Bayesian estimation of the lethargy coefficient for probabilistic fatigue life model

In this study, a model for probabilistic fatigue life that is based on the Zhurkov model is suggested using stochastically and statistically estimated lethargy coefficients. The fatigue life model was derived using the Zhurkov life model, and it was deterministically validated using real fatigue life data as a reference. For this process, firstly, a lethargy coefficient that is related to the failure of materials must be obtained with rupture time and stress from a quasi-static tensile test. These experiments are performed using HS40R steel. However, the lethargy coefficient has discrepancies due to the inherent uncertainty and the variation of material properties in the experiments. The Bayesian approach was employed for estimating the lethargy coefficient of the fatigue life model using the Markov Chain Monte Carlo (MCMC) sampling method and considering its uncertainties. Once the samples are obtained, one can proceed to the posterior predictive inference of the fatigue life. This life model was shown to be reasonable when compared with experimental fatigue life data. As a result, predicted fatigue life was observed to significantly decrease in accordance with increasing relative stress conditions.