Multiscale simulations on the coarsening of Cu-rich precipitates in α-Fe using kinetic Monte Carlo,molecular dynamics and phase-field simulations

The coarsening kinetics of Cu-rich precipitates in an α-Fe matrix for thermally aged Fe–Cu alloys at temperatures above 700 °C is studied using a kinetic Monte Carlo (KMC) simulation and a phase-field method (PFM). In this work, the KMC approach adequately captures the early stage of the system evolution which involves nucleation, growth and coarsening, while the PFM provides a suitable framework for studying late-stage coarsening at large precipitate volume fraction regimes. Hence, both models complement each other by transferring the results of KMC along with precipitate–matrix interface energies from a broken-bond model to a quantitative PFM based on a grand chemical potential formulation and the CALPHAD database. Furthermore, molecular dynamics simulations provide information on the structural coherency of the precipitates and hence justify the sequential parameter transfer. We show that our PFM can be validated quantitatively for the Gibbs–Thomson effect and that it also predicts the coarsening kinetics correctly. It is found that the kinetics closely follow the LSW (Lifshitz–Slyozov–Wagner) law, whereas the coarsening rate constant increases with an increase in volume fraction of precipitates.     

Concurrent growth and coarsening of spheres

A theory is developed of concurrent growth and coarsening of a dispersion of spheres that accounts for the exchange of heat by diffusion among the spheres due to their curvature differences and between the spheres and the environment due to an externally imposed heat extraction rate. The results show that in concurrent growth and coarsening the average particle radius asymptotically increases with the cube root of time, which is the same behavior as in separate growth and coarsening. The growth rate constant increases linearly with the heat extraction rate, from the LSW value in pure coarsening to a value that is 1.89 times larger in concurrent growth and coarsening with a heat extraction rate that just prevents particles from disappearing due to coarsening interactions. For larger heat extraction rates, coarsening has no effect on the particle growth rate, because the distribution becomes mono-sized.     

Unraveling the nature of room temperature grain growth in nanocrystalline materials

We report on the observation of real-time-resolved room temperature grain growth in nanocrystalline metals. We find that neither the time evolution of size can be modeled by standard growth theories nor are there any other systems aware to us that manifest a similar growth behaviour. We detect a transition from an initially self-similar slow growth to abnormal grain growth. Its onset seems to be associated with the simultaneous decrease of microstrain with increasing grain size. Abnormal grain growth is considered as a generic feature of nanocrystallinity but is a transient state since we observed in the late stage of coarsening, using orientational imaging microscopy, a monomodal grain size distribution. We empirically find a nonlinear-response-type of growth law which is in agreement with the observed coarsening kinetics.     

Simulation of the coarsening behavior of intermetallic precipitates in Ni75AlxV25-x alloys

The coarsening behavior of L12 and D022 in Ni75AlxV25-x （x,at.%） alloys including coherent strain was investigated using the microscopic phase-field model. The simulation results indicate that the shape transition and spatial correlation of L12 and D022 are caused by the morphological-dependent anisotropic elastic interactions in the system. The coarsening process of the particles is by means of neighbor particles impingement and aggregation into larger ones. For the strain-induced interactions between the precipitates,the LSW theory is altered for the coarsening behavior of L12 and D022. In addition,the simulation reveals that the growth and coarsening of D022 present two obvious stages at lower Al concentration regions and proceed simultaneously at high Al concentration regions. The growth and coarsening processes of L12 at the same regions is reverse to those of D022.     

CELLULAR AUTOMATA MODELLING OF GRAIN COARSENING DURING REHEATING AND VALIDATION WITH THE EXPERIMENTAL RESULTS

1. IntroductionG rain coarsening isthe processby w hich the m ean grain size ofan aggregate ofcrystalsincreases.A n understanding ofgrain coarsening isoffundam entalim portance forpredicting the average grain sizeand grain size distribution,w hich are dir…     

Experiments and modeling of double-peak precipitation hardening and strengthening mechanisms in Al-Zn-Mg alloy

The aim of the present work is to develop a model for simulating double-peak precipitation hardening kinetics in Al-Zn-Mg alloy with the simultaneous formation of different types of precipitates at elevated temperatures based on the modified Langer-Schwartz approach. The double aging peaks are present in the long time age-hardening curves of Al-Zn-Mg alloys. The physically-based model, while taking explicitly into account nucleation, growth, coarsening of the new phase precipitations and two strengthening mechanisms associated with particle-dislocation interaction (shearing and bypassing), was used for the analysis of precipitates evolution and precipitation hardening during aging of Al-Zn-Mg alloy. Model predictions were compared with the measurements of Al-Zn-Mg alloy. The systematic and quantitative results show that the predicted hardness profiles of double peaks via adding a shape dependent parameter in the growth equation for growth and coarsening generally agree well with the measured ones. Two strengthening mechanisms associated with particle-dislocation interaction (shearing and bypassing) were considered operating simultaneously in view of the particle size-distribution. The transition from shearing to bypassing strengthening mechanism was found to occur at rather early stage of the particle growth. The bypassing was found to be the prevailing strengthening mechanism in the investigated alloys.     

