Elastic behavior of a screw dislocation in the wall of a hollow nanotube

The elastic behavior of a screw dislocation lying in the wall of a hollow cylindrical nanotube is studied theoretically. The corresponding boundary-value problem of the classical theory of elasticity is formulated and solved (for stresses) for a linear elastically isotropic or transversely isotropic body. The elastic energy of the nanotube with the dislocation and the image force exerted on this dislocation by the inner and outer nanotube surfaces are calculated. The internal space of the nanotube is shown to cause the following qualitative differences in the dislocation stress-field distribution: a change in the sign of stress-tensor components near the inner nanotube surface, a high stress concentration at this surface, and a strong stress gradient at this surface. The dislocation has only one position of unstable equilibrium in the nanotube wall, which is always shifted toward the inner nanotube surface. As the internal-space radius increases, the dislocation energy decreases and the position of its equilibrium shifts toward the outer nanotube surface; in the limiting case of a flat plate, it reaches the center of the plate. Near the nanotube free surfaces, the image force on the dislocation is large and can substantially affect the dislocation behavior.     

Dislocations hétéro-interfaciales vis perçant une plaquette mince

A specimen observed in high-resolution transmission electron microscopy is electron transparent and its thickness is often less than about 10 nm. When it contains a linear defect like a screw dislocation, the obtained image can exhibit more or less important perturbations due to elastic relaxation nearby both free surfaces. Therefore, the theoretical interpretation of an image should include this relaxation in the calculation model. In the present work, it is evaluated for screw misfit dislocations piercing normally an elastically heterogeneous bicristalline plate (thickness 2h) from the following assumptions: there is no applied force on the thin plate and any surface stress related to a possible nanometric structure along the two free surfaces is neglected. The solution is found from an appropriate combination of known elastic fields in an infinite medium, which enables total stresses applying on two planes distant of 2h to be cancelled. This solution generalizes for the first time that of Eshelby and Stroh (1951), who consider an isolated screw dislocation normal to a homogeneous plate.     

Surface stress mediated image force and torque on an edge dislocation

The proximity of interfaces gives prominence to image forces experienced by dislocations. The presence of surface stress alters the traction-free boundary conditions existing on free-surfaces and hence is expected to alter the magnitude of the image force. In the current work, using a combined simulation of surface stress and an edge dislocation in a semi-infinite body, we evaluate the configurational effects on the system. We demonstrate that if the extra half-plane of the edge dislocation is parallel to the surface, the image force (glide) is not altered due to surface stress; however, the dislocation experiences a torque. The surface stress breaks the ‘climb image force’ symmetry, thus leading to non-equivalence between positive and negative climb. We discover an equilibrium position for the edge dislocation in the positive ‘climb geometry’, arising due to a competition between the interaction of the dislocation stress fields with the surface stress and the image dislocation. Torque in the climb configuration is not affected by surface stress (remains zero). Surface stress is computed using a recently developed two-scale model based on Shuttleworth’s idea and image forces using a finite element model developed earlier. The effect of surface stress on the image force and torque experienced by the dislocation monopole is analysed using illustrative 3D models.     

晶体缺陷规范场方法处理运动螺型位错

本文用晶体缺陷规范场方法分析了运动螺型位错的性质,在一定规范条件下求解了螺型位错的动力学方程,得到了匀速运动螺型位错的应力场。在K=μ/s(s为耦合常数)趋于零的情况下,其结果与匀速运动的Volterra螺型位错的应力场形式上是一样的,但螺型位错运动的极限速度是2^1/2c。在螺型位错速度为零的情况下,其应力场与Volterra螺型位错的应力场完全一样。最后对所得结果进行了讨论。 关键词：     

Elastic stress fields caused by a dislocation in Ge x Si1−x /Si film-substrate system

