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?• 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. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.)

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

Chapter 8: Mechanical Failure & Failure Analysis

Adapted from chapter-opening photograph, Chapter 8, Callister 7e. (by Neil Boenzi, The New York Times.)

Fracture mechanisms

• Ductile fracture– Occurs with plastic deformation

• Brittle fracture– Occurs with Little or no plastic

deformation– Thus they are Catastrophic meaning

they occur without warning!

Ductile vs Brittle Failure

Very Ductile

ModeratelyDuctile BrittleFracture

behavior:

Large Moderate%Ra or %El Small

• Ductile fracture is nearly always

desirable!

Ductile: warning before

fracture

Brittle: No

warning

• 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

• Evolution to failure:

• Resulting fracture surfaces (steel)

50 mm

Inclusion 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

Ductile vs. Brittle Failure

Adapted from Fig. 8.3, Callister 7e.

cup-and-cone fracture brittle fracture

Brittle FailureArrows indicate point at which failure originated

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

• 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, "Deformation 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: Useful to examine to determine causes of failure

Failure Analysis – Failure Avoidance

• Most failure occur due to the presence of defects in materials– Cracks or Flaws (stress concentrators)– Voids or inclusions

• Presence of defects is best found before hand and they should be determined non-destructively– X-Ray analysis– Ultra-Sonic Inspection– Surface inspection

• Magna-flux• Dye Penetrant

• Stress-strain behavior (Room Temp):

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.

Considering Loading Rate Effect

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

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

y

y

TS

TS

larger

smaller

Impact (high strain rate) Testing

final height initial height

• Impact loading (see ASTM E23 std.): -- severe testing case -- makes material act more brittle -- decreases toughness• Useful to compare alternative materials

for severe applications

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 Specimen)

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

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

Considering Temperature Effects

BCC metals (e.g., iron at T < 914°C)

Impa

ct E

nerg

y

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.

Figure 8.3 Variation in ductile-to-brittle transition temperature with alloy composition. (a) Charpy V-notch impact energy with temperature for plain-carbon steels with various carbon levels (in weight percent). (b) Charpy V-notch impact energy with temperature for Fe–Mn–0.05C alloys with various manganese levels (in weight percent).

(From Metals Handbook, 9th ed., Vol. 1, American Society for Metals, Metals Park, OH, 1978.)

• Pre-WWI: 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: Build Steel Ships Quickly!

As a Designer: Stay Above The DBTT!

Flaws are Stress Concentrators!

Results from crack propagation• Griffith Crack Model:

where t = radius of curvature

of crack tipo = applied stressm = stress at crack tip

ot

/

tom Ka

21

2

t

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

Concentration of Stress at Crack Tip

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

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 tmaxo

=

• Avoid sharp corners!

Adapted from G.H. Neugebauer, Prod. Eng. (NY), Vol. 14, pp. 82-87 1943.)

r , fillet

radius

w

h

o

max max is the concentrated stress in the narrowed region

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

plastic

When Does a Crack Propagate?Crack propagates if applied stress is above critical

stress

where– E = modulus of elasticity s = specific surface energy– a = one half length of internal crack– Kc = c/0

For ductile materials replace s by s + p where p is plastic deformation energy

212 /s

c aE

i.e., m > c

or Kt > Kc

Fracture Toughness

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/ fibersPolymers

5

KIc

(MP

a · m

0.5)

1

Mg alloysAl alloys

Ti alloys

Steels

Si crystalGlass -sodaConcrete

Si carbide

PC

Glass 6

0.5

0.7

2

4

3

10

20

30

<100><111>

Diamond

PVCPP

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

K1c – plane strain stress concentration factor – with edge crack; A Material Property we use for design, developed using ASTM Std: ASTM E399 - 09 Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness K Ic of Metallic Materials

• Crack growth condition:

• Largest, most stressed cracks grow first!

As Engineers we must 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!

21

design

cmax Y

Ka

amax

no fracture

fracture

Y is a material behavior shape factor

• Two designs to consider...Design A --largest flaw is 9 mm --failure occurs at 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 B9 mm112 MPa 4 mm

--Result:

Let’s look at Another Situation• Steel subject to tensile

stress of 1030 MPa, it has K1c of 54.8 MPa(m) – a handbook value

• If it has a ‘largest surface crack’ .5 mm (.0005 m) long will it grow and fracture?

• What crack size will result in failure?