高能球磨制备的Al-Pb纳米相复合结构合金中纳米相Pb的体积分数对其长大行为的影响

利用X射线衍射仪、扫描电子显微镜和透射电子显微镜研究了高能球磨制备的Al-Pb纳米相复合结构合金中纳米相Pb的体积分数对其长大行为的影响。结果表明尽管Al-Pb纳米相复合结构中组成相的尺寸均在纳米量级,不同体积分数的纳米相Pb的长大行为均遵循三次方定律。纳米相Pb的粗化速率随其体积分数的增加而增加,增加幅度大于理论在此成分范围内的预测。纳米相Pb的粗化激活能不随合金成分而变化。纳米相Pb的粗化受溶质原子沿溶剂基体的晶界扩散所控制。     

Coarsening dynamics of self-accommodating coherent patterns

The coarsening kinetics of self-accommodating coherent domain structures is investigated using computer simulations based on a continuum phase-field model. The domain structures are produced from coherent hexagonal to orthorhombic phase transformations. It is found that the long-range elastic interactions arising from the lattice accommodation among different orientation domains of the orthorhombic phase dominate the domain morphologies and the kinetics of domain coarsening. It is shown that the long-range elastic interactions result in several new features for the domain coarsening as compared to normal grain growth. For example, the domain growth rate is reduced significantly and the growth exponent becomes a function of the relative contribution of the elastic energy reduction to the total driving force. In general, the elastic interaction is in favor of fine domains. Although triple junctions are dominant in the microstructure, a significant amount of quadrojunctions exist throughout the domain coarsening process. The average number of sides of the domain is also reduced.     

加热温度对含Nb中碳钢奥氏体晶粒长大的影响

利用微合金析出物与临界晶粒尺寸的定量关系,研究了Si含量较高的中碳Nb微合金钢在不同加热温度下的奥氏体晶粒长大规律。结果表明,随着加热温度的升高,试验钢中奥氏体晶粒逐渐长大,当温度高于1100℃时,晶粒开始粗化。由经验模型可得,随着温度的升高,析出相的体积分数逐渐减少,而颗粒半径逐渐增大,由于二者的共同作用导致了奥氏体晶粒在高于1100℃时迅速粗化;在实验的基础上,得到了适用于试验钢的晶粒长大模型。     

Influence of dendrite arrangement on coarsening during solidification of high-solute Al alloys

Abstract

Coarsening of dendrite arms during continuous solidification is usually characterised by measuring the secondary dendrite arm spacing (SDAS). Images obtained in-situ from X-ray microscopy studies during solidification were used to study SDAS development. Local coarsening and growth kinetics were studied during the solidification of high-solute content aluminium alloys (i.e. Al–30 Cu and Al–20 Cu (wt-%)). Downward and upward solidification conditions were imposed on the sample alloys in order to study the effect of those on coarsening and growth kinetics. The dendritic arrangement, direction of growth and growth fluctuations influence solute-rich liquid distribution which in turn affects solute gradients changing undercooling and thus coarsening and growth kinetics.     

Ti14合金在等温热暴露条件下Ti2Cu相的粗化行为

研究了Ti14合金中Ti_2Cu相在500℃等温热暴露下的静态粗化行为,揭示出Ti_2Cu相的生长速率和形态变化受扩散机制控制。结果表明:静态粗化过程由快速粗化阶段和稳定粗化阶段组成,其中快速粗化阶段主要由末端迁移机制控制,由于条状Ti_2Cu相的末端与长轴方向界面能的差异,溶质原子的扩散过程导致板条状Ti_2Cu的粗化和破碎。而稳定粗化阶段主要由Oswald熟化机制控制,随着时间的延长,合金中Ti_2Cu析出物的尺寸持续增大,而粗化速率降低。Ti_2Cu相的快速粗化会引发第二相的强化,并有效提高快速粗化阶段的可塑性。但是在稳定粗化阶段,由于Ti_2Cu相的长大会增加其位错的有效滑移长度,并进一步影响其裂纹形核阻力同时改变界面构型和晶格失配,从而降低Ti14合金的拉伸塑性。     

