Phase-field theory of grain growth in the presence of mobile second-phase particles

We have developed a phase-field model for grain growth in the presence of mobile second-phase particles. In this model, each grain and particle is represented by a unique order parameter. The grain boundaries sweep the mobile particles during grain growth. The particle velocity is taken to be proportional to the driving force arising from the curvature of the phase boundary in the neighborhood of the particle. The proportionality factor is the constitutive parameter representing the mobility of the particle. We first study the model in a one-dimensional axisymmetric setting and compare the results with theoretical calculations. We then study the interaction of a bicrystal grain boundary with a dilute distribution of particles. Finally we show the effect of particles on polycrystalline grain growth.     

Triple junction drag and grain growth in 2D polycrystals

The process of grain growth in 2D systems is analyzed with respect to the controlling kinetics: from solely boundary kinetics, when grain growth in a polycrystal is determined by the Von Neumann–Mullins relation, to exclusively triple junction kinetics, when grain growth is governed by the mobility of triple junctions. It is shown that in the “intermediate” case, when the driving force for grain boundary motion and the characteristic mobility are grain boundary curvature and grain boundary mobility, respectively, a limited mobility of triple junctions essentially influences grain boundary motion. The Von Neumann–Mullins relation does not hold anymore, and this is the more pronounced the smaller the triple junction mobility. In the case where grain growth is determined by the mobility of grain boundary triple junctions (triple junction kinetics) all grains are transformed into polygons in the course of grain growth. Grain growth would cease if all grains assumed the shape of regular polygons, not only hexagons like in the Von Neumann–Mullins case. The only exceptions are triangles: they collapse without transforming into a polygon. The respective relation for the rate of a change of grain area under triple junction kinetics is obtained and discussed with regard to microstructure evolution.     

Al-Zn-Mg-Cu合金第二相粒子及其无析出区与晶界的作用过程研究

制备一种含Sc和一种含Cr、Mn、Ti、Zr的Al-Zn-Mg-Cu合金,采用透射电镜研究合金中第二相粒子周围的无析出微区和晶界上的无沉淀析出带及其相互的作用过程,给出单个第二相粒子对晶界作用力的方程.当驱使晶界迁移的动力大于粒子及其周围的无析出微区对晶界的阻碍作用时,晶界被粒子穿透而形成孔洞.在晶界扫过粒子的过程中,经历了先加速后减速两个阶段.晶界位于粒子直径区位置时所受的阻力最小、运动速度最大.当晶界能与相界能增量之和等于晶界运动的驱动力时,晶界被粒子钉扎而停止运动.在晶界迁移的过程中,溶质原子倾向于由高浓度区域向低浓度区域扩散,晶界和粒子周围的无析出区对晶界的迁移过程有明显的影响.     

Shape of moving grain boundaries in Al-bicrystals

It is common knowledge that grain boundary migration determines microstructure evolution and thus, affects the properties of polycrystals. The principal parameter which controls the motion of a grain boundary is the grain boundary mobility. In practically all relevant cases the motion of a straight grain boundary is the exception rather than the rule. That is why the shape of a moving grain boundary is of interest, and it will be shown that the grain boundary shape is a source of new, interesting and useful findings concerning grain boundary motion, in particular for the interaction of a moving grain boundary with mobile particles. The experimentally derived shape of a grain boundary “quarter-loop” (Masteller and Bauer, Recrystallization of Metallic Materials, Riederer Verlag, Stuttgart, 1978) in Al-bicrystals of different purity was compared with theoretical calculations in the Lücke–Detert approximation (Lücke and Detert, Acta metall., 1957, 5, 628).     

Computer modeling of particle pushing and clustering during matrix crystallization

Two-dimensional cellular automaton computer simulations were carried out to model the geometric interaction between mobile, equiaxed particles and growing matrix grains, thus simulating crystallization (respectively, recrystallization, phase transformation or solidification) of a matrix material containing a mobile second phase (e.g. solid particles, liquid droplets or gas bubbles). The model allows the study of particle pushing by growing grains, which leads to particle accumulation and clustering at grain boundaries and triple points, and concomitant particle depletion within grains. Parameters explored are particle area fraction, particle settling speed, particle cluster mobility and grain nucleation rate under continuous nucleation conditions. These parameters are found to strongly affect the particle spatial distribution and clustering during and after crystallization. Conversely, the particles have no measurable effect on the grain shape or size. Finally, site-saturated nucleation at the boundaries of the simulation field is investigated, simulating e.g. solidification from crucible walls or recrystallization from sample edges. Pronounced clustering of particles takes place at grain boundaries and is further accentuated by particle settling.     

