Crack-stimulated generation of deformation twins in nanocrystalline metals and ceramics

A theoretical model is proposed that describes the generation of deformation twins near brittle cracks of mixed I and II modes in nanocrystalline metals and ceramics. In the framework of the model, a deformation twin nucleates through stress-driven emission of twinning dislocations from a grain boundary distant from the crack tip. The emission is driven by both the external stress concentrated by the pre-existent crack and the stress field of a neighbouring extrinsic grain boundary dislocation. The ranges of the key parameters, the external shear stress, τ, and the crack length, L, are calculated within which the deformation-twin formation near pre-existent cracks is energetically favourable in a typical nanocrystalline metal (Al) and ceramic (3C-SiC). The results of the proposed model account for experimental data on observation of deformation twins in nanocrystalline materials reported in the literature. The deformation-twin formation is treated as a toughening mechanism effectively operating in nanocrystalline metals and ceramics.     

Emission of Dislocation Loops from Nanovoids in an FCC Crystal Subjected to Shear Deformation under Post-Cascade Shock Waves

The method of molecular dynamics is applied to the study of the effect of post-cascade shock waves generated in a solid irradiated by high-energy particles on the heterogeneous formation of dislocation loops in a simulated gold crystal containing a spherical nanovoid, which is subjected to shear deformation. The interaction between atoms is described with the use of a potential calculated by the embedded atom method. Shock waves are created by assigning a velocity exceeding the speed of sound in the simulated material to the boundary atoms of the computational cell. It is shown that two regions of increased mechanical stress are formed under shear deformation near the surface of a nanovoid, which are the sources of emerging partial dislocations. The main mechanism for the formation of dislocations is the displacement of a group of atoms towards the inner surface of the void, which does not contradict modern ideas about the heterogeneous formation of dislocations. It is shown that, when the values of shear stress are insufficient for the formation of dislocations, loop emission can be initiated by a post-cascade shock wave generated in the computational cell. As temperature increases, the number of nucleated dislocation loops increases, and, in addition, the formation of Lomer–Cottrell dislocations is observed, which is attributed to the additional tangential stresses created by the unloading wave. In this case, the formation of a stable dislocation loop in which the linear tension is balanced by the Peach–Koehler force due to external stress requires that the shock wave front affect the regions of increased stress near the void surface while propagating through the simulated crystal.     

Chain decay of low-angle tilt boundaries in nanocrystalline materials

In terms of two-dimensional dislocation-disclination dynamics, a theoretical model is developed to describe the decay of a low-angle tilt boundary in a deformed nanocrystalline material under the action of an externally applied elastic stress and of the elastic field of a neighboring decayed boundary. The critical external stresses are calculated at which the boundary decays and the dislocations making up this boundary either are trapped by the boundary that decayed earlier or break away from both boundaries. The decay of a low-angle tilt boundary is shown to result in a substantial decrease in the critical decay stresses for the neighboring boundaries, which can cause an avalanche-like chain decay of low-angle boundaries yielding high-density ensembles of mobile dislocations capable of carrying substantial plastic deformations and of forming shear bands in deformed nanocrystalline materials.     

Grain-boundary faceting at a = 3, [110]/{112} grain boundary in a cubic zirconia bicrystal

The atomic structure of a = 3, [110]/{112} grain boundary in a yttria-stabilized cubic zirconia bicrystal has been investigated by high-resolution transmission electron microscopy (HRTEM). It was found that the grain boundary migrated to form periodic facets, although the bicrystal was initially joined so as to have the symmetric boundary plane of {112}. The faceted boundary planes were indexed as {111}/{115}. The structure of the {111}/{115} grain boundary was composed of an alternate array of two types of structure unit: {112}- and {111}-type structure units. HRTEM observations combined with lattice statics calculations verified that both crystals were relatively shifted by (α/4)[110] along the rotation axis to form a stable grain-boundary structure. A weak-beam dark-field image revealed that there was a periodic array of dislocations along the grain boundary. The grain-boundary dislocations were considered to be introduced by the slight misorientation from the perfect = 3 orientation. The fact that the periodicity of the facets corresponded to that of the grain-boundary dislocations must indicate that the introduction of the grain-boundary dislocations is closely related to the periodicity of the facets. An atomic flipping model has been proposed for the facet growth from the initial = 3, {112} grain boundary.     

