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Fatigue Failure Resulting from Variable Loading 283

140 0.5
S' = 0.6
e
Carbon steels
120 S u
Alloy steels 0.4
Wrought irons 105 kpsi
100
Endurance limit S' e , kpsi 80

60

40

20

0
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
, kpsi
Tensile strength S ut
Figure 6–17

Graph of endurance limits versus tensile strengths from actual test results for a large number of wrought

irons and steels. Ratios of S /S ut of 0.60, 0.50, and 0.40 are shown by the solid and dashed lines. Note
e

also the horizontal dashed line for S = 105 kpsi. Points shown having a tensile strength greater than
e

210 kpsi have a mean endurance limit of S = 105 kpsi and a standard deviation of 13.5 kpsi. (Collated
e
from data compiled by H. J. Grover, S. A. Gordon, and L. R. Jackson in Fatigue of Metals and Structures,
Bureau of Naval Weapons Document NAVWEPS 00-25-534, 1960; and from Fatigue Design Handbook,
SAE, 1968, p. 42.)

Steels treated to give different microstructures have different S /S ut ratios. It
e
appears that the more ductile microstructures have a higher ratio. Martensite has a very
brittle nature and is highly susceptible to fatigue-induced cracking; thus the ratio is low.
When designs include detailed heat-treating specifications to obtain specific micro-
structures, it is possible to use an estimate of the endurance limit based on test data for
the particular microstructure; such estimates are much more reliable and indeed should
be used.
The endurance limits for various classes of cast irons, polished or machined, are
given in Table A–24. Aluminum alloys do not have an endurance limit. The fatigue
8
strengths of some aluminum alloys at 5(10 ) cycles of reversed stress are given in
Table A–24.

6–8 Fatigue Strength

As shown in Fig. 6–10, a region of low-cycle fatigue extends from N = 1 to about
3
10 cycles. In this region the fatigue strength S f is only slightly smaller than the tensile
strength S ut . An analytical approach has been given by Shigley, Mischke, and Brown 10

10 J. E. Shigley, C. R. Mischke, and T. H. Brown, Jr., Standard Handbook of Machine Design, 3rd ed.,
McGraw-Hill, New York, 2004, pp. 29.25–29.27.