Chapter 7: Failure Prediction for Cyclic and
Impact Loading
All machines and structural
designs are problems in
fatigue because the forces of
Nature are always at work
and each object must respond
in some fashion.
Carl Osgood, Fatigue
Design
Image: Aloha Airlines flight 243, a Boeing 737-200, taken April 28, 1988. The midflight fuselage failure was caused by corrosion assisted fatigue.
©1998 McGraw-Hill
Hamrock, Jacobson and Schmid
On the Bridge!
Figure 7.1 “On the Bridge,” an
illustration from Punch magazine in
1891 warning the populace that death
was waiting for them on the next bridge.
Note the cracks in the iron bridge.
[From Petroski (1992).]
Cyclic Stress
Cyclic Stress
Figure 7.2 Variation in nonzero cyclic mean stress.
©1998 McGraw-Hill
Text Reference: Figure 7.2, page 261
Hamrock, Jacobson and Schmid
Cyclic Properties of Some Metals
Material
Steel
1015
4340
1045
1045
1045
1045
4142
4142
4142
4142
4142
A luminum
1100
2014
2024
5456
7075
a
Conditio n
Yield
strength,
Sy
Mpa
Fatigue
strength,
’ f,
Mpa
Fatigue
Fatigue
ductility
strength
coefficient exponent,
’ f
a
Fatigue
ductility
exponent,

