CONCENTRATORS!

Sharper cracks amplify stress !More important for brittle materials as in ductile material Plas. Dfm takes place and stress is distributed more uniformly around a crack !

max

t

2o

a

t

NOT SO BAD

Kt=2

Chapter 8 -

Flaws are Stress Concentrators!

Results from crack propagation• Griffith Crack

where t = radius of curvature

o = applied stress

m = stress at crack tip

ot

/

tom K

a

21

2

t

Adapted from Fig. 8.8(a), Callister 7e.

Chapter 8 -

Concentration of Stress at Crack Tip

Adapted from Fig. 8.8(b), Callister 7e.

Chapter 8 -

Engineering Fracture Design

r/h

sharper fillet radius

increasing w/h

0 0.5 1.01.0

1.5

2.0

2.5

Stress Conc. Factor, K t

max

o=

• Avoid sharp corners!

Adapted from Fig. 8.2W(c), Callister 6e. (Fig. 8.2W(c) is from G.H. Neugebauer, Prod. Eng. (NY), Vol. 14, pp. 82-87 1943.)

r , fillet

radius

w

h

o

max

Chapter 8-From http://plane-truth.com/comet.htm

Anything peculiar in this image !

Chapter 8-10

• Condition for crack propagation:

• Values of K for some standard loads & geometries:

2a2a

aa

K a K 1.1 a

K ≥ KcStress Intensity Factor:Depends on applied stress, crack length & component geometry.

Fracture Toughness:Depends on the material, temperature, environment, & rate of loading.

unitsof K :

MPa m

or ksi in

Adapted from Fig. 8.8, Callister 6e.

GEOMETRY, LOAD, & MATERIAL

Chapter 8 -

When Does a Crack Propagate?

Crack propagates if above critical stress

where– E = modulus of elasticity s = specific surface energy

– a = one half length of internal crack

– Kc = c/0

For ductile => replace s by s + p

where p is plastic deformation energy

212

/

sc a

E

i.e., m > c

or Kt > Kc

Chapter 8-

• t at a cracktip is verysmall!

9

• Result: crack tip stress is very large.

• Crack propagates when: the tip stress is large enough to make: distance, x,

from crack tip

tip K2x

tip

increasing K

K ≥ Kc

WHEN DOES A CRACK PROPAGATE?

Chapter 8 -

Crack Propagation

Cracks propagate due to sharpness of crack tip • A plastic material deforms at the tip, “blunting” the

crack.

deformed region

brittle

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

plastic

Chapter 8-

• Energy to break a unit volume of material• Approximate by the area under the stress-strain curve.

20

smaller toughness- unreinforced polymers

Engineering tensile strain,

Engineering tensile stress,

smaller toughness (ceramics)

larger toughness (metals, PMCs)

TOUGHNESS & RESILIENCE

RESILIENCE is energy stored in the material w/o plastic deformation ! U r = σy2 / 2 E

TOUGHNESS is total energy stored in the material upon fracture !

Chapter 8 -

Fracture Toughness

Based on data in Table B5,Callister 7e.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.

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibers

Polymers

5

KIc

(MP

a ·

m0

.5)

1

Mg alloys

Al alloys

Ti alloys

Steels

Si crystalGlass -soda

Concrete

Si carbide

PC

Glass 6

0.5

0.7

2

4

3

10

20

30

<100>

<111>

Diamond

PVC

PP

Polyester

PS

PET

C-C(|| fibers) 1

0.6

67

40506070

100

Al oxideSi nitride

C/C( fibers) 1

Al/Al oxide(sf) 2

Al oxid/SiC(w) 3

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

Glass/SiC(w) 6

Y2O3/ZrO 2(p)4

Kcmetals

Kccomp

KccerKc

poly

incr

easi

ng

Fracture toughness is the resistance of a material to brittle fracture when a crack is present !

Chapter 8 -

• Crack growth condition:

• Largest, most stressed cracks grow first!

Design Against Crack Growth

K ≥ Kc = aY

--Result 1: Max. flaw size dictates design stress.

max

cdesign

aY

K

amax

no fracture

fracture

--Result 2: Design stress dictates max. flaw size.

