臺灣博碩士論文加值系統

摘 要
本文研究的內容共可分為兩個部份，第一部份以微觀力學理論為基礎，求得Eshelby張量，再導入Mori-Tanaka平均場理論及Eshelby等價同質體法之觀念，可推得鐵電/鐵磁複材之等效熱-磁-電-彈模數。文中以BaTiO3/CoFe2O4複材作數值討論，探討熱效應對複材之等效模數的影響，結果發現熱效應的存在使得複材之纖維方向的等效彈性模數會增加，等效壓電及壓磁係數會減小，而鐵電/鐵磁複材所獨特具有的磁電耦合效應也會因壓電與壓磁性質的乘積作用而降低，且複材之電、磁品質因子也會隨之降低。
第二部份係探討電致伸縮同質體任意方向排列與複材之等效模數的關係。文中以包含電致伸縮係數及局部電場的函數取代電致伸縮複材本構方程式中的非線性項，即可將本構方程式改寫如壓電材料之表示式。再以三維空間座標轉換之觀念，求得母材與同質體之局部電場及複材之等效模數。文中以PMN-PT/Epoxy複材作數值討論，結果發現當同質體與母材同向時，由於纖維方向之電致伸縮係數有大幅度的變化，使得等效彈性模數也會因兩者相互對應的關係而變大，有增強的效果；另一方面，為了瞭解等效模數與同質體排列角度之關係，對同質體排列的角度作隨機變化，進一步求得三種同質體特殊排列方式之等效模數的解析解。

Abstract

The composite consisting of ferroelectric and ferromagnetic phases studied in this thesis is characterized as one type of the multi-function intelligent electric ceramics composites. The effective thermal-magneto-electro-elastic properties of the ferroelectric/ferromagnetic composite are explored in the first part of the thesis. Since the performance of the composite is commonly subject to the changing environment under operation, the thermal effect on the composite is extensively addressed. In addition, due to the fact that the effective properties strongly depend upon the shape and volume fraction of inclusions, the ellipsoid is treated as an inclusion in the composites. The coupled thermal-magnetic-electric-elastic Eshelby tensor is obtained from the approach of micromechanics. Then, utilizing the Mori-Tanaka mean-field theory and the Eshelby equivalent inclusion method, the effective thermal-magneto-electro-elastic modules of the composite are obtained successfully. The obtained results show that the effective elastic moduli are increased on account of the thermal effect; on the contrary, piezoelectric and piezomagnetic coefficients, are reduced in the fiber’s direction. Also, the factors regarding the electric as well as magnetic quantities will descend due to the thermal effect. Furthermore, since the product of piezoelectric and piezomagnetic properties, the magneto-electric coupling effect exist only in the composites is decreasing in fiber direction.
For the second part of the thesis, the electrostrictive effect in the electrostriction composite is investigated. Using the effective module theory as developed in the first part of the thesis, firstly, the nonlinear terms in the constitutive equations for the electrostriction composite are treated as a linear electro-elastic coupling coefficient so as to simplify the problem to obtain a linear constitutive equation. Secondly, in order to calculate the electro-elastic coupling coefficient, the numerical iteration method is utilized that a guessed initial value speeding up convergence is obtained from the ratio of local electric fields. It follows that the influence of the electrostrictive effect on the electrostriction composites can readily be analyzed through the obtained numerical results. The analyses show that, parallel to the thermal effect, the electrostriction has a reinforcement effect on the effective elastic moduli, which is especially obvious in the fiber’s direction. Moreover, in order to understand the relationships between the effective moduli of the composite and the distribution of inclusions, the inclusions’ orientation is randomly arranged. At last, three special cases for inclusions’ orientation are discussed with their effective module analytically obtained.

目 錄

摘要i
英文摘要ii
目錄iv
圖目錄vii
表目錄ix
符號表x
第一章 緒論1
1-1背景1
1-2目的3
1-3文獻回顧4
1-4本文內容5
第二章 鐵電及鐵磁材料之性質與應用7
2-1鐵電材料之性質與應用7
2-1.1 壓電材料之性質與應用8
2-1.2 焦電材料之性質與應用11
2-1.3 電致伸縮材料之性質與應用12
2-2鐵磁材料之性質與應用12
2-2.1 磁性材料之性質與應用13
2-2.2 磁致伸縮材料之性質與應用14
2-3電、磁品質因子15
第三章 鐵電(鐵磁)橢球同質體之熱-磁-電-彈耦合Eshelby張量17
3-1熱-磁-電-彈本構方程式17
3-2鐵電(鐵磁)橢球同質體內之熱-磁-電-彈場20
3-3橫向等向性鐵電(鐵磁)材料之 表示式28
3-4橫向等向性鐵電(鐵磁)材料之熱-磁-電-彈耦合Eshelby張量38
3-5本章結論44
第四章 等效熱-磁-電-彈性質45
4-1等效熱-磁-電-彈性質45
4-2邊界上受到拖曳力-電位移-磁感應-熵變化之分析46
4-3邊界上受到位移-電場-磁場-溫度場之分析52
4-4 BaTiO3-CoFe2O4複材的數值結果與討論55
4-5本章結論69
第五章 電致伸縮材料性質之分析71
5-1電致伸縮本構方程式71
5-2三維空間座標轉換73
5-3同質體任意方向排列之等效電致伸縮性質77
5-3.1 母材與同質體之局部電場理論77
5-3.2 同質體任意方向排列之複材材料性質80
5-4 PMN-PT-Epoxy的數值結果與討論86
5-5本章結論98
第六章 結論與展望99
6-1 本文結論99
6-2 未來研究方向101
參考文獻102
附錄 A105
附錄 B106
附錄 C112
誌謝113
作者簡介114

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