The stored energy of cold work: Predictions from discrete dislocation plasticity

The stored energy of cold work is calculated for planar single crystals under tensile loading with plastic deformation occurring through dislocation glide. Superposition is used to represent the solution of boundary value problems in terms of the singular fields for discrete dislocations and image fields that enforce boundary conditions. Constitutive rules are used which account for the effects of line tension and three-dimensional dislocation interactions including dynamic junction formation. The stored energy is calculated both under load and after load removal and methods are devised to estimate the local plastic dissipation and to separate out the contribution of long-range stresses to the energy stored. Calculations are carried out up to imposed strains of 0.05-0.1 and the effects of strain level, dislocation structure and crystal orientation on the evolution of the stored energy are investigated. Although the flow stress and work hardening rate depend mainly on the dislocation density, the stored energy of cold work depends on details of the dislocation structure that forms, with any long-range dislocation stress field playing a significant role. The calculations exhibit a connection between the stored energy of cold work and the Bauschinger effect. It is also found that local energy storage values can differ substantially from the average value.