Simulation of dendritic growth of magnesium al oys with fluid flow

Fluid flow has a significant impact on the microstructure evolution of alloys during solidification. Based on the previous work relating simulation of the dendritic growth of magnesium alloys with hcp(hexagonal closepacked) structure, an extension was made to the formerly established CA(cellular automaton) model with the purpose of studying the effect of fluid flow on the dendritic growth of magnesium alloys. The modified projection method was used to solve the transport equations of flow field. By coupling the flow field with the solute field, simulation results of equiaxed and columnar dendritic growth of magnesium alloys with fluid flow were achieved. The simulated results were quantitatively compared with those without fluid flow. Moreover, a comparison was also made between the present work and previous works conducted by others. It can be concluded that a deep understanding of the dendritic growth of magnesium alloys with fluid flow can be obtained by applying the present numerical model.     

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。     

镁合金枝晶形貌的相场方法模拟

针对hcp晶系的镁合金,建立了其二维枝晶生长的相场模型.根据该模型编写模拟程序,得到了具有六重对称性的晶粒形貌,并根据模拟结果分析了温度场对其枝晶臂形成的影响;根据该模型耦合热扰动进行镁合金微观组织模拟,从计算结果中观察到了枝晶臂相互竞争、改变优先生长方向、颈缩、熔断、融合等现象;计算得到的枝晶形貌与实验结果较为吻合.同时还研究了参数的选取对镁合金枝晶发育的影响.     

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.     

CA-LBM模型模拟自然对流作用下的枝晶生长

建立了一个基于二维的元胞自动机-格子Boltzmann方法(cellular automaton-lattice Boltzmann method,CA-LBM)的耦合模型,对自然对流作用下枝晶的生长行为进行模拟研究.本模型采用CA方法模拟枝品的生长,采用LBM对自然对流及由对流和扩散控制的溶质和热传输进行数值计算.通过计算方腔自然对流问题对模拟自然对流、溶质和热传输的LB模型进行了验证.应用所建市的CA-LBM耦合模型模拟研究了合金中单枝晶和多枝晶在自然对流作用下的生长规律,并将单枝晶上游尖端的稳态生长模拟数据与解析模型的预测结果进行了比较.结果表明,模拟结果与理论预测值吻合良好,自然对流会对枝晶的生长产生重要影响.     

Lattice Boltzmann modeling of dendritic growth in a forced melt convection

A two-dimensional (2D) lattice Boltzmann-based model is developed to simulate solutal dendritic growth of binary alloys in the presence of forced flow. The model adopts the lattice Boltzmann method (LBM) that describes transport phenomena by the evolution of distribution functions of moving pseudoparticles to numerically solve fluid flow and solute transport governed by both convection and diffusion. Based on the LBM-calculated solutal field, the dynamics of dendritic growth is determined according to a previously proposed local solutal equilibrium approach. After detailed model analysis and validation, the model is applied to simulate single and equiaxed multidendritic growth of Al–Cu alloys with forced convection. The results demonstrate the quantitative, numerically stable and computationally efficient capabilities of the proposed model. It is found that the solute distribution and dendritic growth are strongly influenced by convection, producing asymmetrical dendrites that grow faster in the upstream direction, but mostly slower in the downstream direction.     

A three-dimensional cellular automaton model for simulation of dendritic growth of magnesium alloy

A numerical model based on the cellular automaton method for the three-dimensional simulation of dendritic growth of magnesium alloy was developed. The growth kinetics was calculated from the complete solution of the transport equations. By constructing a three-dimensional anisotropy model with the cubic CA cells, simulation of dendritic growth of magnesium alloy with six-fold symmetry in the basal plane was achieved. The model was applied to simulate the equiaxed dendritic growth and columnar dendritic growth under directional solidification, and its capability was addressed by comparing the simulated results to experimental results and those in the previously published works. Meanwhile, the three-dimensional simulated results were also compared with that of in two dimensions, offering a deep insight into the microstructure formation of magnesium alloy during solidification.     

