On dislocation–defect interactions and patterning: stochastic discrete dislocation dynamics (SDD)

Hiratani, Masato; Zbib, Hussein M.

doi:10.1016/j.jnucmat.2003.08.042

Cited by 21 publications

(13 citation statements)

References 33 publications

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“…It presently remains unclear whether such a complex dislocation geometry and reaction sequence could be described by an extension of the simple line-tension model developed here, or instead by the more contemporary segment-tracking dislocation dynamics simulation method within the framework of the Langevin approach-an avenue of methodology that has already been explored in the study of edge dislocation mobility 41 and dislocation patterning. 42,43 In summary, a stochastic differential equation describing a continuum elastic string model has been developed and investigated with the view of developing a simplified description of the collective and internal dynamics of prismatic selfinterstitial and vacancy loops. By exploiting the time-average properties of the stochasticity, relationships between the microscopic parameters of the theory, the friction coefficient, and elastic stiffness per unit length, are given in terms of observables that can be directly obtained from atomistic simulations of prismatic loops.…”

Section: Discussionmentioning

confidence: 99%

Simulating dislocation loop internal dynamics and collective diffusion using stochastic differential equations

2011

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Nanoscale prismatic loops are modeled via a partial stochastic differential equation that describes an overdamped continuum elastic string, with a view to describing both the internal and collective dynamics of the loop as a function of temperature. Within the framework of the Langevin equation, expressions are derived that relate the empirical parameters of the model, the friction per unit length, and the elastic stiffness per unit length, to observables that can be obtained directly via molecular-dynamics simulations of interstitial or vacancy prismatic loop mobility. The resulting expressions naturally exhibit the properties that the collective diffusion coefficient of the loop (i) scales inversely with the square root of the number of interstitials, a feature that has been observed in both atomistic simulation and in situ TEM investigations of loop mobility, and (ii) the collective diffusion coefficient is not at all dependent on the internal interactions within the loop, thus qualitatively rationalizing past simulation results showing that the characteristic migration energy barrier is comparable to that of a single interstitial, and cluster migration is a result of individual (but correlated) interstitial activity.

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Section: Discussionmentioning

confidence: 99%

Simulating dislocation loop internal dynamics and collective diffusion using stochastic differential equations

2011

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“…At the meso-scale, dislocation dynamics is a popular tool to simulate plastic deformation of crystalline structures, where Newtonian-like equations are used to describe the motion of crystal defects within the stress fields. Extended from deterministic models, stochasticity was recently introduced in dislocation dynamics simulations to incorporate the fluctuation effects of internal stress [11] and spatial distributions [12,13] caused by long-range dislocation interaction, and thermal dissipation [14] during plastic flow. The stochastic DD problem then is formulated and solved as Langevin-type evolution equations.…”

Section: Stochastic Models To Simulate With Variabilitiesmentioning

confidence: 99%

Multiscale Variability and Uncertainty Quantification Based on a Generalized Multiscale Markov Model

Wang

2010

Volume 1: 36th Design Automation Conference, Parts a and B

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Variability is inherent randomness in systems, whereas uncertainty is due to lack of knowledge. In this paper, a generalized multiscale Markov (GMM) model is proposed to quantify variability and uncertainty simultaneously in multiscale system analysis. The GMM model is based on a new imprecise probability theory that has the form of generalized interval, which is a Kaucher or modal extension of classical set-based intervals to represent uncertainties. The properties of the new definitions of independence and Bayesian inference are studied. Based on a new Bayes’ rule with generalized intervals, three cross-scale validation approaches that incorporate variability and uncertainty propagation are also developed.

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“…Three-dimensional DD models have mostly been used to examine strain hardening due to dislocation forest interactions [1][2][3] and individual dislocation-defect interactions [4][5][6][7]. However, for complex problems, the use of two-dimensional DD models is common due to the high computational cost of three-dimensional DD [8].…”

Section: Introductionmentioning

confidence: 99%

Macroscopic stress and strain in a doubly periodic array of dislocation dipoles

Gourgiotis

Stupkiewicz

2014

Proc. R. Soc. A.

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It is known that in two-dimensional periodic arrays of dislocations the summation of the periodic image fields is conditionally convergent. This is due to the long-range character of the elastic fields of dislocations. As a result, the stress field obtained for a doubly periodic array of dislocation dipoles may contain a spurious constant stress that depends on the adopted summation scheme. In the present work, we provide, based on micromechanical considerations, a simple physical explanation of the origin of the conditional convergence of lattice sums of image interactions. In this context, the spurious stresses are found in a closed form for an arbitrary elastic anisotropy, and this is achieved without using the stress field of an individual dislocation. An alternative procedure is also developed where the macroscopic spurious stresses are determined using the solution of the Eshelby's inclusion problem.

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On dislocation–defect interactions and patterning: stochastic discrete dislocation dynamics (SDD)

Cited by 21 publications

References 33 publications

Simulating dislocation loop internal dynamics and collective diffusion using stochastic differential equations

Simulating dislocation loop internal dynamics and collective diffusion using stochastic differential equations

Multiscale Variability and Uncertainty Quantification Based on a Generalized Multiscale Markov Model

Macroscopic stress and strain in a doubly periodic array of dislocation dipoles

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