Weibull modeling of the probabilistic S–N curves for rolling contact fatigue

•All the Weibull parameters, confidence parameters and stress–life relation exponent are deduced by test data set.•A least life confidence assessment is incorporated into the probabilistic curves for common applied limited samples case.•Big prediction difference is found in high reliability district for two-parameter and three-parameter Weibull distributions. A Weibull modeling of the probabilistic stress–life (S–N) curves is proposed for rolling contact fatigue (RCF). Shape, scale and location parameters of Weibull distribution, the normal life confidence parameters and the exponent of S–N relation are all deduced from set of test data. Life confidence assessment is incorporated into the probabilistic curves for common applied case of limited samples. Applicability of the present modeling is checked by describing the test data of G20CrNi2Mo bearing steel. Results real that two-parameter (2-P) and three-parameter (3-P) Weibull distributions are acceptable models. But bigger difference is observed in high reliability district. The 3-P one has smaller standard deviation of lives and this deviation is constricted with increasing of stress levels, which is consistency with results of most classical fatigue experiments. While the 2-P modeling fails to well characterizing the test data. This indicates that an appropriate distribution determination is a primary task for RCF analysis. And the 3-P Weibull is a better modeling for the present test data.