大深长比表面裂纹应力强度因子的二维权函数

2D weight function for stress intensity factor of semi-elliptical surface cracks with high aspect ratio

权函数法是求解复杂应力场中表面裂纹应力强度因子的有效手段。本文针对大深长比半椭圆表面裂纹的二维权函数进行了研究。通过三维有限元建模计算了裂纹深长比1≤a/c≤8,裂纹深度比0.01≤a/T≤0.8的有限厚度平板表面裂纹应力强度因子。基于二维权函数统一形式,结合有限元数据,发展了适用于大深长比表面裂纹表面点和最深点应力强度因子计算的二维权函数。新权函数的准确性通过在裂纹面上施加双向变化应力分布载荷进行验证,权函数结果与有限元结果的相对误差均在10%以内。在前期工作基础上,本文将表面裂纹二维权函数的形状适用范围扩大至0.05≤a/c≤8,0.01≤a/T≤0.8。

The weight function method is a powerful tool for calculating stress intensity factor(SIF)of surface cracks under complex stress field.In this paper,the generalized expression of 2D weight function for semi-elliptical surface cracks with high aspect ratio was studied.Three-dimensional finite element analysis was performed to calculate the SIFs for surface cracks in finite-thickness plates over the range of aspect ratio 1≤a/c≤8 and crack depth-to-thickness ratio 0.01≤a/T≤0.8.The unknown parameters in general form were determined from the SIF reference solutions,and then 2D weight function for both surface and deepest point of high-aspect-ratio surface cracks was obtained.The accuracy of the new weight function was validated by several two-dimensional stress distributions,the difference between the SIFs calculated by weight function and FEM is less than 10%.The present results complement the 2D weight function previously developed by the authors with a wider application range of 0.05≤a/c≤8,0.01≤a/T≤0.8.