On the extraction of notch stress intensity factors by the post-processing of stress data on the free edges of the notch

Abstract

Following on the lines of a previous paper dedicated to cracked components by Ciavarella et al., here the case of a notch of semi-angle α is considered. Contrary to the crack case (α = 180°), the free edges of the notch are easily accessible to experimental analysis; moreover they provide information about all the terms of the Williams series expansion of the stress field about the notch apex, including the most important, i.e. the symmetric and antisymmetric singular term notch stress intensity factors (N-SIFs), whereas for the crack case the mode I N-SIFs cannot be extracted from those stresses. Another important different feature is that symmetric and antisymmetric N-SIFs have different singularities, and in several cases they are so close that their contributions tend to overlap. Therefore, a simple procedure is here proposed to use radial stresses, to separate their symmetric and antisymmetric contributions a priori by computing the sum and difference of the stresses on the two edges, to post-process these quantities in the ‘asymptotic region’ with standard least-squares techniques and to extract the N-SIFs. The method is applied to a simple case known in the literature and solved by means of a boundary element code, and the results are almost coincident with previous results, even with quite coarse mesh discretizations.