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

Hamrock, Jacobson and Schmid©1998 McGraw-Hill

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

Hamrock, Jacobson and Schmid©1998 McGraw-Hill

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

Hamrock, Jacobson and Schmid©1998 McGraw-Hill

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