再結晶現象に対するPhasefieldモデルの保存則に基づく構築 [in Japanese] Development of PhaseField Model for Recrystallization Based on Conservation Laws [in Japanese]
Access this Article
Author(s)
Abstract
We modeled previously a crystal lattice as an elastic bar with equivalent atom mass. Applying such a lattice model to recrystallization phenomena, we developed conservation laws of mass, momentum, angular momentum and energy for mixture consisting of recrystallized phase and matrix. Also, the increase law of entropy for mixture was obtained. However, in the previous works, only general principles are formulated and material properties are not introduced into them. Moreover, it is still unclear which conservation laws are corresponding to the governing equations of phasefield models. In this paper, balance equations of mass for single phase and spin angular momentum are rewritten by use of order parameter and crystal orientation, respectively. Constitutive equations for fluxes of order parameter and crystal orientation are thermodynamically derived so that the entropy inequality is not violated. Substituting the constitutive equations of flux into the balance equations, basic equations are obtained. In these equations, the mass source term and diffusion coefficients are modeled so as to synchronize with the temporal change of grain boundary energy. Neglecting the conservative term of the equation of crystal orientation and then integrating it with respect to time, threedimensional KWC type phasefield equations are derived. Finally, reducing the obtained equations to twodimensional ones, it is shown that the present equations result in the conventional KWC type phasefield model.
Journal

 TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A 78(791), 10651078, 2012
The Japan Society of Mechanical Engineers