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An analysis of high cycle fatigue behaviour is undertaken via the numerical simulation of polycrystalline aggregates. The metallic material chosen for investigation is Copper, which has a FCC crystalline structure. The REV, which is composed of 300 randomly orientated equiaxed grains, is loaded at the fatigue limit determined at 107 cycles. The aim is to calculate the mechanical quantities at the mesoscopic scale (average quantities in the grains) after cyclic stabilisation has been achieved. The results highlight the fact that the mechanical quantities at this scale have a large scatter. A statistical analysis of the response of the aggregate for different loading conditions (tensile, torsion, and in-phase tension-torsion) is done. Thanks to the sufficiently large number of different microstructures investigated, a critical analysis of the Dang Van and Crossland multiaxial fatigue criteria has been undertaken, using the local mechanical quantities. [ABSTRACT FROM AUTHOR]