An equivalent domain integral method for fracture analysis of functionally graded materials under thermal stresses

This paper presents the formulation and finite element implementation of the equivalent domain integral (EDI) for fracture analysis of functionally graded materials (FGMs) under thermal stresses. By carrying out the neccesary modifications resulting from material nonhomogeneity and thermal strains, the generalized J-integral is converted to an equivalent domain integral around the crack tip for both plane stress and plane strain problems of thermoelasticity. The developed procedure is integrated in a fracture analysis code FRAC2D using graded and cubic finite elements in order to calculate the stress intensity factor undermode I steady-state and transient thermal loading conditions. Temperature distribution profiles in FGMs are calculated using the finite elements based heat transfer analysis code HEAT2D. Comparisons of the computed thermal stress intensity factors to the results available in the literature and to those calculated by an enriched finite element method show that developed EDI approach produces highly accurate results and possesses the required domain independence. Detailed parametric analyses are performed in order to examine the influences of material property variation profiles and geometrical parameters on the mode I stress intensity factors. It is shown that variation profiles of the thermomechanical parameters such as Poisson's ratio, thermal expansion coefficient and thermal conductivity significantly influence both the amplitude of the stress intensity factors and the transient crack closure behavior.