Interaction of Lomer–Cottrell locks with screw dislocations

In fcc crystals, dislocations are dissociated into partial dislocations and, therefore, restricted to move on {111} glide planes. By junction reactions with dislocations on two intersecting {111} planes, Lomer–Cottrell dislocations along ?110? directions can be formed which are barriers for approaching screw dislocations. Treating the interaction between a dissociated screw dislocation and a LC lock conventionally, using classical continuum theory and assuming the partials to be Volterra dislocations, leads to erroneous conclusions. A realistic result can only be obtained in the framework of the Peierls model, treating the partials as Peierls dislocations and explicitly taking account of the change in atomic misfit energy in the glide plane. At even moderate stresses (at less than 3 × 10^?3 µ in Cu), the screw will combine with the LC lock to form a Hirth lock. As a result, the nature of the repulsive force will change drastically.     

Which stresses affect the glide of screw dislocations in bcc metals?

By direct application of stress in molecular statics calculations we identify the stress components that affect the glide of 1/2?111? screw dislocations in bcc tungsten. These results prove that the hydrostatic stress and the normal stress parallel to the dislocation line do not play any role in the dislocation glide. Therefore, the Peierls stress of the dislocation cannot depend directly on the remaining two normal stresses that are perpendicular to the dislocation but, instead, on their combination that causes an equibiaxial tension-compression (and thus shear) in the plane perpendicular to the dislocation line. The Peierls stress of 1/2?111? screw dislocations then depends only on the orientation of the plane in which the shear stress parallel to the Burgers vector is applied and on the magnitude and orientation of the shear stress perpendicular to the slip direction.     

On slip in AgCl crystals at room temperature

At moderately wavy and branched slip bands on the surfaces of sheets of AgCl crystals the distribution of slip lines has been observed by means of the electron microscope. From the results it can be deduced that the cross slip of screw dislocations takes place. The divergence of the ends of slip bands has also been observed, which can be as well explained by the cross slip. From the active slip direction and the directions of straight slip lines in the cross-slip regions the microscopic slip planes have been determined. They lie in the region roughly limited by the {113} and {331} planes and the problem is discussed whether these planes are low-index crystallographic planes.     

Dislocations in plastically deformed Fe-3% Si alloy single crystals

The plastic deformation of Fe-3%Si alloy single crystals made from the melt is studied by the method of etching of dislocations. At a room-temperature and at static stress deformation by slip occurs in the 1/2〈111〉 directions along planes of maximum resolved shear stress. The plastic properties are determined by the motion of screw dislocations which cause the broadening of slip bands.     

Dislocation kink-pair energetics and pencil glide in body-centered-cubic crystals

When body-centered-cubic crystals undergo plastic deformation, the slip planes are often noncrystallographic. By performing atomistic simulation on the activation pathway of dislocation jumps in bcc iron, we show that the main reason for bcc crystals to exhibit this phenomenon is that one type of kink pair has significantly lower energy than all the other types on the same slip plane. Dislocation motion therefore cannot continue on the same slip plane, and the dislocation has to cross slip onto an intersecting slip plane after each atomic jump. Thus in the long run, the average slip plane would be zigzag and noncrystallographic.     

Theory of strengthening of alpha titanium by interstitial solutes

It is assumed that the core structure of screw dislocations in the h.c.p. lattice of α-Ti can be described by a sessile splitting on the prism plane and on the first order pyramidal plane simultaneously and that slip can proceed after its transformation into a glissile configuration on the prism plane. The strengthening by interstitial solutes O, N, C is explained by their impeding role in these sessile-glissile transformations. A good agreement between the theoretical temperature dependences of the effective stress for different interstitial content and the experimental values can be reached if the effect of impurities on the stacking fault energies is also taken into account. The similarity between the role of screw dislocations in the low temperature deformation of h.c.p. metals with more slip systems operating and of b.c.c. metals is stressed.     

求晶体位错自能的离散弹性方案

考虑到晶体的离散点阵结构,滑移只能在原子之间进行,因此位错中心永远没有原子,位错中心附近分摊到每个原子的离散弹性能量处处有限。在刚性位错假定下,直接应用位错弹性理论解析结果,求出了晶体直奇异位错等效内切半径及其随位错中心位置的周期变化。对于简单四方晶体中奇异螺型位错,一级近似与Peierls模型结果巧合。计算了fcc和bcc两种晶系中各种位错的自能和等效位错内切半径,并初步考虑了各向异性弹性效应。结果表明:位错滑移面不是几何平面,bcc螺型位错滑移面类似于蜂巢结构。指出了用这种离散弹性方法进一步估算各种次级效应的可能。 关键词：     

