Random process model of rough surfaces in plastic contact

Abstract

The plastic contact of a rough surface and a hard, smooth flat is analyzed by modeling the rough surface as an isotropic, Gaussian, random process. The applicability of this model to the contact of two rough surfaces is discussed, and it is shown that the model is appropriate. It is not necessary to analyze interactions of asperity pairs, with the attendant questions of their misalignment, the shape of their caps, etc. Instead, a model involving the interaction of the continuous surfaces is developed, which implicitly takes into account these geometrical factors, as well as allowing for the possibility of the coalescence of microcontacts as the normal pressure is increased. Approximate relations between the density of finite contact patches, their mean area and mean circumference, and the normal pressure/hardness ratio are derived. These relations depend not only on the density and height distribution of maxima, but also on the shape of the Power Spectral Density of the surface. Many surfaces of interest are likely to give rise to multiply-connected contact patches at all except very high separations. The density of holes appearing within the contact patches as well as their area is estimated. Results are derived for surfaces that may be partitioned into two components, one with a large r.m.s. value and a narrow roughness spectrum, and the other with a small r.m.s. value and an arbitrary spectrum. For these surfaces, the density of holes at small separations becomes equal to the density of finite contact patches; the area of the holes remains small, however. It is conjectured that for surfaces that may not be partitioned in this manner, conventional models of contact are inapplicable. Specifically, the contact patches are likely to be perforated by holes at all separations, the hole area being a significant fraction of the contact area. Unit events such as the contact or collision of asperities also appear to become meaningless