Analysis of the energy balance of plastically deformed polycrystals in viscoplastic self-consistent modelling

The viscoplastic self-consistent (VPSC) approach established by Molinari et al. (Acta Metallurgica 35, 1987, 2983–2994) is widely employed for modelling the mechanical behaviour and texture development of polycrystalline materials. In this work, the differences between the macroscopic and grain-level plastic powers were analysed using the isotropic version of the VPSC modelling. It was found that the deviation is maximum at a specific value of the interaction parameter (α) of the interaction equation. This energy discrepancy is related to the inherent stress and strain heterogeneities in VPSC modelling, which is explored in the present work for isotropic textures in cubic (f.c.c., b. c.c.) and hexagonal close-packed (h.c.p.) crystal structures, for several deformation modes. A general observation is that when the stress and strain heterogeneities are expressed in scalar forms for individual grains, high stress levels correspond to low strains and vice-versa. An important consequence of the energy-imbalance is that the Taylor factor, which is frequently employed to scale the stress levels between the grain and macroscopic levels, is dependent on the energy-imbalance between the total strain-energy of the grains and the macroscopic energy.