On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: plane deformation

Abstract

A new multi-layered model is developed for a functionally graded interfacial zone between two dissimilar elastic solids based on the fact that an arbitrary curve can be approached by a continuous but piecewise linear curve. The interfacial zone with both Young’s modulus and Poisson’s ratio varying continuously in an arbitrary manner is divided into multiple layers with the material properties varying linearly in each sub-layer and continuous at the interfaces between sub-layers. With this new model, we analyze the problem of a Griffith crack in the interfacial zone under plane stress-state deformation. The transfer matrix method and Fourier integral transform technique are used to reduce the mixed boundary-value problem to a set of Cauchy singular integral equations. The stress intensity factors are calculated. The paper compares the new model to other existing models and discusses its advantages.