### Abstract

In the previous work, the authors formulated the balance laws of mass, momentum, angular momentum and energy of the lattice element used for recrystallization. These laws were summed up over a phase in a representative volume element (RVE) and averaged in the RVE so as to develop the discrete balance laws for single phase. Furthermore, the balance law of angular momentum was separated into a bulk and a lattice parts through the orderestimation with the representative lengths both in macroscopic and microscopic scales. In this paper, the RVE converges on a material point so that the laws are rewritten in the integration form. When the laws are summed up all over the phases and averaged in them, the balance laws of mass, momentum, angular momentum and energy for nuclei and matrix as mixture are formulated, using an useful theorem proposed for the mixing summation of unsteady terms. At this time, the macroscopic part of the balance law for angular momentum results in the usual equation of angular momentum, so that the stress tensor keeps symmetry even if the lattice rotation is considered. While, the microscopic one is localized as an equation of spin angular momentum for lattice, which is suggested to be equivalent to the evolution equation of crystal orientation in KWC type phase-field model. Moreover, the increase law of entropy for mixture is also formulated. During this process, the entropy flux is defined by use of relative mass flux and chemical potential of phase transformation.

Original language | English |
---|---|

Pages (from-to) | 742-757 |

Number of pages | 16 |

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

Volume | 78 |

Issue number | 789 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- Balance Law
- Heat Treatment
- Micromechanics
- Mixture Theory
- Phase Transformation
- Phase-Field Model
- Recrystallization
- Second Law of Thermodynamics

### ASJC Scopus subject areas

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

### Cite this

**Formulation of balance laws as mixture theory for nuclei and matrix in recrystallization.** / Muramatsu, Mayu; Aoyagi, Yoshiteru; Shizawa, Kazuyuki.

Research output: Contribution to journal › Article

*Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*, vol. 78, no. 789, pp. 742-757. https://doi.org/10.1299/kikaia.78.742

}

TY - JOUR

T1 - Formulation of balance laws as mixture theory for nuclei and matrix in recrystallization

AU - Muramatsu, Mayu

AU - Aoyagi, Yoshiteru

AU - Shizawa, Kazuyuki

PY - 2012

Y1 - 2012

N2 - In the previous work, the authors formulated the balance laws of mass, momentum, angular momentum and energy of the lattice element used for recrystallization. These laws were summed up over a phase in a representative volume element (RVE) and averaged in the RVE so as to develop the discrete balance laws for single phase. Furthermore, the balance law of angular momentum was separated into a bulk and a lattice parts through the orderestimation with the representative lengths both in macroscopic and microscopic scales. In this paper, the RVE converges on a material point so that the laws are rewritten in the integration form. When the laws are summed up all over the phases and averaged in them, the balance laws of mass, momentum, angular momentum and energy for nuclei and matrix as mixture are formulated, using an useful theorem proposed for the mixing summation of unsteady terms. At this time, the macroscopic part of the balance law for angular momentum results in the usual equation of angular momentum, so that the stress tensor keeps symmetry even if the lattice rotation is considered. While, the microscopic one is localized as an equation of spin angular momentum for lattice, which is suggested to be equivalent to the evolution equation of crystal orientation in KWC type phase-field model. Moreover, the increase law of entropy for mixture is also formulated. During this process, the entropy flux is defined by use of relative mass flux and chemical potential of phase transformation.

AB - In the previous work, the authors formulated the balance laws of mass, momentum, angular momentum and energy of the lattice element used for recrystallization. These laws were summed up over a phase in a representative volume element (RVE) and averaged in the RVE so as to develop the discrete balance laws for single phase. Furthermore, the balance law of angular momentum was separated into a bulk and a lattice parts through the orderestimation with the representative lengths both in macroscopic and microscopic scales. In this paper, the RVE converges on a material point so that the laws are rewritten in the integration form. When the laws are summed up all over the phases and averaged in them, the balance laws of mass, momentum, angular momentum and energy for nuclei and matrix as mixture are formulated, using an useful theorem proposed for the mixing summation of unsteady terms. At this time, the macroscopic part of the balance law for angular momentum results in the usual equation of angular momentum, so that the stress tensor keeps symmetry even if the lattice rotation is considered. While, the microscopic one is localized as an equation of spin angular momentum for lattice, which is suggested to be equivalent to the evolution equation of crystal orientation in KWC type phase-field model. Moreover, the increase law of entropy for mixture is also formulated. During this process, the entropy flux is defined by use of relative mass flux and chemical potential of phase transformation.

KW - Balance Law

KW - Heat Treatment

KW - Micromechanics

KW - Mixture Theory

KW - Phase Transformation

KW - Phase-Field Model

KW - Recrystallization

KW - Second Law of Thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=84861634770&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861634770&partnerID=8YFLogxK

U2 - 10.1299/kikaia.78.742

DO - 10.1299/kikaia.78.742

M3 - Article

AN - SCOPUS:84861634770

VL - 78

SP - 742

EP - 757

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 - 789

ER -