Mesoscale cyclic crystal plasticity with dislocation substructures

Abstract

Constitutive formulations have increasingly focused on physically-based approaches that are less phenomenological and incorporate information from multiple scales. Most dislocation-based plasticity approaches reflect many-body dislocation physics without considering the length scales introduced by the self-organization of dislocations into mesoscale structures. These structures promote internal stresses or back stresses that are heterogeneous and long-range in nature and play a critical intermediary role in distinguishing the stress at micro-and nano-scales under cyclic loading. We present a framework that explicitly incorporates length-scales and evolution laws associated with mesoscale dislocation substructures such as cells and persistent slip bands (PSBs) in metallic materials under cyclic loading. A physically-based formulation for the back stress based on the Eshelby inclusion formalism is introduced that explicitly depends on morphology of mesoscale dislocation structures. The approach employs material parameters that can be measured or computed at lower length scales to contrast the response of models and experiments for multiple single crystals orientation and polycrystals for a wide range of strains.

A rationale for modeling hydrogen effects on plastic deformation across scales in FCC metals

“…Hence, the approach introduced earlier by Castelluccio and McDowell (2017) is followed, in which the flow rule specifies the shearing rate of the 12 slip systems in an FCC crystal according to the parametrization proposed by Kocks et al, 1975 , i.e.,…”

“…The back stress evolution is based on an Eshelby mean field approach that incorporates dislocation substructure effects (Castelluccio and McDowell, 2017),…”

“…We proceed with the hypothesis that hydrogen affects mostly the behavior of dislocations at the atomistic level with negligible effects on the mesoscale structure. Therefore, our simulations will consider precisely the same mesoscale attributes as those in Castelluccio and McDowell, 2017, and we will assume that the role of hydrogen is only to affect parameters associated with atomic scale unit processes. A fully hydrogen-dependent crystal plasticity model would require atomistic parametrizations that depend on the local concentration of hydrogen and vacancies.…”

“…Mesoscale structures are determined based on the plastic shear ranges per cycle at the slip system level. Further details about meshes, time scale decoupling, and model implementation may be found in Castelluccio and McDowell, (2017).…”

“…following the scheme proposed byCastelluccio and McDowell, 2017. Thus, the mean advance distance is determined by identifying the appropriate dislocation mesoscale substructures.…”