Multiscale modelling of hardening in BCC crystal plasticity

Abstract

: 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.

Stochastic simulation of dislocation glide in tantalum and Ta-based alloys

“…Such a description replaces the true kink dynamics of a dislocation with a mean field measure of the average mobility of a dislocation line. Ortiz and co-workers (Cuitino and Ortiz, 1993;Ortiz, 1999;Stainier et al, 2003) performed studies of crystal plasticity using phase field methods to define a dislocation loop and employing universality classes to determine the onset of yielding.…”

Dislocation-dynamics based crystal plasticity law for the low- and high-temperature deformation regimes of bcc crystal

“…Stainier et al [14] proposed a probability density of obstacles along the Burgers vector direction: pðlÞ ¼ ffiffiffiffiffiffiffi ffi q s obs p expðÀpq s obs l 2 Þ. The average obstacle spacing obtained with this distribution is:…”

“…This is why specific CLs have been proposed for hcp [12,13] and bcc [14,15] structures. However, the full complexity of the observed plastic properties has not really been addressed.…”

Shear pipe effects and dynamic shear-strain localization in martensitic steels

“…The martensitic phase will be represented as (body-centered tetragonal (bct)/bcc) with 24 potential slip systems with {1 1 0} and {1 1 2} slip planes of for easy and pencil glide, and slip directions of h1 1 1i (e.g. [29,30]). …”