Fitting Method of Small Sample P-S-N Curve Based on Weibull Distribution

Abstract

Abstract In order to obtain the probabilistic stress-fatigue life curve of materials with small samples, a small sample P-S-N curve fitting method is proposed. This method is based on the premise that Weibull distribution can be applied to fatigue test data the method first uses the sample mean fitting to obtain the median S-N curve. Secondly, constructs the random variable function based on the Weibull distribution characteristics, in addition, the sample median is used as the initial value of iteration to perform perturbation optimization to determine the shape parameter a and the scale parameter β of Weibull distribution. The fitting of P-S-N curve is realized. Taking the fatigue data of aluminum alloy 2425-T3 as an example, the results show that the intercept relative error and slope error are less than 0.5% by comparing the fitting results of the proposed method with those of the traditional method, and the intercept error between the proposed method and the traditional method is less than 1.5% and the slope error is small when designing three groups of small sample fitting schemes (7-7-7-7, 5-5-5, 3-3-3) at 3.0%. The proposed method can obtain high-precision P-S-N curve fitting results in the case of small samples, which have a certain significance for engineering applications.