Micromechanical modelling of the cyclic stress–strain behaviour of nickel polycrystals

A crystalline elastoplasticity model is proposed to describe the cyclic behaviour of face-centred cubic crystals. It is based on many experimental observations correlating the observed dislocation structures with the orientations of corresponding crystals. The model distinguishes between two families of crystals. The first family gathers crystals for which the tension–compression loading axis is located in the centre of the standard stereographic triangle. These crystals, in which bundle and/or slip band dislocation structures are usually observed, are subjected to single slip deformation. The second family gathers crystals in which labyrinths or wall dislocation structures develop. These crystals are subjected to multiple slip deformation. Crystalline plasticity parameters are adjusted using only the single crystal cyclic stress strain curves measured for one orientation of each of the two families. The relevance of the model is evaluated through finite elements calculations of the uniaxial cyclic deformation of texture-free nickel polycrystals at room temperature. The macroscopic predictions are in reasonable agreement with experimental data concerning both the cyclic stress–strain curve and the hysteresis loops provided either large grain sizes or intermediate to high plastic strains are considered. By construction, the modelling is unable to predict grain size effect observed at low plastic strain. The distributions of the mean grain plastic strains become narrower as the macroscopic plastic strain amplitude increases, which appears consistent with the large scattering in high-cycle fatigue lifetimes usually observed. On the contrary, the distributions of mean grain axial stresses get broader, in agreement with neutron and X-ray diffraction measurement values published in the literature. The influence of the material parameters is then discussed. Finally, the cumulative probability curves of the number of cycles to fatigue microcrack nucleation are deduced and discussed with respect to scattering mentioned previously.