A Bayesian approach in deriving Paris law parameters from S-N curve data

Probabilistic fatigue analysis is often carried out based on traditional S-N curve data and/or fracture mechanics in consideration of uncertainty. One of the basic equations, which is governed by the theory of fracture mechanics, is the Paris law. However, it is not an easy task to determine the Paris law parameters experimentally, because various sources of uncertainty are involved and experimental data is limited, whereas plenty of experimental data exists for S-N curves. This paper proposes a novel method termed the S-N Paris law (SNPL) method to quantify the uncertainties lying in 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 helps determine 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. When more S-N test data is available, the prior statistical parameters are updated, which provides more reliable information on the Paris law parameters. To test the proposed method, it is applied to two numerical examples with various assumptions on the S-N curve experiments and the Paris law, and the analysis from the SNPL method successfully provides results that show good agreement with the assumptions