Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics

Abstract

A three-dimensional discrete dislocation dynamics plasticity model is presented. The approach allows realistic boundary conditions on the specimen, as both stress and displacement fields of the dislocations are incorporated in the formulation. Emphasis is placed on various technical details in the formulation as well as on the implementation. The current implementation includes features necessary to model conservative motion of dislocations in presence of surfaces. These include details of the discretization of the evolving dislocation structure, the handling of junction formation and destruction, cross-slip and boundary conditions. Special attention is given to the treatment of dislocations that partly glide out of the material, including the treatment of image forces via the finite-element method.

Evolution of mechanical response and dislocation microstructures in small-scale specimens under slightly different loading conditions

“…Simulations of deformation experiments on small-scale columns are performed with the 3-dimensional discrete dislocation dynamics simulation tool described in [17,18].…”

The role of free surfaces on the formation of prismatic dislocation loops

“…Moreover, we approximate free surface effects on the dislocation self energy by removing line-tension forces at the surface. We connect dislocation surface nodes via so-called virtual dislocations to the center of the void as to maintain a zero net Burgers vector for the surface terminated dislocations [15]. We point out that the above modifications are in addition to the image stresses being computed by the corrective boundary value problem.…”

Submicron Plasticity: Yield Stress, Dislocation Avalanches, and Velocity Distribution

“…To study the submicron plastic response by DDD we simulated in 3D several statistically equivalent realizations of the yielding of an L = 0.46 µm edge size aluminium cube subject to compression with constant stress rate and free side boundaries (for simulation details see [21]). The initial dislocation density was 8 × 10 13 m −2 .…”