Al-0.035Ni合金凝固过程微观组织的相场法数值模拟

采用相场法对Al-0.035Ni合金在凝固过程中的微观组织进行数值模拟。分别模拟时间步长、各向异性系数和过冷度下Al-0.035Ni合金的枝晶生长过程;分析了Al-0.035Ni合金中过冷度对溶质分布的影响。结果表明:随着时间步长的不断增大,晶粒生长由最初的近圆形向枝晶状形貌转变,沿晶轴方向的枝晶生长速率明显快于其他方向。当各向异性系数较小时晶体生长缓慢,晶核在各个方向上的生长速度并没有太大的差异;随着各向异性系数的增大,晶粒在主轴方向上的生长优势越发明显。合金等轴枝晶周围的热扩散层由于受过冷度的影响,其枝晶尖端具有不同的生长速率;当增大过冷度时,枝晶尖端的生长速率随之增大,尖端形核半径呈减小趋势。此外,过冷度对合金枝晶内的溶质偏析影响不容忽视,会在枝晶内形成明显的溶质梯度。     

Fe-C合金等温凝固过程的相场法模拟

基于KKS模型,采用耦合相场和溶质场的方法,对Fe-0．5mol％C合金凝固过程中的枝晶生长进行了模拟,并研究了过冷度、各向异性强度和扰动强度对枝晶生长形貌的影响。结果表明：随着过冷度的减小,枝晶主干细化,各向异性程度增大,晶粒生长速度减小,溶质扩散层厚度增加,枝晶的最高溶质浓度降低,溶质梯度减小;随着各向异性的增加,晶粒由海藻状转变为枝晶态,枝晶生长速度也随之增大;扰动强度引发了侧向分枝,侧枝间互相竞争生长,根部出现“颈缩”现象,但扰动强度的加入并不改变枝晶尖端的稳态行为。     

强界面能各向异性下二元Ni-Cu合金枝晶生长过程的相场法模拟

基于Wheeler模型和Eggleston修正强界面能各向异性的方法,建立耦合溶质场和温度场的相场模型,模拟强界面能各向异性下Ni-Cu合金枝晶生长过程.结果表明:在强界面能各向异性作用下,界面方向枝晶生长不连续且枝晶出现棱角;由于枝晶尖端温度梯度和溶质梯度较大,枝晶生长迅速.当界面能各向异性强度低于临界值时,枝晶尖端生长速度随界面能各向异性强度的增加而增大;当界面能各向异性强度等于临界值时,枝晶尖端生长速度下降4.34％;当界面能各向异性强度大于临界值时,枝晶尖端生长速度随界面能各向异性强度的增加先增大到极大值后逐渐减小.当无量纲热过冷度较小时,晶体平衡形貌为类矩形;随着无量纲热过冷度的增加,晶体平衡形貌向枝晶转变,枝晶尖端生长速度先呈幂指数增加,然后呈线性增加,枝晶生长由扩散控制转变为动力学控制.     

Fe-C合金枝晶生长的相场模拟

采用相场法模拟了Fe-C0.5mol%合金等温凝固中的枝晶生长过程,研究了各向异性模数、各向异性强度和过冷度对枝晶生长的影响.结果表明,在二维平面上,枝晶沿<100>方向生长时,形成四重对称的枝晶形貌;枝晶沿<110>方向生长时,形成六重对称的枝晶形貌.随着各向异性强度增加,枝晶生长速度增加,晶粒由类球状向枝晶转变.随着过冷度的增加,枝晶生长速度增大,溶质扩散层减小,枝晶变的粗大.     

