具弱非完美交界面多鐵性纖維複合材料 : 廣義面內問題

Abstract

本研究探討具弱非完美交界面壓電壓磁纖維複合材料在平面應變與橫向電磁場下之等效材料性質與磁電耦合行為。弱非完美意旨在交界面上法線方向之廣義應力:應力、電位移、磁通量密度傳遞連續，廣義勢能:應變、電場、磁場傳遞不連續，而本研究假設此不連續變化值與所對應之法線方向廣義應力項呈一線性比例關係(Linear spring-type interface)，並藉由複變函數與微觀力學模型Mori-Tanaka模式、Ad hoc approximation模式以及雙層法(Two-level recursive scheme)來計算上述等效材料性質。 研究成果顯示，上述方法所預測之等效材料性質在不同內含物體積比下，皆有良好的一致性，除了C11 、C12 與(C11-C12)/2 在Ad hoc approximation模式預測上，只在些微弱非完美時(Slightly weakened interfaces)才會接近正確值；而雙層法的成功應用，得到非完美交界面可用三相複合材料來模擬。受到弱非完美交界面影響，本研究得到最大磁電電壓係數 分別為0.0048V/cmOe (BTO/CFO，fi=0.147 )與0.0038V/cmOe (CFO/BTO，fi=0.91 )，此數值相較完美交界面最大值0.9194V/cmOe (BTO/CFO，fi=0.063 )與0.9827V/cmOe (CFO/BTO，fi=0.937 )分別下降190倍與260倍，遠不及實際元件應用範圍；此外，等效材料性質因交界面弱非完美影響，具有內含物尺寸效應(Size-dependent effect)。

This research studies the effective properties and magneto-electric (ME) coupling of piezoelectric-piezomagnetic fibrous composites with mechanically compliant and weakly electromagnetic conducting interface under generalized plane strain with transverse electromagnetic fields. In this case, we assume that the displacement and potential have a jump across the interface and proportional to the normal components of the stress, electric displacement and magnetic flux density. The closed-form formula of the effective properties is obtained by using the complex variable approach and adopting micromechanical models. The numerical results obtained from different methods are shown in agreement, while the result of ad hoc approximation of C11 、C12 and (C11-C12)/2 is only correct for the interface condition of slightly weakened. The results obtained from the Mori-Tanaka method and the two-level recursive scheme show that the imperfect effect is equivalent to a three-phase composite. Due to the interface imperfection, the maximum magnetoelectric voltage coefficients become 0.0048V/cmOe (BTO/CFO,fi=0.147) and 0.0038V/cmOe (CFO/BTO,fi=0.91), which decrease by 190 times and 260 times compared to the case of perfect interface. Finally, we also study the size-dependent effect numerically.