The stored energy of cold work, thermal annealing, and other thermodynamic issues in single crystal plasticity at small length scales

• We present a thermo-mechanically coupled gradient theory of single-crystal plasticity.
• Central to our theory are an internal energy and entropy which depend on the accumulation of a dislocation density.
• We provide a discussion of the reduction of the dislocation density in a cold-worked material upon subsequent thermal annealing.
• We also provide a detailed discussion of the fraction of plastic stress-power that goes into heating.

This paper develops a thermodynamically consistent gradient theory of single-crystal plasticity using the principle of virtual power as a paradigm to develop appropriate balance laws for forces and energy. The resulting theory leads to a system of microscopic force balances, one balance for each slip system, and to an energy balance that accounts for power expended during plastic flow via microscopic forces acting in concert with slip-rates and slip-rate gradients. Central to the theory are an internal energy and entropy, plastic in nature, dependent on densities that account for the accumulation of glide dislocations as well as geometrically necessary dislocations – and that, consequently, represent quantities associated with cold work. Our theory allows us to discuss – within the framework of a gradient theory – the fraction of plastic stress-power that goes into heating, as well as the reduction of the dislocation density in a cold-worked material upon subsequent (or concurrent) thermal annealing.