压电-正交基体复合半圆柱的界面端部开裂问题研究

Research on Interface-end Cracking in a Compound Semi-cylinder of Piezoelectric and Orthotropic Substrate

建立了半圆柱形压电-正交基体复合材料界面端部开裂问题的力学模型,其中压电层为锆钛酸铅铁电陶瓷,基体为正交异性聚乙烯复合材料。综合利用位错模拟法、格林函数法和奇异积分方程法,对裂纹问题进行了理论分析。通过对应力强度因子进行数值求解和讨论,揭示了几何、物理参数对断裂行为的影响规律。从界面端部止裂的角度出发,找到了压电复合半圆柱的2种优化设计形式:一种是将"较软的内部基体"和"较硬的外部压电层"相结合;另一种是采用正交各向异性介电材料作为基体。另外,数值计算还表明:与剪切模量变化对应力强度因子的影响相比,压电系数和介电系数变化的影响至少要小2个数量级,因此后面二者对结构防断裂优化设计没有显著的实际意义。

Abstract：A mechanical model is established for the problem of interface-end cracking in a semi-cylindrical composite consisting of a piezoelectric layer of PZT ceramics and a central orthotropic polythene substrate. The methods of generalized dislocation simulation, Green＇s function and singular integral equation are combined together to analyze the crack problem theoretically. The Stress Intensity Factor （SIF） is obtained numerically, and the effects of the geometrical and physical parameters on the fracture behavior are revealed. From the viewpoint of prevention against interface-end cracking, two kinds of optimized designs are put forward for the compound piezoelectric semi-cylinder： 1 ） a softer inner substrate and a stiffer out-er piezoelectric layer are combined; 2） the orthotropic dielectric material rather than isotropic one should be adopted as substrate. In addition, numerical computation also indicates that the effect of piezoelectricor dielectric coefficient on the SIF is at least two orders of magnitude smaller than that of the shear modulus. Therefore, changing the piezoelectric or dielectric coefficient contributes nothing to the optimization design of fracture prevention.