A revisited generalized self-consistent polycrystal model following an incremental small strain formulation and including grain-size distribution effect

A generalized self-consistent approach, recently proposed by Jiang and Weng (2004) [B. Jiang, G.J. Weng, A generalized self-consistent polycrystal model for the yield strength of Nanocrystalline materials, Journal of the Mechanics and Physics of Solids 52 (2004a) 1125–1149; B. Jiang, G.J. Weng, A theory of compressive yield strength of nano-grained ceramics, International Journal of Plasticity 20 (2004b) 2007-2056.] for investigating the so-called “breakdown” of the Hall–Petch law in the case of nanocrystalline (NC) materials, is revisited and reformulated following an incremental small strain scheme. The NC material is modelled as a composite material that takes each oriented grain and its immediate grain boundary to form a pair, which in turn is embedded in the infinite effective medium with a property representing the average orientation of all these pairs. The plastic deformation of the inclusion phase takes into account the dislocation glide mechanism whereas boundary phase is modelled as an amorphous material. As an application, the model’s parameters are identified under an optimization code with respect to data stated from pure copper submitted to tensile load. The aggregate is composed of spherical randomly distributed grains with a grain-size distribution following a log-normal statistical function.