Determination of interaction forces between parallel dislocations by the evaluation of J integrals of plane elasticity

Lubarda, Vlado A.

doi:10.1007/s00161-015-0438-1

Cited by 5 publications

(2 citation statements)

References 31 publications

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“…When the singularity takes the form of a dislocation, changes in total energy are defined in terms of a virtual force acting on the dislocation. Lubarda [29], for example, used this fact to calculate the interaction forces between parallel dislocations. Moreover, the ideas corresponding to the use of the J-integral were expanded to the case of couple stress theory by Atkinson and Leppington [19] and Lubarda and Markenscoff [20].…”

Section: Screw Dislocation Near the Bi-materials Interfacementioning

confidence: 99%

Interaction of a screw dislocation with a bi-material interface in anti-plane couple stress elasticity

Gharahi

Dai

Wang

et al. 2017

Mathematics and Mechanics of Solids

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We analyze the contribution of couple stresses to the interaction between a screw dislocation and a bi-material interface. Using Fourier integral transforms, we develop analytical representations for the stress distributions in each of the adjoining materials as well as the interaction force acting on the dislocation. Our results are illustrated with several numerical examples, which indicate that couple stresses significantly influence the corresponding stress distributions and the mobility of the dislocation when the distance between the dislocation and the material interface remains below or near the characteristic length of the materials.

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Section: Screw Dislocation Near the Bi-materials Interfacementioning

confidence: 99%

Interaction of a screw dislocation with a bi-material interface in anti-plane couple stress elasticity

Gharahi

Dai

Wang

et al. 2017

Mathematics and Mechanics of Solids

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“…When the J integral is applied to the stationary dislocation, the J integral is equal to the Peach-Koehler (PK) force acting on it (Eshelby, 1956). The J integral has been widely applied to characterize various states of dislocations upon consideration of simple to complex cases (Lubarda and Markenscoff, 2007;Baxevanakis and Giannakopoulos, 2015;Ballarini and Royer-Carfagni, 2016;Lubarda, 2015;Seo et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Configurational force on a dynamic dislocation with localized oscillation

Kim

2021

International Journal of Plasticity

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Upon employing the conservation theorem and continuum theory, the configurational force on a singularity, or a defect, is given by a pathindependent integral called the J integral. According to the continuum elasticity theory, the J integral around a steadily moving dislocation is equal to the Peach-Koehler force acting on the dislocation and is independent of the integration path. However, using a discrete lattice dynamics method, we theoretically prove that the J integral is not path-independent in practice even under uniform motion. This is because of the generation of phonons during the dislocation motion. In general, phonons are generated upon localized oscillation of the dislocation, and they dissipate energy from the dislocation core; consequently, a drag force is produced. As the drag force disturbs the dislocation motion, the J integral around the moving dislocation is smaller than that around a stationary one, and its deviation from the stationary one corresponds to the drag force. In this study, we analytically derive the drag force for each oscillation mode by adopting dislocation-phonon coordinates. We classify the oscillation mode simply as symmetric or anti-symmetric after assuming the dislocation to be a localized defect having a finite core width. Consequently, the drag force is numerically calculated upon consideration of the discrete nature of the dislocation core. In particular, our study reveals that the anti-symmetric oscillation mode mainly contributes to the drag force in the limit of high dislocation velocity. Furthermore, we show that the resulting relation between the drag force and dislocation frequency can reproduce the dislocation velocity-stress curve. This work is expected to contribute to mesoand macro-scale plasticity when the material is loaded under extreme conditions or transient dislocation motion can be assumed.

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An edge dislocation near an anticrack in a confocal elliptical coating

Wang

Schiavone

2020

Continuum Mech. Thermodyn.

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Determination of interaction forces between parallel dislocations by the evaluation of J integrals of plane elasticity

Cited by 5 publications

References 31 publications

Interaction of a screw dislocation with a bi-material interface in anti-plane couple stress elasticity

Interaction of a screw dislocation with a bi-material interface in anti-plane couple stress elasticity

Configurational force on a dynamic dislocation with localized oscillation

An edge dislocation near an anticrack in a confocal elliptical coating

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