Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates

The paper deals with the evaluation of linear elastic stress fields in the neighbourhood of U- and V-shaped notches in plane plates. The main aim is to improve the accuracy of an approximate solution already proposed in the literature by changing the polynomial arrangement of complex potential functions and properly adapting the boundary conditions. In some special cases, the solution matches Williams, Westergaard–Irwin and Creager–Paris’ equations universally used in the case of sharp corners, cracks, and blunt cracks, respectively. In the presence of notches with a tip radius different from zero and a large opening angle, the equations obtained are compared with finite element results, showing a very good agreement. Due to their reduced complexity, such equations turn out to be particularly useful when applied to rounded V-notches as well as welded-like geometries under mixed loading conditions. Finally, some limits of the solution when applied to the notch free edges are highlighted