Ni基耐热合金凝固过程的元胞自动机方法模拟

以温度扩散方程、多组元的溶质扩散方程以及枝晶尖端生长的LGK模型为基础,建立了Ni基耐热合金凝固过程的元胞自动化模型。利用这个模型模拟了凝固过程中不同冷却速率上晶粒微观结构的演化。对模基表面与铸件内部的均匀形核、晶粒生长、扩散过程以及固／液晶面的曲率等对凝固过程中晶粒微观结构演化的影响分别进行了讨论。     

Simulation of Grain Growth during Solidification of Twin-Roll Continuously Cast Pure Aluminum with a Modified CA Model

基于枝晶生长的基本传输过程和元胞自动机(Cellular Automaton,简称CA)-有限元(Finite Element,简称FE)模型基本原理,建立了适应双辊连续铸轧纯铝薄带工艺特点的凝固过程形核和晶体生长的数学模型。模型耦合了宏观温度场和微观组织模拟计算,考虑了溶质扩散、曲率过冷和潜热释放等重要因素的影响,能够模拟凝固过程中枝晶生长的形态。应用本模型对双辊连续铸轧纯铝薄带凝固过程中等轴晶生长、等轴晶多晶粒生长及柱状晶生长、柱状晶向等轴晶演化进行模拟并与实验结果进行对比,模拟结果与实验结果吻合较好     

焊缝金属凝固组织元胞自动机模拟

应用元胞自动机方法进行了焊缝金属凝固组织的模拟.所建立的焊缝凝固组织二维元胞自动机模型考虑了晶粒的概率性成核、曲率过冷、温度过冷、成分过冷、潜热的释放、溶质浓度的再分布以及焊接熔池晶粒的联生长大等影响因素.模型在统一网格下分别采用差分法计算温度和溶质的扩散,应用元胞自动机方法模拟晶粒形核及生长.模拟结果能够定性地再现焊缝金属晶粒择优取向与竞争长大机制.结果表明,元胞自动机方法较好地反映了焊缝金属凝固的特点,是焊缝凝固组织模拟的新途径.     

用宏微观耦合模型模拟铝合金凝固过程

用一种宏微观耦合模型对Al-2．5Si在金属型中的凝固情况进行了模拟。该模型结合改进的元胞自动机模型与有限差分法，考虑了温度场、浓度场和微观生长过程。该改进的元胞自动机模型与经典元胞自动机相比较，不仅考虑了温度场扩散，而且考虑了溶质在液相中的扩散、界面曲率和溶质富集对枝晶尖端过冷度的影响。在宏微观耦合模型中采用大小两套网格分别进行宏观温度场和微观组织演变的计算。在3种不同的浇注温度下得到了3种典型的柱状晶向等轴晶转变的图形。考虑边界条件后的模拟结果发现等轴晶的形核情况与理论分析有所差别。     

A coupled model of grain growth and solute transfer in molten pool of nickel-based alloy

A coupled model of grain growth and solute transfer based on cellular automaton (CA) method was established and applied to grain growth simulation in molten pool of nickel-based alloy.The CA method was used to simulate welding solidification process successfully,but few researches had taken the effect of convection on dendrite morphology into account.In this paper,solute transfer model was used to calculate the effect of convection and diffusion on solute field with CA method simulating grain growth.The results indicate that convection has a significant effect on the morphology of equiaxed grain.Dendrite growth in the upstream direction is amplified,while it is inhibited in the downstream direction.With inlet velocity increasing,this effect becomes more severe.     

基于宏微观耦合三维模型的铝合金凝固模拟

采用一种宏微观耦合模型对铝合金的凝固情况进行了模拟。该模型结合了元胞自动机法与有限差分法,与传统的元胞自动机模型不同,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。模型中采用大小两套网格分别进行宏观温度场和微观组织演变的计算,极大地提高了计算效率。利用该模型模拟了铝合金微观多晶生长,以及铝合金在金属模具中的凝固情况,获得了3种不同浇注温度下典型的柱状晶向等轴晶转变的三维图形。     

Numerical simulation of microstructure evolution and microsegregation of U-Nb alloy during solidification process

In this work, a cellular automaton model has been developed to simulate the microstructure evolution of U-Nb alloy during the solidification process. The preferential growth orientation, solute redistribution in both liquid and solid, solid/liquid interface solute conservation, interface curvature and the growth anisotropy were considered in the model. The model was applied to simulate the dendrite growth and Nb microsegregation behavior of U-5.5Nb alloy during solidification, and the predicted results showed a reasonable agreement with the experimental results. The effects of cooling rates on the solidification microstructure and composition distribution of U-5.5Nb were investigated by using the developed model. The results show that with the increase of the cooling rate, the average grain size decreases and the Nb microsegregation increases.     

基于有限体积法的Al-Cu合金中Cu枝晶生长过程模拟

考虑成分过冷、曲率过冷、界面能各向异性等因素,将有限体积法与元胞自动机相结合,对枝晶生长过程进行模拟,改进了界面推进和溶质扩散过程的计算.结果发现,过冷度、溶质浓度等因素对于枝晶的形貌和生长速度有着重要影响,而在合金的各种物性参数中,液相溶质扩散系数对于枝晶的生长影响尤为显著.     

