臺灣博碩士論文加值系統

本研究探討弱非完美交界面對多鐵層狀複合材料場量分佈的影響。壓電壓磁複合材料可以改善單相磁電材料之磁電耦合效應過低而難以應用於生活中的問題，成為近年重點研究的智能材料。過往的文獻中常假設複合物交界面為完美交界面，然而在複合材料的製造過程中必定有無法避免的瑕疵，造成交界面上場量分佈有不連續的現象，為非完美交界面。非完美交界面上常區分為曳引力不連續的強非完美交界面與勢能不連續的弱非完美交界面。
本研究運用雙重傅立葉級數表示彈性層狀複合材料之位移、法向應力與切平面向應力，及壓電壓磁層狀複合材料之廣義位移、廣義法向應力與廣義切平面向應力，並運用傳播矩陣連結層狀複合材料各場量與厚度的關係，將弱非完美交界面的性質以弱非完美交界面傳播矩陣表示，並運用傳播矩陣與弱非完美交界面條件串聯層狀複合材料兩厚度位置的場量關係，最後代入邊界條件計算各場量隨厚度位置之分佈。
從結果中可得知弱非完美交界面對彈性層狀複合材料與壓電壓磁層狀複合材料在廣義位移與廣義應力的影響。壓電壓磁層狀複合材料中在交界面為弱非完美交界面的情況下，電位移和電勢能量值在壓電材料及壓磁材料間的比值較完美交界面來的大；同樣的在弱非完美交界面下，磁通量密度和磁勢能在壓磁材料與壓電材料之間的比值也較完美交界面來的大。此外在附錄中會利用施加表面法向電位移在各材料組合中分析磁通量密度與磁勢能，及施加表面磁通量密度分析多鐵層狀複合材料之電位移與電勢能，可以得知弱非完美交界面會降低磁電耦合效應。

In this work, we study the field distributions of laminated multiferroic composites with the spring-type imperfect interfaces. Multiferroic composites were invented for enhancing magnetoelectric coupling effect and have been investigated in recent years. In early studies, potential and traction in interfaces were assumed continuous. However, some defects are unavoidable in the process of manufacturing composites. Imperfect interfaces can be divided into stress-type imperfect interfaces, which represent discontinuity in potential and spring-type interfaces, which represent discontinuity in traction.
We use double Fourier series to express displacement, in-plane stresses, and normal stresses in elastic laminated composites, and extend to the generalized displacement and generalized stresses in multiferroic laminated composites. By adopting propagator matrix, the field of two thickness locations can be connected and the feature of spring-type imperfect interfaces can transform into spring-type imperfect interface matrix. By giving boundary condition, the field distributions along the thickness can be derived.
In numerical studies, we can learn that electric displacement ratio and electric potential ratio of in piezoelectric material and in piezomagnetic material with spring-type imperfect interfaces are larger than perfect interfaces. Similarly, magnetic potential ratio and magnetic flux density ratio of in piezomagnetic material and in piezoelectric material with spring-type imperfect interfaces are larger than perfect interfaces. By the result of exerting the surface normal electric displacement and surface normal magnetic flux density on laminated multiferroic composites, we find that spring-type imperfect interfaces reduce the magnetoelectric coupling effect.

中文摘要 I
Abstract II
誌謝 IV
目錄 V
圖目錄 VIII
表目錄 XII
符號表 XIII
第一章 導論 1
1-1 研究背景與目的 1
1-2 多鐵性材料 2
1-2-1 壓電材料 3
1-2-2 磁致伸縮材料 4
1-2-2 壓磁材料 4
1-2-3 磁電材料 5
1-2-4 非完美交界面 5
1-3 複合材料結構形式 6
1-4 文獻回顧 6
1-4-1 雙相多鐵性複合材料 6
1-4-2 交界面問題 7
1-5 本文架構 8
第二章 彈性層狀複合材料 9
2-1 材料組成律與傳播矩陣 9
2-1-1 材料組成律 9
2-1-2 彈性層狀材料的通解 11
2-1-3 彈性層狀複合材料的傳播矩陣(Propagator Matrix) 16
2-1-4 材料選擇 19
2-2交界面問題 20
2-2-1 完美交界面 20
2-2-2 弱非完美交界面 22
2-3結果與分析 25
2-3-1 Ag/Ag 28
2-3-2 Ag/Ni 32
2-3-3 Ag/Ni/Ag 36
第三章 壓電壓磁層狀複合材料 40
3-1壓電壓磁材料的材料組成律與傳播矩陣 40
3-1-1 磁、電、彈耦合之材料組成律 40
3-1-2 壓電壓磁層狀材料的通解 44
3-1-3 壓電壓磁層狀複合材料的傳播矩陣 48
3-1-4 材料選擇 51
3-2 交界面性質與傳播矩陣的關係 53
3-2-1 完美交界面 53
3-2-2 弱非完美交界面 55
3-3 結果與分析 58
3-3-1 BTO/BTO 61
3-3-2 BTO/CFO 67
3-3-4 CFO/BTO/CFO 80
第四章 結論與未來展望 87
4-1 結論 87
4-2 未來展望 88
參考文獻 90
附錄A 弱非完美交界面條件 94
附錄B 多鐵性層狀複合材料在弱非完美交界面之磁電耦合效應 97
B-1 BTO/CFO 99
B-2 CFO/BTO 102
B-3 BTO/CFO/BTO 105
B-4 CFO/BTO/CFO 108

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