双周期裂纹压电材料反平面剪切问题断裂力学分析

FRACTURE ANALYSIS OF DOUBLE PERIODICAL CRACKED PIEZOELECTRIC MATERIALS UNDER ANTIPLANE SHEAR

研究压电材料双周期裂纹反平面剪切与平面电场作用的问题.运用复交函数方法,获得了该问题严格的闭合解,并由此给出了裂纹尖端应力强度因子和电位移强度因子的精确公式.数值算例显示了裂纹分布特征对材料断裂行为的重要影响.叠间小裂纹能够对主裂纹的应力和电位移场起着屏蔽作用,相反行间小裂纹却起着放大作用,至于钻石形分布裂纹的影响规律则更为复杂.对于某些特殊情形给予了解答并导出一系列有意义的结果.

This work addresses piezoelectric materials with periodically distributed cracks under antiplane shear and inplane electrical field. By using the complex variable method, an analytical solution to this problem is obtained. The stress intensity factor and electrical displacement intensity factor are given. It is found that crack distribution plays an important role in fracture behavior of materials. The stack-interleaving small cracks shield the stress and electrical displacement fields at the main crack tip, whereas the row-interleaving small cracks intensify them. A diamond-shaped array of small cracks has a more complex influence on the field intensities at the main crack tip. The present solution is rather general. A series of novel and existing solutions for particular periodic cracks can be obtained as special cases. This work can be useful in developing a technique to estimate the strength of piezoelectric materials.