Edge Crack Solution Through Use of Dislocation Shielding/Antishielding

Abstract

The edge crack problem in an elastic solid has been treated by a number of investigators. The crack tip stress intensity factor, under uniform loading, of a mode I edge crack of length a has been shown to be 12% greater than a crack of half-length a within an infinite solid. In this paper a new method of solution for this old problem is presented. The crack within an infinite solid can be considered to be a distribution of infinitesimal dislocations on the (horizontal) crack plane. The edge crack is made up of both an infinitesimal edge dislocation distribution on the (horizontal) crack plane and an infinitesimal edge dislocation distribution on the (vertical) free surface when the edge crack is treated by the image dislocation method. (That is, the edge crack is considered to be within an infinite solid and image dislocations are used to cancel surface tractions on the free surface.) The image dislocations on the free surface shield or antishield the crack tip. The dislocation crack tip stress shielding/antishielding stress intensity factor L for a dislocation (of arbitrary Burgers vector) situated at an arbitrary position about a crack was derived earlier. The edge crack solution is derived with use of this L. The use of L is the novel feature of the solution. The crack intensity factor for the mode I edge crack under uniform loading is found to be 12% greater than the equivalent crack within an infinite solid.