We present a computational method for identifying partial and interfacial dislocations in atomistic models of crystals with defects. Our automated algorithm is based on a discrete Burgers circuit integral over the elastic displacement field and is not limited to specific lattices or dislocation types. Dislocations in grain boundaries and other interfaces are identified by mapping atomic bonds from the dislocated interface to an ideal template configuration of the coherent interface to reveal incompatible displacements induced by dislocations and to determine their Burgers vectors. In addition, the algorithm generates a continuous line representation of each dislocation segment in the crystal and also identifies dislocation junctions.

https://iopscience.iop.org/article/10.1088/0965-0393/20/8/085007/pdf

Automated identification and indexing of dislocations in crystal interfaces

Deformation twinning in nanocrystalline materials

We discuss existing and new computational analysis techniques to classify local atomic arrangements in large-scale atomistic computer simulations of crystalline solids. This article includes a performance comparison of typical analysis algorithms such as common neighbor analysis (CNA), centrosymmetry analysis, bond angle analysis, bond order analysis and Voronoi analysis. In addition we propose a simple extension to the CNA method that makes it suitable for multi-phase systems. Finally, we introduce a new structure identification algorithm, the neighbor distance analysis, which is designed to identify atomic structure units in grain boundaries.

https://iopscience.iop.org/article/10.1088/0965-0393/20/4/045021/pdf

Structure identification methods for atomistic simulations of crystalline materials

We discuss existing and new computational analysis techniques to classify local atomic arrangements in large-scale atomistic computer simulations of crystalline solids. This article includes a performance comparison of typical analysis algorithms such as Common Neighbor Analysis, Centrosymmetry Analysis, Bond Angle Analysis, Bond Order Analysis, and Voronoi Analysis. In addition we propose a simple extension to the Common Neighbor Analysis method that makes it suitable for multi-phase systems. Finally, we introduce a new structure identification algorithm, the Neighbor Distance Analysis, that is designed to identify atomic structure units in grain boundaries.

A method for solving small-strain plasticity problems with plastic flow represented by the collective motion of a large number of discrete dislocations is presented. The dislocations are modelled as line defects in a linear elastic medium. At each instant, superposition is used to represent the solution in terms of the infinite-medium solution for the discrete dislocations and a complementary solution that enforces the boundary conditions on the finite body. The complementary solution is nonsingular and is obtained from a finite-element solution of a linear elastic boundary value problem. The lattice resistance to dislocation motion, dislocation nucleation and annihilation are incorporated into the formulation through a set of constitutive rules. Obstacles leading to possible dislocation pile-ups are also accounted for. The deformation history is calculated in a linear incremental manner. Plane-strain boundary value problems are solved for a solid having edge dislocations on parallel slip planes. Monophase and composite materials subject to simple shear parallel to the slip plane are analysed. Typically, a peak in the shear stress versus shear strain curve is found, after which the stress falls to a plateau at which the material deforms steadily. The plateau is associated with the localization of dislocation activity on more or less isolated systems. The results for composite materials are compared with solutions for a phenomenological continuum slip characterization of plastic flow.

/pdf/discrete-dislocation-plasticity-a-simple-planar-model-3yaflv8n1m.pdf

Discrete dislocation plasticity: a simple planar model

http://physics.gmu.edu/~ymishin/Nye_tensor.pdf

Characterization and visualization of the lattice misfit associated with dislocation cores

This paper presents a crystallographically-based constitutive model of a single crystal deforming by climb and glide. The proposed constitutive law is an extension of the rate-sensitivity approach for single crystal plasticity by dislocation glide. Based on this description at single crystal level, a homogenization-based polycrystal model for aggregates deforming in a climb-controlled thermal creep regime is developed. To illustrate the capabilities of the proposed model, we present calculations of effective behavior of olivine and texture evolution of aluminum at warm temperature and low strain rate. In both cases, the addition of climb as a complementary single-crystal deformation mechanism improves the polycrystal model predictions.

/pdf/modeling-the-mechanical-response-of-polycrystals-deforming-3ua05s51ko.pdf

Modeling the mechanical response of polycrystals deforming by climb and glide

The Nye tensor characterizes the strength of infinitesimal dislocations at each point in a continuously dislocated crystal, and provides a measure of the Burgers vector and the extent of dislocation dissociation. The present work employs this description to analyze ½ screw dislocations in bcc Mo obtained by Finnis–Sinclair, Bond Order Potential and first-principles simulations in an attempt to detect misfit in the core region. The spatial distribution and strength of the fractional dislocations are calculated and compared between the different simulated core structures. The Nye tensor technique is also applied to HREM images of end-on screw dislocations in Mo to detect the edge fractional dislocations predicted by simulation. The advantage of the Nye tensor for this purpose arises from its insensitivity to the Eshelby twist due to surface relaxation in a thin TEM foil (this is not the case for the more conventional methods of depicting misfit, such as direct and differential displacement maps). Although t...

Use of the Nye tensor in analyzing HREM images of bcc screw dislocations

This work combines classical continuum mechanics, the continuously dislocated continuum theory as developed by Kroner and Bilby with discrete dislocation theory to develop quantities that permit models involving interactions between individual dislocations to be incorporated into a description of multiaxial yielding of a material. Two quantities distinguish this approach from earlier efforts: firstly, a dislocation mobility tensor relating the velocity of a dislocation configuration to the net Peach–Koehler force on the configuration and, secondly, a vector quantity representing the dislocation content of the materials. The theory of thermally activated motion of dislocations past obstacles is employed to relate the dislocation velocity to stress by a stress-dependent mobility tensor whose components are determined by the nature of the interaction of the moving dislocation with the obstacle. An example is presented in which the obstacle is a forest dislocation that affects a gliding dislocation through mu...

A method for linking thermally activated dislocation mechanisms of yielding with continuum plasticity theory

The stability of extended dislocation barriers in face‐centered cubic metals is determined using the theory of anisotropic elasticity. It is found that the results typically differ from the isotropic elasticity solution by 25%, but the difference can in special cases amount to as much as a factor of four. The anisotropic results are in qualitative agreement with earlier isotropic results in predicting the relative strength of the barriers to dislocation glide. The results suggest that the measurement of barrier extension should provide the most accurate available means of estimating the stacking‐fault energy in fcc metals.

C. S. Hartley

Papers

Characterization and visualization of the lattice misfit associated with dislocation cores

Modeling the mechanical response of polycrystals deforming by climb and glide

Use of the Nye tensor in analyzing HREM images of bcc screw dislocations

A method for linking thermally activated dislocation mechanisms of yielding with continuum plasticity theory

Anisotropic Elasticity Solutions for Dislocation Barriers in Face‐Centered Cubic Crystals