Analogies between spectral methods and multiaxial criteria in fatigue damage evaluation

Abstract This work aims to emphasize some analogies existing between multiaxial fatigue criteria and spectral methods in the context of fatigue damage assessment for uniaxial stochastic loadings in the frequency domain. Among multiaxial criteria available in literature, attention is focused on the so-called “Projection-by-Projection” (PbP) approach, in which fatigue damage of a multiaxial process is computed by using a non-linear summation rule of single damage contributions of uncorrelated projected loadings. In this work the theoretical framework of PbP method will be used to provide a possible mathematical interpretation of the so-called “single moment” (SM) approach, a spectral method for estimating fatigue damage in uniaxial stochastic loadings that was elaborated in 1990 on a purely “empirical” basis. The idea here formalized is to split the spectrum of a uniaxial process into an infinite set of narrow-band spectral contributions, so to define a set of mutually uncorrelated uniaxial narrow-band stochastic processes. The analogy between the damage of a multiaxial process and that of a uniaxial process split into infinitesimal spectral components is shown. Once the formal analogy between uniaxial and multiaxial spectral methods is established, numerical simulations are used to evaluate the accuracy of SM method with reference to different types of stochastic processes with bimodal spectral density.