Contact Distribution Encodes Frictional Strength

Abstract

The static friction coefficient, $\mu$, is a central quantity in modeling mechanical phenomena. However, experiments show that it is highly variable, even for a single interface under carefully controlled experimental conditions. Traditionally, this inconsistency is attributed to fluctuations in the real area of contact between samples, $A_R$. In this work, we perform a variety of experimental protocols on three pairs of solid blocks while imaging the contact interface and measuring $\mu$. Using linear regression and images of the interface taken prior to tangential loading, we predict the static friction coefficient. Our model strongly outperforms two benchmarks, the Bowden and Tabor picture ($\mu \propto A_R$) and prediction using experimental variables, indicating that a large portion of the observed variance in the initialization of slip is encoded in the contact plane. We perform the same analysis using only sub-sections of the interface, and find that regions as small as $1\%$ of the interface can still can beat both benchmarks. However, bigger sub-sections of the interface, even when comprised of many small regions with bad individual predictive power, outperform the best small regions alone, suggesting that the interfacial state is not dependent on any single point, but is rather distributed across the contact ensemble.Comment: 5 pages 4 figure