The elastic contact of a rough surface

The elastic contact of an isotropically rough surface with a plane is treated by approximating the summits of a random process model by paraboloids with the same principal curvatures and applying the classical Hertzian solution for their deformation. The errors in this approximation are computed in terms of the separation and of a bandwidth parameter α. Load and real contact area are derived as functions of separation. For large separation the fractional area of real contact is found to be half the bearing area fraction and the separation may be eliminated to give direct porportionality between load and area. For all separations the load is approximately proportional to the contact area. The constant of proportionality depends only on the Hertzian elastic modulus and the profile absolute mean slope. Experimental measurements of the latter and of α for a variety of surfaces show little variation in either, and the measured values of α are within the range of applicability of the model. The theory is critically compared with existing theories.