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.     

The unique attractor in the theory of Ostwald ripening

It is shown that time-independence of the inverse rate constant implies a time-independent probability distribution of particles sizes, and that this probability distribution arises from the form of the asymptotic characteristic curves of the solution to the continuity equation. From this an expression for the distribution is derived, valid for finite volume fraction.     

To the theory of Ostwald ripening in metallic alloys

The mechanism of growth (dissolution) of nanoparticles controlled simultaneously by the matrix diffusion, diffusion along dislocations, and the rate of the passage of atoms through the interphase boundary (by the rate of formation of interatomic bonds) has been studied in alloys of CuNiAl and AlLi metallic systems at the stage of Ostwald ripening. An expression for the nanoparticle-size distribution function has been obtained, which was calculated based on the dependence of the rate of growth on three fluxes, i.e., diffusion flux j_V, dislocation flux j_d, and kinetic flux j_i. A comparison of the experimental histograms with the theoretically calculated curves indicates their good agreement, which can indicate the opportunity of the realization in practice of the proposed mechanism of growth of nanoparticles in alloys of metallic systems.     

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.     

低体积分数相析出过程的相场模拟

通过构建局域自由能函数,并考虑晶界对析出过程的影响,建立了低体积分数相析出过程的相场模型,模拟了溶质体积分数为2%的体系中第二相在晶界和晶内析出及其演变过程.结果表明,在相同相场步条件下,晶粒空间矢量平方和的幂指数项(∑(η)2)μ决定了第二相在晶界和晶内的析出比例;晶内析出相的比例随μ值的减小而增加;析出相尺寸的大小取决于浓度场梯度能系数к(ζ)值的高低;μ=1或较大к(ζ)时,析出相全部集中于晶界上.     

高体积分数MWCNTs/AZ80复合材料的显微组织

采用搅拌摩擦加工技术制备体积分数为19.5%的多壁碳纳米管(MWCNTs)增强AZ80镁基复合材料,研究经多道次搅拌摩擦加工(FSP)加工后复合材料的显微组织和MWCNTs在基体中的分布和稳定性,分析MWCNTs与基体的界面结构特征。结果表明:多道次FSP能提高MWCNTs在基体中的分散性,并在基体中形成了纳米晶,晶体尺寸仅5 nm左右。经多道次FSP后,MWCNTs在径向上的多壁结构未受到机械损伤,但经7道次加工后,在复合材料中发现有少量Al4C3相;碳纳米管与镁基体以半共格的界面形式相接。     

Phase-field simulation of void migration in a temperature gradient

A phase-field model simulating vacancy diffusion in a solid with a strong vacancy mobility inhomogeneity is presented. The model is used to study void migration via bulk and surface diffusion in a temperature gradient. The simulations demonstrate that voids migrate up the temperature gradient, and the migration velocity varies inversely with the void size, in agreement with theory. It is also shown that the current model has the capability to investigate the effects of surface diffusion, temperature gradient and vacancy concentration on the void migration velocity. An interesting potential application of the model is to study the kinetics of void migration and the formation of a central hole in nuclear fuels.     

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.     

Phase-field simulation of dendritic sidebranching induced by thermal noise

The influence of undercooling and noise magnitude on dendritic sidebranching during crystal growth was investigated by simulation of a phase-field model which incorporates thermal noise. It is shown that, the sidebranching is not influenced with inclusion of the nonconserved noise, therefore, in order to save the computational costs it is often neglected; while conserved noise drives the morphological instability and is dominant origin of sidebranching. The dependence of temperature field on magnitude of thermal noise is apparent, when Fu gets an appropriate value, noise can induce sidebranching but not influence the dendritic tip operating state. In the small undercooled melt, the thermal diffusion layer collected around the dendrite is thick, which suppresses the growth of its sidebranching and makes the dendrite take on the morphology of no sidebranching, but when the undercooling is great, the thermal diffusion layer is thin, which is advantageous to the growth of the sidebranching and the dendrite presents the morphology of the developed sidebranching.     

Fracture of high volume fraction ceramic particle reinforced aluminium under multiaxial stress

Circumferentially notched cylindrical bars of high volume fraction Al₂O₃ particle reinforced aluminium are tested in tension to probe the role of tensile stress triaxiality on damage and failure of such materials. The transverse strain is monitored with a specially designed video extensometer. A significant dependence of the peak average stress and failure strain on notch radius is observed. Finite-element simulations of the tests are conducted on the basis of a micromechanical model derived from earlier studies of damage and failure of these composites under uniaxial tensile deformation (Journal of the Mechanics and Physics of Solids 2009;57:1781). The simulations show that stress and strain distributions within the notched composite samples deviate significantly from predictions of Bridgman’s simplified analysis. Comparison with data shows that, whereas calculations capture satisfactorily the evolution of the average composite flow stress as a function of notch radius at small strains, the notched samples damage faster and fail at strains lower than predicted. Two phenomena may explain the discrepancy, namely (i) damage coalescence beyond a threshold level, and (ii) the incapacity of the matrix to sustain large hydrostatic stresses, which results from the presence of internal surfaces (cracked particles and possibly matrix voiding).     

