A comparison between numerical and approximate methods for rapid calculation of NSIFs

Abstract

To more rapidly predicting the integrity of components weakened by sharp notches, notch stress intensity factors (NSIFs) are usually evaluated. Many methods have been proposed evaluating NSIFs, ranging from the stress gradient based formulation to methods evaluating strain energy density averaged over a control region. Here, we compare different numerical and approximate methods applied to a square plate with a 45° tilted crack, positioned at the center of the plate. Hence, approximate methods need to FE solutions, obtained from models discretized with fine mesh or, alternatively, with coarse mesh, having to consider the mean value of the local Strain Energy Density (SED) to calculate NSIFs. Furthermore, 2D and 3D numerical simulations have been carried out to investigate the solutions provided by these analytical methods. For this aim, two software based on the Finite Element Method (FEM) and on the Dual Boundary Element Method (DBEM), respectively, have been adopted to solve the proposed study case of the square plate with a 45° tilted crack. These methods can supply accurate predictions of SIFs by means of J-integral calculation. Then, the NSIFs have been calculated at the intersection between the crack front and the free surface of the plate and, to assess the thickness effect on the provided solutions, they have also been calculated at half the thickness along the crack front and for increasing thickness values. Finally, the NSIFs obtained from the analytical and numerical methods have been compared each other to evaluate the level of agreement.