Distinctions of dendritic behavior influenced by constant pressure and periodic pressure

The distinctions of dendritic morphology and sidebranching behavior when solidified under atmosphere pressure, constant pressure which is higher than atmosphere pressure (hereinafter referred to as constant pressure) and periodic pressure were investigated using 3-D phase field method. When growing at atmosphere pressure, side branches (secondary dendritic arms) are irregular. When solidified under constant pressure with a relatively high value, side branches are much more luxuriant, with more developed high-order side branches. When applied with periodic pressure, resonant sidebranching happens, leading to many more regular side branches and the smallest secondary dendritic arm spacing (SDAS) in the three cases. The significant difference in dendritic morphology is associated with tip velocity modulated by total undercooling including pressure and temperature undercooling. In the case of constant pressure, tip velocity increases linearly with total undercooling, and it varies periodically in periodic pressure case. The different variation trend in tip velocity is the reason for the distinct dendrite growth behavior in different cases. Unlike the phenomenon in constant pressure case where the dendrite grows faster with higher pressure, the dendrite grows slower under periodic pressure with higher amplitude, resulting in less developed primary dendrite and side branches. This is influenced by tip remelting due to low undercooling or even negative undercooling. It is revealed that the accelerated velocity of tip remelting increases with the decline of undercooling. The greater the amplitude of periodic pressure, the faster the tip remelting velocity during one period. This is the reason why the average tip velocity decreases with the rise of amplitude of periodic pressure.

     

Comparison of Johnson–Mehl–Avrami–Kologoromov (JMAK) kinetics with a phase field simulation for polycrystalline solidification

Polycrystalline solidification in binary alloys proceeding by nucleation and subsequent anisotropic growth is studied by a newly developed phase field model. Simulation results show that, although the growth rates at different locations of the dendrite arm are diverse and cannot be correlated through a multiplicative factor, the time dependence of the dendritic growth area also satisfies a certain simple power function as in the case of linear growth or parabolic growth of a convex particle, but the growth exponent is different from those cases. Through phase field simulation it can be obtained that the growth exponent in two dimensions approximately equals 2 for the dendrite with well-developed side branches and 1.5 for one without side branches. The transformation kinetics of polycrystalline solidification obtained by phase field simulation is compared with the Johnson–Mehl–Avrami–Kologoromov (JMAK) theory based on analyzing the growth kinetics of a single dendrite. For the dendrites grow without side branches, it is found that the JMAK model will overestimate the transformed fraction because of the neglecting of the blocking effect. For the impingement of dendrites with fully developed side branches, the blocking effect is negligible because of the small anisotropy of the dendrictic envelope shape.     

Al-Si合金枝晶形貌的三维相场模拟

基于包含固相扩散系数的Karma薄界面相场模型,采用三维自适应网格划分法,研究了界面宽度、热噪声幅值对Al-Si合金过冷熔体中枝晶生长行为的影响。模拟结果表明：随着界面宽度的增加,枝晶形貌的复杂度下降,枝晶尖端速度下降,尖端液相处溶质的富集程度下降;随着热噪声幅值的增加,枝晶尖端变化较小,位于枝晶主干两侧的二次枝晶的数量和不对称度增加。     

相场法模拟热耦合强度对纯Ni枝晶生长的影响

基于Karma的薄界面极限相场模型,研究了相场和温度场耦合强度对过冷纯Ni熔体中枝晶生长行为的影响。模拟结果表明:随着热耦合强度的减弱,相场受温度场的影响作用减弱,固-液相界面前沿扰动变大,主枝出现二次枝晶并逐渐发达粗化,其粗化方式由缩颈熔断向枝晶臂合并方式转变。同时,枝晶尖端的生长速率增大、曲率半径减小。瞬态过程中枝晶尖端生长速度大于稳态生长速度,随着生长过程的进行,枝晶尖端生长速度逐渐降低,直至达到稳态值,计算结果与微观可解理论吻合良好。     

