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

¹ Soft Matter Science and Engineering Laboratory, UMR CNRS 7615, Ecole Supérieure de Physique et Chimie Industrielles (ESPCI), Univ Pierre et Marie Curie, Paris (UPMC) - F-75005, Paris, France
² CNRS / UPMC Univ Paris 06, FRE 3231, Laboratoire Jean Perrin - F-75005, Paris, France
³ Manufacture Française des Pneumatiques Michelin - F-63040 Cedex 9, Clermont-Ferrand, France

Received: 14 October 2013
Accepted: 16 December 2013

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 . For a glass surface whose topography is self-affine with a Gaussian height asperity distribution, the local frictional shear stress is found to vary 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.