Multiple Parallel Symmetric Mode-III Cracks in a Functionally Graded Material Plane

Abstract

In this paper, the basic solutions of multiple parallel symmetric finite length cracks in a functionally graded material plane subjected to anti-plane shear stress loading were studied by the Schmidt method. The problem was formulated through Fourier transform into dual integral equations, respectively, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The results show that the stress intensity factors at the crack tips depend on the crack lengths, spacing of the cracks and the functionally graded parameter. It is also revealed that the crack shielding effect presents in functionally graded materials.