A model of friction with plastic contact nudging: Amontons-Coulomb laws, aging of static friction, and non-monotonic Stribeck curves with finite quasistatic limit

TL;DR

This paper presents a friction model based on rough surface contact that captures static and dynamic friction behaviors, including aging and non-monotonic Stribeck curves, by introducing plastic nudging of bumps.

Contribution

The model introduces plastic contact nudging to explain static friction aging and velocity-dependent dynamic friction, extending prior elastic-only models.

Findings

Captures Amontons-Coulomb laws of friction.

Reproduces static friction aging with contact time.

Shows non-monotonic Stribeck curves with finite quasistatic limit.

Abstract

We introduce a model of friction between two contacting (stationary or co-sliding) rough surfaces, each comprising a random ensemble of polydisperse hemispherical bumps. In the simplest version of the model, the bumps experience on contact with each other only pairwise elastic repulsion and dissipative drag. These minimal ingredients are sufficient to capture a static state of jammed, interlocking contacting bumps, below a critical frictional force that is proportional to the normal load and independent of the apparent contact area, consistent with the Amontons-Coulomb laws of friction. However, they fail to capture two widespread observations: (i) that the dynamic friction coefficient (ratio of frictional to normal force in steady sliding) is a roughly constant or slightly weakening function of the sliding velocity $U$, at low $U$, with a non-zero quasistatic limit as $U\to 0$, and (ii) that the static friction coefficient (ratio of frictional to normal force needed to initiate sliding) increases ("ages") as a function of the time that surfaces are pressed together in stationary contact, before sliding commences. To remedy these shortcomings, we incorporate a single additional model ingredient: that contacting bumps plastically nudge one another slightly sideways, above a critical contact-contact load. With this additional insight, the model also captures observations (i) and (ii).