The stress field of an infinite set of discrete dislocations
TL;DR: The two-dimensional stress fields induced by a set of infinitely many parallel edge dislocations are difficult to estimate as those of individual dislocation decay slowly as discussed by the authors, and a simple numerical metho...
Abstract: The two-dimensional stress fields induced by a set of infinitely many parallel edge dislocations are difficult to estimate as those of individual dislocations decay slowly. A simple numerical metho...
References
More filters
[...]
02 Nov 2006
TL;DR: In this paper, the Peierls-Nabarroar model of dislocations is used to find transition pathways in atomistic models, and the phase field method is used for phase field simulations.
Abstract: 1. Introduction to crystal dislocations Atomistic Models 2. Fundamentals of atomistic simulations 3. Case study of static simulation 4. Case study of dynamic simulation 5. More about periodic boundary conditions 6. Free energy calculations 7. Finding transition pathways PART 2 Continuum Models 8. Peierls-Nabarro model of dislocations 9. Kinetic Monte Carlo method 10. Line Dislocation Dynamics 11. The Phase Field method
428 citations
"The stress field of an infinite set..." refers background in this paper
[...]
[...]
[...]
TL;DR: In this paper, the origin of conditional convergence and the numerical artefacts associated with it are analyzed and a mathematically consistent and numerically efficient procedure for regularization of the lattice sums and the corresponding image fields is established.
Abstract: The use of periodic boundary conditions for modelling crystal dislocations is predicated on one’s ability to handle the inevitable image effects. This communication deals with an often overlooked mathematical subtlety involved indealin g with the periodic dislocationarrays, that is conditional convergence of the lattice sums of image fields. By analysing the origin of conditional convergence and the numerical artefacts associated with it, we establish a mathematically consistent and numerically efficient procedure for regularization of the lattice sums and the corresponding image fields. The regularized solutions are free from the artefacts caused by conditional convergence and regain periodicity and translational invariance of the periodic supercells. Unlike the other existing methods, our approach is applicable to general anisotropic elasticity and arbitrary dislocation arrangements. The capabilities of this general methodology are demonstrated by application to a variety of situations encountered in atomistic and continuum modelling of crystal dislocations. The applications include introduction of dislocations in the periodic supercell for subsequent atomistic simulations, atomistic calculations of the core energies and the Peierls stress and continuum dislocation dynamics simulations in three dimensions.
161 citations
[...]
TL;DR: In this paper, an extension of the fast-multipole method of Greengard and Rokhlin to the case of the long-range interactions between parallel edge and screw dislocations is presented.
Abstract: We present an extension of the fast-multipole method of Greengard and Rokhlin to the case of the long-range interactions between parallel edge (in arbitrary orientations) and screw dislocations. By finding complex potentials from which the stress terms can be calculated, and expanding those potentials in multipole series, we convert a computationally difficult O(N 2) problem into a much faster O(N) approach. To reach sufficient numerical accuracy, only a few terms are needed in the multipole expansions (four screws and six for edges) so that the interactions between millions of dislocations can be calculated in a few minutes on a workstation. We present results of a study of the relaxed configurations of 16384 edge dislocations of arbitrary orientations.
81 citations
[...]
TL;DR: In this paper, the results of molecular dynamics calculations of the two-dimensional one-component plasma with logarithmic interactions between the particles are reported, and a solid-fluid transition is observed for Γ = q 2 kT ≈ 135.
Abstract: We report the results of molecular dynamics calculations of the two-dimensional one-component plasma with logarithmic interactions between the particles. A solid-fluid transition is observed for Γ = q 2 kT ≈ 135 . The hysteresis observed on traversing the transition region indicates that the transition is first order. The velocity autocorrelation function shows marked oscillations in the strong coupling region, with a frequency, almost independent of Γ, close to the plasma frequency.
69 citations
[...]
TL;DR: In this article, the authors employ discrete dislocation dynamics to establish a continuum-based model for the evolution of the dislocation structure in polycrystalline thin films and demonstrate how size effect naturally enters the evolution equation.
Abstract: Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their fitting parameters. In this paper, we employ discrete dislocation dynamics to establish a continuum-based model for the evolution of the dislocation structure in polycrystalline thin films. Expressions are developed for the density of activated dislocation sources, as well as dislocation nucleation and annihilation rates. We demonstrate how size effect naturally enters the evolution equation. Good agreement between the simulation and the model results is obtained. The current approach is based on a two-dimensional discrete dislocation dynamics model but can be extended to three-dimensional models.
39 citations