應用離散元素法與同步輻射X光斷層掃描探討不同固相分率半固態鋁合金之晶粒形貌變化與變形機制

Abstract

鑄造是一項人類傳承千年的傳統金屬加工工藝，其低廉的成本與高效的生產能力，使其在製造業中扮演著重要角色。然而，與其他加工方法相比，鑄造工藝通常在相對高溫的環境下進行。在金屬冷卻過程中，由於固液體積差異、表面氧化物生成，以及固液間對氣體溶解度的不同，鑄件內部常產生孔洞。目前最有效消除孔洞的方法之一，是在凝固過程中施加壓力，藉由擠壓初晶晶粒以促使其移動與變形來填補孔洞。但後續研究發現，若施加壓力過大，不僅無法消除孔洞，反而可能導致孔洞擴張，甚至造成鑄件破裂。此外，由於鑄件內部不同位置冷卻速率不一，導致晶粒形貌與尺寸差異顯著，使得受壓行為也存在不均。因此，理解壓力與初晶晶粒運動行為之間的關係，成為鑄造工藝優化的重要研究方向。 隨著同步輻射技術的進展，研究發現晶粒在半固態階段呈現出類似於土壤顆粒的準剛性特性，這促使學者開始以土壤力學的角度探討晶粒的運動行為。Altuhafi 等人便以三軸壓縮試驗研究半固態鋁合金晶粒的機械性質。然而，由於實驗設備限制，其研究未能深入觀察晶粒受剪後的微觀運動過程。因此本研究參考 Su 等人之方法，利用第六代離散元素法模擬軟體 Particle Flow Code 3D (PFC3D)，模擬半固態鋁合金的三軸壓縮行為。我們首先以 Avizo 重建同步輻射斷層掃描所得之晶粒結構，並導入 PFC 模擬系統中。接著採用 Su 等人於排水壓縮測試中提出的接觸模型，以 Hertz 模型模擬顆粒與牆體間的非線性接觸，並以 Burgers 模型描述顆粒間的黏彈性作用，所需參數則依據文獻中提出的微觀壓縮模型決定。 此外，為了提高模擬效率，我們參考 Ng 等人提出的方法，透過增加顆粒質量以提升時間步長，降低總計算量。根據微觀模型評估結果，即使質量增加，只要系統維持連續接觸狀態，應力-應變曲線的變化趨勢幾乎不受影響。因此，本研究將伺服牆之最大應變速率設定為 5×10^(-4) s^(-1)，以確保整體顆粒系統處於準靜態(quasi-static) 狀態。 三軸壓縮測試中，首先施加圍壓以模擬鑄造過程中晶粒所受環境壓力，隨後自試樣上方以固定應變速率施加軸向偏應力，觀察顆粒在剪切作用下的運動行為。剪切階段結束後，我們將模擬所得之偏應力、體積應變與孔隙率變化，與 Altuhafi 等人之實驗結果進行比較。模擬結果顯示，在固相率較高 (550°C) 的條件下，施加偏應力後試樣體積呈壓縮趨勢，與 Altuhafi 等人觀察到的膨脹現象不符。為探究差異原因，我們建立了混合接觸模型 (mixed contact model)，並進一步發現體積應變在剪切過程中呈現先壓縮後膨脹之行為。我們推測此差異可能源於模擬中忽略了間隙液體壓力對晶粒運動的影響。 相較於 Su 等人進行的排水壓縮模擬，本研究在三軸剪切條件下更明顯觀察到晶粒滑移與變形對宏觀機械性質的影響，並深化了對間隙液體在半固態行為中所扮演角色的理解。此外，我們亦進一步分析剪切過程中的接觸力分佈與應力傳遞變化，為未來探索高壓鑄造中晶粒行為提供了新的模擬視角與參考依據。

Casting is a traditional metal processing technique that has been passed down for thousands of years. Due to its low cost and high production efficiency, it plays a vital role in the manufacturing industry. However, compared to other processing methods, casting is typically carried out at relatively high temperatures. During the cooling process, internal porosity often forms in the castings as a result of volume differences between solid and liquid phases, the formation of surface oxides, and differing gas solubility between the solid and liquid states.One of the most effective ways to eliminate such porosity is to apply pressure during solidification. This compressive force promotes the movement and deformation of primary solid grains to fill in the voids. However, subsequent studies have shown that excessive pressure can not only fail to eliminate porosity but may even enlarge the voids or cause cracking in the castings.Additionally, variations in cooling rates across different regions of the casting result in significant differences in grain morphology and size, leading to uneven responses to applied pressure. Therefore, understanding the relationship between pressure and the motion of primary grains has become a key research direction in the optimization of casting processes. With advances in synchrotron radiation technology, studies have revealed that grains in the semi-solid state exhibit quasi-rigid behavior similar to that of soil particles. This finding has led researchers to analyze grain motion from a geomechanics perspective. For instance, Altuhafi et al. conducted triaxial compression tests to investigate the mechanical properties of semi-solid aluminum alloys. However, due to experimental limitations, their study was unable to capture the detailed micro-scale motion of grains under shear. To address this, the present study adopts the approach proposed by Su et al., using the sixth-generation Discrete Element Method (DEM) simulation software, Particle Flow Code 3D (PFC3D), to simulate the triaxial compression behavior of semi-solid aluminum alloys. We first reconstructed the grain structure from synchrotron tomography data using Avizo, and then imported it into the PFC simulation system. The contact model follows that used by Su et al. in drained compression tests: the nonlinear contact between particles and walls is modeled using the Hertz contact law, while the viscoelastic behavior between particles is described using the Burgers model. The required parameters are determined based on micro-scale compression models reported in the literature. To improve computational efficiency, we adopted the method proposed by Ng et al., increasing the particle mass to enlarge the time step and thus reduce total computation time. According to the micro-scale model evaluation, even with increased mass, the stress–strain response remains nearly unaffected as long as continuous contact within the system is maintained. Therefore, the maximum strain rate of the servo-controlled walls was set to 5×10⁻⁴ s⁻¹ to ensure quasi-static conditions for the entire granular system. In the triaxial compression test, confining pressure was first applied to simulate the ambient pressure experienced by grains during casting. Axial deviatoric stress was then applied from the top of the specimen at a fixed strain rate to observe grain motion under shear. After the shear phase, the simulated results—such as deviatoric stress, volumetric strain, and porosity evolution—were compared with the experimental results from Altuhafi et al. The simulation results revealed that under higher solid fraction conditions (550 °C), the specimen exhibited volumetric compression after applying deviatoric stress, which contrasts with the dilation observed by Altuhafi et al. To investigate the cause of this discrepancy, a mixed contact model was developed. It was found that the volumetric strain exhibited a compress-then-dilate trend during shearing. We speculate that this difference arises from the simulation's omission of interstitial liquid pressure, which influences grain movement. Compared to Su et al.’s drained compression simulation, this study more clearly observes the influence of grain sliding and deformation on macroscopic mechanical behavior under triaxial shear conditions. It also deepens our understanding of the role of interstitial liquid in semi-solid behavior. Furthermore, we analyzed contact force distributions and stress transmission during shear, providing new simulation perspectives and references for investigating grain behavior in high-pressure casting applications.