On the dynamic propagation of a finite crack in functionally graded materials

This article provides a comprehensive theoretical investigation of the singular behaviour of a propagating crack in a functionally graded material (FGM) with spatially varying elastic properties under plane elastic deformation. The analytical formulations are developed in terms of Fourier transforms and the solution of the resulting singular integral equations by using Chebyshev polynomials. In this study, we examine the effect of the gradient of material properties and the speed of crack propagation upon the stress intensity factors, the strain energy release rate and the crack opening displacement. The results reveal that although the singular stress field around the tip of a crack in this FGM is governed by the traditional square root singularity, significant discrepancy in the local stress field exist between it and a homogeneous solid. This indicates that the presence of a gradient in the mechanical properties affects the local stress distribution significantly and, ultimately, the fracture behaviour of the solid.