一维六方压电准晶中具有双对称分支裂纹的断裂问题  

Fracture Problem of Type Ⅲ Deflection Crack in One-dimensional Hexagonal Piezoelectric Quasicrystals

作　　者：张也 刘官厅[1,2] ZHANG Ye;LIU Guanting(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematical Science,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（自然科学版）》2024年第5期517-523,共7页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目“压电准晶材料弹塑性断裂力学模型及广义复变方法研究”(12162027);内蒙古自治区自然科学基金重点资助项目“稀土准晶材料的弹性理论及多尺度断裂力学问题研究”(2024ZD21);内蒙古自治区高等学校科学技术研究重点资助项目“准晶压电材料纳米缺陷断裂力学问题研究”(NJZZ22574);无穷维哈密顿系统及其算法应用教育部重点实验室(内蒙古师范大学)开放课题资助项目“哈密顿方法在稀土、石墨烯、准晶等新材料力学问题中的应用”(2023KFZD02);内蒙古师范大学研究生科研创新基金资助项目“一维六方压电准晶中Ⅲ型裂纹的断裂问题”(S20231070Z)。

摘　　要：研究一维六方压电准晶体中具有两条对称分支裂纹的断裂问题,利用复变函数方法分析得出双对称分支裂纹的应力场、电位移场和能量释放率的解析形式,分析讨论双对称分支裂纹尖端场强度因子受分支裂纹偏折角和裂纹长度的影响。经过研究得出:当0 <λπ<π/2时,随着裂纹偏折角的增大,主支裂纹尖端的无量纲应力强度因子逐渐减小;随着主支裂纹长度的增加,主支裂纹尖端的无量纲应力强度因子增加;随着分支裂纹长度的增加,主支裂纹尖端的无量纲应力强度因子增加。The fracture problem of two symmetric branch cracks in one-dimensional hexagonal piezoelectric quasicrystals is studied and the analytical forms of the stress field,potential shift field,and energy release rate of the double symmetric branch crack are derived through analysis using the complex function method.And furthermore,the influence of branch crack deflection angle and crack length on the strength factor of the double symmetric branch crack tip field is analyzed and discussed.The results indicate that when the angle is within the range of 0 < λπ <π/2,as the crack deflection angle increases,the dimensionless stress intensity factor at the tip of the main support crack gradually decreases;as the length of the main branch crack increases,the dimensionless stress intensity factor at the tip of the main branch crack increases;as the length of the branch crack increases,the dimensionless stress intensity factor at the tip of the main branch crack increases.

关 键 词：一维六方压电准晶 双对称分支裂纹 应力强度因子 能量释放率 

分 类 号：O346.1[理学—固体力学]