摘要
采用Ｇｒｅｅｎ函数法研究任意有限长度的孔边裂纹对ＳＨ波的散射和裂纹尖端场动应力强度因子的求解．取含有半圆形缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解作为Ｇｒｅｅｎ函数，采用裂纹“切割”方法并根据连接条件建立起问题的定解积分方程，得到动应力强度因子的封闭解答．最后给出了孔边裂纹动应力强度因子的算例和结果。
In the category of elastodynamic fracture, the present paper investigates the problem of SH-wave scattering by cracks of any limited lengths originating at the boundary of a cylindrical hole, and gives the solutions of dynamic stress intensify factor at the crack tip. The Green's Function method is used. That means a special Green's function, which is a fundamental solution of displacement field for an elastic half space possessing a half cylindrical gap while bearing out of plane harmonic line source force at any point of its horizontal boundary, is constructed for the present problem. In terms of the solution of SH wave scattering by a cylindrical hole, the material is divided into two parts along X axis and cracks can be made out with crack-division technique. There are two important steps in the technique of crack division. On one hand, anti plane stresses, which are the same in quantity but opposite in direction to those produced by SH waves mentioned before, are loaded at the region where cracks will appear. If the region begins at hole edge and extends to a limited distance, the composite crack is made out in the medium. On the other hand, anti plane stresses that are unknown must be applied in the non crack region of division interface in order to satisfy the continuity conditions at division plane. Then, integral equations for solution of the unknown stresses, which is connected with crack tip DSIF, can be established, and the solution of dynamic stress intensity factor in mode III can be obtained. Finally, some examples and results for dynamic stress intensity factor are given, and the influence of circular hole to dynamic stress intensity factor at crack tip is discussed. It is indicated that the traditional opinion about composite crack simplification is not right in dynamic case. Simplifying composite crack to Griffith linear crack is not always safety in dynamic fracture.
出处
《力学学报》
EI
CSCD
北大核心
1999年第3期292-299,共8页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
国家教委博士点基金
关键词
孔边裂纹
SH波散射
动应力强度因子
composite cracks, Green's function, SH wave scattering, integral equation, dynamic stress intensity factor (DSIF)
