On the non-uniform motion of dislocations: the retarded elastic fields,the retarded dislocation tensor potentials and the Liénard–Wiechert tensor potentials

The topic 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 derived (Jefimenko type and Heaviside–Feynman type equations of dislocations). In addition, exact closed-form solutions of the elastic fields produced by a dislocation loop are calculated as retarded line integral expressions for subsonic motion. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocation loop are given explicitly in terms of the so-called three-dimensional elastodynamic Liénard–Wiechert tensor potentials. The two-dimensional elastodynamic Liénard–Wiechert tensor potentials and the near-field approximation of the elastic fields for straight dislocations are calculated. The singularities of the near-fields of accelerating screw and edge dislocations are determined.     

New method for in-situ observation of moving dislocations in KCl crystal using laser-light scattering

Abstract

The dislocations moving on slip planes in a KCl single crystal under an applied load were observed successfully by a 90° angle light scattering method using a high-power Ar-ion laser (2W for a wavelength of 514 nm). The photographs of stationary dislocations were taken by an scanning type optical microscope. The image of such dislocations was very sharp and uniform compared with that of grown-in dislocations. The dynamic behavior of moving dislocations was observed by an image intensifier to intensify the scattered light from dislocations. The motion of dislocations was jerkey under a constant load in almost all cases.     

Dislocation behaviour during anelastic strain recovery in zinc single crystals prestrained under basal glide

Anelastic strain recovery experiments of zinc single crystals strained under basal glide were performed as a function of the forest pyramidal dislocation density at room temperature. The instantaneous strain recovery of specimens unloaded after prestraining in compression is proportional to lγ_p^1.8 where l is the average spacing between forest dislocations and γ_p is the prestrain. It is suggested that the instantaneous strain recovery results from the back motion of basal dislocations which multiplied under prestraining. The basal dislocations move to back under the influence of the internal stress unless they are impeded by intersection with forest dislocations. The time dependent strain recovery was measured on all specimens in either the unloaded or partially unloaded states, which enabled the activation volume of the process to be determined. The time dependent strain recovery is explainable in terms of the thermally activated back motion of basal dislocations via cutting the forest dislocations.     

Dynamics of Martensitic Interfaces

The basic dynamic behavior of martensitic interfaces has been analyzed within the framework of lattice dislocation dynamics. Two limiting cases of the martensitic interface structure have been considered: (a) the case when the interface can be appropriately described in terms of an array of non-interacting (well-spaced) interfacial dislocations and; (b) the case when the interfacial dislocations are so closely spaced that the interface can be approximated by a continuous distribution of dislocations. In the first case, it was demonstrated that, after the inclusion of a chemical driving force in the equation of motion, the dynamics of lattice dislocations can be directly applied to analyze the interfacial dynamics. In the second case, on the other hand, while the lattice dislocation dynamics is still quite relevant, several parameters in the equation of motion have to be redefined to reflect the fact that the interface now acts as a planar defect. For both of the cases of interfacial dislocation structure, we have analyzed the two basic modes of interfacial motion: (a) the continuous mode in which the motion is controlled by various energy-dissipative processes (e.g., phonon and electron drag) and; (b) the discontinuous or jerky mode in which the motion is controlled by the thermal activation of the interface/obstacle interactions.     

扩展位错低频内耗的模型

本文提出面心立方合金中扩展位错引起低频内耗峰的一个模型,用来解释高浓度Cu-Al和Cu-Zn合金经过冷加工后在210K附近出现的弛豫型内耗峰(测量频率约为1Hz)。文中指出,扩展位错在外力作用下的运动,可以分解为相对运动(两个部分位错之间的相对位移)和整体运动(扩展位错中心的位移)。除了考虑两个部分位错之间交互作用引起的回复力和位错线张力引起的回复力以外,本文引入了邻近位错之间长程交互作用引起的回复力,并且论证了这种回复力只影响扩展位错的整体运动,但不影响其相对运动。扩展位错的相对运动和整体运动,分别导致相对运动内耗峰和整体运动内耗峰。二者峰温相近。实验上观察到的内耗峰是这两个内耗峰的叠加。本文模型的推论与实验结果相符。 关键词：     

