Burgers tensor flow accounting for cold work and thermal annealing

Abstract

This paper proposes a kinematical-thermal-based constitutive law for the evolution of Burgers tensor during cold work and upon subsequent thermal annealing of a polycrystalline. The proposal is based on the paper by Anand et al. [L. Anand., M. E. Gurtin., B. D. Reddy, The stored energy of cold work, thermal annealing, and other thermodynamic issues in single crystal plasticity at small length scales, Int. J. Plast. 64 (2015), 1–25]. The principle of virtual work and thermodynamic laws are employed to obtain balance of forces, balance of energy, and free-energy imbalance. Non-recoverable energetic microscopic stresses are obtained as features for materials that are cold-worked whenever the defect energy is dependent on Burgers tensor. Consequently, it is observed that internal-energetic plastic power is not less than entropic plastic power. The recovery rate during thermal annealing is shown to mimic dissipative behavior, leading to a reduction in the accumulation of dislocation densities. Furthermore, the free energy function –approximated as a quadratic form– is used to obtain the constitutive relations for the macroscopic and microscopic stresses.

Keywords

• gradient plasticity
• cold work
• burgers tensor
• recovery rate
• nonrecoverable free energy