The importance of being curved: bowing dislocations in a continuum description

Sedláček, Radan; Kratochvı́l, Jan; Werner, Ewald

doi:10.1080/14786430310001600213

Cited by 64 publications

(76 citation statements)

References 18 publications

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“…The dislocation curvature can then be determined from the orientation of the neighboring segments belonging to the same dislocation. To this end, the concept of single-valued dislocation fields has been proposed by Sedláček et al [23,24]. This concept, which is central to this paper as well, is recalled in the next Section.…”

Section: Incompleteness Of the Continuum Descriptionmentioning

confidence: 99%

“…This approach, pioneered by Kratochvíl and Saxlová [34], and used e.g. by Sedláček et al [35,22], has been developed as a concise theory by Sedláček et al [23,24] and it is employed also here. As for the mutual dislocation interactions in a continuum description, a rigorous statistical approach using dislocation correlation functions has been developed for straight parallel dislocations by Groma et al [13,14].…”

Section: Elastic Fields Of Continuously Distributed Dislocationsmentioning

confidence: 99%

“…An alternative approach to the density-based modelling of dislocations is to start with the continuum theory of dislocations that was developed originally to deal with the description of incompatibility and internal stresses resulting from a prescribed dislocation distribution [16]. In the present work, we further develop the non-local continuum theory of evolving dislocation fields based on the continuum theory of moving dislocations [16,17,18,19,20,21] that we have proposed earlier [22,23,24,25]. The length-scale dependency of this approach results from the line tension of the curved dislocations squeezing through small deforming volumes.…”

Section: Introductionmentioning

confidence: 99%

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Continuum theory of evolving dislocation fields

Sedláček

Schwarz

Kratochvı́l

et al. 2007

Philosophical Magazine

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International audienceContinuum theory of moving dislocations is used to set up a non-local constitutive law for crystal plasticity in the form of partial differential equations for evolving dislocation fields. The concept of single-valued dislocation fields that enables to keep track of the curvature of the continuously distributed gliding dislocations with line tension is utilized. The theory is formulated in the Eulerian as well as in so-called dislocation-Lagrangian forms. The general theory is then specialized to a form appropriate to formulate and solve plane-strain problems of continuum mechanics. The key equation of the specialized theory is identified as a transport equation of diffusion-convection type. The numerical instabilities resulting from the dominating convection are eliminated by resorting to the dislocation-Lagrangian approach. Several examples illustrate the application of the theory

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Section: Incompleteness Of the Continuum Descriptionmentioning

confidence: 99%

Section: Elastic Fields Of Continuously Distributed Dislocationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Continuum theory of evolving dislocation fields

Sedláček

Schwarz

Kratochvı́l

et al. 2007

Philosophical Magazine

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“…However, some of the details of the model are not completely developed. A recent promising approach is to apply statistical methods to treat the collective behavior of large dislocation ensembles [8][9][10][11][12][13]. Up to now, however, these investigations have not lead to conclusive results on dislocation pattern formation.…”

Section: Introductionmentioning

confidence: 99%

Dislocation patterning: The role of climb in meso-scale simulations

Bakó

Groma

Györgyi

et al. 2006

Computational Materials Science

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Simulation of parallel dynamics of edge dislocations in a 2D hexagonal lattice is carried out on a large scale by means of coarse graining, in the absence of external strain. In order to study the effect of climb on dislocation pattern formation, we allowed (i) isotropic (ii) biased (iii) only glide mobility. Moreover we annihilated dislocations with opposite Burgers vectors close to each other. The main result is that in cases (i) and (ii) cellular structure emerges, for (ii) this happens after a longer transient, while (iii) gives a diffuse looking pattern, similar to former single slip plane simulations. In the course of the evolution of dislocation number and cell size they statistically well satisfy Holt's relation. The cell structure found appears to have a characteristic cell size, in contrast to fractal examples in the presence of mechanical strain. Despite the simplicity of our model, the results are consistent with the recently detected low-density dislocation patterns in melt-grown, non-post-deformed crystals.

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“…Several such theories have been proposed so far both for two [5,6,7,8,9] and three dimensions [10,11,12,13,14]. In all these models a key problem is to take into account dislocation-dislocation correlations during the coarse graining of the microstructure.…”

Section: Introductionmentioning

confidence: 99%

The probability distribution of internal stresses in externally loaded 2D dislocation systems

Ispánovity

Groma

2008

J. Stat. Mech.

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Abstract. The distribution of internal shear stresses in a 2D dislocation system is investigated when external shear stress is applied. This problem serves as a natural continuation of the previous work of Csikor and Groma (Csikor F F and Groma I 2004 Phys. Rev. B 58 2969), where analytical result was given for the stress distribution function at zero applied stress. First, the internal stress distribution generated by a set of randomly positioned ideal dislocation dipoles is studied. Analytical calculations are carried out for this case. The theoretical predictions are checked by numerical simulations showing perfect agreement. It is found that for real relaxed dislocation configurations the role of dislocation multipoles cannot be neglected, but the theory presented can still be applied.

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The importance of being curved: bowing dislocations in a continuum description

Cited by 64 publications

References 18 publications

Continuum theory of evolving dislocation fields

Continuum theory of evolving dislocation fields

Dislocation patterning: The role of climb in meso-scale simulations

The probability distribution of internal stresses in externally loaded 2D dislocation systems

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