On the Mechanical Modeling of Functionally Graded Interfacial Zone With a Griffith Crack: Anti-Plane Deformation

Abstract

An analytical 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 broken line, the interfacial zone with material properties varying continuously in an arbitrary manner is modeled as a multilayered medium with the elastic modulus varying linearly in each sublayer and continuous on the interfaces between sublayers. With this new multilayered model, we analyze the problem of a Griffith crack in the interfacial zone. The transfer matrix method and Fourier integral transform technique are used to reduce the mixed boundary-value problem to a Cauchy singular integral equation. The stress intensity factors are calculated. The paper compares the new model to other models and discusses its advantages.