The mean stress effect on the high-cycle fatigue strength from a multiaxial fatigue point of view

In the presence of non-proportional multiaxial fatigue loadings, principal stress directions at critical points rotate during the application of the cyclic load. The complexity of the stress field distribution can also be increased by the presence of non-zero mean stress components. In this case, one of the main challenges for researchers engaged in fatigue problems is to propose simple rules capable of accounting for these complex situations. In this study, by starting from the assumption that uniaxial fatigue is a simpler sub-set of the more complex multiaxial fatigue reality, both classical expressions accounting for the mean stress effect in uniaxial fatigue and three different critical plane approaches have been critically reviewed. In particular, the expressions due to Gerber, Dietman, Goodman, Soderberg and the so-called 'elliptical relationship' have been reformulated in terms of the critical plane approach in order to extend them to multiaxial fatigue conditions. In parallel, reliability and accuracy of the multiaxial fatigue criteria proposed by Matake and McDiarmid, respectively, have been checked in the presence of high values of the ratio between the maximum normal stresses and the shear stress amplitudes relative to the critical plane. All the performed analyses suggest that an upper value exists, depending on the material fatigue properties, beyond which the critical plane approach no longer has a physical sense, because the material failure is no longer governed only by the shear stress amplitude. The limit value of this approach has been calculated by using Susmel and Lazzarin's criterion, which has an intrinsic threshold value over which its use is not justified. The correspondence between this mathematical limit and the experimental reality has been investigated by using a number of data sets taken from the literature and generated under uniaxial as well as under multiaxial fatigue loadings. Susmel and Lazzarin's criterion is seen to be a useful tool for fatigue strength assessments in most situations of practical interes