Molecular dynamics simulation of triple junction migration

We present a molecular dynamics simulation study of the migration of grain boundaries with triple junctions. We have monitored the grain boundary profile, triple junction angles and rate of grain boundary migration with and without triple junctions as a function of grain size, grain misorientation, direction of migration and temperature in a series of configurations designed to ensure steady-state migration. The present results demonstrate that triple junction mobility is finite and can be sufficiently small to limit the rate of grain boundary migration. The drag on grain boundaries due to limited triple junction mobility is important at small grain sizes, low temperature and near high symmetry grain misorientations. This drag limits the rate of grain boundary migration and leads to triple junction angles that differ substantially from their equilibrium value. Simulation data suggest that triple junction drag is much more a factor at low temperature than at high temperature. The triple junction mobility is shown to depend upon the direction of triple junction migration. The present results are in excellent qualitative agreement with experimental observations.     

Analysis of the growth of individual grains during recrystallization in pure nickel

The growth of individual grains during recrystallization in 96% cold-rolled pure nickel has been followed using electron backscatter pattern maps of the same surface area taken after each of several annealing steps. It was found that the growth is quite complex, with boundaries moving, stopping and moving again. The growth kinetics differ from grain to grain and, on average, cube-oriented grains grow the fastest. The growth of the grains has also been analyzed as a function of boundary misorientation. This analysis shows that there is no significant difference in misorientation distribution between boundaries that move and those that do not. This is contrary to the usual assumption that the boundary mobility and the migration rate depend on the misorientation across a boundary. This observation and the reasons for the faster growth of cube-oriented grains are discussed.     

Effect of second-phase particle morphology on grain growth kinetics

Second-phase particles are often employed to inhibit grain growth in polycrystalline metals and ceramics. In this work, we studied the effect of second-phase particle morphology on the effectiveness of inhibiting grain boundary migration using the phase-field method. We employed a multi-order parameter phase-field model in combination with an efficient memory allocation strategy which allows large-scale and coalescence-free grain growth simulations. We analyzed the dependence of pinning forces on the particle size and shape, and performed computer simulations of grain growth in the presence of second-phase particles with different sizes and varying aspect ratios. We also discuss the relationship between the pinned grain size and size distributions.     

Recovery,recrystallization and grain growth in Fe3Al-based alloys

The recovery, recrystallization and grain growth of particle-free and particle-containing Fe₃Al intermetallics with a total warm reduction of 70% were investigated in the temperature range from 750 to 1115 °C. The physical phenomena during annealing were characterized and analyzed based on the observations of microstructure, measurement of long-range order degree and determination of micro-hardness. The reordering occurs due to the removal of antiphase boundary trails resulting from the dislocation rearrangement during annealing. The micro-hardness depends on both the dislocation density and the change of long-range order degree. The addition of alloying elements affects the dependence of hardness on reordering. It also has a great effect on the recovery and recrystallization. The recrystallized nuclei are formed by preferential subgrain growth and grain boundary migration. Due to strong anisotropy of Fe₃Al-based alloys, the grain boundary migration resulting from inhomogeneous deformation was frequently observed and the distribution of grain size after annealing was also inhomogeneous. The recrystallization kinetics follows the Kolmogorov-Johnson-Mehl-Avrami (KJMA) relationship. Long-range order and second phase are beneficial in decreasing the grain-boundary mobility. The grain growth kinetics of Fe₃Al intermetallics investigated follows the conventional power law equation with a high grain growth exponent of more than 4. Abnormal grain growth in the Fe–28% Al–5% Cr–0.1% Zr–0.5% Mo–0.5% Nb–0.05B% (at.%) alloy was found when it was annealed at 1115 °C for 72 h.     

TC17钛合金自表面纳米化机制及组织演化

采用二元合金晶体相场模型,耦合原子密度场和浓度场,在扩散时间尺度上模拟过冷熔体的形核,生长及粗化过程.研究表明:增加冷却速率,模拟区域内晶核富集,快速长大;一定范围内,随着冷却速率增大,晶粒尺寸减小,组织细化;晶粒长大过程中,晶界主要依靠位错的迁移或攀移进行运动.二元合金模拟还可以应用到枝晶凝固、外延生长,调幅分解中,前景广阔.     

