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The sensitivity of recrystallization kinetics in metals to the heterogeneity of microstructure and deformation history is a widely accepted experimental fact. However, most of the available recrystallization models employ either a mean field approach or use grain-averaged parameters, and thus neglecting the mesoscopic heterogeneity induced by prior deformation. In the present study, we investigate the impact of deformation-induced dislocation (subgrain) structure on the kinetics of recrystallization in metals using the phase-field approach. The primary focus here is upon the role of dislocation cell boundaries. The free energy formulation of the phase-field model accounts for the heterogeneity of the microstructure by assigning localized energy to the resulting dislocation microstructure realizations generated from experimental data. These microstructure realizations are created using the universal scaling laws for the spacing and the misorientation angles of both the geometrically necessary and incidental dislocation boundaries. The resulting free energy is used into an Allen-Cahn based model of recrystallization kinetics, which are solved using the finite element method. The solutions thus obtained shed light on the critical role of the spatial heterogeneity of deformation in the non-smooth growth of recrystallization nuclei and on the final grain structure. The results showed that, in agreement with experiment, the morphology of recrystallization front exhibits protrusions and retrusions. By resolving the subgrain structure, the presented algorithm paves the way for developing predictive kinetic models that fully account for the deformed state of recrystallizing metals. 

The equations of dislocation transport at finite crystal deformation were developed, with a special emphasis on a vector density representation of dislocations. A companion thermodynamic analysis yielded a generalized expression for the driving force of dislocations that depend on Mandel (Cauchy) stress in the reference (spatial) configurations and the contribution of the dislocation core energy to the free energy of the crystal. Our formulation relied on several dislocation density tensor measures linked to the incompatibility of the plastic distortion in the crystal. While previous works develop such tensors starting from the multiplicative decomposition of the deformation gradient, we developed the tensor measures of the dislocation density and the dislocation flux from the additive decomposition of the displacement gradient and the crystal velocity fields. The two-point dislocation density measures defined by the referential curl of the plastic distortion and the spatial curl of the inverse elastic distortion and the associate dislocation currents were found to be more useful in deriving the referential and spatial forms of the transport equations for the vector density of dislocations. A few test problems showing the effect of finite deformation on the static dislocation fields are presented, with a particular attention to lattice rotation. The framework developed provides the theoretical basis for investigating crystal plasticity and dislocation patterning at the mesoscale, and it bears the potential for realistic comparison with experiments upon numerical solution.