The dendrite growth in casting and additive manufacturing is rather important and related to the formation of some defects. However, quantitatively simulating the growth of dendrites with arbitrary crystallographic orientations in 3-dimension(3D) is still very challenging. In the present work, we develop a multi-grid Cellular Automaton (CA) model for the dendrite growth. In this model, the interfacial area is further discretized into a child grid, on which the decentered octahedron growth algorithm is performed. The model is comprehensively and quantitatively verified by comparing with the prediction of analytical models and a published x-ray imaging observation result, proving that the model is quantitatively and morphologically accurate. After that, with the temperature gradient and cooling rate extracted from a finite-volume-method(FVM)-based thermal-fluid model, the model was applied in reproducing the dendrite growth process of nickel-based superalloy during a single-track electron beam melting process. The simulation results agree fairly well with the experimental observation, demonstrating the feasibility and effectiveness of using the model in additive manufacturing.

铸造和增材制造中的枝晶生长相当重要，并且与某些缺陷的形成有关。然而，在 3 维（3D）中定量模拟具有任意晶体取向的枝晶的生长仍然非常具有挑战性。在目前的工作中，我们开发了一种用于枝晶生长的多网格元胞自动机 (CA) 模型。在该模型中，界面区域进一步离散为子网格，在该子网格上执行偏心八面体生长算法。通过与解析模型的预测和已发表的X射线成像观测结果的对比，对该模型进行了全面定量验证，证明该模型在定量和形态上是准确的。在那之后，利用从基于有限体积法 (FVM) 的热流体模型中提取的温度梯度和冷却速率，该模型被应用于再现镍基高温合金在单轨电子束熔化过程中的枝晶生长过程。仿真结果与实验观察非常吻合，证明了在增材制造中使用该模型的可行性和有效性。