Dislocation dynamic modelling of the brittle–ductile transition in tungsten

Brittle–ductile transitions in metals, ceramics and semiconductors are closely connected with dislocation activity emanating near to crack-tips. We have simulated the evolution of crack-tip plasticity using a two-dimensional dislocation dynamics model which has been developed to include two symmetric slip planes intersecting the crack-tip, and applied to single-crystal tungsten. The dislocation mobility law used was physically based on double-kink nucleation on screw dislocations, with an activation energy reduced by the local stress. Even in the strong stress gradients near a crack-tip, the dislocations are found to self-organise so that the internal stress in the array is effectively constant with time and position over a wide range of strain rates and temperatures. The resultant net activation energy for dislocation motion is found to be constant and close to the activation energy experimentally measured for the brittle–ductile transition. Use of a fracture criterion based on the local crack-tip stress intensity factor, as modified by the stresses from the emitted dislocations, allows explicit prediction of the form and temperature of the brittle–ductile transition. Predictions are found to be in very close agreement with experiment.     

Etude des transitions ferroelectrique-paraelectrique des composes du systeme NaNbO3LiNbO3

We consider infinite arrays of dislocations in simple lattice models and show that stress-free uniform motion of an array of screw dislocations in a twist boundary can occur for a range of values of the spacing between dislocations.     

前视声呐圆弧接收阵列结构优化设计

针对前视声呐线阵波束形成各向同性较差及半圆阵有效孔径受限的问题,提出了一种优化的圆弧接收阵列结构设计方法。根据不同的成像开角,设计圆弧接收阵圆心角使全部阵元参与所有来波方向的波束形成。建立圆弧接收阵的远近场聚焦模型,并推导圆弧接收阵的指向性函数,根据边界波束栅瓣阈值条件计算具有最佳波束性能的圆弧接收阵半径。对圆弧阵、线阵及半圆阵在不同扇区开角下的波束性能及扫查开角120°、纵深100 m的仿真图像对比表明,在成像开角为90°到130°时,圆弧接收阵主瓣性能提升了8%,边界波束栅瓣级优化了4%,交叉向分辨深度相对线阵与半圆阵分别增加了20 m和45 m,同时参数存储量仅为线阵的2.7%。该阵列兼具有效孔径大、波束各向同性的优点,能有效提高前视声呐系统探测性能,并降低算法实现难度。      

Critical current of an inhomogeneous Josephson junction at an intergrain boundary with a random distribution of dislocations

The critical current J _c(θ) of an intergrain boundary is calculated as a function of the contact misorientation angle θ of the granules. It is assumed that the ordering parameter is suppressed in regions near boundaries with an enhanced mechanical stress induced by randomly distributed surface dislocations. The stress distribution function is determined using a probabilistic approach. Assuming that the weak coupling at the boundary is Josephson coupling, an analytic expression is found for the angular dependence J _c(θ) (for tilt and twist boundaries). The magnitude of the residual critical current of a boundary in a strong magnetic field is estimated. Fiz. Tverd. Tela (St. Petersburg) 40, 393–402 (March 1998)     

A computational approach towards modelling dislocation transmission across phase boundaries

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with its specific material properties, separated by a fully coherent and non-damaging phase boundary. Each phase is modelled as a continuum enriched with a Peierls–Nabarro (PN) dislocation region, confining dislocation motion to a discrete plane, the glide plane. In this paper, a single glide plane perpendicular to and continuous across the phase boundary is considered. Along the glide plane bulk induced shear tractions are balanced by glide plane shear tractions based on the classical PN model. The model's ability to capture dislocation obstruction at phase boundaries, dislocation pile-ups and dislocation transmission is studied. Results show that the phase contrast in material properties (e.g. elastic stiffness, glide plane properties) alone creates a barrier to the motion of dislocations from a soft to a hard phase. The proposed model accounts for the interplay between dislocations, external boundaries and phase boundary and thus represents a suitable tool for studying edge dislocation–phase boundary interaction in two-phase microstructures.     

