The contact-hardening behaviour, due to multiple dislocations in a two-dimensional dislocation model, was analyzed. Continuum micro-mechanical methods were used to derive the configurational force on the dislocation, while a modified Rice-Thomson criterion was used to model dislocation nucleation. Dislocations, nucleated from the surface step, were stabilized and piled up as a result of the balance between the resolved driving force and the non-zero lattice resistance in the solid. The dislocation pile-up then exerted a strong back-stress which prevented further dislocation nucleation and thus led to the contact-hardening behaviour; the degree of which depended upon the slip-plane orientation. In particular, it was found that dislocation interactions between two slip-planes could make the contact-loading, which was required tomultiple dislocations, an order-of-magnitude easier. This was so-called latent softening. A mechanistic explanation showed that the latent softening was closely related to the stress-concentration mode-mix at the surface step. Dislocation nucleation modified the geometrical characteristics of the surface step, so that the contact-induced stress-state near to the step as described by the mode-mix, changed. This influenced the subsequent dislocation nucleation. The calculations showed that the dislocation pile-up on one slip-plane could even cause spontaneous dislocation nucleation on the other slip plane without further increase in the contact load. It was found that rough surface contacts at small length-scales could lead to dislocation segregation and to the formation of a surface tensile sub-layer.

Micro-Plasticity of Surface Steps under Adhesive Contact - Part II. Multiple-Dislocation Mediated Contact Hardening. Y.F.Gao, H.H.Yu, K.S.Kim: Journal of the Mechanics and Physics of Solids, 2008, 56[9], 2759-72nucleate