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通过构造新保角映射,利用Stroh公式研究了远场受反平面剪应力和面内电载荷共同作用下无限大压电复合材料中幂函数型曲线裂纹的断裂行为。给出了电不可渗透边界条件下裂纹尖端场强度因子和机械应变能释放率的解析解。该解析解在幂函数的幂次为零时,可退化为已有文献中无限大压电复合材料含直线裂纹的结果,证明了其合理性。由解析解可知,裂纹几何形状一定时,电场分布将不受机械载荷的影响。最后,通过数值算例讨论了幂函数的幂次、系数及其在x1轴上的投影长度对机械应变能释放率的影响。结果表明,当压电体仅受x2方向载荷作用时,对于给定幂次与开口的曲线裂纹,在x1轴上的投影长度存在一临界值使其最容易开裂;而对于给定投影长度与幂次的曲线裂纹,开口越大裂纹越容易扩展。
By means of constructing a new conformal mapping, the fracture behavior of exponential curve crack in an infinite piezoelectric composite under far field interaction with an in-plane shear stress and an in-plane electrical load was studied by Stroh formula. The analytic solution of the field strength factor at crack tip and the release rate of mechanical strain energy is given under the condition of impervious boundary. When the power of the power function is zero, the analytical solution can be degenerated into the result of linear crack in an infinite piezoelectric composite material in the prior literature, which proves its rationality. From the analytic solution we can see that the electric field distribution will not be affected by the mechanical load when the crack geometry is constant. Finally, numerical examples are given to discuss the power of the power function, the coefficient and its length on the x1 axis of the mechanical strain energy release rate. The results show that when the piezoelectric body is only subjected to the load in the x2 direction, there is a critical value for the projection length of the curve on the x1 axis for the given power and the opening of the curve to crack most easily. For a given projection length and Power of the curve crack, the larger the crack the more easy to expand.