Modeling of Dislocation Structures in Materials

A Phenomenological Mesoscopic Field Dislocation Mechanics (PMFDM) model is developed, extending continuum plasticity theory for studying initial-boundary value problems of small-scale plasticity. PMFDM results from an elementary space-time averaging of the equations of Field Dislocation Mechanics (FDM), followed by a closure assumption from any strain-gradient plasticity model that attempts to model effects of geometrically-necessary dislocations (GND) only in work-hardening.

This article is written in memory of Pierre Hohenberg with appreciation for his deep commitment to the basic principles of theoretical physics. I summarize recent developments in the theory of dislocation-enabled deformation of crystalline solids. This topic is especially appropriate for the Journal of Statistical Physics because materials scientists, for decades, have asserted that statistical thermodynamics is inapplicable to dislocations. By use of simple, first-principles...

A computational approach has been developed for analyzing the characteristics of 3D dislocation substructures generated by the vector-density based continuum dislocation dynamics (CDD). In this CDD framework, the dislocation density on the individual slip systems is represented by vector fields with a unique dislocation line direction at each point in space. The evolution of these density fields is governed by a set of transport equations coupled with crystal mechanics. Such ...

The continuum dislocation dynamics framework for mesoscale plasticity is intended to capture the dislocation density evolution and the deformation of crystals when subjected to mechanical loading. It does so by solving a set of transport equations for dislocations concurrently with crystal mechanics equations, with the latter being cast in the form of an eigenstrain problem. Incorporating dislocation reactions in the dislocation transport equations is essential for making suc...

As a guide to constitutive specification, driving forces for dislocation velocity and nucleation rates are derived for a field theory of dislocation mechanics. A condition of closure for the theory in the form of a boundary condition for dislocation density is also derived. Kinematical features of dislocation evolution like initiation of bowing of a pinned screw segment, and initiation of cross-slip of a screw segment are discussed. An exact solution for the expansion of a po...

Dislocations - linear defects within the crystal lattice of, e.g., metals - already have been directly observed and analyzed for nearly a century. While experimental characterization methods can nowadays reconstruct three-dimensional pictures of complex dislocation networks, simulation methods are at the same time more and more able to predict the evolution of such systems in great detail. Concise methods for analyzing and comparing dislocation microstructure, however, are st...

Intriguing analogies were found between a model of plastic deformation in crystals and turbulence in fluids. A study of this model provides remarkable explanations of known experiments and predicts fractal dislocation pattern formation. Further, the challenges encountered resemble those in turbulence, which is exemplified in a comparison with the Rayleigh-Taylor instability.

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...

Dislocations are the main carriers of plastic deformation in crystalline materials. Physically based constitutive equations of crystal plasticity typically incorporate dislocation mechanisms, using a dislocation density based description of dislocation microstructure evolution and plastic flow. Typically, such constitutive models are not formulated in a thermodynamic framework. Nevertheless, fundamental considerations of thermodynamic consistency impose constraints on the adm...

Because of the enormous range of time and space scales involved in dislocation dynamics, plastic modeling at macroscale requires a continuous formulation. In this paper, we present a rigorous formulation of the transition between the discrete, where plastic flow is resolved at the scale of individual dislocations, and the continuum, where dislocations are represented by densities. First, we focus on the underlying coarse-graining procedure and show that the emerging correlati...