Abstract:
Current strategies of computational crystal plasticity that focus on individual atoms or dislocations are impractical for real-scale, large-strain problems even with today’s computing power. Dislocation-density based approaches are a way forward but most schemes published to-date give a heavier weight on the consideration of geometrically necessary dislocations (GNDs), while statistically stored dislocations (SSDs) are either ignored or treated in ad hoc manners. In reality, however, the motions of GNDs and SSDs are intricately linked through their mutual (e.g. Taylor) interactions, and in fact, GNDs and SSDs are indistinguishable on a microstructural level, notwithstanding the fact that the GNDs are simply the portion of dislocations associated with the overall shape change of the crystal. A correct scheme for dislocation dynamics should therefore be the one commonly used in discrete dislocation dynamics (DDD) simulations, namely, an “all-dislocation” treatment that is equally applicable for all dislocations comprising both the GNDs and SSDs, with a rigorous description of the interactions between them.
In this paper, a new formulation for computational dynamics of dislocation-density functions, based on the above “all-dislocation” principle, is discussed. The dynamic evolution laws for the dislocation densities are derived by coarse-graining the individual density vector fields of all the discrete dislocation lines in the system, without distinguishing between GNDs and SSDs. The mutual elastic interactions between dislocations are treated in full by generalizing the elastic interactions between dislocation segments for dislocation densities, and reducing the Hirth-Lothe line-integral formulation into an algebraic form comprising only elementary functions which are straightforward enough for efficient numerical implementation. Other features in the model include forest (Taylor) hardening, generation due to the connectivity nature of dislocations, and dipole annihilation.
|