The elastic stress fields caused by a dislocation in Ge_xSi_(1-x) epitaxial layer on Si substrate are investigated in this work. Based on the previous results in an anisotropic bimaterial system,the image method is further developed to determine the stress field of a dislocation in the film-substrate system under coupled condition. The film-substrate system is firstly transformed into a bimaterial system by distributing image dislocation densities on the position of the free surface. Then,the unknown image dislocation densities are solved by using boundary conditions,i.e.,traction free conditions on the free surface. Numerical simulation focuses on the Ge0.1Si0.9/Si film-substrate system. The effects of layer thickness,position of the dislocation and crystallographic orientation on the stress fields are discussed. Results reveal that both the stresses σxx,σxz at the free surface and the stress σxy,σyy,σyz on the interface are influenced by the layer thickness,but the former is stronger. In contrast to the weak dependence of stress field on the crystallographic orientation the stress field was strongly affected by dislocation position. The stress fields both in the film-substrate system and bimaterial system are plotted.     

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack are dealt with in this paper. Utilizing the conformal mapping technique, the closed-form solutions are derived for complex potentials and stress fields due to a screw dislocation located near the interfacial blunt crack. The stress intensity factor on the crack tips and the critical stress intensity factor for dislocation emission are also calculated. The influence of the orientation of the dislocation and the morphology of the blunt crack as well as the material elastic dissimilarity on the shielding effect and the emission criterion is discussed in detail. The results show that positive screw dislocations can reduce the stress intensity factor of the interfacial blunt crack tip (shielding effect). The shielding effect increases with the increase of the shear modulus of the lower half-plane, but it decreases with the increase of the dislocation azimuth angle. The critical loads at infinity for dislocation emission increases with the increase of emission angle and curvature radius of blunt crack tip, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as special cases.     

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 elastic field and image force of dislocations in anisotropic solids and its application to GaN nanostructures

The determination of the elastic field and image force of dislocation in anisotropic media is a nontrivial problem. This work revisits Eshelby’s sextic anisotropic elasticity theory to obtain the stress field of a screw dislocation in an infinite anisotropic solid. The image force of a dislocation in an anisotropic nanowire is then derived by using the concept of ‘image dislocation’. Moreover, this work proposes to study the image force of nanorods by approximating the three-dimensional shape effect as a height-dependent shape function, which could be obtained through curve fitting of the finite element data. The analytical solution is applied to analyse image forces on different dislocations in GaN nanorods oriented along polar (c-axis) and nonpolar (a, m-axis) directions. The result shows the dislocation dissipation could be more effective in a-GaN but less in m-GaN by comparing with the standard growth of c-GaN. The approach developed in this work is applicable to other material systems. Therefore, it could contribute to a wide range of nanostructure design and fabrication for dislocation-free devices.     

Nucleation of cracks near the free surface in deformed metallic nanomaterials with a bimodal structure

A theoretical model that effectively describes the nucleation of cracks in stress fields of dislocation pile-ups near the free surface in metallic nanomaterials with a bimodal structure has been developed. The dependences of the critical shear stress τ_c (for the formation of a crack with an equilibrium length of 10 nm on a dislocation pile-up near the surface) on the size d of a grain containing the dislocation pile-up have been calculated for copper with a bimodal structure. Theoretically, it has been found that the critical shear stress τ_c for the nucleation of a crack near the free surface in a nanomaterial with a bimodal structure is approximately 30% higher than that for the crack nucleation within the nanomaterial at a distance from the free surface.     

Determination of the sign of screw dislocations viewed end-on by weak-beam diffraction contrast

This paper describes how the sign of a screw dislocation or of the screw component of a mixed dislocation in a thin elastically isotropic foil, viewed end-on, can be determined from the dark-field weak-beam diffraction contrast arising from surface relaxation displacements. The contrast consists of black-white lobes, with the line of no-contrast parallel to g , similar to that found previously by Tunstall et al . [Phil. Mag. 9 99 (1964)] for bright-field imaging of screw dislocations in thick foils. Unlike weak-beam images of inclined dislocations, the image profiles are very broad (～10?nm for the strongest) owing to the long-range nature of surface relaxation strain-field. For dislocations spaced at ～10?nm or less, the overlap of the strain-field from nearby dislocations has to be taken into account. The paper also discusses the nature of the contrast from mixed dislocations slightly tilted from the incident beam direction, when contrast from the edge component is expected, and the possibility of determining the sign of the screw component in this case.     

