New data analysis of probabilistic stress-life (P–S–N) curve and its application for structural materials

Conventional S–N fatigue curves, the so-called Wöhler curves are generally considered as the experimental fatigue life plots for several stress amplitudes. The curves are usually expressed as median ranks and each life distribution is supposed to follow the log-normal distributions. Therefore, it can be said that not enough work on the theoretical relationship between the life distributions and the S–N curve exists till today. This paper unveils a new data analysis method for a probabilistic stress-life (P–S–N) curve. It was used to define the physical meaning of the statistical parameters in the Weibull and the lognormal life distribution function as well as the P–S–N curve. At first, it was applied to conventional S–N test results for bearing steel (no fatigue limit) and rail steel (showing fatigue limit) in the literature. The test data for the material showing no fatigue limit on a log–log (not a semi-log) paper results in a straight line plot, but for the materials showing fatigue limit the data plot is an asymptote to the fatigue limit for any of the probabilities of failure. Following this, the alternating torsion life test data for two P–S–N test series of through hardened bearing steels were examined. The three-parameter Weibull as well as the log-normal distribution function fit fairy well to the life distribution data for the two test materials. No fatigue limit was observed on both materials for the projected data onto the P–S–N curves; and the P–S–N life formulas were successively conducted.