3D J-integral for functionally graded and temperature dependent thermoelastic materials

In order to mitigate the thermal shock impact, many ceramics, refractories or heat protecting layers are made of functionally graded (FGM) or layered structures. Fracture mechanical methods are needed to evaluate the resistance of such structures against failure under thermal shock. Despite a lot of theoretical work has been done for two-dimensional crack configurations in thermoelastic FGM, real defects and structural components are of three-dimensional (3D) nature. In most cases the real gradation of the thermoelastic material properties does not obey simple mathematical functions, but show a complex dependency on location due to manufacturing. Moreover, the elastic and thermodynamic properties depend on temperature itself. In the paper, we present the derivation of the 3D J-integral for arbitrary location and temperature dependent material behavior. The J-integral is implemented in FEM by means of the equivalent domain integral technique. The method is applied to a thermally loaded plate of FGM with a surface crack. The influence of the material gradation on the results is investigated in various examples. Copyright (C) 2016 The Authors. Published by Elsevier B.V.