A grain-boundary diffusion model of dynamic grain growth during superplastic deformation

Dynamic grain growth during superplastic deformation is modelled on the basis of a grain-boundary diffusion mechanism. On the grain boundary where a static and a dynamic potential difference coexist, matter transport along the boundary is assumed to contribute to dynamic grain growth through depositing the matter on the grain surface located opposite to the direction of grain-boundary migration. The amount of the diffusive matter during deformation is calculated for an aggregate of spherical grains and is converted to the increment of mean boundary migration velocity. The obtained relationship between the strain rate and the dynamic grain growth rate is shown to be independent of deformation mechanisms, provided that the grain growth is controlled by grain-boundary diffusion. The strain dependence, strain-rate dependence and temperature dependence of grain growth predicted from this model are consistent with those observed in superplastic ZrO₂-dispersed Al₂O₃.     

Simulation of the influence of particles on grain structure evolution in two-dimensional systems and thin films

A two-dimensional front-tracking simulation of grain growth has been extended to treat the effects of particles on the evolution of grain structures during annealing. When grain boundaries come into contact with particles, boundary motion is assumed to be pinned. It is found that even a small volume fraction of particles retards grain growth, lowers the ultimate average grain size, and leads to significant changes in the grain-size and number-of-sides distributions. These changes differ in detail from the changes in the grain-size distribution predicted using the Potts model. The changes in the nature of the grain-size distribution are explained by considering the topology of the evolving and of the stagnant grain structures. The average grain size in the stagnant structure scales with the number of particles in a way consistent with a scaling with area fraction of the particles to the power 0.46, in near agreement with the expected dependence from a Zener-pinning analysis in two dimensions. Particle pinning is also simulated in conjunction with the effects of other mechanisms impeding grain growth such as solute drag or grain boundary grooving. In this case it is found that the stagnant grain-size distribution is determined by the competing stagnation forces, and that the Zener-pinning analysis is not obeyed and must be modified.     

第二相粒子尺寸对基体晶粒长大影响的仿真研究

根据第二相粒子与基体晶界交互作用的微观物理基础,建立了复相材料晶粒长大的三维图象的仿真方法,设计了含有相同体积分数,不同尺寸第二相粒子的复相体系,并全程仿真了三维复相材料的晶粒长大过程,对粒子尺寸影响基体粒长大的直接观察和定量分析表明,粒子尺寸越大,晶界的“脱钉”趋势越弱,晶粒长大到达停滞状态所经历的时间越长,停滞状态下基体晶粒尺寸越大且尺寸分布的均匀性越近,极限晶粒尺寸与粒子尺寸之间并不存在简单     

ON THE MIGRATION OF AUSTENITE GRAIN BOUNDARY

<正> 采用高温金相显微镜研究奥氏体晶粒长大,将受晶界原子蒸发滞后现象的影响,尤其在奥氏体晶粒急剧长大的温度下,不能清晰观察到晶界迁移的过程。本文通过定位高温金相照片的观察,研究奥氏体晶粒长大过程中晶界的行为,为晶界迁移机制提供实验依据。 试验用西宁钢厂电弧炉生产的40CrNiMoA钢,钢的化学成分如下(wt-％):     

Evolution of grain structure in AA2195 A1-Li alloy plate during recrystallization

The evolution of the grain structures in AA2195 Al-Li alloy plate warm-rolled by 80% reduction during recrystallization annealing at 500℃ was investigated by electron backscatter diffraction, scanning electron microscopy and transmission electron microscopy. It is found that the elongated grain structures are caused by the lamellar distribution of recrystaUization nucleation sites, being lack of large second phase particles （〉 1μm）, and dispersive coherent particles （such as δ′ and β′concentrated in planar bands. The recrystallization process may be separated into three stages： firstly, recrystallization nucleation occurs heterogeneously, and the nuclei are concentrated in some planar zones parallel to rolling plane. Secondly, the grain boundaries interacted with small particles concentrate in planar bands, which is able to result in the elongated grain structures. The rate of the grain growth is controlled by the dissolution of these small particles. Thirdly, after most of small particles are dissolved, their hindrance to migration of the grain boundaries fades away, and the unrecrystallized zones are consumed by adjacent recrystallized grains. The migration of high angle grain boundaries along normal direction leads a gradual transformation from the elongated grains to the nearly equiaxed, which is driven by the tension of the grain boundaries.     

