Systematic Breakdown of Amontons' Law of Friction for an Elastic Object Locally Obeying Amontons' Law

TL;DR

This paper demonstrates that Amontons' law, which states friction is proportional to load and independent of contact area, breaks down for elastic objects under certain conditions, revealing complex precursor slip behaviors.

Contribution

The study provides a systematic analysis showing how Amontons' law fails for elastic objects due to precursor slips, with analytical and numerical evidence.

Findings

Friction coefficient decreases with pressure and system length.

Precursor slips occur before bulk sliding, affecting static friction.

Results align with some previous experimental observations.

Abstract

In many sliding systems consisting of solid object on a solid substrate under dry condition, the friction force does not depend on the apparent contact area and is proportional to the loading force. This behaviour is called Amontons' law and indicates that the friction coefficient, or the ratio of the friction force to the loading force, is constant. Here, however, using numerical and analytical methods, we show that Amontons' law breaks down systematically under certain conditions for an elastic object experiencing a friction force that locally obeys Amontons' law. The macroscopic static friction coefficient, which corresponds to the onset of bulk sliding of the object, decreases as pressure or system length increases. This decrease results from precursor slips before the onset of bulk sliding, and is consistent with the results of certain previous experiments. The mechanisms for these behaviours are clarified. These results will provide new insight into controlling friction.