A strain-gradient thermodynamic theory of plasticity based on dislocation density and incompatibility tensors

Kazuyuki Shizawa, Kanto Kikuchi, Hussein M. Zbib

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

In this work, we discuss a thermodynamic theory of plasticity for self-organization of collective dislocations in FCC metals. The theory is described by geometrical tensor of crystal defect fields such as dislocation density tensor, representing net mobile dislocation density and geometrically necessary boundaries, and the incompatibility tensor representing immobile dislocation density. Conservation laws for the two kinds of dislocation density are formulated with dislocation products and interactions terms. Based on the second law of thermodynamics, we drive basic constitutive equations for the dislocation flux, production and interaction terms of dislocations. We also derive a set of reaction-diffusion equations for the dislocation density tensor and incompatibility tensor which describes the vein and persistent slip band (PSB) ladders structures. These equations are analyzed using linear stability and bifurcation analysis. An intrinsic mesoscopic length scale is determined which provides an estimate for the wavelength of the PSBs. The basic aspects of the model are motivated and substantiated by analyzing the stress fields of various possible dislocation configurations using discrete dislocation dynamics.

Original languageEnglish
Pages (from-to)416-419
Number of pages4
JournalMaterials Science and Engineering A
Volume309-310
DOIs
Publication statusPublished - 2001 Jul 15

Fingerprint

incompatibility
plastic properties
Tensors
Plasticity
Thermodynamics
tensors
gradients
thermodynamics
Crystal defects
Ladders
Constitutive equations
Dislocations (crystals)
Conservation
Metals
Fluxes
Wavelength
reaction-diffusion equations
edge dislocations
constitutive equations
conservation laws

Keywords

  • Dislocation density
  • PSB
  • Thermodynamics

ASJC Scopus subject areas

  • Materials Science(all)

Cite this

A strain-gradient thermodynamic theory of plasticity based on dislocation density and incompatibility tensors. / Shizawa, Kazuyuki; Kikuchi, Kanto; Zbib, Hussein M.

In: Materials Science and Engineering A, Vol. 309-310, 15.07.2001, p. 416-419.

Research output: Contribution to journalArticle

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