A Universal Approach Towards Computational Characterization of Dislocation Microstructure

Abstract

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 still lagging behind. We introduce a universal microstructure "language" which could be used for direct comparisons and detailed analysis of very different experimental and simulation methods.

Machine Learning-Based Classification of Dislocation Microstructures

“…The D2C framework (Sandfeld and Po, 2015;Steinberger et al, 2016) is based on treating dislocations as directed curves with additional physical properties, i.e., the slip plane normal, and the Burgers vector. Dislocations represent the boundary of an area over which slip displacement between two adjacent lattice planes has occurred.…”

“…This makes it problematic to directly operate with these objects. We will therefore take a new approach: Based on the discrete-to-continuous (D2C) framework (Sandfeld and Po, 2015;Steinberger et al, 2016), which "borrows" the field variables of a continuum theory of dislocation dynamics. This method was already successfully used to study the emergent microstructural features of molecular dynamics simulations of plastic deformation via scratching (Gunkelmann et al, 2017) and during shock loading (Kositski et al, 2018).…”

Nanoscratching of iron: A novel approach to characterize dislocation microstructures

“…The reason is that the curvature is independent of the density, such that even averaging voxels with very low density will have a finite curvature value. In Steinberger et al [22] the authors have already shown that this counter-intuitive behavior does not exist if the curvature density, which is a product of density and curvature, is used.…”

FETI‐DP Solvers and Deal.II for Problems in Dislocation Mechanics

“…To compute the stresses associated with dislocations within a specimen for the characterization of the microstructure [1,2], we start by considering a linear elastic model described by div σ = 0, σ = σ T , σ = C : ε el , and ε el = 1 2 ∇u + (∇u) T to solve for the displacements u. Here, σ is the stress tensor, ε el the elastic strain tensor, and C the stiffness tensor.…”