On the sensitivity of adhesion between rough surfaces to asperity height distribution

Abstract

There has been a long debate about the validity of asperity models in the contact between rough surfaces, much of it concentrated on relatively minor aspects of the solution for the special case of Gaussian random processes for roughness, like the exact value of the area–load slope or the extent of the linear regime. It is shown here that in the case of adhesion, the behavior is extremely sensitive to the shape of the height distribution. We show for example results for Weibull distributions, which has been suggested in a number of practical cases from macroscopic to nanoscopic roughness. Pull-off force is found to vary by several orders of magnitude both lower and higher than in the Gaussian case, whereas the “stickiness” criterion on the adhesion parameter changes by an order of magnitude. Additionally, in some operations like chemical-mechanical polishing, tails are almost completely removed and a sharp peak develops instead of a tail: modeling this with contact on the bounded side of the Weibull distribution, stickiness seems to occur for any level of roughness. Some qualitative comparison with recent numerical experiments is attempted.