Accuracy and limit of a least-squares method to calculate 3D notch SIR

To evaluate the three-dimensional (3D) stress intensity factors (SIFs) of a sharp V-notch using the finite element result is limited in the literature. Thus, this study developed a least-squares method to solve this problem as well as study its restriction and accuracy. First, the William's eigenfunction and complex stress function approach are deduced into a least-squares form, and then stress field from the finite element analysis is substituted into the least-squares equation to evaluate the 3D SIFs. Numerical simulations in this article show that the least-squares method can be used to calculate SIFs accurately if more than two stress terms are included. The calculated SIFs of this least-squares method are not sensitive to the maximum and minimum radiuses of the area from which data are included. The major advantage of the proposed method is that the procedure is simple and systematic, so it can be applied to any finite element code without difficulties.