On applying the Neuber's rule to spectral fatigue damage estimation under elasto-plastic strain

Spectral methods (adopting a frequency domain approach) are commonly used for estimating the fatigue damage of vibrating structures in the high-cycle fatigue regime, where the material is linear elastic. In the low-cycle fatigue regime, by contrast, material exhibits plasticity, so the structural response is non-linear. For this reason, the application of spectral methods in low-cycle fatigue regime is more challenging. Few studies exist in the literature that include material plasticity in the spectral methods by means of Neuber's rule and the Ramberg-Osgood constitutive model. After a review of the existing strain-based spectral methods, this paper develops a more rigorous theoretical formulation for the transformation of the stress amplitude probability distribution based on Neuber's rule. It then presents preliminary results of a comparison between strain-based spectral estimations and simulation results obtained in the time domain by the use of kinematic cyclic plasticity models. The findings are useful to shed light on the range of applicability of the strain-based spectral approach while also providing ideas for possible further improvements.