  Crystalline materials exhibit an hysteresis behaviour when deformed
cyclically. The origins of this tension-compression asymmetry have been fully
understood only recently as being caused by an asymmetry in the junction
strength and a reduced mean free path of dislocations inherited from previous
deformation stage. Here, we investigate the saturation stress in fcc single-
and poly-crystals using a Crystal Plasticity framework derived from dislocation
dynamics simulations. In the absence of plastic localization and damage
mechanism, the single-crystal mechanical response eventually saturates. We show
that the cyclic saturation stress converges asymptotically to the monotonic
saturation stress as the cycle plastic increment increases, and this
convergence can be observed for some experimental conditions. The analysis of
the experimental literature suggests that the mechanisms controlling the
saturation in single crystals are the same controlling the cyclic response of
polycrystals with large grains. We propose also analytical and approximated
models to predict the saturation stress over the considered loading conditions.
The saturation stress appears as a fundamental property of dislocations,
explaining the consistency observed in the experimental literature. This work
provides a unified view on the monotonous and cyclic responses of fcc single
and poly-crystals, which may help in interpreting experimental data.
