An approximate equation of motion is proposed for screw and edge dislocations, which accounts for retardation and for relativistic effects in the subsonic range. Good quantitative agreement is found, in accelerated or in decelerated regimes, with numerical results of a more fundamental nature.
A new formulation for the equation of motion of interacting dislocations is derived. From this solution it is shown that additional coupling forces, of kinetic and inertial origin, should be considered in Dislocation Dynamics (DD) simulations at high strain rates. A heuristic modification of this general equation of motion enables one to introduce retardation into inertial and elastic forces, in accordance with a progressive rearrangement of fields through wave propagation. The influence of the corresponding coupling terms and retardation effects are then illustrated in the case of dislocation…
Dislocation pinning plays a vital role in the plastic behaviour of a crystalline solid. Here we report the first observation of the damped oscillations of a mobile dislocation after it gets pinned at an obstacle in the presence of a constant static shear load. These oscillations are found to be inertial, instead of forced as obtained in the studies of internal friction of solid. The rate of damping enables us to determine the effective mass of the dislocation. Nevertheless, the observed relation between the oscillation frequency and the link length is found to be anomalous, when compared with …
In this paper, we present a continuum model for the dynamics of low angle grain boundaries in two dimensions based on the motion of constituent dislocations of the grain boundaries. The continuum model consists of an equation for the motion of grain boundaries (i.e., motion of the constituent dislocations in the grain boundary normal direction) and equations for the dislocation structure evolution on the grain boundaries. This model is derived from the discrete dislocation dynamics model. The long-range elastic interaction between dislocations is included in the continuum model, which ensures …
We develop a continuum model for the dynamics of grain boundaries in three dimensions that incorporates the motion and reaction of the constituent dislocations. The continuum model is based on a simple representation of densities of curved dislocations on the grain boundary. Illposedness due to nonconvexity of the total energy is fixed by a numerical treatment based on a projection method that maintains the connectivity of the constituent dislocations. An efficient simulation method is developed, in which the critical but computationally expensive long-range interaction of dislocations is repl…
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.
A consistent, small scale description of plastic motion in a crystalline solid is presented based on a phase field description. By allowing for independent mass motion given by the phase field, and lattice distortion, the solid can remain in mechanical equilibrium on the timescale of plastic motion. Singular (incompatible) strains are determined by the phase field, to which smooth distortions are added to satisfy mechanical equilibrium. A numerical implementation of the model is presented, and used to study a benchmark problem: the motion of an edge dislocation dipole in a hexagonal lattice. T…
Linear complexions are defect phases that form in the presence of dislocations and thus are promising for the direct control of plasticity. In this study, atomistic simulations are used to model the effect of linear complexions on dislocation-based mechanisms for plasticity, demonstrating unique behaviors that differ from classical dislocation glide mechanisms. Linear complexions impart higher resistance to the initiation and continuation of dislocation motion when compared to solid solution strengthening in all of the face-centered cubic alloys investigated here, with the exact strengthening …
A number of recent Molecular Dynamics (MD) simulations have demonstrated that screw dislocations in face centered cubic (fcc) metals can achieve stable steady state motion above the lowest shear wave speed ($v_\text{shear}$) which is parallel to their direction of motion (often referred to as transonic motion). This is in direct contrast to classical continuum analyses which predict a divergence in the elastic energy of the host material at a crystal geometry dependent `critical' velocity $v_\text{crit}$. Within this work, we first demonstrate through analytic analyses that the elastic energy …
The aim of this paper is to provide new results and insights for a screw dislocation in functionally graded media within the gauge theory of dislocations. We present the equations of motion for dislocations in inhomogeneous media. We specify the equations of motion for a screw dislocation in a functionally graded material. The material properties are assumed to vary exponentially along the x and y-directions. In the present work we give the analytical gauge field theoretic solution to the problem of a screw dislocation in inhomogeneous media. Using the dislocation gauge approach, rigorous anal…
A novel implementation of the dislocation flux boundary condition in discrete dislocation dynamics is presented. The continuity of the individual dislocation loops in a periodic representative crystal volume (RVE) is enforced across the boundary of the RVE with the help of a dual topological description for representing dislocation line kinematics in two equivalent spaces representing the deforming crystal, the RVE and the unbounded crystal spaces. The former describes the motion of the dislocations in the simulated crystal RVE whereas the latter represents the motion of dislocations in an inf…
Isolated kinks on thermally fluctuating (1/2)<111> screw, <100> edge and (1/2)<111> edge dislocations in bcc iron are simulated under zero stress conditions using molecular dynamics (MD). Kinks are seen to perform stochastic motion in a potential landscape that depends on the dislocation character and geometry, and their motion provides fresh insight into the coupling of dislocations to a heat bath. The kink formation energy, migration barrier and friction parameter are deduced from the simulations. A discrete Frenkel-Kontorova-Langevin (FKL) model is able to reproduce the coarse grained data …
