A non-singular continuum theory of dislocations

Cai, Wei; Arsenlis, A.; Weinberger, Christopher R.; Bulatov, Vasily V.

doi:10.1016/j.jmps.2005.09.005

Cited by 397 publications

(431 citation statements)

References 26 publications

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“…The former fields are computed assuming that dislocations are embedded in an infinite elastic medium. Adopting the regularized approximation (Cai et al, 2006) to avoid singularities in the classical expressions, the infinite medium contribution to the elastic strain and lattice rotation tensors are expressed in the form: …”

Section: Theoretical Formalism For the Elastic Fields In A Deformed Cmentioning

confidence: 99%

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

Mohamed¹,

Larson²,

Tischler³

et al. 2015

Journal of the Mechanics and Physics of Solids

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CitationA statistical analysis of the elastic distortion and dislocation density fields in deformed crystals This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Abstract.The statistical properties of the elastic distortion fields of dislocations in deforming crystals are investigated using the method of discrete dislocation dynamics to simulate dislocation structures and dislocation density evolution under tensile loading. Probability distribution functions (PDF) and pair correlation functions (PCF) of the simulated internal elastic strains and lattice rotations are generated for tensile strain levels up to 0.85%. The PDFs of simulated lattice rotation are compared with sub-micrometer resolution three-dimensional X-ray microscopy measurements of rotation magnitudes and deformation length scales in 1.0% and 2.3% compression strained Cu single crystals to explore the linkage between experiment and the theoretical analysis. The statistical properties of the deformation simulations are analyzed through determinations of the Nye and Kröner dislocation density tensors. The significance of the magnitudes and the length scales of the elastic strain and the rotation parts of dislocation density tensors are demonstrated, and their relevance to understanding the fundamental aspects of deformation is discussed.

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Section: Theoretical Formalism For the Elastic Fields In A Deformed Cmentioning

confidence: 99%

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

Mohamed¹,

Larson²,

Tischler³

et al. 2015

Journal of the Mechanics and Physics of Solids

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“…The ParaDis dislocation dynamics model, see [16,18] for details, has been used to obtain numerical data to implement the definitions developed in section 2. In the ParaDis model, the dislocation configuration is a collection of piece-wise linear segments connected at nodes.…”

Section: The Dislocation Dynamics Modelmentioning

confidence: 99%

“…The velocities are computed using a force-velocity law in which the (Peach-Koehler) force is computed either as the negative gradient of the energy of the dislocation system with respect to the nodal coordinates, or by the integral over segments incident with each node, of the point-wise forces on the Philosophical Magazine 14 segments times some weight function. Non-singular expressions of the dislocation stress field and energy that have been recently derived are used for this purpose [18].…”

Section: The Dislocation Dynamics Modelmentioning

confidence: 99%

Statistical characterization of dislocation ensembles

El–Azab

Deng

Tang

2007

Philosophical Magazine

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We outline a method to study the spatial and orientation statistics of dynamical dislocation systems by modeling the dislocations as a stochastic fiber process. Statistical measures have been introduced for the density, velocity, and flux of dislocations, and the connection between these measures and the dislocation state and plastic distortion rate in the crystal is explained. A dislocation dynamics simulation model has been used to extract numerical data to study the evolution of these statistical measures numerically in a body-centered cubic crystal under deformation. The orientation distribution of the dislocation density, velocity and dislocation flux, as well as the dislocation correlations have been computed. The importance of the statistical measures introduced here in building continuum models of dislocation systems is highlighted.

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“…It is worth mentioning that a singularity is present at the dislocation line, which can be regularized according to Ref. [242]. The definition of the local strain field for a generic geometry is quite more complex as it requires to numerically solve, e.g.…”

Section: Dislocationsmentioning

confidence: 99%

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

Bergamaschini

Salvalaglio

Backofen

et al. 2016

Advances in Physics: X

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Semiconductor heteroepitaxy involves a wealth of qualitatively different, competing phenomena. Examples include threedimensional island formation, injection of dislocations, mixing between film and substrate atoms. Their relative importance depends on the specific growth conditions, giving rise to a very complex scenario. The need for an optimal control over heteroepitaxial films and/or nanostructures is widespread: semiconductor epitaxy by molecular beam epitaxy or chemical vapour deposition is nowadays exploited also in industrial environments. Simulation models can be precious in limiting the parameter space to be sampled while aiming at films/nanostructures with the desired properties. In order to be appealing (and useful) to an applied audience, such models must yield predictions directly comparable with experimental data. This implies matching typical time scales and sizes, while offering a satisfactory description of the main physical driving forces. It is the aim of the present review to show that continuum models of semiconductor heteroepitaxy evolved significantly, providing a promising tool (even a working tool, in some cases) to comply with the above requirements. Several examples, spanning from the nanometre to the micron scale, are illustrated. Current limitations and future research directions are also discussed.

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A non-singular continuum theory of dislocations

Cited by 397 publications

References 26 publications

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

Statistical characterization of dislocation ensembles

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

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