裂纹群各向异性与同性各类边值应力强度因子的关系

THE RELATIONSHIPS OF STRESS INTENSITY FACTORS FOR THE COLLINEAR CRACKS BETWEEN ANISOTROPIC AND ISOTROPIC INFINITE PLANES

本文采用复变函数方法和叠加原理,推导出带共线裂纹各向异性板各类边值问题的第一与第二类Fredholm积分方程,通过与各向同性体比较,得出了以下三个结论:Ⅰ.对第一类边值问题,只要裂纹面上作用平衡力系,则各向异性与同性体裂纹尖端应力强度因子完全相同;Ⅱ.各向异性体裂纹面第二类边值问题与各向同性体相应问题应力强度因子仅相差一常系数λ_0/λ;Ⅲ.对第三类混合边值问题,由应力边值产生的应力强度因子两材料相同,但由位移边值产生的因子则相差常系数λ_0/λ。最后,提出了求解具有奇性核积分方程组的数值方法,并给出了计算公式。

According to the superposition principle, the first and second kinds Fredholm integral equa-tions for any boundary value problem about anisotropic infinite plane with collinear cracks havebeen deduced in this paper. Comparing it with isotropic problem, we have got three conclusions.Ⅰ. Only if the loads on the upper and lower crack surfaces are equilibrium system, the stress in-tensity factors at crack tip are independent on the anisotropic material parameters; Ⅱ. Consideringthe second kind boundary value problem, there is a difference between these two materials on con-stant coefficient λ_0/λ; Ⅲ. For mix-boundary value problem, the stress intensity factor caused bystress bound conditions is just the same as isotropic body and different from isotropic on the con-stant coefficient λ_0/λ caused by displacement bound conditions.