Some Closed-Form Results for Adhesive Rough Contacts Near Complete Contact on Loading and Unloading in the Johnson, Kendall, and Roberts Regime

Michele Ciavarella  Yang Xu Robert L. Jackson

Some Closed-Form Results for Adhesive Rough Contacts Near Complete Contact on Loading and Unloading in the Johnson, Kendall, and Roberts Regime

Journal of Tribology Copyright VC 2018 by ASME JANUARY 2018, Vol. 140 / 011402-1

Recently, generalizing the solution of the adhesiveless random rough contact proposed

by Xu, Jackson, and Marghitu (XJM model), the first author has obtained a model for

adhesive contact near full contact, under the Johnson, Kendall, and Roberts (JKR)

assumptions, which leads to quite strong effect of the fractal dimension. We extend here

the results with closed-form equations, including both loading and unloading which were

not previously discussed, showing that the conclusions are confirmed. A large effect of

hysteresis is found, as was expected. The solution is therefore competitive with Persson’s

JKR solution, at least in the range of nearly full contact, with an enormous advantage in

terms of simplicity. Two examples of real surfaces are discussed.

[DOI: 10.1115/1.4036915]

Keywords: Greenwood–Williamson (GW) model, roughness, adhesion, hysteresis,

fractals