Towards a modeling of the time dependence of contact area between solid bodies

TL;DR

This paper introduces a simple model to describe how contact area between solid bodies evolves over time, accounting for surface roughness and relaxation effects, with results aligning with experimental observations.

Contribution

It presents a novel model incorporating relaxation effects for contact area evolution, applicable to both uncorrelated and self-affine surface roughness.

Findings

Contact area increases over time following a power-law decay towards an asymptotic value.

The exponent q depends on the normal load as q ~ F_N^β, with β close to 0.5.

Logarithmic time increase of contact area observed at low loads, matching experimental data.

Abstract

I present a simple model of the time dependence of the contact area between solid bodies, assuming either a totally uncorrelated surface topography, or a self affine surface roughness. The existence of relaxation effects (that I incorporate using a recently proposed model) produces the time increase of the contact area $A(t)$ towards an asymptotic value that can be much smaller than the nominal contact area. For an uncorrelated surface topography, the time evolution of $A(t)$ is numerically found to be well fitted by expressions of the form [$A(\infty)-A(t)]\sim (t+t_0)^{-q}$, where the exponent $q$ depends on the normal load $F_N$ as $q\sim F_N^{\beta}$, with $\beta$ close to 0.5. In particular, when the contact area is much lower than the nominal area I obtain $A(t)/A(0) \sim 1+C\ln(t/t_0+1)$, i.e., a logarithmic time increase of the contact area, in accordance with experimental observations. The logarithmic increase for low loads is also obtained analytically in this case. For the more realistic case of self affine surfaces, the results are qualitatively similar.