Building on ideas introduced by Eshelby in 1953, and on recent dynamical extensions of the Peierls model for screw and edge dislocations, an approximate equation of motion (EoM) to govern non-uniform dislocation motion under time-varying stress is derived, allowing for time variations of the core width. Non-local in time, it accounts for radiative visco-inertial effects and non-radiative drag. It is completely determined by energy functions computed at constant velocity. Various limits are examined, including that of vanishing core width. Known results are retrieved as particular cases. Notabl…
A three-dimensional continuum dislocation theory for single crystals containing curved dislocations is proposed. A set of governing equations and boundary conditions is derived for the true placement, plastic slips, and loop functions in equilibrium that minimize the free energy of crystal among all admissible functions, provided the resistance to the dislocation motion is negligible. For the non-vanishing resistance to dislocation motion the governing equations are derived from the variational equation that includes the dissipation function. A simplified theory for small strains is also provi…
Interactions among dislocations and solute atoms are the basis of several important processes in metals plasticity. In body-centered cubic (bcc) metals and alloys, low-temperature plastic flow is controlled by screw dislocation glide, which is known to take place by the nucleation and sideward relaxation of kink pairs across two consecutive \emph{Peierls} valleys. In alloys, dislocations and solutes affect each other's kinetics via long-range stress field coupling and short-range inelastic interactions. It is known that in certain substitutional bcc alloys a transition from solute softening to…
Quantum motion of atoms known as zero-point vibrations is recognized to be important at low temperatures in condensed matter systems comprised of light atoms or ions, affecting such properties and behaviors as proton-transfer reactions, vibrational spectra of water and ice, and mechanical properties of low temperature helium. Recently, quantum motion of atoms was proposed to explain a long-standing discrepancy between theoretically computed and experimentally measured low-temperature resistance (Peierls stress) to dislocation motion in iron and possibly other metals with high atomic masses. He…
The stress-driven motion of dislocations in crystalline solids, and thus the ensuing plastic deformation process, is greatly influenced by the presence or absence of various point-like defects such as precipitates or solute atoms. These defects act as obstacles for dislocation motion and hence affect the mechanical properties of the material. Here we combine molecular dynamics studies with three-dimensional discrete dislocation dynamics simulations in order to model the interaction between different kinds of precipitates and a $\frac{1}{2}\langle 1 1 1\rangle$ $\{1 1 0\}$ edge dislocation in B…
Dislocations in single-phase concentrated random alloys, including high- entropy alloys (HEAs), repeatedly encounter pinning during glide, resulting in jerky dislocation motion. While solute-dislocation interaction is well understood in conventional alloys, the origin of individual pinning points in concentrated random alloys is a matter of debate. In this work, we investigate the origin of dislocation pinning in the CoCrFeMnNi HEA. In- situ transmission electron microscopy studies reveal wavy dislocation lines and a jagged glide motion under external loading, even though no segregation or clu…
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…
Crystal plasticity is the result of the motion and interaction of dislocations. There is, however, still a major gap between microscopic and mesoscopic simulations and continuum crystal plasticity models. Only recently a higher dimensional dislocation density tensor was defined which overcomes some drawbacks of earlier dislocation density measures. The evolution equation for this tensor can be considered as a continuum version of dislocation dynamics. We use this evolution equation to develop evolution equations for the total dislocation density and an average curvature which together govern a…
A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy and show that it obeys the stress strain relation of linear elasticity. Dislocations in a two dimensional hexagonal lattice are shown to be composite topological defects in the amplitude expansion of the phase field, with topological charges given by the Burgers vector. This allows us to introduce a formal relation between dislocation velocity and the evolu…
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 …
Compression experiments on micron-scale specimens and acoustic emission (AE) measurements on bulk samples revealed that the dislocation motion resembles a stick-slip process - a series of unpredictable local strain bursts with a scale-free size distribution. Here we present a unique experimental set-up, which detects weak AE waves of dislocation slip during the compression of Zn micropillars. Profound correlation is observed between the energies of deformation events and the emitted AE signals that, as we conclude, are induced by the collective dissipative motion of dislocations. The AE data a…
The interaction between screw dislocations and oxygen interstitial atoms is studied with ab initio calculations in hexagonal close-packed titanium. Our calculations evidence a strong repulsion when the solute atoms are located in the dislocation glide plane, leading to spontaneous cross-slip, which allows the dislocation to bypass the atomic obstacle. This avoidance process explains several experimental observations in titanium in presence of oxygen: (1) a larger lattice friction against screw dislocation motion, (2) a reduction of the dislocation glide distance in prismatic planes and (3) an …
The present paper extends the thermodynamic dislocation theory initiated by Langer, Bouchbinder and Lookman [2010] to non-uniform finite plastic deformations. The equations of motion are derived from the variational equation involving the free energy density and the positive definite dissipation function. We also consider the simplified theory by neglecting the excess dislocations. For illustration, the problem of finite strain constrained shear of single crystals with one active slip system is solved within the proposed theory.
