Advances in low cycle fatigue probabilistic modeling

New advances in the probabilistic S-N model proposed by Castillo and Canteli are presented. The requirements for a S-N model derivation to be valid are emphasized, in particular, that of the compatibility between the statistical distributions of lifetime and stress reference variable. The definition of the generalized reference variable (GRV) in the S-N field, as $\mathrm{GRV}=\psi ·{\sigma }_M$, where $\psi$ is a non-dimensional factor derived from the $\sigma -\epsilon$ law of the material, allows the former model to be applied to LCF data. The new model ensures the incontrovertible and unitary definition of the scatter band in the S-N field and the justification of an asymptotic lower limit of the lifetime, $N_0.$ As a result, the stress- and strain-based approaches can be envisaged as a unique probabilistic $\psi {\sigma }_M-N$ approach applicable in the three conventional, i.e., LCF, HCF and VHCF domains. An extension as the $\psi {\sigma }_M-R-N$ model that includes the stress ratio effect is presented. The utility of the model is confirmed with the assessment of LCF data from different external experimental campaigns.