Contact mechanics for randomly rough surfaces

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.

Shearing Nanometer-Thick Confined Hydrocarbon Films: Friction and Adhesion

“…For elastic solids with randomly rough surfaces, and assuming non-adhesive contact, the area of real contact A is given by [19][20][21][22] …”

Relation between Interfacial Separation and Load: A General Theory of Contact Mechanics

“…This is an important result as U el u is relevant for many important applications. Theories show that, for low squeezing pressure, the area of real contact A varies linearly with the squeezing force pA 0 and that the interfacial stress distribution and the size distribution of contact spots are independent of the squeezing pressure [12,13]. That is, with increasing p, existing contact areas grow and new contact areas form in such a way that, in the thermodynamic limit (infinite-sized system), the quantities referred to above remain unchanged.…”

Physio-mechanical Materials Testing Using Scanning Contact Potentiometry Method

“…The Degree of surface deformation is evaluated on the basis of function, power spectral density C(q) [4] and used in the analysis of surface stresses Eq(1):…”