CHAPTER 8Failure Analysis and

Prevention

The repetitive loading of engineering materi-als opens up additional opportunities for struc-tural failure. Shown here is a mechanical test-ing machine, introduced in Chapter 6, modifiedto provide rapid cycling of a given level of me-chanical stress. The resulting fatigue failure is amajor concern for design engineers. ( Courtesyof Instron Corporation)

Anvil

End of swing

Pointer

Specimenh

h′

Starting position

Hammer

Scale

Figure 8-1 Charpy test of impact energy. (From H. W. Hayden, W. G. Moffatt,and J. Wulff, The Structure and Properties of Materials, Vol. 3: MechanicalBehavior, John Wiley & Sons, Inc., New York, 1965.)

Cu: 23000-061

–200 0 +200

Testing temperature, ºF

Testing temperature, ºC

400

70

Impa

ct e

nerg

y, ft

•lb

Impa

ct e

nerg

y, J

100

80

60

40

20

0–200 –100 0 +100 200 300

60

50

40

30

20

10

0

Mg: AM100A

Figure 8-2 Impact energy for a ductile fcc alloy (copper C23000–061, “red brass”) is generally high over a wide temperaturerange. Conversely, the impact energy for a brittle hcp alloy(magnesium AM100A) is generally low over the same range.(From Metals Handbook, 9th Ed., Vol. 2, American Societyfor Metals, Metals Park, Ohio, 1979.)

Temperature, F

Temperature, F

Temperature, C

Impa

ct e

nerg

y, J

Impa

ct e

nerg

y, ft

•lb

Impa

ct e

nerg

y, J

Impa

ct e

nerg

y, ft

•lb

(a)

Temperature, C

(b)

250

200

150

100

50

0

0–100

–100

0

50

100

150

200

250

300

–50 –25 0 25 50 75 100 125 150

–50

2% Mn

0.5% Mn

0% Mn

1% Mn

0 50 100 150 200 250 300

–50 0 50 100 150 200 250

175

150

125

100

75

50

25

200

150

100

50

0

0

100 200 300 400

0.11% C

0.20% C

0.31% C 0.60% C0.41% C

0.80% C

0.49% C0.69% C

Figure 8-3 Variation in ductile-to-brittletransition temperature with alloy com-position. (a) Charpy V-notch impactenergy with temperature for plain-carbonsteels with various carbon levels (inweight percent). (b) Charpy V-notchimpact energy with temperature for Fe–Mn–0.05C alloys with various man-ganese levels (in weight percent). (FromMetals Handbook, 9th Ed., Vol. 1, Amer-ican Society for Metals, Metals Park,Ohio, 1978.)

(a) (b)

Figure 8-4 (a) Typical “cup and cone” ductile fracture surface. Fractureoriginates near the center and spreads outward with a dimpled tex-ture. Near the surface, the stress state changes from tension to shearwith fracture continuing at approximately 45◦. (From Metals Hand-book, 9th Ed., Vol. 12, ASM International, Metals Park, Ohio, 1987.)(b) Typical cleavage texture of brittle fracture surface. (From MetalsHandbook, 9th Ed., Vol. 11, American Society Metals, Metals Park,Ohio, 1986.)

a

Figure 8-5 Fracturetoughness test.

Log flaw size (log a)

a critical

(flaw-induced fracture)

1a1 2!!

Figure 8-6 A design plot of stress versus flaw size for a pressure vesselmaterial in which general yielding occurs for flaw sizes less than acritical size, acritical, but catastrophic “fast fracture” occurs for flawslarger than acritical.

Figure 8-7 Two mechanisms for improv-ing fracture toughness of ceramics bycrack arrest. (a) Transformation tough-ening of partially stabilized zirconiainvolves the stress-induced transforma-tion of tetragonal grains to the mono-clinic structure which has a larger spe-cific volume. The result is a local vol-ume expansion at the crack tip, squeez-ing the crack shut and producing a resid-ual compressive stress. (b) Microc-racks produced during fabrication ofthe ceramic can blunt the advancingcrack tip.

TetragonalZrO2 grain

MonoclinicZrO2 grain

Microcrack

(a)

Cubic ZrO2matrix

(b)

StressTensile strength (T.S.)

Fracture

Time

Figure 8-8 Fatigue corresponds to the brittle fracture of an alloy after a total of N cycles to a stressbelow the tensile strength.

Bearing housing

Bearing housing

Flexible coupling Counter

High-speed motor

Specimen

FulcrumFulcrum

P/2 P/2

Figure 8-9 Fatigue test. (From C. A. Keyser, Materials Science in Engineering,4th Ed., Charles E. Merrill Publishing Company, Columbus, Ohio, 1986.)

1000

500

T.S.

Fatigue strengthor endurance limit

01 102 104

Number of cycles to failure, N

App

lied

stre

ss, S

(M

Pa)

10 103 105 107106 108

Figure 8-10 Typical fatigue curve. (Note that a log scale is required for the horizontal axis.)

Specimen surface

Localized slip

Intrusion

(a)

(b)

(c)

(d)

Figure 8-11 An illustration of how repeatedstress applications can generate local-ized plastic deformation at the alloy sur-face leading eventually to sharp discon-tinuities.

