Dynamics Of Disclinations Research Articles

Couple-stress elasticity of intrinsic and extrinsic dislocations in three-dimensional multilayered materials

This work investigates the influence of couple stresses on intrinsic and extrinsic dislocations within three-dimensional heterogeneous multilayered structures. The materials consist of orthotropic and dissimilar layers with different elastic properties, incorporating the microstructural lengths from a special version of the anisotropic couple-stress elasticity. Double Fourier series expansions are used to describe extended displacements and tractions, considering rotation and couple-stress components and accounting for arbitrary displacement and rotation discontinuities associated with dislocation and disclination loops as well as periodic dislocation and disclination networks at semi-coherent interfaces. The dual-variable and position technique is used to recursively determine the field responses at any point in the multilayered laminate. The application examples focus on dislocation problems with couple stresses, revealing the effects of the core-spreading dislocation technique, free surfaces, anisotropic elasticity, and couple stresses on the field solutions. The analysis also uncovers pressure and von Mises stress amplitudes, non-zero rotation, and non-symmetric stress profiles due to couple stresses in copper/niobium bimaterials. Changes in the sign and magnitude of the Peach-Koehler forces are observed when couple stresses are introduced, which deviate from the classical theory of dislocations. The investigation finds a significant 29% reduction in energy per unit area at a semi-coherent interface between copper and niobium influenced by couple stresses. These results deepen our understanding of how couple stresses affect dislocation behavior in multilayered materials, and provide prospects for future discrete dislocation and disclination dynamics simulations with engineering applications in various nano- and micro-structured materials.

Shear-enhanced elasticity in the cubic blue phase I.

We present results of the linear and nonlinear rheology of the cubic blue phase I (BPI). The elasticity of BPI is dominated by double-twist cylinders assembled in a body-centered cubic lattice, which can be specified by disclination lines. We find that the elasticity of BPI is enhanced by an order of magnitude by applying pre-shear. The shear-enhanced elasticity is attributed to a rearrangement of the disclination lines that are arrested in a metastable state. Our results are relevant for the understanding of the dynamics of disclinations in the cubic blue phases.

A non-traditional view on the modeling of nematic disclination dynamics

Non-singular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of identifying these line defects with singularities of a unit vector field representing the nematic director. It is well known that the universally accepted Oseen-Frank energy is infinite for configurations that contain disclination line defects. We devise a natural augmentation of the Oseen-Frank energy to account for physical situations where, under certain conditions, infinite director gradients have zero associated energy cost, as would be necessary for modeling half-integer strength disclinations within the framework of the director theory. Equilibria and dynamics (in the absence of flow) of line defects are studied within the proposed model. Using appropriate initial/boundary data, the gradient-flow dynamics of this energy leads to non-singular, line defect equilibrium solutions, including those of half-integer strength. However, we demonstrate that the gradient flow dynamics for this energy is not able to adequately describe defect evolution. Motivated by similarity with dislocation dynamics in solids, a novel 2D-model of disclination dynamics in nematics is proposed. The model is based on the extended Oseen-Frank energy and takes into account thermodynamics and the kinematics of conservation of defect topological charge. We validate this model through computations of disclination equilibria, annihilation, repulsion, and splitting. We show that the energy function we devise, suitably interpreted, can serve as well for the modeling of equilibria and dynamics of dislocation line defects in solids, making the conclusions of this paper relevant to mechanics of both solids and liquid crystals.

Dynamics of formation of low-angle tilt boundaries in metals and alloys at high loading rates

A computer model has been developed in which the process of formation of low-angle tilt boundaries and fragmentation of initial subgrains during shock loading of metals and alloys is clearly demonstrated by the of two-dimensional discrete dislocation–disclination dynamics method. The formation and evolution of such grains proceeds under the action of an external stress and the stress field of grain boundary disclinations distributed on the subgrain boundaries. With the D16 aluminum alloy as an example, three cases of fragmented structures formed in accordance with the initial configuration of the disclination ensemble have been considered for a dipole, quadrupole, and arbitrary octupole of wedge disclinations. It has been shown that, in all these cases, the formation of a stable fragmented structure requires a stress of ~0.5 GPa and time of 10 ns. The main results of computer simulation (the finite form of a fragmented structure, typical level of applied stress, and small fragmentation time) agree well with known experimental results on shock compression of the D16 aluminum alloy.

Ultraslow Oscillation of Nematic Disclination after Abrupt Switching of DC Voltage

The slow damped oscillation of a nematic disclination was observed after an abrupt (stepwise) change in the DC electric field. The oscillation was not observed under a high-frequency AC field. These results imply that molecular reorientation influences disclination dynamics after abrupt switching. An effective model, which is not a simple elastic theory, was proposed to analyze the results.

The dynamics of dislocation wall generation in metals and alloys under shock loading

Two-dimensional discrete dislocation–disclination dynamics is applied to model the formation of dislocation walls in shock loaded metals and alloys. The dislocation walls are generated under an external stress impulse and the stress fields of pre-existed wedge disclinations distributed over the subgrain boundary. The case of an aluminum alloy is analyzed. It is shown that the typical shock duration is enough to complete the fragmentation process within the initial subgrain, and the necessary stress magnitude well agrees with experiments.

Equivalent Theories of Liquid Crystal Dynamics

There are two competing descriptions of nematic liquid crystal dynamics: the Ericksen-Leslie director theory and the Eringen micropolar approach. Up to this day, these two descriptions have remained distinct in spite of several attempts to show that the micropolar theory comprises the director theory. In this paper we show that this is the case by using symmetry reduction techniques and introducing a new system that is equivalent to the Ericksen-Leslie equations and includes disclination dynamics. The resulting equations of motion are verified to be completely equivalent, although one of the two different reductions offers the possibility of accounting for orientational defects. After applying these two approaches to the ordered micropolar theory of Lhuiller and Rey, all the results are eventually extended to flowing complex fluids, such as nematic liquid crystals.

