The action functional for a linear elastic medium with dislocations is given. The equations of motion following from this action reproduce the Peach-Köhler and Lorentzian forces experienced by dislocations. The explicit expressions for singular and finite parts of the self-force acting on a curved dislocation are derived in the framework of linear theory of elasticity of an isotropic medium. The velocity of dislocation is assumed to be arbitrary but less than the shear wave velocity. The slow speed and near-sonic motions of a dislocation are investigated. In the near-sonic limit, the explicit expression for the leading contribution to the self-force is obtained. In the case of slowly moving dislocations, the effective equations of motion derived in the present paper reproduce the known results.
We investigate the nonuniform motion of a straight screw dislocation in infinite media in the framework of the translational gauge theory of dislocations. The equations of motion are derived for an arbitrary moving screw dislocation. The fields of the elastic velocity, elastic distortion, dislocation density and dislocation current surrounding the arbitrarily moving screw dislocation are derived explicitely in the form of integral representations. We calculate the radiation fields and the fields depending on the dislocation velocities.
In this paper we present the equations of motion of a moving screw dislocation in the framework of the translation gauge theory of dislocations. In the gauge field theoretical formulation, a dislocation is a massive gauge field. We calculate the gauge field theoretical solutions of a uniformly moving screw dislocation. We give the subsonic and supersonic solutions. Thus, supersonic dislocations are not forbidden from the field theoretical point of view. We show that the elastic divergences at the dislocation core are removed. We also discuss the Mach cones produced by supersonic screw dislocat…
A theoretical framework for dislocation dynamics in quasicrystals is provided according to the continuum theory of dislocations. Firstly, we present the fundamental theory for moving dislocations in quasicrystals giving the dislocation density tensors and introducing the dislocation current tensors for the phonon and phason fields, including the Bianchi identities. Next, we give the equations of motion for the incompatible elastodynamics as well as for the incompatible elasto-hydrodynamics of quasicrystals. We continue with the derivation of the balance law of pseudomomentum thereby obtaining …
Plastic deformation, at all strain rates, is accommodated by the collective motion of crystalline defects known as dislocations. Here, we extend an analysis for the energetic stability of a straight dislocation, the so-called line tension ($Γ$), to steady-state moving dislocations within elastically anisotropic media. Upon simplification to isotropy, our model reduces to an explicit analytical form yielding insight into the behavior of $Γ$ with increasing velocity. We find that at the first shear wave speed within an isotropic solid, the screw dislocation line tension diverges positively indic…
Although continuum theory has been widely used to describe the long-range elastic behavior of dislocations, it is limited in its ability to describe mechanical behaviors that occur near dislocation cores. This limit of the continuum theory mainly stems from the discrete nature of the core region, which induces a drag force on the dislocation core during glide. Depending on external conditions, different drag mechanisms are activated that govern the dynamics of dislocations in their own way. This is revealed by the resultant speed of the dislocation. In this work, we develop a theoretical frame…
In this work, Stroh's formalism is endowed with causal properties on the basis of an analysis of the radiation condition in the Green tensor of the elastodynamic wave equation. The modified formalism is applied to dislocations moving uniformly in an anisotropic medium. In practice, accounting for causality amounts to a simple analytic continuation procedure whereby to the dislocation velocity is added an infinitesimal positive imaginary part. This device allows for a straightforward computation of velocity-dependent field expressions that are valid whatever the dislocation velocity ---includin…
To allow for `relativistic'-like core contraction effects, an anisotropic regularization of steadily-moving straight dislocations of arbitrary orientation is introduced, with two scale parameters $a_\parallel$ and $a_\perp$ along the direction of motion and transverse to it, respectively. The dislocation core shape is an ellipse. When $a_\perp/a_\parallel\to 0$, the model reduces to the Peierls-Eshelby dislocation, the fields of which are non-differentiable on the slip plane. For finite $a_\parallel$ and $a_\perp$, fields are everywhere differentiable. Applying the author's so-called `causal' …
Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled by singularities at certain `critical' velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied s…
This work introduces original explicit solutions for the elastic fields radiated by non-uniformly moving, straight, screw or edge dislocations in an isotropic medium, in the form of time-integral representations in which acceleration-dependent contributions are explicitly separated out. These solutions are obtained by applying an isotropic regularization procedure to distributional expressions of the elastodynamic fields built on the Green tensor of the Navier equation. The obtained regularized field expressions are singularity-free, and depend on the dislocation density rather than on the pla…
We previously observed that an intrinsic staking fault shrunk through a glide of a Shockley partial dislocation terminating its lower end in a hard-sphere crystal under gravity coherently grown in <001> by Monte Carlo simulations [Mori et al., Molec. Phys. 105, 1377 (2007)]; it was an answer to a one-decade long standing question why the stacking disorder in colloidal crystals reduced under gravity [Zhu et al., Nature 387, 883 (1997)]. Here, we present an elastic energy calculation; in addition to the self-energy of the partial dislocation [Mori et al., Prog. Theor. Phys. Suppl. 178, 33 (2009)…
The purpose of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space-dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving dislocations. The retarded elastic fields produced by a distribution of dislocations and the retarded dislocation tensor potentials are determined. New fundamental key-formulae for the dynamics of dislocations are …
Dislocation dynamics in a dodecagonal quasiperiodic structure
我们已经开发了一套数值工具，用于准周期结构中缺陷动力学的定量分析。我们已经应用这些工具来研究Lifshitz和Petrich [Phys. Rev. Lett. 79（1997）1261]，其稳态解包括具有十二角对称性的准周期结构。任意的位错，参数化的同伦群的D-环面，注入作为初始条件，并定量地跟随方程的实时演变。我们发现，对于强扩散的位错攀移速度的结果是类似的十二边形和六边形的图案，但对于弱扩散的十二边形图案具有独特的钉扎的位错，反映其准周期性质。
