Effect of lateral displacement on the surface stress distribution for cone and sphere contact

Abstract

The effect of lateral displacement on the normal surface stress distribution in conical and spherical contact problems is studied. After deriving the governing contact equations, including lateral displacement, the new normal surface stress distributions are evaluated for a variety of lateral displacements and compared with the classical solutions of Hertz and Sneddon. It is shown that Poisson's ratio is the main determinant of lateral displacement. In addition, the effect of sample and indenter and the contact radius on the resulting combined approach is evaluated as a function of the Poisson's ratio. It is also shown, that for spherical indenters due to a rather surprising compensating effect of two approximations introduced by Hertz, the classical Hertzian solution appears to be relatively immune to the effect of lateral displacement.