微裂纹群对主裂纹尖端损伤行为的影响

Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip

在单轴拉伸荷载作用下,运用Muskhelishvili复变函数法和逐步递推法对无限大平面内含一个主裂纹和多个任意分布的微裂纹问题进行求解,得到了裂纹尖端的应力场和应力强度因子K.在此基础上,结合损伤力学,重新定义了单轴拉伸条件下主裂纹和微裂纹尖端的损伤参量D,分析了不同的损伤区形式对主裂纹尖端损伤的影响.结果表明,正向链式和反向链式分布的微裂纹均对主裂纹尖端损伤有增强作用,并且主裂纹尖端的损伤参量随微裂纹的倾斜角度和裂纹间距的减小而增大.当微裂纹的倾斜角度较小时,主裂纹和微裂纹尖端损伤均有增强作用,并且主裂纹尖端损伤的增强作用随着微裂纹的长度增加而增大.在连续损伤区内,均匀分布的微裂纹对主裂纹尖端损伤的增强作用随着微裂纹的数量增加而逐渐增大.

The solution of an infinite plane containing a macro crack and a cluster of micro cracks under uniaxial tensile load was presented based on Muskhelishvili’s complex function method and the stepwise recursive method.The stress field and stress intensity factor K were obtained.Combined with the damage mechanics,damage parameter D of the macro-crack tip and the micro-crack tip under uniaxial tension was redefined,and the influence of different damage zone forms on the damage of the crack tip was analyzed.The results show that,both the chain-distribution and the reverse-chain-distribution micro cracks have an amplifying effect on the macro crack growth,and the damage parameter increases with the decrease of the inclination angle of the micro crack and the reduction of the distance between the macro crack and the micro cracks.For a relatively small inclination angle of the micro crack,the damage parameters of the macro crack and the micro crack heightens,and the damage parameter of the macro crack increases with the micro-crack length.For evenly distributed micro cracks in the continuous damage zone,the micro cracks have an amplifying effect on the macro-crack growth,and the damage parameter of the macro crack increases with the micro-crack number.