The second transition in the frictional slip of single-asperity contacts, which took place at large contact sizes, was explored. This was a transition from single-dislocation assisted slip to multiple-dislocation cooperative slip. It was found that the friction stress was controlled by dislocation nucleation for single-dislocation assisted slip, and by dislocation mobility for multiple-dislocation cooperative slip. A model involving concentric dislocation loops was introduced in order to analyse dislocation pile-up processes and their relationship to the friction stress. Dislocations were stabilized and piled up as a result of the non-zero effective Peierls stress of the interface. The analysis showed that slip occurred when the condition for the nucleation of a new dislocation, and the condition for destabilization of the leading dislocation of the pile-up, were satisfied simultaneously. It was also shown that, as the contact size increased, the friction stress asymptotically approached a constant value that was equal to the effective Peierls stress of the interface. This result was in agreement with reported experimental results, obtained using the surface-force apparatus. The case of a large number of dislocations in a pile-up was studied via an asymptotic analysis whose key concept was the existence of a dislocation-free zone that controlled the dislocation nucleation process. The analysis provided a connection between the discrete dislocation model and the continuous cohesive zone model of single-asperity friction.

Scale Effects in Friction of Single-Asperity Contacts - II. Multiple-Dislocation Cooperative Slip. J.A.Hurtado, K.S.Kim: Proceedings of the Royal Society A, 1999, 455, 3385-400