A Fractal Analysis of Adhesion at the Contact between Rough Solids

Abstract
Analyses of adhesion between rough solids hitherto relied on a random rough surface model which is appropriate for engineering surfaces. Adhesion occurs at the peaks of the asperities and is pronounced when the surface roughness effect is small, down to the nanometre level. It therefore follows that while the microscopic roughness would inhibit the two surfaces to come to close separation, adhesive bonds may still form at the peaks of the small-scale asperities. In order to account for the effect of asperities ranging from the nanometre to the micrometre level, it is necessary to introduce a scale-independent model. A fractal approach essentially gives this. The paper describes analysis of adhesion between rough solids using a fractal model and the results are compared with those using the conventional approach and experimental results. Some of the existing experimental observations such as adhesion-induced plasticity have been confirmed. The present analysis also gives a generalized solution and, depending on the values of fractal parameters D, the dimension, and G, the roughness parameter, specific solutions may be obtained. The solution obtained using the conventional stochastic model is thus a specific case in the generalized fractal solution.

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