Four parallel non-symmetric Mode-III cracks with different lengths in a functionally graded material plane

Abstract

The behavior of four parallel non-symmetric cracks with different lengths in a functionally graded material plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through Fourier transform into four pairs of dual integral equations, 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 cracks and the material parameters. It was also revealed that the crack shielding effect presents in functionally graded materials.