A non-local crystal plasticity constitutive model for hexagonal close-packed polycrystals

Abstract

A strain gradient crystal plasticity finite element model is developed to study the evolution of internal and localized elastic strains in hexagonal close-packed polycrystals. The results of the model are firstly compared to the previously published data for a series of in-situ neutron diffraction experiments conducted on α-zirconium specimens. The development of internal lattice strains is studied first without considering the possible effects of grain morphologies and locations. This is followed by importing the “as-measured” grain maps into the model, and investigating the development of localized lattice rotation fields, geometrically necessary dislocation densities, and statistically stored dislocation densities in the vicinity of twins. The numerical results are compared to those measured for a deformed α-zirconium specimen using high angular resolution electron back scatter diffraction technique. To understand the benefits of using non-local formulation, numerical results are further compared to those from a conventional crystal plasticity model. It is shown that while the calculated lattice strains and lattice rotations from both models are in agreement with the measured ones, the non-local model provides a better estimation of localized stresses in the regions with a sharp strain gradient. This difference is more pronounced in the vicinity of twins, where the calculated stresses and geometrically necessary dislocation densities by the non-local model are in better agreement with the measurements.