Fracture mechanics simple calculations to explain small reduction of the real contact area under shear

Abstract

In a very recent paper, Sahli and coauthors [12] (R. Sahli et al., 2018, “Evolution of real contact area under shear”, PNAS, 115(3), pp. 471-476) studied the contact area evolution for macroscopic smooth spheres under shear load in presence of adhesion. It was found that contact area AA reduces quadratically with respect to shear load T, i.e. A=A0 -αAT2, where A0 is the contact area with no shearing, and αA is the "area reduction parameter" found to be approximately proportional to A0-3/2 across 4 orders of magnitude of A0. In this note we focus on the smooth sphere/plane contact because we believe that the case of a rough contact requires separate investigations, and we use a known model of fracture mechanics, which contains a fitting parameter β which governs the interplay between fractures modes, in order to find very good agreement between the data and the analytical predictions, developing relatively simple equations. The interaction with modes is limited.