Elastic interaction between a dilatation centre and split dislocations in b.c.c. metals

The elastic interaction energy between a dilatation centre and 1/2[111] dislocation split on {110} planes in b.c.c. metals is calculated for sessile and planar splittings of screw dislocation and for planar splitting of edge dislocation; the splitting is considered as a model of the dislocation core. It is concluded that the interstitial impurity atom has three or four possible minimum energy positions in the dislocation core. A hypothesis on the impurity jumps in the dislocation core is proposed.On leave from theInstitute of Physics, Hanoi, VDR.     

Interactions of glide dislocations in a channel of a persistent slip band

Two unlike dislocations gliding in parallel slip planes in a channel of a persistent slip band are considered. Initially they are kept apart in straight screw positions. As the dislocations are pushed by the applied stress between two walls in the opposite directions, they bow out and attract one another forming a dipole. With the increasing stress the dislocations become more and more curved, until they separate. The walls of the channel are represented by elastic fields of rigid edge dipoles. The dislocations are modelled as planar curves approximated by moving polygons. The objective of the simulations is to determine the stress in the channel needed for the dislocations to escape one another. The stress and strain controlled regimes considered provide upper and lower estimates of the escape stress. The results are compared with the studies by Mughrabi and Pschenitzka, and Brown and the recent dislocation dynamics estimates. Problems encountered in the dislocation dynamics evaluation of the escape stress are analyzed.     

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.     

Initial stages of misfit stress relaxation through the formation of prismatic dislocation loops in GaN–Ga<Subscript>2</Subscript>O<Subscript>3</Subscript> composite nanostructures

The initial stages of misfit stress relaxation through the formation of rectangular prismatic dislocation loops in model composite nanostructures have been considered. The nanostructures are either spherical or cylindrical GaN shells grown on solid or hollow β-Ga²O₃ cores or planar thin GaN films on β-Ga²O₃ substrates. Three characteristic configurations of prismatic dislocation loops, namely, square loops, loops elongated along the GaN/Ga²O₃ interface, and loops elongated along the normal to the GaN/Ga²O₃ interface, have been analyzed. The generation of prismatic dislocation loops from the interface into the bulk of the GaN shell (film), from the free surface into the GaN shell (film), and from the interface into the β-Ga²O₃ core (substrate) has been investigated. It has been shown that, for the minimum known estimate of the lattice misfit (2.6%) in some of the considered nanostructures, no any prismatic dislocation loops can be generated. If the generation of prismatic dislocation loops is possible, then in all the considered nanostructures, the energetically more favorable case corresponds to prismatic dislocation loops elongated along the GaN/Ga²O₃ interfaces, and the more preferred generation of prismatic dislocation loops occurs from the GaN free surface. The GaN/Ga²O₃ nanostructures that are the most and least resistant to the formation of prismatic dislocation loops have been determined. It has been found that, among the considered nanostructures, the planar two-layer GaN/Ga²O₃ plate is the most resistant to the generation of prismatic dislocation loops, which is explained by the action of an alternative mechanism for the relaxation of misfit stresses due to the bending of the plate. The least resistant nanostructure is the planar three-layer GaN/Ga²O₃/GaN plate, in which GaN films have an identical thickness and which itself as a whole does not undergo bending. The critical thicknesses of the GaN shells (films), which must be exceeded to ensure the growth of these shells (films) so as to avoid the formation of prismatic dislocation loops, have been calculated for all the studied nanostructures and three known estimates of the lattice misfits (2.6, 4.7, and 10.1%).     

二相介质中的运动位错

本文考虑二相介质中与平面相界平行的匀速运动直线位错。采用了与位错相对静止的运动坐标系,在此坐标系中推广位错各向异性弹性理论的普遍方法,并利用弹性力学中的格林函数方法处理相界面,计算得到此位错在介质中所产生的总弹性场,以及其所受到的“像力”。本文所提出的理论方法有一般的适用性,结果可以用于考虑此位错与其它缺陷的相互作用,以及二相介质的力学性质。 关键词：     

Collective properties of defects,multiscale plasticity,and shock induced phenomena in solids

A statistically based approach is developed for the construction of constitutive equations that provides linkages between defect-induced mechanisms of structural relaxation, thermally activated plastic flow, and material response to extreme loading conditions. The collective properties of defects have been studied to establish the interaction of multiscale defect dynamics and plastic flow, and to explain the mechanisms leading to the universal self-similar structure of shock wave fronts. Pn explanation for structural universality of the steady-state plastic shock front (the four power law) and the self-similarity of shock wave profiles under reloading (unloading) is proposed. Structural characterization under transition from thermally activated dislocation glide to nonlinear dislocation drag effects is developed in terms of scaling invariants (effective temperatures) related to mesodefect induced morphology formed during the different stages of plastic deformation.     

On the vibrational spectrum of a parallel dislocation array

The free vibrations of dislocation arrays of different types (monopole and dipole dislocation walls and a planar dislocation array) have been investigated on the basis of the dispersion equation derived within the self-consistent dynamic theory of dislocations. The relaxation spectrum of a planar dislocation array in the strong damping mode has also been analyzed.     

Dislocation field theory in 2D: Application to graphene

A two-dimensional (2D) dislocation continuum theory is being introduced. The present theory adds elastic rotation, dislocation density, and background stress to the classical energy density of elasticity. This theory contains four material moduli. Two characteristic length scales are defined in terms of the four material moduli. Non-singular solutions of the stresses and elastic distortions of an edge dislocation are calculated. It has been pointed out that the elastic strain agrees well with experimental data found recently for an edge dislocation in graphene.     

