Calculating Strain Energy Release Rate, Stress Intensity Factor and Crack Propagation of an FGM Plate by Finite Element Method Based on Energy Methods

Abstract

In the field of crack mechanics, predicting the direction of a crack is important because this will evaluate whether, when the crack propagates, it penetrates into important areas and whether the structure is dangerous or not. This paper will refer to three theories that predict the propagation direction of cracks: a theory of maximum tangential normal stress, a theory of maximum energy release, and a theory of minimum strain energy density. At the same time, the finite element method (FEM)–ANSYS program will be used to calculate stress intensity factors (SIFs), strain energy release rate (J-integral), stress field, displacement near a crack tip, and crack propagation phenomenon based on the above theories. The calculated results were compared with the results in other scientific papers and experimental results. This research used ANSYS program, an experimental method combined with FEM based on the above energy theories to simulate the J-integral, the SIFs, and the crack propagation. The errors of the SIFs of the FGM rectangular plate has a through-thickness center crack of 1.77%, J-integral of 4.49%, and crack propagation angle ${\theta }_c$ of 0.15%. The FEM gave good errors compared to experimental and exact methods.