球墨铸铁中的奥氏体枝晶与缩松

采用着色腐蚀技术,金相显示了球墨铸铁缩松区中奥氏体枝晶组织形貌,分析了球铁缩松的形成机制。研究表明,奥氏体枝晶对缩松缺陷的类型及形成机制具有显著影响;宏观缩松常常出现在枝晶晶簇的间隙,产生于共晶凝固前期树枝晶骨架形成以后,是异地凝固收缩造成的对热节中心（厚壁处）铁水抽吸流动的结果;显微缩松是于凝固末期,晶簇间隙中的凝固收缩得不到补偿而产生的微小孔洞;枝晶数量增多,形态趋于发达,液态金属异地抽吸作用增强,易于形成宏观缩松;反之,枝晶数量减少,形态粗壮,倾向于形成显微缩松;共晶石墨化膨胀有利于消除缩松,而不是缩松形成的原因。     

Oscillatory growth of nonfaceted dendrite and faceted plate during unidirectional solidification

Nonfaceted dendrite and faceted plate in succinonitrile-0.7 wt.% salol and camphor-47.4 wt.% and −35 wt.% naphthalene mixtures were in situ observed during unidirectional solidification. Nonfaceted dendrite oscillates in the growth direction during unidirectional solidification, alternatively repeating fast and slow growth. The faceted phase, whose growth is operated by a two dimensional nucleation mode, also shows oscillation of growth velocity. The oscillation in the faceted phase is due to the intrinsic growth nature, while in the nonfaceted phase it is due to experimental artifacts, that is, thermal fluctuations in the cold and hot zones. The implications of the observed dendrite tip fluctuation in relation with the initiation of dendrite sidebranching have been discussed.     

相场参数对枝晶生长形貌的影响

基于相场与温度场耦合的相场法原理对Ni-Cu二元合金枝晶长大过程进行二维数值模拟。研究了不同过冷度和各向异性系数等相场参数对枝晶生长的影响,最后采用加入非平衡扰动的方式,进行了二次及三次枝晶生长的模拟。模拟结果表明:随着过冷度的增加,越有利于侧向分枝的生长;各项异性γ系数影响枝晶尖端的稳态行为,γ越大,枝晶生长速度越大,侧向分枝越发达,二次枝晶间距越小。     

铝合金中孪生枝晶的研究进展

羽状晶是铸造组织中与柱状晶、等轴晶并列的第三类组织,在凝固理论研究和工业应用中有重要价值。近年来研究表明孪生枝晶是羽状晶最基本的微观组织特征。综述了孪生枝晶尖端形貌、增殖机制、与常规枝晶的竞争生长规律以及羽状晶力学性能等方面的研究进展,讨论了不同因素对孪生枝晶形成和生长的影响,总结了研究中尚未解决的问题。     

HCP材料强界面能各向异性的相场模型

基于Karma模型和Eggleston修正强界面能各向异性的方法,建立HCP材料的强界面能各向异性相场模型。采用有限差分法对控制方程进行数值求解,模拟研究HCP材料的枝晶生长行为。结果表明：枝晶形貌呈现出明显的六重对称性,界面方向不连续,导致在主枝和侧枝的尖端出现棱角。当界面能的各向异性强度低于临界值（1/35）时,枝晶尖端稳态生长速度随着各向异性强度的增加而增加;当界面能各向异性强度值超过临界值时,尖端稳态生长速度降低0.89%;当进一步增加各向异性强度值时,尖端稳态速度增加且在各向异性强度值为0.04时达到极大值,随后减小。     

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.     

Phase field simulation of dendrite growth under convection

The phase-field model coupled with a flow field was used to simulate the solidification of pure materials by the finite difference method. The effects of initial crystal radius, the space step and the interface thickness on the dendrite growth were studied. Results indicate that the grain grows into an equiaxial dendrite during free flow and into a typical branched structure under forced flow. The radius of an initial crystal can affect the growth of side-branches but not the stability of the dendrite's tip when an appropriate value is assigned to it. With an increase in space steps, side-branches appear at the upstream of the longitudinal principal branch and they grow rapidly. With an increase in the interface thickness, the trunk of the longitudinal upstream and lateral principal branches grow longer and become more slender while the number of secondary branches increases.     

