Kinetics of Grain Boundary Recovery in Deformed Polycrystals

Annealing kinetics are studied for nonequilibrium ensembles of dislocations occurring in grain boundaries during plastic deformation. Two types of dislocation ensembles are considered: 1) walls of sessile extrinsic grain boundary dislocations (EGBDs), which cause a change of the GB misorientation angle, and 2) arrays of glissile EGBDs having a Burgers vector tangential to the grain boundary plane. For both types similar exponential relationships are obtained for the relaxation of the average EGBD density, with approximately the same characteristic time proportional to the cube of grain size.     

A disclination model for twinning and de-twinning of nanotwinned copper

The twinning and de-twinning processes within grains of nanotwinned copper (nt-Cu) are schematically demonstrated using the concept of wedge disclination quadrupoles. The stable twin nucleus size and the equilibrium equation of the applied shear stress and twin width during twin growth are obtained. The dependence of the critical resolved shear stress for twinning on the grain size, which conforms to the classic Hall–Petch relationship, is theoretically modelled. Additionally, the disclination quadrupole model for de-twinning is used to interpret the strength softening in nt-Cu. Relative to the classic kinetic and energetic models, this novel approach is more compatible with the experiments.     

Effect of screening of the elastic field of the disclination located at the interface of two half-spaces by a dislocation ensemble

The self-consisted dynamics of a dislocation ensemble in the elastic field of the disclination located at the interface of two half-spaces has been considered for two cases, namely, for half-spaces with different densities of mobile dislocations and for a bicrystal where dislocations are absent in one half-space. The elastic energy W of the disclination screened by the dislocation ensemble has been calculated for the rectangular zone centered relative to the disclination. It has been shown that W increases as ～ $\sqrt R $ (R is the transverse size of the zone in the plastically deformed half-space).     

Competing relaxation mechanisms in a disclinated nanowire: temperature and size effects

This Letter reports a molecular dynamics study of the temperature and size dependence of disclination relaxation in a bicrystalline titanium nanowire. The simulations show that an unstable disclination may relax via crack nucleation and/or structural transformation. The critical disclination strength to nucleate a crack decreases with the nanowire diameter at 0 K, but an inverse relation may exist at higher temperatures. Similar relaxation mechanisms are operative in other hcp materials. The results suggest that grain boundaries in nanostructured materials can be disordered through disclinations which relax via amorphization.     

Redistribution of dislocations in silicon near stress concentrators

The distribution of defects in dislocation tracks in silicon plates was studied for various indentation angles. The regularities of variations in the linear density and maximum path of dislocations in slip bands are established. A model is proposed to describe the distribution of dislocations in the dislocation tracks. By fitting the theory to the experimental data, the dependence of this distribution on the energy relaxation time is determined.     

Contribution from dislocation to deformation resistance in polycrystals of copper-based solid solutions

The evolution of dislocation structure in solid solutions of Cu-Al and Cu-Mn systems with different grain sizes and at different test temperatures is studied by means of transmission electron diffraction microscopy. The scalar density of dislocations is measured and its relationship to the flow stress of alloys is determined. Changes in the contribution from dislocation hardening to deformation resistance upon variations in the contributions associated with changes in grain size, solid-solution hardening, and test temperature are analyzed.     

Non-singular dislocation continuum theories: strain gradient elasticity vs. Peierls–Nabarro model

Abstract

Non-singular dislocation continuum theories are studied. A comparison between Peierls–Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses, plastic distortions and dislocation core shapes are analysed and compared for the two models. The main conclusion of this study is that due to their characteristic properties, the non-singular displacement fields, non-singular stresses and dislocation core shape of screw and edge dislocations obtained in the framework of strain gradient elasticity are more realistic and physical than the corresponding fields of the Peierls–Nabarro model. Strain gradient elasticity of dislocations is a continuum dislocation theory including a weak non-locality within the dislocation core and predicting the size and shape of the dislocation core. The dislocation core is narrower in the strain gradient elasticity dislocation model than in the Peierls–Nabarro model and more evenly distributed in two dimensions. The present analysis shows that for the modelling of the dislocation core structure the non-singular dislocation fields of strain gradient elasticity are the suitable ones.     

