压电效应下一维六方准晶双材料孔边裂纹的反平面问题研究

On the Anti-Plane Problem of a Crack Emanating from a Hole in One-Dimensional Hexagonal Quasicrystal Bi-Material with Piezoelectric Effect

利用复变函数方法和保角变换技术研究了压电效应下一维六方准晶双材料中圆孔边单裂纹的反平面问题.考虑电不可渗透型边界条件,运用保角变换和Stroh公式得到了弹性体受远场剪切力和面内电载荷作用下裂纹尖端应力强度因子和能量释放率的解析解.数值算例分析了几何参数、远场受力、电位移载荷对能量释放率的影响.结果表明:裂纹长度、耦合系数和远场剪切力的减小可以抑制裂纹的扩展.不考虑电场时,声子场应力对能量释放率的影响较小.本文的研究结果可作为研究一维六方压电准晶双材料孔边裂纹问题的理论基础,同时为压电准晶及其复合材料的设计、制备、优化和性能评估提供理论依据.

The anti-plane problem of a single crack emanating from a circular hole in one-dimensional(1D)hexagonal quasicrystal(QC)bi-material with piezoelectric effect is investigated using the complex function method and the conformal mapping technique.Considering the electrically impermeable boundary conditions,the analytic solutions of stress intensity factors(SIFs)and energy release rate(ERR)at the crack tip of the elastic body under the far-field shear force and the in-plane electrical load were obtained using the conformal transformation and Stroh formula.Numerical examples were given to analyze the influences of geometric parameters,far-field stress and electric displacement load on the ERR.The results show that,the decrease of crack length,coupling coefficient and far-field shear force will inhibit the crack propagation.In the absence of the electric field,the phonon field stress has little effect on the ERR.The results of this paper can be used as a theoretical basis for the study of a crack emanating from a hole in 1D hexagonal piezoelectric QCs,and provide theoretical reference for the design,preparation,optimization and performance evaluation of piezoelectric QCs and piezoelectric QC components.