Grain boundary curvature and grain growth kinetics with particle pinning

Second-phase particles are used extensively in design of polycrystalline materials to control the grain size. According to Zener’s theory, a distribution of particles creates a pinning pressure on a moving grain boundary. As a result, a limiting grain size is observed, but the effect of pinning on the detail of grain growth kinetics is less known. The influence of the particles on the microstructure occurs in multiple length scales, established by particle radius and the grain size. In this article, we use a meso-scale phase-field model that simulates grain growth in the presence of a uniform pinning pressure. The curvature of the grain boundary network is measured to determine the driving pressure of grain growth in 2D and 3D systems. It was observed that the grain growth continues, even under conditions where the average driving pressure is smaller than the pinning pressure. The limiting grain size is reached when the maximum of driving pressure distribution in the structure is equal to the pinning pressure. This results in a limiting grain size, larger than the one predicted by conventional models, and further analysis shows consistency with experimental observations. A physical model is proposed for the kinetics of grain growth using parameters based on the curvature analysis of the grain boundaries. This model can describe the simulated grain growth kinetics.     

Deformation-induced changes in single-phase Al-0.1Mg alloy

Al-0.1wt.%Mg has been chosen to explore the effects of deformation on the microstructure of nominally single-phase materials. For these materials, the rate of static grain growth is much higher compared to that of Zener pinned systems and dual-phase alloys, where growth is hindered due to the pinning force exerted by second-phase particles on grain boundaries. Therefore, deformation-induced microstructural changes in single-phase alloys occur without any restricting pinning pressure. This paper illustrates the complex effect of deformation on the microstructural changes mainly associated with dynamic recovery. The process affects the initial microstructure due to an intensive substructure development. Dynamic recrystallisation, associated with the formation of new grains, is considered to be a transient phenomenon that quantitatively influences the mean grain size formed during straining. This work also aims to estimate the stored energy of the deformed regions and texture components to explore their contribution to the migration of high-angle grain boundaries.     

相场法模拟第二相颗粒对柱状晶形成的影响

基于定向退火条件下的移动热区模型,采用相场法研究第二相颗粒对多晶材料中柱状晶结构形成的影响.结果表明:第二相颗粒对柱状晶结构的形成具有抑制作用,其抑制作用随第二相颗粒体积分数的增加和第二相颗粒尺寸的减小而增强.定向退火条件下第二相颗粒对晶粒极限尺寸的影响遵循Zener关系.为了获得良好的柱状晶结构,应尽量减少材料中第二相颗粒的体积分数及其在晶界上的弥散分布.     

Phase-field study of the second phase particle effect on texture evolution of polycrystalline material

The second phase particle effect on texture evolution of polycrystalline material is studied through phase-field method. A unique field variable is introduced into the phase-field model to represent the second phase particles. Elastic interaction between particles and grains is also considered. Results indicate that in the presence of second phase particles the average particle diameter turns smaller than in the absence of these particles and retards texture formation by pinning effect. The second phase particles change the strain energy profile, which tremendously influences the pinning effect.     

Grain boundary pinning in two-phase materials

The calculation of the Zener stress involves two parts (1) the determination of the force between a particle and a grain boundary, and the shape of the resulting dimple on the grain boundary and (2) the statistical problem of summing the forces over the boundary. Calculations of the forces from spherical, needle-shaped and plate shaped particles are used to estimate the Zener stress by means of a point obstacle model and statistical dimple model. The results are compared with experimental determinations of stable grain sizes, with a computer simulation growth and with experimental measurements of retarded primary recrystallisation. When the particles are non-spherical or inhomogeneously distributed the Zener stress is anisotropic; this effect has been observed experimentally.     

Contributions of different strengthening mechanisms to the shear strength of an extruded Mg–4Zn–0.5Ca alloy

The shear deformation behaviour of an extruded Mg–4Zn–0.5Ca alloy was studied using shear punch testing at room temperature. The extrusion process effectively refined the microstructure, leading to a grain size of 4.6 ± 1.4 μm. Contributions of different strengthening mechanisms to the room temperature shear yield stress, and overall flow stress of the material, were calculated. These mechanisms include dislocation strengthening, grain boundary strengthening, solid solution hardening and strengthening resulting from second-phase particles. Grain boundary strengthening and solid solution hardening made significant contributions to the overall strength of the material, while the contributions of second-phase particles and dislocations were trivial. The observed differences between calculated and experimental strength values were discussed based on the textural softening of the material.     

