# Non-Amontons-Coulomb local friction law of randomly rough contact interfaces with rubber

## TL;DR

This study investigates the local friction law at rubber-glass interfaces, revealing that the classical Amontons-Coulomb law does not hold at the local contact scale, with shear stress varying sub-linearly with contact pressure.

## Contribution

It provides direct measurements of local shear stress and contact pressure distributions, demonstrating non-Amontons-Coulomb behavior in multi-contact rubber interfaces.

## Key findings

- Local shear stress varies sub-linearly with contact pressure.
- Amontons-Coulomb law does not apply at the local scale.
- Sub-linear behavior observed for different surface topographies.

## Abstract

We report on measurements of the local friction law at a multi-contact interface formed between a smooth rubber and statistically rough glass lenses, under steady state friction. Using contact imaging, surface displacements are measured, and inverted to extract both distributions of frictional shear stress and contact pressure with a spatial resolution of about 10~$\mu$m. For a glass surface whose topography is self-affine with a Gaussian height asperity distribution, the local frictional shear stress is found to vary strongly sub-linearly with the local contact pressure over the whole investigated pressure range. Such sub-linear behavior is also evidenced for a surface with a non Gaussian height asperity distribution, demonstrating that, for such multi-contact interfaces, Amontons-Coulomb's friction law does not prevail at the local scale.