定向凝固过程中NH_4Cl-H_2O枝晶生长的数值模拟

建立了一种改进的元胞自动机模型(MCA),通过考虑成分过冷、曲率过冷、择优取向系数、温度梯度和抽拉速度等因素,模拟了不同温度梯度方向、不同择优取向及不同抽拉速度对柱状晶形态的影响.模拟结果较好地刻画了温度梯度和生长方向夹角的变化对一次枝晶臂间距的影响,不同择优生长取向的柱状晶竞争生长过程以及柱状晶尖端分叉机制.为了验证模型的可靠性,使用NH_4Cl-H_2O透明合金进行了定向凝固实验,实验结果和模拟结果吻合较好.     

A cellular automaton investigation of the transformation from austenite to ferrite during continuous cooling

A cellular automaton model has been employed to investigate the transformation from austenite to ferrite in low carbon steels during continuous cooling. An important aspect of this approach is the implementation of incorporating local concentration changes into a nucleation or growth function, which is utilized by the automaton in a probabilistic fashion. The modeling gives a visual insight into the effect of cooling conditions on this transformation. The final nucleation number, the number of ferrite grains per austenite grain, ferrite grain size and the kinetics of ferrite formation are obtained as a function of the cooling rate or the undercooling temperature.     

A three-dimensional cellular automaton model of dendrite growth with stochastic orientation during the solidification in the molten pool of binary alloy

A three-dimensional (3D) cellular automaton model is developed for the prediction of dendrite growth with stochastic orientation during solidification process in the molten pool of binary alloy. An angle-information transfer method is proposed for improving cellular automaton technique to simulate the growth of the dendrites whose preferred growth direction owns stochastic misorientation with respect to the direction of the coordinate system. Dendrite morphologies and solute distributions of single dendrite growth and multi-dendrite growth are able to be obtained by the simulation using present model. The model is also employed to study the difference between two-dimensional simulation and 3D simulation on solute segregation and dendritic growth. Using the established model, 3D multi-columnar dendrites with stochastic crystallographic orientations can be obtained efficiently, and the competitive growth and impinging of dendrites can be reproduced in practice. The simulation results agree well with the experimental results.     

Modelling of dendritic growth under forced convection in solidification of Al–7Si alloy

Abstract

An integrated microscale model is used to describe the dendritic growth morphology of Al–7Si alloy under forced convection, which combines the two-dimensional finite difference method (FDM) with the cellular automaton (CA) model. The FDM is used to simulate the induced fluid flow and solute transfer. The CA model is used to depict the dendritic morphology. Simulations are performed to investigate the influences of processing variables on morphological evolution under stirring. Calculated results reveal that at the intermediate undercooling, the growth morphology changes from dendritic to rosette as the rotation speed increases. The dendritic growth is promoted by increasing the undercooling. The rotation speed has a minor influence on microstructure formation for the cases of lower and higher undercoolings. A globulitic structure is formed as the nucleation density is increased. Changing the rotation speed is found to have a negligible influence on morphological evolution for the grain refined alloy.     

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.     

Fe-C合金焊接熔池凝固过程CET转变的数值模拟

基于元胞自动机方法建立了枝晶生长的数值模型,应用该模型模拟了Fe-C合金焊接熔池凝固期间柱状晶向等轴晶(CET)转变过程中枝晶生长形貌与溶质浓度分布状况. 模拟过程主要考虑不同扰动振幅和冷却速率对柱状晶向等轴晶转变的影响. 结果表明,随着时间步长增大,晶粒数逐渐增多,最终趋于稳定值;当冷却速率增加时,生长速度增大,枝晶生长的越充分,显微偏析越严重,而CET转变所需时间越短;当扰动振幅增大时,一次枝晶生长的越细,二次、三次枝晶竞争越激烈.     

Columnar and Equiaxed Solidification of Al-7 wt.% Si Alloys in Reduced Gravity in the Framework of the CETSOL Project

During casting, often a dendritic microstructure is formed, resulting in a columnar or an equiaxed grain structure, or leading to a transition from columnar to equiaxed growth (CET). The detailed knowledge of the critical parameters for the CET is important because the microstructure affects materials properties. To provide unique data for testing of fundamental theories of grain and microstructure formation, solidification experiments in microgravity environment were performed within the European Space Agency Microgravity Application Promotion (ESA MAP) project Columnar-to-Equiaxed Transition in SOLidification Processing (CETSOL). Reduced gravity allows for purely diffusive solidification conditions, i.e., suppressing melt flow and sedimentation and floatation effects. On-board the International Space Station, Al-7 wt.% Si alloys with and without grain refiners were solidified in different temperature gradients and with different cooling conditions. Detailed analysis of the microstructure and the grain structure showed purely columnar growth for nonrefined alloys. The CET was detected only for refined alloys, either as a sharp CET in the case of a sudden increase in the solidification velocity or as a progressive CET in the case of a continuous decrease of the temperature gradient. The present experimental data were used for numerical modeling of the CET with three different approaches: (1) a front tracking model using an equiaxed growth model, (2) a three-dimensional (3D) cellular automaton–finite element model, and (3) a 3D dendrite needle network method. Each model allows for predicting the columnar dendrite tip undercooling and the growth rate with respect to time. Furthermore, the positions of CET and the spatial extent of the CET, being sharp or progressive, are in reasonably good quantitative agreement with experimental measurements.     

