Modelling of dislocation structures in materials

J. M. Rickman, Jorge Viñals

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39 Scopus citations


A phenomenological model of the evolution of an ensemble of interacting dislocations in an isotropic elastic medium is formulated. The line-defect microstructure is described in terms of a spatially coarse-grained order parameter, the dislocation density tensor. The tensor field satisfies a conservation law that derives from the conservation of Burgers vector. Dislocation motion is entirely dissipative and is assumed to be locally driven by the minimization of plastic free energy. We first outline the method and resulting equations of motion to linear order in the dislocation density tensor, obtain various stationary solutions, and give their geometric interpretation. The coupling of the dislocation density to an externally imposed stress field is also addressed, as well as the impact of the field on the stationary solutions.

Original languageEnglish (US)
Pages (from-to)1251-1262
Number of pages12
JournalPhilosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties
Issue number5
StatePublished - May 1997
Externally publishedYes

Bibliographical note

Funding Information:
We are indebted to Y. T. Chou, Hamid Garmestani, W. W. Mullins and David Srolovitz for useful discussions. The work of J. M. R. is supported by the National Science Foundation under contract DMR-9458028. J. V. is supported by the US Department of Energy, contract No. DE-FG05-95ER14566, and also in part by the Supercomputer Computations Research Institute, which is partially funded by the US Department of Energy, contract No. DE-FC05-85ER25000.


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