Large-scale simulations of Ostwald ripening in elastically stressed solids. II. Coarsening kinetics and particle size distribution

Ostwald ripening of misfitting second-phase particles in an elastically anisotropic solid is studied by large-scale simulations. The coarsening kinetics for the average particle size are described by a t^1/3 power law with a rate constant equal to its stress-free value when the particles are fourfold symmetric. However, the rate constant increases when the elastic stress is sufficient to induce a large number of twofold-symmetric particles. We find that interparticle elastic interactions at a 10% area fraction of particles do not affect the overall coarsening kinetics. A mean-field approach was used to develop a theory of Ostwald ripening in the presence of elastic stress. The simulation results on the coarsening kinetics agree well with the theoretical predictions. The particle size distribution scaled by the average particle size is not time invariant, but widens slightly with an increasing ratio of elastic to interfacial energies. No time-independent steady state under scaling is found, but a unique time-dependent state exists that is characterized by the ratio of elastic energy to interfacial energy.     

The effect of rare earth elements on the kinetics of the isothermal coarsening of the globular solid phase in semisolid AZ91 alloy produced via SIMA process

In the present study, the effects of rare earth (RE) elements on the microstructure and coarsening kinetics of the solid globular particle in the semisolid slurry of AZ91 magnesium alloy have been studied at 570 °C and 580 °C. The results showed that the coarsening kinetics of the solid globular particles in semisolid slurry of AZ91 alloy satisfies the Ostwald ripening theory. It was shown that the coarsening rate of the solid particles decreases by adding RE elements into AZ91 alloy, specially at 580 °C, which results in the smaller particles size. It was attributed to the solid–liquid interfacial energy reduction due to the addition of RE elements.     

Large-scale three-dimensional simulation of Ostwald ripening

Large-scale three-dimensional simulations of Ostwald ripening were carried out using a multiphase-field model for accurate and efficient computation of multiparticle diffusional interaction in order to clarify coarsening kinetics in systems with finite particle fractions. The simulations were performed on 400³ grid systems in a particle fraction range of 0.25–0.86, where the initial microstructures with 20,000–100,000 solid particles in a liquid matrix evolve into structures with 1500–3000 particles. The simulation results were carefully analyzed and compared with those from the previous simulations and experiments, which have data range relevant to the present simulation range. The present results are in excellent agreement with the simulations by Akaiwa and Voorhees at low particle volume fractions, with the recent results from the 3-D reconstruction of serial sections at high fractions and with the grain size distribution of ideal grain growth at very high fractions.     

Analytical description of phase coarsening at high volume fractions

An analytical theory of volume fraction effects in diffusion-controlled phase coarsening is developed. It is based on the application of the Lifshitz–Slyozov–Wagner procedure of Ostwald ripening theory to a self-similar particle volume evolution equation which is approximated by a quadratic polynomial of the scaled particle size. A family of analytical particle size distributions with the scaled maximum particle size as a parameter is derived, which contains the size distribution of normal grain growth as a genuine limit distribution at ultra-high volume fraction without changing the t^1/3-Ostwald ripening kinetics. This reflects an important characteristic feature of particle coarsening at nearly space filling, which was first noted by Ardell and which is in principle in agreement with recent observations. The obtained analytical expressions for the maximum particle size, the particle size distribution and the coarsening rate constant are easy to use for evaluating coarsening data. The results compare well with a number of experimental and simulation results at intermediate and high volume fractions of the second phase.     

强制对流流变成形制备7075铝合金半固态浆料及其数值模拟(英文)

采用自主研发的强制对流流变装置,研究搅拌速度对7075铝合金半固态组织的影响规律。实验结果表明,随着搅拌速度的增加,半固态组织的晶粒尺寸减小,形状因子及粒子数增加。同时,对强制对流流变成形浆料制备过程进行数值模拟,研究熔体在筒体内的流动规律和搅拌速度对合金熔体温度场和固相率的影响。模拟结果表明,合金熔体在FCR筒体内存在复杂的对流运动,熔体对流极大地改变了合金熔体温度场和固相率的分布。增加对流强度有利于减小合金熔体的过冷度梯度和改善初生晶粒的分布。     

