无限压电体内共线周期裂纹间的相互作用  

Interaction Between Collinear Periodic Cracks in an Infinite Piezoelectric Body

作　　者：崔之健[1] 胡洪平[2] 杨峰[2] 

机构地区：[1]西安石油大学石油工程学院,西安710065 [2]华中科技大学力学系,武汉430074

出　　处：《应用数学和力学》2008年第7期783-789,共7页Applied Mathematics and Mechanics

基　　金：中国博士后科学基金资助项目(20070410944)

摘　　要：研究了无限压电体内共线周期裂纹间的相互作用的问题,并且考虑了裂纹尖端的饱和条带作用.应用Stroh理论和保角变换方法,得到了共线裂纹的一般周期解.对应力强度因子和饱和条带尺寸进行了理论推导,详细分析了它们与周期长和半裂纹长的比值h/l之间的关系.数值结果表明:1)当h/l大于4.0时,裂纹之间的相互作用对应力强度因子影响较小,无限压电体内周期裂纹和单裂纹的值几乎相等.这表明当h大于4.0l时,建立裂纹扩展判据时可以近似忽略裂纹之间的相互作用;2)周期裂纹的饱和条带尺寸趋近于单裂纹值的速度,取决于无穷远处的电载荷,通常无穷远处的电载荷越大,趋近速度越慢.The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips was taken into account. By means of Stroh formalism and the conformal mapping technique, the general periodic solutions for collinear cracks were obtained. The stress intensity factors and the size of saturation strips were derived analytically and their dependencies on the ratio of the periodicity to haft-length of the crack h/l were analyzed in detail. Numerical results show that： 1） when h/l is higher than 4.0, the stress intensity factors become almost identical to the ones for a single crack in an infinite piezoelectric body. It indicates that the infraction between cracks can be ignored in establishing the criterion for crack initiation in the case that h is larger than 4.0 l; 2） the speed of saturation strip size of periodic cracks approaching one of a single crack depends on the electric load applied at infinity. In general, a larger electric load applied at infinity is with a slower approaching speed.

关 键 词：共线周期裂纹 应力强度因子 饱和条带 周期长和半裂纹长比值 趋近速度 

分 类 号：O346.1[理学—固体力学]