Computation of thermal fracture parameters for orthotropic functionally graded materials using Jk-integral

This article introduces a computational method based on the J_k-integral for mixed-mode fracture analysis of orthotropic functionally graded materials (FGMs) that are subjected to thermal stresses. The generalized definition of the J_k-integral is recast into a domain independent form composed of line and area integrals by utilizing the constitutive relations of plane orthotropic thermoelasticity. Implementation of the domain independent J_k-integral is realized through a numerical procedure developed by means of the finite element method. The outlined computational approach enables the evaluation of the modes I and II stress intensity factors, the energy release rate, and the T-stress. The developed technique is validated numerically by considering two different problems, the first of which is the problem of an embedded crack in an orthotropic FGM layer subjected to steady-state thermal stresses; and the second one is that of periodic cracks under transient thermal loading. Comparisons of the mixed-mode stress intensity factors evaluated by the J_k-integral based method to those calculated through the displacement correlation technique (DCT) and to those available in the literature point out that, the proposed form of the J_k-integral possesses the required domain independence and leads to numerical results of high accuracy. Further results are presented to illustrate the influences of the geometric and material constants on the thermal fracture parameters.