A generalized J-integral for thermal shock analyses of 3D surface cracks in spatially and temperature dependent materials

In this paper, we present the derivation of the 3D J-integral for arbitrary location and temperature dependent anisotropic material behavior. The functionally varying material properties are implemented in the finite element method (FEM) by means of »graded elements«. The J-integral is calculated in post-processing using the equivalent domain integral technique. The method is applied to surface cracks in a functionally graded plate under mechanical and thermal shock loading. Hereby, the real measured variation of all thermal and mechanical properties with porosity and temperature is exploited for a CaAl ceramic. The influence of the material gradation on the fracture parameters J and KI is investigated in various examples in order to find optimal gradation functions. It could be shown that the temperature dependency of thermoelastic material properties has an important effect on the results and must not be neglected.