JKR, DMT and More: Gauging Adhesion of Randomly Rough Surfaces

Widely known adhesion contact mechanics theories are the Derjaguin, Muller & Toporov (DMT) and Johnson, Kendall & Roberts (JKR) ones. For the case of the smooth contact of elastic spheres, the Tabor parameter allows identifying when the DMT and JKR approaches are expected to work. In this paper, we demonstrate that the same scheme observed in the contact of elastic spheres also applies in the contact of randomly rough surfaces for which an equivalent Tabor parameter can be defined as a function of the mean radius of the surface curvature. Specifically, we discuss results obtained with a recent multi-asperity contact model, the Interacting and Coalescing Hertzian Asperities (ICHA) model, conveniently modified to take account of adhesion in the DMT and JKR limits. From a comparison with data of the literature, we find that the model returns the correct dependence of the adhesion-induced extra contact area on the surface energy γrrs, a quantity introduced in Ref. [25] as a unique measure of the surface energy for randomly rough surfaces.