竹編織強化高分子複合材料等效彈性常數之量測與多層級模型之建構

Abstract

纖維強化高分子複合材料 (Fiber Reinforced Polymer, FRP) 是工程中重要的一種材料利用形式，藉由高性能的纖維提供剛性與強度而高延展性的基質用於傳遞應力、保護纖維並提供外形。在淨零碳排的時空背景下，竹纖維是一種同時具備短纖維與連續纖維加工潛力的材料，在固碳效益、再生速度、集運效率與力學性能均在多種天然纖維中脫穎而出。本研究利用真空轉注成形技術開發一種竹編織加固環氧樹脂複合材料 (Bamboo Textile Reinforced-Polymer, BTRP)。研究旨在發展出此一新材料並探究其物理與力學性能，更針對彈性常數進行深度的剖析與理論模型的建構。據此，研究分為三個主題。首先是 (1) 基礎物理力學性能的研究，目的是評估BTRP工程所需的基本性能數據並討論不同編織結構因子所造成的影響。首先從密度、含水率、水分吸附、尺寸變異、準靜態、應變能與破壞模式等多種角度切入，廣泛評估此一材料受編法、疊層數、疊層結構、受力方向與荷重條件的影響。結果發現，BTRP在輕量化、尺寸穩定性與耐水性方面均有相當潛力。力學性能方面，楊氏模數至高可達19 GPa，波松比則分布於0.13–0.23之間；抗彎強度最高的組別可達193.40 MPa，而模數可達17.90 GPa，並與編織法、層數、尺寸效應、軸向纖維比例有關。搭配3D X-ray 成像、一階導函數以及應變能分析，也辨識出多種由編織結構引起的破壞模式。由此可見，竹材的彈性常數影響最後的力學表現甚劇，而編織結構對BTRP彈性常數的影響也相當重要，影響抗彎、拉伸行為，甚至因儲存能量的方式不同進而影響破壞發生。 由於編織結構會造成彈性常數明顯的變動進而影響許多力學行為，彈性常數的建構又是複合材料設計的重要基礎，因此第二個主題 (2) 編織FRP的彈性常數預測的目標是推導適用於竹編織FRP的多層級線彈性常數模型。針對竹編結構建立可從竹纖維的彈性，到竹編單層行為直到疊層複合材料彈性反應的解析模型。此模型聚焦在目前較少研究探究的斜紋編織結構，並選定應用性較高且求解較於簡便的解析模型盡可能從物理現象與幾何結構推知不同層級間彈性行為交互作用。此模型共分為四個層級。第一層級將竹篾視為一橫向等向性 (Transverse isotropic) 的等向 (Unidirectional) 材料，利用多種微觀力學模型來描述竹材維管束鞘 (Vascular Bundle Sheath) 與基質組織 (Ground Tissue) 的天然複合結構；第二層級是將竹篾在編織單元中的幾何狀態與疊壓造成的彎折型態以數學式描述，並額外加入描述纖維束彎曲結構的參數；第三層級是將樹脂基質區域與纖維束區域在經緯雙向對彈性的各自貢獻進行組合，求得單層的簡化勁度矩陣並加入修正表面樹脂分布的新參數。第四層級則依循古典疊層理論計算多疊層或多角度的BTRP成品的外力與變形關係。此外，由於竹材料天生的變異性與梯度分布特性，多層級模型亦納入了一種用於解釋竹材變異性的理論；藉由參數分析得知，各種彈性常數對纖維束斷面的敏感度不同。纖維束斷面結構不僅會影響纖維體積分數還會造成疊壓角度不同進而影響彈性常數計算結果。 本研究的最後一個主題是 (3) 各層級的面內彈性常數量測，核心目的是比較不同彈性常數測量的方式，並針對目前較缺乏討論的彈性項發展或測試對應的測定方法 (如竹材顯微單元的估算、竹材側向彈性常數、竹材面內面外剪切模數與編織FRP面內剪切)。本研究利用竹材纖維方向的拉伸試驗量測波松比與縱向彈性模數，討論了包含試片類型與應變量測方式等因子在內的影響。接著利用一種特殊設計過的試片，藉由微觀力學模型來反算橫向的彈性模數，並利用了有限元素分析與旋切的竹單板進行橫向拉伸試驗當作驗證。剪切模數方面，將竹材當成等向FRP，借助V-notched短樑試驗測量面內的剪切模數與剪切強度。為了檢視是否創造真正的面內剪切，我們額外做了竹材與夾具內外側的剪應變比對、數位影像相關法以及破壞模式的比對。最後，以Timoshenko 樑彎理論為基礎，發展一種測得面外剪切模數的方法。本文亦利用數值擬合的方式估計了竹材彈性顯微層級的彈性常數，並成功將之用來描述竹材的梯度變異性。 本研究中，以斜紋編BTRP為材料，比較了多種方法量測雙方向彈性模數、波松比、面內剪切模數的差異。結果顯示，測量方法對彈性模數與波松比的影響不大。而疊層前後會使材料的彈性常數有所不同，可能與編織材料的特有的嵌套效應 (Nesting) 與表面編織結構有關。剪切模數則會因為受力模式與應變量測方式的不同有明顯的差異。 總結而言，本文成功利用編織、連續竹纖維與真空轉注成形三者的優勢發展出一種高性能輕量化的樹脂複合材料，並建構一個能輸入少量因子便計算BTRP成品彈性常數的解析模型。除詳細討論模型中各種幾何因子與編織參數的行為敏感度，更輔以多種不同編織結構的試驗驗證。另一方面，原先缺乏特定數值的竹材與BTRP兩層級彈性常數，本研究系統性的建構新測定方法或取得對應數據。無論是新方法或新理論的討論、基礎研究的積累與材料設計的創新等三個層面，均期望本研究的結果能為竹材料的高值化應用與複合材料工業的低碳轉型做出貢獻。

