一维六方压电准晶体中Ⅲ型偏折裂纹的断裂问题  

Fracture Problem of TypeⅢDeflection Crack in One‐dimensional Hexagonal Piezoelectric Quasicrystals

作　　者：张也 刘官厅[1,2] 周彦斌 ZHANG Ye;LIU Guanting;ZHOU Yanbin(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematics,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2023年第5期521-529,535,共10页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12162027);内蒙古自治区高等学校科学技术研究重点资助项目(NJZZ22574);内蒙古师范大学基本科研业务费专项基金资助项目(2022JBXC013);内蒙古师范大学研究生科研创新基金资助项目(CXJJS22095)。

摘　　要：利用复变函数方法分析得出偏折裂纹的应力场、能量释放率和J积分的解析形式,研究一维六方压电准晶体中Ⅲ型偏折裂纹的断裂问题,分析讨论偏折裂纹尖端场强度因子受分支裂纹偏折角和裂纹相对尺寸的影响。经过研究发现,随着裂纹偏折角的增加,主支和分支裂纹尖端的无量纲应力强度因子减小。随着裂纹相对尺寸的增加,主支和分支裂纹尖端的无量纲应力强度因子增加。The fracture problem of typeⅢdeflection crack in one-dimensional hexagonal piezoelectric quasicrystals is studied in the paper.The analytical forms of stress field,energy release rate and J-integral of the deflection crack are obtained by complex variable function method.The effects of the deflection angle and the relative size of the crack on the field intensity factor of the tip of the deflection crack are analyzed.The results show that the dimensionless stress intensity factor decreases at the crack tip of main branch and branch with the increase of crack deflection angle;the dimensionless stress intensity factor at the crack tip increases with the increase of the crack relative size.

关 键 词：一维六方准晶 偏折裂纹 应力强度因子 能量释放率 J积分 

分 类 号：O346.1[理学—固体力学]