彈壓電複合材料介層擴展裂紋之應力波傳與動力破壞的暫態解析

Theoretical Transient Analyses of Stress Wave Propagation and Dynamic Fracture for Interfacial Crack in Elastic-Piezoelectric Bi-materials

陳熙洪(Xi-Hong Chen)

指導教授 ： 馬劍清

國立臺灣大學/工學院/機械工程學研究所/博士(2006年)

https://doi.org/10.6342/NTU.2006.00689

摘要

近年來，壓電材料由於其內部機電耦合的性質而被逐漸重視，尤以複合壓電材料在高科技的電子電機與精密機械工業上有十分廣泛的應用。但由於壓電材料大多為脆性物質所構成且複合壓電材料會衍生介面裂紋，因此容易遭受破壞而無法修補，所以壓電元件在設計與應用之初，複合壓電材料的力學破壞考量就非常重要。本文使用積分轉換法與Wiener-Hopf技巧推導內含擴展裂紋之彈壓電複合材料於一次拉普拉斯轉換域中受空間指數應力之基本解，其中詳細探討在不同材料的搭配下是否在介面處會產生MT表面波，利用此基本解來解析包含特徵長度的彈壓電複合材料動力破壞問題，接著使用Cagniard-de Hoop方法來做拉普拉斯逆轉換得到時域解，此展示了應用拉氏域疊加方法的優越性，最後針對應力強度因子與電位移強度因子等解析解，作詳細的數值計算與討論。此外，在多數的工程運用上，靜力破壞理論已不敷現實狀況，因此本文的研究著重於受動力載荷時的動力破壞解析，無論在學術研究上或工程應用方面將能提供更有利的參考。

關鍵字

擴展裂紋 ； 壓電材料 ； 表面波 ； 疊加法 ； 動力強度因子

並列摘要

In transversely isotropic elastic solids, there is no surface wave for anti-plane deformation. However, for certain orientations of piezoelectric materials, a surface wave propagating along the free surface (interface) will occur and is called the Bleustein-Gulyaev (Maerfeld-Tournois) surface wave. The existence of the surface wave strongly influences the crack propagation event. Hence the existence condition and velocity of the interfacial surface wave between two piezoelectric materials are analyzed. The nature of anti-plane dynamic fracture in piezoelectric materials is fundamentally different from that in purely elastic solids. Piezoelectric surface wave phenomena are clearly seen to be critical to the behavior of the moving crack. In this study, the problem has characteristic lengths and a direct attempt towards solving this problem by transform and Wiener-Hopf techniques is not applicable. A new fundamental solution for propagating interfacial crack between elastic-piezoelectric bi-materials is proposed and the transient response of the propagating crack is determined by superposition of the fundamental solution in the Laplace transform domain. The fundamental solution to be used is the responses of applying exponentially distributed traction in the Laplace transform domain on the propagating crack surface. Four situations for different combination of shear wave velocity and the existence of MT surface wave are discussed to completely analyze this problem. Exact analytical transient solutions are obtained by using the Cagniard-de Hoop method of Laplace inversion and are expressed in explicit forms. Finally, numerical results for the transient solutions are evaluated and discussed in detail.

並列關鍵字

Crack propagation ； Piezoelectric material ； Surface wave ； Superposition ； Dynamic intensity factor

參考文獻

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

Achenbach, J. D. 1976 Wave Propagation in Elastic Solids. New York: Elsevier.

Bleustein, J. L. 1968 A new surface wave in piezoelectric materials. Applied Physics Letters 13, 412-413.

Cagnard, L. 1939 Reflexion et refraction des ondes seismiques progressives. New York: McGraw-Hill.

Chen, Z. T. and Yu, S. W. 1997 Anti-plane Yoffe crack problem in piezoelectric materials. International Journal of Fracture 84, L41-L45.