1

Chapter 8: Mechanical Failure ISSUES 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 loading rate, loading history, and temperature

affect the failure behavior of materials?

Ship-cyclic loading

from waves.

Computer chip-cyclic

thermal loading.

Hip implant-cyclic

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 plastic deformation

2

• Brittle fracture

– Little or no plastic deformation

– Catastrophic

Ductile vs Brittle Failure

3

Very

Ductile

Moderately

Ductile Brittle

Fracture

behavior:

Large Moderate %AR or %EL Small

• Ductile fracture is

usually more desirable

than brittle fracture!

Adapted from Fig. 8.1,

Callister & Rethwisch 8e.

• Classification:

Ductile:

Warning before

fracture

Brittle:

No

warning

DUCTILE FRACTURE

• Highly ductile materials – Pure gold and lead at room temperature, and other metals,

polymers, and inorganic glasses at elevated temperatures.

– They neck down to a point fracture

– Showing virtually 100% reduction in area.

4

• Moderate ductile fracture • The most common type of tensile fracture profile for ductile

materials

• Brittle fracture • Happens without any appreciable deformation and by rapid

crack growth

• The direction of crack growth is very nearly perpendicular to the

direction of the applied stress and yields a briefly flat surface.

5

Example: Pipe Failures

• 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.

• Brittle failure: -- many pieces

-- small deformations

6

Moderately Ductile Failure

• Resulting

fracture

surfaces

(steel)

50 mm

particles

serve as void

nucleation

sites.

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 mm

Fracture surface of tire cord wire

loaded in tension. Courtesy of F.

Roehrig, CC Technologies, Dublin,

OH. Used with permission.

• Failure Stages: necking

s

void nucleation

void growth and coalescence

shearing at surface

fracture

Moderately Ductile vs. Brittle Failure

7

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

cup-and-cone fracture brittle fracture

Moderately Ductile Failure

8

– Occurs in several stages: 1) initial necking, 2) small cavity

formation, 3) coalescence of cavities to form a crack, 4)

crack propagation, 5) final shear fracture at a 45 angle

relative to the tensile direction

– 45° with the tensile axis is the angle at which the shear

stress is maximum

Fractography-Ductile materials

9

– In a cop-and-cone fracture, the central interior region of the

surface has an irregular and fibrous appearance, which is

indicative of plastic deformation

– High magnification: consists of numerous spherical

“dimples”. Each dimple is one half of a microvoid that formed

and then separated during fracture process (elongated and

C-shaped).

Figure 8.4

Fractography-Brittle materials

10

– In brittle fracture, the sign of gross plastic

deformation is absent. A series of V-shaped

“chevron” marking may form near the center of the

fracture cross section that point back toward the

crack initiation site.

– Other brittle fracture surfaces contain lines or ridges that

radiate from the origin of the crack in a fanlike pattern

– Brittle fracture in amorphous materials, such as

ceramic glasses, yields a relatively shiny and

smooth surface

Brittle Failure

Arrows indicate point at which failure originated

11 Adapted from Fig. 8.5(a), Callister & Rethwisch 8e.

CLEAVAGE FRACTURE

12

– For most brittle crystalline materials, crack

propagation corresponds to the successive and

repeated breaking of atomic bonds along specific

crystallographic planes (Cleavage).

– This type of fracture is transgranular (or

transcrystalline), as the fracture cracks pass

through the grains.

– Macroscopically, the fracture surface may have a

grainy or faceted texture, because the orientation

of the cleavage planes were changed from grain

to grain.

13

Brittle Fracture Surfaces • Intergranular (between grains) 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.

4 mm

• Transgranular (through 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.)

3 mm

160 mm

1 mm (Orig. source: K. Friedrick, Fracture 1977, Vol.

3, ICF4, Waterloo, CA, 1977, p. 1119.)

INETRGRANULAR FRACTURE

14

– Normally results subsequent to the occurrence of

processes that weaken or embrittle grain

boundary regions.

15

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

TS << TS engineering

materials

perfect

materials

s

e

E/10

E/100

0.1

perfect mat’l-no flaws

carefully produced glass fiber

typical ceramic typical strengthened metal typical polymer

• DaVinci (500 yrs ago!) observed... -- the longer the wire, the

smaller the load for failure.

• Reasons:

-- flaws cause premature failure.

-- larger samples contain longer 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.

STRESS CONCENTRATION

16

– Theoretical calculations of fracture strength is

based on atomic bonding energies.

– The measured fracture strengths of materials are

significantly lower than the theoretical values,

because of the presence of microvoid flaws or

cracks that always exist under normal conditions.

– The applied stress is amplified or concentrated at

the crack tips.

– The flaws are called stress risers

Flaws are Stress Concentrators!

• Griffith Crack

where t = radius of curvature

so = applied stress

sm = stress at crack tip

17

t

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

ott

om Ks

ss2/1

2a

Concentration of Stress at Crack Tip

18

Adapted from Fig. 8.8(b),

Callister & Rethwisch 8e.

