Numerical implementation of a 3D continuum theory of dislocation dynamics and application to micro-bending

S. Sandfeld, Thomas Hochrainer, P. Gumbsch, M. Zaiser

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Crystal plasticity is governed by the motion of lattice dislocations. Although continuum theories of static dislocation assemblies date back to the 1950s, the line-like character of these defects posed serious problems for the development of a continuum theory of plasticity which is based on the averaged dynamics of dislocation systems. Only recently the geometrical problem of performing meaningful averages over systems of moving, oriented lines has been solved. Such averaging leads to the definition of a dislocation density tensor of second order along with its evolution equation. This tensor can be envisaged as the analogue of the classical dislocation density tensor in an extended space which includes the line orientation as an independent variable. In the current work, we discuss the numerical implementation of a continuum theory of dislocation evolution that is based on this dislocation density measure and apply this to some simple benchmark problems as well as to plane-strain micro-bending. © 2010 Taylor & Francis.
Original languageEnglish
Pages (from-to)3697-3728
JournalPhilosophical magazine (London) / Letters
Volume90
Issue number27-28
DOIs
Publication statusPublished - 2010

Fingerprint

Dislocations (crystals)
Tensors
continuums
Plasticity
Crystal lattices
tensors
plastic properties
Defects
Crystals
plane strain
assemblies
analogs
defects
crystals

Keywords

  • continuum theory of dislocation
  • dislocation density
  • dislocations dynamics
  • micro-bending

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Numerical implementation of a 3D continuum theory of dislocation dynamics and application to micro-bending. / Sandfeld, S.; Hochrainer, Thomas; Gumbsch, P.; Zaiser, M.

In: Philosophical magazine (London) / Letters, Vol. 90, No. 27-28, 2010, p. 3697-3728.

Research output: Contribution to journalArticleResearchpeer-review

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