压电复合材料中圆孔边Ⅲ型非对称裂纹的场强度因子

Field intensity factors of a mode-Ⅲ non-symmetrical cracks originating from circular hole in piezoelectric composite material

研究了压电复合材料中圆孔边4个非对称裂纹在远处受面内电载荷和面外力载荷共同作用下的断裂行为。利用复变函数方法和新映射函数将问题转化为Cauchy积分方程组。通过求解Cauchy积分方程组,得到了电非渗透型和电渗透型两种边界条件下裂纹尖端电弹性场和场强度因子的解析解。所得结果不仅可退化为已有解,而且可模拟出若干新的缺陷构型,如压电复合材料中圆孔边三裂纹、半无限压电复合材料中半圆孔边单裂纹及半无限压电体中边界裂纹。将所得结果与有限元结果进行比较,吻合很好,证实了文中方法的正确性和有效性。数值算例分析了缺陷的几何参数对场强度因子的影响规律。

The fracture behavior of four non-symmetric radial cracks originating from a circular hole in piezoelectric composite materials subjected to remotely uniform inplane electric loading and antiplane mechanical loading was studied in this paper. The problem was transformed using the complex variable method and a new mapping function into Cauchy integral equations. By solving the Cauchy integral equations, the analytical solutions of electric and elastic fields and field intensity factors near the crack tip were obtained under the electrically impermeable and permeable assumptions. Several known results were the special cases of the present results and new models used for simulating more practical defects in piezoelectric composite materials were derived as well, such as three radial cracks originating from a circular hole, semi-circular hole with an edge crack originating from a semi-infinite plane and a semi-infinite plane with an edge crack. A well agreement of the analytical solutions with the finite element results shows the accuracy and efficiency of the present method. Numerical examples are provided graphically to show the effects of the geometrical parameters on the field intensity factors.