基於COMSOL多物理模擬以及CALPHAD方法探討 CoCrNiSi0.3中熵合金凝固和熱傳分析問題

Abstract

CoCrNi中熵合金具有優異的強度和延展性，在低溫環境下強度高達1.3GPa和超過70%的延展率，且發現CoCrNi系中熵合金有比CoCrFeMnNi之Cantor Alloy還更低的疊差能，在低溫受到快速變形時能產生大量的變形雙晶，使得其低溫延性遠優於其他的金屬。因此以CoCrNi系中熵合金為基底，開發輕量化與高降伏強度之合金為目前重要的研究方向。添加價錢合宜以及質輕的元素如Al或Si等，形成輕量型高熵合金CoCrNi(Si/Al)，不僅能減少合金整體的熔配成本和重量密度，如添加量適當，其產生的第二相能有效增加降伏強度。過去研究利用小批量的真空電弧再熔融技術，研究Al或Si的添加固溶及第二相強化CoCrNi中熵合金的程度。但為了拓展輕量型高熵合金應用如工業級低溫抗衝擊合金板材製造，必須研究由工業級真空澆鑄、氬氣保護澆鑄或精密鑄造方胚或扁胚之凝固微結構特性，以讓輕量型高熵合金的優異性能產生出實際價值。 本研究添加Si來輕量化CoCrNi中熵合金精密鑄造方胚時，對凝固組織、熱傳現象、元素偏析以及均質化動力學進行實驗研究以及模擬探討。這些鑄造微結構的訊息強烈地影響鑄態金屬的機械性質和後續均質化熱處理的所需時間，故應理解輕量化CoCrNiSi0.3中熵合金所使用的製程技術之熱傳特性，並且研析驗證製程特性、冷卻速率和凝固微結構的連結，以利後續藉由理論模擬預測來減少實驗試製的成本。而研究過程使用到Thermo-Calc軟體所推出最新高熵合金數據庫TCHEA6以及Thermo-Calc DICTRA模組計算以獲得更可靠的參數組，其預測參數後續將應用於COMSOL Multiphysics®宏觀暫態熱傳以及介觀尺度相場模型的建立。 本研究針對低缺陷且適合後續塑性加工的9 cm × 9 cm × 3 cm精密鑄造方胚之微結構。經過比較此精密鑄造方胚或真空電弧再熔融取得鑄態試片以及其均質化後試片之結果，我們發現精密鑄造方胚的二次枝晶臂間距約為170 μm，明顯高於真空電弧再熔融試片的25 μm，這結果使得精密鑄造方胚要花超過12小時的時間於1100℃均質化。由於相關CoCrNi中熵合金的凝固特性文獻有限，我們也藉由統整Cantor alloy和鎳基超合金相關精密鑄造凝固學理探討文獻，反推精密鑄造方胚和真空電弧再熔融的冷卻速率各落在0.018 - 0.05 K/s和2.75 – 5.94 K/s之間。 宏觀熱傳模型方面，我們利用COMSOL Multiphysics®軟體模擬精密鑄造方胚製程，並針對陶瓷模與銅模、陶瓷模厚及模溫進行分析，由於意鑫方胚與林新智實驗室自熔材所使用的模具分別為陶瓷模具與銅模具，因此我們分別將兩種模具之基參數輸入其中銅模的熱導率為400 W⁄((m∙K) )而陶瓷模之熱導率為1.22 W⁄((m∙K) )，而在高的熱導率下金屬熔湯倒入模具中使其可以快速降溫，進而形成較細小的樹枝晶顯微結構。另外，為了比較陶瓷模厚1 mm 與4 mm之差異，我們取方胚的四分之一位置且t=350 s進行冷卻速率以及溫度梯度的比較，其中4 mm陶瓷模之冷卻速率與溫度梯度分別為0.73 K/s和4.13 K/mm，而1 mm 陶瓷模之冷卻速率與溫度梯度分別為1.12 K/s和4.6 K/mm，可發現4 mm陶瓷模的溫度梯度和冷卻速率皆約比1 mm陶瓷模還低，由此可知陶瓷模具厚度的增加會降低冷卻速率進而使凝固時間增加。 而在介觀尺度方面，我們仍使用COMSOL Multiphysics®軟體建立長18 l_0、寬18 l_0塊材之邊界，其中l_0=852 μm為特徵長度，為簡化模型我們以CoCrNi作為溶劑Si為溶質，並透過增加成核點使生長方式接近於等軸晶。本研究我們透過改變其凝固初始溫度T_0，觀察不同過冷度T_0=0以及T_0=0.1的情況下樹枝晶的生長情形，其結果顯示隨著過冷度的增加，為了使溶質能夠更快速的擴散至液相，因此需要長出更多二次枝臂甚至三次枝臂以加速Si原子的排出，進而使樹枝晶較為細小。另外，為量測二次枝臂間距大小，我們透過COMSOL模擬軟體沿著scan-line方向分析溶質原子(Si)的濃度分佈，再藉由量測Si濃度曲線波峰與波峰之距離取平均得到平均二次枝臂間距大小，其模擬結果T_0=0與T_0=0.1分別為164.7±81.9 μm以及177.13±75.8 μm，模擬結果與實驗端測量結果170±30 μm吻合。 宏觀尺度暫態熱傳模型以及介觀尺度相場方法模擬枝晶凝固，能合理地再現潛熱釋放與熱逸散、四重對稱枝晶生長以及溶質微觀偏析現象。後續研究可在實驗與模擬方面持續使用Thermo-Calc分析比較不同輕量型高熵合金，以幫助最佳化工業級製造高熵合金凝固與均質化過程的熱傳、質傳和相變化行為，並且在介觀尺度相場模擬方面持續在COMSOL Multiphysics®軟體中進行以非等溫條件凝固以觀察樹枝晶結構演變以及溶質微觀偏析現象，所驗證的計算模型能在低成本之下進行更多且更系統性的參數變異，幫助為輕量型高熵合金凝固製程與均質化熱處理微結構控制建立理論模型。

CoCrNi high-entropy alloys exhibit excellent strength and ductility, with high strength of up to 1.3 GPa and over 70% elongation at low temperatures. It has been found that CoCrNi-based high-entropy alloys have lower stacking fault energy than the CoCrFeMnNi-based Cantor Alloy, resulting in the generation of a large number of deformation twin boundaries at low temperatures during rapid deformation. This property gives it superior low-temperature ductility compared to other metals. Therefore, the development of lightweight and high-yield strength alloys based on CoCrNi-based high-entropy alloys is currently an important research direction. By adding cost-effective and lightweight elements such as Al or Si, a lightweight high-entropy alloy, CoCrNi(Si/Al), can be formed. It not only reduces the melting and alloying costs but also decreases the density of the alloy. The resulting second phase can effectively increase the yield strength with