Fracture in Functionally Gradient Materials Subjected to the Time-Dependent Anti-Plane Shear Load

Abstract

In this article, a finite crack subjected to a general time-dependent anti-plane shear load in functionally gradient materials is studied. The elastic properties of the interfacial layer are assumed to vary continuously between those of two dissimilar homogeneous bonding layers. Laplace and Fourier transforms are applied to reduce this mixed boundary value problem to a system of dual integral equations which in turn will be reduced to a standard Fredholm integral equation of the second kind. The dynamic crack tip stress fields are determined analytically while the dynamic stress intensity factors are evaluated numerically from the standard Fredholm integral equation. The Laplace inversion is performed numerically by using Gauss-quadrature and Jacobi polynomials. In general, the dynamic stress intensity factor is found to be a function of the crack length, location of the crack in interfacial layer, and material properties of the surrounding layers as well as interfacial layer.