On the plastic contact of rough surfaces

Abstract

The treatment of plastic contact developed in this paper is based on three physical observations: that the total volume of metal is not changed by plastic deformation; that the mean indentation pressure is a well-defined material constant applicable to the whole range of likely asperity shapes; and that the displaced material reappears as a uniform rise in the non-contacting surface. An energy-balance argument is used to obtain dimensionless relations between the load, separation, and degree of contact, in terms of the height distribution of the surface. A fourth observation is then added: that the height distributions of many engineering surfaces are, to a good approximation, Gaussian. The relations are worked out in detail for this height distribution and compared with experimental observations. The treatment accurately predicts the behaviour up to extremely high loads; and accounts for the remarkable persistence of asperities on rough surfaces in plastic contact. The argument, and the main supporting experiments, were conceived in terms of the contact of a uniformly loaded nominally flat surface, but the extention to local indentations is quite straightforward. It is shown that for local indentations in homogeneous bodies the real area of contact is always one half of the nominal area. This unexpected result is in fact accurately confirmed by experiment. The treatment also discusses the effect of a hard or soft surface layer on the indented body, and again the predictions are supported by practical measurements.