Periodic Array of Cracks in a Half-Plane Subjected to Arbitrary Loading

Abstract

The plane elastic problem for a periodic array of cracks in a half-plane subjected to equal, but otherwise arbitrary normal crack surface tractions is examined. The mixed boundary value problem, which is formulated directly in terms of the crack surface displacements, results in a hypersingular integral equation in which the unknown function is the crack opening displacement. Based on the theory of finite part integrals, a least squares numerical algorithm is employed to efficiently solve the singular integral equation. Numerical results include crack opening displacements, stress intensity factors, and Green’s functions for the entire range of possible periodic crack spacing.