Consolidation of cryomilled Al–Si using spark plasma sintering

Cryomilled eutectic aluminum–12% silicon powder was sintered using spark plasma sintering (SPS) to create bulk compacts. The cryomilling serves to break up and disperse the eutectic phase in the powder to create a well-distributed Si phase throughout the matrix and to modify the morphology of the Si phase from plate-like to spherical, whilst refining the aluminium grain size to the nanometric level. The effects of different sintering times and temperatures using SPS on the densification of the powder, the aluminium grain size evolution, the growth of the Si phase and the morphology change of the Si phase were investigated. The compacts were analysed using X-ray diffraction, scanning electron microscopy and optical microscopy. The initial stages of densification appear to be highly dependent on the yield strength of the powder. An estimate of the temperature gradient seen in the powder bed was made and calculated to be near 200?°C at the highest point. The Al and Si phase growth was investigated and it was observed that the Si coarsening rate is increased due to the increased volume of grain boundaries. As the Si coarsens, any pinning effect on the Al grains is lost, resulting in a highly unstable microstructure that coarsens rapidly.     

Atomistic calculation of internal stress in nanoscale polycrystalline materials

Internal stress in polycrystalline materials is an intrinsic attribute of the microstructure that affects a broad range of material properties. It is usually acquired through experiment in conjunction with continuum mechanics modelling, but its determination at nanometre and submicron scales is extremely difficult. Here, we report a bottom-up approach using atomistic calculation. We obtain the internal stress in polycrystalline copper with nanosized grains by first computing the stress associated with each atom and then sorting the stress into those associated with different self-equilibrating length scales, i.e. sample scale and grain cell, which gives type I, II and III residual stresses, respectively. The result shows highly non-uniform internal stress distribution; the internal stress depends sensitively on grain size and the grain shape anisotropy. Statistical distributions of the internal stresses, along with the means and variance, are calculated as a function of the mean grain size and temperature. The implementation of this work in assisting the interpretation of experimental results and predicting material properties is discussed.     

The Effect of Severe Plastic Deformation on the Structure and Mechanical Properties of Al–Mg–Li Alloys

The structural-phase state and mechanical properties of commercial aluminum alloys produced by severe plastic deformation are studied and compared to the initial polycrystalline state. This kind of treatment is found to give rise to the formation of a homogeneous ultrafine-grained structure with second-phase particles occurring predominantly along grain boundaries. With this structure, the strain-temperature and strain-rate intervals wherein the superplastic properties of the alloys under study are observed are shifted to lower temperatures and higher rates.     

多晶材料晶粒生长粗化过程的相场方法模拟

基于采用晶体有序化程度参量ψ和晶体学取向θ来表示多晶粒结构的相场模型,利用自适应有限元方法模拟了多晶材料等温过程中的晶粒粗化现象.模拟结果显示,在曲率作用下,通过晶界迁移弯曲晶界逐渐平直化,小晶粒逐渐被大晶粒吞并,当晶界之间的取向差较小时,满足一定能量和几何条件的两晶粒在界面能作用下会发生转动,合并为单个晶粒.模拟结果与实验结果符合较好.因此,该相场模型可以很好地用来模拟固态相变中多晶材料的生长粗化等现象. 关键词： 相场 晶界迁移 晶粒转动 粗化     

The Shape of the Moving Grain Boundary in the Reversed-Capillary Technique Under Consideration of the Drag Effect

The shape of the curved part of the migrating grain boundary driven by capillary forces was studied for the reversed-capillary bicrystal technique. A comparison of experimentally observed and theoretically calculated shapes showed good agreement when the drag effect by mobile obstacles was taken into account. So far previous studies dealing with the reversed-capillary technique have not considered the drag effect. Consequently, they assume a scaling behavior of the shape of the moving grain boundary. In this study it is shown that this assumption generally is not possible for the reversed-capillary technique. Furthermore, it is shown that the geometry factor used for determination of the driving force is dependent on the displacement. Problems specific to the reversed-capillary technique due to the drag effect are discussed. The analysis of the boundary shape is presented as a tool to distinguish free and dragged motion.     

Three-dimensional finite-element simulation of Zener pinning dynamics

The Zener pinning dynamics of a moving boundary interacting with one or more particles is described by a three-dimensional (3D) finite-element model. The model, based upon a variational formulation for boundary motion by viscous drag, is solved by a finite-element method to obtain the velocity at each node of triangular linear elements on the grain boundary. It is first applied to relatively simple and validated cases, for which analytical and numerical results are available. These cases correspond to an axisymmetrical geometry, in which the grain boundary interacts with a centred particle. A simple analytical pinning criterion is derived from these simulations. The model is then applied to general 3D cases, in which the grain boundary interacts with arbitrarily localized and sized particles. The aim of these 3D simulations is to quantify the influence of the position and the number of particles on the average grain-boundary velocity. It is shown, for example, that the drag effect is enhanced when the particle, or the cluster of particles, is off-centre and that pinning is less efficient with several particles than with a single particle producing the same Zener force.     

Current percolation and anisotropy in polycrystalline MgB(2)

The influence of anisotropy on the transport current in MgB(2) polycrystalline bulk samples and wires is discussed. A model for the critical current density is proposed, which is based on anisotropic London theory, grain boundary pinning, and percolation theory. The calculated currents agree convincingly with experimental data, and the fit parameters, especially the anisotropy, obtained from percolation theory agree with experiment or theoretical predictions.     

