Scale effects in friction of single-asperity contacts. II. Multiple-dislocation-cooperated slip

In this paper we explore the second transition in the mechanism of frictional slip of single-asperity contacts, which takes place at large contact sizes. This is a transition from single-dislocation-assisted (SDA) slip to multiple-dislocation-cooperated (MDC) slip. It is found that the friction stress is controlled by dislocation nucleation for SDA slip, and by dislocation mobility for MDC slip. A model of concentric dislocation loops is introduced to analyse dislocation pile-up processes and their relationship to the friction stress. Dislocations are stabilized to be piled up as a result of the non-zero effective Peierls stress of the interface. The analysis shows that slip occurs when the condition for the nucleation of a new dislocation and the condition for destabilizing the leading dislocation of the pile-up are simultaneously satisfied. It is also shown that, as the contact size increases, the friction stress approaches asymptotically a constant value equal to the effective Peierls stress of the interface. This result is in agreement with reported experimental results in the surface force apparatus (SFA). The case of a large number of dislocations in the pile-up is studied via an asymptotic analysis, a key concept of which is the existence of a dislocation-free zone that controls the dislocation nucleation process. The analysis provides the connection between the discrete dislocation model and the continuous cohesive zone model of single-asperity friction.