淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-1707200615015900
中文論文名稱 含裂紋之壓電材料受反平面動力點載荷之全場解析
英文論文名稱 Transient Full-Field Analysis of a Piezoelectric Crack Subjected to Dynamic Anti-plane Concentrated Loading
校院名稱 淡江大學
系所名稱(中) 航空太空工程學系碩士班
系所名稱(英) Department of Aerospace Engineering
學年度 94
學期 2
出版年 95
研究生中文姓名 吳盈稷
研究生英文姓名 Ying-Chi Wu
電子信箱 693370172@s93.tku.edu.tw
學號 693370172
學位類別 碩士
語文別 中文
口試日期 2006-06-28
論文頁數 174頁
口試委員 指導教授-應宜雄
委員-馬劍清
委員-劉昭華
中文關鍵字 壓電材料  裂紋  應力強度因子  電位移強度因子  動力破壞 
英文關鍵字 piezoelectric  crack  stress intensity factor  electric displacement intensity factor  dynamic fracture 
學科別分類 學科別應用科學航空太空
中文摘要 本文研究主題為含真空邊界靜止裂紋之壓電材料動力破壞問題,解析一含半無限長靜止裂紋之壓電材料,於域內任意處施予一應力型反平面動力點載荷之暫態效應,本文使用積分轉換法與Wiener-Hopf技巧推導壓電材料於一次拉普拉斯轉換域中,受空間指數應力與電位移分佈型之基本解,並利用此基本解來解析此包含特徵長度的壓電材料動力破壞問題,文中使用Cagniard-de Hoop方法來作拉普拉斯逆轉換得到時域中的解。最後,本文將針對應力場、應力強度因子與電位移強度因子等解析解,做詳細的數值計算與討論。
英文摘要 In this study, the transient response of a semi-infinite crack subjected to dynamic anti-plane concentrated loading in a hexagonal piezoelectric medium with vacuum boundary conditions is investigated. Two 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 problems are the problems of applying exponentially distributed traction or electric displacements (in Laplace transform domain) on the crack faces. The Cagniard-de Hoop method of Laplace inversion is used to obtain the transient solutions in time domain. Exact transient Full-Field solutions and exact transient solutions of intensity factors to the problem are both derived. Finally, numerical results are evaluated and discussed in detail.
論文目次 目錄 ………………………………………………………………… I
圖表目錄 …………………………………………………………… III
第一章 緒論 ………………………………………………………1
1.1 研究動機與文獻回顧 …………………………………1
1.2 研究方法與內容簡介 …………………………………6
第二章 理論基礎與基本解 ………………………………………8
2.1 線彈性壓電控制與本構方程式 ………………………8
2.2 拉普拉斯轉換與Cagniard-de Hoop method …………9
2.2.1 拉普拉斯轉換 ………………………………………9
2.2.2 Cagniard-de Hoop method ………………………10
2.3 含真空邊界靜止裂紋之壓電材料受反平面應力型基本解 ………………………………………………11
2.4 含真空邊界靜止裂紋之壓電材料受平面電位移型基本解 ………………………………………………23
2.5 無窮域壓電材料受反平面動力點載荷之全場解 ………………………………………………………29
第三章 含半無限長裂紋之壓電材料受反平面動力點載荷之全場解析 …………………………………………………………37
3.1 問題描述 ……………………………………………37
3.2 上半平面之全場解 ……………………………………37
3.3 下半平面之全場解 ……………………………………60
3.4 強度因子 …………………………………………76
第四章 數值計算與討論 …………………………………………80
4.1 波傳的分析與討論(上半平面) …………………80
4.2 波傳的分析與討論(下半平面) …………………83
4.3 強度因子 ……………………………………………86
第五章 結論 ………………………………………………………87
5.1 本文結論 ……………………………………………87
5.2 本文成果 ……………………………………………87
5.3 尚待研究的方向 ……………………………………89
附錄 …………………………………………………………………91
A. 觀察點位於上半平面 全場解 ………………………91
B. 觀察點位於下半平面 全場解 ………………………95
C. 觀察點位於上半平面 與 全場解 …………………99
D. 觀察點位於下半平面 與 全場解 ………………102
E. 電位移暫態圖(上半平面) ……………………………106
F. 電位移暫態圖(下半平面) ……………………………112
參考文獻 …………………………………………………………118

