On a recent stickiness criterion using a very simple generalization of DMT theory of adhesion

Abstract

In the contact of rough surfaces, contact occurs on smaller and smaller scales, the well-known Tabor adhesion parameter decreases and the so-called Derjaguin–Muller–Toporov (DMT) theory is the appropriate limit. Fuller and Tabor developed 40 years ago a model based on asperities and JKR theory, and more recently the author developed an asperity theory using asperities and DMT theory in the form given by Maugis. Both lead to adhesion parameters which do not depend on the range of attractive forces, in contrast to the parameter recently suggested by Pastewka and Robbins (PNAS, 111(9), 3298–3303, 2014). As it is well known from random process theory that contact of rough surfaces can be described reasonably well by asperity summits at least for low bandwidths, the Pastewka–Robbins DMT model and stickiness criterion should correspond in the limit case of a spherical contact. We therefore consider this limit case, and show that Pastewka–Robbins DMT model introduces a dependence on range of attractive forces, or on Tabor parameter, which is not correct for the sphere, and therefore may be incorrect also in general.

Keywords:

• Adhesion
• Greenwood–Williamson theory
• rough surfaces

Notes

1. We avoid the notation d_att as d_att will have to do with an annulus shape, whereas x_att here is a radius of a circular region.

2. JKR is presented in a curve fitted form in order to be easily used.