1

1

1*1030* 3.141*.0005 40.82Since K < K the part won't fail!

a a

a

a c

K Y ahereY

Y a

1

221 54.8

1*10303.1416

.0009 .9

c c

c

c

K Y a

KYa

a m mm

Figure 8.7 Two mechanisms for improving fracture toughness of ceramics by crack arrest. (a) Transformation toughening of partially stabilized zirconia involves the stress-induced transformation of tetragonal grains to the monoclinic structure, which has a larger specific volume. The result is a local volume expansion at the crack tip, squeezing the crack shut and producing a residual compressive stress. (b) Microcracks produced during fabrication of the ceramic can blunt the advancing crack tip

Fatigue behavior:• Fatigue = failure under cyclic stress

• Stress varies with time. -- key parameters are S (stress amplitude), m, and frequency

max

min

time

mS

• Key points when designing in Fatigue inducing situations: -- fatigue can cause part failure, even though max < c. -- fatigue causes ~ 90% of mechanical engineering failures.• Because of its importance, ASTM and ISO have developed many special standards to assess Fatigue Strength of materials

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

tension on bottom

compression on top

countermotor

flex coupling

specimen

bearing bearing

Some important Calculations in Fatigue Testing

2 5max 3

2 5min 3

max

A Material 6.4 mm in is subject to (fatiguing) loads:5340 - tensile then compressive

5340 5340 165.993.22 106.4*10

25340 5340 165.993.22 106.4*10

2

mean stressm

N

MPa

MPa

min

min

165.99 165.990

2 2 stress range 331.99

stress amplitude 165.992

r Max

ra

MPa

MPa

S MPa

Figure 8.8 Fatigue corresponds to the brittle fracture of an alloy after a total of N cycles to a stress below the tensile strength.

• Fatigue limit, Sfat: --no fatigue failure if

S < Sfat

Fatigue Limit is defined in: ASTM D671

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

• However, 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

Let’s look at an Example

2 5max 3

2min 3

Given: 2014-T6 Alum. Alloy bar (6.4 mm )find its fatigue life if a part is subject to loads:

5340 - tensile then compressive5340 5340 165.993.22 106.4*10

25340 5340

3.6.4*102

N

MPa

5

max min

min

6

165.9922 10

165.99 165.990

2 2331.99

165.992Examining Fig (right) at S = 165.99

Fatigue Life = Cycles to Failure 7 10

m

r Max

ra

MPa

MPa

MPa

S MPa

For metals other than Ferrous alloys, F.S. is taken as the stress that will cause failure

after 108 cycles

Figure 8.21 Fatigue behavior for an acetal polymer at various temperatures.

(From Design Handbook for Du Pont Engineering Plastics, used by permission.)

For polymers, we consider fatigue life to be (only) 106 cycles to

failure thus fatigue strength is the stress that will lead to failure

after 106 cycles

• Cracks in Material grows incrementallytyp. 1 to 6

a~

increase in crack length per loading cycle

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

crack origin

Adapted fromfrom D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.

Fatigue Mechanism

mKdNda

Figure 8.11 An illustration of how repeated stress applications can generate localized plastic deformation at the alloy surface leading eventually to sharp discontinuities.

Figure 8.12 Illustration of crack growth with number of stress cycles, N, at two different stress levels. Note that, at a given stress level, the crack growth rate, da/dN, increases with increasing crack length, and, for a given crack length such as a1, the rate of crack growth is significantly increased with increasing magnitude of stress.

Improving Fatigue Life1. Impose a compressive surface stresses (to suppress surface crack growth)

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.

Figure 8.17 Fatigue strength is increased by prior mechanical deformation or reduction of structural discontinuities.

Other Issues in Failure – Stress Corrosion Cracking

• Water can greatly accelerate crack growth and shorten life performance – in metals, ceramics and glasses

• Other chemicals – that can generate (or provide H+ or O2-)

ions – also effectively reduce fatigue life as these ions react with the metal or oxide in the material

Figure 8.18 The drop in strength of glasses with duration of load (and without cyclic-load applications) is termed static fatigue.

(From W. D. Kingery, Introduction to Ceramics, John Wiley & Sons, Inc., New York, 1960.)

Figure 8.19 The role of H2O in static fatigue depends on its reaction with the silicate network. One H2O molecule and one –Si– O–Si– segment generate two Si–OH units, which is equivalent to a break in the network.

Figure 8.20 Comparison of (a) cyclic fatigue in metals and (b) static fatigue in ceramics.

• 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