Analysis of the Contact Problem of an Elastic Body with a Surface Crack.

Abstract

In the field of tribology, the contact pressure is usually assumed to be distributed elliptically according to the well-known Hertz's contact theory. However, the existence of defects near the contact area may require some modifications of this theory. In this study, the effect of a surface crack in contact problems is investigated. In the present analysis, with considering the effect of the surface crack on the contact pressure distribution, the problem is formulated into the singular integral equations in which the dislocation density on the crack surface and the contact pressure distribution are unknown. Furthermore, the numerical method for solving the singular integral equations is shown and some typical examples are solved by the present method. Calculated contact pressure distributions are compared with those obtained by assuming the Hertz's theory. It is concluded that there are some cases when the Hertz's theory does not give sufficiently accurate solutions.