二元合金非等温凝固相场法模拟

利用耦合温度场与溶质场的相场模型对Al-Cu二元合金非等温凝固时枝晶生长过程进行了模拟。研究了人为变化的不同热扩散系数对枝晶生长行为的影响。计算结果表明：随着热扩散系数的减小，潜热释放对熔体内原有温度场的影响也减小，熔体内过冷度能够更好地保持；而枝晶尖端生长速度将增大．枝晶呈现出更发达的侧向分支；同时，溶质偏析程度也越小。将计算模拟结果和实验结果进行了比较，两者吻合良好。     

纯Ni枝晶生长过程的相场法数值模拟

采用凝固过程相场模型,对纯Ni过冷熔体中的枝晶生长过程进行了计算模拟,研究了各向异性强度、过冷度、扰动等对枝晶生长的影响.结果表明:随着各向异性强度的增大,枝晶尖端生长速度加快,枝晶结构特征愈加明显;随着过冷度的增加,枝晶尖端稳定性遭到破坏,甚至出现分叉;扰动会促发侧向分枝的形成,但不影响枝晶尖端的稳态生长行为.     

相场法模拟Ni-Cu合金枝晶生长中过冷度的影响

用相场法模拟了Ni30Cu70合金非等温凝固中的枝晶生长过程。研究了过冷度对过冷合金熔体中的枝晶生长以及溶质场和温度场的分布的影响。模拟结果表明：随着过冷度的增大，二次枝晶臂发达，溶质扩散层厚度减小、溶质浓度梯度增大，热扩散层厚度减小。     

来流对Al-Cu合金三维树枝晶生长的影响

建立了模拟二元合金树枝晶生长的三维元胞自动机模型,以Al-4%Cu(质量分数)为模型合金,模拟了合金过冷熔体中树枝晶的生长过程,研究了来流对枝晶生长的影响.结果表明,来流对合金过冷熔体中三维树枝晶生长影响显著,迎流侧枝晶尖端生长速度随来流速度的增大而增大,枝晶尖端半径随来流速度的增大而减小;随着来流速度的增大,枝晶尖端选择参数减小;在给定过冷度条件下,随界面能各向异性的增大,来流对枝晶尖端选择参数的影响增强;对于给定的合金(或界面能各向异性),来流对枝晶尖端选择参数的影响随着过冷度的增大而增强.     

对流作用下枝晶生长行为的相场法

基于Wheeler等提出的纯扩散相场模型,建立耦合溶质场、温度场和流场的相场模型,采用有限差分法对控制方程进行数值求解,研究Ni-Cu合金凝固过程中单晶粒枝晶和多晶粒枝晶在强制对流作用下的生长行为。结果表明:熔体的流动显著改变凝固前沿的传热和传质,从而改变枝晶的生长行为。在流速为6.43m/s的垂直强制对流作用下,上游枝晶受过冷熔体冲刷,枝晶尖端溶质浓度和温度低,实际过冷度大,枝晶生长迅速,稳态生长速度比纯扩散时增加28%;热量和溶质在下游富集,下游枝晶尖端溶质浓度和温度高,实际过冷度小,枝晶生长缓慢,稳态生长速度比纯扩散时减小26%。     

晶粒生长中高界面能各向异性的相场模拟

建立了一个能够模拟纯物质的计算有效的相场模型,该模型考虑了强动力学各向异性和高各向异性界面能。采用数值计算模拟了各种程度的各向异性（强动力学和高各向异性界面能）。在界面各向异性系数变化中,平衡晶体形貌从光滑过渡到出现角部,这之间有一临界值。小于临界值时,生长速度随界面能各向系数的增加单调增加;各向异性系数大于临界值时,随界面能各向系数的增加生长速度减小。在过冷度的变化过程中,生长速度从受热扩散控制转变到动力学控制,在热扩散控制时,生长速度随过冷度增加而增加,枝晶尖端半径随温度增加而减小;在动力学控制时生长速度和枝晶尖端半径随过冷度增加而增加,这与传统的微观可解理论认为R^2V=CONSTANT有所违背。     

Phase-field models for eutectic solidification

This article discusses two methods for modeling eutectic solidification using the phase-field approach. First, a multi-phase-field model is used to study the three-dimensional morphological evolution of binary eutectics. Performing the calculations in three dimensions allows observation of both lamellar and rod-like structures as well as transient phenomena such as lamellar fault motion, rod-branching, and nucleation or elimination of phases as solidification progresses. The second approach models multiple eutectic grains where the crystallizing phases have an orientation relationship. This approach is promising for modeling complex solidification microstructures. For more information, contact Daniel Lewis, General Electric Co., Ceramic and Metallurgy Technologies, Building MB223, One Research Circle, Niskayuna, NY 12309; (518) 387-4538; fax (518) 387-5576; e-mail lewis@research.ge.com.     