Shielding effect of a nano-circular inclusion acting on semi-infinite wedge cracks

The model of a screw dislocation near a semi-infinite wedge crack tip inside a nano-circular inclusion is proposed to investigate the shielding effect of nano inclusions acting on cracks. Utilizing the complex function method, the closed-form solutions of the stress fields in the matrix and the inclusion region are derived. The stress intensity factor, the image force, as well as the critical loads for dislocation emission are discussed in detail. The results show that the nano inclusion not only enhances the shielding effect exerted by the dislocation, but also provides a shielding effect itself. Moreover, dislocations may be trapped in the nano inclusion even if the matrix is softer than the inclusion. This helps the dislocation shield crack, and reduces the dislocation density within the matrix.     

Dislocations in an inhomogeneous anisotropic medium

The general expressions for the stress field of a dislocation situated near a welded, slipping and free boundary are derived employing the method of Fourier transformations. As an example the stress field of a screw dislocation near a simple type of welded boundary is explicitly given.     

The Peierls stress for coupled dislocation partials near a free surface

The effect of a free surface on the Peierls stress of a perfect dislocation, as well as on one of two dislocation partials under a free surface, has been accounted for by considering the Lubarda–Markenscoff variable-core dislocation model (VCM). The VCM dislocation smears the Burgers vector, while producing on the slip plane the Peierls–Nabarro sinusoidal relation between the stress and the slip discontinuity with a variable width. Here the core radius is allowed to depend on the distance to the free surface and the other partial. The Peierls stress is computed as a configurational force by accounting for all the energies and the image stresses to satisfy the traction-free boundary conditions. The results are applied to aluminum and copper and comparisons are made with atomistic calculations in the literature that show that the partials merge as they approach the free surface.     

Multiscale modelling of dislocation/grain boundary interactions. II. Screw dislocations impinging on tilt boundaries in Al

The interaction of dislocations with grain boundaries (GBs) determines a number of important aspects of the mechanical performance of materials, including strengthening and fatigue resistance. Here, the coupled atomistic/discrete-dislocation (CADD) multiscale method, which couples a discrete dislocation continuum region to a fully atomistic region, is used to study screw-dislocations interacting with Σ3, Σ11, and Σ9 symmetric tilt boundaries in Al. The low-energy Σ3 and Σ11 boundaries absorb lattice dislocations and generate extrinsic grain boundary dislocations (GBDs). As multiple screw dislocations impinge on the GB, the GBDs form a pile-up along the GB and provide a back stress that requires increasing applied load to push the lattice dislocations into the GB. Dislocation transmission is never observed, even with large GBD pile-ups near the dislocation/GB intersection. Results are compared with experiments and previous, related simulations. The Σ9 grain boundary, composed from a more complex set of structural units, absorbs screw dislocations that remain localized, with no GBD formation. With increasing applied stress, new screw dislocations are then nucleated into the opposite grain from structural units in the GB that are nearby but not at the location where the original dislocation intersected the boundary. The detailed behaviour depends on the precise location of the incident dislocations and the extent of the pile-up. Transmission can occur on both Schmid and non-Schmid planes and can depend on the shear stresses on the GB plane. A continuum yield locus for transmission is formulated. In general, the overall dissociation and/or transmission behaviour is also determined by the Burgers vectors and associated steps of the primitive vectors of the grain boundary, and the criteria for dislocation transmission formulated by Lee et al . [Scripta Metall. 23 799 (1989); Phil. Mag. A 62 131 (1990); Metall. Trans. A 21 2437 (1990)] are extended to account for these factors.     

