臺灣博碩士論文加值系統

本論文利用電場與磁場大小和方向的改變，使用能量密度理論(Strain energy density theory)探討含裂縫之單一磁壓電複合材料BaTiO3-CoFe2O4的破壞行為-預測裂縫成長角度及裂縫成長的驅動力。能量密度因子S為應力強度因子、電位移(電場)強度因子及磁感(磁場)強度因子函數。藉由改變電場與磁場的方向和壓電壓磁的大小來判斷所施加外力負載在過程中扮演的角色。

In this studying, the fracture problem of an arbitrarily oriented crack in a magnetoelectroelastic solid has been analyzed by using the energy density theory. The solution for the energy density factor S is modified to include the stress intensity factors, the electric displacement intensity factor(or the electrical field intensity factor) and the magnetic induction intensity factor(or the magnetic field intensity factor). The driving force and crack growth are also found to be significantly influenced by the polarization direction. Change in the directions of the applied magnetic and electric fields may influence the character of crack growth which could be enhanced or retarded. The ratios R and V are used as the parameters to judge the significance of mechanical load, electric field or magnetic field.

摘要.......................I
Abstract.......................II
誌謝.......................III
目錄.......................IV
表目錄.......................VII
圖目錄.......................VIII
符號說明.......................XI
第一章 緒論.......................1
1.1 前言.......................1
1.2 文獻回顧.......................2
1.3 研究主旨.......................6
1.4 本文架構.......................6
第二章 磁壓電材料之廣義Lekhnitskii複變函數公式.......................7
2.1 廣義Lekhnitskii表示法.......................7
2.2 應力函數、電位移函數、磁感函數複變表示法.......................17
2.3 各種特殊退化問題之探討.......................25
2.3.1 退化條件A：.......................25
2.3.2 退化條件B：.......................26
2.3.3 退化條件C：.......................28
2.3.4 退化條件D：.......................29
第三章 含裂縫之磁壓電材料破壞研究.......................31
3.1 問題描述.......................31
3.2 基本公式.......................32
3.3 裂縫尖端之磁電彈場解.......................41
3.4 能量密度理論.......................45
第四章 結果與討論.......................48
4.1 BaTiO3-CoFe2O4的材料係數.......................48
4.2 無窮遠處沿y-軸施加張應力.......................50
4.3 無窮遠處沿x-軸施加剪應力.......................52
4.4 無窮遠處沿y-軸施加電場.......................54
4.5 無窮遠處沿y-軸施加磁場.......................56
4.6 CoFe2O4導磁係數和BaTiO3-CoFe2O4之間比例對最小能量密度因子的影響.......................58
4.6.1 CoFe2O4導磁係數的影響.......................58
4.6.2 BaTiO3體積比例對最小能量密度因子的影響.......................60
4.7 無窮遠處施加機械力、電場與磁場.......................62
4.7.1 電場效應.......................62
4.7.2 磁場效應.......................66
4.8 無窮遠處施加歪斜之機械力、電場與磁場.......................71
第五章 結論.......................81
參考文獻.......................84
附錄A.......................88
附錄B.......................90
附錄C.......................92
附錄D.......................104

[1] Van Suchtelen, J., 1972. “Product properties: a new application of composite materials”, Philips Research Reports, 27, 28-37.

[2] Van Den Boomgaard, J., Terrell, D.R., Born, R.A.J., Giller, H.F.J.I., 1974. “An in situ grown eutectic magnetoelectric composite material. PartⅠ: Composition and unidirectional solidification”, Journal of Materials Science, 9, 1705-1709.

[3] Van Run, A.M.J.G., Terrell, D.R., Scholing, J.H., 1974. “An in situ grown eutectic magnetoelectric composite material. PartⅡ: Physical properties”, Journal of Materials Science, 9, 1710-1714.

[4] Jinxi, L., Xianglin, L., Yongbin, Z., 2001. “Green’s functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack”, International Journal of Engineering Science, 39, 1405-1418.

[5] Gao, C.F., Kessler, H., Balke, H., 2003. “Crack problems in magnetoelectroelastic solids. PartⅠ: Exact solution of a crack”, International Journal of Engineering Science, 41, 969-981.

[6] Gao, C.F., Kessler, H., Balke, H., 2003. “Crack problems in magnetoelectroelastic solids. PartⅡ: General solution of collinear cracks”, International Journal of Engineering Science, 41, 983-994.

