Discrete Dislocation Predictions for Single Crystal Hardening: Tension VS Bending

Two boundary value problems are solved for a planar single crystal strip: tension and bending. Plastic flow arises from the motion of discrete dislocations, which are modeled as line defects in a linear elastic medium. Two sets of constitutive rules for sources and obstacles are used: (i) rules that only account for a static set of initial point sources and obstacles; (ii) rules that, in addition, account for the dynamic creation (and possible destruction) of dislocation junctions that can act as sources or obstacles. In tension, the overall stress-strain response is essentially ideally plastic when rule set (i) is employed while a two-stage hardening behavior, with a high hardening second stage, occurs when the number of sources and obstacles evolves dynamically. No major difference between the predictions of the two sets of constitutive rules is found in bending where the density of geometrically necessary dislocations dominates.