Critical Current Density Through Grain Boundaries in High-Temperature Superconductors

In this paper, a theoretical study is proposed based on the assumption that the vortices on low-angle grain boundaries (GBs) in high-temperature superconductor (HTS) are mixed Abrikosov-Josephson (AJ) vortices. The critical current density through GB is obtained on the basis of the Bean critical model and the assumption that the periods of AJ vortices coincide with the ones of Abrikosov (A) vortices. The model also enables us to calculate J _c of HTS with an inclined GB. In addition, the effect of strain on critical current density is also taken into account in this model by considering the strain dependence of deparing current density within GB. There is a good agreement of our results with the classical power-law expression. The model proposed in this work can be used for simultaneous studies of the effects of misorientation angles, GB-inclined angles, and applied fields on the critical current density of polycrystalline HTS.     

Stress-dependent deformation behaviour in bulk nanocrystalline titanium–nickel alloys

In this study, the deformation mechanisms operating with stress in bulk nanocrystalline (NC) titanium–nickel with an average grain size below a critical size of 10–20?nm have been investigated. We demonstrate a sequential variation of the deformation mechanism from grain boundary (GB) sliding and grain rotation to grain growth and dislocation activity with the increase of the deformation stress. These deformation mechanisms are different from the previous understanding that below a critical grain size of 10–20?nm, GB sliding and grain rotation govern plastic deformation of NC materials.     

Effect of an Elliptical Inclusion on Critical Current Density of a Long Cylindrical High-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> Superconductor

An analytical investigation is presented to display the distribution of critical current flow and trapped magnetic field around an elliptical nonsuperconducting inclusion within a long cylindrical superconductor. The current streamlines, the critical current density, and the trapped field around the inclusion in the superconductor without deformation are obtained based on the Bean model and the method of conformal mapping. The results show that the critical current density of a superconductor will be decreased dramatically due to a macroscopic nonsuperconducting inclusion. Besides, the maximum trapped magnetic field is limited by the inclusion.     

An Exponential Model for Critical Current Density Through a Low-Angle Grain Boundary in a High-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Bold">c</Emphasis></Subscript> Superconductor

An analytical investigation is presented to display the distribution of critical current flow through a low-angle grain boundary in a high-T _c superconductor such as YBCO or Bi-2212 film. When a superconductor is subjected to a transport current or a magnetic field, the fluxoids are redistributed between the dislocations which comprise a low-angle grain boundary. A model considering the elastic interaction between a flux line and an edge dislocation is developed in this paper. Results of our model are consistent with those of the classic exponential model, while for high-angle grain boundaries with the misorientation angles ?? > 4^°, this model is invalid. It is helpful by using our model to understand the mechanisms of the effect of low-angle grain boundaries on critical current density.     

Grain size, grain boundary sliding, and grain boundary interaction effects on nanocrystalline behavior

A dislocation–density grain boundary (GB) interaction scheme, a GB misorientation dependent dislocation–density relation, and a grain boundary sliding (GBS) model are presented to account for the behavior of nanocrystalline aggregates with grain sizes ranging from 25 nm to 200 nm. These schemes are coupled to a dislocation–density multiple slip crystalline plasticity formulation and specialized finite element algorithms to predict the response of nanocrystalline aggregates. These schemes are based on slip system compatibility, local resolved shear stresses, and immobile and mobile dislocation–density evolution. A conservation law for dislocation–densities is used to balance dislocation–density absorption, transmission and emission from the GB. The relation between yield stresses and grain sizes is consistent with the Hall–Petch relation. The results also indicate that GB sliding and grain-size effects affect crack behavior by local dislocation–density and slip evolution at critical GBs. Furthermore, the predictions indicate that GBS increases with decreasing grain sizes, and results in lower normal stresses in critical locations. Hence, GBS may offset strength increases associated with decreases in grain size.     

Simultaneous grain boundary motion,grain rotation,and sliding in a tricrystal

Grain rotation and grain boundary (GB) sliding are two important mechanisms for grain coarsening and plastic deformation in nanocrystalline materials. They are in general coupled with GB migration and the resulting dynamics, driven by capillary and external stress, is significantly affected by the presence of junctions. Our aim is to develop and apply a novel continuum theory of incoherent interfaces with junctions to derive the kinetic relations for the coupled motion in a tricrystalline arrangement. The considered tricrystal consists of a columnar grain embedded at the center of a non-planar GB of a much larger bicrystal made of two rectangular grains. We examine the shape evolution of the embedded grain numerically using a finite difference scheme while emphasizing the role of coupled motion as well as junction mobility and external stress. The shape accommodation at the GB, necessary to maintain coherency, is achieved by allowing for GB diffusion along the boundary.     