Interaction of dislocation pile-up with a low-angle tilt boundary: a discrete dislocation dynamics study

Abstract

The pile-up of dislocations between two low-angle tilt boundaries (LATB) in an fcc crystal was simulated using three-dimensional discrete dislocation dynamics. The LATB was constructed using glissile edge dislocations stacked on each other. The dislocations in the pile-up were chosen such that their reactions with the dislocations in the LATB resulted in glissile junctions. Parallel pairs of dislocations were inserted to a maximum allowable value estimated from theoretical expressions. A resolved shear stress was applied and increased in steps so as to move the dislocations in the pile-up towards the boundaries. The shear stress required to break the lead dislocation from the wall was determined for varying spacings between the two boundaries. The shear stress and boundary spacing followed the Hall–Petch type relation. Dislocation pile-ups without a LATB were also simulated. The spacing of the dislocations in the pile-up with LATB was found to be closer (ie higher dislocation density) than that without LATB. It was shown through analytical expressions that LATB exerts an attractive force on the dislocations in the pile-up thereby creating a denser pile-up.     

Generation of dislocations introduced by bending stress in a Si wafer

Distribution and morphology for dislocations introduced in (001) Si wafers subjected to bending stress at 800°, 900°, and 1100°C were investigated. For wafers bent around a [110] axis at 900° and 1100°C, straight dislocations appeared along the [110] direction only near the neutral plane, and were absent at the surfaces where bending stress is greatest. However, for wafers bent at 800 °C, such straight dislocations were not formed. Dependence of the dislocation distribution and morphology on heat treatment temperature is explained on the basis of interaction between bending stress and SiO₂ precipitates introduced in bulk. Also, it was found that the straight [110] dislocations remained still near the neutral plane, even when additional reverse bending stress was applied around an axis parallel to the dislocations, but were transfered toward the tensile surface by bending around an axis normal to the dislocation direction.     

Towards a further understanding of dislocation pileups in the presence of stress gradients

This study is an essential complement and extension to the stress-gradient concept recently proposed by Hirth. An analytic method is presented for studying the behaviour of double-ended dislocation pileup in the presence of various stress gradients by solving a singular integral equation based on the continuous approximation of dislocations. Four special cases of double-ended pileup in the presence of stress gradients are discussed in detail. The corresponding dislocation distribution, the length of pileup, the total number of dislocations within the pileup and the force on the leading dislocations at the pileup ends are derived, respectively. It is shown that both the number of dislocations and the force on the leading dislocation in a pileup are sensitive to the relative magnitude of stress near the dislocation source and both are less than that in constant stress case. Of particular importance, it is indicated that the small-scaled materials subjected to a stress involving a gradient would be stronger than that under a constant stress. Applied to wire torsion and foil bending, the stress gradient model predicts an increase in the initial yielding, which is in reasonable agreement with the recent experimental data. The proposed stress gradient concept may provide a new physical insight into the size-dependent plasticity phenomena at small length scale.     

Grain Growth During Superplastic Deformation

Significant grain growth occurring during superplastic deformation is related to the micro-mechanism of superplastic flow. Observations performed on the deformed surface of superplastically deformed tensile and shear Pb-62%Sn samples and bi-axially formed AA7475 samples directly indicate that cooperative grain boundary sliding, i.e. sliding of grain groups, is accompanied by cooperative grain boundary migration that can result in an enhanced grain growth. Such a long range correlation in migration of sliding grain boundaries is related to movement of grain boundary dislocations having a step associated with its core. Observed correlation between grain size and strain measured in different regions of a superplastically formed Ti-alloy part and alignment of grain boundaries along shear surfaces support coupling of grain boundary sliding and migration. A model of grain growth considering climb of cellular dislocations, topological defects in a grain array, has been expanded to incorporate gliding and mixed cellular dislocations.     

