Effect of screening of the elastic field of the disclination located at the interface of two half-spaces by a dislocation ensemble

The self-consisted dynamics of a dislocation ensemble in the elastic field of the disclination located at the interface of two half-spaces has been considered for two cases, namely, for half-spaces with different densities of mobile dislocations and for a bicrystal where dislocations are absent in one half-space. The elastic energy W of the disclination screened by the dislocation ensemble has been calculated for the rectangular zone centered relative to the disclination. It has been shown that W increases as ～ $\sqrt R $ (R is the transverse size of the zone in the plastically deformed half-space).     

Specific features of low-temperature phonon scattering in materials with tilted disclination loops

Phonon scattering by static stress fields of circular wedge disclination loops is investigated in the framework of the deformation potential approach. Numerical calculations of the mean free path l and thermal conductivity κ demonstrate that the temperature dependence of κ exhibits a minimum at a certain temperature T* in the low-temperature range. The thermal conductivity κ sharply increases as T ^?3 with a decrease in temperature (T<T*) and exhibits a dislocation behavior (κ ～ T ²) with an increase in temperature (T>T*). The results obtained for the wedge disclination loop are compared with the available data for uniaxial disclination dipoles. It is shown that the properties of uniaxial disclination dipoles serving as sources of phonon scattering are similar to those of wedge disclination loops.     

On the annealing of junction disclinations in deformed polycrystals

The kinetics of relaxation of disclination quadrupoles formed within triple junctions of grains during plastic deformation are studied. The calculations are made using the discrete dislocation model for disclinations by simulating the climb of dislocations. Exponential relationships are obtained for the relaxation of the strength and elastic energy of disclination quadrupoles with a characteristic time proportional to the cube of grain size. The distribution of vacancy fluxes along grain boundaries (GBs) during the relaxation of a disclination quadrupole is studied in detail. The relation between continuum and discrete dislocation approaches to a study of the GB recovery process is considered. Characteristics of each relaxation stage are studied. A hierarchy of characteristic relaxation times for dimerent grain size ranges is constructed and it is show that in nanocrystalline materials the spreading time of trapped lattice dislocations can depend on the grain size.     

Continuous description of a grain boundary in forsterite from atomic scale simulations: the role of disclinations

We present continuous modelling at inter-atomic scale of a high-angle symmetric tilt boundary in forsterite. The model is grounded in periodic arrays of dislocation and disclination dipoles built on information gathered from discrete atomistic configurations generated by molecular dynamics simulations. The displacement, distortion (strain and rotation), curvature, dislocation and disclination density fields are determined in the boundary area using finite difference and interpolation techniques between atomic sites. The distortion fields of the O, Si and Mg sub-lattices are detailed to compare their roles in the accommodation of lattice incompatibility along the boundary. It is shown that the strain and curvature fields associated with the dislocation and disclination fields in the ‘skeleton’ O and Si sub-lattices accommodate the tilt incompatibility, whereas the elastic strain and rotation fields of the Mg sub-lattice are essentially compatible and induce stresses balancing the incompatibility stresses in the overall equilibrium.     

Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional,anisotropic, elastic,and piezoelectric media. II. Infinite straight dislocation and Frank disclination

The fields of stress and electric displacement caused by infinitely extended straight dislocations and Frank disclinations are deduced from the author's statements for the fields caused by a continuous distribution of dislocations and disclinations (S. Minagawa, Phil. Mag. 84 2229 (2004)). The multiple integrals in the original statements are converted into functions of space coordinates. Cauchy's theorem plays an important part. The improper integral that appears in computations of the fields around a Frank disclination is interpreted as its finite part by Hadamard. Examples are the fields around an infinite straight defect in caesium copper chloride, as well as those in gallium arsenide. The contours and zero lines are plotted to illustrate the fields caused by a dislocation and a disclination dipole.     

Effects of self-consistent dynamics of dislocations in the elastic field of a planar mesodefect

The self-consistent dynamics of a dislocation ensemble in an elastic field of a planar mesodefect has been considered within the kinetic approach. The effective Airy stress function for a planar mesodefect, which takes into account the screening effect of a system of distributed dislocation charges, has been obtained. Coordinate dependences of the stress tensor components and the dislocation charge density for the considered screened system have been found. Its elastic energy and misorientation of the regions adjacent to the planar mesodefect have been calculated.     

