Physically-based modeling of the cyclic macroscopic behaviour of metals

Grain size seems to have only a minor influence on the cyclic strain strain curves (CSSCs) of metallic polycrystals of medium to high stacking fault energy (SFE). That is why many authors tried to deduce the macroscopic CSSCs curves from the single crystals ones. Either crystals oriented for single slip or crystals oriented for multiple slip could be considered. In addition, a scale transition law should be used (from the grain scale to the macroscopic scale). Authors generally used either the Sachs rule (homogeneous single slip) or the Taylor one (homogeneous plastic strain, multiple slip). But the predicted macroscopic CSSCs do not generally agree with the experimental data for metals and alloys, presenting various SFE values. In order to avoid the choice of a particular scale transition rule, many finite element (FE) computations have been carried out using meshes of polycrystals including more than one hundred grains without texture. This allows the study of the influence of the crystalline constitutive laws on the macroscopic CSSCs. Activation of a secondary slip system in grains oriented for single slip is either allowed or hindered (slip planarity), which affects strongly the macroscopic CSSCs. The more planar the slip, the higher the predicted macroscopic stress amplitudes. If grains oriented for single slip obey slip planarity and two crystalline CSSCs are used (one for single slip grains and one for multiple slip grains), then the predicted macroscopic CSSCs agree well with experimental data provided the SFE is not too low (316L, copper, nickel, aluminium). Finally, the incremental self-consistent Hill-Hutchinson homogeneization model is used for predicting CSS curves and partially validated with respect to the curves computed by the FE method.