Viscous grain-boundary sliding with rotating particles or grains

We evaluate the sliding rate and stress distribution on the boundary when the sliding of grain boundary containing particles is accommodated by grain-boundary diffusion, by taking the particle rotation and the intrinsic boundary viscosity into account. The particle rotation enhances the sliding rate, and can occur in the reverse direction with respect to the grain-boundary sliding. We investigate the sliding behavior for various particle shapes and boundary viscosities. A similar analysis is also conducted for the shear deformation of regular hexagonal grains.     

The effect of cryogenic temperature and change in deformation mode on the limiting grain size in a severely deformed dilute aluminium alloy

With the aim of investigating the factors that limit the production of true nanograined materials by cryogenic severe deformation, the grain structures formed in an Al–0.1%Mg alloy have been studied in plane strain compression at temperatures down to 77 K, following prior severe plastic deformation (SPD) by equal channel angular extrusion. Changing the deformation mode alone had little effect on increasing the rate of grain refinement. At the minimum cryogenic temperature (77 K) the samples still contained ∼30% low angle boundaries and a nanoscale high-angle boundary (HAB) spacing was only obtained in one dimension. At high strains a steady-state minimum HAB spacing was approached, irrespective of the temperature, where the rate of grain refinement stagnated. It is shown that the minimum grain size achievable in SPD is limited by a balance between the rate of compression of the HAB spacing and dynamic grain coarsening. At low temperatures this is controlled by abnormally high boundary migration rates, which are difficult to explain with existing theories of grain boundary mobility.     

Measurements of grain boundary mobility during recrystallization of a single-phase aluminium alloy

A combination of in situ annealing and electron backscattered diffraction in the SEM has been used to determine the mobility of high angle grain boundaries in a deformed single-phase Al–Si alloy. It is found that the boundary velocity is directly proportional to the driving pressure and that the activation energy for boundary migration over all the conditions investigated is consistent with control by lattice diffusion of the solute. It is confirmed that tilt boundaries of recrystallized grains misoriented by 40±10° about axes within ±10° of 〈111〉 have an increased mobility compared to other high angle boundaries, whereas the mobilities of 40°〈111〉 twist boundaries are similar to those of general high angle boundaries. The mobility maximum for the 40°〈111〉 tilt boundaries is very broad, which is in contrast to the sharp mobility peaks reported for curvature-driven grain growth, and possible reasons for these differences are discussed.     

A size effect in grain boundary migration: A molecular dynamics study of bicrystal thin films

Molecular dynamics simulations of stress-driven grain boundary migration in bicrystal thin films demonstrate that the grain boundary mobility decreases as the films are made thinner. Examination of the surface morphology proves that this effect is not associated with grain boundary grooving. The simulation data demonstrate that the grain boundary mobility is a linear function of the inverse thickness. We present a simple model to explain this effect based upon the fundamental mechanism of grain boundary migration: the collective rearrangement of a large group of atoms. Decreasing system size implies that more of the boundary is near the surface. The presence of the free surface interferes with the collective rearrangement of the atoms during boundary motion and hence slows the migration. A simple heuristic analysis, based on this effect, is consistent with the observed functional dependence of boundary mobility on bicrystal thickness.     

纳米复合银基电触头材料的研究

利用高能球磨技术及热压烧结工艺制备出第二相弥散均匀分布于Ag基体中的纳米复合AgNi和AgSnO2触头，对复合粉末和合金触头进行了X射线衍射(XRD)、扫描电镜(SEM)和透射电镜(TEM)分析。结果发现：经长时间高能球磨后，复合粉末的晶粒明显细化，第二相粒子尺寸已达到40nm左右，并在球磨过程中通过嵌入、焊合弥散分布于Ag基体中，消除了传统方法第二相聚集及在晶界处的连续析出等缺陷。在退火、热压过程中第二相并未明显长大，仍保持在50nm左右。对触头进行SEM观察时发现，2种触头的晶界处都保持着有利于电性能的Ag膜。与常规商用触头相比，纳米复合触头有分散电弧作用，表面没有明显的熔池和液体喷溅，呈现出较好的耐电弧侵蚀特性。