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

Abstract

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.