Local density approximation for the energy functional of three-dimensional dislocation systems

Abstract

The elastic energy functional of a system of discrete dislocation lines is well known from dislocation theory. In this paper we demonstrate how the discrete functional can be used to systematically derive approximations which express the elastic energy in terms of dislocation density-like variables which average over the discrete dislocation configurations and represent the dislocation system on scales above the spacing of the individual dislocation lines. We study the simple case of two-dimensional systems of straight dislocation lines before we proceed to derive energy functionals for systems of three-dimensionally curved dislocation lines pertaining to a single, as well as to multiple slip systems. We then illustrate several applications of the theory including Debye screening of dislocations in two and three dimensions, and the derivation of back stress and friction stress terms entering the stress balance from the free energy functionals.

References in corpus (3)

• Scaling Properties of Dislocation Simulations in the Similitude Regime
• Scale-free phase field theory of dislocations
• Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum plasticity theory

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• On the dynamics of curved dislocation ensembles
• Data-mining of dislocation microstructures: concepts for coarse-graining of internal energies
• A computationally efficient implementation of continuum dislocation dynamics: Formulation and application to ultrafine-grained Mg polycrystals
• Cell structure formation in a two-dimensional density-based dislocation dynamics model
• Cyclic-loading microstructure-property relations from a mesoscale perspective: An example of single crystal Nickel-based superalloys