Mixed-Mode Fatigue Crack Growth Reliability Analysis: An Extended Finite Element Method-Based Framework

Structural fatigue cracking is an important cause of the failure of engineering structures. Accurately predicting the crack growth behavior of structures and evaluating the structural reliability are crucial for ensuring structural safety and extending the service life. To address this challenge, this paper proposes a reliability analysis method for fatigue crack growth based on the extended finite element method (XFEM). Due to the nonlinear relationship between the uncertain parameters of the cracked structure and the crack length, as well as the stress intensity factor (SIF), the limit state function (LSF) is highly complex. Consequently, the surrogate model is used to establish this relationship. The uncertain structural parameters are sampled using Latin hypercube sampling (LHS), and then XFEM is employed to simulate the crack propagation to obtain a sample dataset. Based on the sample data set, the response surface method (RSM) is applied to establish a surrogate model of the LSF between the uncertain parameters of the cracked structure and the crack growth length, as well as the SIF. The reliability index and failure probability are obtained through the first-order reliability method (FORM), the second-order reliability method (SORM) and the subset simulation (SS) method. By comparing with the Monte Carlo (MC) method, it is found that the SS method has a high accuracy and can provide a new idea for the reliability analysis of structural crack growth.