A Finite Element Analysis for Evaluation of J-Integral in Plates Made of Functionally Graded Materials with a Semicircular Notch

Abstract

This work introduces a numerical investigation using finite element method to evaluate the J-integral at crack tip in titanium boride (TiB)–titanium (Ti) ceramic–metal functionally graded materials plate with a semicircular notch at side subjected to different mechanical load conditions (mode I and mixed mode). Young’s modulus of the functionally graded material plate varies along the specimen width (notch radius direction r-FGM) with power-law and exponential-law functions. Further, the Poisson’s ratio is taken as a constant in normal direction to the hole with a power-law function. The relation of J-integral with functionally graded material plate parameters (i.e., power-law index, thickness of plate) and geometrical parameters (i.e., normalized crack length, notch radius ratio) is highlighted; these parameters must be optimized in order to improve the performance. The obtained results show that it requires estimating the length of the crack, the plate thickness, the notch root radius, the variation in the material properties of the FGM plate constituents and the crack direction that they have a significant influence on the J-integral at the crack tip, and the controlled it can be significantly reduce the J-integral. It is noticed also that in the mixed mode the J-integral is more affected than in mode I.