hamrock, jacobson and schmid©1998 mcgraw-hill chapter 7: failure prediction for cyclic and impact...
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Hamrock, Jacobson and Schmid©1998 McGraw-Hill
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 mid-flight fuselage failure was caused by corrosion assisted fatigue.
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
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Cyclic Stress
Figure 7.2 Variation in nonzero cyclic mean stress.
Text Reference: Figure 7.2, page 261
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Cyclic Properties of Some Metals
Material Condition
Yieldstrength,
Sy
Mpa
Fatiguestrength,
’f,Mpa
Fatigueductility
coefficient’f
Fatiguestrength
exponent,a
Fatigueductility
exponent,
Steel10154340104510451045104541424142414241424142
NormalizedTemperedQ&Ta 80°FQ&T 360°FQ&T 500°FQ&T 600°FQ&T 80°FQ&T 400°FQ&T 600°FQ&T 700°FQ&T 840°F
2281172
-17201275965
2070172013401070900
8271655214027202275179025852650217020001550
0.950.73
-0.070.250.35
-0.070.090.400.45
-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
Aluminum11002014202454567075
AnnealedT6
T351H311
T6
97462379234469
19384811037241317
1.800.420.220.460.19
-0.106-0.106-0.124-0.110-0.126
-0.69-0.65-0.59-0.67-0.52
aQuenched and tempered
Table 7.1 Cyclic properties of some metals [From Shigley and Mischke (1989) and Suresh (1991)]
Text Reference: Table 7.1, page 263
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
R.R. Moore Specimen
Figure 7.3 R.R. Moore machine fatigue test specimen.
Text Reference: Figure 7.3, page 264
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
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.
Text Reference: Figure 7.4, page 266
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
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.
Text Reference: Figure 7.4, page 266
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
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.
Text Reference: Figure 7.4, page 266
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Endurance Limit vs. Ultimate Strength
Figure 7.5 Endurance limit as a function of ultimate strength for wrought steels.
Text Reference: Figure 7.5, page 267
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Approximate Endurance Limit for Various Materials
Material Number of Cycles Relation Magnesium alloys 108 S’e=0.35Su Copper alloys 108 0.25Su< S’e <0.5 Su Nickel alloys 108 0.35 Su < S’e <0.65
Su Titanium 107 0.45 Su < S’e <0.65
Su Aluminum alloys 5 x 108 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)].
Text Reference: Table 7.2, page 267
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
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)].
Text Reference: Figure 7.6, page 272
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
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).]
Text Reference: Figure 7.7, page 273
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Surface Finish Factors (cont.)
Text Reference: Figure 7.7, page 274
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).]
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Surface Finish Factor
Manufacturing
Factor e
Exponent f
Process Mpa ksi Grinding 1.58 1.34 -0.085 Machining or cold drawing
4.51 2.70 -0.265
Hot rolling 57.7 14.4 -0.718 None (as forged)
272.0 39.9 -0.995
Table 7.3 Surface finish factor [From Shigley and Mischke (1989)].
Usage:
kf=e(Sut)f (ref: Eq. 7.21)
Text Reference: Table 7.3, page 274
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Reliability Correction Factors
Probability ofsurvival, percent
Reliability facto r,k r
50909599
99.999.99
1.000.900.870.820.750.70
Table 7.4 Reliability correction factors for six probabilities of survival.
Text Reference: Table 7.4, page 275
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Example 7.4
Figure 7.8 Tensile-loaded bar. (a) Unnotched; (b) notched.
Text Reference: Figure 7.8, page 277
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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.
Text Reference: Figure 7.9, page 280
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Modified Goodman Diagram
Figure 7.10 Complete modified Goodman diagram, plotting stress as ordinate and mean stress as abscissa.
Text Reference: Figure 7.10, page 283
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Example 7.7
Figure 7.11 Modified Goodman diagram for Example 7.7.
Text Reference: Figure 7.11, page 285
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
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.
Text Reference: Figure 7.12, page 287
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
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).]
Text Reference: Figure 7.13, page 289
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
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).]
Text Reference: Figure 7.14, page 291
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
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.
Text Reference: Figure 7.15, page 293
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Brake Stud
Figure 7.16 Dimensions of existing brake stud design. Note that no radius has been specified at point A-A.
Text Reference: Figure 7.16, page 296
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Applied Loads and Resultant Stress Cycle
Figure 7.17 Press brake loads. (a) Shear and bending moment diagram for applied load; (b) stress cycle.
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Daño Acumulativo
Regla de Daño lineal o de Palgrem Miner
1...2
2
1
1 N
n
N
n
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.
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Daño Acumulativo
1...2
2
1
1 N
n
N
n
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
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Daño Acumulativo
1...2
2
1
1 N
n
N
n
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