等温热处理过程中铸态AZ91镁合金的微观组织演化

铸态AZ91镁合金加热至液固相温度区间内等温热处理后演变成半固态金属,对淬火组织形态分析的试验表明:在高固相体积分数条件下,网状分布的共晶组织首先熔化,二次枝晶臂消失或熔断脱落并重新沉淀在枝晶主干上,在Gibbs-Thomson效应下,发生Ostwald熟化,固相颗粒由枝晶逐渐演变成球形颗粒,并随着热处理时间的延长发生合并现象,而且热处理温度越高晶粒间合并现象越严重。同时在界面能降低的驱使下,晶粒内部包裹的液滴以两种方式形成:晶粒内富Al、Zn的质点经过熔化、扩散、合并、或者脱落的二次枝晶臂沉淀后搭桥生长形成。     

糊状区变形及浓度再分布的模拟实验

用丁二腈－丙酮合金实验研究试样变形开始时间、初始厚度及变形量对枝晶变形及溶质再分布的影响。结果表明，枝晶变形满足幂次大于1的能量函数关系；枝晶变形能力主要与变形时糊状区固相分数有关；从糊状区挤出的液相相对浓度与固相分数、变形比率成线性关系。实验结果对建立糊状区变形与宏观偏析数学模型及优化连铸液芯压下工艺有意义。     

侧向凝固通道偏析的数值模拟

建立了二元系凝固过程通道偏析形成的数学模型,给出了描述焓与温度及固相分数耦合关系的表达式.在实验验证的基础上,对亚共晶与过共晶成分的NH4Cl-H2O侧向凝固通道偏析的形成位置与生长方向进行了数值模拟研究.模拟计算结果表明,偏析通道起源于糊状区,偏析通道中的富集溶质从糊状区流向液相区.为了维持偏析通道中的液体流动,枝晶间液体可通过糊状区从液相区得到补充.糊状区中富集溶质的流动方向取决于析出溶质的密度.NH4Cl-70%H2O侧向凝固时,析出的溶质密度较小,偏析通道倾斜向上生长,在糊状区上部形成A偏析.NH4Cl-90%H2O侧向凝固时,析出的溶质密度较大,在糊状区下部偏析通道倾斜向下生长.     

等温热处理对AZ91D+Ce镁合金半固态组织的影响

研究了等温热处理对AZ91D+Ce镁合金半固态组织的影响,获得了较理想的球状或类球状晶粒组织。结果表明,在等温热处理的过程中,加入稀土Ce会阻碍原子向固相粒子聚集和结合,抑制固相颗粒的长大,形成细小圆整的半固态组织。随等温热处理温度的升高,原子活动能力增强,熔化速度加快,液相量增加,固相颗粒尺寸先减小后增大。在等温初始阶段,熔化对初生固相颗粒尺寸起决定作用,使得颗粒尺寸减小。但是,随等温时间的进一步增加,由于合并粗化和Ostwald熟化的作用,固相颗粒开始长大。     

镍基高温合金定向凝固斑点偏析的数值模拟研究

为了研究铸造高温合金中的斑点偏析，建立了描述多元合金凝固过程传输行为的数学模型。基于伪二元相图方法，模型给出了液相线温度与固相分数及液相多元溶质浓度的耦合关系式。利用该模型对Ni-5．8Al-15．2Ta（质量分数，％）合金铸锭的垂直定向凝固过程进行了模拟。结果表明：该模型能够反映多组元镍基高温合金凝固过程中斑点偏析的形成及发展过程。凝固界面前沿附近热-溶质双扩散对流引起的密度倒置，是诱发斑点偏析的主要原因。在糊状区中形成的偏析通道中，富集溶质从糊状区流向液相区，通道周围局部流动可以通过糊状区从液相区补充通道中的流动。凝固初期形成的通道不能稳定存在，多个通道合并促使局部凝固前沿优先生长，最终形成稳定的偏析通道。     

The development of spatial correlations during Ostwald ripening: a test of theory

The coarsening of solid-Sn particles in a Pb–Sn liquid was studied under microgravity conditions. Spatial correlation functions were measured on plane sections in a low-volume fraction system undergoing Ostwald ripening. The correlation functions changed with time in a way that indicated that the microstructure initially consisted of clusters of particles and evolved into one which was more dispersed. The model by Akaiwa and Voorhees (AV) was used to study the effect of spatial correlations on the ripening process. We found that the initially highly correlated structure had no observable effect on the evolution of particle size distributions, but did have an effect on the coarsening rate of the system. Specifically, we determined that a structure consisting of clusters of particles coarsened faster than a system with a random, spatial arrangement of non-overlapping particles. We also found that the approach of the microstructure towards the steady-state regime could be monitored more sensitively using spatial correlations rather than using particle size distributions. The spacial correlations and the particle size distributions measured from the experiment agreed well with those calculated from the AV simulations using the initial experimental correlations and size distribution.     

