Thermomechanical discussions on constitutive equations for plastic spin and back stress in a theory of dislocation drift rate

Kazuyuki Shizawa, Hiroki Wakabayashi

Research output: Contribution to journalArticle

Abstract

A thermomechanical theory of elastoplasticity, including kinematic hardening at finite strain, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. The thermomechanically consistent constitutive equations for plastic deformation rate, plastic spin and dislocation drift rate are rigorously derived. Constitutive equation of the plastic spin is directly obtained by taking account of a work associating with plastic spin and deriving stress. An expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present theory is sufficiently consistent with the theory of non-Riemannian plasticity.

Original languageEnglish
Pages (from-to)1290-1296
Number of pages7
JournalNihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
Volume66
Issue number647
Publication statusPublished - 2000

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Constitutive equations
Plastics
Tensors
Entropy
Elastoplasticity
Plasticity
Hardening
Residual stresses
Plastic deformation
Kinematics

Keywords

  • Back stress
  • Constitutive equation
  • Dislocation density
  • Non-riemannian plasticity
  • Plastic spin
  • Plasticity
  • Rational mechanics
  • Thermomechanics

ASJC Scopus subject areas

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

Cite this

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title = "Thermomechanical discussions on constitutive equations for plastic spin and back stress in a theory of dislocation drift rate",
abstract = "A thermomechanical theory of elastoplasticity, including kinematic hardening at finite strain, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. The thermomechanically consistent constitutive equations for plastic deformation rate, plastic spin and dislocation drift rate are rigorously derived. Constitutive equation of the plastic spin is directly obtained by taking account of a work associating with plastic spin and deriving stress. An expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present theory is sufficiently consistent with the theory of non-Riemannian plasticity.",
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AU - Shizawa, Kazuyuki

AU - Wakabayashi, Hiroki

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N2 - A thermomechanical theory of elastoplasticity, including kinematic hardening at finite strain, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. The thermomechanically consistent constitutive equations for plastic deformation rate, plastic spin and dislocation drift rate are rigorously derived. Constitutive equation of the plastic spin is directly obtained by taking account of a work associating with plastic spin and deriving stress. An expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present theory is sufficiently consistent with the theory of non-Riemannian plasticity.

AB - A thermomechanical theory of elastoplasticity, including kinematic hardening at finite strain, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. The thermomechanically consistent constitutive equations for plastic deformation rate, plastic spin and dislocation drift rate are rigorously derived. Constitutive equation of the plastic spin is directly obtained by taking account of a work associating with plastic spin and deriving stress. An expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present theory is sufficiently consistent with the theory of non-Riemannian plasticity.

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KW - Constitutive equation

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