Chap8fatiguepart1

Fundamentals of Machine Component Design, 4/E by Robert C. Juvinall and Kurt M. Marshek

Copyright © 2006 by John Wiley & Sons, Inc. All rights reserved.

Fatigue

• Progressive fracture that begins at small microscopic cracks

• Beach mark- smooth velvety texture- the fatigue zone

• Final rough fracture



Figure 8.1 (p. 291)Fatigue failure originating in the fillet of an aircraft crank-shaft [SAE 4340 steel 320-

Bhn].



Fatigue

• Results from repeated plastic deformation

• Failures occur after 1,000 or more cycles

• Failures can occur at stress levels far below static yield criteria (i.e. Sy)

• Avoid highly localized plastic yielding if loads are cyclic

• Strain strengthening possible if local yielding is small enough; local yielding then ceases– Loss of ductility if local yielding is not sufficiently minute

• Initial fatigue crack produces increase in local stress concentration.– Decrease in cross sectional area for carrying load as crack

propagates



Figure 8.2 (p. 292)Enlarged view of a notched region.



Fatigue Life Models

• Based on empirical data

• 4 pt bending specimen results in pure bending

• Add rotation of specimen to fully reverse and cycle stresses

• R.R. Moore Rotating Beam Fatigue Test

– i.e. σ(t) = σmax sin(ωt)



Figure 8.3 (p. 293)R.R. Moore rotating-beam fatigue-testing machine.



Figure 8.4a (p. 294)Three S-N plots of representative fatigue data for 120 Bhn steel. (Continued on next two slides.)



Figure 8.4b (cont.)



Figure 8.4c (cont.)

For a given life, small scatter

in fatigue strength

For a given fatigue strength,

large scatter in life



Figure 8.5 (p. 295)Generalized S-N curve for wrought steel with superimposed data points.



Figure 8.6 (p. 295)Endurance limit versus hardness for four alloy steels. [From M.F. Garwood et al., Interpretation of Tests and Correlation with Service. American Society of Metals, 1951. p. 13.]



Figure 8.7 (p. 296)Representation of maximum bending stress at low fatigue life (1000 cycles). (Note: Calculated maximum stress is used in S-N plots.)



Figure 8.8 (p. 296)S-N bands for representative aluminum alloys, excluding wrought alloys with Su < 38 ksi.

No knee in diagram!

No infinite life!



Figure 8.9 (p. 297)Fatigue strength at 5 x 108 cycles, common wrought-aluminum alloys..

400,000 miles before cylinder fires this

many times



Rotating Bending Verses Reversed Bending

W

θ = ωt

F(t) = Fmax sin(ωt)

If Fmax = W, which test would result in failure first?

Fatigue strength in reversed bending slightly greater than in rotating bending



Rotating Bending Verses Reversed Axial Loading

W

θ = ωt

F(t) = Fmax sin(ωt)

If Fmax and W are such that σmax is same, which test would result in failure first?

Fatigue strength in reversed axial loading 10 percent or more lower than in

Reversed bending

Reduce by gradient factor CG = 0.9 for pure axial

loading of precision parts, 0.7 – 0.9 for axial loading of

nonprecision parts

nS′



Reversed Torsional Loading

Endurance limit in reversed torsion is about 58 percent of endurance limit in

reversed bending

103 cycle strength 0.9 appropriate ultimate strength i.e. ultimate shear strength

Sus = 0.8 Su for steel

Sus = 0.7 Su for other ductile materials



Figure 8.12 (p. 300)A σ1–σ2 plot for completely

reversed loading, ductile

materials. [Data from Walter Sawert, Germany, 1943, for annealed mild steel; and H.J. Gough, "Engineering Steels under Combined Cyclic and Static Stresses." J. Appl. Mech., 72: 113–125 (March 1950).]-



Figure 8.11 (p. 299)Generalized S-N curves for polished 0.3=in. diameter steel specimens (based

on calculated elastic stresses ignoring possible yielding).



Figure 8.13 (p. 301)Reduction in endurance limit owing to surface finish–steel parts.



Figure 8.14 (p. 302)Stress gradients versus diameter for bending and torsion.

Parts that are greater than 0.4” diameter and are subjected to reversed bending

or torsion should carry a gradient factor of CG = 0.9, the same as parts subjected

to axial loading



Summary

n n L G S T RS S C C C C C′=

Load factorGradient

factor Surface

finish factor

Temperature

factor

Reliability

factor



Table 8.1a (p.

303)Generalized Fatigue

Strength Factors for

Ductile Materials

(S-N curves).

(Continued on next slide.)



Table 8.1b (cont.)



Figure 8.15 (p. 305)Fluctuating stress notation illustrated with two examples.



Figure 8.16 (p. 305)Constant-life fatigue diagram – ductile materials.

Yield free zone



Figure 8.17 (p. 306)Fatigue-strength diagram for alloy steel, Su = 125 to 180 ksi, axial loading. Average of test data for polished specimens of AISI 4340 steel (also applicable

to other alloy steels, such as AISI 2330, 4130, 8630). (Courtesy Grumman

Aerospace Corporation.)



Figure 8.18 (p. 306)Fatigue strength diagram for 2024-T3, 2024-T4, and 2014-T6 aluminum alloys

axial loading. Average of test data for polished specimens (unclad) from rolled and drawn sheet and bar. Static properties for 2024: Su = 72 ksi, Sy = 52 ksi; for 2014, Su = 72 ksi. Sy = 63 ksi. (Courtesy Grumman Aerospace Corporation.)



Figure 8.19 (p. 307)Fatigue stress diagram for 7075-T6 aluminum alloy, axial loading. Average of test data for polished specimens (unclad) from rolled and drawn sheet and bar.

Static properties: Su = 82 ksi, Sy = 75 ksi. (Courtesy Grummon Aerospace

Corporation.)



Figure 8.20 (p. 307)Various fluctuating uniaxial stresses, all of which correspond to equal fatigue life.



Figure 8.21 (p. 308)Axial loading of precision steel part.



Figure 8.22 (p. 310)Sample Problem 8.1 – estimate S-N and σm and σa curves for steel, Su = 150 ksi, axial loading, commercially polished surfaces.

Chap8fatiguepart1

Documents

Transcript of Chap8fatiguepart1