压电薄板板边导电裂纹尖端的力电场分析

采用有限元方法，分析了压电薄板板边不同长度导电裂纹尖端的力电场分布规律，发现导电裂纹尖端的应力场和电场强度存在明显的集中和奇异现象，集中和奇异的程度与裂纹长度有关。而且，在裂纹延长线上分别存在两点，这里的应力和电场对裂纹长度不太敏感，总等于无裂纹时薄板的均匀应力和均匀电场强度；同时，还研究了导电裂纹尖端的应力强度因子和电场强度因子对裂纹长度的依赖关系，发现在线性本构的前提下，导电裂纹尖端的应力强度因子与电场强度因子之间具有近似的线性关系。

Analysis of tip fields of conducting cracks in the edge of a thin piezoelectric plate

Electro-mechanical coupling fields ahead of tips of conducting cracks with different length lying near the edge of a thin piezoelectric plate are analyzed using the finite element method in this paper. The numerical results indicate that concentration and singularity of stress and electric fields evidently occur near the crack tip and there are two fixing regions ahead of the conducting cracks in which the mechanical or electric field is not affected by the crack-length. At the same time, the dependence of the stress intensity factor and the electric field intensity factor on the crack length is also studied, and it is verified that the relation between the two factors is approximately linear in the sense of the linear constitutive model.