Cell Gap Dependence of Nematic Backflow around Annihilating Disclination Pair

This paper reports an experimental study of the dynamics of s = ±1/2 disclinations in the nematic liquid crystalline (LC) phase of 4-cyano-4'- n -pentylbiphenyl (5CB) under strong anchoring condition. The backflow brings asymmetry in annihilation dynamics of disclinations. To reveal the surface effect on backflow, we observed the motion of disclination pair for a various cell gap d . Although the velocity ratio of s = ±1/2 disclinations is comparable with a theoretical prediction, it decreased around the cell gap d = 1 µm when velocity ratio was reduced. This observation shows that the backflow is suppressed in the LC cell with d = 1 µm. The anchoring effect is analyzed through a model calculation within an elastic theory.

Disclination Models of Misorientation Band Generation and Propagation

The generation and propagation of misorientation bands in polycrystalline metals under large deformation are theoretically investigated and discussed. Disclination models are proposed to describe the generation of misorientation bands at grain boundary kinks and junctions. The models consider edge disclination dipole and quadrupole configurations and predict the value for the critical external shear stress τg, above which nucleation of misorientation bands takes place. The numerical estimates for τg give values of G/1000 – G/400 (G being the shear modulus), which correspond to the level of the deforming stress observed in the materials with fine grain structure. The critical stress τg is shown to be strongly dependent on the geometry and strengths of initial disclinations at grain boundary faults. The further development of the disclination structure at an isolated grain boundary fault demonstrates two main regimes of misorientation band development: stable and unstable propagation. The transition between the two regimes is controlled by another critical value for external stress τp which is several times higher than τg. To better understand the cooperative behavior of dislocations and disclinations in metals at late stages of plastic deformation, computer simulation of dislocation–disclination interaction has also been performed, using a 2D dislocation–disclination dynamics code. Some preliminary results of these calculations are reported and discussed.

A theory for flowing nematic polymers with orientational distortion

Synopsis Using a nonlocal nematic potential, we generalize the Doi theory for nematic polymers to include distortional elasticity. We derive an evolution equation for the configuration tensor and a constitutive equation for a nonlocal stress tensor which is consistent with the long-range order in nematic polymers. One of the interesting effects of distortional elasticity is the appearance of a mean-field torque on the molecules as they are forced away by flow from their preferred orientation. This torque gives rise to an antisymmetric part of the stress tensor. With a few molecular parameters, the complete system of equations is capable, we believe, of describing the evolution of the texture and the dynamics of disclinations in flowing nematic polymers. Thus, for the first time, a suitable platform for exploring complex flows of nematic polymers is established. In the limit of weak flows and small distortions, the theory properly reduces to the Leslie‐Ericksen theory. The Leslie viscosities are derived in terms of molecular parameters. © 2000 The Society of Rheology. @S0148-6055~00!00705-7#

Hydrodynamics of Defects in the Abelian–Higgs Model: An Application to Nematic Liquid Crystals

The Abelian–Higgs model is the basis for a gauge covariant form of the distortion free energy for nematic liquid crystals. This is used to derive a new form of the Ericksen–Leslie equations incorporating the dynamics of disclinations in nematic films. The zero liquid flow case is treated in detail for simplicity. The equations are reduced to dynamic equations for disclination points in moduli space for a small deviation from the Bogomol'nyi limit. We are able to derive analytically the dynamics of disclinations with winding numbers of the same sign. A set of such disclinations close to one another, i.e., with overlapping cores, can result from the disintegration of a larger disclination, and they repel one another. For a pair of such dis- clinations far apart from one another we find that they move on a straight line where their separation increases logarithmically over time.

Dynamics of disclinations in liquid crystals

Dynamics of disclinations in liquid crystals

Zig-Zag Defects and Disclinations in the Surface-Stabilized Ferroelectric Liquid Crystals

Characteristic features of zig-zag defects and disclinations in surface-stabilized ferroelectric liquid crystal cells are presented. It is pointed out that there exist two kinds of zig-zag defects, i.e., a lightning type and a hairpin type, which appear alternatively along the smectic layer normal. This fact indicates that two types of mismatching of a layer bend structure cause two kinds of zig-zag defects. Switching between two twisted states occurs with the formation of internal boat-shaped disclination loops in relation to the zig-zag defects. The nucleation process of the boat-shaped domains is quite characteristic; the bows appear on each side of the bright hairpin-type lines, while the sterns appear on both sides of the dark lightning-type lines. A model structure is proposed in order to interpret the experimental observation around the zig-zag defect lines on the basis of disclination dynamics.

Dynamics of Disclinations in the Non-Orthogonally Twisted Nematics

The equation of motion of disclinations in the non-orthogonally twisted nematic cell is derived. The experimental results on a liquid crystal MBBA are presented and discussed.

Dynamics of Disclinations in Twisted Nematics Quenched below the Clearing Point

Dynamics of Disclinations in Twisted Nematics Quenched below the Clearing Point

Dynamics of Disclinations in Twisted Nematics Quenched below the Clearing Point

We have investigated the dynamical behavior of twisted nematic crystals quenched from an isotropic phase into a nematic phase. In such a system the collective motion of an assembly of disclination can be observed and a dynamical scaling law was found. The u-field theory developed by Ohta, Jasnow and Kawasaki was applied to analyze the obtained data.