Disclination Dipole Research Articles

Special strain hardening mechanism and nanocrack generation in nanocrystalline materials

A special mechanism of strain hardening in deformed nanocrystalline materials (NCMs) is suggested and theoretically described. The mechanism represents generation of disclination dipoles at grain boundaries (GBs) due to GB sliding. It is shown that special strain hardening can effectively suppress plastic flow instability in metallic and ceramic NCMs and thus enhance their ductility. At the same time, the disclination dipoles formed due to GB sliding serve as dangerous stress sources that can induce nucleation of nanocracks, decreasing ductility of NCMs.

Inclusions in Chiral and Non-Chiral Smectic C Free-Standing Films

Director distributions around small inclusions in chiral (Sm C*) and non-chiral (Sm C) smectic C free standing films are approximately analytically determined. These director distributions are equivalent to disclination configurations. Disclination models describing small inclusions can be also generalized to model greater inclusions. In Sm C films greater inclusions can be represented by (+1)-wedge disclination in its centre and two accompanying (−1/2)-wedge disclinations on its surface. Both (−1/2)-disclinations stay on inclusion surface because the anchoring energy is not enough high to expel them. Growing inclusions in Sm C* films can be approximately described by disclination dipole with (+1)-wedge disclination in the inclusion centre and (−1)-wedge disclination inside inclusion approaching the surface. When an inclusion is large enough that (−1)-disclination reaches the surface, it is usually expulsed from the surface to film bulk. The presence of disclination on the surface leads to the perturbation of the radial director anchoring and creation of local electric charge on the inclusion surface namely in Sm C* films with relatively high spontaneous polarisation. The disclination expulsion is then connected with the elimination of the surface electric charge.

Residual resistivity due to wedge disclination dipoles in metals with rotational plasticity

The residual resistivity $\rho $ in metals caused by wedge disclination dipoles is studied in the framework of the Drude formula. It is shown that $\rho\sim L^{-p}$ with $p=3$ for biaxial and $p=2$ for uniaxial dipoles ($L$ is a size of dipole arm)

Elastic interaction between wedge disclination dipole and internal crack

The system of a wedge disclination dipole interacting with an internal crack was investigated. By using the complex variable method, the closed form solutions of complex potentials to this problem were presented. The analytic formulae of the physics variables, such as stress intensity factors at the tips of the crack produced by the wedge disclination dipole and the image force acting on disclination dipole center were obtained. The influence of the orientation, the dipole arm and the location of the disclination dipole on the stress intensity factors was discussed in detail. Furthermore, the equilibrium position of the wedge disclination dipole was also examined. It is shown that the shielding or antishielding effect of the wedge disclination to the stress intensity factors is significant when the disclination dipole moves to the crack tips.

Between microscopic and mesoscopic descriptions of twin–twin interaction

On a microscopic scale, deformation twinning is carried by the motion of twinning disconnections. A disconnection is an interfacial line defect characterized by a Burgers vector, a line vector, and a step vector. The Burgers vector (dislocation component of the disconnection) carries the deformation while the step vector (ledge component) carries the transformation from one twin variant to the other. On a mesoscopic scale, the deformation produced by twinning is a simple shear. A moving disclination dipole provides a mesoscopic model accounting for the twinning shear. Twin-twin interaction processes including the intersection of twins, the formation of structured twins, and the nucleation of cracks, may feature very complex mechanisms when analyzed on a microscopic scale. It turns out, however, that these mechanisms are controlled by the properties of large disconnection groups containing up to 10000 disconnections and more. These properties are sufficiently well approximated in the disclination dipole model. The disclination model for twin-twin interaction predicts orientation and volume fractions of secondary twins. The model also predicts the nucleation of cracks and crack growth. The disclination model was used to analyze the ductile-to-brittle transition of austenitic steel deformed at low temperature. The mesoscopic disclination model for twinning is successful because it accounts for the properties and mechanisms of disconnection groups.

Interaction of a wedge disclination dipole with interfacial cracks

The elastic interaction between a wedge disclination dipole and collinear interfacial cracks in bimaterials is investigated. The general solutions of complex potentials to this problem are presented by using complex potential theory. As illustrative examples, the closed-form solutions for a wedge disclination dipole interacting with a finite interfacial crack and a semi-infinite interfacial crack are obtained. The stress intensity factors at the tips of the crack and the force acting on the disclination dipole center are also given. The shield and anti-shield effect of the wedge disclination dipole upon the stress intensity factors is evaluated, and the equilibrium position of the disclination dipole is discussed for various crack geometries and material mismatch. The results indicate that the shielding or anti-shielding effect to the stress intensity factors increases acutely when the disclination dipole approaches the tip of the crack. If the center of the dipole is fixed, there always exists a critical value of angle of the dipole arm which the shielding or anti-shielding effect to the stress intensity factor is maximal. In addition, the length of the dipole arm and the material mismatch have significant influence on the stress intensity factors. The results also show that the interfacial crack always attracts the wedge disclination dipole and an equilibrium position of the disclination dipole may be available near the interface, which differs from the case of a perfect bonded interface, when the dipole approaches the surface of the crack from infinity. The present solutions contain a series of new and previously known results which can be shown to be special cases.

