A Generalization of Neuber's Rule for Numerical Applications

Abstract

In this paper, a generalization of Neuber's rule for a quick and easy elastic/plastic notch analysis is established and discussed. The proposed generalization allows for a numerical and/or graphical solution for any notch geometry as well as its associated stress concentration factor, kt, and fatigue notch factor, kf. It is shown that the so called Neuber's “master” curve, involved in such analysis, is unique and is only material dependent. This is obtained by a simultaneous solution of the Ramberg-Osgood relationship and Neuber's rule. These solutions are plotted in terms of the product of nominal stress, S, times stress concentration factor, kt (or kf), versus the actual notch root strain, ε. The Neuber's “master” curve can be interactive and is applicable for both monotonic and cyclic loading situations. The present formulation is pertinent to conditions when applied nominal stresses, S, is below material's yield stress, σ0, i.e. |S| ≤ σ0. The proposed method is particularly suitable for rapid fatigue life predictions and material screening during pre-prototype phase of notched component design.