Effect of cooperative nanograin boundary sliding and migration on dislocation emission from a blunt nanocrack tip in nanocrystalline materials

Theoretical model is suggested that describes the effects of the cooperative nanograin boundary sliding and stress-driven nanograin boundary migration (CNGBSM) process on the lattice dislocation emission from an elliptically blunt nanocrack tip in deformed nanocrystalline materials. Within the model, CNGBSM deformation near the tip of growing nanocrack carries plastic flow, produces two dipoles of disclination defects and creates high local stresses in nanocrystalline materials. By using the complex variable method, the complex form expression of dislocation force is derived, and critical stress intensity factors for the first lattice dislocation emission are obtained under mode I and mode II loading conditions, respectively. The combined effects of the geometric features and strengths of CNGBSM deformation, nanocrack blunting and length on critical SIFs for dislocation emission depend upon nanograin size and material parameters in a typical situation where nanocrack blunting and growth processes are controlled by dislocation emission from nanocrack tips. It is theoretically shown that the cooperative CNGBSM deformation and nanocrack blunting have great influence on dislocation emission from blunt nanocrack tip.     

Electron on a cylinder with topological defects in a homogeneous magnetic field

In this work we study the effects of the geometry and topology of a cylinder on the energy levels of an electron moving in a homogeneous magnetic field. We consider the existence of topological defects as a screw dislocation and a disclination. When we take the region of movement as the full cylindrical surface, we find that, by increasing the strength of the screw dislocation, the dispersion on the electronic energy levels is affected and monotonically increasing. For an electron moving in an almost flat region we show that the dispersion on the Landau levels decrease monotonically as we increase the strength of the screw dislocation. The lowest Landau level can reach a zero value, leaving the energy of the system solely given by the geometry of the cylinder, which does not depend on the magnetic field. In both situations, as we change the deficit angle of the disclination, we observe that the energy levels are shifted and the magnitude of such shift depends on the magnetic field. The Landau levels for a flat sample are recovered in the limit of an infinite cylinder radius.     

Elastic behaviour of a wedge disclination dipole near a sharp crack emanating from a semi-elliptical blunt crack

The interaction between a wedge disclination dipole and a crack emanating from a semi-elliptic hole is investigated. Utilising the complex variable method, the closed form solutions are derived for complex potentials and stress fields. The stress intensity factor at the tip of the crack and the image force acting on the disclination dipole center are also calculated. The influence of the morphology of the blunt crack and the position of the disclination dipole on the shielding effect to the crack and the image force is examined in detail. The results indicate that the shielding or anti-shielding effect to the stress intensity factor increases when the wedge disclination dipole approaches the tip of the crack. The effects of the morphology of the blunt crack on the stress intensity factor of the crack and the image force are very significant.     

Simulation of the dynamics of a two-dimensional dislocation-disclination ensemble

A computer code for simulating the dynamics of an arbitrary 2D dislocation-disclination ensemble is developed. The code is constructed according to the molecular-dynamics principles; individual interacting particles are taken to be edge dislocations and dipoles of partial wedge disclinations. Pure copper is considered as an example for simulating the glide of one dislocation near an immobile dipole for various orientations of the dipole and under various initial conditions of the problem. The dislocation dynamics is shown to be mainly determined by the distribution of the elastic field of the disclination dipole rather than by the initial velocity of the dislocation.     

A disclination model for twinning and de-twinning of nanotwinned copper

The twinning and de-twinning processes within grains of nanotwinned copper (nt-Cu) are schematically demonstrated using the concept of wedge disclination quadrupoles. The stable twin nucleus size and the equilibrium equation of the applied shear stress and twin width during twin growth are obtained. The dependence of the critical resolved shear stress for twinning on the grain size, which conforms to the classic Hall–Petch relationship, is theoretically modelled. Additionally, the disclination quadrupole model for de-twinning is used to interpret the strength softening in nt-Cu. Relative to the classic kinetic and energetic models, this novel approach is more compatible with the experiments.     