Normalized
Tempered
Q&Ta 80°F
Q&T 360 °F
Q&T 500 °F
Q&T 600 °F
Q&T 80°F
Q&T 400 °F
Q&T 600 °F
Q&T 700 °F
Q&T 840 °F
228
1 172
1 720
1 275
965
2 070
1 720
1 340
1 070
900
82 7
1655
2140
2720
2275
1790
2585
2650
2170
2000
1550
0.95
0.73
0.07
0.25
0.35
0.07
0.09
0.40
0.45
-0.110
-0.076
-0.065
-0.055
-0.080
-0.070
-0.075
-0.076
-0.081
-0.080
-0.080
-0.64
-0.62
-1.00
-0.60
-0.68
-0.69
-1.00
-0.76
-0.66
-0.73
-0.75
Annealed
T6
T351
H3 11
T6
97
462
379
234
469
19 3
84 8
1103
72 4
1317
1.80
0.42
0.22
0.46
0.19
-0.106
-0.106
-0.124
-0.110
-0.126
-0.69
-0.65
-0.59
-0.67
-0.52
Quenched and tempered
Table 7.1 Cyclic properties of some metals [From Shigley and Mischke (1989) and Suresh (1991)]
©1998 McGraw-Hill
Text Reference: Table 7.1, page 263
Hamrock, Jacobson and Schmid
R.R. Moore Specimen
Figure 7.3 R.R. Moore machine fatigue test specimen.
©1998 McGraw-Hill
Text Reference: Figure 7.3, page 264
Hamrock, Jacobson and Schmid
Fatigue Strength vs. Cycles to Failure
Figure 7.4 Fatigue strengths as a function of number of loading cycles.
Ferrous alloys, showing clear endurance limit.
©1998 McGraw-Hill
Text Reference: Figure 7.4, page 266
Hamrock, Jacobson and Schmid
Fatigue Strength vs. Cycles to Failure (cont.)
Figure 7.4 Fatigue strengths as a function of number of loading cycles.
Aluminum alloys, with less pronounced knee and no endurance limit.
©1998 McGraw-Hill
Text Reference: Figure 7.4, page 266
Hamrock, Jacobson and Schmid
Fatigue Strength vs. Cycles to Failure (cont.)
Figure 7.4 Fatigue strengths as a function of number of loading cycles. (c)
Selected properties of assorted polymer classes.
©1998 McGraw-Hill
Text Reference: Figure 7.4, page 266
Hamrock, Jacobson and Schmid
Endurance Limit vs. Ultimate Strength
Figure 7.5 Endurance limit as a function of ultimate strength for wrought steels.
©1998 McGraw-Hill
Text Reference: Figure 7.5, page 267
Hamrock, Jacobson and Schmid
Approximate Endurance Limit
for Various Materials
Material
Magnesium alloys
Copper alloys
Nickel alloys
Titanium
Aluminum alloys
Number of Cycles
108
108
108
107
5 x 108
Relation
S’e=0.35Su
0.25Su< S’e <0.5 Su
0.35 Su < S’e <0.65
Su
0.45 Su < S’e <0.65
Su
S’e =0.45 Su (Su
<48ksi)
S’e =19 ksi (Su
≥48ksi)
Table 7.2 Approximate endurance limit for various materials [From Juvinall and Marshek (1991)].
©1998 McGraw-Hill
Text Reference: Table 7.2, page 267
Hamrock, Jacobson and Schmid
Notch Sensitivity
Figure 7.6 Notch sensitivity as a function of notch radius for several materials
and types of loading. [From Sines and Waisman (1959)].
©1998 McGraw-Hill
Text Reference: Figure 7.6, page 272
Hamrock, Jacobson and Schmid
Surface Finish Factors
Figure 7.7 Surface finish factors
for steel Function of ultimate
strength in tension for different
machine processes. [From Shigley
and Mitchell (1983).]
©1998 McGraw-Hill
Text Reference: Figure 7.7, page 273
Hamrock, Jacobson and Schmid
Surface Finish Factors (cont.)
Figure 7.7 Surface finish factors for steel (b) Function of ultimate strength and
surface roughness as measured with a stylus profilometer. [From Johnson (1967).]
©1998 McGraw-Hill
Text Reference: Figure 7.7, page 274
Hamrock, Jacobson and Schmid
Surface Finish Factor
Factor e
Manufacturin
g
Process
Grinding
Machining or
cold drawing
Hot rolling
None (as
forged)
Exponent f
Mpa
1.58
4.51
ksi
1.34
2.70
-0.085
-0.265
57.7
272.0
14.4
39.9
-0.718
-0.995
Table 7.3 Surface finish factor [From Shigley and Mischke (1989)].
Usage:
kf=e(Sut)f (ref: Eq. 7.21)
©1998 McGraw-Hill
Text Reference: Table 7.3, page 274
Hamrock, Jacobson and Schmid
Reliability Correction Factors
Probability of
survival, percent
50
90
95
99
99. 9
99.99
©1998 McGraw-Hill
Reliability facto r,
kr
1.00
0.90
0.87
0.82
0.75
0.70
Table 7.4 Reliability correction
factors for six probabilities of
survival.
Text Reference: Table 7.4, page 275
Hamrock, Jacobson and Schmid
Example 7.4
Figure 7.8 Tensile-loaded bar. (a) Unnotched; (b) notched.
©1998 McGraw-Hill
Text Reference: Figure 7.8, page 277
Hamrock, Jacobson and Schmid
Influence of Non-Zero Mean Stress
Figure 7.9 Influence of nonzero mean stress on fatigue life for
tensile loading as estimated by four empirical relationships.
©1998 McGraw-Hill
Text Reference: Figure 7.9, page 280
Hamrock, Jacobson and Schmid
Modified Goodman Diagram
Figure 7.10 Complete
modified Goodman diagram,
plotting stress as ordinate and
mean stress as abscissa.
©1998 McGraw-Hill
Text Reference: Figure 7.10, page 283
Hamrock, Jacobson and Schmid
Example 7.7
Figure 7.11 Modified Goodman diagram for Example 7.7.
©1998 McGraw-Hill
Text Reference: Figure 7.11, page 285
Hamrock, Jacobson and Schmid
Alternating Stress Ratio vs. Mean Stress Ratio
Figure 7.12 Alternating stress ratio as a function of mean stress
ratio for axially loaded cast iron.
©1998 McGraw-Hill
Text Reference: Figure 7.12, page 287
Hamrock, Jacobson and Schmid
Correction
Factor Y
Figure 7.13 Correction factor Y to compensate for plate width in fracture mechanics
approach to fatigue crack propogation. [From Suresh (1991).]
©1998 McGraw-Hill
Text Reference: Figure 7.13, page 289
Hamrock, Jacobson and Schmid
Properties vs. Strain Rate
Figure 7.14 Mechanical properties of mild steel at room temperature as
a function of average strain rate. [From Manjoine (1994).]
©1998 McGraw-Hill
Text Reference: Figure 7.14, page 291
Hamrock, Jacobson and Schmid
Example 7.10
Figure 7.15 Diver impacting diving board, used in Example 7.10. (a) Side
view; (b) front view; (c) side view showing forces and coordinates.
©1998 McGraw-Hill
Text Reference: Figure 7.15, page 293
Hamrock, Jacobson and Schmid
Brake Stud
Figure 7.16 Dimensions of existing brake stud design. Note that
no radius has been specified at point A-A.
©1998 McGraw-Hill
Text Reference: Figure 7.16, page 296
Hamrock, Jacobson and Schmid
Applied Loads and Resultant Stress Cycle
Figure 7.17 Press brake loads. (a) Shear and bending moment diagram for
applied load; (b) stress cycle.
©1998 McGraw-Hill
Hamrock, Jacobson and Schmid
Daño Acumulativo
Regla de Daño lineal o de Palgrem Miner
n1 n2

 ...  1
N1 N 2
Se predice la falla cuando la fracción de daño por niveles diferentes de esfuerzo
excede la unidad.
El nivel de daño es directamente proporcional al número de ciclos, donde no
importa la secuencia de los mismos.
©1998 McGraw-Hill
Hamrock, Jacobson and Schmid
Daño Acumulativo
Para la barra sin muesca, el esfuerzo de fatiga se refleja en la siguiente tabla:
% tiempo
Esfuerzo(ksi)
20
25
30
30
40
35
10
40
Hallar el número de ciclos hasta la falla acumulativa
n1 n2

 ...  1
N1 N 2
©1998 McGraw-Hill
Hamrock, Jacobson and Schmid
Daño Acumulativo
Para la barra sin muesca, el esfuerzo de fatiga se refleja en la siguiente tabla:
% tiempo
Esfuerzo(ksi)
20
25
30
30
40
35
10
40
n1 n2

 ...  1
N1 N 2
©1998 McGraw-Hill
Hamrock, Jacobson and Schmid