Elastoplastic nominal stress effects in the estimation of the notch-tip behavior in tension

The evaluation of notch effects in low-cycle fatigue problems in general requires local plasticity calculations via the solution of a global Finite Element (FE) problem to obtain the cyclic elastoplastic (EP) stresses and strains at the notch tip, as well as the stress gradient effects around it. Moreover, this EP global FE approach needs to adopt an incremental plasticity formulation in every element of the studied piece that suffers plastic strains. Besides being not trivial to implement, these calculations are computationally intensive, especially when dealing with long loading histories, since they imply in having to solve the EP FE problem for the entire piece for every load increment of every load cycle. A much simpler approach is to perform a single linear elastic (LE) FE calculation on the entire piece for a static unit value of each applied loading, to find the stress and strain influence factors. The resulting LE values then require EP corrections to reproduce the true stresses and strains at the critical point of the component. Thus, an EP strain concentration rule must be assumed to estimate the actual notch-tip stresses and strains from the LE values. Perhaps the most used concentration rules are the ones proposed by Neuber and Glinka, which usually result in reasonable estimates in tension, especially under plane-stress conditions. However, most implementations of Neuber's and Glinka's rules assume the nominal stresses (which act away from the notch tip) are purely elastic, which can induce significant numeric errors even at stress levels much below the yield strength. In this work, Neuber's and Glinka's rules are presented in a formulation that assumes nominal stresses as EP instead of LE, highly improving the EP notch corrections, even under gross yielding of the net section. EP FE simulations on thin and thick specimens are used to verify the effectiveness of the proposed formulation, as well as to study 3D notch effects.