本文研究內含電極邊界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質壓電材料複合層板，於裂紋面上施加反平面動力點載荷在有限光速影響下之暫態效應，本文利用積分轉換法與Wiener-Hopf技巧推導壓電材料於拉普拉斯轉換域中之基本解，接著利用疊加的技巧求得一次拉普拉斯轉換域中之解，最後在使用Cagniard-de Hoop Method來做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。最後，將針對應力與電位移之暫態解作數值計算與討論。

In this study, the transient response of a semi-infinite interface crack due to Quasi-hyperbolic approximation between two dissimilar piezoelectric materials with the electrode boundary condition is investigated. The useful fundamental solutions are derived and the solutions can be determined by superposition of the fundamental solutions in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in Laplace transform domain) on the interface crack faces. The Cagniard-de Hoop method of Laplace inversion is used to obtain the transient solution in time domain. Exact transient Full-Field solution and exact transient solution of intensity factors to the problem with concentrated loads are derived. Finally, numerical results are evaluated and discussed in detail.

目錄
目錄......................................................I
圖表目錄................................................III
附錄.....................................................VI
第一章	緒論
  1.1研究動機顧...........................................1
  1.2文獻回顧.............................................3
  1.3內容簡介.............................................7
第二章	理論基礎
  2.1麥斯威爾方程式.......................................8
  2.2線性壓電控制與本構方程式............................10
  2.3拉普拉斯轉換與Cagniard-de Hoop method...............18
  2.4含靜止裂紋之雙異質壓電材料在有限光速影響下受反平面應力
     型負載基本解........................................19
  2.5存在MT表面波N(λ)有實根之理論分析....................30
  2.6無MT表面波N(λ)無實根之理論分析......................38
第三章	界面裂紋受反平面動力點載荷之暫態解析
  3.1問題描述.............................................46
  3.2存在MT表面波之解析...................................47
  3.3無MT表面波之解析.....................................72
  3.4結果驗證.............................................89
第四章 數值計算與討論.....................................96
第五章 成果與討論........................................102
  5.1本文結論............................................102
  5.2本文成果............................................103
  5.3尚待研究方向........................................103
參考文獻.................................................105
圖表目錄
圖3-1 介面裂紋之問題描述.................................109
圖3-2  逆轉換路徑圖有剪力頭前波..........................110
圖3-3  逆轉換路徑圖無剪力頭前波..........................111
圖3-4  逆轉換路徑圖有剪力頭前波..........................112
圖3-5  逆轉換路徑圖無剪力頭前波..........................113
圖3-6a  之雙異質壓電材料裂紋面施加動力點載荷波前.........114
圖3-6b  之雙異質壓電材料裂紋面施加動力點載荷波前放圖.....115
圖3-7  時，有MT表面波圍線積分路徑圖......................116
圖3-8  時，有MT表面波圍線積分路徑圖......................117
圖3-9  時，無MT表面波圍線積分路徑圖......................118
圖3-10  時無MT表面波圍線積分路徑圖.......................119
表4.1 壓電材料常數表.....................................120
表4.2 有限光速影響下與光速趨近無限大之應力強度因子數值比較
      (ZnO-PZT4).........................................121
表4.3 有限光速影響下與光速趨近無限大之電位移強度因子
      數值比較(ZnO-PZT4).................................122
圖4-1a  積分路徑圖.......................................123
圖4-1b  積分路徑圖.......................................124
圖4-2數值積分示意圖......................................125
圖4-3 (4.1)式圍線積分路徑圖..............................126
圖4-4 受應力負載含界面裂紋在有限光速影響下之應力強度因子
      (ZnO-PZT4) ........................................127
圖4-5 受應力負載含界面裂紋在有限光速影響下之電位移強度因子
      (ZnO-PZT4) ........................................128
圖4-6 受應力負載含界面裂紋在有限光速影響下之應力強度因子 
      (PZT4-CdS) ........................................129
圖4-7 受應力負載含界面裂紋在有限光速影響下之應力強度因子
       (虛擬材料-PZT4) ..................................130
圖4-8 受應力負載含界面裂紋在有限光速影響下之電位移強因子
      (虛擬材料-PZT4)....................................131
圖4-9 受應力負載含界面裂紋在光速趨近無限大之應力強度因子
      (ZnO-PZT4) ........................................132
圖4-10 受應力負載含界面裂紋在光速趨近無限大之電位移強度因子
       (ZnO-PZT4) .......................................133
圖4-11 受應力負載含界面裂紋在光速趨近無限大之應力強度因子
       (虛擬材料-PZT4) ..................................134
圖4-12 受應力負載含界面裂紋在光速趨近無限大之電位移強度因子
       (虛擬材料-PZT4) ..................................135
圖4-13 受應力負載含界面裂紋在有限光速影響下與光速趨近無限大
       之應力強度因子比較 (虛擬材料-PZT4)................136
圖4-14 受應力負載含界面裂紋在有限光速影響下與光速趨近無限大
       之電位移強度因子比較 (虛擬材料-PZT4)..............137
圖4-15 受應力負載含界面裂紋單一壓電材料在有限光速影響下之應
       力強度因子(PZT4)..................................138
圖4-16 受應力負載含界面裂紋單一壓電材料在有限光速影響下之電
       位移強度因子(PZT4)................................139
附錄
附錄一...................................................140

Albert C. To, Shaofan Li and Steven D. Glaser ,(2005) “On scattering in dissimilar piezoelectric materials by a semi-infinite interfaceial crack ”Q.JI Mech.Appl.Math,Vol. 58, pp. 309-331.

Bleustein, J. L., (1968) “A new surface wave in piezoelectric materials,’ Applied Physics Letters, Vol. 13, pp. 412-413.

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,X.H., Ing,Y.S., and Ma,C.C.,(2007)“Transient analysis of dynamic crack propagation in piezoelectric materials”Journal of the Chinese Institute of Engineers, Vol 30, No.3, pp.491-502. 

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.

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)“Transient analysis of a mode-III crack propagating in a piezoelectric medium”International Journal of Solids and structures, Vol.41, pp. 6197-6214

Ing, Y. S. and Ma, C. C., (1997a) “Dynamic analysis of a propagating anti-plane interface crack,” Journal of engineering Mechanics, Vol.123, pp.783-791.

Li, S., (2000) “Transient wave propagation in a transversely isotropic piezoelectric half space,” Zeitschrift fur Angewandte Mathematik und Physik, Vol.51,pp.236-266.

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.

Ma, C. C., Chen, X. H. and Ing, Y. S.,(2007) “Theoretical transient analysis and wave propagation of piezoelectric bi-materials”International Journal of Solids and Structures,Vol. 44, pp.7110-7142.

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

   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.

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.

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.

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.

Zhou, Z. G., and Wang, B.,(2006)“Investigation of behavior of mode-I interface crack in piezoelectric materials by using Schmidt method,”Applied Mathematics and Mechanics(English Edition),Vol. 27,pp. 871-882.
 
王茂榮, (2003)，含擴展裂紋之壓電材料動力破壞解析，淡江大學航空太空工程學所碩士論文。

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。

黃俊元, (2006)，含界面裂紋之雙異質壓電材料暫態解析，淡江大學航空太空工程學所碩士論文。

 謝友誌, (2007)，半雙曲線近似對含裂紋之壓電材料動態特性影響之研究，淡江大學航空太空工程學所碩士論文。

陳冠志, (2008)，含界層裂紋之雙層壓電材料受反平面動力點載荷之暫態效應，淡江大學航空太空工程學所碩士論文。