On the second non-singular stress term of the V-notch solution: a new engineering solution

The non-singular stress terms are expressed by means complex eigenvalues and their corresponding complex coefficients for a number of sharp V-notches with varying notch opening angles. According to the literature the complex part of the solution introduces in the stress field equations an oscillatory function depending also on the logarithm of the radial distance from the notch tip. The intensity of the non-singular term depends on two parameters contrary to the conventional representation of the singular term the intensity of which is expressed by the notch stress intensity factor (NSIF). The aim of this paper is to investigate whether the stress field and the strain energy density can be described with sufficient accuracy by the real part of the Williams’ solution, neglecting the complex part of the eigenvalue and the corresponding complex coefficient. This engineering proposal strongly simplifies the problem allowing to define a real, unique, non-singular NSIF (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{ H }_\mathrm{ns}$$\end{document}) which governs the intensity of the non-singular part of the stress field.