Motion of dislocations through ensembles of forest dislocations and point obstacles upon the simultaneous action of static and cyclic loads

Methods of computer simulation developed for hcp crystals were used to analyze the motion of gliding dislocations through composite ensembles of points obstacles and vibrating forest dislocations. It is shown that the possibility for forest dislocations to suffer forced vibrations increases the transparency of a composite ensemble. It was established that as the amplitude of dislocation vibrations reaches a certain limit depending on the strength of point obstacles, such obstacles in a composite ensemble almost completely lose their ability to hinder the motion of gliding dislocations.     

On the elastic fields produced by non-uniformly moving dislocations: a revisit

We investigate the non-uniform motion of straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving screw dislocations, gliding edge and climbing edge dislocations. The exact closed-form solutions of the elastic fields are calculated. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocations are given explicitly in the form of integral representations free of non-integrable singularities. The elastic fields describe the response in the form of non-uniformly moving elastic waves caused by the motion of the dislocation.     

Elastic interaction between two parallel dislocations in non-parallel slip planes

The elastic interaction between two parallel dislocations which can glide in non-parallel slip planes is studied under the simplifying assumption that the dislocation glide velocity is proportional to stress. The motion of the two dislocations is represented by a motion of one reference point in a configuration plane. It is concluded that the contribution of the long-range elastic interaction between individual dislocations from different slip systems to work hardening is negligible, compared to the contribution from the formed attractive junctions. Especially, two parallel edge dislocations with mutually perpendicular Burgers vectors can co-exist in minimum energy positions, however, they can be separated by an arbitrarily small external stress.     

Investigation of the motion kinetics of screw dislocations in sodium chloride and potassium chloride crystals

The kinetics of the motion and the surmounting of detents by dislocations in sodium chloride and potassium chloride crystals is investigated herein. Special attention is paid to a comparative study of the mean free paths of the screw and edge dislocations. It is established that the mean free paths of the screw dislocations is somewhat less than for edge dislocations under identical test conditions. The kinetic curves obtained were processed within the frame-work of theoretical representations about the motion of dislocations in crystals containing detents of two kinds.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 17–21, September, 1973.     

In situ investigation of the effect of a magnetic field on the mobility of dislocations in deformed KCl:Ca single crystals

This paper presents the results of an experimental investigation into the mobility of edge dislocations in KCl:Ca single crystals and the effect of a static magnetic field of 0.3 T on the dislocation mobility. The experiments on the effect of a magnetic field on the dislocation mobility were carried out with the use of a high-resolution (1 ms) method that permits in situ measurements of the sample dipole moment induced by the motion of charged dislocations as the crystal is being deformed. It is found that the starting stress is reduced in a magnetic field and the activation volume for overcoming of point defects by the dislocations is increased. It is further found that the magnetic field increases the rate of motion of the dislocations at the initial stage of deformation (to the point of dislocation multiplication) but has no effect on the mobility in the multiplication stage. Fiz. Tverd. Tela (St. Petersburg) 39, 630–633 (April 1997)     

Hopping motion of nonisolated dislocations in KC1 crystals

An investigation was made of hopping of nonisolated dislocations in KC1 crystals. It was found that hopping of dislocations in bands was characterized by a correlation between the lengths of successive jumps, rest periods, and numbers of jumps. Irradiation with rays and quenching did not change these results, which was explained by the motion of dislocations together with their atmospheres.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 60–64, July, 1980.The authors are grateful to Prof. A. A. Predvoditelev for his valuable advice and help.     

