位错与纳米裂纹干涉的反平面问题  

Anti-plane Problem of Interaction between Dislocation and Nanoscale Crack

作　　者：肖万伸[1] 席俊平 XIAO Wanshen;XI Junping(College of Mechanical and Vehicle Engineering,Hunan University,Changsha410082,China)

机构地区：[1]湖南大学机械与运载工程学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2018年第12期80-84,共5页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(11572118)~~

摘　　要：针对位错与纳米裂纹干涉的反平面问题,提出了一种新方法,得出了精确解.首先利用复变函数中的保角变换方法,将直线裂纹问题化为孔板问题,再借助于柯西积分,获得了该问题的精确解答,然后分别推导出有、无表面效应作用时的应力场和位错力的解析表达式.数值结果表明:当裂纹尺寸缩减到纳米量级时,表面效应的影响使裂纹尖端附近的应力场和位错力减小,但随着裂纹长度的增大,表面效应的影响能力逐渐减弱,含表面效应的解答逐渐趋近于无表面效应的经典弹性理论解答.A new method was presented to exactly solve the anti-plane problem of the interaction between a dislocation and nanoscale crack.Firstly,the problem of straight line crack was turned into an orifice plate problem by using conformal mapping method of the complex function.Secondly,the exact solutions of this problem were obtained by Cauchy integral theorem.Then,the stress field and image force with and without surface effect were formulated.The numerical results show that the stress field near crack tip and image force are decreased due to the surface effect when crack size is reduced to the nanometer level.However the influence of the surface effect can be gradually weakened with the increase of the crack length,and the solutions considering the surface effect approach to the classical elastic theory solutions without the surface effect.

关 键 词：表面效应 纳米裂纹 螺型位错 应力场 位错力 

分 类 号：O343.1[理学—固体力学]