具非完美交界面功能梯度多鐵纖維複合材料

Abstract

本文探討具非完美交界面，且內含物為功能梯度材料之多鐵纖維複合材料在廣義反平面問題下的磁電耦合效應。功能梯度材料(Functionally graded material)之漸變性質可減少交界面因材料差異造成的應力集中，而達到增強材料結構效果。在理論探討上，多鐵性複合材料之交界面多假設為完美連續，而現實複合材料製程中交界面上多有裂縫或孔洞等瑕疵，進而影響其整體行為。本研究探討兩種非完美交界面，分別為擁有高磁電彈性質的強非完美交界面與低磁電彈性質的弱非完美交界面，並利用廣義Rayleigh方法與聚合複合圓柱模型(Composite cylinder assemblage model)求出等效材料性質並相互驗證；最後分別探討漸變參數、非完美交界面係數以及材料係數對等效磁電電壓耦合係數的影響。 數值結果顯示，不同方法之正確性比較時，除了六邊形排列在漸變參數不為零時有偏差外，在不同體積比下其數值與趨勢皆有良好一致性。會受漸變參數、非完美交界面係數、體積比以及材料性質影響，其中提高強非完美交界面係數有持續提升的效果。最後，選擇較低彈性係數、介電常數與較高磁導率之壓電材料，以及較低彈性係數、磁導率與較高壓磁係數之壓磁材料亦能有效提升 。

This research studies the effective magneto-electric (ME) coupling effect of multiferroic fibrous composites consisting of functionally graded cylinders with imperfect interfaces subjected to anti-plane shear strain with in-plane electromagnetic fields. Functionally graded materials can reduce the stress concentration at the interface and enhance the strength of materials. Studies on the multiferroic composites are usually assumed that the interfaces are perfectly bonded. In reality, however, cracks and voids at the interfaces affect the overall behavior. In this work, we study two kinds of imperfect interfaces: mechanically stiff and electromagnetic highly conducting interfaces, and mechanically soft and electromagnetic weakly conduction interfaces. We generalize Rayleigh’s method and composite cylinder assemblage model to estimate the effective property of the proposed composites. Further, we investigate the influence of the grading parameter, imperfect interface parameters, and material properties on the ME voltage coupling coefficient . Numerical results show that the magnitudes and trends of agree well between the two methods mentioned above, except that the hexagonal arrangement has deviation for the non-zero grading parameter. Based on the model, we study the dependence of on the grading parameter, imperfect interface coefficients, volume fraction of the fiber phase, and the material properties of each phase. We observe that larger can be obtained by increasing the mechanically stiff and electromagnetic highly conducting interface coefficients. Further, it is desirable to have smaller elastic coefficient and dielectric permittivity but larger magnetic permeability in the piezoelectric phase, while smaller elastic coefficient and magnetic permeability but larger piezomagnetic coefficient in the piezomagnetic phase for improving ‬‬‬‬‬.