Prediction of dislocation formation in epitaxial multilayers subject to in-plane loading

A theoretical model is described to predict equilibrium distributions of misfit dislocations in one or more anisotropic epitaxial layers of a multilayered system deposited on a thick substrate. Each layer is regarded as having differing elastic and lattice constants, and the system is subject to biaxial in-plane mechanical loading. A stress transfer methodology is developed enabling both the stress and displacement distributions in the system to be estimated for cases where the interacting dislocations are of a pure edge configuration. Energy methods are used to determine equilibrium distributions of the dislocations for given external applied stress states. It is shown that the new model accurately reproduces known exact analytical solutions for the special case of just one isotropic epitaxial layer applied to an isotropic semi-infinite substrate having the elastic constants of the substrate but differing lattice constants. The model is used to consider equilibrium dislocation distributions in capped epitaxial systems with misfit dislocations. It is shown that the simplifying assumptions often made in the literature, regarding the uniformity of elastic properties and the neglect of anisotropy, can lead to critical thicknesses being underestimated by 15–18%. The application of uniaxial tensile stresses increases the value of critical thicknesses. The model can be used to analyse dislocations in various non-neighbouring layers provided the dislocation density has the same value in all layers in which dislocations have formed. This type of analysis enables the prediction of the deformation of metallic multilayers subject to mechanical and thermal loading.     

Interbranch scattering of an X-ray wave field in a strongly distorted region of the elastic field around a dislocation

The case of a diffraction image of screw dislocations arranged parallel to the surface of a specimen has been studied experimentally and by methods of computer simulation. Special features of scattering of an X-ray wave field in a strongly distorted region near the dislocation core have been considered. It has been shown that the diffraction image in the vicinity of the defect is formed due to a superposition of new wave fields generated at each point of the elastic field around a dislocation with the existing fields.     

Numerical implementation of static Field Dislocation Mechanics theory for periodic media

This paper investigates the implementation of Field Dislocation Mechanics (FDM) theory for media with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are considered as spatially periodic continuous fields). In this context, the uniqueness of the stress and elastic distortion fields is established. This allows to propose an efficient numerical scheme based on Fourier transform to compute the internal stress field, for a given spatial distribution of dislocations and applied macroscopic stress. This numerical implementation is assessed by comparison with analytical solutions for homogeneous as well as heterogeneous elastic media. A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the FDM theory.     

Screening of the elastic field of disclinations by a dislocation ensemble

A self-consistent dynamics of a dislocation ensemble in the disclination field is analyzed within the kinetic approach. The effective Airy stress functions for the wedge disclination and the disclination dipole with due regard for the screening effect of the system of distributed dislocation charges are determined. The coordinate dependences of the stress tensor components and dislocation charge density for the screened disclination systems are found. The elastic energies of the screened disclination systems are calculated.     

冲击加载下20钢中弹性前驱波衰减与应力松弛行为实验研究

 通过改变样品厚度，对平面冲击加载下20钢的弹性前驱波的波幅衰减和应力松弛进行了实验研究。采用激光速度干涉测速仪（VISAR）实测了样品后自由面速度历史，采样频率达到1 ns，保证了实验结果的准确性。实验结果显示：Hugoniot弹性极限随着传播距离呈指数衰减，在所研究的样品厚度范围内，Hugoniot弹性极限减小了44%；应力松弛行为和弹性前驱波的上升沿时间也依赖于传播距离；冲击加载的强度对材料动态屈服行为的影响很小。     

钢中脆硬粒子裂纹形成机理

钢中的脆硬粒子对钢的解理脆断有直接的影响，解理断裂源大都发生在脆硬粒子上.根据微裂纹形成的热力学模型，利用钢中脆硬粒子开裂时所释放的弹性应变能、位错塞积弹性能，所产生的表面能，对脆硬粒子裂纹形成机理进行分析.模型计算表明，正应力和位错塞积力都是脆硬粒子开裂的必要条件，这与实验事实相符；同时给出脆硬粒子开裂的临界条件计算方法，计算发现，脆硬粒子临界开裂应力不仅取决于脆硬粒子尺寸及表面能，而且与晶粒直径有一定的相关关系，当晶粒直径较小时，这种关系与实验测定的材料解理断裂应力与晶粒尺寸的关系一致，说明整体失稳解 关键词： 解理断裂 裂纹形核 脆硬粒子     

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.     

Change in the plastic properties of ionic crystals under UV irradiation

The effect of UV irradiation on the dislocation motion in ionic crystals and relaxation growth of elastic twin in Iceland spar has been investigated. It is shown that UV radiation causes stress relaxation in crack tips, which is related to a change in the dislocation structure. It is suggested that the observed effects are based on the interaction of dislocations with low-energy excitons.     

Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classical Peierls--Nabarro (P-N) theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.     

GENERALIZATION OF ESHELBY''S METHOD TO THE ANISOTROPIC ELASTICITY THEORY OF DISLOCATIONS IN QUASICRYSTALS

The general expressions of the elastic fields induced by straight dislocations in quasicrystals have been given according to Eshelby's method which was used to treat the anisotropic elasticity of dislocations in crystals. As an example, the elastic displacement vector, the stress tensor and the elastic energy density of a screw dislocation line lying on the quasiperiodic plane of decagonal quasicrystals are calculated.