A wedge disclination dipole interacting with a circular inclusion

AbstractThe problem involving the interaction effects between a wedge disclination dipole and an elastic circular inclusion is investigated. Utilizing the Muskhelishvili complex variable method, the closed form solutions are derived for complex potentials and stress fields due to a wedge disclination dipole located near the circular inclusion. The strain energy and the force acting on the disclination dipole center are also calculated. The influence of the orientation and the location of the disclination dipole as well as the material elastic dissimilarity upon the equilibrium position of the disclination dipole is discussed in detail. The results show that for certain combinations of materials constants, the disclination dipole has a stable equilibrium point near the inclusion. Moreover, the force on the disclination dipole is very much affected by the orientation of the disclination dipole. The present solutions contain previously known results as the special cases. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Disclinations as a source of thermal resistance in icosahedral i-AlPdMn quasicrystals

We propose a model to analyse the experimental data for thermal conductivity ofsingle-grain i-AlPdMn quasicrystals. The interpretation is based on the picture in whichdisclination pairs of wedge type are the main source of phonon scattering at lowtemperatures. The scattering of phonons due to strain fields of these dipoles isconsidered. Our numerical calculations show that experimentally observed thermalconductivity in a wide temperature range can be well fitted by a combinationof wedge disclination dipole scattering and quasi-umklapp scattering processes.

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.

Nucleation of dislocations from [0 0 1] bicrystal interfaces in aluminum

It is well established from molecular dynamics simulations that grain boundaries in nanocrystalline samples serve as sources of dislocations. In this work, we use molecular dynamics simulations to study the mechanisms associated with dislocation nucleation from bicrystal [0 0 1] interfaces in aluminum. Three interface misorientations are studied, including the Σ5 (3 1 0) boundary, which has a high density of coincident atomic sites. Molecular dynamics simulations show that full dislocation loops are nucleated from each interface during uniaxial tension. After the second partial dislocation is emitted, a ledge remains within the interface at the intersection of the slip plane and the bicrystal boundary. A disclination dipole model is proposed for the structure of the distorted interface accounting for local lattice rotations and the ledge at the nucleation site.

Exact Solutions for Periodic Interfacial Wedge Disclination Dipoles in a Hexagonal Bicrystal

In this paper, exact closed-form solutions for the elastic stress and strain energy density of an infinite, periodic array of interfacial wedge disclination dipoles in a hexagonal bicrystal with arbitrary in-plane c-axis orientations are derived by the method of image dislocations. These solutions are shown to be of the form of the logarithm of hyperbolic and trigonometric functions of complex parameters. The strain energy of the dipole array is also calculated by numerical integration of the density field. The results show that the stress, strain energy density and strain energy all depend significantly on the orientational and material inhomogeneities, and the importance of using an anisotropic bicrystal model over a homogeneous model for calculations is emphasized. For bicrystals with symmetric c-axis orientations, it is also shown that the strain energy of the dipole array can be a strong function of the orientations, with the maximum and minimum at specific orientations that depend on the bicrystal materials.

Misorientation dependence of the energy of symmetrical tilt boundaries in hcp metals: prediction by the disclination-structural unit model

The misorientation dependence of the energy of grain boundaries in hcp metals is predicted by application of the disclination-structural unit model and continuum solutions for interfacial disclination dipoles in elastically anisotropic and inhomogeneous bicrystals. For symmetrical tilt boundaries in cobalt and titanium, it is shown that the dipole stress field and the grain-boundary energy depend strongly on the misorientation. In particular, the dipole stress field is more localized in large-angle boundaries than in small-angle boundaries, severe distortion of the stress field results from even a small inhomogeneity, and homogeneous isotropic solutions fail to capture the dependence of the stress field on misorientation. The energy–misorientation curve is characterized by cusps associated with favoured boundaries, local energy maxima between the cusps, and regions of high and low average energies demarcated by the favoured boundary. The maximum energy occurs near the misorientation of 23° corresponding to the () plane. The grain-boundary energy of cobalt is approximately twice that of titanium for most misorientations.

An Analysis of Lattice Strain due to Disclination Dipole Walls in Fe-Pd Martensite

The martensite structure in Fe–Pd is shown to possess disclination dipole walls, which induce a locally fluctuating residual stress field. In a polycrystal, the residual stress averaged over each (former austenite) grain vanishes, since the average t

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.