Critical conditions for dislocation nucleation at surface steps

Dislocation nucleation at a surface step is analyzed based on a general variational boundary integral formulation of the Peierls–Nabarro dislocation model. By modelling the surface step as part of the surface of a three-dimensional crack, the free surface effect is taken into account by transferring the half space problem into an equivalent one in the infinite medium. The profiles of embryonic dislocations, corresponding to the relative displacements between the two adjacent atomic layers along the slip planes, are then rigorously solved through the variational boundary integral method. The critical conditions for dislocation nucleation are determined by solving the stress-dependent activation energies required to activate the embryonic dislocations from their stable to unstable saddle-point configurations. In particular, the effect of the step geometry, such as the height of the step, the dip angle of the slip plane and the inclined angle of the step surface on dislocation nucleation, is quantitatively ascertained. The results show that the atomic-scale surface step can rapidly reduce the critical stress required for dislocation nucleation from the surface by nearly an order of magnitude. The decrease in critical stress as a function of the height of the step is more significant for slip planes with smaller dip angles and surface steps with smaller inclined angles.     

Elastic interaction between two parallel dislocations in non-parallel slip planes

The elastic interaction between two parallel dislocations which can glide in non-parallel slip planes is studied under the simplifying assumption that the dislocation glide velocity is proportional to stress. The motion of the two dislocations is represented by a motion of one reference point in a configuration plane. It is concluded that the contribution of the long-range elastic interaction between individual dislocations from different slip systems to work hardening is negligible, compared to the contribution from the formed attractive junctions. Especially, two parallel edge dislocations with mutually perpendicular Burgers vectors can co-exist in minimum energy positions, however, they can be separated by an arbitrarily small external stress.     

Peierls-Nabarro model of non-planar screw dislocation cores

The Peierls-Nabarro model originally developed for dislocations with planar cores is modified to describe the cores of screw dislocations extended along two or three intersecting slip planes, under the action of external stress. This concept generalizes the simplified concept of sessile splitting of screw dislocations into singular partials and enables an instructive interpretation of fully atomistic models of screw dislocation cores developed recently for b.c.c. metals. As an example, a numerical solution of the modified Peierls-Nabarro equation is given for the equilibrium configuration of a 1/2 [111] screw dislocation core in -Fe extended along three {110} planes.     

The peierls energy and kink energy in fcc metals

In fcc crystals, dislocations are dissociated on the {111} glide plane into pairs of partial dislocations. Since each partial interacts individually with the Peierls potential and is coupled to its neighbour by a stacking fault, periodic variations in the separation distance d of the partials occur when dislocations running along closed packed lattice directions are displaced. This can drastically reduce the effective Peierls stress. By using the Peierls model the structure of 0°, 30°, 60° and 90° dislocations in a typical fcc metal with the elastic properties of Cu and a stacking-fault energy γ₀ in the interval 0.04?≤?γ₀?≤?0.05?J/m² was studied, and the magnitude of the Peierls energy ΔE _P and the resulting kink energies E _K were determined. Since the energies involved are of the order of 10^?3?eV/b or less, their magnitude cannot be asserted with high confidence, considering the simplifying assumptions in the model. The difference in the changes of the core configuration during displacement of dislocations of different orientations should, however, be of physical significance. It is found that a dissociated 60° dislocation generally has a higher effective Peierls energy than a screw dislocation, but the reverse is true for the kink energy, at least in Cu.     

Effects of size on the dynamics of dislocations in ice single crystals

Single crystals of ice subjected to primary creep in torsion exhibit a softening behavior: the plastic strain rate increases with time. In a cylindrical sample, the size of the radius affects this response. The smaller the radius of the sample becomes while keeping constant the average shear stress across a section, the softer the response. The size-dependent behavior is interpreted by using a field dislocation theory, in terms of the coupled dynamics of excess screw dislocations gliding in basal planes and statistical dislocations developed through cross slip occurring in prismatic planes. The differences in the results caused by sample height effects and variations in the initial dislocation microstructure are discussed.     

Dislocation structure of calcium fluorapatite

Using etching of single crystals of calcium fluorapatite (FAP), we investigated the geometry of the distribution of dislocations emerging to the face surfaces, and the crystallography of their slip. It was shown that the application of a constant electric field of fixed orientation with respect to the crystal planes leads to motion of the dislocations. The mechanism of motion of edge and screw dislocations was determined by the presence of an effective charge created by steps and kinks.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 89–91, April, 1978.     

The cross slip of a dislocation in an ultrasound field and its dependence on the ultrasound amplitude and frequency,sample orientation,and dynamic viscosity

The motion of a screw dislocation under the action of ultrasound is simulated with account taken of its cross slip in a spatially nonuniform stress field created by a fixed dislocation of the same sense. Only dislocations started from certain regions in the space are shown to undergo cross slip. The variations in the sizes and shapes of these regions with the ultrasound parameters, crystallographic orientation of the sample, and coefficient of dynamic viscosity are given.     

