两条等长共线裂纹尖端塑性区扩展理论研究

Theoretical study on expansion of plastic zone at crock tips of isometric collinear cracks

采用Kachanov法基本思想求解2条等长共线裂纹相互作用下裂纹的应力强度因子,分别基于Mises屈服准则和D-P屈服准则推导了裂纹尖端塑性区半径的表达式,并求得裂纹相互作用下塑性区半径的扩大倍数,其值为2条裂纹相互作用下的应力强度因子与单裂纹状态下应力强度因子比值的平方。在此基础上,分析了裂纹间距对塑性区扩展的影响。研究发现,同一裂纹倾角下裂纹间距与裂纹长度比值越小,2条裂纹尖端的塑性区半径越大,裂纹尖端塑性区扩展速度越快,直至塑性区发生接触,且不同的裂纹倾角,裂纹尖端塑性区发生接触的条件不同。

Based on the basic idea of the Kachanov method, the stress intensity factors for the interaction of isometric collinear cracks are computed. Moreover, according to the Mises failure criterion and the D-P failure criterion, the expression of the plastic zone radius at the crack tip and the expansion ratio of plastic zone radius under the crack interaction are derived based on the small-area yield condition under the uniaxial tension. The radius enlargement of the plastic zone is the square of the ratio of the stress intensity factor under the interaction of two cracks to the stress intensity factor of a single crack. And, the influence of crack spacing on the plastic zone expansion is also analyzed. The results show that, for a same inclining angle of crack, the plastic zone radius of crack tip increases with the decrease of crack spacing, and its increasing rate increase as well. For different crack angles, the contact conditions at the plastic zone of crack tip are also different. Therefore, the combination conditions of double cracks need to be determined according to the inclining angle of crack.