A unified rule to estimate multiaxial elastoplastic notch stresses and strains under in-phase proportional loadings

Several methods can be used to estimate elastoplastic (EP) notchtip stresses and strains from linear elastic calculations, providing EP stress and strain concentration factors. For uniaxial load histories, Neuber's and Glinka's rules are perhaps the most used. For non-proportional multiaxial histories, such corrections require incremental plasticity calculations to correlate stresses and strains at the notch root, 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 methods can be used without requiring an incremental approach. Most of these methods are based on Neuber's rule, so they usually result in conservative predictions, especially in plane strain-dominated cases associated with sharp notches. In this work, a Unified Notch Rule (UNR) is proposed for uniaxial and in-phase proportional multiaxial histories. The UNR can reproduce Neuber's or Glinka's rules, interpolate their notch-tip behaviors, or even extrapolate them for notches with increased constraint. Moreover, the UNR also allows a non-zero normal stress perpendicular to the free-surface. The proposed method predictions are compared with elastoplastic Finite Element calculations on notched shafts.