An engineering method for reliability analyses of mechanical structures for long fatigue lives

Reliability analyses of mechanical structures designed for long fatigue lives require: some information on the probability distribution of material fatigue strength at long fatigue lives. In order to address this need, three-parameter P-S-N curves are adopted to represent the results of fatigue tests based on the conventional method. The parameters of the P-S-N curves are estimated by using the least squares fitting method and maximizing the correlation coefficient. The three-parameter P-S-N curves obtained are then used to estimate the fatigue strengths for different survival probabilities at an arbitrarily long fatigue life. These fatigue strengths are used to define the probability distribution of fatigue strength at the long fatigue life when a normal. distribution is used to approximate the probability distribution of fatigue strength. The method is illustrated by analyzing the results of fatigue tests of steel #45 (Chinese steel) notched specimens subject to axial loads with a stress concentration factor kt = 2·0. Then, the method is applied to the fatigue reliability analysis of the runner of a hydraulic turbine. It is shown here that the reliability at long lifetimes can be easily estimated by the proposed engineering method and the conventional method may give a non-conservative design at long fatigue lives due to the assumption of bi-linear P-S-N curves.