穿透夹杂界面的半无限楔形裂纹尖端螺型位错的发射研究

研究了穿透圆形夹杂界面的半无限楔形裂纹与裂纹尖端螺型位错的干涉问题.应用复变函数解析延拓技术与奇性主部分析方法,得到了位错位于半圆形夹杂内部时,半无限基体和半圆形夹杂内复势函数的解析解.然后利用保角映射技术得到了穿透圆形夹杂界面的半无限楔形裂纹尖端螺型位错产生的应力场以及作用在位错上的位错力的解析表达式.主要讨论了螺型位错对裂纹的屏蔽效应以及从楔形裂纹尖端发射位错的临界载荷条件.研究结果表明正的螺型位错可以削弱楔形裂纹尖端的应力强度因子,屏蔽裂纹的扩展,屏蔽效应随位错方位角的增大而减小.位错发射所需的无穷远临界应力随发射角的增加而增大,最可能的位错发射角度为零度,直线裂纹尖端位错的发射比楔形裂纹尖端位错的发射更容易,硬基体抑制位错的发射.

EMISSION CRITERION OF A SCREW DISLOCATION FROM A SEMI-INFINITE WEDGE CRACK PENETRATING AN INHOMOGENEITY

Abstract: The interaction between a screw dislocation and a semi-infinite wedge crack penetrating a circular inhomogeneity is investigated. Using Riemann-Schwartz's symmetry principle integrated with the analysis of singularity of complex functions, the closed form solutions of the complex potentials in both the semi-infinite matrix and the semi-circular inhomogeneity are obtained when screw dislocation located in the semi-circular inhomogeneity. The expressions of stress fields in the inhomogeneity and the force acting on dislocation are derived by using the conformal mapping technique. The shielding effect and the emission criterion of the screw dislocation are discussed in detail. The results show that positive dislocation can reduce the stress intensity factor of the wedge crack and shield the crack growth. The shielding effect decreases with the increment of dislocation azimuth angle. The critical load at infinity for dislocation emission increases with the increment of emission angle, and the most probable angle for screw dislocation emission is zero. Comparing with the case for a straight-line crack, the emission of the dislocation from a wedge crack becomes more difficult. In addition, the hard matrix can enhance the critical load for the dislocation emission.