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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 asymmetric cracks near the circular hole in the piezoelectric composite under the combined action of the internal and external loads is studied. The problem is transformed into Cauchy integral equations by using the complex function method and the new mapping function. By solving the Cauchy integral equations, the analytic solutions of the electric field and the field strength factor at crack tip under two kinds of boundary conditions of electro-infiltration and electro-osmosis are obtained. The results obtained not only degenerate into the existing solutions, but also simulate a number of new defect configurations, such as the three cracks in the circular hole edge of the piezoelectric composite material, the semi-circular hole edge cracks in the semi-infinite piezoelectric composite material and the semi-infinite piezoelectric Body boundary crack. The results obtained are compared with the finite element results, and the results are in good agreement, which proves the correctness and effectiveness of the proposed method. Numerical examples analyze the influence of geometrical parameters of defects on the field strength factor.