To the Question of Forming Geometrically Necessary Disclinations in Triple Junctions of Grain Boundaries in Metals

The Bollman and King models are tested by means of molecular dynamics simulation for the formation of geometrically necessary disclinations in triple junctions of grain boundaries in metals. It is shown that the stresses arising in a triple junction due to the non-multiple lengths of low-angle tilt boundaries to the distance between grain boundary dislocations is not compensated for mainly by the formation of an additional disclination in the junction (the King model) but by the bending of one or several grain boundaries, accompanied by the displacement of grain boundary dislocations. A triple junction of the Bollman U-type (containing a geometrically necessary disclination) is not formed at the conjugation of tilt boundaries with common misorientation along the junction or at the conjugation of mixed-type boundaries.     

Quantifying the grain boundary resistance against slip transfer by experimental combination of geometric and stress approach using stage-I-fatigue cracks

In recent studies, many groups have investigated the interaction of dislocations and grain boundaries by bi-crystals and micro-specimen experiments. Partially, these experiments were combined with supplementary simulations by discrete dislocation dynamics, but quantitative data for the grain boundary resistance against slip transfer is still missing. In this feasibility study with first results, we use stage-I-fatigue cracks as highly localised sources for dislocations with well-known Burgers vectors to study the interaction between dislocations in the plastic zone in front of the crack tip and selected grain boundaries. The stress concentration at the grain boundary is calculated with the dislocation-free zone model of fracture using the dislocation density distribution in the plastic zone from slip trace height profile measurements by atomic force microscopy. The grain boundary resistance values calculated from common geometric models are compared to the local stress distribution at the grain boundaries. Hence, it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer to a self-contained concept. As a result, the prediction of the grain boundary resistance effect based on a critical stress concept is possible with knowledge of the geometric parameters of the grain boundary only, namely the orientations of both participating grains and the orientation of the grain boundary plane.     

Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional,anisotropic, elastic,and piezoelectric media. II. Infinite straight dislocation and Frank disclination

The fields of stress and electric displacement caused by infinitely extended straight dislocations and Frank disclinations are deduced from the author's statements for the fields caused by a continuous distribution of dislocations and disclinations (S. Minagawa, Phil. Mag. 84 2229 (2004)). The multiple integrals in the original statements are converted into functions of space coordinates. Cauchy's theorem plays an important part. The improper integral that appears in computations of the fields around a Frank disclination is interpreted as its finite part by Hadamard. Examples are the fields around an infinite straight defect in caesium copper chloride, as well as those in gallium arsenide. The contours and zero lines are plotted to illustrate the fields caused by a dislocation and a disclination dipole.     

Dynamics of threading dislocations in porous heteroepitaxial GaN films

Behavior of threading dislocations in porous heteroepitaxial gallium nitride (GaN) films has been studied using computer simulation by the two-dimensional discrete dislocation dynamics approach. A computational scheme, where pores are modeled as cross sections of cylindrical cavities, elastically interacting with unidirectional parallel edge dislocations, which imitate threading dislocations, is used. Time dependences of coordinates and velocities of each dislocation from dislocation ensembles under investigation are obtained. Visualization of current structure of dislocation ensemble is performed in the form of a location map of dislocations at any time. It has been shown that the density of appearing dislocation structures significantly depends on the ratio of area of a pore cross section to area of the simulation region. In particular, increasing the portion of pores surface on the layer surface up to 2% should lead to about a 1.5-times decrease of the final density of threading dislocations, and increase of this portion up to 15% should lead to approximately a 4.5-times decrease of it.     

Theory of magnetic cold-work peak in ferromagnetic materials

The magnetic after effect due to dislocations is investigated for three types of configurations: i) randomly distributed immobile point defects, ii) Cottrell clouds, iii) strongly bound defects in the dislocation core. It is shown that only the case of the mobile Cottrell cloud leads to a simple Debye process, whereas the other cases must be described by a more general relaxation function. The role of point defects in the core of dislocations is studied in some details. In this case the relaxation time is found to be determined mainly by the binding energy of the impurity atoms to the dislocation core.     

