摘要
研究了一维六方准晶中带两条纳米裂纹的圆形纳米孔的解析解,基于复变方法和表面弹性理论得到了考虑表面效应时圆形纳米孔附近裂纹的声子场应力强度因子和相位子场应力强度因子的解析解.在数值分析中分析了考虑表面效应时孔口尺寸、声子场机械载荷和相位子场机械载荷对无量纲声子场应力强度因子和无量纲相位子场应力强度因子的影响,分析了孔口半径和裂纹长度对无量纲应力强度因子的影响.结论表明,在有纳米级缺陷的一维六方准晶中,由于受到表面效应的影响,无量纲场强度因子表现出明显的尺寸依赖效应.当纳米孔扩大到一定程度时,各结果趋于经典弹性理论中的结果.无量纲场强度因子随着孔口尺寸的增加而减小,随着裂纹长度的增大而增大.
In this paper,the analytical solution of two nano-cracks emanating from circular nano-hole in one-dimensional hexagonal quasicrystalsis is studied.Based on the complex method and the surface elasticity theory,the exact solutions of stress intensity factor of phonon field and stress intensity factor of phason field of the cracks emanating from circular nano-hole considering surface effect are obtained.In the numerical analysis,the influence of the size of the cracked hole,mechanical loads of the phonon field and the phason field on the stress intensity factor of the phason field and the phason field are analyzed.The influence of the size of the cracked hole and crack length on the dimensionless stress intensity factor are also analyzed.The results show that in one-dimensional hexagonal quasicrystals with nanoscale defects,the field intensity factor shows obvious size dependent effect due to the influence of surface effect.When the nano-hole is expanded to a certain extent,the results tend to the results of the classical elastic theory.The dimensionless field intensity factor decreases with the increase of the size of the cracked hole and increases with the increase of crack length.
作者
武志林
刘官厅
杨东升
WU Zhi-lin;LIU Guan-ting;YANG Dong-sheng(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China)
出处
《数学的实践与认识》
2021年第16期164-172,共9页
Mathematics in Practice and Theory
基金
内蒙古自然科学基金(2018MS01005)
内蒙古师范大学研究生科研创新基金项目支持(CXJJS19098)。
关键词
一维六方准晶
应力强度因子
表面效应
纳米尺度
one-dimensional hexagonal quasicrystals
stress intensity factor
surface effect
nanoscale
