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From a microscopic point of view, the frictional force associated with the relative sliding of rough surfaces originates from deformation of the material in contact, by adhesion in the contact interface or both. We know that plastic deformation at the size scale of micrometres is not only dependent on the size of the contact, but also on the rate of deformation. Moreover, depending on its physical origin, adhesion can also be size and rate dependent, albeit different from plasticity. We present a two-dimensional model that incorporates both discrete dislocation plasticity inside a face-centred cubic crystal and adhesion in the interface to understand the rate dependence of friction caused by micrometre-size asperities. The friction strength is the outcome of the competition between adhesion and discrete dislocation plasticity. As a function of contact size, the friction strength contains two plateaus: at small contact length ( ≲ 0.6 μ m ) , the onset of sliding is fully controlled by adhesion while for large contact length ( ≳ 10 μ m ) , the friction strength approaches the size-independent plastic shear yield strength. The transition regime at intermediate contact size is a result of partial de-cohesion and size-dependent dislocation plasticity, and is determined by dislocation properties, interfacial properties as well as by the loading rate.

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.

The plane strain indentation of single crystal films on a rigid substrate by a rigid wedge indenter is analyzed using discrete dislocation plasticity. The crystals have three slip systems at ± 35 . 3 ∘ and 90 ∘ with respect to the indentation direction. The analyses are carried out for three values of the film thickness, 2 , 10 and 50 μ m , and with the dislocations all of edge character modeled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated through a set of constitutive rules. Over the range of indentation depths considered, the indentation pressure for the 10 and 50 μ m thick films decreases with increasing contact size and attains a contact size-independent value for contact lengths A > 4 μ m . On the other hand, for the 2 μ m films, the indentation pressure first decreases with increasing contact size and subsequently increases as the plastic zone reaches the rigid substrate. For the 10 and 50 μ m thick films sink-in occurs around the indenter, while pile-up occurs in the 2 μ m film when the plastic zone reaches the substrate. Comparisons are made with predictions obtained from other formulations: (i) the contact size-independent indentation pressure is compared with that given by continuum crystal plasticity; (ii) the scaling of the indentation pressure with indentation depth is compared with the relation proposed by Nix and Gao [1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 43, 411–423]; and (iii) the computed contact area is compared with that obtained from the estimation procedure of Oliver and Pharr [1992. An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7, 1564–1583].