Phase field simulations of elastic deformation-driven grain growth in 2D copper polycrystals

In this work, a phase field grain growth model coupled with a spectral stress calculation method is used to investigate the effect of applied elastic deformation on grain growth in 2D copper polycrystals with isotropic grain boundary properties. The applied deformation accelerates the grain growth compared to a relaxed polycrystal, though the effect of the deformation decreases rapidly with time. The softest grain orientations with respect to the applied deformation grow at the expense of other orientations, though they have higher elastic energy density. Due to a rapid decrease in the elastic energy stored in the system, the GB energy eventually dominates the growth leading to a linear change in the average grain area with time. Increasing the magnitude of the applied deformation accelerates the growth, while increasing the temperature accelerates the growth but decreases the effect of the applied deformation.     

Effect of cooperative grain boundary sliding and migration on dislocation emitting from a semi-elliptical blunt crack tip in nanocrystalline solids

A theoretical model is established to investigate the interaction between the cooperative grain boundary (GB) sliding and migration and a semi-elliptical blunt crack in deformed nanocrystalline materials. By using the complex variable method, the effect of two disclination dipoles produced by the cooperative GB sliding and migration process on the emission of lattice dislocations from a semi-elliptical blunt crack tip is explored. Closed-form solutions for the stress field and the force acting on the dislocation are obtained in complex form, and the critical stress intensity factors for the first dislocation emission from a blunt crack under mode I and mode II loadings are calculated. Then, the influence of disclination strength, curvature radius of blunt crack tip, crack length, locations and geometry of disclination dipoles, and grain size on the critical stress intensity factors is presented detailedly. It is shown that the cooperative GB sliding and migration and the grain size have significant influence on the dislocation emission from a blunt crack tip.     

新型含铝奥氏体耐热合金Fe-20Cr-30Ni-0.6Nb-2Al-Mo的动态再结晶行为

在Gleeble-3500热力模拟试验机上对一种新型奥氏体耐热合金(Fe-20Cr-30Ni-0.6Nb-2Al-Mo)进行单道次热压缩实验,结合OM、EBSD及TEM等表征手段,研究了该合金在950~1 100℃和0.01~1s-1热变形参数下的动态再结晶行为,采用回归法确定了合金的热变形激活能和表观应力指数,并以此构建其高温本构模型。实验结果表明,新型奥氏体耐热合金的应力水平随变形温度的升高而降低,随应变速率的增大而升高;动态再结晶行为更易发生在较高变形温度或较低应变速率下。采用lnθ-ε曲线的三次多项式拟合求解临界再结晶拐点的方法,较准确地预测了合金的动态再结晶临界点。此外,归纳出该合金在动态再结晶过程中的形核机制,主要包括应变诱导晶界迁移、晶粒碎化以及亚晶的合并。     

Grain Distribution for Optimal Strength in Homogeneous and Gradient Nano-Grained Coppers

The distribution of grains plays a crucial role in determining the strength of polycrystalline copper when the grain size is constant. Herein, the mechanical properties of homogeneous nano-grained (HNG) and gradient nano-grained (GNG) coppers with different grain distributions are examined using molecular dynamics (MD) simulations. The HNG-ordered structure has all triple junctions (TJs), whereas the random structure contains many quadruple and quintuple junctions. When grain size is below the critical size in the inverse Hall–Petch relationship, the high-density TJs in the HNG-ordered structure effectively inhibit grain boundary (GB) softening compared with the random structure, leading to higher strength. However, when grain size is above the critical size, subgrains are produced inside the large grains due to dislocation slip. In addition, disordered atoms in HNG-random structure are stacked in the quadruple and quintuple junctions, resulting in thicker GBs. This triggers grain boundary migration, and forms more subgrains at GBs. Subsequently, grain boundary sliding and grain rotation of subgrains induce partial recrystallization in the structure. This consecutively triggered deformation mechanism leads to extra strengthening in the random structure. Further research indicates that combining small-grained ordered and large-grained random structures can be a new approach to effectively strengthen GNG materials.     

