Finite Strain Discrete Dislocation Plasticity

Alan Needleman
Brown University
Division of Engineering

For a wide range of crystalline solids, room temperature plastic deformation occurs due to the collective motion of dislocations gliding on specific slip planes. The mobility of dislocations is what gives rise to plastic flow at stress levels relatively low compared to the theoretical strength. Dislocations can also form organized structures that increase local stress levels. As a consequence dislocations play a dual role in a variety of deformation and fracture processes. In particular, plastic flow in confined volumes can lead to dislocation structures that increase apparent strength levels leading to a size effect that is not present in classical theories of plasticity. Considerable effort has been directed toward developing theories of plasticity that can describe observed size effects. One approach has been to develop phenomenological continuum theories, another approach is to represent crystalline plastic flow directly in terms of the dynamics of large numbers of interacting dislocations, with the dislocations represented as line singularities in an elastic solid. Such discrete dislocation plasticity formulations have been restricted to infinitesimal deformations; both the effect of lattice reorientation on dislocation glide and the effect of geometry changes on the momentum balance have been neglected. Here, we describe a finite deformation discrete dislocation plasticity framework. The discrete dislocations are still presumed to be adequately represented by the singular linear elastic fields so that the large deformations near dislocation cores are not modeled. A key difference from phenomenological continuum plasticity formulations is that the displacement field is only piecewise continuous. This is in contrast to current phenomenological continuum plasticity theories, both classical and size-dependent, where there is an underlying assumption that the deformation gradient can be derived from a single valued, continuous displacement field. Furthermore, in discrete dislocation plasticity interior material points can become boundary material points. Numerical implementation issues will be discussed and examples presented. Possible implications of the lack of displacement continuity for phenomenological models will also bediscussed.