电半渗透边界条件下一维六方压电准晶纳米弯折裂纹反平面问题研究  

On Anti-Plane Problem of Nano-Bending Crack in One-Dimensional Hexagonal Piezoelectric Quasicrystals With the Electrically Semi-Permeable Boundary Condition

作　　者：卢绍楠 赵雪芬[2] 马园园 LU Shaonan;ZHAO Xuefen;MA Yuanyuan(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,Ningxia,China;Xinhua College,Ningxia University,Yinchuan 750021,Ningxia,China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021 [2]宁夏大学新华学院,宁夏银川750021

出　　处：《力学季刊》2023年第2期444-455,共12页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11762016,11762017);宁夏自然科学基金(2022AAC03013);宁夏大学新华学院科学研究基金重点项目(23XHKY01)。

摘　　要：利用复变函数方法及G-M(Gurtin-Murdoch)表/界面理论,研究了电半渗透条件下一维六方压电准晶纳米弯折裂纹反平面问题.引入弯折裂纹的保角映射,得到电半渗透条件下场强度因子以及能量释放率的解析解.数值分析了纳米弯折裂纹的介电常数、弯折角度、外载荷对无量纲场强度因子以及能量释放率的影响.结果表明:介电常数对相位子场无量纲应力强度因子以及电位移无量纲强度因子影响较为显著;场强度因子均随着裂纹与坐标轴夹角的增大而减小;随着外载荷的增加,场强度因子以及能量释放率有显著的变化且变化趋势具有差异性.本文可以为准晶及其复合材料的断裂行为的进一步研究奠定基础,也可以为纳米准晶材料的制备及应用提供一定的理论依据.Using the complex function method and Gurtin-Murdoch surface/interface theory,the anti-plane problem of nanobending cracks in one-dimensional hexagonal piezoelectric quasicrystals under electric semi-permeable conditions is studied.By constructing the conformal map of the bending crack,the analytical solutions of the field strength factor and the energy release rate under electric semi-permeability condition are obtained.The influences of the dielectric constant,bending angle,and external load on the dimensionless field strength factor and the energy release rate of the nano-bending crack are numerically analyzed.The results indicate that the dielectric constant has a significant influence on the dimensionless strength factors of the stress and the electric displacement.The field strength factors decrease with the increase of the angle between the crack and the coordinate axis.As the external load increases,the field intensity factor and energy release rate change significantly,with different change trend.This paper can provide basis for further study of the fracture mechanical behavior of quasicystalline materials and their composites,and provide theoretical reference for the preparation and application of nano-quasicystalline materials.

关 键 词：一维六方压电准晶 纳米弯折裂纹 复变函数方法 场强度因子 能量释放率 

分 类 号：O0343.8[理学]