P–S–N curves fitting method of small samples obeying Weibull distribution

Abstract

A three‐parameter Weibull small sample aggregation method is proposed to address the problem of small sample fatigue data in practical engineering. First, based on the empirical assumption that the shape parameter is a constant and data equivalent conversion and aggregation, the small sample fatigue life data are converted into “equivalent large samples.” Second, through the linear relationship between logarithmic scale parameter and stress, an iterative procedure is established to estimate the scale parameters of small sample data. At the same time, the moment and rank estimation methods are used to solve the location parameters quickly. Finally, P–S–N curves with different survival rates are given, and a 7‐series aluminum alloy is selected to verify the correctness and reliability of the method proposed in this study. The results show that the predicted life obtained by the method still has high accuracy under a high survival rate, which can provide a theoretical basis for solving practical engineering problems.