凝固過程是金屬的材料製程中一個重要的階段，對凝固微結構進行數值模擬，可預測鑄件的凝固組織變化，有助於改善鑄件材料品質。
本文採用修正後自動細胞機方法(Modified cellular automaton method, MCA method)模擬鋁銅合金凝固過程中枝狀晶之微組織變化。本文以巨觀熱傳為基礎，結合微觀的成核、成長及溶質擴散，建立一個可同時計算巨觀與微觀尺度之二維模型，預測枝狀晶成長之型態。其中，考慮溫度、濃度與表面曲率所造成過冷度之變化，並根據 KGT (Kurz-Giovanola-Trivedi)模型來計算枝狀晶頂端之速度。此外，加入一個受液固介面法線方向影響之Gibbs-Thomson係數來修正過冷度與成長速度，對角度之型態進行修正。
本文以此模式模擬自由枝狀晶在凝固過程之成長型態，由濃度、表面曲率與溫度來探討過冷度所造成之影響。晶粒形態經由修正後在優先成長方向上有明顯的改善。在模擬一般鑄模凝固時，可得到柱狀晶向等軸晶之轉變(CET, Columnar-to-Equiaxed)之現象；在模擬方向性凝固時，可獲得與熱傳方向相反的枝狀晶，並將模擬結果與文獻和實驗相較之下趨勢大致吻合。

Solidification process is an important stage for manufacturing metal materials. Thus, to operate the numerical simulation on solidification microstructures can predict the variation of casting solidification and helps the improvement on the quality of a casting material.
A modified cellular automaton (MCA) model was adopted to simulate the evolution of dendritic microstructures in solidification processes of Al-Cu alloy. This study combined the micro-models of nucleation, growth and solute diffusion with the macro-model of heat transfer to establish a two-dimensional macro-micro model to predict the growth morphology of dendrites. In this model, the tip velocity was calculated according to KGT (Kurz-Giovanola-Trivedi) model, in which the effects of temperature, solute and curvature are considered to evaluate the total undercooling. Besides, this work modified the growth angle along the preferential growth orientation by adding a variable Gibbs-Thomson coefficient, which is constrained by the parameters of the normal direction on solid/liquid interface, to calculate the undercooling and tip velocity.
This work simulated the morphology of a free dendrite in the melt, based on MCA model. The influences caused by the temperature undercooling, solutal undercooling and curvature undercooling were discussed. Also, there was a significant improvement to the growth morphology due to the modification of growth angle. Furthermore, this study simulated the competitively dendritic structures in the directional casting and rectangular casting, in which the Columnar-to-Equiaxed (CET) phenomenon was discussed. Finally, the proposed study compares the simulated results with those in references and they acquire a fine matching trend in result.

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