含裂紋之壓電材料受反平面動力點載荷之全場解析

Transient Full-Field Analysis of a Piezoelectric Crack Subjected to Dynamic Anti-plane Concentrated Loading

吳盈稷(Ying-Chi Wu)

指導教授 ： 應宜雄

淡江大學/工學院/航空太空工程學系碩士班/碩士(2006年)

https://doi.org/10.6846/TKU.2006.00493

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。

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

並列摘要

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.

並列關鍵字

piezoelectric ； crack ； stress intensity factor ； electric displacement intensity factor ； dynamic fracture

參考文獻

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.

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.

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 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.