A thorough review of the state-of-the-art of determining fatigue life of machine and structural members considering cumulative damage effect under varying stress amplitudes is given. Among the many proposed theories, Miner’s linear damage rule is seen to be as reliable as any other rule alleged to be an improvement for predicting fatigue life under cumulative damage effects. Its simplicity and amenability for easy modification have in fact been the basis for some other theories and used in design codes. In its original form, Miner’s rule, however does not account for fatigue strength reducing factors. Observing fatigue data on the effects of fatigue strength reducing factors, the article offers a modified form of the Miner’s rule to consider the effects of fatigue strength reducing factors, such as the notch, reliability, surface finish, size, and environmental factors. The mean stress effect and material properties are incorporated utilizing Bagci’s mean stress line and the S-N diagram. The safe fatigue life of a component subjected to stresses of varying magnitudes becomes
$Ns=df/∑i=1s(αi/10zi)$
where
$zi=A{B−log(pig/Rf)$
$+log[1−(pi/mi)r]}$
in the ith block of stress range, Rf being the resultant of fatigue strength reducing factors; A, B, g are parameters defined by material properties, pi is the ratio of the basic alternating stress times the factor of safety (the failure value) to the yield strength of the material, and mi is the slope of the load line in the ith block of loading. Design charts for zi for steel and aluminum alloys for cases with and without basic mean stress for r=4 are given. Numerical examples are included. Therefore, the article offers the most general form of the Miner’s rule for designers’ use for fatigue design considering cumulative damage effect.
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