2

1

design

cmax Y

Ka

amax

no fracture

fracture

Chapter 8 -

• Two designs to consider...Design A --largest flaw is 9 mm --failure stress = 112 MPa

Design B --use same material --largest flaw is 4 mm --failure stress = ?

• Key point: Y and Kc are the same in both designs.

Answer: MPa 168)( B c• Reducing flaw size pays off!

• Material has Kc = 26 MPa-m0.5

Design Example: Aircraft Wing

• Use...max

cc

aY

K

c amax A

c amax B

9 mm112 MPa 4 mm --Result:

Chapter 8 -

Loading Rate

• Increased loading rate... -- increases y and TS -- decreases %EL

• Why? An increased rate gives less time for dislocations to move past obstacles.

y

y

TS

TS

larger

smaller

Chapter 8 -

Impact Testing

final height initial height

• Impact loading: -- 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.)

(Charpy)

Chapter 8 -

• Increasing temperature... --increases %EL and Kc

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

Temperature

BCC metals (e.g., iron at T < 914°C)

Imp

act

Ene

rgy

Temperature

High strength materials (y > E/150)

polymers

More Ductile Brittle

Ductile-to-brittle transition temperature

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

Adapted from Fig. 8.15, Callister 7e.

Chapter 8-

DBTT

1. As temperature decreases a ductile material can become behave brittle - ductile-to-brittle transition

2. FCC metals remain ductile down to very low temperatures.3. For ceramics, this type of transition occurs at much higher

temperatures than for metals.4. The ductile-to-brittle transition can be measured by impact testing:

the impact energy needed for fracture drops suddenly over a relatively narrow temperature range – temperature of the ductile-to-brittle transition.

Chapter 8 -

• Pre-WWII: The Titanic • WWII: Liberty ships

• Problem: Used a type of steel with a DBTT ~ Room temp.

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.)

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.)

Design Strategy:Stay Above The DBTT!

Chapter 8-17

• Fatigue = failure under cyclic stress.

tension on bottom

compression on top

countermotor

flex coupling

bearing bearing

specimen

• Stress varies with time. --key parameters are S and

m

max

min

time

mS

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

critical. --causes ~ 90% of mechanical engineering failures.

Adapted from Fig. 8.16, Callister 6e. (Fig. 8.16 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.)

FATIGUE

Load

Explain!

Chapter 8-

FATIGUE

• How ?– Under fluctuating / cyclic stresses, failure can occur at loads considerably

lower than tensile or yield strengths of material under a static load:

• Important ?– Estimated to causes 90% of all failures of metallic structures (bridges,

aircraft, machine components, etc.)

• What is the failure type ?– Fatigue failure is brittle-like (relatively little plastic deformation) - even in

normally ductile materials. Thus sudden and catastrophic!

• Applied stresses causing fatigue may be axial (tension or compression), flextural (bending) or torsional (twisting).

• Fatigue failure proceeds in three distinct stages: – Crack initiation in the areas of stress concentration (near stress raisers), – incremental crack propagation, – final catastrophic failure.

Chapter 8-

Periodic and symmetricalRotating Car axle

Periodic and asymmetrical

Random stress fluctuations

Chapter 8 -

• Fatigue limit, Sfat:

--no fatigue if S < Sfat

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

Fatigue Design Parameters

Sfat

case for steel (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe

S = stress amplitude

• Sometimes, the fatigue limit is zero!

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

case for Al (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe

S = stress amplitude

Chapter 8-18

• Fatigue limit, Sfat: --no fatigue if S < Sfat

• Sometimes, the fatigue limit is zero!

Adapted from Fig. 8.17(a), Callister 6e.

Adapted from Fig. 8.17(b), Callister 6e.