Fiber reinforced polymers (FRP) are composites used in engineering to provide stiffness and strength through high-performance fibers, while a ductile matrix is used to transfer stress, protect the fibers, and provide form. In line with the trend towards net-zero carbon emissions, bamboo fiber is a material with potential as both a short and continuous fiber processing material. It stands out among various natural fibers in terms of carbon sequestration efficiency, regeneration rate, transportation efficiency, and mechanical properties. In this study, a Bamboo Textile Reinforced-Polymer (BTRP) was developed using vacuum-assisted resin transfer molding (VA-RTM). The research aims to develop this new composite and investigate its physical-mechanical properties, as well as conduct an in-depth analysis and theoretical modeling of the elastic constants. The research is divided into three topics. The first topic is (1) a study of the physical-mechanical properties of BTRP to evaluate the performance required for engineering and discuss the effects caused by different woven structural factors. The BTRP is extensively evaluated from various perspectives such as density, moisture content, moisture adsorption, dimensional variation, quasi-static behavior, strain energy, and fracture mode. The effects of woven type, number of plies, lamination sequence, loading direction, and conditions are also evaluated. It was found that BTRP has considerable potential in terms of light weight, dimensional stability, and water resistance. Young's modulus can reach up to 19 GPa, Poisson's ratio is distributed between 0.13 and 0.23, and the flexural strength can reach 193.40 MPa, which is affected by the weaving type, number of plies, size effect, and axial fiber content. Various fracture patterns caused by woven structures are also identified using 3D X-ray imaging, first-order derivatives, and strain energy analysis. The elastic constants of bamboo affect the final mechanical performance significantly, and the influence of the woven structure on the elastic constants of BTRP is also critical. The second topic is (2) the prediction of the elastic constants for woven FRP to derive a hierarchical linear elasticity model applicable to BTRP. An analytical model was developed for bamboo woven structures from the elastic properties of bamboo fibers to the elastic properties of lamina up to laminates. The model focuses on twill weave structure, which has been less investigated, and is an easily applied and solved analytical model to deduce the interaction of elastic behaviors between different levels from physical phenomena and geometry. The first level treats the strip as a transversely isotropic unidirectional composite and uses various micromechanical models to describe the natural complex structure of the vascular sheath and the ground tissue of the bamboo. The second level describes the geometry and undulation of the strip in the repeating woven unit. An additional parameter to describe the undulation of strip was proposed; The third level combines the respective contributions of the matrix and the strip to elasticity to obtain a reduced stiffness matrix for a lamina and new parameters which modify the surface matrix distribution was added. The fourth level follows the classical lamination theory to calculate the force–deformation relationship of BTRP laminates. The hierarchical model predicted the inherent variability and gradient distribution properties of bamboo and elastic constants of each level well; the parametric analysis shows that the sensitivity of various elastic constants to strip cross-sections varies. The tow cross-sectional structure not only affects the fiber volume fraction but also causes different crimp angles, which in turn affects the results of elastic constants. The final topic is (3) the measurement of in-plane constants of each level. The main objective of this topic includes a comparative study of measuring approaches and the development of a method for determining specific constants. For instance, this topic focuses on the estimation of anatomical tissue, transverse elastic modulus, in-plane and out-of-plane shear modulus of bamboo, and in-plane shear of woven FRP. The differences between the specimen types and the strain measurement are also discussed. A novel designed specimen was used to invert the transverse modulus using a micromechanical and finite element model, and a transverse tensile test of spin-cut bamboo veneer was conducted as validation. The in-plane shear modulus and shear strength were measured using the Iosipescu approach. To verify the in-plane shear loading, the shear strain, fracture mode were analyzed through digital image correlation . Finally, an approach was developed to measure the out-of-plane shear modulus based on Timoshenko's assumption. In this study, the differences between various measurements for the biaxial elastic modulus, Poisson's ratio, and in-plane shear modulus of BTRP were compared. The results showed that the measurement did not have much effect on the elastic modulus and Poisson's ratio. The effect of ply number on constants may be related to the nesting effect of the woven FRP and the surface deformation characteristics. In addition, the measured shear modulus is significantly different depending on the loading mode and strain measurement. In conclusion, this work successfully developed a high-performance lightweight composite by utilizing the advantages of weaving, continuous bamboo fiber, and VA-RTM. An analytical model describing the elastic constants of BTRP with simple inputs was developed theoretically and verified experimentally. Additionally, a series of new measurements were systematically constructed, and the elastic constants of bamboo and BTRP were obtained. The results of this study are expected to contribute to the high-value application of bamboo and composite materials in the industry.