Brittle fracture under a sliding line contact

When an indenter slides over the surface of a brittle solid, cracks form in its wake. A simple analysis of this process is presented. The solid is modelled as an ideally brittle elastic half-space, which contains a distribution of short cracks near the surface, and is loaded by a cylindrical indenter. Two limiting cases of friction between the indenter and the half-space are considered. The cylinder may slide freely over the surface, with a fixed coefficient of friction between the contacting surfaces. Alternatively, the indenter may be perfectly bonded to the surface of the half-space. The loads necessary to cause fracture under the indenter are calculated, and compared to the loads required to initiate plastic deformation in the solid. In addition, the pattern of fracture which occurs under the indenter is analysed in detail. The residual tensile strength of a solid which has been damaged by contact loading is calculated. Finally, the influence of a residual stress near the surface of the half-space is investigated. It is shown that there is a critical tensile stress which leads to catastrophic failure under the indenter, while if the stresses are compressive, they may prevent fracture.