ENGINEERING FRACTURE DESIGN

19

– Stress amplification is not restricted to these

microscopic defects, and may occur at

macroscopic internal discontinuities (e.g., voids or

inclusions), at sharp corers, scratches, and

notches.

– When the magnitude of a tensile stress at the tip

of one of the flaws exceeds the value of critical

stress, a crack forms and then propagate, which

result in fracture.

ENGINEERING FRACTURE DESIGN

20

Engineering Fracture Design

21

r/h

sharper fillet radius

increasing w/h

0 0.5 1.0 1.0

1.5

2.0

2.5

Stress Conc. Factor, K t =

• Avoid sharp corners! s

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

s max

smax

s0

Crack Propagation

22

Cracks having sharp tips propagate easier than cracks

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

“blunts” 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

ductile

Criterion for Crack Propagation

23

Crack propagates if crack-tip stress (sm) exceeds a critical stress (sc)

where – E = modulus of elasticity

– s = specific surface energy

– a = one half length of internal crack

For ductile materials => replace s with s + p

where p is plastic deformation energy

2/12

sas

cE

i.e., sm > sc

Example – Brittle Fracture • Given Glass Sheet with

– Tensile Stress,

s = 40 Mpa

– E = 69 GPa

– = 0.3 J/m

• Find Maximum Length

of a

Surface Flaw

• Plan

• Set sc = 40Mpa

• Solve Griffith Eqn for

Edge-Crack Length

2

2

applied

sEa

s

Solving

µm2.8m102.8

N/m1040

N/m3.0N/m10692

6

226

29

a

a

Fracture Toughness Ranges

25

Based on data in Table B.5,

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.,

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

K Ic

(MP

a ·

m 0.

5 )

1

Mg alloys

Al alloys

Ti alloys

Steels

Si crystal

Glass - soda

Concrete

Si carbide

PC

Glass 6

0.5

0.7

2

4

3

10

2 0

3 0

<100>

<111>

Diamond

PVC

PP

Polyester

PS

PET

C-C (|| fibers) 1

0.6

6 7

4 0

5 0 6 0 7 0

100

Al oxide Si nitride

C/C ( fibers) 1

Al/Al oxide(sf) 2

Al oxid/SiC(w) 3

Al oxid/ZrO 2 (p) 4

Si nitr/SiC(w) 5

Glass/SiC(w) 6

Y 2 O 3 /ZrO 2 (p) 4

26

Design Against Crack Growth • Crack growth condition:

• Largest, most highly stressed cracks grow first!

K ≥ Kc = asY

--Scenario 1: Max. flaw

size dictates design stress.

maxas

YKc

design

s

amax no fracture

fracture

--Scenario 2: Design stress

dictates max. flaw size. 2

max1

s

design

c

YKa

amax

s no fracture

fracture

27

Design Example: Aircraft Wing

Answer: MPa 168)( Bsc

• 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 KIc are the same for both designs.

• Material has KIc = 26 MPa-m0.5

• Use... maxa

sY

KIcc

B max Amax aa cc ss

9 mm 112 MPa 4 mm --Result:

= a = sY

KIc constant

Design using fracture mechanics

Example:

Compare the critical flaw sizes in the following metals subjected to

tensile stress 1500MPa and K = 1.12 sa.

KIc (MPa.m1/2)

Al 250

Steel 50

Zirconia(ZrO2) 2

Toughened Zirconia 12

Critical flaw size (microns)

7000

280

0.45

16

Where Y = 1.12. Substitute values

SOLUTION

Impact Testing

31

final height initial height

• Impact loading: -- severe testing case

-- makes material more brittle

-- decreases toughness

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,

Mechanical Behavior, John Wiley

and Sons, Inc. (1965) p. 13.)

(Charpy)

32

Influence of Temperature on Impact Energy

Adapted from Fig. 8.15,

Callister & Rethwisch 8e.

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

BCC metals (e.g., iron at T < 914ºC)

Imp

act E

ne

rgy

Temperature

High strength materials ( s y > E/150)

polymers

More Ductile Brittle

Ductile-to-brittle transition temperature

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

33

Design Strategy: Stay Above The DBTT!

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

• Problem: Steels were used having DBTT’s just below

room temperature.

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.)

FATIGUE

34

Adapted from Fig. 8.18,

Callister & Rethwisch 8e.

(Fig. 8.18 is from Materials

Science in Engineering, 4/E

by Carl. A. Keyser, Pearson

Education, Inc., Upper

Saddle River, NJ.)

• Fatigue = failure under applied cyclic stress.

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

cycling frequency

S = stress amplitude

s max

s min

s

time

s m S

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

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

-- occurs suddenly and catastrophically (brittle-like)

tension on bottom

compression on top

counter motor

flex coupling

specimen

bearing bearing

Fatigue

35

Adapted from Fig. 8.17,

Callister & Rethwisch 8e.

• Fatigue = failure under applied cyclic stress.

• max and min stresses are

asymmetrical relative to the

zero stress

Fatigue

36

Source: https://youtu.be/LhUclxBUV_E

RANGE OF STRESS,STRESS

AMPLITUDE, AND STRESS RATIO

37

• Mean stress

• Range of stresses

• One-half of the range

(stress amplitude)

• Stress ratio

Question

38

• make a schematic sketch of a stress-versus-time plot

for the situation when the stress ratio R has a value of

+1.

