一维六方准晶压电材料中螺型位错与椭圆孔口的相互作用  

The interaction of elliptical hole and screw dislocation of piezoelectricity of one-dimensional hexagonal quasicrystals

作　　者：周彦斌[1] 刘官厅[1] 

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《宝鸡文理学院学报（自然科学版）》2015年第2期17-24,共8页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然基金项目(11262017;11262012);教育部科技研究重点项目(No.212029);内蒙古师范大学"十百千人才工程"研究项目(No.RCPY-2-2012-K-035);研究生科研创新基金项目(No.CXJJS13042)

摘　　要：目的根据点群6mm一维六方准晶的位错理论,通过一维六方准晶压电材料反平面问题的控制方程,研究含螺型位错与椭圆孔口相互作用时的应力场和电场的相互关系。方法根据复变函数方法,引入适当的保角变换,将椭圆孔口问题映射到单位圆来讨论。结果 1)得到了一维六方准晶压电材料含螺型位错时电弹性场的解析表达式;2)得到了椭圆孔口与螺型位错相互作用时应力强度因子解析表达式。结论由螺型位错与椭圆孔口的相互作用结果,这为研究一维六方准晶压电材料位错问题和断裂问题提供了重要依据。Objective--To investigate the correlation of stress fields and electric field under the interaction between elliptical hole and screw dislocation in the material on the basis of the dislocation theory of point group 6mm of one-dimensional hexagonal quasicrystals and the anti-plane problem of piezoelectricity of one-dimensional hexagonal quasicrystals. Methods--According to the complex varia- ble method, introducing appropriate conformal mapping was introduced to map the elliptical hole to the unit circle. Results-1） The analytic expression of the stress fields and electric field were obtained when there existed screw dislocation in the material; 2） The analytic expression of stress intensity factors was gained under the interaction between elliptical hole and screw dislocation. Conclusion--The results of interaction between elliptical hole and screw dislocation provides an important basis for studying the dislocation and the fracture problem of the piezoelectricity of one-dimensional hexagonal quasicrystals.

关 键 词：点群6mm 一维六方准晶压电材料 椭圆孔口 螺型位错 应力强度因子 

分 类 号：O346.1[理学—固体力学]