一维六方压电准晶中圆孔边周期裂纹分析  

Analysis of periodic cracks emanating from a circular hole in one-dimensional hexagonal piezoelectric quasicrystals

作　　者：杨娟[1,2] 李星 周跃亭 YANG Juan;LI Xing;ZHOU Yueting(School of Preparatory Education for Nationalities,Ningxia University,Yinchuan 750002,China;School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China;School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]宁夏大学民族预科教育学院,银川750002 [2]宁夏大学数学统计学院,银川750021 [3]同济大学航空航天与力学学院,上海200092

出　　处：《振动与冲击》2019年第18期62-71,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(11832014;11762017;11762016);国家留学基金委员会(CSC);中央高校基本科研业务费项目(22120180223)

摘　　要：利用复变函数和保角变换的方法,结合柯西积分,针对一维六方压电准晶中圆孔边周期裂纹问题进行了分析研究,导出了电不可导通边界条件和电可导通边界条件下Ⅲ型裂纹问题的场强度因子和能量释放率。在缺失相位子场或电场时,所得结果和已有结果做对比分析,以此验证方法的有效性。通过数值算例讨论了裂纹数、几何参数、耦合参数、声子场应力、相位子场应力和电载荷对材料断裂特性的影响规律,以便在实践中得到更好的应用。本研究为压电准晶元件的优化设计和可靠性分析提供理论基础。By using the complex variable method and the conformal mapping function,combined with the Cauchy integral,the anti-plane problem about a circular hole with periodic cracks in one-dimensional(1D)hexagonal piezoelectric quasicrystals(QCs)was investigated.The field intensity factors and the energy release rates with electrically impermeable and permeable conditions were obtained,respectively.In the absence of phase field or electric field,the obtained results were analysed contrastively with existing literature results in order to verify the validity of the method.A numerical analysis was then conducted to discuss the influences of the geometric parameters,coupling coefficient,phonon load,phason load and applied electric loads on the fracture characteristics of material.The research provides a theoretical basis for the optimization design and reliability analysis of piezoelectric quasicrystal elements.

关 键 词：一维六方压电准晶 周期裂纹 圆孔 保角变换 场强度因子 能量释放率 

分 类 号：O346.1[理学—固体力学]