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提出了一种基于两套网格的元胞自动机(CA)模型,用来模拟铸造镁合金凝固过程的枝晶形貌演化.模型中采用的两套网格,一套为四边形正交网格,用来求解溶质扩散方程;另一套为正六边形网格,用来进行CA方法的计算,以反映镁合金枝晶形貌的六重对称特征.模型中,枝晶尖端生长驱动力由界面平衡溶质浓度和求解扩散方程得出的界面实际溶质浓度的差值决定.应用该模型计算了AZ91D镁合金自由凝同条件下的单个等轴晶生长和定向凝固条件下的柱状枝晶生长以及Mg-10Gd-2Y-O.5Zr(质量分数,%)镁合金多晶粒等轴晶生长.将模拟结果与浇铸AZ91D镁合金的块状试件和Mg-10Gd-2Y-0.5Zr合金的阶梯试件进行了对比.

The texture of Mg alloy dendrites is quite different from that of fcc or bee metals because of the influence of hcp crystal lattice on the dendrite morphology evolutions during solidification. Although the simulations of dendrite morphologies for fee or bcc metals by cellular automaton (CA) methods have been widely reported, CA simulations of magnesium alloys with hcp crystal lattice have just appeared in recent years. When performing the simulation of Mg alloy dendrites with a CA method on a square mesh, the artificial anisotropy of growth kinetics introduced by the square mesh makes it hard to reflect the texture of Mg alloy dendrites, which shows the six-fold symmetry instead of four-fold symmetry of bcc or fee metal dendrites.In the present paper, a two dimensional CA model has been developed for simulating the dendrite morphology evolution of cast Mg alloys. The model employs two sets of meshes to perform the numerical simulation, where a hexagonal mesh is used to perform CA calculation to reflect the texture of Mg alloy dendrites, and an orthogonal mesh is used to solve the mass transportation equation. The two sets of meshes are coupled by an interpolation method. By employing the two-set mesh method, the texture of Mg alloy dendrites is well reflected and the undesired artificial growth kinetics introduced by square mesh is avoided. In the model, the growth kinetics of dendrite tips was determined by the difference between local equilibrium and local actual compositions obtained by solving the solute transport equation. With this calculation method for growth kinetics, the solid fraction of interface CA cell can be obtained directly from the solute field, which decreases the computational cost greatly. The model was applied to simulate the single dendrite evolution and columnar dendrite growth of AZ91D Mg alloy, as well as multi-dendrite growth and grain size of Mg-10Gd-2Y-0.5Zr (mass fraction, %) alloy step-shaped castings. To validate the current model, permanent mold sample castings of AZ91D Mg alloy and step-shaped castings of Mg-10Gd-2Y-0.5Zr alloy were produced. Optical metallographic examinations were performed on specimens of these two Mg alloys, and grain sizes were measured on solution treated specimens of Mg-10Gd-2Y-0.5Zr alloy. The simulated and experimental results were compared.