A probabilistic model for fatigue crack growth prediction based on closed-form solution

Abstract

The stochastic property of fatigue crack growth is well-known, and brings a challenge for accuracy fatigue life prediction. This paper proposes a probabilistic model for predicting the fatigue crack growth under the framework of linear elastic fracture mechanics. The stress intensity factor is related to the crack length and load condition through finite element model. The material parameters and model error are regarded as random variables. Based on conjugate Bayesian analysis, a closed-form solution is derived to update the posterior distribution of material parameters according to the crack growth observation. Given the posterior distribution, a modified Paris–Erdogan model is adopted to predict the crack growth in a probabilistic view. The contribution of this paper is providing a closed-form solution for updating the well-known Paris–Erdogan equation, and predicting the crack propagation more efficiently and accurately. Comprehensive experiments show the superiority of the proposed method over existing Markov Chain Monte Carlo (MCMC) approaches.