Most of mechanical components in the engineering are frequently subjected to the fatigue damaging process because of the great number of stress cycles they have to undergo. This paper presents an elaboration of two of the most studied methods for the computation of fatigue life in multiaxial fatigue. We describe the reformulation of Sines and Crossland fatigue criteria, which have been adapted so that they could preserve the observed detrimental influence of a tensile mean stress and the observed beneficial effect of a compressive mean bending stress. The proposed reformulation of Crossland and Sines criteria is applied to a general sinusoidal in-phase or out-of-phase bending and torsion stress state, for which analytical formulae can be derived. From the theoretical results calculated according to the present propositions, the criterion proposed by Sines was found to be the most precise in preserving the detrimental influence of a tensile mean stress and the observed beneficial effect of a compressive mean bending stress. On the other hand, the criterion proposed by Crossland was found to be precise in the multiaxial fatigue limit prediction. This analysis shows that the proposed procedure is very efficient, suggesting that Sines and Crossland fatigue criteria remain valuable fatigue evaluation tools for the mechanical design industry.

In many situations encountered in engineering practice, structures or structural elements are under thermomechanical cycles of loading. The use in this condition of traditional fatigue criteria in high cycle fatigue is no more advisable because on structures, these criteria are formulated for the prediction of the number of cycles for the nucleation of cracks in the isothermal situation. In this paper, we propose an extension of stress invariants based criteria, for the anisothermal high cycle fatigue. Our proposal is essentially based on the hypothesis of accommodation at macroscopic and microscopic levels. The simulation made from the fatigue strength of the proposed ansiothermal criterion reproduced qualitatively the expected results. The proposed modified criteria will enhance the account the account of the multiaxial and anisothermal character of thermomechanical loadings.