Geodesic
Burgers tensor flow accounting for cold work and thermal annealing
Theoretical and applied mechanics, Tome 51 (2024) no. 1.

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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, \emph{The stored energy of cold work, thermal annealing, and other thermodynamic issues in single crystal plasticity at small length scales}, Int. J. Plast. extbf{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, non-recoverable free energy 
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     author = {A. S. Borokinni and O. O. Fadodun and B. A. Olokuntoye and O. P. Layeni and A. P. Akinola},
     title = {Burgers tensor flow accounting for cold work and thermal annealing},
     journal = {Theoretical and applied mechanics},
     pages = {39 - 56},
     publisher = {mathdoc},
     volume = {51},
     number = {1},
     year = {2024},
     url = {http://geodesic.mathdoc.fr/item/TAM_2024_51_1_a3/}
}
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A. S. Borokinni; O. O. Fadodun; B. A. Olokuntoye; O. P. Layeni; A. P. Akinola. Burgers tensor flow accounting for cold work and thermal annealing. Theoretical and applied mechanics, Tome 51 (2024) no. 1. http://geodesic.mathdoc.fr/item/TAM_2024_51_1_a3/