Morphological development of solidification structures under forced fluid flow: a Monte-Carlo simulation

A Monte-Carlo simulation of microstructural development under forced convection is presented. The model takes into account both diffusive and forced fluid flow, kinetics of atomic attachment at the solid–liquid interface and structural modification under the influence of capillary forces. It has been shown that the nature of fluid flow has a very significant influence on the morphology of the solidification structure. A laminar type flow is shown to destabilize the solid–liquid interface promoting dendritic growth for solid growing from fixed substrate. Particle rotation under streamlined flow, or a periodic change in the fluid flow direction around the growing solid is, however, shown to produce the rosette type solidification morphology. A turbulent type flow penetrating into the interdendritic region produces fine and compact solidification structures with or without liquid entrapment.     

Transient Ostwald ripening and the disagreement between steady-state coarsening theory and experiment

The coarsening of solid-Sn particles in a Pb–Sn liquid has been studied under microgravity conditions. These experiments permit an unambiguous comparison between theory and experiment to be made. In contrast to steady-state theories, such as those due to Lifshitz and Slyozov and Wagner, the scaled particle size distributions evolve in samples containing 0.1 and 0.2 volume fractions of solid. Steady state was not reached even though the average particle radius increased by a factor of three during the experiment. In addition, the scaled spatial correlation functions were also found to be time dependent in samples containing 0.1, 0.2, and 0.3 volume fractions of solid. The size distributions and correlation functions for all coarsening times at the fractions ≤0.3 agree with the predictions of a theory for transient coarsening. We show that the microstructures have not reached the steady-state regime for all volume fractions, are thus not self-similar, and that given our initial experimental conditions the time required to reach steady-state coarsening increases with increasing volume fraction. In these experiments, and we suspect in others as well, the transients are sufficiently long that steady-state theories cannot adequately describe the evolution of the microstructure.     

自孕育法制备AZ31镁合金半固态流变成形组织(英文)

采用新型自孕育流变铸造技术对变形镁合金半固态组织进行控制。该工艺过程为将合金熔体与一定量的合金固体颗粒(自孕育剂)混合,然后将混合金属通过一个多流股导流器浇入铸型或收集器。结果表明:采用自孕育工艺,合金熔体处理温度690~710℃,孕育剂的加入量为3%~7%时能有效将AZ31镁合金传统铸造中的粗大枝晶组织转变为细小、近球状的非枝晶组织;当合金熔体处理温度较高时,增加孕育剂的加入量或减小导流器的倾斜角度有利于获得非枝晶组织。自孕育工艺制备的AZ31镁合金半固态浆料在620℃等温保温30s后能有效改善初生α-Mg颗粒的圆整度;延长保温时间有助于减小颗粒的圆整度,但同时颗粒发生粗化。利用Lifshitz-Slyozov-Wagner(LSW)理论对初生相颗粒在等温保温过程中的组织圆整、粗化过程进行了分析。     

Induction heating process of an Al–Si aluminum alloy for semi-solid die casting and its resulting microstructure

During induction heating, the relationship between time and temperature must be controlled exactly to obtain a homogeneous temperature distribution over the entire cross-sectional area. Because the initial solid fraction in the semi-solid die casting (SDC) process is the main parameter to achieve a homogeneous flow behavior of the liquid and solid phases and to prevent macro-segregation effects in the SDC process, an accurately controllable induction heating method must be selected for the reheating process. The purpose of this work is not just to obtain the desire solid fraction, generally about 50%, but also to ensure the optimal induction heating conditions of A356 alloy to reduce the temperature gradient of a 76 mmdiameter×90 mmlength billet and to obtain a fine globular microstructure without grain coarsening (resulting microstructure). This work shows that, in the case of a three-step reheating process for the SDC process, the final holding time is the most important factor to maintain a fine globular microstructure without grain coarsening.     

