Crack Propagation Simulation for Metal-Ceramic FGMs by Enriched Natural Element Method

The structural failure of functionally graded materials (FGMs) is mostly triggered by the micro-cracks so that the crack propagation is an important research subject. In this connection, the goal of this study is to develop a reliable numerical method for solving the crack propagation in 2-D inhomogeneous FGMs. To accomplish this goal, this paper introduces an improved crack propagation simulation method for 2-D FGMs by applying the enrichment technique to the natural element method (NEM). The global displacement field is interpolated using Laplace interpolation (LI) functions in NEM, and it is enhanced by the crack-tip singular displacement field. The stress intensity factors (SIFs) of FGMs having the varying Young's modulus in space was computed by the modified interaction integral M-(1,M-2), while the trajectories in crack propagation were predicted using the maximum principal stress (MPS) criterion and the effective SIF K-leqv at mode I. The present method was validated from the comparison with ANSYS and the unriched PG-NEM. It is found that the enriched NEM greatly enhances the simulation reliability of crack trajectory, such that it produces the crack trajectory close to one obtained by ANSYS. As well, it successfully predicted the remarkable variation of crack trajectories of FGM with exponentially varying elastic modulus.