一维六方压电准晶双材料椭圆孔边不对称裂纹断裂行为

Fracture Behavior of Asymmetrical Cracks Emanating from an Elliptical Hole in One-dimensional Hexagonal Piezoelectric Quasicrystal Bi-material

基于一维六方压电准晶理论,利用复变函数方法研究了一维六方压电准晶双材料椭圆孔边不对称裂纹的反平面问题。利用保角变换将椭圆孔孔边裂纹问题转化为直裂纹问题,结合Stroh公式求解得到电不可通和电可通两种条件下场强度因子和能量释放率的解析表达式。数值算例结果显示:一维六方压电准晶双材料界面Griffith裂纹比椭圆孔边裂纹更易促进裂纹扩展;考虑相位子场可使能量释放率变化更显著,表明压电准晶材料相比压电材料更脆。此研究可为压电准晶元件的设计和制备提供理论依据。

Based on the theory of one-dimensional hexagonal piezoelectric quasicrystals,using complex function method,the anti-plane problem of asymmetrical cracks emanating from an elliptical hole in one-dimensional hexagonal piezoelectric quasicrystal bi-material was studied.Using conformal transformation,the crack problem on the edge of elliptical hole was transformed into the straight crack problem,combined with the Stroh formula,the analytical expressions of field intensity factors and energy release rates under the electrically impermeable and permeable conditions were obtained.Numerical example results show that the Griffith crack at the one-dimensional hexagonal piezoelectric quasicrystal interface is more likely to promote crack propagation than the cracks emanating from an elliptical hole.The more significant change in energy release rate takes into account the phason field,indicating that piezoelectric quasicrystal materials are more brittle than piezoelectric materials.The research provides a theoretical basis for the design and preparation of piezoelectric quasicrystal elements.