A model of solidification microstructures in nickel-based superalloys: predicting primary dendrite spacing selection

A combined cellular automaton-finite difference (CA-FD) model has been developed to simulate solute diffusion controlled solidification of binary alloys. Constitutional and curvature undercooling were both solved to determine the growth velocity of the solid/liquid interface. A modified decentered square/octahedron (in two or three dimensions) growth technique was implemented in the cellular automaton to account for the effect of crystallographic anisotropy. The resulting model is capable of simulating the growth of equiaxed and columnar dendritic grains in 2D and 3D, with the <100> directions either aligned or inclined with the grid. The algorithm used can also be used on coarser grids, with a concomitant loss in resolution, allowing simulation of sufficiently large numbers of dendrites in 3D to investigate the distribution of spacings, as well as average behavior.Simulations were performed for directional solidification with a range of withdrawal velocities and nucleation conditions, but a constant thermal gradient. The simulations capture the full microstructural development and primary spacing selection by both branching and overgrowth mechanisms. The model illustrates that there is a range of possible stable spacings, and that the final spacing is history dependent. It was also found that a minimum deviation from the steady state dendrite spacing is required before the spacing adjustment mechanisms are activated. The influence of perturbing the withdrawal velocity upon the stability of the spacing was also investigated. It was found that perturbations significantly reduce the range of stable primary dendrite spacing.     

Cellular automaton modeling of semisolid microstructure formation

Computer modeling of semi-solid structure formation is of significance in both understanding the mechanisms of globular structure formation and determining the effect of solidification conditions on final microstructure. A modified cellular automaton (mCA) model has been developed, which is coupled with macroscopic models for heat transfer calculation and microscopic models for nucleation and grain growth. The InCA model is applied to A356 Al alloy - one of the most widely used semi-solid alloys, to predict grain morphology and grain size during semi-solid solidification, and determines the effects of pouring temperature on the final microstructure. The modeling results show that the lower the initial temperature, the finer grain size will be obtained. In addition, the model can be used to predict the solutal micro-segregation.     

定向凝固共晶生长的元胞自动机数值模拟

本文在已有的二元初生相元胞自动机（CA）方法的基础上,针对二元共晶凝固过程提出了改进的元胞自动机（MCA）模型.该模型考虑成分过冷和曲率过冷对界面形态的影响,通过界面溶质浓度守恒来获得共晶α相和β相生长速率,模拟了层片的湮灭、分叉与稳态生长.为了验证模型的可靠性,对常见的CBr₄-C₂Cl₆共晶透明合金进行了模拟,研究了抽拉速率对共晶层片间距大小的影响,模拟结果与文献中的实验结果吻合良好;同时模拟了共晶层片间距调整过程的形貌演化以及层片振荡不稳定性现象.本文将MCA模型扩展到三维定向凝固过程中,研究了共晶形态的层棒状转变机制.     

镍基合金焊缝凝固组织演变过程模拟和仿真

建立了一个元胞自动机与有限差分的耦合模型,并将其应用于镍基合金TIG焊熔池凝固过程的模拟.首先对焊接熔池内的各种凝固组织的生长进行了模拟,成功地模拟了平面晶、胞状晶、树枝晶、等轴晶的形态,并与试验结果进行了比照.进一步模拟熔池凝固时的凝固组织不同形态的演变过程,再现了胞状晶到树枝晶、树枝晶到等轴晶的转变过程.同时,采用溶质扩散模型模拟了扩散对溶质场分布的影响.结果表明,模拟结果与试验结果吻合良好.     

Simulation of α-Al grain formation in high vacuum die-casting Al-Si-Mg alloys with multi-component quantitative cellular automaton method

Al-Si-Mg alloys are the most commonly used material in high vacuum die-casting(HVDC),in which the morphology and distribution ofα-Al grains have important effect on mechanical properties.A multi-component quantitative cellular automaton(CA)model was developed to simulate the microstructure and microsegregation of HVDC Al-Si-Mg alloys with different Si contents(7%and 10%)and cooling rates during solidification.The grain number and average grain size with electron backscatter diffraction(EBSD)analysis were used to verify the simulation.The relationship between grain size and nucleation order as well as nuclei density was investigated and discussed.It is found that the growth of grains will be restrained in the location with higher nuclei density.The influence of composition and cooling rate on the solute transport reveals that for AlSi7Mg0.3 alloy the concentration of solute Mg in liquid is higher at the beginning of eutectic solidification.The comparison between simulation and experiment results shows that externally solidified crystals(ESCs)have a significant effect for samples with high cooling rate and narrow solidification interval.