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

Thanks to their favorable mechanical properties and modern manufacturing technologies, functionally graded materials (FGM) and structures have gained increasing utilization in engineering. One major applications of functionally graded ceramics, refractories or heat protecting layers is to improve the resistance against thermal shock impact. Here, fracture mechanical methods are needed to evaluate the strength and durability of such structures exposed to transient thermomechanical loading. 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 shows a complex physical dependency on location due to manufacturing. Moreover, the elastic and thermodynamic properties depend on temperature itself. In this paper, we present the derivation of the 3D f-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 f-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] and K-1 is intrestigated 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. (C) 2017 Elsevier Ltd. All rights reserved.