A thermodynamical theory of plastic spin and internal stress with dislocation density tensor

Kazuyuki Shizawa, H. M. Zbib

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

A thermodynamical theory of elastoplasticity including kinematic hardening and dislocation density tensor is developed. The theory is self-consistent and is based on two fundamental principles of thermodynamics, i.e., the principle of increase of entropy and maximal entropy production rate. The thermodynamically consistent governing equations of plastic spin and back stress are rigorously derived. An expression for the plastic spin tensor is obtained from the constitutive equation of dislocation drift rate tensor and an expression for the back stress tensor is given as a balance equation expressing an equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that, in order to obtain a thermodynamically consistent theory for kinematic hardening, the free energy density should have the dislocation density tensor as one of its arguments.

Original languageEnglish
Pages (from-to)247-253
Number of pages7
JournalJournal of Engineering Materials and Technology, Transactions of the ASME
Volume121
Issue number2
Publication statusPublished - 1999 Apr

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residual stress
Tensors
Residual stresses
plastics
tensors
Plastics
hardening
kinematics
elastoplasticity
Hardening
entropy
Kinematics
drift rate
Entropy
Elastoplasticity
constitutive equations
stress tensors
Constitutive equations
flux density
Free energy

ASJC Scopus subject areas

  • Mechanical Engineering
  • Materials Science(all)

Cite this

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AB - A thermodynamical theory of elastoplasticity including kinematic hardening and dislocation density tensor is developed. The theory is self-consistent and is based on two fundamental principles of thermodynamics, i.e., the principle of increase of entropy and maximal entropy production rate. The thermodynamically consistent governing equations of plastic spin and back stress are rigorously derived. An expression for the plastic spin tensor is obtained from the constitutive equation of dislocation drift rate tensor and an expression for the back stress tensor is given as a balance equation expressing an equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that, in order to obtain a thermodynamically consistent theory for kinematic hardening, the free energy density should have the dislocation density tensor as one of its arguments.

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