应力集中部位裂纹自由表面处应力强度因子的计算与分析

Calculation and analysis of stress intensity factor at the free surface of crack at the stress concentration position

针对采用最小二乘法拟合的三次多项式计算应力集中部位裂纹自由表面处应力强度因子,结果往往存在较大偏差的问题,基于椭圆形表面裂纹的通用权函数,提出了将应力分布数据进行离散化分段插值的思路,并具体给出了基于常数插值、线性插值、二次插值的计算公式。结合工程实例,将分段插值与常规最小二乘法的计算结果进行对比与分析,发现两者的计算结果有较大偏差;采用线性插值方法能够较好地表征应力分布,计算出的应力强度因子值也能较快趋于收敛,更适合于工程计算。此外,将有限元法与线性插值、最小二乘法的计算结果进行对比,结果表明运用最小二乘法拟合计算出的结果偏冒进,而运用分段线性插值法的结果则偏安全,从而验证了基于线性插值法计算的可靠性。

The stress intensity factor at the free surface of the crack at the stress concentration position is calculated by the cubic polynomial fitted by the least square method,and the results often have large deviation.Based on the general weight function of elliptical surface crack,the idea of discrete piecewise interpolation of stress distribution data was proposed,and the calculation formulas based on constant interpolation,linear interpolation and quadratic interpolation were given in detail.Combined with engineering examples,the calculation results of piecewise interpolation and conventional least square method were compared and analyzed,and it was found that there is a large deviation between the two calculation results;It is considered that the linear interpolation method can better characterize the stress distribution,and the calculated stress intensity factor value can also quickly converge,which is more suitable for engineering calculation.In addition,the finite element method was compared with the results of linear interpolation and least square method,and it is considered that the results calculated by using the least square method are more aggressive,while the results calculated by using piecewise linear interpolation are safer,which shows the reliability of calculation based on linear interpolation method.