Formulation of discrete balance laws of single phase in lattice scale for recrystallization

Mayu Muramatsu, Yoshiteru Aoyagi, Kazuyuki Shizawa

Research output: Contribution to journalArticle

Abstract

A crystal lattice in a metal during recrystallization process is modeled as an elastic bar element subject only to stretch and its kinematics is discussed. The balance laws of mass, momentum, angular momentum and energy of the lattice element are formulated. These laws are summed up over a phase in a representative volume element (RVE) and averaged in the RVE so as to prepare to develop macroscopic balance laws for a continuum mixture consisting of several phases. When the RVE converges on a material point at the final procedure of formulation, the present model can be regarded as a director model whose direction vector expressing the crystal orientation is attached to a material point of simple body. During the averaging process, two useful theorems are proposed for averaging terms associated with mass source and then these theorems are verified. Moreover, defining the representative lengths both in macroscopic and microscopic scales and performing an order-estimation for the balance law of angular momentum, this law can be separated into the bulk and lattice parts. The former results in the usual form, so that the Cauchy stress keeps symmetric even though the spin angular momentum of crystal lattice is taken into account. On the other hand, the latter corresponds to the evolution equation of crystal orientation of KWC type phase-field model.

Original languageEnglish
Pages (from-to)1304-1319
Number of pages16
JournalNihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
Volume77
Issue number780
DOIs
Publication statusPublished - 2011

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Angular momentum
Crystal lattices
Crystal orientation
Momentum
Kinematics
Metals

Keywords

  • Balance law
  • Heat treatment
  • Lattice scale
  • Mesoscopic
  • Micromechanics
  • Phase transformation
  • Phase-field model
  • Recrystallization
  • Representative volume element

ASJC Scopus subject areas

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

Cite this

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title = "Formulation of discrete balance laws of single phase in lattice scale for recrystallization",
abstract = "A crystal lattice in a metal during recrystallization process is modeled as an elastic bar element subject only to stretch and its kinematics is discussed. The balance laws of mass, momentum, angular momentum and energy of the lattice element are formulated. These laws are summed up over a phase in a representative volume element (RVE) and averaged in the RVE so as to prepare to develop macroscopic balance laws for a continuum mixture consisting of several phases. When the RVE converges on a material point at the final procedure of formulation, the present model can be regarded as a director model whose direction vector expressing the crystal orientation is attached to a material point of simple body. During the averaging process, two useful theorems are proposed for averaging terms associated with mass source and then these theorems are verified. Moreover, defining the representative lengths both in macroscopic and microscopic scales and performing an order-estimation for the balance law of angular momentum, this law can be separated into the bulk and lattice parts. The former results in the usual form, so that the Cauchy stress keeps symmetric even though the spin angular momentum of crystal lattice is taken into account. On the other hand, the latter corresponds to the evolution equation of crystal orientation of KWC type phase-field model.",
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author = "Mayu Muramatsu and Yoshiteru Aoyagi and Kazuyuki Shizawa",
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AU - Aoyagi, Yoshiteru

AU - Shizawa, Kazuyuki

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AB - A crystal lattice in a metal during recrystallization process is modeled as an elastic bar element subject only to stretch and its kinematics is discussed. The balance laws of mass, momentum, angular momentum and energy of the lattice element are formulated. These laws are summed up over a phase in a representative volume element (RVE) and averaged in the RVE so as to prepare to develop macroscopic balance laws for a continuum mixture consisting of several phases. When the RVE converges on a material point at the final procedure of formulation, the present model can be regarded as a director model whose direction vector expressing the crystal orientation is attached to a material point of simple body. During the averaging process, two useful theorems are proposed for averaging terms associated with mass source and then these theorems are verified. Moreover, defining the representative lengths both in macroscopic and microscopic scales and performing an order-estimation for the balance law of angular momentum, this law can be separated into the bulk and lattice parts. The former results in the usual form, so that the Cauchy stress keeps symmetric even though the spin angular momentum of crystal lattice is taken into account. On the other hand, the latter corresponds to the evolution equation of crystal orientation of KWC type phase-field model.

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KW - Heat treatment

KW - Lattice scale

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KW - Micromechanics

KW - Phase transformation

KW - Phase-field model

KW - Recrystallization

KW - Representative volume element

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