圖 表 目 錄
圖2.1 真空基本解的邊界描述 ……………………………………125
圖2.2 積分路徑 …………………………………………………126
圖2.3 無窮域基本解的邊界描述 ………………………………127
表3.1 上半平面之波前統整 …………………………………128
表3.2 下半平面之波前統整 …………………………………129
圖3.1 靜止裂紋之問題描述 ………………………………………130
圖3.2.1(a) 情況一:聲波積分路徑圖 ……………………………131
圖3.2.1(b) 情況一:電磁波積分路徑圖 …………………………132
圖3.2.2(a) 情況二:聲波積分路徑圖 ……………………………133
圖3.2.2(b) 情況二:電磁波積分路徑圖 …………………………134
圖3.2.3(a) 情況三:聲波積分路徑圖 ……………………………135
圖3.2.3(b) 情況三: 積分路徑圖 ……………………………136
圖3.2.3(c) 情況三:電磁波積分路徑圖 …………………………137
圖3.2.4(a) 情況四:聲波積分路徑圖 ……………………………138
圖3.2.4(b) 情況四:電磁波積分路徑圖 …………………………139
圖3.2.5(a) 情況五:聲波積分路徑圖 ……………………………140
圖3.2.5(b) 情況五: 積分路徑圖 ……………………………141
圖3.2.5(c) 情況五:電磁波積分路徑圖 …………………………142
圖3.2.6(a) 情況六:聲波積分路徑圖 ……………………………143
圖3.2.6(b) 情況六:電磁波積分路徑圖 …………………………144
圖3.3.1(a) 情況一:聲波積分路徑圖 ……………………………145
圖3.3.1(b) 情況一:電磁波積分路徑圖 …………………………146
圖3.3.2(a) 情況二:聲波積分路徑圖 ……………………………147
圖3.3.2(b) 情況二:電磁波積分路徑圖 …………………………148
圖3.3.3(a) 情況三:聲波積分路徑圖 ……………………………149
圖3.3.3(b) 情況三:電磁波積分路徑圖 …………………………150
圖3.3.4(a) 情況四:聲波積分路徑圖 ……………………………151
圖3.3.4(b) 情況四:電磁波積分路徑圖 …………………………152
圖3.3.5(a) 情況五:聲波積分路徑圖 ……………………………153
圖3.3.5(b) 情況五:電磁波積分路徑圖 …………………………154
圖3.3.6(a) 情況六:聲波積分路徑圖 ……………………………155
圖3.3.6(b) 情況六:電磁波積分路徑圖 …………………………156
圖3.4 積分路徑圖 ………………………………………………157
表4.1 壓電材料常數表 ……………………………………………158
圖4.1 應力在第一象限波前圖 ……………………………………159
圖4.2 應力在第二象限波前圖 ……………………………………160
圖4.3.1 情況一: , 應力暫態圖 …………………161
圖4.3.2 情況二: , 應力暫態圖 …………………162
圖4.3.3 情況三: , 應力暫態圖 …………………163
圖4.3.4 情況四: , 應力暫態圖 …………………164
圖4.3.5 情況五: , 應力暫態圖 …………………165
圖4.3.6 情況六: , 應力暫態圖 …………………166
圖4.4.1 情況一: , 應力暫態圖 …………………167
圖4.4.2 情況二: , 應力暫態圖 ………………168
圖4.4.3 情況三: , 應力暫態圖 ………………169
圖4.4.4 情況四: , 應力暫態圖 ………………170
圖4.4.5 情況五: , 應力暫態圖 ………………171
圖4.4.6 情況六: , 應力暫態圖 ………………172
圖4.5 含靜止裂紋之壓電材料之應力強度因子 …………………173
圖4.6 含靜止裂紋之壓電材料之電位移強度因子 ………………174
參考文獻 Auld, B, A., (1973) “Acoustic Field and Waves in Solids,” John Wiley &Sons, NEW York.

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).

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

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.

Gulayev, Y. V., (1969) “Electroacoustic surface waves in solids,” Soviet Physics JETP, Vol. 9, pp.37-38.

Ing, Y. S. and Lin, J. T., (2002) “ The stress intensity factor for a surface crack due to movig impact loading”, accepted to publish in Tamkang Journal of Science and Engineering.

Ing, Y. S. and Ma, C. C., (1996) “Transient response if a finite crack subjected to dynamic anti-plane loading,” International Journal of Fracture, Vol. 82. pp. 345-362.

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

Ing, Y. S. and Ma, C. C., (1997b) “Dynamic fracture analysis of a finite crack subjected to an incident horizontally polarized shear wave,” International Journal of Solids and Structures, Vol.34, pp. 895-910.

Ing, Y. S. and Ma, C. C., (1999) “Transient analysis of a propagating crack with finite length subjected to a horizontally polarized shear wave,” International Journal of Solids and Structures, Vol. 36, pp. 4609-4627.

Ing, Y. S. and Ma, C. C., (2001) “Transient response of a surface crack subjected to dynamic anti-plane concentrated loadings”, International Journal of Fracture, Vol.109, pp. 239-261.