Plastic deformation of crystals is a physical phenomenon, which has immensely driven the development of human civilisation since the onset of the Chalcolithic period. This process is primarily governed by the motion of line defects, called dislocations. Each dislocation traps a quantum of plastic deformation expressible in terms of its Burgers vector[1,2]. Theorising the mechanisms of dislocation motion at the atomistic scales of length and time remains a challenging task on account of the extreme complexities associated with the dynamics. We present a new concept of modelling a moving disloca…
The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion tensor are given; that is the generalized Burgers equation for arbitrary sources and the generalized Mura-Willis formula, …
Plasticity is governed by the evolution of, in general anisotropic, systems of dislocations. We seek to faithfully represent this evolution in terms of density-like variables which average over the discrete dislocation microstructure. Starting from T. Hochrainer's continuum theory of dislocations (CDD), we introduce a methodology based on the 'Maximum Information Entropy Principle' (MIEP) for deriving closed-form evolution equations for dislocation density measures of different order. These equations provide an optimum representation of the kinematic properties of systems of curved and connect…
We theoretically examine the validity of Matthiessen's rule caused by strong dislocation-dislocation interaction using a fully quantized dislocation field, where its degree of deviation is quantified at arbitrary electron energy, dislocation-electron and dislocation-dislocation distances and interaction strengths. Contrary to intuition, we show that the electron relaxation rate deviates from the Matthiessen's rule in an oscillatory way as a function of inter-dislocation distance, instead of monotonically. This study could serve as a computational tool to investigate the electronic behavior of …
We study the mechanics and statistical physics of dislocations interacting on cylinders, motivated by the elongation of rod-shaped bacterial cell walls and cylindrical assemblies of colloidal particles subject to external stresses. The interaction energy and forces between dislocations are solved analytically, and analyzed asymptotically. The results of continuum elastic theory agree well with numerical simulations on finite lattices even for relatively small systems. Isolated dislocations on a cylinder act like grain boundaries. With colloidal crystals in mind, we show that saddle points are …
Structural transitions are invariably affected by lattice distortions. If the body is to remain crack-free, the strain field cannot be arbitrary but has to satisfy the Saint-Venant compatibility constraint. Equivalently, an incompatibility constraint consistent with the actual dislocation network has to be satisfied in media with dislocations. This constraint can be incorporated into strain-based free energy functionals to study the influence of dislocations on phase stability. We provide a systematic analysis of this constraint in three dimensions and show how three incompatibility equations …
To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science.During the last two decades such a theory has been developed for the time evolution of a system of parallel edge dislocations. The evolution equations were derived by a systematic coarse-graining of the equations of motion of the individual dislocations and later retrieved from a functional of the dislocation densities and the stress potential by applying the standard formalism of phase field theories. It is, however, a long standing issue if a similar procedure can be es…
The exceptional combination of strength and ductility in multi-component alloys is often attributed to the interaction of dislocations with the various solute atoms in the alloy. To study these effects on the mechanical properties of such alloys there is a need to develop a modeling framework capable of quantifying the effect of these solutes on the evolution of dislocation networks. Large scale three-dimensional (3D) Discrete dislocation dynamics (DDD) simulations can provide access to such studies but to date no relevant approaches are available that aim for a complete representation of real…
A theory for conduction electron scattering by inhomogeneous crystal lattice strains is developed, based on the differential geometric treatment of deformations in solids. The resulting fully covariant Schrödinger equation shows that the electrons can be described as moving in a non-Euclidean background space in the continuum limit of the deformed lattice. Unlike previous work, the formalism is applicable to cases involving purely elastic strains as well as discrete and continuous distributions of dislocations --- in the latter two cases it clearly demarcates the effects of the dislocation str…
Detailed dynamics of a moving magnetic skyrmion lattice in MnSi observed using a small-angle neutron scattering under an alternating electric current flow
Uniqueness of solutions in the linear theory of non-singular dislocations, studied as a special case of plasticity theory, is examined. The status of the classical, singular Volterra dislocation problem as a limit of plasticity problems is illustrated by a specific example that clarifies the use of the plasticity formulation in the study of classical dislocation theory. Stationary, quasi-static, and dynamical problems for continuous dislocation distributions are investigated subject not only to standard boundary and initial conditions, but also to prescribed dislocation density. In particular,…
A canonical quantization procedure is applied to the interaction of elastic waves --phonons-- with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach-Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line, and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are poin…
We develop a non-singular theory of three-dimensional dislocation loops in a particular version of Mindlin's anisotropic gradient elasticity with up to six length scale parameters. The theory is systematically developed as a generalization of the classical anisotropic theory in the framework of linearized incompatible elasticity. The non-singular version of all key equations of anisotropic dislocation theory are derived as line integrals, including the Burgers displacement equation with isolated solid angle, the Peach-Koehler stress equation, the Mura-Willis equation for the elastic distortion…
A rectangular "shifting cloak", which visually shifts the cloaked object for a certain distance from the original place, is proposed. Comparing with the previously proposed similar cloaks, this rectangular shifting cloak has a much simpler structure, for it is constructed with only four blocks of homogeneous materials. The shifting distance can be arbitrarily tuned from zero to infinity in principle, thus the shifted image can be either in or out of the cloak. Various kinds of objects that have different sizes, shapes and constitutive parameters can be cloaked using the same device. Numerical …
