The stored energy of cold work was calculated for planar single crystals under tensile loading with plastic deformation occurring through dislocation glide. Superposition was 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 were used which account for the effects of line tension and 3-dimensional dislocation interactions including dynamic junction formation. The stored energy was calculated both under load and after load removal and methods were devised to estimate the local plastic dissipation and to separate out the contribution of long-range stresses to the energy stored. Calculations were 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 were 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 was also found that local energy storage values could differ substantially from the average value.

The Stored Energy of Cold Work - Predictions from Discrete Dislocation Plasticity. A.A.Benzerga, Y.Bréchet, A.Needleman, E.Van der Giessen: Acta Materialia, 2005, 53[18], 4765-79