A Mechanics Approach to Static Friction of Elastic-Plastic Fractal Surfaces

A contact mechanics theory of static friction is presented for isotropic rough surfaces exhibiting fractal behavior. The analysis is based on a piece-wise power-law size distribution and a normal slope distribution of the asperity contacts and elastic-fully plastic deformation models. Numerical integration yields solutions for the normal and friction forces in terms of fractal parameters, elastic-plastic material properties, and interfacial shear strength. The variation of the static coefficient of friction with normal load is related to the effect of the surface topography on the dominant deformation mode at the asperity contacts. Plastic deformation of the smaller asperity contacts dominates at low loads and elastic deformation of the larger asperity contacts at high loads. The critical load signifying the transition from predominantly plastic to elastic deformation depends on the fractal parameters and material properties. In the low-load range, the static coefficient of friction decreases with the increase of the load, while in the high-load range it increases relatively faster with the load. Numerical results for copper fractal surfaces illustrate the effects of normal load, surface topography, and interfacial shear strength on the static coefficient of friction.