Solidification behaviour of AZ91D alloy under intensive forced convection in the RDC process

Rheo-diecasting (RDC) is a new semisolid processing technology for production of near net shape components. In this work, the solidification behaviour of AZ91D alloy under intensive forced convection in the RDC process was investigated experimentally to understand the effects of the intensity of forced convection, shearing time and shearing temperature on the nucleation and growth behaviour. It was found that under intensive forced convection, heterogeneous nucleation occurred continuously throughout the entire volume of the solidifying melt. All the nuclei could survive due to the uniform temperature and composition fields created by the forced convection. This has been named as continuous effective nucleation. It is also found that the nuclei grow spherically with an extremely fast growth rate. This makes the primary solidification essentially a coarsening process, in which Ostwald ripening takes place by dissolution of the smaller particles. Secondary solidification of the intensively sheared semisolid slurry takes place also through effective nucleation, but with dendritic growth. Increasing the intensity of forced convection enhances nucleation and promotes the formation of the primary phase during the secondary solidification in the shot sleeve. The final solidification microstructure is strongly dependent on the presence of turbulence rather than the shear rate.     

Experimental and simulation studies on grain growth in TiC and WC-based cermets during liquid phase sintering

The grain growth behaviors of TiC and WC particles in TiC-Ni, TiC-Mo₂C-Ni, WC-Co and WC-VC-Co alloys during liquid phase sintering were investigated for different Ni or Co contents and compared with the results of Monte Carlo simulations. In the experimental study, TiC-Ni and WC-Co alloys had a maximum grain size at a certain liquid volume fraction, while the grain size in TiC-Mo₂C-Ni and WC-VC-Co alloys increased monotonically with an increasing liquid volume fraction. These results mean that the grain growth of these alloys cannot be explained by the conventional mechanisms for Ostwald ripening, namely diffusion or reaction controlled processes. Monte Carlo simulations with different energy relationships between solidliquid interfaces predicted the effect of the liquid volume fraction on grain size similar to the experimental results. The contiguous boundaries between solid (carbide) particles appear to influence the grain growth behavior in TiC- and WC-based alloys during liquid phase sintering.     

快速凝固Al-In偏晶合金的显微结构

采用单辊法快速凝固工艺制备均质的Ａｌ－Ｉｎ偏晶合金,并对所获得的快速凝固组织和形貌进行了观察和研究。结果表明,细小的Ｉｎ颗料均匀分布在Ａｌ基体中：在甩带厚度方向上,随着与激冷面距离的增大,Ｉｎ颗粒尺寸逐渐增大;在同一辊速条件下（同一冷却速率）,随着Ｉｎ含量的增加,Ｉｎ颗粒的平均尺寸也不断增大;同一成分条件下,随着辊速的升高,Ｉｎ颗粒的平均尺寸不断减少;单辊法快速凝固过程中第二相液滴通过Ｂｒｏｗｎｉ     

Coarsening of grain-refined semi-solid Al–Ge32 alloy: X-ray microtomography and in situ radiography

The Lifshitz, Slyozov and Wagner theory (LSW) describes the coarsening of low volume fraction dispersed particles in a supersaturated solution as governed by a t^1/3 power law, while stating that ripening occurs in a self-similar manner. Only a few experiments have reported three-dimensional (3D) coarsening in binary semi-solid alloys, which differs from the LSW theory. We report here on in situ coarsening of Al–Ge32 (wt.%), which is used as a model system for a large variety of technical alloys. Numerical analysis of 2D and 3D images of the microstructure measured by X-ray radiography and microtomography reveals the evolution of the solid particles during annealing. Ripening of a grain-refined particle network is found to be quite well described by LSW theory, although somewhat smaller exponents (t^1/4–t^1/5) are found. Changes in coarsening behavior are observed in samples which are thinner than 0.5 mm, as well as in non-equiaxed alloy microstructures, characterized by anisotropic dendrites.     

Ag-Ni电接触材料快速/亚快速凝固过程研究

采用快速/亚快速凝固方法制备了富Ni相粒子弥散分布于Ag基体的Ag-Ni合金。建立了Ag-Ni合金凝固过程中组织演变的动力学模型,模拟计算了Ag-Ni合金凝固组织形成过程,分析讨论了合金成分对Ag-Ni合金凝固组织形成过程的影响。结果表明,合金的Ni含量越高,凝固组织中富Ni相粒子平均尺寸越大;Ag-Ni合金熔体冷却凝固时,富Ni相液滴/粒子的尺寸主要受形核和长大控制,Ostwald粗化作用很弱。