Probabilistic analysis of fatigue crack growth using efficient surrogate model

Abstract

In this paper probabilistic analysis of a fatigue crack growth process governed by the Walker law is performed. Sensitivity of its parameters to uncertainties related to the material properties is considered. Based on statistical analysis of experimental data, they are modelled as independent normal random variables. The effect of these uncertainties on the fatigue crack growth behaviour of Centre Cracked Plate specimen is assessed using Monte-Carlo simulations and surrogate model based on polynomial chaos expansion. An efficient truncation scheme allows to discard the high order interactions having a weak effect on the mechanical response and consequently reduce the number of finite elements calls when identifying the unknown coefficients of the polynomial chaos expansion. The statistical moments namely the mean and the standard deviation in addition to the probability density function of the mechanical response are derived with a good accuracy. The obtained results show that the fatigue crack growth life is significantly affected by the uncertainties on the material properties since its coefficient of variation reaches 21% and that it follows a log-normal distribution law.