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Fatigue Failure Resulting from Variable Loading 291
Table 6–4 Temperature, °C S T/S RT Temperature, °F S T/S RT

Effect of Operating 20 1.000 70 1.000
Temperature on the 50 1.010 100 1.008
Tensile Strength of 100 1.020 200 1.020
Steel.* (S T = tensile 150 1.025 300 1.024
strength at operating 200 1.020 400 1.018
temperature; 250 1.000 500 0.995
S RT = tensile strength 300 0.975 600 0.963
at room temperature; 350 0.943 700 0.927
0.099 ≤ˆσ ≤ 0.110) 400 0.900 800 0.872
450 0.843 900 0.797
500 0.768 1000 0.698
550 0.672 1100 0.567
600 0.549

*Data source: Fig. 2–9.

Finally, it may be true that there is no fatigue limit for materials operating at high tem-
peratures. Because of the reduced fatigue resistance, the failure process is, to some
extent, dependent on time.
The limited amount of data available show that the endurance limit for steels
increases slightly as the temperature rises and then begins to fall off in the 400 to 700°F
range, not unlike the behavior of the tensile strength shown in Fig. 2–9. For this reason
it is probably true that the endurance limit is related to tensile strength at elevated tem-
18
peratures in the same manner as at room temperature. It seems quite logical, therefore,
to employ the same relations to predict endurance limit at elevated temperatures as are
used at room temperature, at least until more comprehensive data become available. At
the very least, this practice will provide a useful standard against which the perfor-
mance of various materials can be compared.
Table 6–4 has been obtained from Fig. 2–9 by using only the tensile-strength data.
Note that the table represents 145 tests of 21 different carbon and alloy steels. A fourth-
order polynomial curve fit to the data underlying Fig. 2–9 gives

−3
−5
k d = 0.975 + 0.432(10 )T F − 0.115(10 )T 2
F
(6–27)
−8
3
+ 0.104(10 )T − 0.595(10 −12 )T 4
F F
◦
where 70 ≤ T F ≤ 1000 F.
Two types of problems arise when temperature is a consideration. If the rotating-
beam endurance limit is known at room temperature, then use
S T
k d = (6–28)
S RT
18 For more, see Table 2 of ANSI/ASME B106. 1M-1985 shaft standard, and E. A. Brandes (ed.), Smithell’s
Metals Reference Book, 6th ed., Butterworth, London, 1983, pp. 22–134 to 22–136, where endurance limits
from 100 to 650°C are tabulated.