基于三维裂纹尖端应力场的应力强度因子计算方法

提出一种基于无限大体裂纹尖端弹性应力场理论解的前几项多项式函数,对实际裂纹体弹性应力场有限元解进行拟合来计算应力强度因子的方法.该方法在计算应力强度因子时不需要预先假设裂纹尖端的应力应变状态,应力强度因子计算结果更符合三维裂纹体裂纹尖端实际的应力应变状态.首先基于二维无限大板中心穿透裂纹应力场理论解验证了方法的有效性,探讨了拟合确定应力强度因子需要的多项式应力函数的项数.然后分别以二维大板中心穿透裂纹、三维大体内埋圆裂纹和三维有限厚板中心穿透裂纹的应力强度因子计算为例,通过与无限大板和无限大体应力强度因子理论解以及基于位移外推法和1/4节点张开位移法的应力强度因子有限元解的对比分析,验证了该方法的有效性和合理性.研究表明该方法能够合理反映三维裂纹体裂纹尖端的实际应力应变状态,计算得到的应力强度因子数值更合理. 

Calculation method of stress intensity factor based on the three-dimensional stress field at the crack tip

An approach for calculating stress intensity factors was proposed based on the first several items of the theoretical polynomial solution of the elastic crack tip stress field in infinite body, and the stress intensity factors were calculated by fitting the finite element solution of elastic crack tip stress field in actual crack bodies. This method did not need assuming the stress and strain state at crack tip in calculated of stress intensity factors, and the calculated results were more in line with the actual stress and strain state in the three-dimensional crack bodies. First, the availability of this method was validated based on the theoretical solution of center-through-crack stress field in a two-dimensional infinite plate, and the fitting item of the polynomial function to determine the stress intensity factors was explored. Then by calculating the stress intensity factors of center through crack in two-dimensional infinite plate, embedded circle crack in three-dimensional infinite body and center through crack in three-dimensional finite thickness plate, the validity and rationality of the proposed method had been verified by comparative analysis with theoretical solutions of the infinite plate and infinite body, and also with the finite element solutions based on displacement extrapolation method and 1/4 point opening displacement method. Studies show that this method can reasonably reflect the actual stress and strain state of crack tip in three dimensional crack bodies, and the calculated stress intensity factors are more reasonable.