Adhesion and friction between a smooth elastic spherical asperity and a plane surface

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 nanotribology, 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. In this paper these models are extended to include both static and sliding friction. The approach is through the concept of fracture mechanics, in which the rate of release of elastic strain energy is equated to the work done against surface forces, both frictional and adhesive. The model appears to be consistent with currently available experimental data.