Simulations of isothermal and thermomechanical fatigue of a polycrystal made out of austenitic stainless steels and relation to the Coffin-Manson law

Based on an experimental result of the literature showing that the crack remains in the grain of its initiation up to about 20% of the lifetime at low cycle fatigue of austenitic stainless steels, the lifetime of a polycrystal made out of these steels undergoing uniaxial isothermal or thermomechanical fatigue from 30 to 340 degrees C at constant total strain amplitude is calculated. The stresses and strains in the grains and polycrystal are determined in term of mean field with the Hill-Hutchinson model. Dipolar slip markings in the grains are predicted and assumed sites of initiation and propagation of the cracks calculated in terms of critical stress and of shear plastic strain, depth and grain boundary, respectively. There is agreement of the macroscopic stress and plastic strain, but at the residual stress, making the modelling not suitable for thermomechanical fatigue. For isothermal fatigue, the lifetime is in agreement. The lifetime - plastic strain power relationships are addressed to the Coffin-Manson law assumed to derive from the kinetic equation of the crack in a dimensional approach. The calculated constants of the power relationship of five austenitic steels of the literature are in qualitative agreement with those measured of the law. The relationships between the constants of the power relationship, law and kinetic equation are determined. The results and modelling are discussed.