Modeling of Dislocation Structures in Materials

Details Modeling of Dislocation Structures in Materials Modeling of Dislocation Structures in Materials

1996-04-09

arxiv.org/abs/mtrl-th/9604001v1

Phil. Mag. A 75, 1251 (1997).

Physics

Condensed Matter

Materials Science

RevTeX, 19 pages. Also at http://www.scri.fsu.edu/~vinals/jeff1.ps

Scientific paper

10.1080/01418619708209855

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.

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