以相場法模擬冷凍鑄造法合成之仿生材料微結構

冷凍鑄造法是極具潛力的仿生多孔材料合成方法，不但製程單純、成本低廉，且可透過多種參數來調控多孔材料內部的微結構組成，擁有夠大規模量產的特性，極具商品化價值。此方法主要是以冷凍固化的方式形成冰晶與粉體的二相結構，透過生長出的冰晶作為材料微結構模型，並藉由調控冷凍溫度梯度、冷凍速度、漿料濃度、溶劑添加物等變因來形塑出不同的多孔材料微結構，最後經冰晶昇華與粉體燒結，生成最終的陶瓷坯體。其中最關鍵的步驟為冷凍固化的調控，藉由具方向性的冰晶推開懸浮液中的粉體，成長出複雜的片狀(lamellar)與樹枝狀(dendritic)冰晶，直接決定最終坯體的內部微結構。本研究提出針對冷凍鑄造法在參數調控下合成仿生多功能孔洞材料內部微結構成長的數值模型，啟發自Peppin等人所提出之一維冷凍鑄造模型，並由二元合金固化模型延伸而來。陶瓷微粒在模型中被視為一質量流(mass flow)，以濃度場表示；而溫度場則是被定義為一個能夠自由調控的給定參數。透過兩者與相場方程式的耦合得以模擬冰晶於陶瓷微粒懸浮液中成長的動態過程，同時可對實驗中最具主導性的漿料濃度與冷凍速度兩操作變因進行分析。首先，透過相場法(phase-field method)可將不連續邊界物理模型(sharp interface model)轉化為在數值上較易處理的連續邊界值問題(continuous boundary value problem)，再應用自適應有限元素法大幅提升計算效率，最終得以重現冷凍鑄造過程中陶瓷微粒與冰晶間的交互作用，更能夠看出兩相界面處異向性的微結構演化。此數值模型的模擬結果與實驗量測相當吻合，無論是參數調控對微結構的影響趨勢，還是量化數值的分析比較，兩者都具有一致的結論。此外，本研究深化了漿料濃度與冷凍速度對陶瓷坯體微結構控制的理解，也為冷凍鑄造法相關領域的研究者在材料設計上，提供一個更清晰的參考憑藉。不但奠定了冷凍鑄造數值模擬最基本的原型，更開啟冷凍鑄造法製程模擬的扉頁，給予日後數值模擬與冷凍鑄造法實驗領域能夠緊密結合的前景，也開啟材料微結構模擬另一種新的可能。

關鍵字

相場法；仿生材料；樹枝狀孔洞微結構；冷凍鑄造法；自適應有限元素法

並列摘要

In this research, a numerical model for microstructure evolution in the freeze-casting process is established. The theoretical mechanism behind the ceramic colloidal suspension solidification process is revealed; also, the relationship between the critical factors and the porous structures is quantitatively described. The model is benchmarked with experimental results and found to be in good agreement. In recent decades, freeze-casting, with an excellent flexibility in microstructure control, has attracted great attention as a potential manufacture method of bioinspired materials. Solidification of ice crystal in ceramic colloidal suspension is found as an important role in freeze-casting dynamical process. The formation of microstructure in solidification results in a dendritic pattern within the ice-template crystallization, determining the macroscopic properties of the materials. In this dissertation, a phase-field model is proposed to describe the crystallization of the ice-template and the particle evolution during the solidification. The ceramic particle is regarded as a mass flow, namely a concentration field. Following the 1D freeze-casting model by Peppin and a general phase-field model for binary alloy casting, a sharp interface model is built up and transformed into a continuous boundary value problem by the phase-field method. The adaptive finite element technique is employed to decrease the computational cost; furthermore, the algorithm reconstructs the details of microstructure, and the influence of the anisotropy may be exhibited. Finally, the numerical results are compared with the experimental data, which demonstrate a good agreement. Both results identify several essential physical parameters controlling the ice-template morphology and the formation of microstructure, such as front velocity, temperature gradient, and particle concentration. The first numerical model to simulate the structural detail in freeze-casting is constructed in the study; moreover, significant perspectives on designing the bioinspired material is presented.

並列關鍵字

Phase-Field Method ； Bioinspired Material ； Dendritic Microstructure ； Freeze-Casting Process ； Adaptive Finite Element Method

參考文獻

Meyers, M. A., Chen, P.-Y., Lin, A. Y.-M., and Seki, Y. (2008). "Biological materials: Structure and mechanical properties." Progress in Materials Science, 53(1), 1-206.

Allen, S. M., and Cahn, J. W. (1979). "A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening." Acta Metallurgica, 27(6), 1085-1095.

Ascher, U. M., and Petzold, L. R. (1998). Computer methods for ordinary differential equations and differential-algebraic equations, Siam.

Badalassi, V., Ceniceros, H., and Banerjee, S. (2003). "Computation of multiphase systems with phase field models." Journal of Computational Physics, 190(2), 371-397.

Bangerth, W., Burstedde, C., Heister, T., and Kronbichler, M. (2011). "Algorithms and Data Structures for Massively Parallel Generic Adaptive Finite Element Codes." Acm T Math Software, 38(2), 14.

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以相場法模擬冷凍鑄造法合成之仿生材料微結構

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