Probing the micromechanics of a multi-contact interface at the onset of frictional sliding

TL;DR

This study uses Digital Image Correlation to investigate the micromechanics of a multi-contact interface during the transition from static to sliding, revealing deviations from classical models and proposing an elasto-plastic friction law.

Contribution

It provides the first quantitative validation of the Cattaneo and Mindlin model at mesoscopic scales and introduces an elasto-plastic constitutive law for rough interfaces.

Findings

Cattaneo and Mindlin model captures most local behaviors but shows deviations.

The interface exhibits elasto-plastic rheology, not rigid-plastic.

Finite compliance of the rough interface causes small deviations from classical laws.

Abstract

Digital Image Correlation is used to study the micromechanics of a multi-contact interface formed between a rough elastomer and a smooth glass surface. The in-plane elastomer deformation is monitored during the incipient sliding regime, i.e. the transition between static and sliding contact. As the shear load is increased, an annular slip region, in coexistence with a central stick region, is found to progressively invade the contact. From the interfacial displacement field, the tangential stress field can be further computed using a numerical inversion procedure. These local mechanical measurements are found to be correctly captured by Cattaneo and Mindlin (CM)'s model. However, close comparison reveals significant discrepancies in both the displacements and stress fields that reflect the oversimplifying hypothesis underlying CM's scenario. In particular, our optical measurements allow us to exhibit an elasto-plastic like friction constitutive equation that differs from the rigid-plastic behavior assumed in CM's model. This local constitutive law, which involves a roughness-related length scale, is consistent with the model of Bureau \textit{et al.} [Proc. R. Soc. London A \textbf{459}, 2787 (2003)] derived for homogeneously loaded macroscopic multi-contact interfaces, thus extending its validity to mesoscopic scales.measurements allow for the first quantitative test of Cattaneo and Mindlin (CM) classical model of the incipient sliding of a smooth interface. Small deviations are observed and interpreted as a result of the finite compliance of the rough interface, a behavior which contrasts with Amontons' law of friction assumed to be valid locally in CM's model. We illustrate how these measurements actually provide a method for probing the rheology of the rough interface, which we find to be of the elasto-plastic type.