Discrete dislocation plasticity analysis of static friction

The initiation of frictional sliding between a flat-bottomed indenter and a planar single-crystal substrate is analyzed using discrete dislocation dynamics. Plastic deformation is modeled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The adhesion between the indenter and the substrate is modeled using a shear traction versus sliding displacement cohesive relation. Two cohesive relations are used. In both relations, the shear traction increases to a maximum value, subsequently in one relation the shear traction decays to zero with increasing sliding, while in the other relation the shear traction remains at its maximum value. Predictions obtained using these two cohesive relations do not differ qualitatively and the quantitative differences are small. The shear stress needed to initiate sliding is a function of contact size; for large contacts sliding initiates at a value approximately equal to the tensile yield strength while for small contacts sliding initiates at the cohesive strength. The effects of superposed normal pressure on the contact, of cohesive strength and of dislocation source density are investigated. (C) 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.