枝晶生长的数值模拟

对朱、洪已发展的一种微观尺度cellular automaton(CA)模型做了进一步改进．在改进的模型中用二元合金的Gibbs-Thomson方程建立固／液界面的平衡关系．考虑了动力学和表面能各向异性对枝晶择优生长方向的影响．应用改进的模型模拟了不同择优取向的单枝晶在过冷熔体中的自由生长、定向凝固过程中柱状晶的竞争生长以及等轴晶的演变过程．模拟结果表明,改进后的模型成功地模拟出各种不同择优取向的单枝晶和多枝晶的生长形貌。     

外加磁场对镁合金焊接熔池形态的影响

以镁合金焊接熔池为研究对象,建立了移动热源作用下焊接熔池的三维数学模型. 利用大型通用有限元软件ANSYS将电磁场分析结果导入到热流场分析中,实现电磁场和热流场之间的耦合分析. 模拟了无外加磁场作用下以及外加磁场作用下镁合金焊接熔池的温度场分布和流体流动的速度矢量分布. 结果表明,外加磁场产生的电磁力驱动熔池中熔融的液态金属发生旋转运动,改变了液态金属原有的运动方式和传热方式,流体流动速度和流动范围增加,焊缝熔宽增大,熔深减小. 试验结果验证了模拟结果的可靠性.     

Characterization and Modeling Study on Interfacial Heat Transfer Behavior and Solidified Microstructure of Die Cast Magnesium AlloysEI北大核心CSCD

Magnesium alloys are widely used in various fields because of their outstanding properties. High-pressure die casting (HPDC) is one of the primary manufacturing methods of magnesium alloys. During the HPDC process, the solidification manner of casting is highly dependent on the heat transfer behavior at metal-die interface, which directly affects the solidified microstructure evolution, defect distribution and mechanical properties of the cast products. As common solidified microstructures of die cast magnesium alloys, the externally solidified crystals (ESCs), divorced eutectics and primary dendrites have important influences on the final performance of castings. Therefore, investigations on the interfacial heat transfer behavior and the solidified microstructures of magnesium alloys have considerable significance on the optimization of die-casting process and the prediction of casting quality. In this paper, recent research progress on theoretical simulation and experimental characterization of the heat transfer behaviors and the solidified microstructures of die cast magnesium alloys was systematically presented. The contents include: (1) A boundary-condition model developed based on the interfacial heat transfer coefficients (IHTCs), which could precisely simulate the boundary condition at the metal-die interface during solidification process. Accordingly, the IHTCs can be divided into four stages, namely the initial increasing stage, the high value maintaining stage, the fast decreasing stage and the low value maintaining stage. (2) A numerical model developed to simulate and predict the flow patterns of the externally solidified crystals (ESCs) in the shot sleeve during mold filling process, together with discussion on the influence of the ESCs distribution on the defect bands of die cast magnesium alloys. (3) Nucleation and growth models of the primary alpha-Mg phases developed by considering the ESCs in the shot sleeve. (4) Nucleation and growth models of the divorced eutectic phase, which can be used to simulate the microstructure evolution of die cast magnesium alloys. (5) The 3D morphology and orientation selection of magnesium alloy dendrite. It was found that magnesium alloy dendrite exhibits an eighteen-primary branch pattern in 3D, with six growing along < 11(2)over bar0 > in the basal plane and the other twelve along < 11(2)over bar3 > in non-basal planes. Accordingly, an anisotropy growth function was developed and coupled into the phase field model to achieve the 3D simulation of magnesium alloy dendrite.     