an appropriate amount of addition. Previous studies have employed small-scale vacuum arc remelting techniques to investigate the solubility and second-phase strengthening of CoCrNi-based high-entropy alloys with Al or Si additions. However, to expand the application of lightweight high-entropy alloys in industrial-grade low-temperature impact-resistant alloy plate manufacturing, it is necessary to study the solidification microstructure characteristics of industrial-grade vacuum casting, argon-protected casting, or precision casting billets or slabs. This will help to demonstrate the practical value of the excellent properties of lightweight high-entropy alloys. This study used Si addition for lightweight CoCrNi-based high-entropy alloy precision casting billets. Experimental investigations and simulations were conducted to study the solidification structure, heat transfer phenomena, elemental segregation, and homogenization kinetics. The information obtained from these casting microstructures strongly influences the mechanical properties of the as-cast metal and the required time for subsequent homogenization heat treatment. Therefore, it is important to understand the thermal transfer characteristics of lightweight CoCrNiSi0.3 high-entropy alloys and analyze the relationship between process characteristics, cooling rate, and solidification microstructure. This will facilitate cost reduction through theoretical simulations and predictions, reducing the need for experimental trial production. Thermo-Calc software, with the latest high-entropy alloy database TCHEA6 and the Thermo-Calc DICTRA module, was used in the research process to obtain more reliable parameter sets. The predicted parameters will be applied to the establishment of macroscopic transient heat transfer and mesoscale phase field models in COMSOL Multiphysics®. In this study, the microstructure of a low-defect and suitable for subsequent plastic processing 9 cm × 9 cm × 3 cm precision casting billet was examined. By comparing the results of the precision casting billet with the as-cast specimens obtained from vacuum arc remelting and their homogenized counterparts, it was found that the secondary dendrite arm spacing in the precision casting billet was approximately 170 μm, significantly higher than the 25 μm in the vacuum arc remelted specimens. This resulted in a homogenization time of over 12 hours at 1100℃ for the precision casting billet. Due to the limited literature on the solidification characteristics of related CoCrNi-based high-entropy alloys, a comprehensive study of the solidification science of Cantor alloys and nickel-based superalloys was conducted to infer the cooling rates of the precision casting billet and vacuum arc remelting, which fell between 0.018 - 0.05 K/s and 2.75 - 5.94 K/s, respectively.. In terms of macroscopic heat transfer modeling, we utilized COMSOL Multiphysics® software to simulate the precision casting billet process. We analyzed the effects of ceramic molds versus copper molds, ceramic mold thickness, and mold temperature. The copper mold used in the TCA billet had