Dislocations in cubic crystals described by discrete models

Bonilla, L. L.; Carpio, Ana; Plans, I.

doi:10.1016/j.physa.2006.10.082

Cited by 9 publications

(6 citation statements)

References 25 publications

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“…If we Taylor expand these finite difference combinations about (x, y), insert the result in ( 1) and ( 2) and write the displacement vector in cartesian coordinates, we recover the equations of linear elasticity [26]. The role of the periodic function g is to allow dislocation gliding [28,29,30]. When a defect moves, a few atoms change some of their nearest neighbors.…”

Section: Periodized Discrete Elasticity and Stability Of Defectsmentioning

confidence: 99%

Dislocations in graphene

et al. 2008

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We study the stability and evolution of various elastic defects in a flat graphene sheet and the electronic properties of the most stable configurations. Two types of dislocations are found to be stable: "glide" dislocations consisting of heptagon-pentagon pairs, and "shuffle" dislocations, an octagon with a dangling bond. Unlike the most studied case of carbon nanotubes, Stone Wales defects are unstable in the planar graphene sheet. Similar defects in which one of the pentagonheptagon pairs is displaced vertically with respect to the other one are found to be dynamically stable. Shuffle dislocations will give rise to local magnetic moments that can provide an alternative route to magnetism in graphene.

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Section: Periodized Discrete Elasticity and Stability Of Defectsmentioning

confidence: 99%

Dislocations in graphene

et al. 2008

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“…Our approach follows the original proposal by Ericksen that the energy periodicity in the space of tensors should be made compatible with geometrically nonlinear kinematics of crystal lattices [46][47][48][49], and we also build upon subsequent important developments of the mathematical formalism in [50][51][52][53][54].This general program can be viewed as far reaching generalization of the Frenkel-Kontorova-Peierls-Nabarro model accounting for energy periodicity along a single slip plane [55][56][57]. Scalar models with periodic energies, dealing with multiple slip planes, have been used before to describe dislocation cores [58][59][60], to simulate dislocation nucleation [61][62][63][64] and to capture intermittency of plastic flows [65,66]. Their tensorial versions with linearized kinematics were considered in [67][68][69][70].In the proposed kinematically nonlinear theory the role of the order parameter is played by the metric ten-arXiv:1904.03429v2 [cond-mat.mtrl-sci]…”

mentioning

confidence: 99%

“…This general program can be viewed as far reaching generalization of the Frenkel-Kontorova-Peierls-Nabarro model accounting for energy periodicity along a single slip plane [55][56][57]. Scalar models with periodic energies, dealing with multiple slip planes, have been used before to describe dislocation cores [58][59][60], to simulate dislocation nucleation [61][62][63][64] and to capture intermittency of plastic flows [65,66]. Their tensorial versions with linearized kinematics were considered in [67][68][69][70].…”

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confidence: 99%

Landau-Type Theory of Planar Crystal Plasticity

et al. 2019

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We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group GL (3, Z). Quasi-static loading can be then handled by athermal dynamics, while lattice based discretization can play the role of regularization. As a proof of principle we study in this Letter dislocation nucleation in a homogeneously sheared 2D crystal and show that the global tensorial invariance of the elastic energy foments the development of complexity in the configuration of collectively nucleating defects. A crucial role in this process is played by the unstable higher symmetry crystallographic phases, traditionally thought to be unrelated to plastic flow in lower symmetry lattices.Crystal plasticity is the simplest among yield phenomena in solids [1], and yet it has been compared in complexity to fluid turbulence [2,3]. The intrinsic irregularity of plastic flow in crystals [4] is due to short and long range interaction of crystal defects (dislocations) [5] dragged by the applied loading through a rugged energy landscape [6][7][8]. Fundamental understanding of plastic flow in crystals is crucial for improving hardening properties of materials [9], extending their fatigue life [10], controlling their forming at sub-micron scales [11] and building new materials [12].Macroscopic crystal plasticity relies on a phenomenological continuum description of plastic deformation in terms of a finite number of order parameters representing amplitudes of pre-designed mechanisms. These mechanisms are coupled elastically and operate according to friction type dynamics [13][14][15][16][17]. The alternative microscopic approaches, relying instead on molecular dynamics [18][19][20][21][22][23][24][25], can handle only macroscopically insignificant time and length scales [26]. An intermediate discrete dislocation dynamics approach focuses on long range interaction of few dislocations, while their short range interaction is still treated phenomenologically [27][28][29]. Collective dynamics of many dislocations can be also described by the dislocation density field, however, rigorous coarse-graining in such strongly interacting system still remains a major challenge [30][31][32][33][34][35][36][37].A highly successful computational bridge between microscopic and macroscopic approaches is provided by the quasi-continuum finite element method which uses adaptive meshing and employs ab initio approaches to guide the constitutive response at different mesh scales [38][39][40][41][42]. Its drawbacks, however, are spurious effects due to matching of FEM representations at different scales and a high computational cost of reconstructing the constitutive response at the smallest scales [43].In this Letter we propose a synthetic approach dea-Figure 1. Schematic representation of a lattice invariant shear and the associated energy barriers along the simple shear loading path ∇y = 1 + α(e1 ⊗ e ⊥ 1 ). Alt...

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“…The corresponding scalar approaches [38,165,166] can be viewed as generalizations of the minimalistic 1D Frenkel-Kontorova model [167][168][169] for the 2D case when only one slip system is activated. Despite their simplicity such models have been successful in describing dislocation cores [170], in simulating dislocation nucleation [75,[171][172][173][174] and even in modeling of plastic intermittency [39,68]. The tensorial models with linearized kinematics were proposed in [175][176][177][178].…”

Section: Mesoscopic Tensorial Model (Mtm)mentioning

confidence: 99%

Discontinuous yielding of pristine micro-crystals

Salman¹,

Baggio²,

Bacroix³

et al. 2021

Comptes Rendus. Physique

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We study the mechanical response of a dislocation-free 2D crystal under homogenous shear using a new mesoscopic approach to crystal plasticity, a Landau-type theory, accounting for the global invariance of the energy in the space of strain tensors while operating with an infinite number of equivalent energy wells. The advantage of this approach is that it eliminates arbitrariness in dealing with topological transitions involved, for instance, in nucleation and annihilation of dislocations. We use discontinuous yielding of pristine micro-crystals as a benchmark problem for the new theory and show that the nature of the catastrophic instability, which in this setting inevitably follows the standard affine response, depends not only on lattice symmetry but also on the orientation of the crystal in the loading device. The ensuing dislocation avalanche involves cooperative dislocation nucleation, resulting in the formation of complex microstructures controlled by a nontrivial self-induced coupling between different plastic mechanisms.

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Dislocations in cubic crystals described by discrete models

Cited by 9 publications

References 25 publications

Dislocations in graphene

Dislocations in graphene

Landau-Type Theory of Planar Crystal Plasticity

Discontinuous yielding of pristine micro-crystals

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