Physics. — Some considerations on the fields of stress connected with dislocations in a regular crystal lattice. I

Burgers, J. M.

doi:10.1007/978-94-011-0195-0_11

Cited by 62 publications

(61 citation statements)

References 3 publications

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“…T he central role of dislocations in determining the behavior of solid-state matter has been extensively investigated in materials sciences since the first formulation of the dislocation concept at the beginning of the twentieth century [1][2][3] and their experimental discovery 50 years later 4 . However, up until now, atomic-scale studies of creation, migration and annihilation of dislocations have been reserved for theory and atomistic simulations, as monitoring changes in the structure of materials with atomic resolution has been well beyond the spatial and temporal limits of experimental characterization techniques.…”

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confidence: 99%

Atomic scale study of the life cycle of a dislocation in graphene from birth to annihilation

et al. 2013

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Dislocations, one of the key entities in materials science, govern the properties of any crystalline material. Thus, understanding their life cycle, from creation to annihilation via motion and interaction with other dislocations, point defects and surfaces, is of fundamental importance. Unfortunately, atomic-scale investigations of dislocation evolution in a bulk object are well beyond the spatial and temporal resolution limits of current characterization techniques. Here we overcome the experimental limits by investigating the two-dimensional graphene in an aberration-corrected transmission electron microscope, exploiting the impinging energetic electrons both to image and stimulate atomic-scale morphological changes in the material. The resulting transformations are followed in situ, atom-by-atom, showing the full life cycle of a dislocation from birth to annihilation. Our experiments, combined with atomistic simulations, reveal the evolution of dislocations in two-dimensional systems to be governed by markedly long-ranging out-of-plane buckling.

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confidence: 99%

Atomic scale study of the life cycle of a dislocation in graphene from birth to annihilation

et al. 2013

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“…where u 0 i , v 0 i and w 0 i are the components of the incomplete displacements of the ith angular dislocation and ϕ TD is the Burgers function (Burgers 1939) that corresponds to the TD. We elaborate on the calculation of ϕ TD in Section 2.3.…”

Section: The Implementation Proceduresmentioning

confidence: 99%

Triangular dislocation: an analytical, artefact-free solution

Nikkhoo

Walter

2015

Geophysical Journal International

108

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S U M M A R YDisplacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space R 3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.Key words: Geomechanics; Kinematics of crustal and mantle deformation. I N T RO D U C T I O NCrustal deformations associated with earthquakes, volcanoes, landslides and human activities can be observed at a high level of detail using modern geodetic techniques, including synthetic aperture radar interferometry (InSAR) and GPS (Segall 1997;Bürgmann et al. 2000). These deformation data are often analysed using modelling techniques that are typically very computationally intense. The primary objective of such modelling is to understand the underlying processes through indirect imaging of the so-called sources, such as seismogenic faults, magma chambers and other reservoirs. The position and geometry of these sources, as well as the slip or the forces acting on them, are typically regarded as the source parameters. The source parameters, in other words, the outputs of the implemented modelling, are relevant to earthquake aftershock studies, the assessment of volcanic eruption precursors, tsunami modelling and many other applications (Feigl et al. 2002).The majority of methods that are applied for crustal deformation modelling are based on the theory of elasticity in general and the concept of dislocations in particular (Segall 2010). Elastic dislocation theory concerns the state of deformations in a strained solid body that is subject to the action of a dislocation embedded inside it (Love 1944). The Volterra model (Volterra 1907) describes a dislocation as a surface of displacement discontinuity with a uniform distribution of the slip throughout. The edges of the Volterra dislocation, also known as ...

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“…the characteristic lengths of the meso-and macro-scale are well separated. 4 The term Bravais strain aims at not considering a-priori that it consists of a purely elastic quantity. In fact, the Bravais strain is the homogenized strain but is not the complete macroscopic strain.…”

Section: Definition 6 (Macroscopic Measures) the Macroscopic Strain mentioning

confidence: 99%

“…The theory of dislocations is an old topic going back to the pioneer work of Volterra [39]. Crucial steps have later been provided by Burgers [4], Eshelby, Frank, and Nabarro [11], among others (cf. survey results in, e.g., [28]).…”

Section: Introductionmentioning

confidence: 99%

A multiscale model for dislocations: From mesoscopic elasticity to macroscopic plasticity

Goethem

2012

Z Angew Math Mech

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A multiscale model for dislocations in single crystals is proposed. The aim of this paper is to provide homogenization of dislocations from the meso-to the macro-scale. In particular we prove a new formula relating macroscopic strain incompatibility and dislocation density. Moreover, it is shown that plasticity is recovered from homogenization of purely elastic mesoscopic crystals with dislocations, where the appropriate functional space of Special functions of Bounded Deformation appears as a natural choice. Nonstandard defect and deformation internal variables and their evolution in time appear while novel differential relations are sketched in the non-Riemannian crystal with a thermodynamical model as based on those results.

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Physics. — Some considerations on the fields of stress connected with dislocations in a regular crystal lattice. I

Cited by 62 publications

References 3 publications

Atomic scale study of the life cycle of a dislocation in graphene from birth to annihilation

Atomic scale study of the life cycle of a dislocation in graphene from birth to annihilation

Triangular dislocation: an analytical, artefact-free solution

A multiscale model for dislocations: From mesoscopic elasticity to macroscopic plasticity

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