Multiaxial fatigue limits and material sensitivity to non-zero mean stresses normal to the critical planes

This paper is concerned with an attempt to reformulate the so-called Modified Wöhler Curve Method (MWCM) in order to more efficiently account for the detrimental effect of non-zero mean stresses perpendicular to the critical planes. In more detail, by taking as a starting point the well-established experimental evidence that engineering materials exhibit different sensitivities to superimposed tensile static stresses, an effective value of the normal mean stress relative to the critical plane was attempted to be calculated by introducing a suitable correction factor. Such a mean stress sensitivity index was assumed to be a material constant, i.e. a material parameter to be determined by running appropriate experiments. The accuracy of the novel reformulation of the MWCM proposed here was systematically checked by using several experimental data taken from the literature. In particular, in order to better explore the main features of the improved MWCM, its accuracy in estimating multiaxial high-cycle fatigue damage was evaluated by considering fatigue results generated not only under non-zero mean stresses but also under non-proportional loading. Such a validation exercise allowed us to prove that the systematic use of the mean stress sensitivity index resulted in estimates falling within an error interval equal to about ±10%, and this held true independently of considered material and complexity of the investigated loading path. Finally, such a novel reformulation of the MWCM was also applied along with the Theory of Critical Distances (TCD) to predict the high-cycle fatigue strength of notched samples tested under in-phase bending and torsion with superimposed tensile and torsional static stresses: again our method was seen to be highly accurate, correctly predicting high-cycle multiaxial fatigue damage also in the presence of stress concentration phenomena.