摘要
理论研究了纳米尺度孔边均布径向多裂纹的Ⅲ型断裂性能.基于Gurtin-Murdoch表面弹性理论和保角映射技术,获得了孔和裂纹应力场的解析解,给出了裂纹尖端应力强度因子的闭合解.基于解答分析了应力强度因子的尺寸效应,讨论了裂纹数量、裂纹/孔径比和缺陷表面性能对应力强度因子的影响.结果表明:当孔和裂纹尺寸在纳米量级时,无量纲应力强度因子具有显著的尺寸效应;应力强度因子随裂纹数量的变化规律受裂纹/孔径比的影响;裂纹/孔径比对应力强度因子的影响受到缺陷表面性能的制约,同时表面性能对应力强度因子的影响也受限于裂纹/孔径比;表面效应对应力强度因子的影响与裂纹数量无关.
The mode-Ⅲfracture properties of the radial multi cracks on the edge of a nanoscale circular hole were theoretically investigated.Based on the Gurtin-Murdoch surface elasticity theory and the conformal mapping technique,the analytical solutions of the stress fields around the hole and cracks were given,and the closed form solution of the stress intensity factor at the crack tip was obtained.The size effect of the stress intensity factor was analyzed based on the solution.The effects of the crack number,the ratio of crack/hole radius and the surface defects on the stress intensity factor were discussed.The results indicate that,the dimensionless stress intensity factor has remarkable size-dependent effects when the sizes of the cracked hole are at the nanoscale.The variation of the stress intensity factor with the number of cracks is influenced by the crack/hole size ratio.The effects of the crack/hole size ratio on the stress intensity factors are restricted by the surface defects,and the effects of the surface properties on the stress intensity factor are also limited by the crack/hole size ratio.The surface effects on the stress intensity factors are independent of the number of cracks.
作者
冯国益
肖俊华
苏梦雨
FENG Guoyi;XIAO Junhua;SU Mengyu(Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures of Hebei Province,Yanshan University,Qinhuangdao,Hebei 066004,P.R.China)
出处
《应用数学和力学》
CSCD
北大核心
2020年第4期376-385,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11302186)。
