旋转盘型件表面半椭圆裂纹K_I的权函数解法

A weight function method for modeⅠstress intensity factor calculation of surface semi-elliptical cracks in disk-shaped part under centrifugal load

计算半椭圆裂纹的Ⅰ型应力强度因子(K_I)是研究含缺陷部件损伤容限、评估剩余寿命的关键技术。针对机械设备类盘型件应力分布复杂、有限元建模繁琐耗时等问题,建立一种计算高速旋转条件下复杂结构盘状部件表面半椭圆裂纹K_I的权函数方法。在一定的适用条件下,将盘型件局部小裂纹简化为平板表面裂纹。在半椭圆形状参数0.2≤α≤2、0.05≤β≤0.6的范围内,通过平板表面裂纹模型,拟合得到表面半椭圆裂纹权函数参数M的多元线性表达式,其中拟合值与有限元计算值的残差平方和均值为0.00975。结合某机械设备盘型件的设计特点,研究该权函数法在不等厚及中部突起型圆盘表面径向、切向裂纹问题的适用性。经验证,权函数解与有限元结果的相对误差为-4.45%~2.80%。

The assessment of modeⅠstress intensity factors(K_I)is a crucial step to calculate the damage tolerance and evaluate the residual life of structures with defects.Solving the problem of time consuming in finite element modeling,general weight function is developed to calculate K_I of surface cracks on the rotating disk-shaped part with complex structure.A cracked finite plate model based on some hypothesis was presented to describe the fracture performance for small semi-elliptical cracks on surface of disk-shaped part.Within the range ofαfrom 0.2 to 2,βfrom 0.05 to 0.6,correction coefficients of surface semi-elliptical cracks on finite plate of aluminium alloy were fitted by multiple linear regression,which was applied to calculate the weight function of cracked disk-shaped part.The average squared residual of FEM and analytical solutions is 0.00975.Based on calculated stress distribution of certain parts,weight function method was used to obtain K_I factors of surface semi-elliptical cracks on rotating disks with non-uniform thickness and central bulge,whose feature is similar with that in special purpose equipment.The comparison between the results obtained from proposed weight function method and numerical solutions by FEM is presented,the relative error is from-4.45%to 2.80%.