本文研究內含電極邊界條件之界面裂紋的壓電複合材料動力破壞問題，解析一含半無限長界面裂紋之六角雙異層壓電材料複合層板，於裂紋面上施加反平面均佈動力載荷之暫態效應。本文使用積分轉換法與Wiener-Hopf技巧推導壓電材料於拉普拉氏轉換域中之解，接著使用Cagniard-de Hoop方法來作拉普拉斯逆轉換得到時域中的全場暫態解析解，並求出應力強度因子與電位移強度因子等解析解。文中並對表面波存在的條件做詳細之研究，最後，將針對應力與電位移之暫態解做數值計算與討論。

In this study, the transient response of a semi-infinite interface crack between two dissimilar piezoelectric materials with the electrode boundary condition is investigated. The interface crack is subjected to dynamic anti-plane uniform loading on the crack faces. The problem is solved by the application of integral transform methods and the Wiener-Hopf technique. Exact analytical transient full-field solutions for displacements, shear stresses, electric potentials, electric displacements,  and intensity factors are obtained by using the Cagniard-de Hoop method of Laplace inversion. The existence condition of a propagating surface wave along the interface is studied in detail. Finally, numerical results are evaluated and discussed in detail.

目錄
目錄	I
圖表目錄	III

第一章 緒論	1
1.1研究動機	1
1.3內容簡介	6
第二章 理論基礎	7
2.1 線性壓電控制與本構方程式	7
2.2 拉普拉斯轉換與Cagniard-de Hoop method	15  
第三章 界面裂紋受反平面動力均佈載荷之暫態解析	16  
3.1 問題描述	16
3.2 理論解析	17
3.3  之有無實根判斷以及有實根拆解	24  
3.4  函數之無根拆解	31
3.5  函數拆解	33
3.6存在MT表面波之理論解析	37
3.7無MT表面波之理論解析	43
3.8存在MT表面波之時域解	49
3.9 無MT表面波之時域解	61
第四章 數值計算與討論	70
第五章 成果與討論	75
5.1本文結論	75
5.2 本文成果	75
5.3 尚待研究方向	76
參考文獻	78
 
圖表目錄

圖3-1界面裂紋之問題描述	84
圖3-2  之 平面圖	85
圖3-3  有根形式之 平面圖	86
圖3-4  無根形式之 平面圖	87
圖3-5 有根形式之 積分路徑	88
圖3-6無根形式之 積分路徑	89
圖3-7  積分路徑圖	90
圖3-8  積分路徑圖	91
圖3-9  逆轉換路徑圖有剪力頭前波	92
圖3-10  逆轉換路徑圖無剪力頭前波	93
表4.1壓電材料常數表	94
圖4-1a   之剪應力暫態圖	95
圖4-1b   之剪應力暫態圖	96
圖4-2a   之剪應力暫態圖	97
圖4-2b   之剪應力暫態圖	98
圖4-3 之雙異質壓電材料裂紋面施加均佈載荷波前圖	99
圖4-4   之不同壓電材料剪應力暫態圖	100
圖4-5   之不同壓電材料剪應力暫態圖	101
圖4-6   之不同壓電材料剪應力暫態圖	102
圖4-7   之不同壓電材料剪應力暫態圖	103
圖4-8   之不同壓電材料剪應力暫態圖	104
圖4-9   之不同壓電材料剪應力暫態圖	105 
圖4-10a   之上半平面電位移暫態圖	106
圖4-10b   之上半平面電位移暫態圖	107 
圖4-11a   之下半平面電位移暫態圖	108 
圖4-11b   之下半平面電位移暫態圖	109 
圖4-12   之不同壓電材料電位移暫態圖	110
圖4-13   之不同壓電材料電位移暫態圖	111
圖4-14   之不同壓電材料電位移暫態圖	112 
圖4-15   之不同壓電材料電位移暫態圖	113 
圖4-16   之不同壓電材料電位移暫態圖	114 
圖4-17   之不同壓電材料電位移暫態圖	115 
圖4-18搭配虛擬材料之有根情況剪應力暫態圖	116 
圖4-19搭配虛擬材料之有根情況剪應力暫態圖	117

參考文獻

  Albert C. To, Shaofan Li and Steven D. Glaser (2005) “On scattering in dissimilar piezoelectric materials by a semi-infinite interfaceial crack ”

Achenbach, J. D., (1973) “Wave Propagation in Elastic Solids,” Elsevier, New Work.
	
Bleustein, J. L., (1968) “A new surface wave in piezoelectric materials,’ Applied Physics Letters, Vol. 13, pp. 412-413.

Cagniard, L., (1939) “Reflexion et Refraction des Ondes Seismiques Progressives,” Cauthiers-Villars, Paris (Translated into English and revised by Flinn, E.A., Dix, C.H., 1962 Reflection and Refraction of Progressive Seismic Waves. McGraw-Hill, New York).

Chen, Z. T., (1998) “Crack tip field of an infinite piezoelectric strip under anti-plane impact,”Machenics Research Communications, Vol. 25, pp. 313-319.

Chen, Z. T., Karihaloo, B. L. and Yu, S. W., (1998) “A Griffith crack moving along the interface of two dissimilar piezoelectric materials,” International Journal of Fracture, Vol. 91, pp. 197-203.

De Hoop, A. T., (1958) Representation theorems for the displacement in an elastic solid and their application to elastodynamic diffraction theory, Doctoral dissertation, Technische hoegschool, Delft.

