电致伸缩材料三维断裂问题研究

The poor toughness of electrostrictive materials is a difficult problem to application of smart materials in the world. One of the reasons is that defects existing in these materials will lead to high local fields, resulting from cracking and crack growth in electrostrictive materials under high electric loading. Usually, cracks can be filled with air. Since the dielectric of air is much less than that of electrostrictive material, the electric field strength inside cracks can be enhanced about 1000 times higher in magnitude than the applied electric field. Under such a high local electric field, air discharge may occur inside the crack and result in fracture of these materials. By theoretical analysis, numerical simulation and experimental observations, the three-dimensional fracture problem of electrostrictive materials is studied. Firstly, based on the assumption that the elastic strain of electrostrictive materials is a higher-order small quantity, we studies the three-dimensional problem of an infinite electrostrictive solid with a spheroidal inclusion or a penny-shaped crack. With the displacement function method, we first derived explicit experssion for displacement potential function and obtained stress field near the crack and open displacement of crack surface. Then, the general solution for the stress intensity factor was derived. Secondly, We derived Green fuctions and boundary integral functions for electrostrictive materials. Using the boundary element method, we solved the problems of the three-dimensional in a finite or infinite area. In experimental research, the loading platform of mechanical-electric-magnetic-thermal is used to observe the crack growth under different fracture factors. Based on the researches above, it is our purpose to find out the key factros of the fracture problem in electrostrictive materials and provide scientific basis for electrostrictive materials toughening design and fracture analysis.

电致伸缩材料较差的韧性是当今国际智能材料应用的难题，其原因之一在于当内部含有裂纹的电致伸缩材料在受到外加强电场作用时，由于裂纹内部空气的介电常数远小于电致伸缩材料的，因此裂纹内部的电场被放大到外加电场的近1000倍，在裂纹的尖端处发生了电击穿现象，由此导致了裂纹的扩展，最终使得材料发生断裂。本项目采用理论分析、数值计算与实验观测相结合的方法，研究了三维电致伸缩材料的断裂问题。首先，基于势函数理论，建立了三维电致伸缩材料的位移势函数方程，求解出了椭球夹杂、钱币型裂纹等缺陷内外部的位移场、应力场以及应力强度因子；其次，推导出三维电致伸缩材料的基本解和边界积分方程，利用边界元方法，对三维任意形状有限/无线域内的裂纹问题进行数值模拟；最后，利用力-电-磁-热多场耦合加载平台，观测裂纹在不同因素影响下的扩展情况。通过上述研究，探索电致伸缩材料中电致失效的机理，为电致伸缩材料的增韧设计提供科学依据。