Anchoring screening of defects interaction in a nematic liquid crystal

The relaxation dynamic of a dipole of +1/2 and -1/2 parallel disclination lines in a confined geometry is measured. The confinement and the planar anchoring conditions force the disclinations to be normal to the glass plates. In a first asymptotic regime, the direct elastic interaction between disclination is completely screened out by the anchoring energy. In a second regime, corresponding to the final annihilation steps, the dynamic follows the square-root law predicted by de Gennes for two isolated and parallel disclinations. The annihilation dynamic, in the asymptotic regime, is in good agreement with an elastic model based on an electrostatic analogy.     

Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional,anisotropic, elastic and piezoelectric media: elliptical Frank disclination

A statement is made on the theory of continuous distributions of dislocations and disclinations in anisotropic elastopiezoelectric media. The basic field equations governing the fields of stress functions, electric vector potential and incompatibility are presented and solved to give the fields of stress and electric displacement caused by a distribution of dislocations and disclinations. They are expressed in terms of the dislocation- and disclination-density tensors by means of the convolution integrals, extended throughout the medium, and the Fourier integrals. To treat the fields around discrete defects, that is dislocation and/or Frank disclination, the convolution integrals are replaced by the line integrals belonging to the loop of the defect. The fields of stress and electric displacement are given in terms of three quadruple integrals, which are converted into single integrals of explicitly given functions, in the case where the loop of the defect is elliptical. Numerical computations are carried out to estimate the fields in gallium arsenide. The values of those fields at a certain point of the body are presented. The contours and zero lines of the fields of dilatational stress and electric displacement in the plane placed parallel to and at a certain distance from the loop are illustrated.     

Dislocation and disclination loops in the virtual-defect method

A method of virtual circular defect loops is developed for determining the elastic fields produced by defects in a bounded medium in the case of an axially symmetric geometry. In this method, continuously distributed virtual circular Volterra and Somigliana dislocation loops are adjusted in such a way as to satisfy the boundary conditions imposed at free surfaces and interfaces. Original calculations of the elastic fields of circular defect loops of different types are carried out. The elastic fields are found for the case of straight dislocations and disclinations in a plate that are perpendicular to the plate plane and for the case of circular disclination loops parallel to the plate plane or to an interface.     

Physics of megaplastic (Severe) deformation in solids

The main regularities of structural and phase transformations occurring in solids have been analyzed experimentally and theoretically within the framework of the concept of manifestation of additional channels providing the dissipation of an elastic energy introduced into a solid under megaplastic deformation. It has been demonstrated that an active participation of low-temperature dynamical recrystallization processes, phase transitions of the type crystal ai amorphous state, and thermal effects under the conditions of an insufficient efficiency of the dislocation and disclination relaxation modes can consistently explain almost all the experimental results obtained for very severe plastic deformations.     

Microstructure of Mo – 47% Re – 0.4% Zr alloys after rolling at room temperature. I. Anisotropy of microband structure and peculiarities of internal structure of microbands

The results of an electron microscopy investigation of microstructure of a Mo – 47% Re – 0.4% Zr alloy after rolling deformation (ε ≈ 90%) at room temperature are presented. A special focus is made on investigation of anisotropy of microband nanostructured states and high-energy defect substructures with high values of the crystal lattice curvature, dislocation density and local internal stresses. A disclination mechanism of reorientation as a mechanism of fragmentation of the internal microband structure is proposed.     

Melting transition of a network model in two dimensions

The freezing transition of a network model for tensionless membranes confined to two dimensions is investigated by Monte Carlo simulations and scaling arguments. In this model, a freezing transition is induced by reducing the tether length. Translational and bond-orientational order parameters and elastic constants are determined as a function of the tether length. A finite-size scaling analysis is used to show that the crystal melts via successive dislocation and disclination unbinding transitions, in qualitative agreement with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. The hexatic phase is found to be stable over only a very small interval of tether lengths. Received 4 June 1999 and Revised in final form 1 September 1999