The interface crack problem for a functionally graded coating-substrate structure with general coating properties

A piecewise-exponential model (PE model) is developed for the interface crack problem of a functionally graded coating-substrate structure in which the coating mechanical properties are generally continuous while the substrate is homogeneous. By this way, the coating properties can be approached by a series of exponential functions without losing the continuity. Through a series of mathematical manipulations, the problem is reduced into a group of singular integral equations that can be solved by numerical methods. After analyzing the mix-mode stress intensity factors (SIFs) and the strain energy release rates (SERRs) of some typical examples under plane loadings, the influences of the geometric parameters and coating properties variations on the fracture behaviors of the interface crack are presented. Those analyses can greatly benefit the designs and the manufactures of FGM coating-substrate structures.