In this work we investigate the theory of dynamics of dislocations in quasicrystals. We consider three models: the elastodynamic model of wave type, the elasto-hydrodynamic model, and the elastodynamic model of wave-telegraph type. Similarities and differences between the three models are pointed out and discussed. Using the framework of linear incompatible elastodynamic theory, the equations of motion of dislocations are deduced for these three models. Especially, the equations of motion for the phonon and phason elastic distortion tensors and elastic velocity vectors are derived, where the s…
Thermally-activated $\small{\nicefrac{1}{2}}<111>$ screw dislocation motion is the controlling plastic mechanism at low temperatures in body-centered cubic (bcc) crystals. Motion proceeds by the nucleation and propagation of atomic-sized kink pairs susceptible of being studied using molecular dynamics (MD). However, MD's natural inability to properly sample thermally-activated processes as well as to capture $\{110\}$ screw dislocation glide calls for the development of other methods capable of overcoming these limitations. Here we develop a kinetic Monte Carlo (kMC) approach to study single s…
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…
A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in Ref. [48]. The model is based on the motion and reaction of the constituent dislocations of the grain boundaries. The long-range elastic interaction between dislocations is included in the continuum model, and it maintains a stable dislocation structure described by the Frank's formula for grain boundaries. In this paper, we develop a new continuum model for the coupling and sliding motions of grain boundaries that avoids the time-consum…
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 …
We introduce a phenomenological theory of dislocation motion appropriate for two dimensional lattices. A coarse grained description is proposed that involves as primitive variables local lattice rotation and Burgers vector densities along distinguished slip systems of the lattice. We then use symmetry considerations to propose phenomenological equations for both defect energies and their dissipative motion. As a consequence, the model includes explicit dependences on the local state of lattice orientation, and allows for differential defect mobilities along distinguished directions. Defect den…
The classical motion of gliding dislocation lines in slip planes of crystalline solid helium leads to plastic deformation even at temperatures far below the Debye temperature and can affect elastic properties. In this work we argue that the gliding of dislocations and plasticity may be the origin of many observed elastic anomalies in solid He-4, which have been argued to be connected to supersolidity. We present a dislocation motion model that describes the stress-strain $τ$-$ε$ curves and work hardening rate $dτ/dε$ of a shear experiment performed at constant strain rate $\dotε$ in solid heli…
Unlike the tensile mode, compressive deformation of a bcc metallic nanostructure is mediated by the glide of screw dislocation. Although the bcc screw dislocations are well known to possess unusual attributes, it is still unclear how these unique effects manifest in a nanoscale solid. In the present study, atomistic simulations render a close look at the dislocation activities underlying the compressive deformation of bcc iron nanopillars. It is found that instead of performing simple glide motion, the line defects exhibit a host of complex features. In this regard, the temperature is observed…
High-entropy alloys (HEAs) with concentrated solid solutions are conceived to possess a rugged atomic and energy landscape in which dislocation motion necessarily proceeds to accommodate mechanical deformation. Fundamental questions remain as to how rough the energy landscape is and to what extent it can be influenced by the local ordering of their constituent elements. Here, we construct and report the potential energy landscape (PEL) governing screw dislocation motion in refractory HEAs that reveals a hierarchical and multilevel structure with a collection of small basins nested in large met…
A theoretical framework is proposed to derive a dynamic equation motion for rectilinear dislocations within isotropic continuum elastodynamics. The theory relies on a recent dynamic extension of the Peierls-Nabarro equation, so as to account for core-width generalized stacking-fault energy effects. The degrees of freedom of the solution of the latter equation are reduced by means of the collective-variable method, well known in soliton theory, which we reformulate in a way suitable to the problem at hand. Through these means, two coupled governing equations for the dislocation position and cor…
Plasticity in hexagonal close-packed zirconium is controlled by screw dislocations which easily glide in the prismatic planes where they are dissociated. At high enough temperatures, these dislocations can deviate out of the prism planes to also glide in the first order pyramidal and basal planes. To get a better understanding of these secondary slip systems, we have performed molecular dynamics (MD) simulations of a screw dislocation gliding in a basal plane. The gliding dislocation remains dissociated in the prism plane where it performs a random motion and occasionally cross-slips out of it…
Dislocations are a central concept in materials science, which dictate the plastic deformation and damage evolution in materials. Layered materials such as graphite admit two general types of interlayer dislocations: basal and prismatic dislocations, of which prismatic dislocations have been relatively less studied. Using density functional theory (DFT) calculations, we have examined different prismatic core structures in graphite and evaluated their structure, energetics and mobility. We find close energetic interplay between bonded and "free-standing" core structures in both zigzag and armch…