一维六方压电准晶中圆孔边周期裂纹分析

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摘要本文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。

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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

Abstract：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.

Key words： 1D hexagonal piezoelectric quasicrystals Periodic Crack Circular hole Conformal mapping The field intensity factors The energy release rate

收稿日期: 2018-06-08 出版日期: 2019-09-15

引用本文:

杨娟1，2, 李星2，周跃亭3. 一维六方压电准晶中圆孔边周期裂纹分析[J]. 振动与冲击, 2019, 38(18): 62-71.
Juan Yang,Xing Li Yue Ting Zhou . Analysis of periodic cracks emanating from a circular hole in one-dimensional hexagonal piezoelectric quasicrystals. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(18): 62-71.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2019/V38/I18/62

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