From systems of discrete dislocations to a continuous field description: Stresses and averaging aspects

摘要

Metal plasticity is governed by the motion of dislocations, and predicting the interactions and resulting collective motion of dislocations is a major task in understanding and modeling plastically deforming materials. This task has, despite all the efforts and advances of the last few decades, not yet been fully accomplished. The reason for this is that discrete models which describe the dislocation system with high accuracy are only computationally feasible for small systems, small strains, and high strain rates. Classical continuum models do not suffer from these restrictions but lack sufficiently detailed information about dislocation microstructure. In this paper we present the steps that are needed for averaging systems of discrete dislocations toward a continuous and hence more efficient representation. Our main emphasis lies on investigating the effects of averaging on the description of stress fields and dislocation interactions. We show how the evolution of continuous dislocation fields can then be appropriately described by a dislocation density-based model and validate our results by comparison with discrete dislocation dynamic simulations.