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Chiqun Zhang's picture

On the relevance of generalized disclinations in defect mechanics

Chiqun Zhang            Amit Acharya

The utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects like defected grain and phase boundaries, dislocations and disclinations. The Burgers vector of a disclination dipole in linear elasticity is derived, clearly demonstrating the equivalence of its stress field to that of an edge dislocation. We also prove that the inverse deformation/displacement jump of a defect line is independent of the cut-surface when its g.disclination strength vanishes. An explicit formula for the displacement jump of a single localized composite defect line in terms of given g.disclination and dislocation strengths is deduced based on the Weingarten theorem for g.disclination theory at finite deformation. The Burgers vector of a g.disclination dipole at finite deformation is also derived.

Chiqun Zhang's picture

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

Chiqun Zhang          Xiaohan Zhang         Amit Acharya          Dmitry Golovaty          Noel Walkington

Nonsingular 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.

Influence of anisotropic elasticity on the mechanical properties of fivefold twinned nanowires


In this paper in the Journal of the Mechanics and Physics of Solids (vol. 84, p. 358, ) we propose a
new theory for the mechanical properties of fivefold twinned nanowires.

We show that the Frank vector of the central wedge disclination depends on the uniaxial strain,

Mohammad Aramfard's picture

Disclination mediated dynamic recrystallization in metals at low temperature

Recrystallization is one of the most important physical phenomena in condensed matter that has been utilized for materials processing for thousands of years in human history. It is generally believed that recrystallization is thermally activated and a minimum temperature must be achieved for the necessary atomic mechanisms to occur. Here, using atomistic simulations, we report a new mechanism of dynamic recrystallization that can operate at temperature as low as T = 10 K in metals during deformation.

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