Diffusive fluxes associated with interfacial defeet motion and interaction

The diffusional flux associated with the motion of interfacial defects is described by an equation expressed in terms of the topological parameters which characterise defects, namely their Burgers vectors and step heights, the defect velocity and the concentration of each atomic species in the two adjacent crystals. This expression demonstrates that glide/climb behaviour of grain boundary defects is analogous to motion of dislocations in single crystals; climb motion results if a component of b is perpendicular to the interface plane. However, the situation is more complex in the case of interphase interface defects, but the present approach, which considers the step and dislocation portions of defects separately, enables a straightforward analysis. Several examples are illustrated to show the various possibilities, such as climb motion even when b is parallel to the interface, and glide motion when b is not. The latter case arises in martensitic transformation where the existence of an invariant-plane-strain relation at the interface leads to equal and opposite fluxes to the step and dislocation portions of transformation defects so that overall the motion is diffusionless.Interfacial processes involve the motion and interaction of defects. The present analysis facilitates the consideration of diffusive fluxes associated with defect interaction since the step and dislocation portions can be treated independently. A general expression is derived for the total flux arising, and a particular case, the interaction of transformation dislocations with crystal dislocations which have reached the interface during lattice-invariant deformation in martensite formation, is considered.     

A note on the geometry of slip controlled by the Peierls mechanism

The macroscopic slip plane in solids with undissociated dislocations is determined as the average plane of motion of screw dislocations. It is assumed that their motion is controlled by thermally activated overcoming of the Peierls potential into different crystallographic planes. The screw dislocations have a unit motion or jump of one atomic distance and they are free to jump into a number of different positions. Under these circumstances cross slip jumps are frequent and the macroscopic slip plane for a given applied stress is determined by the Peierls potential in the different planes of cross slip. The geometry of slip in b.c.c. metals is discussed in some detail and it is shown that experimental results can be described formally using this approach.     

Specific features in the generation and motion of dislocations in silicon single crystals doped with nitrogen

The specific features in the generation and motion of dislocations are investigated in Si: N single crystals grown by the Czochralski method. The motion of dislocation loops is analyzed by the four-point bending technique in the temperature range 500–800°C. The dislocation loops are preliminarily introduced into the samples with the use of a Knoopp indenter at room temperature. It is found that doping with nitrogen leads to a considerable increase in the critical stress of the onset of dislocation motion from surface sources (indentations) and in the stress of the generation of dislocations from internal sources. The velocity of dislocation motion in Si: N crystals is less than that in undoped crystals (under comparable loads). The hardening effect of nitrogen is explained by the fact that nitrogen promotes the decomposition of a solid solution of oxygen in silicon during postcrystallization cooling.     

热应力作用降低LPE层中的位错

提出由温差造成热剪切应力,引起衬底穿线位错滑移,形成<110>界面位错,从而降低LPE层中位错的模型。稳定自然对流下的温度梯度液相外延,存在衬底厚度方向的温差,能在边缘固定的衬底中造成热剪切应力。生长了厚GaAs和Ga_1-xAl_xAs层(x<0.3),估算的热剪切应力大于产生<110>暗线缺陷的临界剪切应力。表面腐蚀坑观察表明,外延层位错密度下降,或无位错。界面蚀槽和阴极荧光观察表明,衬底穿线位错在界面弯曲成<110>界面位错。透射电子显微镜观察表明,界面位错多 关键词：     

Recovery mechanisms in nanostructured aluminium

Commercial purity aluminium (99.5%) has been cold rolled to a true strain of 5.5 (99.6% reduction in thickness). The material is very strong but low temperature recovery may be a limiting factor. This has been investigated by isothermal annealing treatments in the temperature range 5–100°C. Hardness tests, microstructural investigations by electron backscattered diffraction (EBSD) and transmission electron microscopy (TEM) were carried out to identify and characterise possible recovery mechanisms. Annihilation of zigzagged dislocations, positioned between deformation-induced lamellar boundaries of medium-to-high angles, and annihilation of dislocations in boundaries were found to be important recovery mechanisms, whereas other mechanisms, such as triple junction motion, subgrain coalescence, and boundary migration, were less important or negligible. The recovery kinetics was analysed based on hardness data, showing that the apparent activation energy for recovery at low temperatures was 60–86?kJ?mol^?1, consistent with thermally activated glide of jogged interior dislocations and the climb of dislocations in boundaries. These mechanisms are restricted by the presence of small intermetallic particles, which pin dislocations and boundaries and thereby raise the stability of the heavily deformed material.     

