A self-consistent model for the elastic contact of rough surfaces

Abstract

The interaction of asperities plays an important role in the contact of rough surfaces. This paper develops a self-consistent contact model, in which the effect of asperity interaction is accounted for by applying the mean pressure around a representative asperity. Based on the Boussinesq’s solution of a point force acting on an elastic half-plane, the problem is transformed into a singular integral equation. Using the Gauss–Legendre quadrature formula, we solve the integral equation numerically. The results demonstrate that when the ratio between the real contact area and the nominal one is small, the effect of asperity interaction is negligible and the present mode coincides with the Greenwood–Williamson model. However, when the area ratio gets larger, the interaction of asperities becomes prominent. For a given ratio between the real contact area to the nominal one, the self-consistent contact model predicts a higher load than the Greenwood–Williamson model, in agreement with relevant experimental results.