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 journalArticlepeer-review

21 Citations (Scopus)


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 & Engineering A: Structural Materials: Properties, Microstructure and Processing
Publication statusPublished - 2001 Jul 15


  • Dislocation density
  • PSB
  • Thermodynamics

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'A strain-gradient thermodynamic theory of plasticity based on dislocation density and incompatibility tensors'. Together they form a unique fingerprint.

Cite this