Statistical characterization of dislocation ensembles

Abstract

We outline a method to study the spatial and orientation statistics of dynamical dislocation systems by modeling the dislocations as a stochastic fiber process. Statistical measures have been introduced for the density, velocity, and flux of dislocations, and the connection between these measures and the dislocation state and plastic distortion rate in the crystal is explained. A dislocation dynamics simulation model has been used to extract numerical data to study the evolution of these statistical measures numerically in a body-centered cubic crystal under deformation. The orientation distribution of the dislocation density, velocity and dislocation flux, as well as the dislocation correlations have been computed. The importance of the statistical measures introduced here in building continuum models of dislocation systems is highlighted.

Dislocation pair correlations from dislocation dynamics simulations

“…The density fluctuations in 3D systems thus appear into the statistical models in ways that are fundamentally different from the case of 2D systems. For example, as pointed out in [7,8], correlation effects arise due to both long-range interactions as well as short range dislocation reactions. Also, the presence of distinct dislocation densities associated with various slip systems in the crystal makes it essential to model and incorporate the cross correlations between various dislocation types as a part of modeling the correlation effects.…”

“…In that investigation, the dislocation correlations themselves were computed from numerical simulation of the relaxation of undriven edge dislocation systems. Although some works have already pointed out the critical role of dislocation fluctuations in statistical modeling of 3D dislocation systems, see for example [6][7][8] and related works in a recent volume [10], no detailed investigations have been conducted yet to explore the nature of the dislocation correlations in driven 3D dislocation systems. The lack of such investigations as well as the anticipated differences between dislocation correlations in 2D and 3D systems motivate the current study.…”

“…The fact that dislocations in a deforming crystal can be considered as a dynamical system with large numbers of degrees of freedom has inspired the use of the principles of statistical mechanics to address the question of collective dynamical behavior of dislocations in crystals [1][2][3][4][5][6][7][8]. In a typical statistical model the dislocation system is described in terms of phase densities governed by kinetic equations, a treatment that bears some similarities with the classical kinetic theory of particle systems [9].…”

“…This investigation makes use of the concept of stochastic fiber process and the method of dislocation dynamics simulation to model and compute the dislocation correlations. The work takes advantage of the connection between kinetic dislocation models and the method of dislocation dynamics simulation [11,12], on one hand, and between geometrical and statistical characteristics of dislocations and the concept of stochastic fiber process [7,8,13], on the other hand. The Parallel Dislocation Simulator (ParaDiS) model [14] is used to obtain the spatial statistical data of the dislocation system for subsequent analysis of the correlation using the framework of stochastic fiber process.…”

The probability distribution of internal stresses in externally loaded 2D dislocation systems

“…Several such theories have been proposed so far both for two [5,6,7,8,9] and three dimensions [10,11,12,13,14]. In all these models a key problem is to take into account dislocation-dislocation correlations during the coarse graining of the microstructure.…”