Numerical evaluation of the original “Neuber’s rule” for pure out-of-plane shear loading

Abstract

Neuber’s rule has become a popular analytical tool for evaluating notch root stress and strain for fatigue life estimation. The original study was based on the geometry of prismatic bodies with hyperbolic notches under pure out-of-plane shear with a nonlinear material model. From this study, the author observed that “The geometric mean of stress and strain concentration factors is equal to theoretical elastic stress concentration factor, K_t.” Although this conclusion was based on a “special deformation law,” Neuber suggested that it can be approximately extended to any stress–strain law and to tensile and bending loads replacing shear stress and strain with equivalent von Mises stress and strain and Neuber’s rule evolved. Extensive research has been conducted to evaluate and generalize Neuber’s rule for fatigue analysis. However, the applicability of Neuber’s rule to a specific situation requires consideration of the material model utilized, in addition to the notch geometry and loading conditions. This article presents a detailed finite element analysis of Neuber’s rule using out-of-plane shear loading on prismatic bodies with hyperbolic notch geometries identical to those considered by Neuber. Neuber’s nonlinear material model (special deformation law) is compared to the Ramberg–Osgood material model, and discernable differences were observed. Neuber’s observations were approximately valid for conditions congruent with his constitutive model. For the Ramberg–Osgood model, this happens to occur only for a strain hardening exponent of about 0.2. For other values of the strain hardening exponent, Neuber’s model cannot emulate the shape of the Ramberg–Osgood curve, and notch strain predictions from Neuber’s rule are less accurate.