摘要
为更深入了解多场载荷作用下含裂纹压电材料断裂扩展情况,采用理论计算和数值模拟研究了在温度场、电场复合作用下含一定绝缘系数裂纹的无限大压电平板的二维断裂问题。横观各向同性压电平板在无穷远处受均匀热流q∞2以及电场D∞2的作用,在裂纹上产生的效应分别为αq∞2和βD∞2。基于广义二维热问题的复变函数方法及Hilbert问题解法,求得温度场和电弹性场以及场强度因子,并在给定的材料常数下针对绝缘系数对应力强度因子的影响、裂纹延长线上热流的分布以及裂纹长度对场强度因子的影响等进行数值模拟。研究结果表明,在裂纹尖端处,热流存在奇异性;无电位移作用、α=0时,KD取最大值,相当于扰流;α=1时,KD取最小值,相当于没有裂纹的情况;在电绝缘系数一定时,强度因子随热绝缘系数呈线性增长。
In order to better understand the fracture propagation of piezoelectric materials with cracks under multi-field loads,the two-dimensional fracture problem of an infinite piezoelectric plate with a certain insulation coefficient under the combined action of temperature field and electric field is studied by theoretical calculation and numerical simulation.The transverse isotropic piezoelectric plate is subjected to electric displacement D∞2 and uniform heat flowq∞2 at infinity,the effects on crack areβD∞2 andαq∞2,respectively.The effects on the crackαq∞2 are andβD∞2 respectively.The temperature field,electroelastic field and the intensity factors based on complex function method and Hilbert Problem Solutions are obtained.Then,numerical results are given to discuss the effects of insulation coefficient on stress intensity factors and the distribution of heat flow on the crack extension line,simultaneously including the effects of crack length on intensity factor.At the crack tip,the heat flux is singular.Suppose that whenα = 0 is applied without any potential shift,the maximum value of KDis obtained,which is equal to the disturbance flow.Whenα =1 is applied,the minimum value of KDis equal to that without cracks.When the electrical insulation coefficient is constant,the intensity factor increases linearly with the thermal insulation coefficient.
出处
《长江大学学报（自然科学版）》
CAS
2018年第9期63-67,共5页
Journal of Yangtze University(Natural Science Edition)
基金
铜陵学院校级科学研究项目(2016tlxy26)