Geometry and grain size effects on the fracture behavior of sheet metal in micro-scale plastic deformation

The demand on micro-parts is significantly increasing in the last decade due to the trend of product miniaturization. When the part size is scaled down to micro-scale, the billet material consists of only a few grains and the material properties and deformation behaviors are quite different from the conventional ones in macro-scale. The size effect phenomena occur in micro-scale plastic deformation or micro-forming and there are still many unknown phenomena related to size effect, including geometry and grain size effects. It is thus critical to investigate the size effect on deformation behavior, especially for the fracture behavior in micro-scale plastic deformation. In this research, tensile test was conducted with annealed pure copper foils with different thicknesses and grain sizes to study the size effects on fracture behavior. It is found that flow stress, fracture stress and strain, and the number of micro-voids on the fracture surface decrease with the decreasing ratio of specimen size to grain size. Based on the experimental results, dislocation density based models which consider the interactive effect of specimen and grain sizes on fracture stress and strain are developed and their accuracies are further verified and validated with the experimental results obtained from this research and prior arts.     

Size and microstructure effects on the mechanical behavior of FCC bicrystals by quasicontinuum method

The effects of structure and size on the deformation of <110> tilt bicrystals in copper are investigated by concurrent multiscale simulations at zero temperature. In the simulation of eleven grain boundary (GB) structures, a direct relation is shown between structural units and sliding at GBs. We find that GB sliding operates by atom shuffling events localized on one particular type of structural units, which are present in the GB period. When this type of unit is absent, the GB deformation process occurs by migration, or GB-mediated nucleation of partial dislocations with no sliding, depending on the initial GB configuration. The elastic limit causing sliding is found to vary slightly at zero temperature, but no correlation was obtained with the GB energy at equilibrium. Additionally, both modulus of rigidity, and elastic limit remain constant as the bicrystal size varies from 1 nm up to 25 nm. However, differences in the stress relaxation after sliding are observed with respect to the size.     

Modelling the strongest grain size in nanocrystalline FCC metals

A physical model is proposed to predict the critical grain size at which nanocrystalline FCC metals reach a maximum steady state flow stress. The model considers that nanocrystalline metals are composed of two phases. One is the grain boundary phase and the other is the grain interior phase. The grain boundary phase has specific deformation mechanism different to the grain interior phase. The critical grain size with the maximum steady state flow stress is predicted to decrease with deformation temperature and to increase with strain rate. Both normal and abnormal Hall–Petch relations can be described simultaneously by the model.     

The role of grain boundary sliding and reinforcement morphology on the creep deformation behaviour of discontinuously reinforced composites

In this study, the role of grain boundary sliding behaviour on the creep deformation characteristics of discontinuously reinforced composites is investigated numerically together with the other influencing parameters: reinforcement aspect ratio, grain size and interfacial behaviour between the reinforcement and the matrix. The results obtained for the composites are compared with results obtained for a polycrystalline matrix material having identical grain size and morphology. The results indicate that, with sliding grain boundaries, the stress enhancement factor for the composites is much higher than the one observed for the matrix material and its value increases with increasing reinforcement aspect ratio, reduction in the matrix grain size and sliding interfacial behaviour between the reinforcement and the matrix. In the composites, the contribution of the grain boundary sliding to overall steady state creep rates occurs in a larger stress range in comparison to the matrix material. Experimentally observed higher creep exponent values or stress dependent creep exponent values for the composites could not be explained solely by the mechanism of grain boundary sliding. However, experimentally observed large scale triple point grain boundary cavitation in the composites could occur due to large grain rotations resulting from grain boundary sliding.     

Grain Boundary Triple Junction Effects on the Fatigue Deformation and Cracking Behaviors of Copper Tricrystal and Tetracrystals

Cyclic symmetrical tension-compression fatigue tests in an axial plastic strain range of 2.0×10-4 to 1.5×10-3 were performed on three copper tetracrystal specimens containing two grain boundary triple lines as well as one copper tricrystal specimen employing a multiple step method. Experimental results show that the strengthening effect of triple junction (TJ) on axial saturation stress increased with increasing plastic strain amplitude. The strengthening effects owe much to the strain incompatibilities at TJ. The cyclic stress-strain (CSS) curves of tetracrystals are higher than that of tricrystal. At low strain amplitude, deformation at TJ is smaller than that near grain boundary (GB), which results in that the width of TJ effect zone is smaller than that near GB. Whether GB split or not is associated with the angle between GB and loading axis, activation of slip systems beside GB and the accommodation and annihilation of residual dislocations on GB planes.     

