Bayesian model updating and prognosis of fatigue crack growth

This paper presents a framework to update and predict crack length as a function of the number of cycles in structural elements subjected to fatigue. The framework has two main components: (i) a model updating section to identify the probability density function of the fracture mechanics parameters and (ii) a prognosis component used to estimate the crack length of the specimen as a function of the number of cycles. The form of the equation describing the stress intensity range is considered unknown and it is modeled as a polynomial equation function of the crack length. The polynomial coefficients are treated as random variables and their joint probability distribution, together with the probability distribution of other fracture mechanics parameters are computed using Bayesian inference. Markov Chain Monte Carlo (MCMC) is used to predict the crack length at some number of cycles in the future. The methodology is verified using experimental data from a compact tension specimen under constant amplitude load (CAL), a plate with a center crack under variable amplitude load (VAL) and numerically validated using a T-section beam girder with a crack in the web under CAL, and a plate with an inclined center through crack subjected to CAL.