A solution to the problem of elastic half-plane with a cohesive edge crack

Abstract

This paper considers the problem of extension of an elastic half-plane slackened by a rectilinear edge crack. The opposite edges of the crack are attracted to each other. The intensity of attracting forces – the forces of cohesion – depends on displacements of the edges; this dependence is nonlinear in the general case. External load and cohesive forces are related to each other by the condition of finite stresses at the crack tip. The authors apply Picard’s method of successive approximation. In each iteration, Irwin’s method is used to solve the problem of a half-plane with a crack, the edges of which are subjected to irregularly distributed load. The solution of the resulting integral equation is found by Galerkin’s method. The paper includes examples of calculations and their results. Some of them are compared with the data of previous studies.