K. N. Mikaelyan

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 τ g , above which nucleation of misorientation bands takes place. The numerical estimates for τ g 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 τ g 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 τ p which is several times higher than τ g . 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.

Screw dislocation near interface in gradient elasticity

Michigan Technological University, Houghton, MI 49931, USA(Received July 28, 1999)(Accepted in revised form May 4, 2000)Keywords: Gradient elasticity; Interface dislocations1. IntroductionA description of the elastic interaction of dislocations with interphase boundaries has been one of thekey problems in the theory of defects, with applications to materials science and engineering and specialattention to polycrystalline, multilayered and thin-film solid systems (e. g. [1–4]). This description istraditionally based on solutions of appropriate boundary value problems in the classical linear theory ofelasticity. The corresponding solutions provide the elastic fields of dislocations far from both theinterface and the dislocation line, thus being satisfactory for the cases when long-range elasticinteractions are of interest. However, when short-range interactions are of interest, the classicalsolutions lead to unreasonable results. These concern the elastic singularity at the dislocation line, aswell as the “image” force which acts on dislocations from the side of an interface which also becomessingular when the dislocation approaches the interface. Moreover, some components of the elastic stressfield of a dislocation suffer jumps at the interface, a fact which may be acceptable from a macroscopicpoint of view but physically unrealistic from a nano- or microscopic point of view. To avoid theaforementioned three difficulties, we reconsider the boundary value problem of a screw dislocation neara flat interface within the theory of gradient elasticity.In fact, the present paper is a continuation of our systematic studies [5–9] of defects (dislocations[5–9] and disclinations [8, 9]) within the theory of gradient elasticity. Our main results so far, have beenthe elimination of displacement [5–8], strain [5–9], stress [7, 9] and energy [7, 8] singularities at thedefect line. Starting [5, 6, 8] with a simle gradient modification of the linear theory of elasticityproposed in [10] and applied first for crack problems [10–14], we have found new nonsingular solutionsfor displacements, strains and energies of dislocations, as well as for the strains of disclinations.However, within that theory, solutions for elastic stresses remain singular and as in the classical theoryof elasticity. To dispense with this difficulty, we have employed recently [7, 9] a more general gradienttheory first used by Ru and Aifantis [15] (see also [16]) whose constitutive equation reads~1 2 c

Grain growth and collective migration of grain boundaries during plastic deformation of nanocrystalline materials

A theoretical model is proposed for the collective migration of two neighboring grain boundaries (GBs) in a nanocrystalline material under applied elastic stress. By analyzing the change in the energy of the system, it is shown that GBs can remain immobile or migrate toward each other depending on the values of the applied shear stress and misorientation angles. The process of GB migration can proceed either in a stable regime, wherein the GBs occupy equilibrium positions corresponding to a minimum of the energy of the system under relatively small applied stress, or in an unstable regime, wherein the motion of GBs under relatively high stress is accompanied by a continuous decrease in the system energy and becomes uncontrollable. The stable migration of GBs leads to a decrease of the grain bounded by them at the cost of growth of the neighbor grains and can result in complete or partial annihilation of the GBs and the collapse of this grain. Unstable migration leads either to annihilation of GBs or to passage of them through each other, which can be considered as the disappearance of the grain and nucleation and growth of a new grain.

Generation and Evolution of Partial Misfit Dislocations and Stacking Faults in Thin-Film Heterostructures

An analysis is made of the specific features in the generation and evolution of partial misfit dislocations at the vertices of V-shaped configurations of stacking fault bands, which terminate in the bulk of the growing film at 90° partial Shockley dislocations. The critical thicknesses hc of an epitaxial film, at which generation of such defect configurations becomes energetically favorable, are calculated. It is shown that at small misfits, the first to be generated are perfect misfit dislocations and at large misfits, partial ones, which are located at the vertices of V-shaped stacking-fault band configurations emerging onto the film surface. Possible further evolution of stacking-fault band configurations with increasing film thickness are studied.

Edge dislocations near phase boundaries in the gradient theory of elasticity

A solution of the boundary-value problem in the gradient theory of elasticity concerning a rectilinear edge dislocation parallel to the interface between phases with different elastic moduli and gradient coefficients is obtained. The interaction between the dislocation and the interface is considered on a nanoscopic level. It is shown that the stress field has no singularities on the dislocation line and remains continuous at the interface, unlike the classical solution, which is singular at the dislocation line and allows a discontinuity of two stress components at the interface. The gradient solution also removes the classical singularity of the image force for the dislocation on the interface. An additional elastic image force associated with the difference in the gradient coefficients of contacting phases is also determined. It is found that this force, which has a short range and a maximum at the interface, expels the edge dislocation into the material with a smaller gradient coefficient.

On the role of disclinations in relaxation and deformation processes in nanostructured materials

Abstract The features of grain boundary disclination splitting in nanocrystals are theoretically examined. It is shown that there are three basic variants of such splitting as a relaxation process which are specified by different values of elastic-energy decrease. Also, the contribution of disclinations as strengthening elements to processes of plastic deformation in metallic glass nanocrystal composites is discussed.

Behavior of screw dislocations near phase boundaries in the gradient theory of elasticity

The solution of the boundary-value problem on a rectilinear screw dislocation parallel to the interface between phases with different elastic moduli and gradient coefficients is obtained in one of the versions of the gradient theory of elasticity. The stress field of the dislocation and the force of its interaction with the interface (image force) are presented in integral form. Peculiarities of the short-range interaction between the dislocation and the interface are described, which is impossible in the classical linear theory of elasticity. It is shown that neither component of the stress field has singularities on the dislocation line and remains continuous at the interface in contrast to the classical solution, which has a singularity on the dislocation line and permits a discontinuity of one of the stress components at the interface. This results in the removal of the classical singularity of the image force for the dislocation at the interface. An additional elastic image force associated with the difference in the gradient coefficients of contacting phases is also determined. It is found that this force, which has a short range and a maximum value at the interface, expels a screw dislocation into the material with a larger gradient coefficient. At the same time, new gradient solutions for the stress field and the image force coincide with the classical solutions at distances from the dislocation line and the interface, which exceed several atomic spacings.

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.

Equilibrium configurations of partial misfit dislocations in thin-film heterosystems

The energy characteristics of orthogonal rows of partial misfit dislocations with V-shaped stacking faults in thin-film heteroepitaxial systems are analyzed theoretically. It is shown that they should appear only in very thin epitaxial films of nanoscopic thickness and for high values of the mismatch exceeding a definite value. Under these conditions partial misfit dislocations associated with V-shaped stacking faults are typical elements of the defect structure of nanolayer heterosystems. For smaller mismatches and larger films thicknesses total misfit dislocations should form.

Viscoelasticity and plasticity mechanisms of human dentin

Theoretical models of viscoelastic behavior and plastic deformation mechanisms of human dentin are considered. Using the linear viscoelasticity theory in which creep and relaxation kernels have the form of fraction-exponential functions, numerical values of instantaneous and long-time Young’s moduli and other characteristics of dentin viscoelasticity under uniaxial compression are found. As dentin plastic deformation mechanisms, mutual collagen fiber sliding in the region of contact of their side surfaces, separation of these fibers from each other, and irreversible tension of some collagen fibers, are proposed. It is shown that the second mechanism activation requires a smaller stress than that for activating others. The models of plastic zones at the mode I crack tip, which correspond to these mechanisms, are studied. It is shown that the plastic zone size can increase from a few hundreds of nanometers to hundreds of micrometers with increasing applied stress.