Phase-field simulations of non-isothermal binary alloy solidification

A phase-field method for two-dimensional simulations of binary alloy solidification is studied. Phase-field equations that involve both temperature and solute redistribution are formulated. The equations are solved using the finite element method with triangular elements on unstructured meshes, which are adapted to the solution. Dendritic growth into a supersaturated melt is simulated for two temperature regimes: (a) the temperature is prescribed on the boundary of the computational domain; and (b) the heat is extracted through the domain boundary at a constant rate. In the former regime the solute redistribution is compared with the one given by an isothermal model. In the latter case the influence of the size of the computational domain and of the heat extraction rate on dendritic structure is investigated. It is shown that at high cooling rates the supersaturation is replaced by thermal undercooling as the driving force for growth.     

Phase-field simulations of solidification of AI-Cu binary alloys

The dendrite growth process during the solidification of the Al-4.5 %Cu binary alloy was simulated using the phase-field model, proposed by Kim et al. Solute diffusion equation and heat transfer equation were solved simultaneously. The effects of the noise on the dendrite growth, solute and temperature profile in the undercooled alloy melt were investigated. The results indicate that the noise can trigger the growth of the secondary arms, and increase the highest temperature and solute concentration, but not influence the tip operating state. The solute and temperature gradients in the tip are the highest.     

Phase-field modelling of self-propagating high-temperature synthesis of NiAl

A phase-field model is developed and used to simulate high-temperature synthesis of intermetallic compounds. The model is based on a thermodynamic formulation, which incorporates the formation of chemically ordered phases and the associated heat generation. In contrast to previous approaches to modelling of high-temperature synthesis of intermetallics, the present model can be used to analyse the kinetics of the process at the microstructure level. The model takes general thermodynamic and kinetic parameters as input and gives as output a spatially resolved sequence of phase formation, from which the overall reaction kinetics can be inferred. Thus, no additional assumption has to be made on the nature of the kinetic mechanisms or on the magnitude of the overall reaction rate. Beside prediction of the microstructure, the model captures the key thermal characteristics of the combustion synthesis in both modes of thermal explosion and self-propagation. The results of simulations, as applied to the case of intermetallic formation in a simplified Ni–Al system, are shown to be consistent with the existing experimental data.     

二元合金非等温凝固过程的相场法模拟

基于Ginzburg-Landau理论,发展了一个新的相场模型.并利用该相场模型与溶质场、温度场进行耦合计算,以Al-6.5Cu合金为例模拟了二元合金非等温凝固和等温凝固的等轴枝晶生长过程.研究了凝固潜热对过冷合金熔液中的等轴枝晶生长以及溶质场和温度场的分布的影响.结果表明:潜热的释放在一定程度上抑制了枝晶的生长,使非等温凝固时枝晶没有等温凝固时发达,并且凝固界面的溶质浓度也会降低,但不会改变在枝晶生长过程中浓度分布情况.而且非等温凝固时的Peclet数值与Ivantsov理论值符合得更好.     

Phase-field simulations of solidification of Al-Cu binary alloys

The dendrite growth process during the solidification of the Al-4.5%Cu binary alloy was simulated using the phase-field model, proposed by Kim et al. Solute diffusion equation and heat transfer equation were solved simultaneously. The effects of the noise on the dendrite growth, solute and temperature profile in the undercooled alloy melt were investigated. The results indicate that the noise can trigger the growth of the secondary arms, and increase the highest temperature and solute concentration, but not influence the tip operating state. The solute and temperature gradients in the tip are the highest.