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Comparison of Cellular Automaton and Phase Field Models to Simulate Dendrite Growth in Hexagonal Crystals

Mohsen Asle Zaeem

材料科学技术(英)

A cellular automaton (CA)-finite element (FE) model and a phase field (PF){FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals. In the CA-FE model, the conservation equations of mass and energy were solved in order to calculate the temperature field, solute concentration, and the dendritic growth morphology. CA{FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing (SDAS) vs cooling rate. In the PF model, a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidification of pure materials. Another PF variable was considered to determine the evolution of solute concentration. Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton-Glicksman-Kurz (LGK), showing quantitatively good agreement in the tip growth velocity at a given melt undercooling. Application to magnesium alloy AZ91 (approximated with the binary Mg-8.9 wt% Al) illustrates the di±culty of modeling dendrite growth in hexagonal systems using CA-FE regarding mesh-induced anisotropy and a better performance of PF{FE in modeling multiple arbitrarily-oriented dendrites growth.

关键词: Dendrite growth

铸造镁合金的枝晶生长模拟

刘志勇 , 许庆彦 , 柳百成

金属学报

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.

关键词: 数值模拟 , Magnesium alloy , Dendrite growth , Compact hexagonal

Phase field modeling of dendrite growth

Yutuo ZHANG , Chengzhi WANG , Dianzhong LI , Yiyi LI

金属学报(英文版) doi:10.1016/S1006-7191(08)60089-7

Single dendrite and multi-dendrite growth for Al-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 during 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.

关键词: Phase field modeling , null , null , null

Phase field simulation of dendrite growth under convection

Yutian DING

金属学报(英文版)

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.

关键词: Phase field method , 强制对流 , 枝晶生长 , 模拟

Numerical Modelling and Experimental Investigation of Microse-gregation in Al-4.45 wt pct Cu: Effect of Dendrite Joining

H.B.Dong

材料科学技术(英)

A numerical model Alloy/M has been applied to investigate the microsegregation in Al-4.45 wt pct Cu alloy. The calculated data were compared with the experimental measurements for samples solidified at different cooling rates. Discrepancies in solute concentration occur between the experimental observations and calculated results. Reasons for the discrepancies were discussed, and the effect of dendrite joining at a later stage of solidification on the microsegregation was investigated. Calculations that have included this effect showed a better fit with experimental results.

关键词: Microsegregation , null , null , null , null

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