A continuum framework for recrystallization was presented in which the driving force was the energy stored in dislocation sub-structures; here characterized by the dislocation content. Grain boundary kinetics were derived from a configurational force balance, a mechanical version of the second law, and suitable constitutive assumptions. A relationship was obtained which characterized the efficiency with which the dislocation sub-structure was eliminated by moving grain boundaries. By using a system of micro-force balances, the sharp interface theory was shown to have a phase-field regularization that removed the need to track individual grain boundaries. The sharp interface theory was recovered, asymptotically, as a limiting case.

Sharp-Interface and Phase-Field Theories of Recrystallization in the Plane. M.E.Gurtin, M.T.Lusk: Physica D, 1999, 130[1-2], 133-54