A recent PNAS paper explained! FRACTURE MECHANICS SIMPLE CALCULATIONS TO EXPLAIN SMALL REDUCTION OF THE REAL CONTACT AREA UNDER SHEAR

If you have seen the very nice PNAS paper which just appeared

Sahli, R., Pallares, G., Ducottet, C., Ben Ali, I.E., Al Akhrass, S., Guibert, M., Scheibert, J., 2018, Evolution of real contact area under shear, Proceedings of the National Academy of Sciences, 115(3), pp. 471-476.

Here we provide a simple explanation.

FACTA UNIVERSITATIS

Series: Mechanical Engineering

DOI: 10.22190/FUME180108007C

Short Communication

FRACTURE MECHANICS SIMPLE CALCULATIONS TO EXPLAIN SMALL REDUCTION OF THE REAL CONTACT AREA UNDER SHEAR

UDC 539.6

Michele Ciavarella

Politecnico di Bari, Department of Mechanics, Mathematics and Management, Italy

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 -AT2, where A0 is the contact area with no shearing, and A 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  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.

Key Words: Adhesion, Friction, Fracture Mechanics, Area Reduction, JKR Model

See attached.