Refined short-range interactions in the continuum dislocation-based model of plasticity at the microscale

Schwarz, Cornelia; Sedláček, Radan; Werner, Ewald

doi:10.1016/j.actamat.2007.09.029

Cited by 5 publications

(15 citation statements)

References 20 publications

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“…17 Similar extension was adopted by Schwarz et al too 18 for a continuum theory of interacting curved dislocations 19 . In all mentioned current 3D continuum theories of dislocation dynamics one of the biggest challenges is the precise incorporation of the effects of dislocation correlations, which seems to be unavoidable.…”

Section: 10mentioning

confidence: 98%

Evolution of the correlation functions in two-dimensional dislocation systems

2008

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In this paper spatial correlations of parallel edge dislocations are studied. After closing a hierarchy of equations for the many-particle density functions by the Kirkwood superposition approximation, we derive evolution equations for the correlation functions. It is found that these resulting equations and those governing the evolution of density fields of total as well as geometrically necessary dislocations around a single edge dislocation are formally the same. The second case corresponds to the already described phenomenon of Debye screening of an individual dislocation. This equivalence of the correlation functions and screened densities is demonstrated also by discrete dislocation dynamics simulation results, which confirm the physical correctness of the applied Kirkwood superposition approximation. Relation of this finding and the linear response theory in thermal systems is also discussed.

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Section: 10mentioning

confidence: 98%

Evolution of the correlation functions in two-dimensional dislocation systems

2008

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“…Then, according to (6), P F str is real, and therefore the distribution function P str is symmetric. This case was thoroughly studied recently by Csikor and Groma [23].…”

Section: The Symmetric Part Of the Distribution's Fourier Transformmentioning

confidence: 99%

“…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%

“…(It is known that neglecting the dislocation-dislocation correlations leads to unphysical results [8,9].) It is found that correlation effects enter into the theories through gradientlike stress terms [6,8,14], which were already proposed earlier phenomenologically [15,16]. Motivated by its crucial role many investigations on the properties of dislocation correlations have been published recently [17,18,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

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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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“…By doing so, many details of the short-range interactions are missing. For example, it has been noticed by several research groups that the self-force of dislocations due to the line tension effect proportional to their curvature or the diffusion-like terms, which will lead to size dependent effects, should be added in the dislocation density based plasticity theories [13,14,16,[24][25][26][27][28]. However, different forms of such curvature or gradient terms and adjustable parameters such as the stiffness parameter in the line tension approximation or the diffusion coefficient are included in these models.…”

Section: Introductionmentioning

confidence: 99%

Continuum model for dislocation dynamics in a slip plane

Zhu

Xiang

2010

Philosophical Magazine

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In this paper, we present a continuum model for dislocation dynamics in a slip plane, which accurately incorporates both the long-range interaction and the local line tension effect of dislocations. Unlike the continuum models in the literature using dislocation densities, we use the disregistry across the slip plane to represent the continuous distribution of dislocations in the slip plane, which has the advantage of including the orientation dependence of dislocations in a very simple way. The continuum dislocation dynamics model is validated by linear instability analysis of a uniform dislocation array to small perturbations and comparisons of the results with those of the discrete dislocation dynamics model. Numerical examples for the evolution of distributions of dislocations and plastic slips in a slip plane are presented.

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Refined short-range interactions in the continuum dislocation-based model of plasticity at the microscale

Cited by 5 publications

References 20 publications

Evolution of the correlation functions in two-dimensional dislocation systems

Evolution of the correlation functions in two-dimensional dislocation systems

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

Continuum model for dislocation dynamics in a slip plane

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