A Computational Framework for 2D Crack Growth Based on the Adaptive Finite Element Method

Abstract

As a part of a damage tolerance assessment, the goal of this research is to estimate the two-dimensional crack propagation trajectory and its accompanying stress intensity factors (SIFs) using the adaptive finite element method. The adaptive finite element code was developed using the Visual Fortran language. The advancing-front method is used to construct an adaptive mesh structure, whereas the singularity is represented through construction of quarter-point single elements around the crack tip. To generate an optimal mesh, an adaptive mesh refinement procedure based on the posteriori norm stress error estimator is used. The splitting node strategy is used to model the fracture, and the trajectory follows the successive linear extensions for every crack increment. The stress intensity factors (SIFs) for each crack extension increment are calculated using the displacement extrapolation technique. The direction of crack propagation is determined using the theory of maximum circumferential stress. The present study is carried out for two geometries, namely a rectangular structure with two holes and one central crack, and a cracked plate with four holes. The results demonstrate that, depending on the position of the hole, the crack propagates in the direction of the hole due to the unequal stresses at the crack tip, which are caused by the hole’s influence. The results are consistent with other numerical investigations for predicting crack propagation trajectories and SIFs.