Abstract
The study of micro-plasticity behavior near and at the rough surface is the critical link towards a fundamental understanding of contact, surface failures, friction and adhesion at small length scales. In the companion paper (Part I), we have studied the onset of surface yielding due to single-dislocation nucleation from a stepped surface under adhesive contact. Here we analyze the contact hardening behavior due to multiple dislocations in a two-dimensional dislocation model. Continuum micromechanical analyses are used to derive the configurational force on the dislocation, while a modified Rice-Thomson model is used to describe the dislocation nucleation. Dislocations nucleated from a surface source are stabilized and pile up as a result of the balance between the resolved driving force and the non-zero lattice resistance in the solid. The pileup dislocations will exert a strong back stress to prevent further dislocation nucleation and thus lead to the surface contact hardening, the degree of which depends on the slip-plane orientation. Particularly, we find that the dislocation interactions between two slip planes can make the contact loading order-of-magnitude easy to nucleate multiple dislocations, which is thus named "latent softening". A mechanistic explanation shows that the latent softening is closely related to the mode mixity of the stress concentration at the surface step. Dislocation nucleation will modify the geometric characteristics of the surface step, so that the contact-induced stress state near the step, as described by the mode mixity, changes. The altered stress state affects subsequent dislocation nucleation. Our calculations show that dislocation pileup on one slip plane can even cause spontaneous dislocation nucleation on the other slip plane without further increase of contact pressure. Furthermore, it is found that the rough surface contact at small length scale can lead to the formation of a surface tensile sub-layer caused by segregated dislocation pileups. The discrete-dislocation model provides novel insights to understanding of surface step deformation at a small length scale, which bridge atomistic simulations and continuum plastic flow analysis of surface asperity contact. Implications of the theoretical predictions are also discussed.