界面动力学系数影响枝晶生长的相场模拟

利用相场法对纯金属熔体中的枝晶生长进行了模拟;研究了界面动力学系数取值的影响因素及其取值对枝晶尖端生长速度和尖端半径的影响。结果表明：界面动力学系数的取值由相场和温度场的耦合系数、热扩散系数、界面厚度、界面原子运动时间变量等参数综合决定,随着界面动力学系数的增加,枝晶尖端生长速度减小,尖端半径增大。     

A phase field investigation of dendrite morphology and solute distributions under transient conditions in an Al–Cu welding molten pool

A quantitative phase field model is developed to simulate dendrite morphology and solute distributions of the Al–4?wt-% Cu alloy in Gas Tungsten Arc Welding (GTAW) welding molten pool under transient conditions. The functions of temperature gradient and travel velocity are used to obtain transient conditions of the welding molten pool. Time evolutions of the dendrite morphology, solute distributions of different positions and interfaces are obtained. The dendrite growth process can be divided into four stages, namely linear growth, non-linear growth, competitive growth and short-term steady growth. The solute concentration near the primary dendrite tip region is the smallest, while solute concentration is larger in the front of plane crystals growth interface and the solute concentration in the liquid region among the primary dendrites is obviously the largest, where the solute segregation forms readily. For the given welding parameters, the dendrite morphology and the initial instability of solid/liquid interface agree well with the experimental result.     

基于KKS相场模型模拟强迫对流下镁合金枝晶的生长

基于KKS模型,耦合温度场、浓度场、流场和取向场,建立适合hcp晶系镁合金的相场模型,研究强迫对流下镁合金单晶粒和多晶粒生长过程。结果表明:在v=0.02 m/s的水平强迫对流作用下,晶粒上游侧3个方向的一次枝晶臂生长速度明显快于下游侧3个方向的一次枝晶臂,同一时刻上游方向一次枝晶臂最长,上游侧与水平方向成60o夹角的两枝晶臂次之,下游侧与水平方向成60o夹角的两枝晶臂较短,下游方向枝晶臂最短。多晶粒生长时,晶粒间相互影响,不同晶粒的枝晶臂相互碰撞并彼此抑制,最终形成不对称枝晶形貌。将模拟结果与实验结果进行对比表明,镁合金连续形核下多晶粒枝晶形态的模拟结果与实验结果十分相似,从而验证了本文中相场模型的正确性。     

EFFECT OF LIQUID FLOW ON PRIMARY ARM SPACING OF CONSTRAINED COLUMNAR CRYSTALS

An experimental apparatus,which has a convection generator and an aid-heater,is developedfor the study of the effect of stable laminar liquid flow on the directional solidification processby the use of transparent alloy SCN-2wt-% Ace.The flow is perpendicular to primary arms.By in-situ observation and photographing at different specific moments,it has been found thatsuch a flow can cause a great change in primary spacings of constrained columnar crystals:forcells,the spacings become smaller;but for dendrites,they become larger.The former is mainlydue to the tilted growth of upstreamside branches,while the latter is mainly due to the coup-ling effect of liquid flow with solutal field around dendrite tips.The faster the liquid flows,thefurther smaller the cell spacing and the further larger the dendrite spacing.     