镁合金枝晶生长的试验表征及模拟仿真研究进展

镁合金被誉为21世纪的绿色工程材料,被广泛应用于汽车、航空航天和3C等领域。枝晶作为金属凝固过程中一种常见的晶体形态,其形貌对铸件的力学性能影响很大。综述了具有密排六方晶体结构的镁合金枝晶生长试验表征与模拟仿真研究进展,阐述了采用试验表征与分析得到的镁合金二维及三维枝晶生长形貌与择优取向,分析了通过建立枝晶生长模型耦合溶质场、温度场、流场、压力场等模拟仿真得出的不同凝固工艺条件对镁合金二维及三维枝晶生长形貌的影响规律,最后指出了当前镁合金枝晶生长试验表征及模拟仿真研究存在的问题及未来的发展方向。     

Phase-field modeling of dendritic growth of magnesium alloys with a parallel-adaptive mesh refinement algorithm

A two-dimensional phase field (PF) model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure.By applying a parallel-adaptive mesh refinement (Para-AMR) algorithm,the computational efficiency of the numerical model was greatly improved.Based on the PF model,a series of simulation cases were conducted and the results showed that the anisotropy coefficient and coupling coefficient had a great influence on the dendritic morphology of magnesium alloy.The dendritic growth kinetics was determined by the undercooling and equilibrium solute partition coefficient.A significant finding is acquired that with a large undercooling,the maximum solute concentration is located on both sides of the dendrite tip in the liquid,whereas the maximum solute concentration gradient is located right ahead of the dendrite tip in the liquid.The dendrite tip growth velocity decreases with the increase of the equilibrium solute partition coefficient,while the variation trend of the dendrite tip radius is the opposite.Quantitative analysis was carried out relating to the dendritic morphology and growth kinetics,and the simulated results are consistent with the theoretical models proposed in the previously published works.     

Numerical simulation of the effect of fluid flow on solute distribution and dendritic morphology

Abstract

The presence of bulk and interdendritic flow during solidification can alter the microstructure, potentially leading to the formation of defects. In this paper, a numerical model is presented for the direct simulation of dendritic growth in the presence of fluid flow in both liquid and mushy zones. The Navier–Stokes equations are solved for multiphase flow using a projection method. The energy conservation and solute diffusion equations are solved via a combined stochastic nucleation approach and finite difference solution to simulate dendritic growth. The predicted microstructures illustrate typical asymmetric dendritic growth behaviour under forced convection, which is consistent with prior similar simulations of a single dendrite during unconstrained growth (both 2D and 3D). The micromodel was coupled with a macromodel to investigate the effects of forced fluid flow on equiaxed dendritic growth and micro-segregation during vacuum arc remelting.     

Modeling of Microstructure and Microsegregation in Solidification of Multi-Component Alloys

Driven by industrial demand, extensive efforts have been made to investigate microstructure evolution and microsegregation development during solidification of multicomponent alloys. This paper briefly reviews the recent progress in modeling of microstructures and microsegregation in solidification of multicomponent alloys using various models including micromodel, phase field, front tracking, and cellular automaton approaches. A two-dimensional modified cellular automaton (MCA) model coupled with phase diagram software PanEngine is presented for the prediction of microstructures and microsegregation in the solidification of ternary alloys. The model adopts MCA technique to simulate dendritic growth. The thermodynamic data needed for determining the dynamics of dendritic growth are calculated with PanEngine. After validating the model by comparing the simulated values with the prediction of the Scheil model for solute profiles in the primary dendrites as a function of solid fraction, the model was applied to simulate the microstructure and microsegregation in the solidification of Al-rich ternary alloys. The simulation results demonstrate the capabilities of the present model not only to simulate realistic dendrite morphologies, but also to predict quantitatively the microsegregation profiles in the solidification of multi-component alloys. This article was presented at the Multi-Component Alloy Thermodynamics Symposium sponsored by the Alloy Phase Committee of the joint EMPMD/SMD of The Minerals, Metals, and Materials Society (TMS), held in San Antonio, Texas, March 12-16, 2006, to honor the 2006 William Hume-Rothery Award recipient, Professor W. Alan Oates of the University of Salford, UK. The symposium was organized by Y. Austin Chang of the University of Wisconsin, Madison, WI, Patrice Turchi of the Lawrence Livermore National Laboratory, Livermore, CA, and Rainer Schmid-Fetzer of the Technische Universitat Clausthal, Clauthal-Zellerfeld, Germany.     

