Analysing discrete dislocation data using alignment and curvature tensors

Benedikt Weger,Thomas Hochrainer,Satyapriya Gupta

doi:10.5802/crphys.60

Abstract

Analysis of large scale discrete dislocation data requires the characterisation of complex dislocation networks by suitable average quantities. In the current work, we suggest dislocation alignment tensors and closely related curvature tensors as easily extractable and intelligible measures of geometrical and topological characteristics of dislocation distributions. We provide formulae for extracting these measures from discrete dislocation data based on straight segments. Examples for interpreting and visualising these measures are provided for a simple configuration and two more involved results from discrete dislocation simulations. We suggest the alignment and curvature tensors for wider use in plasticity research.

Highlights

Recent years have seen the establishment of large scale data analysis tools in computational materials science, see, e.g., [1] for a recent review
We suggest dislocation alignment tensors and closely related curvature tensors as extractable and intelligible measures of geometrical and topological characteristics of dislocation distributions
What appears to be mostly overlooked is that there exist more refined dislocation density measures developed in the community dealing with so-called continuum dislocation dynamics (CDD); and that these measures are easy to obtain and relevant for characterising discrete dislocation states

Summary

Introduction

Recent years have seen the establishment of large scale data analysis tools in computational materials science, see, e.g., [1] for a recent review. The total dislocation density does not comprise any topological information and may, for example, not distinguish a small number of large dislocation loops from a high number of small loops; but these two cases represent very different dynamics in further deformation Besides these classical measures, the link length distribution has been considered recently [6, 7], which comprises interesting characteristics of dislocation networks. What appears to be mostly overlooked is that there exist more refined dislocation density measures developed in the community dealing with so-called continuum dislocation dynamics (CDD); and that these measures are easy to obtain and relevant for characterising discrete dislocation states These so-called dislocation alignment tensors [8] allow for a seamless characterisation of orientation distributions of dislocation lines.

Obtaining alignment tensors from discrete dislocation data

Analysis of dislocation distributions obtained from 3-dimensional DD

Validation and analysis of a simple dislocation configuration

Analysis of complex dislocation configurations

Findings

Summary and conclusions