Contact mechanics for randomly rough surfaces

TL;DR

This paper reviews contact mechanics theories, introduces a new boundary condition approach, and applies it to rough surfaces like glass and polymers, explaining experimental friction results and suggesting numerical testing methods.

Contribution

It develops a new boundary condition framework for contact mechanics and applies it to rough surfaces, providing insights into frictional behavior of glassy materials.

Findings

Surface roughness from frozen capillary waves significantly affects contact.

The theory explains the load dependence of frictional shear stress.

Numerical methods like finite element analysis can test the theory.

Abstract

When two solids are squeezed together they will in general not make atomic contact everywhere within the nominal (or apparent) contact area. This fact has huge practical implications and must be considered in many technological applications. In this paper I briefly review basic theories of contact mechanics. I consider in detail a recently developed contact mechanics theory. I derive boundary conditions for the stress probability distribution function for elastic, elastoplastic and adhesive contact between solids and present numerical results illustrating some aspects of the theory. I analyze contact problems for very smooth polymer (PMMA) and Pyrex glass surfaces prepared by cooling liquids of glassy materials from above the glass transition temperature. I show that the surface roughness which results from the frozen capillary waves can have a large influence on the contact between the solids. The analysis suggest a new explanation for puzzling experimental results [L. Bureau, T. Baumberger and C. Caroli, arXiv:cond-mat/0510232] about the dependence of the frictional shear stress on the load for contact between a glassy polymer lens and flat substrates. I discuss the possibility of testing the theory using numerical methods, e.g., finite element calculations.