Non-local energy based fatigue life calculation method under multiaxial variable amplitude loadings

► A fatigue life prediction method for multiaxial variable amplitude loadings is proposed. ► The method is based on strain energy quantity. ► No cycle counting method is needed. ► The method is non-local so that stress strain gradient can be taken into account. ► The approach unifies all loading types on a single master curve. Reliable design of industrial components against high cycle multiaxial fatigue requires a model capable of predicting both stress gradient and load type effects. Indeed, taking into account gradient effects is of prior importance for the applicability of fatigue models to real structures. In this paper, a fatigue life assessment method is proposed for proportional and non-proportional multiaxial variable amplitude loadings in the range 104–107 cycles. This method derives from the fatigue criterion initially proposed by Palin-Luc and Lasserre (1998) [2] and revisited by Banvillet et al. (2003) [16] for multiaxial constant amplitude loading. The new proposal consists of a complete reformulation and extension of the previously cited energy based fatigue strength criteria. It includes two major improvements of the existing criteria. The first one consists in a fatigue criterion for multiaxial variable amplitude loadings while only constant amplitude loadings were considered in the above cited works. The second one is an extension to an incremental fatigue life assessment method for proportional and non-proportional multiaxial variable amplitude loadings. No cycle counting technique is needed whatever the variable amplitude loadings type considered (uniaxial or multiaxial). The predictions of the method for constant and variable amplitude multiaxial loadings are compared with experimental results on specimens from literature and from new experiments on a ferrito-perlitic steel. The above mentioned method has been implemented as a post-processor of a finite element software. An application to a railway wheel is finally presented.