A new Bayesian approach to derive Paris\' law parameters from S-N curve data

The determination of Paris\' law parameters based on crack growth experiments is an important procedure of fatigue life assessment. However, it is a challenging task because it involves various sources of uncertainty. This paper proposes a novel probabilistic method, termed the S-N Paris law (SNPL) method, to quantify the uncertainties underlying the Paris\' law parameters, by finding the best estimates of their statistical parameters from the S-N curve data using a Bayesian approach. Through a series of steps, the SNPL method determines the statistical parameters (e.g., mean and standard deviation) of the Paris\' law parameters that will maximize the likelihood of observing the given S-N data. Because the SNPL method is based on a Bayesian approach, the prior statistical parameters can be updated when additional S-N test data are available. Thus, information on the Paris\' law parameters can be obtained with greater reliability. The proposed method is tested by applying it to S-N curves of 40H steel and 20G steel, and the corresponding analysis results are in good agreement with the experimental observations.