Interface modeling in continuum dislocation transport

Dogge, Mmw Michael; Peerlings, Rhj Ron; Geers, Mgd Marc

doi:10.1016/j.mechmat.2015.04.007

Cited by 8 publications

(9 citation statements)

References 33 publications

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“…al. 42 . However, in this type of analysis an artificial length scale parameter is introduced in terms of the slip plane spacing and, as demonstrated elsewhere 43 , the results depend crucially on the difficult-to-justify assumption of a strictly periodic arrangement of active slip planes.…”

Section: Density Based Representation Of a Dislocation System: Linkin...mentioning

confidence: 99%

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Dislocation patterning in a 2D continuum theory of dislocations

Groma,

Zaiser,

Ispanovity

2016

Preprint

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Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were proposed, but few of them (if any) are derived from microscopic considerations through systematic and controlled averaging procedures. In this paper we present a 2D continuum theory that is obtained by systematic averaging of the equations of motion of discrete dislocations. It is shown that in the evolution equations of the dislocation densities diffusion like terms neglected in earlier considerations play a crucial role in the length scale selection of the dislocation density fluctuations. It is also shown that the formulated continuum theory can be derived from an averaged energy functional using the framework of phase field theories. However, in order to account for the flow stress one has in that case to introduce a nontrivial dislocation mobility function, which proves to be crucial for the instability leading to patterning.

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Section: Density Based Representation Of a Dislocation System: Linkin...mentioning

confidence: 99%

“…For a system of straight parallel edge dislocations with Burgers vectors parallel to the x axis the evolution equations of dislocation densities ρ + and ρ − have the form 22,42…”

Section: Variational Approachmentioning

confidence: 99%

Dislocation patterning in a 2D continuum theory of dislocations

Groma,

Zaiser,

Ispanovity

2016

Preprint

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“…This force originates from the externally applied forces and the forces induced by the interactions with other dislocations. After performing such averaging in the infinite medium considered here, the velocities can be expressed as [6,11,12]…”

Section: Governing Equationsmentioning

confidence: 99%

“…For crystalline solids, inelastic effects have been taken into account at the level of single crystals by various crystal plasticity models [30]. At a higher spatial resolution, plasticity in a single crystal can be modeled using dislocation transport equations [6,12,14].…”

Section: Introductionmentioning

confidence: 99%

Towards an unconditionally stable numerical scheme for continuum dislocation transport

Velazquez¹,

Massart

Peerlings³

et al. 2015

Modelling Simul. Mater. Sci. Eng.

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Recent developments in plasticity modeling for crystalline materials are based on dislocations transport models, formulated for computational efficiency in terms of their densities. This leads to sets of coupled partial differential equations in a continuum description involving diffusion and convection-like processes combined with non-linearity. The properties of these equations cause the most traditional numerical methods to fail when applied to solve them. Therefore, dedicated stabilization techniques must be developed in order to obtain physically meaningful and numerically stable approximations. The objective of this paper is to present a dedicated stabilization technique and to apply it to a system of dislocation transport equations in one dimension. This stabilization technique, based on coefficient perturbations, successfully provides unconditional stability with respect to the spatial discretization. Several of its favorable characteristics are discussed, providing evidence of its versatility and effectiveness through a thorough numerical assessment.

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“…The model of [79] considers the redistribution of defects along the grain boundary in an averaged sense via a diffusion-type equation for the spreading of the net-defect content of the grain boundary along its planar surface. Dislocation transport is considered in the models of [80,81]. In the latter work, flux equations are explicitly accounted for at the interfaces, thereby modeling the transport across them.…”

mentioning

confidence: 99%

Review on slip transmission criteria in experiments and crystal plasticity models

et al. 2015

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A comprehensive overview is given of the literature on slip transmission criteria for grain boundaries in metals, with a focus on slip system and grain boundary orientation. Much of this extensive literature has been informed by experimental investigations. The use of geometric criteria in continuum crystal plasticity models is discussed. The theoretical framework of Gurtin (2008, J. Mech. Phys. Solids 56, p. 640) is reviewed for the single slip case. This highlights the connections to slip transmission criteria from the literature that are not discussed in the work itself. Different geometric criteria are compared for the single slip case with regard to their prediction of slip transmission. Perspectives on additional criteria, investigated in experiments and used in computational simulations, are given.

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Interface modeling in continuum dislocation transport

Cited by 8 publications

References 33 publications

Dislocation patterning in a 2D continuum theory of dislocations

Dislocation patterning in a 2D continuum theory of dislocations

Towards an unconditionally stable numerical scheme for continuum dislocation transport

Review on slip transmission criteria in experiments and crystal plasticity models

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