低频P波荷载下压电介质中共面裂纹的耦合断裂行为  

Coupled fracture behavior of two coplanar cracks in piezoelectric material under low-frequency P-wave

作　　者：张培伟[1,2] 

机构地区：[1]东南大学土木工程学院,南京210096 [2]东南大学江苏省工程力学分析重点实验室,南京210096

出　　处：《东南大学学报（自然科学版）》2013年第5期1024-1033,共10页Journal of Southeast University：Natural Science Edition

基　　金：中国博士后科学基金资助项目(2012M511646);江苏省博士后科学基金资助项目(1102043C)

摘　　要：对压电介质中共面裂纹的动态断裂问题进行建模,并求解该边界值问题.将裂纹形状等效为等面积的矩形以便于理论分析和增加安全评价的可靠性,采用一般Almansi理论得到了广义应力场、广义应力强度因子和能量释放率的解析表达式.考虑部分电导通裂纹边界条件,将边界值问题转换为3组对偶积分方程,并以裂纹上下表面的位移阶跃函数作为未知函数.通过将位移阶跃函数展开成Jacobi多项式,得到裂纹尖端的广义奇异应力、广义强度因子和能量释放率的解析解.最后,通过数值算例研究了P波载荷频率和矩形裂纹几何尺寸对裂纹扩展行为的影响规律.研究结果显示了该方法的正确性及在动载作用下裂纹相互作用引起裂纹扩展行为的复杂性.The dynamic fracture problem of coplanar double rectangular cracks is constructed into a kind of boundary value problem, which is solved to compose the analytical expression of generalized stress fields, generalized intensity factors and energy release rate with the help of generalized Almansi＇ theorem. Rectangular crack is more suitable for analyzing and over-security for reliability. The boundary value problem is first transformed into three pairs of dual integral equations with the jump functions of the displacements across the crack surface as unknown functions. The unknown functions can be expanded directly into series of Jacobi polynomials which can be actually found close-form solution. Then, the analytical expressions for generalized singular stress at crack tip, generalized intensity factors and energy release rate are strictly derived in form of infinite series. The numerical results are graphically shown to demonstrate intuitively effects of loading frequency as well as geometry on fracture criteria of cracks. And the correction of this method and the sophistication of crack propagation laws due to dynamic loads and couple effects are also verified.

关 键 词：共面裂纹 应力强度因子 能量释放率 动态断裂 

分 类 号：U441.4[建筑科学—桥梁与隧道工程]