Generalization of the Weibull probabilistic compatible model to assess fatigue data into three domains: LCF, HCF and VHCF

In this work, three classes of fatigue models are reviewed according to the fatigue regimes commonly considered in the current components design. Particular attention is devoted to the so-called Class III fatigue models, covering the three fatigue regimes, namely, LCF, HCF and VHCF. The applicability and limitations of the proposed analytical sigmoidal solutions are discussed from the viewpoint of practical design. The compatible Weibull S-N model by Castillo and Canteli is revisited and improved by considering a new reference parameter GP = E·σ_M ·(dε/dσ)|_M as the driving force alternative to the conventional stress range. In this way, the requirement, σ_M ≤ σ_u, according to the real experimental conditions, is fulfilled and the parametric limit number of cycles, N₀, recovers its meaning. The probabilistic definition of the model on the HCF and VHCF regimes is maintained and extended to the LCF regime. The strain gradients may be calculated from the monotonic or cyclic stress–strain curve of the material although a direct derivation from the hysteresis loop is recommended. Some Class III fatigue models from the literature and another one improved by the authors are applied to the assessment of one experimental campaign under different stress ratios conditions and the results compared accordingly. Finally, the new probabilistic GP-N field is evaluated. The results confirm the practical confluence of the stress- and the strain-based approaches into a single and advantageous unified methodology.