Mechanics of Plastic Deformation in Small Volumes

Conventional continuum mechanics models of inelastic deformation processes are size scale independent. In contrast, there is considerable experimental evidence that plastic flow in crystalline materials is size dependent over length scales of the order of tens of microns and smaller. Micromachines are in this size range and clearly will be of increasing technological significance. Also, processes that control the mechanical integrity of microelectronic devices, both during processing and in service, take place on this size scale. In addition, this is the size scale for key deformation and fracture processes in structural materials. For crystalline solids, where dislocation motion is the main mechanism of plastic flow, a framework has been developed for solving boundary value problems where plastic flow is represented by the collective motion of discrete dislocations. This framework will be described and solutions to various problems used to illustrate key aspects of plastic flow in small volumes. These solutions will then be compared with the predictions of various nonlocal continuum plasticity theories. The role of higher order boundary conditions will be illustrated, and the capabilities and limitations of currently available nonlocal continuum plasticity theories discussed.