一维六方准晶中螺型位错偶极子与直线纳米裂纹的干涉效应  

The Interaction between a Screw Dislocation Dipole and a Linear Nano Crack in One-dimensional Hexagonal Quasicrystals

作　　者：魏刚[1] 肖万伸[2] 席俊平 Gang Wei;Wanshen Xiao;Junping Xi(College of Engineering,Hunan Agricultural University,Changsha,410128;College of Mechanical and Vehicle Engineering,Hunan University,Changsha,410082;Hubei Huntkey Magna Seating System Co.,Ltd.,Xiangyang,441057)

机构地区：[1]湖南农业大学工学院,长沙410128 [2]湖南大学机械与运载工程学院,长沙410082 [3]湖北航嘉麦格纳座椅系统有限公司,襄阳,441057

出　　处：《固体力学学报》2018年第6期606-613,共8页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金资助项目(11572118);湖南省杰出青年自然科学基金资助项目(2015JJ1006)资助

摘　　要：关于一维六方准晶中螺型位错偶极子与直线纳米裂纹干涉效应的问题,提出了一种可获得精确解的新方法.首先,将Gurtin-Murdoch表/界面理论推广运用到准晶材料中的纳米裂纹问题,建立了裂纹表面上含声子场、相位子场的应力边界模型;然后,利用复变函数中的共形映射方法,将直线裂纹问题化为单位圆孔问题;再借助于柯西积分方法获得了问题的封闭解,将该解退化到无表面效应时与经典解一致;最后,数值结果表明:当裂纹的尺寸减小到纳米量级时,表面效应将对声子场和相位子场中的应力场、像力及像力偶矩产生显著的影响,从而改变其力学性能,即裂纹尺寸越小,表面效应越强,声子场和相位子场中的应力场、像力及像力偶矩的数值变化越大;螺型位错偶极子偶臂的方向对像力的极值和自身平衡亦有较大影响.When the defect size in quasicrystal materials reaches the nanometer level,the ratio of the defect surface/interface area to its volume will become large,and the mechanical properties of the quasic- rystal materials will change significantly.Therefore,the influence of surface effect on the mechanical properties of quasicrystal materials should not be neglected.The equilibrium equation and constitutive equation of the problem are consistent with the classical theory of elasticity,but the non-classical boundary conditions need to be applied on the surface.Here,a new method is presented to obtain the precise results about the interaction between a screw dislocation dipole and a linear nano crack in one-dimensional hexagonal quasicrystals.Firstly,the Gurtin-Murdoch surface/interface theory is successfully applied to the nano crack problem of quasicrystal materials,and the boundary model with surface stresses of phonon field and phason field is established.Secondly,the linear crack problem is turned into a unit circle orifice problem by using the conformal mapping method of complex function.Then,the exact solutions of this problem are obtained via the Cauchy integral theorem.It is consistent with the classical solution when the solution is reduced to a non-surface effect.Finally,the numerical results show that the surface effect significant affects the numerical values of the stress field,image force and image torque of the phonon field and phason field,and further changes the mechanical properties of quasicrystal materials when the linear crack size in quasicrystal materials reduces to the nanometer level.Namely,the smaller the crack size is,the stronger the surface effect is,and the greater the numerical changes in the stress field,image force and image torque of the phonon field and phason field are.The couple arm orientation of the screw dislocation dipole has a great influence on the extreme value of the image force and its self-balance.The method of solving the anti-plane problem in this paper can be extended to

关 键 词：准晶 螺型位错偶极子 直线纳米裂纹 表面效应 像力 像力偶矩 

分 类 号：O753.3[理学—晶体学]