Thermal stability of discontinuous precipitation in the Al-Zn-（Cu） system

The coarsening mechanism and kinetics of discontinuous precipitation (DP) in A1-Zn-(Cu) alloys were studied by means of optical microscopy, scanning electron microscopy, and X-ray diffraction analysis. The results show that the coarsening mechanism is different as the aging temperature varies. At a low temperature (150℃), the coarsening occurs through the dissolution and spheroidization of fme laminar structure of DP; at high temperatures (above 200℃), the discontinuous coarsening (DC) of DP microstructure mainly occurs, forming coarsening cells with a larger laminar distance. The growth velocity of coarsening cells rapidly reaches the maximum, and then decreases with the increase of time. The coarsening velocity of DP microstructure decreases due to the addition of Cu element.     

Evolution of the sidebranch structure in free dendritic growth

The sidebranching behavior in free dendritic growth into a supercooled melt is investigated through a detailed measurement of the sidebranch structure of succinonitrile (SCN) dendrites using images from the microgravity experiment of Glicksman and co-workers. The measurements show that the sidebranching evolution is divided into two regimes: an initial linear regime and a subsequent non-linear coarsening regime. A simple model, based on the Mullins–Sekerka linear stability theory, is developed to describe the initial sidebranching behavior. The excellent agreement of the model prediction with the experimental results indicates that the initial sidebranch spacings are selected by the maximum instability wavelength. In the non-linear regime, two new geometrical parameters, derived from the measurements, are proposed to characterize the coarsening process of the sidebranches and to compare the measurements with available coarsening theories. It is found that coarsening at the sidebranch roots follows closely classical laws for purely capillary-driven isothermal coarsening, but the overall coarsening process of the entire sidebranching dendrite cannot be explained by these isothermal coarsening theories.     

Al-Zn对称成分合金不连续析出组织的再结晶

采用光学显微镜、扫描电镜和透射电镜研究了Al 4 0 %Zn(摩尔分数 )二元合金的不连续析出细片层组织在冷轧后重新加热时所发生的再结晶。根据加热过程中的显微组织变化 ,确定了该合金再结晶的形核及长大机制。结果发现 ,再结晶的 2种机制为非典型形核长大机制的连续粗化和典型形核长大机制的不连续粗化 ,后者又分为在团域界面、滑移带等处发生的以变形储能为主要驱动力的粗化和在变形量很小区域发生的以界面能为主要驱动力的粗化。     

Phase field modeling of dendrite growth

Single dendrite and multi-dendrite growth for A1-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites dur-ing solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms.When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.     

Dynamic grain growth and particle coarsening in Al–3.5Cu

Grain growth and particle coarsening in Al–3.5Cu at a temperature of 450 °C has been studied. Plastic deformation of this Zener-pinned system at strain rates of 10^?3 and 10^?4 s^?1 led to an increase in both the grain growth and particle coarsening rates. The results of mechanical tests and metallography, including in situ studies, showed that the material was deforming primarily by intragranular slip. The dynamic grain growth was ascribed to the geometric effect of deformation on the Zener pinning, and the rate sensitivity of the growth to the dynamic particle coarsening. The principal effect of deformation on particle coarsening was concluded to be increased diffusion due to the dislocation content.     

Recrystallization behaviour of fine-grained magnesium alloy after hot deformation

Annealing behaviors of hot-deformed magnesium alloy AZ31 were studied at temperatures from 300 to 673 K by optical and SEM/EBSD metallographic observation. Temperature dependence of the average grain size（D） is categorized into three temperature regions, i.e. an incubation period for grain growth, rapid grain coarsening, and normal grain growth. The number of fine grains per unit area, however, is reduced remarkably even in incubation period. This leads to grain coarsening taking place continuously in the whole temperature regions. In contrast, the deformation texture scarcely changes even after full annealing at high temperatures. It is concluded that the annealing processes operating in hot-deformed magnesium alloy with continuous dynamic recrystallized grain structures can be mainly controlled by grain coarsening accompanied with no texture change, that is, continuous static recrystallization.     

Uniqueness and self similarity of size distributions in grain growth and coarsening

The late stage statistical self-similarity or scaling observed in normal grain growth and coarsening are derived from a model for their evolution using a Fokker–Planck equation obtained from stochastic considerations. Using a suitably generalized H-theorem, it is shown that there is indeed a unique state (self-similar state) evolving from an arbitrary initial state. The time dependence of the appropriate average sizes in normal grain growth, bubble growth, and coarsening are deduced from this model. Multiple self-similar states in some previous models based on mean field treatment do not appear in the present analysis.