39

Types of Fatigue Behavior

Adapted from Fig.

8.19(a), Callister &

Rethwisch 8e.

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

Sfat

case for steel (typ.)

N = Cycles to failure 10

3 10

5 10

7 10

9

unsafe

safe

S =

str

ess a

mplit

ude

• For some materials,

there is no fatigue

limit!

Adapted from Fig.

8.19(b), Callister &

Rethwisch 8e.

case for Al (typ.)

N = Cycles to failure 10

3 10

5 10

7 10

9

unsafe

safe

S =

str

ess a

mplit

ude

CREEP

40

• time-dependent and permanent deformation of

materials when subjected to constant load or stress

• normally an undesirable phenomenon and reduces the

lifetime of the mechanical parts

• for metals, it becomes important at T>0.4Tm (absolute

temperature)

• amorphous polymers are specially sensitive to creep

deformation

CREEP Sample deformation at a constant load or stress (s) vs. time

(T = constant)

41

Adapted from

Fig. 8.28, Callister &

Rethwisch 8e.

Primary Creep: slope (creep rate)

decreases with time.

Secondary Creep: steady-state

i.e., constant slope De/Dt).

Tertiary Creep: slope (creep rate)

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

s

s,e

0 t

elastic deformation

CREEP CURVE

42

• Primary region: the material is experiencing an

increase in creep resistance or strain hardening (the

deformation becomes more difficult as the material is

strained)

• Secondary region: the longest duration ( a balance

between the competing processes of strain hardening

and recovery)

• Tertiary region: the acceleration of the rate of creep.

The failure is termed “rupture”

•

ENGINEERING DESINS

43

• in the long-life applications (e.g., nuclear power plant),

De/Dt) is the most important parameter from a creep

rupture test.

• in short-life creep situations (e.g., turbine blades), time

to rupture or rupture lifetime is the dominant design

consideration.

•

UNDERESTANDING CREEP

44

Source: https://youtu.be/opPWceW-YKc

45

Creep: Temperature Dependence

• Occurs at elevated temperature, T > 0.4 Tm (in K)

Adapted from Fig. 8.29,

Callister & Rethwisch 8e.

elastic

primary secondary

tertiary

Creep: Temperature Dependence

46

• with either increasing stress or temperature:

• the instantaneous strain at the tie of stress application

increases

• the steady-state creep rate is increased

• the rupture life is diminished

•

47

Secondary Creep • Strain rate is constant at a given T, s

-- strain hardening is balanced by recovery

stress exponent (material parameter)

strain rate

activation energy for creep

(material parameter)

applied stress material const.

• Strain rate

increases

with increasing

T, s

10

2 0

4 0

10 0

2 0 0

10 -2 10 -1 1

Steady state creep rate (%/1000hr) e s

Str

ess (

MP

a) 427ºC

538ºC

649ºC

Adapted from

Fig. 8.31, Callister 7e.

(Fig. 8.31 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.)

se

RTQ

K cns exp2

Prediction of Creep Rupture Lifetime

48

• prolonged creep tests are sometimes not practical!

• one solution is to perform creep rupture tests at

temperatures in excess of those required, for shorter

time periods, and at a comparable stress level, and

then making a suitable extrapolation to the in-service

condition.

• a common extrapolation procedure is Larson-Miller

parameter.

Prediction of Creep Rupture Lifetime • Estimate rupture time S-590 Iron, T = 800ºC, s = 20,000 psi

time to failure (rupture)

function of

applied stress

temperature

LtT r )log20(

Time to rupture, tr

310x24)log20)(K 1073( rt

Ans: tr = 233 hr Adapted from Fig. 8.32, Callister & Rethwisch

8e. (Fig. 8.32 is from F.R. Larson and J.

Miller, Trans. ASME, 74, 765 (1952).)

103 L (K-h)

Str

ess (

10

3 p

si)

100

10

1 12 20 24 28 16

data for

S-590 Iron

20

24

49

Estimate the rupture time for S-590 Iron, T = 750ºC, s = 20,000 psi

• Solution:

50 50

Adapted from Fig. 8.32, Callister & Rethwisch

8e. (Fig. 8.32 is from F.R. Larson and J.

Miller, Trans. ASME, 74, 765 (1952).)

103 L (K-h)

Str

ess (

10

3 p

si)

100

10

1 12 20 24 28 16

data for

S-590 Iron

20

24

310x24)log20)(K 1023( rt

Ans: tr = 2890 hr

time to failure (rupture)

function of

applied stress

temperature

LtT r )log20(

Time to rupture, tr

51

SUMMARY • Failure type depends on T and s :

-For simple fracture (noncyclic s and T < 0.4Tm), failure stress

decreases with:

- increased maximum flaw size,

- decreased T,

- increased rate of loading.

- For fatigue (cyclic s:

- cycles to fail decreases as Ds increases.

- For creep (T > 0.4Tm):

- time to rupture decreases as s or T increases.