Stress intensity factors for a surface‐breaking crack in a half‐plane subject to contact loading

Abstract

Modes I and II stress intensity factors are derived for a crack breaking the surface of a half‐plane which is subject to various forms of contact loading. The method used is that of replacing the crack by a continuous distribution of edge dislocations and assume the crack to be traction‐free over its entire length. A traction free crack is achieved by cancelling the tractions along the crack site that would be present if the half‐plane was uncracked. The stress distribution for an elastic uncracked half‐plane subject to an indenter of arbitrary profile in the presence of friction is derived in terms of a single Muskhelishvili complex stress function from which the stresses and displacements in either the half‐plane or indenter can be determined. The problem of a cracked half‐plane reduces to the numerical solution of a singular integral equation for the determination of the dislocation density distribution from which the modes I and II stress intensity factors can be obtained. Although the method of representing a crack by a continuous distribution of edge dislocations is now a well established procedure, the application of this method to fracture mechanics problems involving contact loading is relatively new. This paper demonstrates that the method of distributed dislocations is well suited to surface‐breaking cracks subject to contact loading and presents new stress intensity factor results for a variety of loading and crack configurations.