点群6一维六方准晶中幂函数型曲线裂纹的反平面问题  

Anti-plane Analysis of Power Function Curved Cracks in an Infinite Point Group 6 of One-dimensional Hexagonal Quasi-crystals

作　　者：施志昱[1] 刘官厅[1] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《内蒙古大学学报（自然科学版）》2012年第3期237-243,共7页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10761005);内蒙古自然科学基金资助项目(2009MS0102)

摘　　要：利用复变函数法,通过引入适当的保角变换,研究了裂纹面受剪切作用下无限大点群6一维六方准晶中幂函数型曲线裂纹的断裂行为,给出了曲线型裂纹在裂纹尖端处应力强度因子公式,得到了裂纹尖端处应力强度因子的解析解.该解析解在幂函数的幂次为零时,可还原为无限大点群6一维六方准晶中Griffith裂纹的结果,证明了其合理性.基于该解析解,得到了一些重要结论.By using the complex variable function method and introducing the appropriate conformal mapping,the fracture problem of a power function curved crack in an infinite point group 6 of one-dimensional hexagonal quasicrystals is studied under anti-plane shear stress loaded in the crack surface.The stress intensity factor formulas at the curved crack tip are given.The analytic solution of the stress intensity factors at the crack tip is obtained.When the power of the curve is zero,the present results can be degenerated to the solutions of a Griffith crack in an infinite point group 6 of one-dimensional hexagonal quasicrystals.Some useful conclusions are drawn on the basic of the analytic solution.

关 键 词：点群6一维六方准晶 幂函数型曲线裂纹 保角变换 应力强度因子 解析解 

分 类 号：O346.1[理学—固体力学]