压电材料中星型裂纹的应力分析

The stress analysis of star cracks in piezoelectric material

基于压电材料力学,利用一个适当的保角变换公式,结合Stroh公式研究了远场受反平面剪应力和面内电载荷同时作用下无限大压电材料中星型裂纹的断裂行为。确定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表达式。该结果在裂纹条数为一或二时,可退化为无限大压电复合材料含直线裂纹结果,验证了其合理性。由解析表达式可以看出,裂纹几何形状一定时,电场分布将不受机械载荷的影响,裂纹的长度越长时,越容易扩展。

Based on mechanics of piezoelectric material, proposing a conformal mapping and using the Stroh formula, the problem of star cracks in an infinite piezoelectric composite is studied under anti-plane shear stress and in-plane electric load at infinity. The expression of the field intensity factors and the mechanical strain energy release rate was obtained with the assumption that the surface of the crack was electrically impermeable. When the number of crack is one or two, the present results can be reduced to the solutions of a Griffith crack in an infinite piezoelectric composite. Based on the analytical expression, it was found that the distribution of electric field was independent on the mechanics load under a fix shape of the cracks. The longer the length of the cracks, the easier crack propagates.