Multiscale Dislocation Dynamics Plasticity

Abstract

A recently developed discrete dislocation dynamics (DD) model for crystalline materials coupled with finite elements (FE) analysis is reviewed. The three-dimensional continuum-based FE formulation for elastoviscoplasticity incorporates the DD simulation, replacing the usual plasticity constitutive relationships, leading to what is called multiscale dislocation dynamics plasticity (MDDP). The coupling involves a nontrivial homogenization to obtain local plastic strains from the contributions of discrete plastic events captured in DD. The superposition principle is used in order to find the effects of the boundaries (free, rigid, or interfaces) on the dislocation movement. The developed computer code can efficiently handle size-dependent small-scale plasticity phenomena and related material instabilities at various length scales ranging from the nano-microscale to the mesoscale. The DD modeling is based on the fundamental physical laws governing dislocation motions and their interactions with various defects, interfaces, and external loadings. The multiscale frame of consideration merges the two scales of nano-microscale, where plasticity is determined, and the continuum scale, where the energy transport is based. In order to illustrate the usefulness of this approach in investigating a wide range of plasticity phenomena, results for a set of case studies are presented. This includes the deformation and dislocation structure during nano-indentation in bcc and fcc single crystals, analyses pertaining to the formation of dislocation boundaries during heavy deformation, dislocations interaction with shock-waves during impact loading conditions, and dislocation–defect interaction.