Elastic interaction between a dislocation and a near-by inclusion

The study of elastic interaction between a dislocation and an inclusion (i.e., a region transformed without change of elastic constants) in an elastic continuum is extended to the cases when the singular dislocation line intersects or touches the inclusion or is situated inside it. The interaction energy is shown to be a finite and continuous function of position of the inclusion. The interaction of an edge dislocation with a dilatation sphere and of a screw dislocation with a sphere transformed into ellipsoid in isotropic continuum are studied in detail. The spherical inclusion which is considered as a rough model of a point defect (e.g. of carbon atom in iron) has a maximum and minimum energy position near the dislocation line so that the binding energy can be calculated in a consistent way.     

位错环与点阵空位间的弹性相互作用

本文分析了点阵空位的弹性模型,给出点阵空位与任意内应力系统的相互作用能量普遍表达式。作为一个物理上有意义的例子,推导了棱柱位错环与点阵空位弹性相互作用能量的具体表达式。给出了关于铝中位错环的数值结果,并对结果进行了讨论。     

Screening of the elastic field in a dislocation ensemble

The phenomenon of screening of the elastic field of screw dislocations is investigated on the basis of a system of self-consistent field equations for a dislocation ensemble. Expressions are derived for the effective dislocation interaction potential, the screening length, and the average elastic field energy associated with the correlation interaction of dislocations. An expression for the correlation dislocation flux is formulated in the slightly inhomogeneous case. Fiz. Tverd. Tela (St. Petersburg) 39, 1575–1579 (September 1997)     

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：     

Correlation effects in an ensemble of edge dislocations

A kinetic theory of correlation interaction in an ensemble of edge dislocations is developed taking into account the effects of the fluctuation dynamics of dislocations. Equations of evolution of a dislocation ensemble are derived including the correlation interaction between dislocations. A criterion of instability of a uniform dislocation distribution is established. It is shown that the nucleation of spatially nonhomogeneous dislocation structures due to correlation instability is mainly determined by the specific features of the elastic interaction between dislocations and depends only slightly on the mechanism of dislocation kinetics. The theory is applied to calculating the dispersion of an internal stress field.     

The elastic interaction of a dislocation dipole with dilatation centres

The elastic interaction of a dilatation centre with edge dislocation dipole is investigated and the share of this elastic interaction in the time dependence of the diffusion of point defects to dislocations in plastically deformed crystalline materials is discussed.Reported on in brief at the International Conference on Electron Diffraction and Crysta Defects, Melbourne, August 1965.     

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.     

Stress field and interaction forces of dislocations in anisotropic multilayer thin films

Utilizing Fourier transforms, the elastic field of three-dimensional dislocation loops in anisotropic multilayer materials is developed. Green's functions and their derivatives, obtained first in the Fourier domain and then in the real domain by numerical inversion, are used in integrals to determine the elastic field of dislocation loops. The interaction forces between dislocations and free surfaces or interfaces in multilayer thin films are then investigated. The developed method is based on rigorous elasticity solutions for dislocations approaching to within one to two atomic planes from the interface. For a dislocation in one layer, the interface image force is determined mainly by the elastic moduli and thicknesses of neighbouring layers. When a dislocation approaches an interface between two layers, within 10–20 atomic planes, the image force changes rapidly. Interaction forces are then kept constant up to the interface. The model shows that, when a dislocation crosses an interface from a soft to a hard layer, additional external forces must be applied to overcome an elastic mismatch barrier. The developed method extends the concept of the Kohler barrier in 2D, and shows that the interface force barrier not only depends on the relative ratio of the elastic moduli of neighbouring layers, but also on the 3D shape of the dislocation, the number of interacting adjacent layers, and on layer thicknesses.     

Dislocation models of mechanoluminescence in γ- and X-irradiated alkali halides crystals

The mechanoluminescence appears in the elastic, plastic and fracture regions of γ- and X-irradiated KCl and NaCl crystals. A linear relation is found between the mechanoluminescence intensity and the newly created dislocations. Four models are proposed for the mechanoluminescence excitation during the movement of dislocations. These models are: dislocation unpinning model, dislocation interaction model, dislocation defect stripping model, and dislocation innihilation model. The dislocation annihilation model seems to be a dominating process for the M.L. excitation in γ- and X-irradiated alkali halide crystals.     

石墨烯/铝基复合材料在纳米压痕过程中位错与石墨烯相互作用机制的模拟研究

石墨烯因其优异的力学性能已成为增强金属基复合材料的理想增强体.然而,目前对石墨烯/金属基复合材料在纳米压痕过程中嵌入石墨烯与位错之间的相互作用仍不清晰.本文采用分子动力学模拟方法,对90°,45°和0°位向的石墨烯/铝基复合材料进行了纳米压痕模拟,研究了压痕加载和卸载过程中石墨烯/铝基复合材料的位错形核及演化,以获取不同位向的石墨烯与位错的相互作用机制,并分析其对塑性区的影响.研究发现,石墨烯可以有效阻碍位错运动,并且石墨烯会沿着位错滑移方向发生弹性变形.在纳米压痕过程中,位错与不同位向石墨烯之间的相互作用差异导致塑性区的变化趋势不同.研究结果表明,在石墨烯/铝基复合材料中,位向不同的石墨烯对位错阻碍强度和方式不同,且石墨烯位向为45°的复合材料的硬度高于其他模型.此外,石墨烯/铝基复合材料的位错线总长度的演化规律与石墨烯位向紧密相关.本文研究可为设计和制备高性能石墨烯/金属基复合材料提供一定的理论指导.     

