对接双材平面中圆弧裂纹问题的数值方法

Numerical Method on Circular Arc Crack in Bi-material Plane

基于超奇异积分方程法的基本原理,以裂纹弧长坐标为基本变量,以裂纹岸位移间断为基本未知函数,得出双材料平面圆弧裂纹问题的超奇异积分方程组,并通过适当的变量与函数代换建立了相应的数值算法,最终将问题转变为对一个线性方程组的求解.针对圆弧裂纹的计算表明,由于裂纹变曲一般产生应力强度因子减小的良性影响,而双材料界面对附近裂纹应力强度因子的影响则在切变模量比G2/G1<1时变大,而在G2/G1>1时则变小.

Based on the principle of the hyper-singular integral equation method, the hyper-singular inte- gral equations of the circular arc crack in the bi-material plane were obtained with the coordinate of crack arc length being the basic variable and the displacement discontinuities of crack being unknown func- tions. The corresponding numerical method was established through appropriate variables and functions substitution. Eventually, the problem could be transformed into the solution for a linear equations. The calculation results on the arc crack showed that the crack bending generally led to the positive impact of the decrease of stress intensity factor. The bi-material interface led to the change of the stress intensity factor near the crack： it became larger when the shear modulus ratio G2/G1 〈 1, and it became smaller when G2/G1 〉 1.