Ing, Y. S. and Ma, C. C., (2003a) “Dynamic Fracture analysis of finite cracks by horizontally polarized shear waves in anisotropic solids,” Journalof the Mechanics and Physics of Solids, Vol. 51, pp. 1987-2021.

Ing, Y. S. and Ma, C. C., (2003b) “Full-field analysis of an anisotropic finite crack subjected to an anti-plane point impact loading(submitted),”

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

Ing, Y. S. and Wang, M. J., (2004b) “Transient analysis of a mode-III crack propagating in a piezoelectric medium,” International Journal of Solids and Structures. (In press)

Kwon, J. H., Lee, K. Y. and Kwon, S. M., (2000) “ Moving crack in a piezoelectric ceramic strip under anti-plane shear loading,” Mechanics Research Communications, Vol. 27, pp. 327-332.

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.

Li, S. and Mataga, P. A., (1996a) “ Dynamic crack propagation in piezoelectric materials-Part I. Electrode solution,” Journal of the Mechanics and Physics of Solids,
Vol. 44, pp. 1799-1830.

Li, S. and Mataga, P. A., (1996b) “ Dynamic crack propagation in piezoelectric materials-Part II. Vacuum solution,” Journal of the Mechanics and Physics of Solids,
Vol. 44, pp. 1831-1866.

Ma, C. C. and Chen, S. K., (1993) “Exact transient analysis of an anti-plane semi-infinite crack subjected to dynamic body forces,” Wave Motion,Vol. 17, pp. 161-171.

Ma, C. C. and Ing, Y. S., (1995) “Transient analysis of dynamic crack propagation with boundary effect,” ASME Journal of Applied Mechanics, Vol. 62, pp. 1029-1038.

Ma, C. C. and Ing, Y. S., (1997a) “Dynamic crack propagation in a layered medium under antiplane shear,” Journal of Applied Mechanics, Vol. 64, pp. 66-72.

Ma, C. C., Ing, Y. S., (1997b) “Transient analysis of a crack in a composite layered medium subjected to dynamic loadings,” AIAA Journal, Vol. 35, pp. 706-711.

McMeeking, R. M., (1989a) “ Electrostricitive stress near crack-like flaws,” Zeitschrift f r Angewandte Mathematik und Physik, Vol. 40, pp. 615-627.

McMeeking, R. M., (1989b) “ On mechanical stresses at cracks in dielectrics with application to dielectric breakdown,” Journal of Applied Physics, Vol. 28, pp. 605-613.

Meguid, S. A. and Wang, X. D., (1998) “ Dynamic antiplane behavior of interacting cracks in a piezoelectric medium,” International Journal of fracture, Vol. 91, pp. 391-403.

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.

Pak, Y. E., (1990) “Crack extension force in a piezoelectric material ,” Journal of Applied Mechanics, Vol. 57, pp.647-653.

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

Park, Y. E. and Sun, C. T., (1995b) “Fracture criteria for piezoelectric ceramics,” J. Am. Ceram. Soc. Vol. 78, pp. 1475-1480.

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

Pohanka, R. C. and Smith, P. L., (1988) “Recent advances in piezoelectric ceramics.” Electronic Ceramics (ed. L. M. Levinson). Marcel Dekker, New York.

Ru, C. Q., (2000) “Exact solution for finite electrode layers embedded at the interface of two piezoelectric half-planes.” Journal of Mechanics and Physics of Solids, Vol. 48, pp. 693-708.

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.

To A. C., Li S., Glaser S. D., (2005) “On Scattering in Dissimialr Piezoelectric Materials by Semi-infinite Interfacial Crack,” The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 58, pp. 309-331

Tsai, C. H., and Ma, C. C., (1992) “Transient analysis of a semi-infinite crack subjected to dynamic concentrated forces,” ASME Journal of Applied Mechanics, Vol. 59, pp. 804-811.

Yang, F., (2001) “Fracture mechanical for a mode I crack in piezoelectric materials,” International Journal of Solids and Structures, Vol. 38, pp. 3913-3830.

Yang, F. and Kao, I., (1999) “Crack problem in piezoelectric materials: general anti-plane mechanical loading,” Mechanics of Materials, Vol. 31, pp. 395-406.

Zhang, T. Y. and Tong, P., (1996) “Fracture mechanics for mode III crack in a piezoelectric material,” International Journal of Solids and Structures, Vol. 33, pp. 343-359.

洪國彬 (2003),含預裂縫之壓電材料的力學行為,國立臺灣大學應用力學研究所碩士論文。

林世皓 (2004),含真空邊界壓電材料之擴展裂紋動力破壞解析,淡江大學航空太空工程學系碩士論文
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2006-07-20公開。
  • 同意授權瀏覽/列印電子全文服務,於2008-07-20起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2281 或 來信