A discussion of the structure and behaviour of dipole walls in cyclic plasticity

Assuming that cross-slip by thermally activated migration of jogs can cause annihilation of screw dislocation dipoles without macroscopic crystallographic confinement of cross-slip to the cross-slip plane, an attempt is made to re-derive earlier equations for the saturation stress and the plastic strain amplitude in persistent slip bands. These equations had been based on the assumption that cross-slip could occur only on a cross-slip plane making an obtuse angle with the slip plane, an assumption which limits the mean free path of screw dislocations. The key new assumption is that the walls of edge dislocation dipoles which dominate the structure of persistent slip bands are penetrable obstacles, which increases the mean free paths of the mobile dislocations. Agreement with experiment is obtained if the penetration probability in cyclic saturation is on average one third, a value for which there is a simple rationalization. Estimates can be made of the wall width, which is independent of temperature, in agreement with recent observations by Tippelt et al. However, the main unresolved difficulty is the role of the very fine dipoles, particularly the faulted dipoles, in the walls. A further weakness in the theory is that it ignores the cutting of dipoles by the cross-slipping screw dislocations. Despite these problems, the distribution of dipole heights can be worked out and is found to be in reasonable agreeement with experiment.     

晶体位错的离散弹性模型——位错中心结构和P-N力

在离散弹性模型中考虑了位错中心位错密度分布的影响,计算了fcc和bcc两种各向同性弹性介质中,不同中心结构的螺型位错的自能、等效内截半径与位错中心位置的关系,估算了不同滑移面上P-N力。讨论了原子热振动对P-N力的影响,比较了离散弹性方法与现有其它方法的结果,据信离散弹性方法是一种进一步进行更深入计算的有效方案。 关键词：     

Dynamic peierls stress in a crystal model with slip anisotropy

The analysis of screw dislocation motion in a lattice is extended to crystals with a preferred slip direction and to force laws of the “dangling bond” type. The external strain required for uniform motion, or the corresponding Peierls stress depends critically on the shape of the interatomic potential. For particular combinations of velocity, crystal anisotropy, and force law, the external strain drops sharply—indicating some modes of dislocation motion that are almost loss-free. Although the relation between dynamic Peierls stress and dislocation width is not monotonie, it shows a general exponential decrease.     

Cross-slip in face centred cubic metals: a general full stress-field dependent activation energy line-tension model

Cross-slip is a thermally activated process by which a screw dislocation changes its slip plane. Understanding and modelling the activation barrier of the cross-slip process as a free-energy barrier that depends on the stress conditions at the vicinity of the dislocation is crucial. In this work, we employ the line-tension model for the cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier when both Escaig stresses are applied on the primary and cross-slip planes and Schmid stress is applied on the cross-slip plane. We propose a closed-form expression for the activation energy for cross-slip in a large range of stresses, without any fitting parameters. The results of the proposed model are in good agreement with previous numerical results and atomistic simulations. We also show that, when Schmid stress is applied on the cross-slip plane, the energy barrier is decreased, and in particular, cross-slip can occur even when the Escaig stress in the primary plane is smaller than that on the cross-slip plane. The proposed closed-form expression for the activation energy can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality. This will allow cross-slip to be more accurately related to macroscopic plasticity.     

Dislocations in Fe-3% Si alloy single crystals deformed at a higher rate

The method of etching dislocations is used to study the distribution of dislocations and twins in Fe-3% Si alloy single crystals prepared from the melt after plastic deformation with higher speed. The crystals are deformed by twinning in the 〈111〉 directions along the {112} planes and by slip in the 〈111〉 directions along the {110} planes. The results prove that the dislocations causing plastic deformation move in the {110} planes during both fast and slow deformation. The difference in the slip surfaces during fast and slow deformation is explained by the different number of cross slips per unit dislocation path.     

Modelling the effect of pressure on the critical shear stress of MgO single crystals

A hierarchical multi-scale model was used to study the effect of high pressure on the critical shear stresses of MgO. The two main slip systems, ½?110?{110} and ½?110?{100}, were considered. Based on a generalised Peierls–Nabarro model, it is shown that the core structure of ½?110? screw dislocations is strongly sensitive to pressure. Mostly planar and spread in {110} at ambient pressure, the core of screw dislocations tends to spread in {100} with increasing pressure. Subsequently, an inversion of the easiest slip systems is observed between 30 and 60?GPa. At high pressure, the plasticity of MgO single crystals is expected to be controlled by ½?110?{100} slip systems, except at high temperature where both slip systems become active. Pressure is also found to increase the critical resolved shear stresses and to shift the athermal temperature toward higher temperatures. Under high pressure, MgO is thus characterised by a significant lattice friction on both slip systems.