Deeg, W. F., (1980) “The analysis of dislocation, crack and inclusion problems in piezoelectric solids,”Ph.D Thesis, Stanford University.

Gao, C.F.and Fan, W. X., (1999a) “A general solution for the plane problem in piezoelectric media with collinear cracks,” International Journal of Engineering Science, Vol. 37,pp. 347-363.

Gao, C. F. and Fan, W. X., (1999b) “Exact solutions for the inplane problem in piezoelectric materials with an elliptic or a crack,” International Journal of Solids and Structures, Vol. 36, pp. 2527-2540.

Gao, C. F. and Wang, M. Z., (2001) “Green’s function of an interfacial crack between two dissimilar piezoelectric media,” International Journal of Solids and Structures, Vol. 38, pp. 5323-5334.

Ing, Y. S. and Wang, M. J., (2004) “Explicit transient aolutions for a mode III crack subjected to dynamic concentrated loading in a piezoelectric material,” Interational Journal of Solids and Structures, Vol. 41, pp. 3849-3864.

Ing, Y. S. and Ma, C. C., (1997a) “Dynamic analysis of a propagating anti-plane interface crack,” Journal of engineering Mechanics,pp.783-791.

Kwon, S. M. and Lee, K. Y., (2001) “ Transient response of a rectangular piezoelectric medium with a center crack,” European Journal of Mechanics A/Solids, Vol. 20, pp. 457-468.

Li, S., (2003) “On global energy release rate of a permeable crack in crack in piezoelectric ceramic,” Journal of Applied Mechanics, Vol.  70, pp. 246-252.

	Maerfeld C. and Tournois P., (1971) “Pure Shear Elastic Surface Wave Guided by the Interface of Two Semi-
Infinite Media”

Meguid, S. A. and Chen, Z. T., (2001) “Transient response of a finite piezoelectric strip containing coplanar insulating cracks under electromechanical impact,” Mechanics of Materials, Vol. 33, pp. 85-96.

Meguid, S. A. and Zhao. X., (2002) “The interface crack problem of bonded piezoelectric and elastic half-space under transient electromechanical loads,” Journal of Applied Mechanics, Vol.  69, pp. 244-253.

Narita, F. and Shindo, Y., (1998a) “Layered piezoelectric medium with interface crack under anti-plane shear,” Theoretical and Applied Fracture Mechanics, Vol. 30, pp.119-126.

Narita, F. and Shindo, Y., (1998b) “Scattering of love waves by a surface-breaking crack in piezoelectric layered media,” JSME Int. J., Series A, Vol. 41, pp. 40-48.

Narita, F. and Shindo, Y., (1999) “Scattering of antiplane shear waves by a finite crack in piezoelectric laminates,” Acta Mechanica, Vol.  134, pp. 27-43.
    
   Pak, Y. E., (1990) “Crack extension force in a piezoelectric material ,” Journal of Applied Mechanics, Vol. 57, pp.647-653.

Park, S. B. and Sun, C. T., (1995a) “Effect of electric field on fracture of piezoelectric ceramics,” International Journal of Fracture, Vol. 70, pp. 203-216.

Park, S. B. and Sun, C. T., (1995b) “Fracture criteria of piezoelectric ceramics,” Journal-American Ceramic Society, Vol. 78, pp. 1475-1480.

	Parton, V. Z., (1976) “Fracture mechanics of piezoelectric materials.” Acta Astronaut, Vol. 3, pp. 671-683.

Shen, S., Kuang, Z. B. and Hu, S., (1999) “Interface crack problems of a laminated piezoelectric plate,” European Journal of Mechanics A/Solids, Vol. 18, pp. 219-238.

	Shindo, Y. and Ozawa, E., (1990) “Dynamics analysis of a piezoelectric material,” In: Hsieh, R.K.T. (Ed.), Mechanical Modeling of New Electromagnetic Materials. Elsevier, Amsterdam, pp. 297-304.

	Sosa, H., (1992) “On the fracture mechanics of piezoelectric solids,” International Journal of Solids and Structures, Vol. 29, pp. 2613-2622.
	Suo, Z., Kuo, C. M., Barnett, D. M. and Willis, J. R., (1992) “Fracture mechanics of piezoelectric ceramics,” Journal of the Mechanics and Physics of Solids, Vol. 40, pp. 739-765.

Ueda, S., (2003) “Diffraction of antiplane shear waves in a piezoelectric laminate with a vertical crack,” European Journal of Mechanics A/Solids, Vol. 22, pp. 413-422.

	Wang, B. L., Han, J. C. and Du, S. Y., (2000) “Electroelastic fracture dynamics for multilayered piezoelectric materials under dynamic anti-plane shearing.” International Journal of Solids and Structures, Vol. 37, pp. 5219-5231.

Wang, X. D., (2001) “On the dynamic behavior of interacting interfacial cracks in piezoelectric media,” International Journal of Solids and Structures, Vol. 38, pp. 815-831.
	
	Yang, F., (2001) “Fracture mechanical for a mode I crack in piezoelectric materials,” International Journal of Solids and Structures, Vol. 38, pp. 3913-3830.

Zhou, Z. G., Wang, B. and Sun, Y. G., (2003) “investigation of the dunamic behavior of two parallel symmetric cracks in piezoelectric materials use of non-local theory,” International Journal of Solids and Structures, Vol. 40, pp. 747-762.

蔡忠翰 (2005)，含界層裂紋之彈壓電複合材料之動力破壞分析，淡江大學航空太空工程學所碩士論文。