Multiscale Modelling of Hardening in BCC Crystal Plasticity

The mechanical behavior of polycrystalline metals can be successfully modeled by macroscopic theories, such as Von Mises plasticity. On the other hand, numerous studies can be performed on the atomic scale, either by atomistic or dislocation dynamics models. The proposed model attempts to bridge those two scales by deriving constitutive relations between slip strains, dislocation densities and resolved shear stresses on crystallographic planes, from mechanisms of deformation playing at the level of the dislocation line. The resulting "mesoscopic" hardening relations are controlled by dislocation self energies and junctions strengths. Temperature and strain rate dependence result from the presence of thermally activated mechanisms such as Peierls barriers or pair annihilation by cross slip. A set of material parameters is identified for Tantalum by fitting the numerical stress strain curves from these tests with experimental results gathered in the literature. These parameters prove to be in very good agreement with the values which can be derived from molecular dynamics computations