On the Errors Induced by the Hookean Modeling of Nominal Stresses in the eN Method

The traditional εN procedures are inconsistent when modeling nominal stresses by Hooke's law and the stresses and strains at the critical notch root by Ramberg-Osgood's equation, since the material is the same at both regions. When the nominal stresses are not substantially smaller than the yielding strength S_Y, the predicted hysteresis loops at the notch root can be significantly non-conservative. In fact, when the nominal stresses are in the order of S_Y, the Hookean model can predict stresses and strains at the notch root that are smaller than the nominal ones, a clear non-sense. To avoid this problem, it is mandatory to use Ramberg-Osgood to model both the nominal and the critical stresses and strains. However, this approach is not trivial to implement, especially when complex loads are involved. In this work, the methodology required to warrant correct numerical predictions of the critical loops under high nominal loads are discussed.