Fatigue phenomena in polycrystals are governed by deterministic laws such as crystal plasticity, but also depend on probabilistic properties, which results in significant scatter of fatigue lifetime at the macroscopic scale. Since crystal plasticity depends on local features of polycrystals (e.g. crystal lattice orientation, grain size and shape etc.) fatigue properties depend on the detailed grain structure. Thus, modeling fatigue phenomena so that the probability of failure is estimated, would be useful for high cycle fatigue involving very large number of cycles (i.e., high experimental costs). Such models rely on full field computations. However, the exact  grain structure is unknown in most industrial applications, only statistical information is known. Thus, to capture the probability density function of rare events, it would be necessary to perform numerous full field computations corresponding to different draws of random grain structures, which seems very difficult to achieve for 3D polycrystals due to high computation costs when using Crystal Plasticity Finite Element Method (CPFEM) for instance [1-3].
In this contribution, a fast direct full field cyclic method is derived to deal with high cycle fatigue of polycrystals. The model relies on the minimization of the total energy composed of the elastic stored energy, minus the external work, and the energy dissipated in crystal plastic mechanisms. For high cycle fatigue, since the applied load is small, one can assume that in each grain, only one slip mechanism is activated and the plastic slip is uniform. Ellipsoid grains weakling interacting with each other are assumed to reach short computation time.
Plastic hardening is based on dislocation density [4] and Hall-Petch effect, and a linear softening regime corresponding to damage is also introduced [5]. On this basis, different failure mechanisms are identified in critical grains undergoing most of the plastic slips, and the fatigue lifetime is computed. A Basquin law [6] is adopted if a stabilized elastic cycle is reached (i.e elastic shakedown) leading to infinite or finite lifetime, while a Manson-Coffin criterion [7] is used if a stabilized plastic cycle is reached (i.e., plastic shakedown). If the cyclic loading does not result in a stabilized elasto-plastic cycle, the lifetime is estimated by the number of cycles needed to completely damage at least one grain (i.e., end of the softening regime leading to zero stress).
A large number of draws of random polycrystals under cyclic loading are computed along with resulting probabilistic SN curves, which opens interesting perspectives to upscale high cycle fatigue at the macroscopic scale while accounting for statistical descriptors of the microstructure as in [8,9].

References
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[9] D. Weisz-Patrault, S. Sakout, A. Ehrlacher, Acta Materialia, 2021, 210, 116805