Nonlinear Fatigue Crack Growth Simulations using J-integral Decomposition and XFEM

Abstract

In the present work, nonlinear fatigue crack growth analysis of an inclined edge crack is performed by extended finite element method (XFEM) [1]. The material behavior is assumed to be nonlinear, which is modelled by Ramberg-Osgood model and von-Mises yield criterion. Due to inherent material nonlinearity, the interaction integral approach cannot be used for evaluating the individual stress intensity factors (SIFs). Hence, the mixed mode crack growth problem is solved by decomposing the mixed mode J-integral into mode-I and mode-II. The decomposition of stress, strain and displacement fields is done by considering the symmetric and anti-symmetric parts of the corresponding field [2]. The symmetric part of these fields is related with the symmetric part of J-integral and provides mode-I SIF (KI) whereas the anti-symmetric part of these fields provides the mode-II SIF (KII). The equivalent KI and KII are used to find the direction of crack growth and the equivalent effective KIeq for the obtained direction of the crack growth. The range of KIeq (ΔKIeq) is used with the Paris law to evaluate the rate of crack growth. For highly nonlinear materials, J-integral decomposition method is more suitable then interaction integral approach.