Thermal response of a partially insulated interface crack in a graded coating-substrate structure under thermo-mechanical disturbance: Energy release and density

Consider the thermal fracture problem of a functionally graded coating-substrate structure of finite thickness with a partially insulated interface crack subjected to thermal-mechanical supply. A new model is proposed that the heat conduction through the crack region occurs and the temperature drop across the crack surfaces is the result of the thermal resistance. For the first time, real fundamental solutions are derived for the fracture analysis of functionally graded materials. The complicated mixed boundary problems of equations of heat conduction and elasticity are converted analytically into singular integral equations, which are solved numerically. The asymptotic expressions with higher order terms for the singular integral kernels are considered to improve the accuracy and efficiency of the numerical integration. Explicit expressions of various failure modes including stress intensity factors, energy release rate and strain energy density, are provided. Numerical results are presented to illustrate the effects of non-homogeneity parameters and the dimensionless thermal resistance on the temperature distribution along the crack surfaces and extended crack line, the thermal stress intensity factors and minimum strain energy density.