Exact Solutions for Piezoelectric Materials with an Elliptic Hole or a Crack under Uniform Internal Pressure  

作　　者：LIU Shuhong SHEN Yingming LIU Jinxi 

机构地区：[1]Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China [2]Department of Science and Technology, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

出　　处：《Chinese Journal of Mechanical Engineering》2012年第4期845-852,共8页中国机械工程学报（英文版）

基　　金：supported by Hebei Provincial Natural Science Foundation of China (Grant No. A2011210033);Foundation of Hebei Education Department of China (Grant No. ZH2011116);Hebei Provincial Research Program for Higher Education and Teaching Reformof China (Grant No. 103024)

摘　　要：The existing investigations on piezoelectric materials containing an elliptic hole or a crack mainly focus on remote uniform tensile loads.In order to have a better understanding for the fracture behavior of piezoelectric materials under different loading conditions,theoretical and numerical solutions are presented for an elliptic hole or a crack in transversely isotropic piezoelectric materials subjected to uniform internal pressure and remote electro-mechanical loads.On the basis of the complex variable approach,analytical solutions of the elastic and electric fields inside and outside the defect are derived by satisfying permeable electric boundary condition at the surface of the elliptical hole.As an example of PZT-4 ceramics,numerical results of electro-elastic fields inside and outside the crack under various electric boundary conditions and electro-mechanical loads are given,and graphs of the electro-elastic fields in the vicinity of the crack tip are presented.The non-singular term is compared to the asymptotic one in the figures.It is shown that the dielectric constant of the air in the crack has no effect on the electric displacement component perpendicular to the crack,and the stresses in the piezoelectric material depend on the material properties and the mechanical loads on the crack surface and at infinity,but not on the electric loads at infinity.The figures obtained are strikingly similar to the available results.Unlike the existing work,the existence of electric fields inside an elliptic hole or a crack is considered,and the piezoelectric solid is subjected to complicated electro-mechanical loads.The existing investigations on piezoelectric materials containing an elliptic hole or a crack mainly focus on remote uniform tensile loads.In order to have a better understanding for the fracture behavior of piezoelectric materials under different loading conditions,theoretical and numerical solutions are presented for an elliptic hole or a crack in transversely isotropic piezoelectric materials subjected to uniform internal pressure and remote electro-mechanical loads.On the basis of the complex variable approach,analytical solutions of the elastic and electric fields inside and outside the defect are derived by satisfying permeable electric boundary condition at the surface of the elliptical hole.As an example of PZT-4 ceramics,numerical results of electro-elastic fields inside and outside the crack under various electric boundary conditions and electro-mechanical loads are given,and graphs of the electro-elastic fields in the vicinity of the crack tip are presented.The non-singular term is compared to the asymptotic one in the figures.It is shown that the dielectric constant of the air in the crack has no effect on the electric displacement component perpendicular to the crack,and the stresses in the piezoelectric material depend on the material properties and the mechanical loads on the crack surface and at infinity,but not on the electric loads at infinity.The figures obtained are strikingly similar to the available results.Unlike the existing work,the existence of electric fields inside an elliptic hole or a crack is considered,and the piezoelectric solid is subjected to complicated electro-mechanical loads.

关 键 词：piezoelectric material elliptic hole CRACK boundary condition electro-elastic fields 

分 类 号：O346.1[理学—固体力学] TM22[理学—力学]