Scale-free phase field theory of dislocations

Abstract

According to recent experimental and numerical investigations if the characteristic size of a specimen is in the submicron size regime several new interesting phenomena emerge during the deformation of the samples. Since in such a systems the boundaries play a crucial role, to model the plastic response of submicron sized crystals it is crucial to determine the dislocation distribution near the boundaries. In this paper a phase field type of continuum theory of the time evolution of an ensemble of parallel edge dislocations with identical Burgers vectors, corresponding to the dislocation geometry near boundaries, is presented. Since the dislocation-dislocation interaction is scale free ($1/r$), apart from the average dislocation spacing the theory cannot contain any length scale parameter. As shown, the continuum theory suggested is able to recover the dislocation distribution near boundaries obtained by discrete dislocation dynamics simulations.

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• Thermodynamic considerations on a class of dislocation-based constitutive models
• The Emergence and Role of Dipolar Dislocation Patterns in Discrete and Continuum Formulations of Plasticity
• On the dynamics of curved dislocation ensembles
• The role of weakest links and system size scaling in multiscale modeling of stochastic plasticity
• Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations
• Convergence and non-convergence of many-particle evolutions with multiple signs
• Efficient numerical method to handle boundary conditions in 2D elastic media
• Variational approach to determine the properties of dislocations at finite deformation