FATIGUE DESIGN PARAMETERS

Sfat

case for Steel % Ti

N = Cycles to failure103 105 107 109

unsafe

safe

S =

str

ess

amp

litu

de

case for Al (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe

S =

str

ess

amp

litu

de

• For steels Sfat = 35%-60% of YS

• Think about design criteria factor, N in chapter 6

Low cycle fatigue: high loads, plastic and elastic deformationHigh cycle fatigue: low loads, elastic deformation (N > 105)

Endurance Limit

Chapter 8-19

• Crack grows incrementally

dadN

K mtyp. 1 to 6

~ a

increase in crack length per loading cycle

• Failed rotating shaft --crack grew even though

Kmax < Kc

--crack grows faster if • increases • crack gets longer • loading freq. increases.

crack origin

Adapted fromFig. 8.19, Callister 6e. (Fig. 8.19 is from D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.)

FATIGUE MECHANISM

Chapter 8 -

Improving Fatigue Life

1. Impose a compressive surface stress (to suppress surface cracks from growing)

N = Cycles to failure

moderate tensile mLarger tensile m

S = stress amplitude

near zero or compressive mIncreasing

m

--Method 1: shot peening

put surface

into compression

shot--Method 2: carburizing

C-rich gas

2. Remove stress concentrators. Adapted from

Fig. 8.25, Callister 7e.

bad

bad

better

better

Adapted fromFig. 8.24, Callister 7e.

Chapter 8-

1. Impose a compressive surface stress (to suppress surface cracks from growing)

20

--Method 1: shot peening

2. Remove stress concentrators.

bad

bad

better

better

--Method 2: carburizing

C-rich gasput

surface into

compression

shot

Adapted fromFig. 8.23, Callister 6e.

N = Cycles to failure

moderate tensile mlarger tensile m

S = stress amplitude

near zero or compressive m

Adapted fromFig. 8.22, Callister 6e.

IMPROVING FATIGUE LIFE

POLISH THE SURFACE !

Chapter 8-

timeelastic

primary secondary

tertiary

T < 0.4 Tm

INCREASING T

0

strain,

• Occurs at elevated temperature, T > 0.4 Tmelt

• Deformation changes with time.

21

Adapted fromFigs. 8.26 and 8.27, Callister 6e.

CREEP

0 t

Chapter 8-

• Most of component life spent here.• Strain rate is constant at a given T, --strain hardening is balanced by recovery

22

stress exponent (material parameter)

strain rateactivation energy for creep(material parameter)

applied stressmaterial const.

• Strain rate increases for larger T,

10

20

40

100

200

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

s

Stress (MPa)427C

538C

649C

Adapted fromFig. 8.29, Callister 6e.(Fig. 8.29 is from Metals Handbook: Properties and Selection: Stainless Steels, Tool Materials, and Special Purpose Metals, Vol. 3, 9th ed., D. Benjamin (Senior Ed.), American Society for Metals, 1980, p. 131.)

s K2nexp

QcRT

.

SECONDARY CREEP

Chapter 8-

• Failure: along grain boundaries.

23

time to failure (rupture)

function ofapplied stress

temperature

T(20 logtr ) L

L(103K-log hr)

Str

ess

, ks

i

100

10

112 20 24 2816

data for S-590 Iron

20appliedstress

g.b. cavities

• Time to rupture, tr

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

T(20 logtr ) L

1073K

24x103 K-log hr

Ans: tr = 233hr

Adapted fromFig. 8.45, Callister 6e.(Fig. 8.45 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).)

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.)

CREEP FAILURE

Chapter 8-24

• Engineering materials don't reach theoretical strength.

• Flaws produce stress concentrations that cause premature failure.

• Sharp corners produce large stress concentrations and premature failure.• Failure type depends on T and stress:

-for noncyclic and T < 0.4Tm, failure stress decreases with: increased maximum flaw size, decreased T, increased rate of loading.-for cyclic : cycles to fail decreases as increases.

-for higher T (T > 0.4Tm): time to fail decreases as or T increases.

SUMMARY (I)

Chapter 8-

SUMMARY (II)

Chapter 8-

Reading: Chapter 8 and Chapter 9 at least twice !Use the CD and review Chapter 7 and 8 !

Core Problems: 8.7,8.10, 8.13, 8.17, 8.22

Self-help Problems: 8.1, 8.2, 8.3, 8.15, 8.20, 8.21

0

ANNOUNCEMENTS

Homework due January 5th , 2009