Development of phase-field model for recrystallization based on conservation laws

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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 phase-field 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, three-dimensional KWC type phase-field equations are derived. Finally, reducing the obtained equations to two-dimensional ones, it is shown that the present equations result in the conventional KWC type phase-field model.

Original languageEnglish
Pages (from-to)1065-1078
Number of pages14
JournalNihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
Volume78
Issue number791
DOIs
Publication statusPublished - 2012

Fingerprint

Crystal orientation
Conservation
Angular momentum
Constitutive equations
Entropy
Fluxes
Crystal lattices
Materials properties
Momentum
Grain boundaries
Atoms

Keywords

  • Balance laws
  • Constitutive equation
  • Continuum mechanics
  • Heat treatments
  • Phase transformation
  • Phase-field model
  • Recrystallization

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)

Cite this

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title = "Development of phase-field model for recrystallization based on conservation laws",
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 phase-field 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, three-dimensional KWC type phase-field equations are derived. Finally, reducing the obtained equations to two-dimensional ones, it is shown that the present equations result in the conventional KWC type phase-field model.",
keywords = "Balance laws, Constitutive equation, Continuum mechanics, Heat treatments, Phase transformation, Phase-field model, Recrystallization",
author = "Mayu Muramatsu and Kazuyuki Shizawa",
year = "2012",
doi = "10.1299/kikaia.78.1065",
language = "English",
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journal = "Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A",
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TY - JOUR

T1 - Development of phase-field model for recrystallization based on conservation laws

AU - Muramatsu, Mayu

AU - Shizawa, Kazuyuki

PY - 2012

Y1 - 2012

N2 - 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 phase-field 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, three-dimensional KWC type phase-field equations are derived. Finally, reducing the obtained equations to two-dimensional ones, it is shown that the present equations result in the conventional KWC type phase-field model.

AB - 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 phase-field 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, three-dimensional KWC type phase-field equations are derived. Finally, reducing the obtained equations to two-dimensional ones, it is shown that the present equations result in the conventional KWC type phase-field model.

KW - Balance laws

KW - Constitutive equation

KW - Continuum mechanics

KW - Heat treatments

KW - Phase transformation

KW - Phase-field model

KW - Recrystallization

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