a thermal conductivity of 400 W/(m·K), while the ceramic mold had a thermal conductivity of 1.22 W/(m·K). The copper mold's high thermal conductivity allowed for the molten metal's rapid cooling, resulting in a finer dendritic microstructure. Additionally, to compare the differences between ceramic mold thicknesses of 1 mm and 4 mm, we selected the quarter position of the billet. We analyzed the cooling rate and temperature gradient at t=350 s. The cooling rate and temperature gradient for the 4 mm ceramic mold were found to be 0.73 K/s and 4.13 K/mm, respectively, while for the 1 mm ceramic mold, they were 1.12 K/s and 4.6 K/mm. It was observed that the temperature gradient and cooling rate were lower for the 4 mm ceramic mold than the 1 mm ceramic mold, indicating that increasing the ceramic mold thickness reduced the cooling rate and extended the solidification time. In terms of mesoscale modeling, we also used COMSOL Multiphysics® software to establish a boundary for a rectangular block of size 18 l_0 × 18 l_0, where l_0 = 852 μm is the characteristic length. To simplify the model, we used CoCrNi as the solvent and Si as the solute, and we increased the nucleation sites to achieve an equiaxed dendritic growth mode. In this study, we varied the initial solidification temperature T_0to observe the growth behavior of dendritic structures under different degrees of undercooling T_0=0 and T_0=0.1). The results showed that as the undercooling increased, more secondary and even tertiary branches needed to grow to facilitate faster diffusion and expulsion of Si atoms, resulting in finer dendritic structures. Furthermore, we analyzed the concentration distribution of Si atoms along a scan line using COMSOL software to measure the interdendritic spacing. We obtained the average interdendritic spacing by measuring the distances between the peaks of Si concentration curves. The simulated results for T_0=0 and T_0=0.1 were 164.7 ± 81.9 μm and 177.13 ± 75.8 μm, respectively, which aligned with the experimental measurement of 170 ± 30 μm. The macroscopic transient heat transfer model and mesoscale phase field method successfully simulated dendritic solidification, capturing latent heat release, thermal dissipation, quadruple symmetry dendritic growth, and solute microsegregation phenomena. Future research can continue using Thermo-Calc for experimental and simulation analysis to compare lightweight high-entropy alloys. This will aid in optimizing the thermal transfer, mass transfer, and phase transformation behaviors during solidification and homogenization processes in industrial-scale manufacturing of high-entropy alloys. Further mesoscale phase field simulations can be performed in COMSOL Multiphysics® under non-isothermal conditions to observe dendritic structure evolution and solute microsegregation phenomena. The validated computational models allow for the cost-effective exploration of a wider range of parameters, facilitating the establishment of theoretical models for controlling solidification and homogenization microstructures in lightweight high-entropy alloy processes.