Mechanics and physics of disclinations in solids

An overview of recent achievements of the disclination approach in mechanics and physics of solids is given and the use of disclination modeling in materials science is demonstrated. Disclinations are defined as linear defects in solids, which manifest themselves as the sources of characteristic singularities in the fields of displacement and rotation. Necessary terminilogy and designations: Volterra dislocations, Frank (rotation) vector of a disclination, wedge and twist disclinations, are provided and discussed. The properties of screened disclination configurations (loops, dipoles, defects in small particles, etc.) with relatively small energies are considered. The methods and results of calculation of elastic energies for screened disclinations (for example, near a free surface) are presented. On the basis of properties of screened disclinations a series of models for the processes in the structure of plastically deformed materials is developed. The bands with misorientated crystal lattice in metals and other materials are described as a result of partial wedge disclination dipole motion. Disclination models are applied to the analysis of workhardening at large strains and to the theory of grain boundaries and their junctions in polycrystals. Disclination models for the structure and properties of nanostructured materials and nanoparticles are also delivered. Finally, the role of disclinations in relaxation of elastic stresses in epitaxial thin films is highlighted.

Importance of Disclinations in Severe Plastically Deformed Materials

AbstractA short overview of recent achievements in disclination approach application to severe plastically deformed materials is given. Necessary definitions and designations: Volterra rotational and translational dislocations, disclination Frank (rotation) vector, wedge and twist disclinations, are introduced and explained. The properties of screened disclination configurations (loops, dipoles, defects in small particles etc.) with relatively small energies are considered. Disclination models for the processes in the structure of plastically deformed materials are reviewed. The bands with misorientated crystal lattice in metals and other materials are described as a result of partial wedge disclination dipole motion. The disclination approach is applied to the description of workhardening at large strains and to the analysis of grain boundaries and their junctions in conventional polycrystals and nanocrystals.

High-resolution TEM Analysis of Defect Structures in Mechanically Milled, Nanocrystalline Fe

Grain interior and grain-boundary structures of mechanically milled ultrafine-grained iron powder were investigated with atomic resolution using high-resolution transmission electron microscopy (HRTEM). Grain boundaries in the powder appear wavy and irregular, with no amorphous or other unusual defect structures present. Diffraction analysis of HRTEM images indicates that elongated grains approximately 100 nm long and 20 nm wide consist of several sub-grains along their length, each rotated by several degrees around a common ‹110› axis. The presence of partial disclination dipoles in the sub-grains was also observed by HRTEM. Such structures indicate that shear, fragmentation and rotation of grains several to tens of nanometers in diameter occurs during severe plastic deformation. A mechanism for the formation of an ultrafine-grained structure in mechanically milled Fe involving partial disclinations is proposed.

Disclinations and rotational deformation in fine-grained materials

A theoretical model is presented which describes a new mechanism of plastic deformation in fine-grained materials. In the framework of the model, rotational deformation occurs via motion of dipoles of grain-boundary disclinations and is associated with the emission of lattice dislocations from grain boundaries into adjacent grain interiors. Ranges of defect system parameters are identified in which the disclination motion is energetically favourable. It is shown that the mechanism can contribute to plastic flow in fine-grained materials prepared by highly non-equilibrium methods such as ball milling, severe deformation and high-pressure compaction.

Thermal transport in materials with disclination dipoles and disclinationloops

The problem of phonon scattering by static strain fields due to biaxial wedgedisclination dipoles (WDDs) of finite length and circular wedge disclinationloops (WDLs) is studied in the framework of the deformation potentialapproach. The specific behaviour of the thermal conductivity, κ,is found for both defects. In particular, for WDDs the crossover fromT2to Tis predicted at low temperatures. For circular WDLs, κ(T) exhibits a minimum atsome temperature T*in the low-temperature range. Above T* κ ∼ T2(dislocation-like behaviour), while belowT*, one findsκ ∼ T−3.

Interfacial Wedge Disclination Dipole in a Hexagonal Bicrystal with Arbitrary In-Plane c-Axis Orientations

The stress field of a wedge disclination dipole located at the boundary of a hexagonal bicrystal is investigated under plane strain. The c-axes of the adjoining crystals are restricted to be in-plane but can otherwise be arbitrarily oriented. Exact closed-form solutions for the stress components, obtained by the method of continuous image dislocations, are of the form of the logarithm of the ratio of the functions of spatial coordinates and disclination and crystal parameters. Numerical results show that the characteristics of the stress distribution depend significantly on the c-axis orientations. Also, the interfacial stress components, plotted as functions of the two c-axis orientations, possess extrema and saddle points. The occurrence of, and the stress magnitude associated with, the extrema and saddle points are dependent on the crystal elastic anisotropy and the bicrystal inhomogeneity.