具強非完美交界面多鐵性纖維複合材料： 廣義面內問題

Abstract

壓電壓磁複合材料因有較高的磁電耦合效應能應用於致動器及感測器，使其成為近代材料研究重點之一。但複合材料於製作過程中往往會因為不同因素，使得交界面產生瑕疵，為研究此一情況，本研究利用理論探討具強非完美交界面的壓電壓磁複合材料在面內應變與橫向電磁場問題下之等效材料性質。而強非完美交界面意指複合材料交界面上廣義勢能（位移、電勢能、磁勢能）連續，但廣義徹體力（徹體力、法線電位移、法線磁通量）不連續。藉由複變函數與微觀模型Mori-Tanaka模式求解等效材料性質，並另外以聚合複合圓柱模型(Composite cylinder assemblages model)、廣義自洽法(Generalized self-consistent method)以及界面相模型(Interphase model)用以驗證其正確性。 數值模擬則選用鈦酸鋇(BaTiO3, BTO)及鈷鐵氧(CoFe2O4 , CFO)進行分析。數值分析結果顯示，除了等效剪力模數G有極大的誤差外，其餘等效材料性質在各微觀模型預測下皆有良好的一致性。而此原因應為非完美交界面條件的近似所致，因此將界面相模型模擬為非完美交界面時需要更高階的近似。而本研究所得到於強非完美交界面下的磁電電壓係數 極值分別為0.809 V/cmOe (BTO/CFO, f=0.075)與0.167 V/cmOe (CFO/BTO, f=0.502)，其值與完美交界面之最大值 1.149 V/cmOe(BTO/CFO, f=0.063)與 1.228 V/cmOe(CFO/BTO, f=0.937)相比分別下降1.4倍及7.4倍。最後，探討強非完美交界面下內含物於奈米尺度存在的尺寸效應，其磁電電壓係數 隨半徑減少而遞減。

Piezoelectric-piezomagnetic composite has received pronounced attention in recent years due to its high magnetoelectric (ME) effect. However, the imperfect interfaces, which can affect the ME effect, may be present in many circumstance such as sliding, debonding and flaws. This research studies the effective properties of piezoelectric-piezomagnetic fibrous composites with membrane-type imperfect interface subjected generalized plane strain deformation coupled to out-of-plane electromagnetic fields. In this case, the generalized traction (traction, normal electric displacement, normal magnetic flux) has a jump across interface, but the generalized potential (displacement, electric potential, magnetic potential) maintains continuously. By using the complex variable approach and several micromechanical models, we obtain the closed-form formula of the effective properties. The micromechanical models employed include the Mori-Tanaka method, composite cylinder assemblages model, generalized self-consistent method, and interphase model. Numerical results show that the effective properties predicted by different models are in good agreement except the effective transverse shear modulus. Therefore, a higher order approximation is required for the equivalency between an interphase and an imperfect interface. Due to the interface imperfection, the maximum ME voltage coefficient becomes 0.809 V/cmOe (BTO/CFO, f=0.075) and 0.167 V/cmOe (CFO/BTO, f=0.502) , which decreases by 1.4 times and 7.4 times compared to the corresponding case of perfect interface. Further, the size-dependent effect indicates that when the radius of fiber decreases, the ME voltage coefficient decreases.