磁电弹性体中螺型位错与唇口裂纹的相互作用

研究磁电弹性体中螺型位错与唇口裂纹的相互作用。结合Muskhelishvili方法和干扰技术, 在假定裂纹面具有不可渗透条件下得到磁电弹性体中由位错和唇口裂纹所诱导的应力场、电场和磁场的解析解。应用广义Peach-Koehler公式,得到作用在位错上的影像力。通过数值算例,得到场强度因子的变化规律及影像力和广义力随位错位置的变化规律。     

Section images of dislocations normal to the surface of a 6H-SiC single crystal

Section topographs of edge and screw dislocations with an axis along [0001] in 6H-SiC are taken and interpreted, and the image formation is explained for this case. The contrast induced by various arrangements of dislocations within the Borrmann triangle is experimentally studied. The sign of the Burgers vector of an edge or screw dislocation normal to the crystal surface is shown to be unambiguously determined from the section-topograph image of this dislocation. The sign of the Burgers vector of a screw dislocation can also be determined from its image taken with Lang projection topography. The contribution of a long-range strain field to the section images of edge and screw dislocations normal to the crystal surface is revealed. The experimental contrasts recorded using section topography and Borrmann-effect-based topography are compared.     

一维六方准晶中螺形位错与楔形裂纹的相互作用

采用保角映射方法和扰动技巧,研究了一维六方准晶中螺形位错和半无限楔形裂纹的相互作用. 讨论了位错的位置和楔形角对作用在位错上的力的影响,得到了应力强度因子和作用在 位错上的力的解析解.此外,还详细地讨论了位错对裂纹的影响.当楔形角参数λ=1/2时, 半无限楔形裂纹退化成半无限尖裂纹,相应的结果 可以作为特殊情况而直接得到.     

自由表面附近运动的位错——各向异性介质情况

本文将Eshelby等人关于无限各向异性介质中静止位错弹性理论加以推广,并结合运用Green张量函数积分法提出计算半无限各向异性介质中在自由表面附近运动位错弹性场的处理方案,作为示例,以γ-Fe/自由空间系统进行数值计算,计算结果显示出位错运动对弹性场的影响,当位错运动速度v→0时,与静止位错的情况一致,离自由表面越近的场点处表面效应越显著,位错所受的“像力”表示自由表面对运动位错有“吸引”作用,本文所提出的简单理论和方法可适用于任意各向异性介质中运动位错的弹性场及所受“像力”的计算,这对研究介质的一些力 关键词：     

位错规范场对于位错芯区的应用

本文用位错连续分布方法分析了位错所产生的应变和应力场,用位错规范场表出了位错芯区的位错分布,并在一定规范条件下求解了位错规范场。得到了螺位错芯区内、外的应力场。在螺位错芯区外,其应力场与Volterra位错的应力场完全一样,而在芯区内,当ρ趋于零时,螺位错的应力场是有解的。最后计算了螺位错的能量。 关键词：     

Evolution of dislocation structure during deformation of γ-irradiated LiF crystals

The effect of γ irradiation on the mechanical characteristics and dislocation structure of slip bands in LiF crystals is studied at doses D⩽7.3×10⁸ R. Irradiation causes a substantial increase (up to a factor of 30) in the yield stress τ _y of the crystals, with τ _y ∝ D ^0.4 in the first approximation. The deformation shear increases in the slip bands of irradiated crystals, as do the densities of the screw and edge dislocation components, while the dislocation mean free paths decrease. Irradiation also raises the probability of twinning cross slip for screw dislocations. The observed effects are assumed to be related to the formation of a different kind of defects in the irradiated crystals, primarily clusters of implanted atoms. Fiz. Tverd. Tela (St. Petersburg) 39, 1072–1075 (June 1997)