A Continuum Mechanics Model of Adhesion and Friction in a Single Asperity Contact

Abstract

Attempts to establish the relationship between adhesion and friction at the contact of solid surfaces has been frustrated by their inevitable roughness. The recent development of nano-tribology, in which a single asperity contact can be modelled in the surface force apparatus (SFA) or the atomic force microscope (AFM), has made possible the simultaneous measurement of friction and adhesion in a sliding experiment. For the case of pure adhesion, continuum mechanics models exist which assist in the interpretation of the measurements. By assuming a ‘Dugdale’ potential, in which the adhesive force is constant in the separation zone, Maugis [1] obtained a solution in closed form to the behaviour in adhesion of elastic spheres. In the limit, when the separation zone is small compared with the size of the contact, the JKR adhesion theory (Johnson, Kendall & Roberts,[2]) is recovered.

Recent observations in both the SFA and AFM suggest that the frictional traction in the sliding contact of unlubricated solid surfaces is approximately independent of the contact pressure. This result forms the basis of a continuum model of friction which includes the transition from static to kinetic friction, This model is then extended to accommodate possible interaction between adhesive and frictional forces in terms of an empirical interaction parameter α. The effect of such interaction is for the application of a tangential force to cause a reduction in the apparent adhesion between the surfaces. The value of the parameter α may be found by observing the reduction in the static contact area brought about by sliding.