Stochastic XFEM based fracture behavior and crack growth analysis of a plate with a hole emanating cracks under biaxial loading

Abstract

In the paper, the stochastic fracture response of an isotropic finite plate with a circular hole emanating radial cracks, having different angles, under biaxial loading with different biaxiality ratio (β=0,1 and −1) is examined. In this direction, the mean values and corresponding coefficient of variations (COVs) of mixed mode stress intensity factor (MMSIFs) using the second order perturbation technique (SOPT) combined with a finite difference method through extended finite element method (XFEM) are evaluated in MATLAB environment. The random system parameters, e.g., normalized crack length, crack angle, the normalized radius of the hole, are assumed as uncorrelated input random variables. The effects, of these input parameters and biaxial load factors, on the statistics of MMSIFs with input individual and combined random system parameters, are analyzed. Also, the stochastic fracture behavior is predicted with the increment in the radius of the hole and with the change in the position of the discontinuities (a hole emanating cracks) in the plate using uncorrelated combined randomness with different input variables. Further, the static crack propagation behavior of the plate with hole emanating cracks under biaxial loading with different biaxiality ratio is analyzed.