压电复合材料中幂函数型曲线裂纹的反平面问题

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。 

Anti-plane analysis of power function curved cracks in piezoelectric composites

By proposing a new conformal mapping and using the Stroh formula, the fracture problem of a power function curved crack in an infinite piezoelectric composite is studied under anti-plane shear stress and in-plane electric load at infinity. The analytical solutions of the field intensity factors and the mechanical strain energy release rate are presented with the assumption that the surface of the crack is electrically impermeable. When the power of the curve is zero, the present results can be reduced to the solutions of a Griffith crack in an infinite piezoelectric composite. Based on the analytical solutions, it is found that the distribution of electric field is independent on the mechanics load under a fixed shape of the curve. Numerical examples are finally conducted to analyze the influences of the projected length along the x1-axis, power and coefficient of curved cracks on the mechanical strain energy release rate. The results show that if the piezoelectric composite is subjected to the only load along the direction of x2-axis, there exists a critical projected length along the x1-axis which can promote the crack growth easily for given power and coefficient of curved cracks. Moreover, for given values of projected length and power of curved cracks, the smaller coefficient of curved crack is, the easier crack propagates.