Cycles, N

Cra

ck le

ngth

, a

a1

a0

dadN 1 2 da

dN 1 2

Figure 8-12 Illustration of crack growth with number of stress cycles, N , at two dif-ferent 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 ofstress.

Stress intensity factor range, DK (log scale)

Cra

ck g

row

th r

ate,

(lo

g sc

ale)

da dN

= A(DK)mdadN

I II III

Figure 8-13 Illustration of logarithmic relationship be-tween crack growth rate, da/dN , and the stress in-tensity factor range, 1K . Region I corresponds tononpropagating fatigue cracks. Region II correspondsto a linear relationship between log da/dN and log1K . Region III represents unstable crack growthprior to catastrophic failure.

(a)

(b) (c)

Figure 8-14 Characteristic fatigue fracture surface. (a) Photograph of an aircraftthrottle-control spring (11

2×) that broke in fatigue after 274 h of service. The al-loy is 17–7PH stainless steel. (b) Optical micrograph (10×) of the fracture ori-gin (arrow) and the adjacent smooth region containing a concentric line patternas a record of cyclic crack growth (an extension of the surface discontinuity shownin Figure 8–11). The granular region identifies the rapid crack propagation atthe time of failure. (c) Scanning electron micrograph (60×), showing a closeupof the fracture origin (arrow) and adjacent “clamshell” pattern. (From MetalsHandbook, 8th Ed., Vol. 9: Fractography and Atlas of Fractographs, AmericanSociety for Metals, Metals Park, Ohio, 1974.)

Pearlitic (80 – 55 – 06 as cast) unnotched

40

400

350

300

250

200

150

100

50104 105 106 107 108

20

Fatigue life, cycles

Fati

gue

stre

ngth

, MP

a

200

150

100

50

Fati

gue

stre

ngth

, MP

a

Fati

gue

stre

ngth

, ksi

26

22

18

14

10

Fati

gue

stre

ngth

, ksi

(a)

21 C (70 F)

65 C (150 F)

100 C (212 F)

107 108106

Stress cycles

(b)

Figure 8-15 Comparison of fatigue curves for (a) ferrous and(b) nonferrous alloys. The ferrous alloy is a ductile iron.The nonferrous alloy is C11000 copper wire. The nonfer-rous data do not show a distinct endurance limit, but thefailure stress at N = 108 cycles is a comparable parameter.(After Metals Handbook, 9th Ed., Vols. 1 and 2, AmericanSociety for Metals, Metals Park, Ohio, 1978, 1979.)

500

00 500

Tensile strength, T.S. (MPa)

Fati

gue

stre

ngth

, F.S

. (M

Pa)

1000

F.S. = T.S.1

2

F.S. = T.S.1

4

Figure 8-16 Plot of data from Table 8.4 showing how fatigue strength is gener-ally one-fourth to one-half of the tensile strength.

Increased cold work or surfacesmoothness

S

Log N

Figure 8-17 Fatigue strength is increased by prior mechanicaldeformation or reduction of structural discontinuities.

25,000

Fused silica glass (wet)

Soda-limesilica glass

(wet)

10–3 10–1 10Stress duration, sec.

Bre

akin

g st

ress

, psi

10–2 1 102 104103 105

20,000

15,000

10,000

5,000

0

Figure 8-18 The drop in strength of glasses with duration of load (and withoutcyclic load applications) is termed static fatigue. (From W. D. Kingery, In-troduction to Ceramics, John Wiley & Sons, Inc., New York, 1960.)

O

O

+

Si

OHSi

Si

HO Si

H H

Figure 8-19 The role of H2O instatic fatigue depends on itsreaction with the silicate net-work. One H2O moleculeand one –Si–O–Si– segmentgenerate two Si–OH units.This is equivalent to a breakin the network.

Crack growth by local shearing mechanism

(a)

H2O H2O

Crack growth by chemical breaking ofoxide network

(b)

Figure 8-20 Comparison of (a) cyclic fatigue inmetals and (b) static fatigue in ceramics.

601800 cycles per minute

23˚C(73˚F)

1

2

3

4

21˚C(73˚F)

66˚C(150˚F)

100˚C(212˚F)

50

40

30

20

10

0

8

7

6

5

4

3

2

1

0103 104 105

Cycles to failure

1. Tensile stress only2. Completely reversed tensile and compressive stress3. Completely reversed tensile and compressive stress4. Completely reversed tensile and compressive stress

106 107

Stre

ss (

MP

a)

Stre

ss (

103 p

si)

Figure 8-21 Fatigue behavior for an acetal polymer at various temper-atures. (From Design Handbook for Du Pont Engineering Plas-tics, used by permission.)

x-ray source

Test piece(containing high-densityinclusion and low-densitypore)

Film(showing correspondinglesser and greater filmdarkening)

Figure 8-22 A schematic of x-radiography.

Waterbath

Frontsurface

Oscilloscopedisplay

Flaw

Backsurface

Flaw

Time

Inte

nsit

y

Sample

Ultrasonic transducer

Initial pulse

Figure 8-23 A schematic of a “pulse echo” ultrasonic test.

(Courtesy of Paramount Pictures and Twentieth Century Fox)