On the estimation of multiaxial elastoplastic notch stresses and strains under in-phase proportional loadings

There are several methods or rules to estimate elastoplastic (EP) notch-tip stresses and strains from simpler linear elastic calculations, an almost indispensable step for practical fatigue damage calculations. Neuber's and Molski-Glinka's rules are perhaps the most popular for fatigue analyses of uniaxial load histories. Their use in such elementary cases is relatively easy, but the general case of non-proportional multiaxial load histories require non-trivial incremental plasticity calculations to correlate EP stresses and strains at the notch tip, a quite challenging task. However, for in-phase proportional multiaxial histories, where the principal directions do not change and the load path in a stress diagram follows a straight line, approximate calculation methods can be used to avoid the need for an incremental EP approach. Most of these methods are based on Neuber's rule, so they may result in conservative predictions, in particular under near plane strain-dominated states associated with sharp notches. To minimize this problem, a Unified Notch Rule (UNR) is proposed and evaluated in this work, by comparing its predictions with EP Finite Element calculations on notched shafts, both for uniaxial and for in-phase proportional multiaxial load histories. The UNR can reproduce Neuber's or Molski-Glinka's rules, interpolate their notch-tip behaviors, or even extrapolate them for notches with increased transversal constraint, which affect the plastic behavior at notch tips. Moreover, the UNR can also consider non-zero normal stresses perpendicular to the free-surface.