Contact induced micro-surface plasticity is of crucial importance in many applications, such as surface treatment via severe plastic deformation. A clear understanding of the evolution of dislocation structure near the surface and the mutual interactions among neighboring asperities is important in understanding micro-surface plasticity. In this dissertation, rough surfaces under contact are analyzed using a discrete dislocation model.

A new Boundary Element Method (BEM) that takes into consideration singular fields due to dislocations is derived to solve the boundary value problem. At the heart of this method, a complex variable boundary integral equation that is weakly singular. First order singular integral equations capable of measuring stresses accurately close to the surface are developed. The new method offers a unified approach where two-dimensional discrete dislocation boundary value problems are solved directly in a similar fashion as in two-dimensional elasticity.

Using the new technique, indentation of single crystals with rough surfaces by flat contacts is analyzed. Simulation results show the size effect where it is very hard to yield small size asperities. If only surface sources are activated, dislocations nucleated form surface-steps exhibit different behavior depending on the asperity width and spacing. For asperities of small widths and large spacing, dislocations nucleated from surface-steps form dipolar bands within which materials are inserted from the surface leading to the formation of zones with high compressive stresses. For asperities of large widths, dislocations nucleated form the surface segregate into anti-load and pro-load dislocations. Anti-load dislocations pile up under the surface leading to the formation of tensile spots at the edges of the asperities. When bulk material yields dislocations nucleated from bulk sources glide towards the surface and relieve the high compressive stresses that may develop within the shear bands. Also, they block the motion of dislocations nucleated from the surface making it harder for subsequent dislocations to nucleate from surface asperities. For small asperity width to asperity spacing ratios, a large material pileup is observed on both sides of the asperity. For big ratios, deformation mode is similar to that of a plane strain compressions. Between these two modes materials experience shear band deformation.