Phase-field simulation of polarization switching and domain evolution in ferroelectric polycrystals

A phase-field model is developed for predicting the polarization switching and domain structure evolution under an applied electric field in ferroelectric polycrystals. The model takes into account realistic grain structures as well as various energetic contributions, including elastic energy, electrostatic energy, and domain wall energy. A hysteresis loop – average polarization as a function of applied electric field – is computed, and the detailed domain evolution process during switching is analyzed. In particular, the role of grain boundaries in the nucleation and growth of new domains is studied. It is shown that switching takes place through the nucleation of 90° domains at grain boundaries and subsequent growth into the grain interiors instead of direct 180° domain switching. A correlation between the domain structures in neighboring grains was observed, and polarization switching in one grain was found to affect the switching in neighboring grains.     

Phase-field simulation of solidification dendritic segregation in Ti-45Al alloy

The microstructures and mechanical properties of Ti Al alloys are directly linked to micro-segregation which cannot be avoided during solidification. So a thorough understanding of the micro-segregation should be a great help to further enhance the mechanical properties of the cast products. Theoretical analysis and experiments have been used to predict the micro-segregation, but it is very difficult to observe and determine the dendritic segregation in the micro region. Phase-field method has been employed for the simulation of dendritic growth. However, due to the complicated quasi-sub regular solution model for Ti-45Al(at.%) alloy, the classic phase-field models have difficulty to deal with the free energy. In this work, a phase-field model by linking thermodynamic calculation was used to simulate solidification dendritic segregation of Ti-45 Al alloy for Liquid→Liquid+β(Ti). The free energies of solid phase and liquid phase for Ti-45 Al alloy were calculated by Thermo-Calc and then coupled with the phase-field equations. The simulation results show the dendritic morphology and Al content variations between liquid and growing solid phase for Ti-45 Al alloy. With the growth of the β(Ti), dendritic segregation is formed in the liquid and solid phases due to the solute partitioning and rejection into the liquid. As a result, the dendrite arms are depleted of Al element, while the inter-dendrites are enriched. The dendritic tip growth velocity decreases with the progress of solidification, whereas the segregation ratio increases.     

Evaluation of drilling characteristics of high volume fraction fibre glass reinforced polymeric composite

This paper aims to understand the dynamics of drilling of high volume fraction glass fibre reinforced composite. This type of composite is currently used in ballistic applications. At high fibre volume, fibres do not show much relaxation and normal hole shrinkage associated with polymeric composites is not observed during drilling. Peak drilling thrust, dimension of holes drilled and vibration induced during drilling are observed to correlate with each other. Vibrations study has been attempted through wavelet packet transform and the results demonstrated its capability in signal characterisation.     

含高体积分数SiC_p的Al复合材料微观组织及弯曲性能

利用无压浸渗法制备高体积分数SiC的SiC_p/Al复合材料.采用XRD和SEM对复合材料的相组成、微观组织及断口形貌进行分析,研究颗粒粒径分布和基体合金成分对复合材料抗弯性能的影响.结果表明:以Al-10Si-8Mg(质量分数,%)合金为基体制备的复合材料组织均匀,致密度好,无明显气孔缺陷;界面反应产物为Mg2Si、MgAl_2O_4和Fe,其弯曲强度高于以Al-10Si合金为基体制备的复合材料的弯曲强度;SiC_p/Al复合材料的弯曲强度随着SiC颗粒粒径的增大而减小;复合材料整体上表现出脆性断裂的特征.     

Phase-field simulation of structure evolution at high growth velocities during directional solidification of Ti55Al45 alloy

A phase-field model whose free energy of the solidification system is derived from Calphad thermodynamic modeling of phase diagram is used to simulate structure evolution of Ti₅₅Al₄₅ alloy during directional solidification at growth velocities sufficiently higher than the critical velocity of transition from cells to dendrites, but lower than the absolute stability. The liquid–solid phase transition of L→L+β(Ti) is chosen. Firstly, the dynamics of the breakdown of initially planar interfaces into cellular structures then cellular dendrites are shown. Then the transition from cellular dendrites to fine cellular structures are shown at higher growth velocities. The solute segregation patterns are investigated at different growth velocities. The appearance of solute trapping is also investigated by determining the solute partition coefficients as a function of growth velocities. Agreement is reached with the theory of rapid directional solidification.