Effect of melt flow on dendritic growth in AlSi7-based alloys during directional solidification

Abstract

High-strength automotive components are often made of AlSi7-based alloys. A very challenging problem with aluminium casting is the influence of melt flow during solidification, because it affects the microstructure formation and therefore the material properties. The scope of this paper is to investigate the effect of forced melt flow on the evolution of the dendritic microstructure in a binary AlSi7 alloy during directional solidification. Global modelling using the software CrysMAS provides typical flow patterns and velocities. These values are used as boundary condition for the flow in the phase field code MICRESS, which allows the numerical simulation of dendritic array solidification in 2D with applied flow. From solidification experiments in a gradient furnace with applied rotating magnetic field the dendrite shapes are determined. It is found consistently that intense melt flow leads to asymmetric dendrite shapes and the growth behaviour of the dendrite arms is directly correlated with the flow direction.     

铸造镁合金的枝晶生长模拟

根据hcp晶体学结构和优先生长方向,建立了铸造镁合金晶体生长的物理模型,提出了一种新的随机性模拟方法--虚拟生长中心计算模型.模型考虑了枝晶生长动力学、各向异性和二次枝晶臂粗化,采用枝晶形状函数揭示了一次枝晶和二次枝晶的生长演化过程.引入坐标变换技术可更快速准确计算任意晶向枝晶的生长捕获.耦合了微观溶质场计算,得到了更准确的枝晶生长形貌和溶质分布情况.对Mg-Al合金定向凝固和等轴晶生长的模拟验证了本模型的正确性.     

镁合金铸造成形过程宏观／微观模拟

通过研究镁合金压铸过程中界面热,采用热传导反算法确定压铸过程的界面换热系数,研究镁合金压铸过程中工艺参数及凝固过程对铸件界面换热系数的影响规律,建立镁合金压铸过程界面换热边界条件的处理模型,以实现镁合金压铸过程中凝固过程的准确预测。通过实验研究镁合金压铸过程中凝固组织,建立了镁合金压铸过程中形核模型。采用CA方法,建立了镁合金枝晶生长模型,以实现镁合金凝固组织的预测。采用相场方法研究了镁合金枝晶生长形貌。     

Multi-scale coupling simulation in directional solidification of superalloy based on cellular automaton-finite difference method

Casting microstructure evolution is difficult to describe quantitatively by only a separate simulation of dendrite scale or grain scale, and the numerical simulation of these two scales is difficult to render compatible. A three-dimensional cellular automaton model couplling both dendritic scale and grain scale is developed to simulate the microstructure evolution of the nickel-based single crystal superalloy DD406. Besides, a macro–mesoscopic/microscopic coupling solution algorithm is proposed to improve computational efficiency. The simulation results of dendrite growth and grain growth of the alloy are obtained and compared with the results given in previous reports. The results show that the primary dendritic arm spacing and secondary dendritic arm spacing of the dendritic growth are consistent with the theoretical and experimental results. The mesoscopic grain simulation can be used to obtain results similar to those of microscopic dendrites simulation. It is indicated that the developed model is feasible and effective.     

元胞自动机法模拟铝合金三维枝晶生长

以元胞自动机模型为基础,基于晶粒形核和生长的物理过程及热质传输过程,建立了铝合金凝固过程微观组织形成及枝晶形貌演化的三维元胞自动机模型.与传统的元胞自动机不同,该模型不仅考虑了温度场扩散而且考虑了固液相中的溶质扩散、曲率过冷等重要因素.枝晶尖端生长速度与局部过冷度的关系采用KGT(Kurz-Giovanola-Trivedi)模型,温度场和浓度场计算采用有限差分法.使用该模型模拟了单晶生长和多晶生长.模拟结果表明,所建立的模型能够合理反映质点形核、单晶粒生长和多晶粒生长,微观组织形貌的模拟计算结果合理.     

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.