When a sample is cyclically loaded under a mean stress or strain, incremental strain ratcheting or mean stress relaxation phenomena are usually observed. Experiments show that for metallic materials there is generally no full mean stress relaxation as well as saturation of macroscopic strain ratcheting. In contrast, most macroscopic constitutive models produce both quantities in excess, and complex sets of additional internal variables must be introduced to improve the modeling. Little attention has been paid to model such phenomena using polycrystal aggregates especially going up to the regime of cyclic mechanical stability. In this work based on an elementary crystal plasticity model for FCC crystals and large scale finite element, it is be shown that the interaction between different grains is sufficient to cater for such complex phenomena. Light is shed on how different regions of the polycrystal accommodate each other and how the classical definition of constant rate strain ratcheting or a zero mean stress is nearly impossible to apply to a polycrystalline aggregate. In addition, it is shown that even if a macroscopic stable hysteresis stress strain loop is observed, ratcheting phenomena can still be observed at the local scale. The distributions of different constitutive quantities within a polycrystal are also analyzed which gives a new insight into what is happening inside a polycrystal in terms of stress and strain redistribution. In particular, the existence of evolving bimodal distributions of stress and accumulated plastic strain is evidenced and related to the occurrence of plastic shakedown and incomplete mean stress relaxation. Two numerical criteria to detect strain ratcheting are finally proposed and discussed. Kang et al., 2010). Mean stress in this article is defined as (Σ max + Σ min )/2 where Σ max and Σ min are the 15 maximum and minimum applied stresses in a cyclically loaded component. The stress amplitude is defined as Σ max −Σ min /2. With regards to asymetric strain controlled cyclic loadings, it is also known that under a given stress amplitude, increasing the mean stress, or increasing the applied mean stress under constant amplitude, both increase the rate of ratcheting (Goodman, 1984). On the other hand, experimental observations indicate levels of mean stress for which there is very low ratcheting and the mechanical state of the material converges 20 towards plastic shakedown (Pellissier-Tanon et al., 1982). Similarly, for asymmetric strain controlled loading conditions, a cyclic mean stress is observed, and several experimental studies (Wehner and Fatemi, 1991;Nikulin et al., 2019;Prithivirajan and Sangid, 2018) have deciphered the corresponding physical mechanisms. These observations show that for a given positive mean strain, and a low strain amplitude, the mean stress does not completely relax to zero. Also, increasing the strain amplitude leads to a nonlinear decrease of the 25

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