Grain boundary sliding and lattice dislocation emission in nanocrystalline materials under plastic deformation

A theoretical model is proposed to describe the physical mechanisms of hardening and softening of nanocrystalline materials during superplastic deformation. According to this model, triple interface junctions are obstacles to glide motion of grain boundary dislocations, which are carriers of grain boundary glide deformation. Transformations of an ensemble of grain boundary dislocations that occur at triple interface junctions bring about the formation of partial dislocations and the local migration of triple junctions. The energy characteristics of these transformations are considered. Pileups of partial dislocations at triple junctions cause hardening and initiate intragrain lattice sliding. When the Burgers vectors of partial dislocations reach a critical value, lattice dislocations are emitted and glide into adjacent grains, thereby smoothing the hardening effect. The local migration of triple interface junctions (caused by grain boundary sliding) and the emission of lattice dislocations bring about softening of a nanocrystalline material. The flow stress is found as a function of the total plastic strain, and the result agrees well with experimental data.     

Energy of a wedge-shaped nanotwin calculated in terms of a dislocation mesoscopic model

The total energy of a wedge-shaped micro- and nanotwin is calculated in terms of a dislocation mesoscopic model. The total energy of the twin is represented as a sum of the elastic energy, energy of interaction between twinning dislocations, and stacking-fault energy of partial dislocations of the wedge-shaped twin. It is found that the evolution of the twin is controlled by the energy of interaction between twinning dislocations: in the case of a microtwin, it is five orders of magnitude higher than the elastic energy and six orders of magnitude higher than the stacking-fault energy. In the case of a nanotwin with the number of twinning dislocations at the twin boundary less than 20, all the three energies listed above are of the same order of magnitude. Therefore, all the components of the total energy contribute to the origination of a wedge-shaped twin. As the length of the twin increases with its width and the number of twinning dislocations at twin boundaries fixed, the total energy modulo grows although the density of twinning dislocations at twin boundaries decreases. This indicates that long-range stress fields due to twinning dislocations play an important part in the evolution of a wedge-shaped twin.     

Examination of Dislocation Mechanism on Grain Boundary Sliding in High Angle Grain Boundaries by Stress Change Test

In order to understand the factors dominating grain boundary sliding, stress change tests and stress reversal tests were conducted on aluminum bicrystal specimens with high angle grain boundaries. It is found that small change in stress results in the remarkable change in the rate of grain boundary sliding. Stress reversal tests showed that grain boundary slide hardening does not work for the sliding to the direction opposite to that before the stress reversal. Mean internal stresses for the dislocations contributing to grain boundary sliding are experimentally measured by a method consisting of stress change and annealing. It is found that the velocity of dislocations in the grain boundary is in proportion to the mean effective stress.     

单向拉伸作用下Cu(100)扭转晶界塑性行为研究

应用分子动力学方法研究了在不同扭转角度下的Cu（100）失配晶界位错结构,以及不同位错结构对晶界强度的影响.模拟结果表明：小角度扭转晶界上将形成失配位错网,失配位错密度随着晶粒之间的失配扭转角度的增加而增加.变形过程中,位错网每个单元中均产生位错形核扩展.位错之间的塞积作用影响晶界的屈服强度：随着位错网格密度的增加,位错之间的塞积作用增强,界面的屈服强度得到提高.大角度扭转晶界将形成面缺陷,在变形中位错由晶界角点处形核扩展,此时由于面缺陷位错开动应力趋于一致,因此晶界的临界屈服强度趋于定值. 关键词： 扭转晶界 失配位错网 强化机理 分子动力学     

Elastic properties of dislocations lying in a planar boundary

The formulae for the stress field, self-energy and interaction energy of a dislocation lying in a planar boundary between two anisotropic media are given. The solution is applied to the twinning dislocations, especially in bcc metals. A similar solution is also given for a dislocation lying in the boundary between two different isotropic media.     

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.     

Flexible Ab initio boundary conditions: simulating isolated dislocations in bcc Mo and Ta

We report the first ab initio density-functional study of the strain field and Peierls stress of isolated <111> screw dislocations in bcc Mo and Ta. The local dislocation strain field is self-consistently coupled to the long-range elastic field using a flexible boundary condition method. This reduces the mesoscopic atomistic calculation to one involving only degrees of freedom near the dislocation core. The predicted equilibrium core for Mo is significantly different from previous atomistic results and the Peierls stress shows significant non-Schmid behavior as expected for the bcc metals.