A micro-mechanical dislocation model for frictional slip between two asperities was presented. The model suggested that, when the contact radius was smaller than a critical value, the friction stress was constant and of the order of the theoretical shear strength; in agreement with reported atomic force microscope friction experiments. However, at the critical value, there was a transition beyond which the friction stress decreased with increasing area until it reached the second transition, where the friction stress gradually became independent of the contact size. This contrasted with previous theories, which had assumed that the friction stress was always independent of the size. The present model also predicted that the slip mechanisms were size-dependent. Before the first transition, the constant friction stress was associated with concurrent slip; without the aid of dislocation motion. The first transition corresponded to the minimum contact size at which a single dislocation loop was nucleated, and swept through the entire contact interface, resulting in single-dislocation assisted slip. This mechanism was predicted to prevail for contact sizes, ranging from 10nm to 10μm in radius, for typical dry adhesive contacts. However, there were no experimental data available for this size range. The second transition was found to be caused by the effective Peierls stress, which stabilized the dislocation loop within the contact region and resulted in dislocation pile-ups. Beyond the second transition, slip was assisted by the cooperative glide of dislocations in the pile-up. For sufficiently large contacts, the mechanism of cooperative glide induced a size-independent friction stress in agreement with observations made using surface force apparatus friction experiments.

Scale Effects in Friction of Single-Asperity Contacts – I. From Concurrent Slip to Single Dislocation-Assisted Slip. J.A.Hurtado, K.S.Kim: Proceedings of the Royal Society A, 1999, 455, 3363-84