This paper is a new proposal of a multiaxial fatigue criterion which takes better into account the mobility of principal directions of stress tensor. The model proposed is based on the Crosland Criterion and start by defining an equivalent stress with zero out-of-phase angles for the stress components with a phase difference, which apply to Crossland criterion gives the Crossland* criterion. Poor predictions are obtained from Crossland criterion for stress states with mobile principal stress directions. We impute this discrepancy not on the capacity of parameters appearing in the criterion to account for the complexity of the loading or to account the additional damage generate by the mobility of principal stress directions, but instead on the procedure of evaluation of parameters appearing in the criterion and also on the formulation of linear combinations of two scalar parameters proposed by Crossland. Assuming that the second invariant of the stress deviator and maximum hydrostatic pressure can account of the additional damage generate by the mobility of principal stress directions. The re-formulated Crossland criterion gives good predictions of experimental data when stress states present mobility of principal stress directions. The results show that the predictions obtained using in general the equivalent stress should be more satisfactory than the initial Crossland criterion and Crossland.
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