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Multiaxial high cycle fatigue modeling of materials is an issue that concernsmany industrial domains (automotive, aerospace, nuclear, etc) and in wich many progress stillremains to be achieved. Several approaches exist in the litterature: invariants, energy, integraland critical plane approaches all of there having their advantages and their drawbacks. Thesedifferent formulations are usually based on mechanical quantities at the micro or meso scalesusing localization schemes and strong assumptions to propose simple analytical forms. Thisstudy aims to revisit these formulations using a numerical approach based on crystal plasticitymodelling coupled with explicit description of microstructure (morphology and texture). Thiswork has three steps: First, 2D periodic digital microstructures based on a random grain sizesdistribution are generated. Multiaxial cyclic load conditions corresponding to the fatiguestrength at 107 cycles are applied to these microstructures. Then, the mesoscopic FatigueIndicator Parameters (FIPs), formulated from the different criteria existing in the literature, areidentified using the FE calculations of the mechanical fields. These mesoscopic FIP show thelimits of the original criteria when it comes to applying them at the grain scale. Finally, astatistical method based on extreme value probability is used to redefine the parameters of thesecriteria. These new criteria contain the sensitivity of the microstructure variability.