### 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 language | English |
---|---|

Pages (from-to) | 1065-1078 |

Number of pages | 14 |

Journal | Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A |

Volume | 78 |

Issue number | 791 |

DOIs | |

Publication status | Published - 2012 |

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### 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

**Development of phase-field model for recrystallization based on conservation laws.** / Muramatsu, Mayu; Shizawa, Kazuyuki.

Research output: Contribution to journal › Article

}

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

UR - http://www.scopus.com/inward/record.url?scp=84864465489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864465489&partnerID=8YFLogxK

U2 - 10.1299/kikaia.78.1065

DO - 10.1299/kikaia.78.1065

M3 - Article

VL - 78

SP - 1065

EP - 1078

JO - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

JF - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

SN - 0387-5008

IS - 791

ER -