颗粒介质尺度效应的抗剪试验及物理机理分析

针对颗粒介质力学特性的颗粒尺度效应研究,选用土矿物颗粒制备不同颗粒尺度的抗剪试样,进行一系列直剪快剪和三轴抗剪试验,测得了不同颗粒粒径和体分比试样的变形曲线及剪应力强度;基于颗粒间微观作用力与重力比值和胞元体模型,首次从微观和细观角度解释颗粒尺度效应的物理机理.结果表明,随着介质中粗颗粒的比例增加和粒径减小,介质变形特性增强,剪应力强度也随之提高;体分比对变形和强度特性的影响比粒径的影响更加显著.基于介质特性尺度效应物理机理分析,提出衡量介质颗粒聚集和摩擦效应的微重比判别参数以及应变梯度和变形协调微裂纹引起颗粒尺度效应的细观机理解释;文中提出的胞元体模型大大减少了颗粒物质体系的计算自由度,为工业和工程设计的计算建模提供一种可行途径.     

On defects in aluminium single crystal thin films

Defects in Al single crystal thin films prepared by epitaxial growth on mica were investigated by transmission electron microscopy. Dislocations, subgrain boundaries, grain of different orientation and separated polycrystalline regions were observed in the single crystal matrix with density dependent on the pressure of residual gases.     

Grain Boundary Dynamics: A Novel Tool for Microstructure Control

The reaction of grain boundaries to a wide spectrum of forces is reviewed. Curvature, volume energy and mechanical forces are considered. The boundary mobility is strongly dependent on misorientation, which is attributed to both grain boundary structure and segregation. In magnetically anisotropic materials grain boundaries can be moved by magnetic forces. For the first time a directionality of boundary mobility is reported. Flat boundaries can also be moved by mechanical forces, which sheds new light on microstructure evolution during elevated temperature deformation. Curvature driven and mechanically moved boundaries can behave differently. A sharp transition between the small and large angle boundary regime is observed. It is shown that grain boundary triple junctions have a finite mobility and thus, may have a serious impact on grain growth in fine grained materials. The various dependencies can be utilized to influence grain boundary motion and thus, microstructure evolution during recrystallization and grain growth.     

Pinning frequencies of the collective modes in alpha-uranium

Uranium is the only known element that features a charge-density wave (CDW) and superconductivity. We report a comparison of the specific heat of single-crystal and polycrystalline alpha-uranium. In the single crystal we find excess contributions to the heat capacity at 41 K, 38 K, and 23 K, with a Debye temperature ThetaD = 265 K. In the polycrystalline sample the heat capacity curve is thermally broadened (ThetaD = 184 K), but no excess heat capacity was observed. The excess heat capacity Cphi (taken as the difference between the single-crystal and polycrystal heat capacities) is well described in terms of collective-mode excitations above their respective pinning frequencies. This attribution is represented by a modified Debye spectrum with two cutoff frequencies, a pinning frequency V0 for the pinned CDW (due to grain boundaries in the polycrystal), and a normal Debye acoustic frequency occurring in the single crystal.     

Effect of thermal fluctuations on the coarsening dynamics of 2D hexagonal system

The dynamics of ordering in a 2D hexagonal system was investigated through the Cahn-Hilliard-Cook model. At low thermal noise amplitudes, pinning forces acting on grain boundaries dominate the dynamics and the coarsening evolves logarithmically in time. As noise amplitude increases, fluctuations becomes large enough to unlock dislocations located along grain boundaries and the grain boundary motion is driven by curvature. The grain boundary relaxation leads to a grain structure with Lifshitz's configurations. In this case the dynamic is also logarithmic as a consequence of the pinning of triple points.     

Coarsening in Sintering: Grain Shape Distribution,Grain Size Distribution,and Grain Growth Kinetics in Solid-Pore Systems

Sintering occurs when packed particles are heated to a temperature where there is sufficient atomic motion to grow bonds between the particles. The conditions that induce sintering depend on the material, its melting temperature, particle size, and a host of processing variables. It is common for sintering to produce a dimensional change, typically shrinkage, where the powder compact densifies, leading to significant strengthening. Microstructure coarsening is inherent to sintering, most evident as grain growth, but it is common for pore growth to occur as density increases. During coarsening, the grain structure converges to a self-similar character seen in both the grain shape distribution and grain size distribution. Coarsening behavior during sintering conforms to classic grain growth kinetics, modified to reflect the evolving microstructure. These modifications involve the grain boundary coverage due to pores, liquid films, or second phases and the altered grain boundary mobility due to these phases. The mass transport rates associated with each of these interfaces are different, with different temperature and composition dependencies. Hence, the coarsening rate during sintering is not constant, but changes with the evolving microstructure. Core aspects treated in this review include models for coarsening, grain shape, grain size distribution, and how pores, liquids, dispersoids, and other phases determine microstructure coarsening during sintering.