Single-asperity friction during quasi-static sliding

The static friction of an asperity is investigated using atomic-scale simulations. We explore scale effects by varying the sphere radius R and the contact radius a from nanometers to micrometers. We first consider commensurate contact between bare lattices with repulsive interactions across the interface. In small contacts, all contacting atoms move coherently and the friction coefficient $\mu$ is independent of contact radius and load. In larger contacts, interfacial slip is mediated by localized dislocations, and the static friction coefficient $\mu$ $\sim$ (Ra$_{0}$/a$^{2})^{2/3}$, where a$_{0}$ is the nearest-neighbor spacing. In very large contacts $\mu$ stops decreasing and begins to increase with a, at fixed R. The results are in sharp contrast to Cattaneo-Mindlin continuum theory where $\mu$ is independent of contact size. Separate simulations are performed to connect the results to the dislocation-based models of contact-size effects due to Hurtado and Kim, and Gao, which assume adhesive interactions between surfaces and find $\mu$ $\sim$ (a$_{0}$/a)$^{1/2}$. Simulations for incommensurate contacts show a transition from superlubricity for rigid contacts to a finite friction associated with the Peierls stress in very large contacts. Support from: DMR-1006805; NSF IGERT-0801471; OCI-0963185; CMMI-0923018