Cu对Zn-27Al二元合金凝固组织的影响

研究了Cu元素的添加量对Zn-27Al二元合金凝固组织的影响,并通过XRD、EPMA、SEM等检测手段分析了随Cu元素含量的变化合金组织中的相变及组织转变过程。结果表明,随着Cu含量的增加,组织由弥散分布的富Cu的ε相逐渐转变为富集于α-Al枝晶晶臂上的CuZn4相;金相组织由粗大的等轴晶逐渐变为发达的树枝晶、长径比大的柱状树枝晶、二次枝晶发达主干相对短小的树枝晶。     

Zn—2.75%Cu合金定向凝固组织及对流的影响

研究了Zn-2.75%Cu合金在传统Bridgeman法和ACRT－B法下定向凝固组织的差别。着重讨论了生长速度和液相强制对流对Zn-Cu包晶定向凝固组织的影响。实验发现,在Bridgeman法定向凝固过程中,生长速度的增加使得液相中的温度梯度减小,一次枝晶间距减小,一次枝晶间距与生长速度和温度梯度的关系式为：λ1=0.6064R^-0.25GL^-0.5。强制对流使得一次枝晶发生分叉和偏转。并且随着对流强度的加大,一次枝晶间距降低,二次枝晶的生长被抑制。包晶反应的存在,使得枝晶的尖端和二次枝晶熔解,造成了固相中枝晶和初生枝晶的差别。     

同步辐射X射线成像法原位研究Al-15％Cu合金柱状晶一等轴晶转变以及无轴柱状枝晶生长

利用上海光源同步辐射装置（SSRF）,通过原位及实时探测研究Al—15％Cu合金定向凝固。结果表明：外部热扰动激发柱状晶一等轴晶转变（CET）。当固一液界面前沿的溶质边界层较薄时,枝晶尖端碎片的分离和漂浮是转变的前奏。而枝晶的三角尖端是断裂敏感区域。只要条件合适,一种新的枝晶形貌将孕育和长大。这种枝晶没有明显的主枝臂,称为无轴柱状枝晶。     

Influence of periodic pressure on dendritic morphology and sidebranching

The influence of periodic pressure with low and high frequencies on microstructure and dendritic sidebranching was studied by using 3-D phase field method.In both low and high frequency cases,the variation trend of SDAS (secondary dendritic arm spacing) with increasing pressure frequency is opposite to that of sidebranching frequency,while the variation trend of the average length of secondary arms is consistent with that of sidebranching frequency.The high sidebranching frequency indicates that more secondary arms share the whole driving force of dendrite growth,resulting in lower driving force for each one and leading to less developed secondary arms.The smallest SDAS is obtained when perturbed by the periodic pressure with the frequency of 0.157/τ_0 (τ_0 is the physical unit of time in the dimensionless phase field model) and 2.200/τ_0 in low and high frequency cases,respectively.Comparisons of dendritic morphology and secondary arms are made between the low and high frequency cases.Firstly,in the low frequency case,secondary arms are luxuriant especially when pressure frequency is low,with many high-order side branches stretching out.Secondly,the average length of secondary arms in primary dendrite is longer in the low frequency case than that without pressure,and much longer than that in the high frequency case.Thirdly,the dendrite tip without side branches in the high frequency case is much longer than that in the low frequency case.All of the differences in dendritic morphology and sidebranching in the two cases can be attributed to the different modulation mechanism.In the low frequency case,periodic pressure determines tip velocity and then modulates sidebranching directly.While in the high frequency case,periodic pressure cannot determine sidebranching directly,but via modulating tiny protuberances in dendrite tip,part of which evolves into side branch.In this case,the tiny protuberances take part of the whole driving force,leading to less developed secondary arms.     

镁合金枝晶生长的相场法研究

采用有限差分法求解考虑界面能各向异性的相场模型,对镁合金枝晶生长过程进行了模拟计算,研究了无量纲过冷度和各向异性强度对枝晶生长行为的影响。结果表明:镁合金枝晶在二维平面上具有6个最优生长方向,优先生长方向上枝晶生长迅速,形成枝晶主干,枝晶形貌具有六重对称性。随着过冷度和各向异性强度的增加,枝晶形貌由光滑的类六边形向具有侧向分支的六重对称形貌转变,温度扩散层由类球形向星形过渡,枝晶尖端生长速率增加,尖端曲率半径和温度值减小。