Prediction of grain boundary stress fields and microcrack initiation induced by slip band impingement

Slip localization is widely observed in metallic polycrystals undergoing cyclic deformation or post-irradiation tensile deformation, whatever their crystallographic structure. Hence, strong strain localization occurs in thin slip bands (SBs) inducing by the way local stress concentrations at their intersections with grain boundaries (GBs). Many GB stress field formulae based on the dislocation pile-up theory have been proposed since the pionnering work of Stroh and others. These allow the use of the Griffith criterion for prediction GB fracture initiation. However, recent observations show that assuming that slip is localized on a single atomic plane leads to unrealistic results. In fact, a large number of slip planes are plastically activated and then finite slip band thickness should be accounted for. Numerous crystalline finite element (FE) computations have been carried out using considering a slip bands with low critical resolved shear stress embedded in an elastic matrix. The computed GB normal and shear stress fields:

are considerable lower than the pile-up ones and exhibit strong dependency on the slip band thickness close to the SB corner

but are in fair agreement with the solution predicted by the pile-up theory far away.

Since the pile-up theory leads to the overestimation of the local GB stress fields, the main goal of the current paper is to perform analytical model of GB stress components based upon FE calculations. The effect of various parameters can be understood in the framework of matching asymptotic expansions which is usually applied to cracks with V notches of finite thickness. Finally, the predicted remote stresses to GB fracture in pre-irradiated austenitic stainless steels subjected to tensile loading in various environment are compared to experimental data and the pile-up based predictions.     

Impurity and vacancy segregation at symmetric tilt grain boundaries in Y<Subscript>2</Subscript>O<Subscript>3</Subscript>-doped ZrO<Subscript>2</Subscript>

Segregation energies of impurity ions and oxygen vacancies at grain boundaries in Y₂O₃-doped ZrO₂ as calculated from atomistic simulations using energy minimization and Monte Carlo methods are reported. Based on these energies, local defect equilibrium concentrations have been estimated. It is found that it is more energetically favorable for an yttrium ion to be accompanied by an oxygen vacancy at grain boundaries, although decrease in energy when associated with an oxygen vacancy differs from boundary to boundary. The segregation energy for a neutral defect complex consisting of a two yttrium ions and an oxygen vacancy at infinitely dilute concentration is highly correlated with the coordination environment of each site in the vicinity of the grain boundary (GB), and, in turn, GB energy. Although the estimated local equilibrium concentrations of these defects are similar, detailed analysis of the atomic coordination and defect distributions in the vicinity of a GB reveal that defect distributions, especially of oxygen vacancies, are dependent on the characteristics of the particular GB and that segregation in effect reduces lattice strains at the GB. Equilibrium concentration distributions of yttrium at grain boundaries are also given as a function of spatial resolution, and are useful for interpretation of experimental results.     

Superconductor Stability Against Quench and Its Correlation with Current Propagation and Limiting

This paper presents a numerical (finite element) analysis of superconductor stability and current propagation under random variations of critical superconductor parameters. Instead of using singular (homogeneous) values, random variations potentially are appropriate to take into account any conductor inhomogeneity that can be considered as an obstacle to current propagation. Traditional assumptions like homogeneous current distribution, critical temperature, critical current density and critical magnetic fields are not justified in general; a local disturbance (for example, release of mechanical stress energy), if not immediately distributed by solid conduction, would generate a transient increase of local conductor temperature. Local critical current density and magnetic field then will be reduced, and current distribution will change. Disturbances may arise also from transport currents that locally exceed the critical current of the superconductor. Disturbances of all kinds may increase the conductor temperature above its critical value. A local analysis of all superconductor states thus is mandatory to safely avoid a quench. As an extension of standard stability models, also flux flow resistive states are taken into account. We will try to find a possibly existing correlation between current propagation and superconductor stability. Fault current limiting is discussed as a special case of current propagation. The analysis is applied to a bundle of high-temperature superconductor (HTSC) filaments. As will be shown, temperature profiles in a superconductor do not allow a clear distinction between Ohmic resistive or flux flow resistive fault current limiting. Though frequently made in the literature, this separation is highly questionable, because Ohmic resistive and flux flow resistive states may locally coexist, side by side, but are not very stable in the superconductor volume.     

Grain boundary sliding and accommodation mechanisms during superplastic deformation of ZK40 alloy processed by ECAP

Controlling mechanism during superplastic deformation of ZK40 alloy processed by ECAP was identified. Effects of twinning and dynamic strain ageing (DSA) on superplasticity were analyzed. Amplitude in stress oscillation was correlated with solute atom concentration theoretically. Twinning can be an enhancing factor in grain boundary sliding and DSA had apparent influence on stress fluctuation; they were accommodation mechanisms for superplastic deformation through grain reorientation and interaction between solute atoms and dislocations, respectively. The interaction between mobile and forest dislocations played a dominant role for the occurrence of DSA, when dislocation density was relatively low in large grains. The effect of DSA became more active with increasing temperature, although grain boundary sliding (GBS) was the controlling mechanism throughout the whole process of superplastic deformation under elevated temperatures.