含界層裂紋之彈壓電複合材料之動力破壞分析

Dynamic Fracture Analysis of an Interface Crack between Purely Elastic and Piezoelectric Materials.

蔡忠翰(Chung-Han Tsai)

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(2005年)

https://doi.org/10.6846/TKU.2005.00027

摘要

本文研究內含電極邊界彈壓電複合材料之界層裂紋的動力破壞問題，解析一含半無限長界面裂紋之彈壓電複合材料，於裂紋面上施予均佈反平面動力載荷之破壞行為，並研究於距離裂紋尖端h處之裂紋面分別為受一對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技巧推導彈壓電複合材料於一次拉普拉氏轉換域中，受空間指數應力之基本解，並利用此基本解來解析此包含特徵長度的複合壓電材料動力暫態問題，接著使用Cagniard-de Hoop方法來作拉普拉斯逆轉換得到時域中的解。最後本文針對應力、電位移、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

複合壓電材料 ； 界面裂紋 ； 應力強度因子 ； 動力破壞

並列摘要

In this study, the transient response of a semi-infinite, interface crack between hexagonal piezoelectric and purly elastic media 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 solutions to the problem with uniform loads, and exact transient solutions of intensity factors to the problem with concentrated loads are both derived. Finally, numerical results are evaluated and discussed in detail.

並列關鍵字

piezoelectric ； interface crack ； stress 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.

Achenbach, J. D., (1970a) “Brittle and ductile extension of a finite crack by a horizontally polarized shear wave,” International Journal of Engineering Science, Vol. 8, pp. 947-966.

Achenbach, J. D., (1970b) “Extension of a crack by a shear wave,” Zeitschrift fur Angewandte Mathematik und Physik (ZAMP), Vol. 21, pp. 887-900.

Achenbach, J. D., (1973) “Wave Propagation in Elastic Solids,” Elsevier, New Work.