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.
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