Scale effects in single-asperity friction

Simulations are used to examine the static friction in model single-asperity contacts between a sphere and a flat elastic substrate. The two surfaces have the same crystalline structure. The radius $R$ of the sphere and $a$ of the contact are varied from nanometers to micrometers. For small contacts the atoms move coherently and the coefficient of friction $\mu$ is independent of load. As contact size increases, $\mu$ begins to drop. Results from a wide range of systems can be collapsed when $\mu$ is plotted against $a^2/R a_0$ where $a_0$ nearest-neighbor spacing. The results are compared to Cattaneo-Mindlin continuum theory and dislocation-based models of contact-size effects from Hurtado and Kim and Gao.