Fictitious notch rounding concept applied to sharp V-notches: Evaluation of the micro structural support factor for different failure hypotheses. Part I: Basic stress equations

With the aim to perform a comprehensive and accurate evaluation of the microstructural support factor of sharp V-notches (Neuber's notch rounding concept), in Part I of this contribution, the indispensable theoretical tools, especially the basic stress equations, are reconsidered and amended in respect of accuracy of results. First, the analytical solution derived by Neuber [Neuber H. Kerbsparmungslehre. 2nd ed. Berlin: Springer-Verlag; 19581 for sharp rounded V-notches with an arbitrary flank angle under tension loading is considered. The equation of the normal stress has been obtained with the restriction to the notch bisector. Using the Airy stress function suggested by Neuber, this solution is extended to the region outside the notch bisector, and the complete stress field is derived in this manner. A comparison between Neuber's solution, a more recent solution due to Filippi et al. [Filippi S, Lazzarin P, Tovo R. Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates. Int J Solids Struct 2002;39:4543-65] and highly accurate FE results is performed. Filippi's equations which include Williams' solution [Williams ML. Stress singularities resulting from various boundary conditions in angular corners on plates in tension. J App] Mech 1952;19:526-8] for pointed V-notches, are shown to be superior.