A statistical consideration of Miner's rule

Abstract

Miner's rule regarding the fatigue behaviour of materials is discussed in statistical terms. The conditions required for both the parameters of the log-normal and Weibull distribution functions of fatigue life and the cumulative damage rule to satisfy the statistical Miner's rule are derived. For the case when the conditions obtained are not satisfied, the reliability of the population and the mean cumulative cycle ratio to failure are considered for two-step fatigue tests, and calculation examples are given. It is found that fatigue life scatter has a fairly large effect on the mean cumulative cycle ratio to failure.