Unified Framework for Dislocation-Based Defect Energetics

Modeling dislocations is an inherently multiscale problem as one needs to simultaneously describe the high stress fields near the dislocation cores, which depend on atomistic length scales, and a surface boundary value problem which depends on boundary conditions on the sample scale. We present a novel approach which is based on a peridynamic dislocation model to deal with the surface boundary value problem. In this model, the singularity of the stress field at the dislocatio...

This work addresses differences in predicted elastic fields created by dislocations either by the Phase Field Crystal (PFC) model, or by static Field Dislocation Mechanics (FDM). The PFC order parameter describes the topological content of the lattice, but it fails to correctly capture the elastic distortion. In contrast, static FDM correctly captures the latter but requires input about defect cores. The case of a dislocation dipole in two dimensional, isotropic, elastic medi...

Grain boundaries (GBs), an important constituent of polycrystalline materials, have a wide range of manifestion and significantly affect the properties of materials. Fully understanding the effects of GBs is stalemated due to lack of complete knowledge of their structures and energetics. Here, for the first time, by taking graphene as an example, we propose an analytical energy functional of GBs in angle space. We find that an arbitrary GB can be characterized by a geometric ...

The common practice of ignoring the elastic strain gradient in measurements of geometrically necessary dislocation (GND) density is critically examined. It is concluded that the practice may result in substantial errors. Our analysis points to the importance of spatial variations of the elastic strain field in relation to its magnitude in inferring estimates of dislocation density from measurements.

In this paper, we present a continuum model for the dynamics of low angle grain boundaries in two dimensions based on the motion of constituent dislocations of the grain boundaries. The continuum model consists of an equation for the motion of grain boundaries (i.e., motion of the constituent dislocations in the grain boundary normal direction) and equations for the dislocation structure evolution on the grain boundaries. This model is derived from the discrete dislocation dy...

We investigate low energy structures of a lattice with dislocations in the context of nonlinear elasticity. We show that these low energy configurations exhibit in the limit a Cosserat-like behavior. Moreover, we give bounds from above and below to the energy of such configurations.

In this paper, we deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal in exam, so that the mathematical formulation will involve a two dimensional variational problem. The dislocations are introduced as point topological defects of the strain fields, for which we compute the elastic energy stored outside the so called core region. We show that the Gamma...

Continuum models of dislocation plasticity require constitutive closure assumptions, e.g., by relating details of the dislocation microstructure to energy densities. Currently, there is no systematic way for deriving or extracting such information from reference simulations, such as discrete dislocation dynamics or molecular dynamics. Here, a novel data-mining approach is proposed through which energy density data from systems of discrete dislocations can be extracted. Our ap...

We introduce a phenomenological theory of dislocation motion appropriate for two dimensional lattices. A coarse grained description is proposed that involves as primitive variables local lattice rotation and Burgers vector densities along distinguished slip systems of the lattice. We then use symmetry considerations to propose phenomenological equations for both defect energies and their dissipative motion. As a consequence, the model includes explicit dependences on the loca...

We analyze the dislocation content of grain boundary (GB) phase junctions, i.e., line defects separating two different GB phases coexisting on the same GB plane. While regular GB disconnections have been characterized for a variety of interfaces, GB phase junctions formed by GBs with different structures and different numbers of excess atoms have not been previously studied. We apply a general Burgers circuit analysis to calculate the Burgers vectors b of junctions in two {\S...