激光冲击690高强钢位错组态与晶粒细化的实验研究

为研究激光冲击材料内部位错组态和晶粒细化的关系,用脉冲激光对690高强钢试样进行了冲击强化处理,采用扫描电镜和透射电镜分别获得了冲击后试样的扫描电子显微像和透射电子显微像、高分辨电子显微像,并对高分辨电子显微像进行快速傅里叶逆变换,从位错组态角度建立了激光冲击690高强钢晶粒细化模型.结果表明,690高强钢试样经功率密度为5.09 GW/cm^2的激光冲击加载后,其材料内部位错增殖、表层晶粒细化,截面晶粒尺寸大小分布在80~200 nm;析出相与基体保持半共格关系,基体中分布着众多刃型位错、位错偶以及扩展位错等缺陷,其中位错偶是由带割阶的螺型位错运动形成;通过由位错、扩展位错、空位等构成的几何位错界面扩展交汇把原始大晶粒分割成细小晶粒;激光冲击690高强钢晶粒细化模型可以描述激光冲击690高强钢位错运动主导的晶粒细化过程.     

Relaxation of a dislocation in a nanocrystallite

Experimental studies of dislocations in nanoparticles are just beginning. The corresponding theoretical models are still lacking. In this context, the author analyzes relaxation of a dislocation in a nanoparticle. Mechanistically, this process is considered to occur primarily via dislocation drift induced by the stress-related image forces. Elementary dislocation displacements include the formation of a kink at one of the sides of the dislocation line, its diffusion along this line, and annihilation at the opposite side. For this mechanism, the dependence of the time of dislocation disappearance on the nanoparticle size has been identified.     

Continuous description of a grain boundary in forsterite from atomic scale simulations: the role of disclinations

We present continuous modelling at inter-atomic scale of a high-angle symmetric tilt boundary in forsterite. The model is grounded in periodic arrays of dislocation and disclination dipoles built on information gathered from discrete atomistic configurations generated by molecular dynamics simulations. The displacement, distortion (strain and rotation), curvature, dislocation and disclination density fields are determined in the boundary area using finite difference and interpolation techniques between atomic sites. The distortion fields of the O, Si and Mg sub-lattices are detailed to compare their roles in the accommodation of lattice incompatibility along the boundary. It is shown that the strain and curvature fields associated with the dislocation and disclination fields in the ‘skeleton’ O and Si sub-lattices accommodate the tilt incompatibility, whereas the elastic strain and rotation fields of the Mg sub-lattice are essentially compatible and induce stresses balancing the incompatibility stresses in the overall equilibrium.     

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.     

Grain size refinement due to relaxation of disclination junction configurations in the course of plastic deformation of polycrystals

A model is proposed for the formation of the substructure in polycrystals during plastic deformation. According to this model, fragmentation of a grain occurs through the formation of a system of diagonal low-angle boundaries, which originate at the edges of a rectangular grain. Misorientation boundaries form through relaxation of a nonsymmetric junction quadrupole disclination configuration accumulated at the grain corners under severe deformation when the disclination strength reaches a certain critical value. The energetics of this process is analyzed. A general case is considered where the disclinations at the junctions of the chosen grain differ in strength. The energetic approach used makes it possible to determine the misorientation angle ω_x of the resulting boundaries corresponding to the maximum energy gain and to find the dependence of this angle on the degree of asymmetry of the quadrupole configuration of junction disclinations. According to the proposed model, the splitting of a grain with a short edge greater than 0.5 μm is energetically favorable and decreases the latent energy of the grain for any ratio between the junction disclination strengths if the grain length-to-width ratio is less than 30. It is shown that the minimum possible grain size in the proposed model does not exceed 0.1 μm.     

Dislocation dynamics in nanocrystalline nickel

It is believed that the dynamics of dislocation processes during the deformation of nanocrystalline materials can only be visualized by computational simulations. Here we demonstrate that observations of dislocation processes during the deformation of nanocrystalline Ni with grain sizes as small as 10 nm can be achieved by using a combination of in situ tensile straining and high-resolution transmission electron microscopy. Trapped unit lattice dislocations are observed in strained grains as small as 5 nm, but subsequent relaxation leads to dislocation recombination.