一维六方准晶压电材料中多缺陷的相互作用  

Interactions among Multi-defects in Piezoelectric Material of One-dimensional Hexagonal Quasicrystals

作　　者：刘官厅[1] 杨丽英[2] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022 [2]内蒙古农业大学理学院,呼和浩特010018

出　　处：《固体力学学报》2017年第2期180-188,共9页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(11262017和11462020);内蒙古自治区高等学校科学研究重点项目(NJZZ14081);内蒙古师范大学"十百千人才工程"研究项目(RCPY-2-2012-K-035);重大培育专项基金项目(2014ZD03)资助

摘　　要：基于准晶压电材料的基本方程,利用解析函数理论和复变方法,研究了一维六方准晶压电材料中多缺陷的相互作用问题,建立了多条平行位错以及它们与半无限裂纹相互作用的断裂力学模型,给出了一维六方准晶压电材料中n条平行位错相互作用的Peach-Koehler公式和n条平行位错的等效作用点,得到了n条平行位错与半无限裂纹相互作用下电弹性场的解析解,数值算例给出了位错位置对裂纹面上应力的影响和位错Burgers矢量的大小对裂纹面上应力的影响,为讨论裂纹尖端的位错发射、位错屏蔽和裂纹钝化奠定了理论基础.这些结果均为本文首次给出,丰富和发展了经典弹性理论中的相应结果.Like the classical materials, there are a variety of defects such as cracks and dislocations in quasicrystalline materials. Based on the fundamental equations of piezoelectricity of quasicrystalline materi- al, by means of the analytic function theory and the complex variable method, the interactions among muhi-de{ects in the piezoelectric material of one-dimensional hexagonal quasicrystals are studied. First, the models of fracture mechanics of the interactions among n parallel dislocations and a semi-infinite crack in the material are established, and the interaction forces and the equivalent action point of the n parallel dis- locations are obtained, which are the versions of the well-known Peach-Koehler formula in the piezoelectric material of one-dimensional hexagonal quasicrystals with n parallel dislocations. Second, the analytic solu- tions of electric-elastic fields of the interactions among n parallel dislocations and a semi-infinite crack in the piezoelectric material of one-dimensional hexagonal quasicrystals are derived. Finally, some numerical examples show that the stress and electric displacement of crack surface vary with the position of disloca- tion and the size of Burgers vector. These results offer the basis of theory to discuss the dislocation emis sion from a crack tip, screening for dislocation and crack shielding in the piezoelectric material of one-di- mensional hexagonal quasicrystals. As the development of the corresponding parts of classical elasticity, these are all firstly given in the present paper. When the electric fields or phason fields disappear, the re- sults of this paper degenerate into those of the classical one.

关 键 词：一维六方准晶压电材料 复变方法 n条平行位错 半无限裂纹 相互作用 

分 类 号：O34[理学—固体力学]