Microstructural comparison of the kinematics of discrete and continuum dislocations models

Abstract

The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation Dynamics (DDD) method are compared based on concise mathematical formulations of the coarse graining of discrete data. A numerical tool for converting from a discrete to a continuum representation of a given dislocation configuration is developed, which allows to directly compare both simulation approaches based on continuum quantities (e.g. scalar density, geometrically necessary densities, mean curvature). Investigating the evolution of selected dislocation configurations within analytically given velocity fields for both DDD and CDD reveals that CDD contains a surprising number of important microstructural details.Submitted to: Modelling Simulation Mater. Sci. Eng.

Nanoscratching of iron: A novel approach to characterize dislocation microstructures

“…The D2C method converts geometrical properties of discrete dislocation lines into continuous field variables [21]. Since geometrical dislocation lines are onedimensional objects embedded in a three-dimensional space a point-wise comparison between two dislocation structures is difficult.…”

“…Then the density and curvature of dislocations with line orientation ϕ (i.e., the angle between the line tangent and the Burgers vector) is given by the variables ρ(r, ϕ) and k(r, ϕ) [39], where r denotes the spatial coordinates of a point. These two variables can easily be obtained from discrete dislocations since the line length and average line orientation in an averaging volume can be computed and also the curvature can be derived from basic geometrical relations (please refer to [18] and [21] for further details).…”

“…Finally, to obtain the fields we integrate or average over all line segments within a voxel, e.g., ρ (1) = i (ρ (1) ) i . Further details, applications and a detailed mathematical description of these discrete-to-continuous (D2C ) steps are presented in [21].…”

“…In order to quantitatively analyze the dislocation microstructure, we apply the recently introduced discreteto-continuum (D2C) method [21,22] to data obtained from atomistic simulations of nanoscratching. D2C is a methodology for converting properties of discrete dislocation lines to continuous field data.…”

A Universal Approach Towards Computational Characterization of Dislocation Microstructure

“…Therefore, we propose a different approach towards characterizing, validating, and data mining of dislocation data based on one of the information-richest CDD models that resulted from the theory by Hochrainer [14,15,20,21]. Although this CDD model is able to describe the evolution of dislocations in great detail [22], we only will use the underlying field variables consisting of density and line curvature data (and possibly higher-order moments thereof). Together with converting data from lower scale methods or experiments into these mesoscale field variables we arrive at a description that is -unlike discrete dislocation data -defined in each point of the volume under consideration, which, e.g., allows to simply "take the difference" between two data sets.…”