Characteristics of a crack propagating along the gradient in functionally gradient materials

Stress and displacement fields for a crack propagating along gradient in a functionally gradient material, which has (1) a linear variation of shear modulus with a constant density and Poisson's ratio, and (2) an exponential variation of shear modulus and density under a constant Poisson's ratio, are developed. The equations of motion in nonhomogeneous materials are first developed using displacement potentials and the solution to the displacement fields and the stress fields for a crack propagating at constant speed though an asymptotic analysis. The influence of nonhomogeneity on the higher order terms of the stress fields are explicitly brought out. Using these stress components, isochromatic fringes around the propagating crack are generated for different crack speeds and nonhomogeneity and the effects of nonhomogeneity on these fringes are discussed. (C) 2004 Elsevier Ltd. All rights reserved.