Numerical study on crack propagation simulation in functionally graded materials by enriched natural element method

Abstract

Most of numerical studies on the crack propagation have dealt with homogeneous materials using FEM. In this context, the purpose of current study is to introduce a numerical method for simulating the crack propagation in 2-D functionally graded materials (FGMs) by an enriched Petrov-Galerkin natural element method (PG-NEM). The displacement field is basically approximated in terms of Laplace interpolation functions in NEM, but it is enriched by the near-tip singular field. Whether the crack is propagated or not is judged in terms of the equivalent mode-I SIF and the fracture toughness. And, the crack propagation direction is predicted by the maximum principal stress (MTS) criterion. Two numerical examples are presented, one for the validation of proposed method and the other for the parametric investigation of crack trajectory in FGMs. It is justified that the enriched PG-NEM successfully and accurately predicts the crack trajectories in FGMs. And, it is found that the power index of Young's modulus of FGMs influences the crack propagation length.