[7] Gao, C.F., Tong, P., Zhang, T.Y., 2003. “Interfacial crack problems in magneto-electroelastic solids”, International Journal of Engineering Science, 41, 2105-2121.

[8] Gao, C.F., Tong, P., Zhang, T.Y., 2004. “Fracture mechanics for a mode Ⅲ crack in a magnetoelectroelastic solid”, International Journal of Solids and Structures. 41, 6613-6629.

[9] Wang, B.L., Mai, Y.W., 2004. “Impermeable crack and permeable crack assumptions, which one is more realistic ?”, ASME Journal of Applied Mechanics, 71, 575-578.

[10] Li, R., Kardomateas, G.A., 2006. “The mode Ⅲ interface crack in piezo-electro-magneto-elastic dissimilar bimaterials”, ASME Journal of Applied Mechanics, 73, 220-227.

[11] Wang, B.L., Mai, Y.W., 2006. “Closed-form solution for an antiplane interface crack between two dissimilar magnetoelectroelastic layers”, ASME Journal of Applied Mechanics, 73, 281-290.

[12] Wang, X., Shen, Y.P., 2002. “The general solution of three-dimensional problems in magnetoelectroelastic media”, International Journal of Engineering Science, 40, 1069-1080.

[13] Song, Z.F., Sih, G.C., 2003. “Crack initiation behavior in magnetoelectroelastic composite under in–plane deformation”, Theoretical and Applied Fracture Mechanics, 39, 189-207.

[14] Sih, G.C., Song, Z.F., 2003. “Magnetic and electric poling effects associated with crack growth in BaTiO3-CoEe2O4 composite”, Theoretical and Applied Fracture Mechanics, 39, 209-227.

[15] Sih, G.C., Jones, R., Song, Z.F., 2003. “Piezomagnetic and piezoelectric poling effects on modeⅠandⅡ crack initiation behavior of magnetoelectroelastic materials”, Theoretical and Applied Fracture Mechanics, 40, 161-186.

[16] Spyropoulos, C.P., Sih, G.C., Song, Z.F., 2003. “Magnetoelectroelastic composite with poling parallel to plane of line crack under out-plane deformation”, Theoretical and Applied Fracture Mechanics, 39, 281-289.

[17] Wang, B.L., Mai, Y.W., 2003. “Crack tip field in piezoelectric/piezomagnetic media”, European Journal of Mechanics, A/Solids, 22, 591-602.

[18] Zhou, Z.G., Wang, B., Sun, Y.G., 2004. “Two collinear interface cracks in magneto-electro-elastic composites”, International Journal of Engineering Science, 42, 1155-1167.

[19] Sih, G.C., Yu, H.Y., 2005. “Volume fraction effect of magnetoelectroelastic composite on enhancement and impediment of crack growth”, Composite Structures, 68, 1-11.

[20] Zhou, Z.G., Wu, L.Z., Wang, B., 2005. “A closed form solution of a crack in magneto-electro-elastic composites under anti-plane shear stress loading”, JSME International Journal, Series A, 48(3), 151-154.

[21] Hu, K., Li, G., 2005. “Constant moving crack in a magnetoelectroelastic material under anti-plane shear loading”, International Journal of Solids and Structures, 42, 2823-2835.

[22] Li, X.F., 2005. “Dynamic analysis of a cracked magnetoelectroelastic medium under antiplane mechanical and inplane electric and magnetic impacts”, International Journal of Solids and Structures, 42, 3185-3205.

[23] Zhou, Z.G., Wu, L.Z., Wang, B., 2005. “The dynamic behavior of two collinear interface cracks in magneto-electro-elastic materials”, European Journal of Mechanics, A/Solids, 24, 253-262.

[24] Zhou, Z.G., Wang, B., 2004. “Two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading”, International Journal of Solids and Structures, 41, 4407-4422.

[25] Zhou, Z.G., Wu, L.Z., Wang, B., 2005. “The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading”, Archive of Applied Mechanics, 74, 526-535.

[26] Soh, A.K., Liu, J.X., 2005. “On the constitutive equations of magnetoelectroelastic solids”, Journal of Intelligent Material Systems and Structures, 16, 597-602.

[27] Lekhnitskii, S.G., 1963. Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, San Francisco.

[28] Huang, J.H., Kuo, W.S., 1997. “The analysis of piezoelectric-piezomagnetic composite materials containing ellipsoidal inclusions”, Journal of Applied Physics, 81(3), 1378-1386.

[29] Edminister, J.A., 1993. Theory and Problems of Electromagnetics. Second edition, McGraw-Hill, New York.