功能梯度壓電壓磁纖維複合材料之磁電耦合效應

Abstract

功能梯度材料(Functionally graded material, FGM)為一種新型的複合材料，透過連續控制材料含量的分布，使材料之間無明顯的交界面，進而降低了應力集中的現象。這樣的特點使功能梯度材料逐漸成為研究材料領域的主流。本研究為探討功能梯度壓電壓磁纖維複合材料在反平面問題下的等效材料性質。其中，內含物的材料性質隨半徑r呈指數函數exp(ρr)漸變(ρ為漸變參數)，並以週期性排列的方式置入於一均質母材內。本文將內含物依方形陣列(Square array)及六邊形陣列(Hexagonal array)排列後，利用Rayleigh方法求出內含物的勢能公式，並求其等效材料性質及勢能圖。另以有限元素法軟體COMSOL Multiphysics v4.4及聚合複合圓柱模型(Composite cylinder assemblages model, CCA model)求其等效材料性質佐以驗證其結果之正確性。 數值分析結果顯示，上述方法所求出的等效材料性質在不同內含物體積百分比下擁有良好的一致性，但等效磁電係數λ11在漸變參數ρ為負時會有較大的偏差。藉由改變漸變參數ρ，勢能圖中內含物的線段會隨著漸變參數ρ為正或負而產生內凹與外擴的差別；而等效磁電電壓係數則會隨著漸變參數ρ的增加而愈趨增高。最後，藉由改變材料係數及漸變參數ρ來探討磁電耦合效應的影響，得到了選擇材料的標準。壓電材料需選擇擁有較低的彈性係數、介電常數及較高的磁導率；壓磁材料則需選擇擁有較低的彈性係數、磁導率及較高的壓磁係數。

Functionally graded materials are composite materials without clear interface between the different phases because the transition from one phase to the other is graded. The smooth transition reduces mechanical stress concentrations that occur in conventional composites. This research studies the effective properties and magneto-electric (ME) coupling of piezoelectric-piezomagnetic fibrous composites consisting of periodic arrays of exponentially graded cylinders under anti-plane shear deformation with in-plane electromagnetic fields. We generalize Rayleigh’s method to account for the periodic arrangements of these cylinders. The potential field and effective properties of composites systems were calculated. For comparisons, we also use finite element analysis (COMSOL Multiphysics v4.4) and composite cylinder assemblages model to compare the results predicated by the Rayleigh’s method. Numerical results show that the magnitude and trend of the effective properties predicted by the proposed methods are all in good agreement except that the ME coupling coefficient has large deviation for the negative grading parameter. It is observed that the grading parameter has great effects on the potential field of the inclusions. If the grading parameter is positive (negative), the potential lines in the inclusions are concave (convex). Further, to enhance the ME voltage coefficient, we can choose materials with higher grading parameter and softer phases. In addition, it is desirable to have larger magnetic permeability but smaller dielectric permittivity in the piezoelectric phase and smaller magnetic permeability but larger piezomagnetic coefficient in the piezomagnetic phase for maximum ME voltage coefficient.