Sharp-interface and phase-field theories of recrystallization in the plane

A continuum framework is presented for recrystallization. The driving force is the energy stored in dislocation substructures, here characterized with the aid of a scalar measure, the dislocation content. Grain boundary kinetics are derived from a configurational force balance, a mechanical version of the second law, and suitable constitutive assumptions. A relation is obtained characterizing the efficiency with which dislocation substructure is eliminated by moving grain boundaries. Using a system of microforce balances, the sharp interface theory is shown to have a phase-field regularization that obviates the need to track individual grain boundaries. The sharp interface theory is recovered, via formal asymptotics, as a limiting case.