三维裂纹裂尖场的高阶项

High Order Stress in Crack Tip Field for Three Dimension Crack

现实中的裂纹一般都属于三维裂纹。绝大多数关于三维裂纹的研究通常只关心裂尖场的奇异项及应力强度因子,而不涉及其高阶项。然而,在疲劳以及小裂纹等问题中,高阶项的影响一般是不能忽略的。针对三维椭圆裂纹,通过特定的坐标转换,得到了沿椭圆长、短轴方向的应力分布及其高阶项,并依据该高阶项,提出了三维裂纹问题的应力强度因子数值外插法,通过有限元分析,证实了所提出的外插法的有效性。

Elliptical crack under normal tension will propagate at the intersections of the major and minor axes with crack border. Until now, the stress field along the major and minor axes used as common is presented by M. K. Kassir and G. C. Sih, but it left the high-order stress, and the high-order stress plays an important role in fatigue and small scale crack. The exact result of mode-I along the major and minor axes was obtained through A. E. Green＇s method. Then K1 was also determined by numerical extrapolation method. The numerical examples show that our results are in good agreement with those of finite element analysis.