A fractal analysis of adhesive friction between rough solids in gentle sliding

Abstract

Studies of adhesive friction have always relied on careful experiments, and many plausible theories based on the observations now exist to describe the fundamental causes of interfacial bonding between rough solids. In this regard, an analytical model based on surface forces that operate within short ranges is probably not out of place. The analysis of friction is closely associated with that of adhesion between rough solids. Such analyses of adhesion and friction using a random rough surface model have already been described elsewhere. Adhesive bonds may occur at the peaks of nanometric size asperities even though the microscopic roughness would inhibit the surfaces from approaching close separation. It is therefore necessary to account for the effect of asperities ranging from nanometre to micrometre level for a true representation of asperity interactions at the interface and this essentially requires a scale-independent model such as a fractal approach. The paper describes friction between rough solids using a fractal model and the results are compared with those using a conventional approach. The results explain some of the earlier experimental observations. It also seems that the variation in the fractal dimension D may produce a broad spectrum of results which may explain phenomenologically some of the experimental observations, hitherto not explained.