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.     

On the interaction between dislocations and cracks in one-dimensional hexagonal quasi-crystals

The solution of elasticity problems involving the interaction between dislocations and cracks plays a fundamental role in many practical and theoretical applications. Although elasticity problems involving dislocation or cracks in quasi-crystals have been investigated in many papers, the analysis is limited to a single defect. This paper investigates the interaction of defects in one-dimensional hexagonal quasi-crystals using the complex variable function method. The interaction force between two parallel dislocations is presented and the analytic solutions of elastic fields of interaction between a dislocation and a crack are obtained. A version of the well-known Peach－Koehler formula in one-dimensional hexagonal quasi-crystals is given.     

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.     

Dislocation interaction with radiation-induced single halogen interstitials in KBr

Mechanism of radiation hardening by single halogen interstitials has been studied in KBr. It is found that the interstitial ions more strongly interrupt dislocation movements than the atoms do. The I_A center-dislocation interaction involves thermal activation. The maximum force in the interaction process is obtained to be 1.6 x 10^-4 dyne. The results of linear elastic calculations suggest that this interaction is elastic in nature.     

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.     

Solute friction and forest interaction

Solute friction is known to prevail in crystals where a solution of point defects results in a diffuse resistance to dislocation motion. This property is often used to strengthen materials. In this paper we show that it also affects dislocation–dislocation interactions. Dislocation dynamics simulations are used to investigate and quantify this property. The solute friction results in a shielding of elastic interactions leading to a significant decrease of the intrinsic strengths of junction and annihilation reactions. Simulations in static and dynamic conditions show that the interaction stability decreases with the friction stress. A model is proposed to account for the modification of the interaction coefficient predicted by massive simulations in latent hardening conditions. Results suggest that the observed softening is mainly due to the decrease of the line tension of dislocations involved in the dislocation–dislocation interactions.     

An improvement of the lattice theory of dislocation for a two-dimensional triangular crystal

The structure of dislocation in a two-dimensional triangular crystal has been studied theoretically on the basis of atomic interaction and lattice statics. The theory presented in this paper is an improvement to that published previously.Within a reasonable interaction approximation, a new dislocation equation is obtained, which remedies a fault existing in the lattice theory of dislocation. A better simplification of non-diagonal terms of the kernel is given. The solution of the new dislocation equation asymptotically becomes the same as that obtained in the elastic theory, and agrees with experimental data. It is found that the solution is formally identical with that proposed phenomenologically by Foreman et al, where the parameter can be chosen freely, but cannot uniquely determined from theory. Indeed, if the parameter in the expression of the solution is selected suitably, the expression can be well applied to describe the fine structure of the dislocation.     

Interaction of dislocations with ordered cylindrical precipitates

The size and antiphase boundary effects of a cylindrical inclusion with zero axial misfit in f.c.c. alloys are calculated using the linear isotropic elasticity.The plane strain gives rise to nonzero elastic interaction even inside inclusions with zero misfit direction inclined to the Burgers vector. The extreme value of the total force on a straight dislocation cutting the inclusion axis is determined for different dislocation and inclusion orientations.     

Elastic stress field beneath an arbitrary axisymmetric punch

The nanoindentation test is commonly used for the local determination of mechanical properties (hardness, elastic modulus, etc.) and also to study the initial stages of plasticity (dislocation nucleation, dislocation interaction mechanisms) at the nanometre scale. In the latter case, the determination of the elastic stress field beneath the indenter is of primary interest. An analytical expression is derived for the elastic stress and strain fields beneath an axisymmetric punch. Most solutions, in the literature, are given for simple indenter shapes, such as flat, conical or spherical indenters. The complete solution proposed for an arbitrary indenter profile is described by a power law, in which the exponent can be an integer or not. The stress is given as the real part of complex analytical expressions.     

Dislocation decoration and raft formation in irradiated materials

Experimental observations of dislocation decoration with self-interstitial atom (SIA) clusters and of SIA cluster rafts are analysed to establish the mechanisms controlling these phenomena in bcc metals. The elastic interaction between SIA clusters, and between clusters and dislocations is included in kinetic Monte Carlo (KMC) simulations of damage evolution in irradiated bcc metals. The results indicate that SIA clusters, which normally migrate by 1D glide, rotate due to their elastic interactions, and that this rotation is necessary to explain experimentally-observed dislocation decoration and raft formation in neutron-irradiated pure iron. The critical dose for raft formation in iron is shown to depend on the intrinsic glide/rotation characteristics of SIA clusters. The model is compared with experimental observations for the evolution of defect cluster densities (sessile SIA clusters and nano-voids), dislocation decoration characteristics and the conditions for raft formation.