Emission of partial dislocations by grain boundaries in nanocrystalline metals

A theoretical model is proposed to describe the emission of partial dislocations by grain boundaries in nanocrystalline materials during plastic deformation. Partial dislocations are assumed to be emitted during the motion of grain-boundary disclinations, which are carriers of rotational plastic deformation. The ranges of the parameters of a defect structure in which the emission of partial dislocations by grain boundaries in nanocrystalline metals are energetically favorable are calculated. It is shown that, as the size of a grain decreases, the emission of partial dislocations by its boundary becomes more favorable as compared to the emission of perfect lattice dislocations.     

In-situ transmission electron microscopy observations and molecular dynamics simulations of dislocation-defect interactions in ion-irradiated copper

An in-situ transmission electron microscopy straining technique has been used to investigate the dynamics of dislocation-defect interactions in ion-irradiated copper and the subsequent formation of defect-free channels. Defect removal frequently required interaction with multiple dislocations, although screw dislocations were more efficient at annihilating defects than edge dislocations were. The defect pinning strength was determined from the dislocation curvature prior to breakaway and exhibited values ranging from 15 to 175 MPa. Pre-existing dislocations percolated through the defect field but did not show long-range motion, indicating that they are not responsible for creating the defect-free channels and have a limited contribution to the total plasticity. Defect-free channels were associated with the movement of many dislocations, which originated from grain boundaries or regions of high stress concentration such as at a crack tip. These experimental results are compared with atomistic simulations of the interaction of partial dislocations with defects in copper and a dispersed-barrier-hardening crystal plasticity model to correlate the observations to bulk mechanical properties.     

Supersonic dislocation stability and nano-twin formation at high strain rate

Improved understanding of the plastic deformation of metals during high-strain-rate shock loading is key to predicting their resulting material properties. This paper presents the results of molecular-dynamics simulations which address two fundamental questions related to materials deformation: the stability of supersonic dislocations and the mechanism of nano-twin formation. The results show that aluminium plastically deforms by the subsonic motion of edge dislocations when subjected to applied shear stresses of up to 600?MPa. Although higher applied stresses initially drive transonic dislocations, this motion is transient, and the dislocations decelerate to a sustained subsonic saturation velocity. Slowing of the transonic dislocation is controlled by the interaction with excited Rayleigh waves. 800?MPa marks a critical shear stress at which dislocation glide gives way to nano-twin formation via the homogeneous nucleation of Shockley partial dislocation dipoles. At still higher applied stresses, additional dislocation dipole nucleation produces a mid-stacking fault transformation of the twinned material.     

Edge stacking dislocations in two-dimensional bilayers with a small lattice mismatch

Incomplete stacking dislocations are predicted to form at edges of the shorter upper layer in two-dimensional hexagonal bilayers upon stretching the longer bottom layer. A concept of the edge Burgers vector is introduced to describe such dislocations by analogy with the Burgers vector of standard bulk dislocations. Analytical solutions for the structure and energy of edge stacking dislocations in bilayer graphene are obtained depending on the magnitude of elongation and angles between the edge Burgers vector, direction of elongation and edge. The barrier for penetration of stacking dislocations inside the bilayer is estimated. The possibilities to measure the barrier to relative motion of graphene layers and strain of graphene on a substrate by observation of edge stacking dislocations are discussed.