A Cosserat crystal plasticity and phase field theory for grain boundary migration

Abstract

The microstructure evolution due to thermomechanical treatment of metals can largely be described by viscoplastic deformation, nucleation and grain growth. These processes take place over different length and time scales which present significant challenges when formulating simulation models. In particular, no overall unified field framework exists to model concurrent viscoplastic deformation and recrystallization and grain growth in metal polycrystals. In this work a thermodynamically consistent diffuse interface framework incorporating crystal viscoplasticity and grain boundary migration is elaborated.The Kobayashi-Warren-Carter (KWC) phase field model is extended to incorporate the full mechanical coupling with material and lattice rotations and evolution of dislocation densities. The Cosserat crystal plasticity theory is shown to be the appropriate framework to formulate the coupling between phase field and mechanics with proper distinction between bulk and grain boundary behaviour.

A Cosserat–phase-field theory of crystal plasticity and grain boundary migration at finite deformation

“…In [4], a coupled model for large deformation crystal plasticity was formulated inspired by the KWC approach. The approach is very similar to the one in [7] and the one proposed in this work. Instead of working with the torsion-curvature tensor of the Cosserat theory, the energy density in [4] contains corresponding contributions due to the full dislocation density tensor.…”

“…However, the proposed methodology represents rather a sequential algorithmic procedure and cannot be regarded as a unified field theory of viscoplastic deformation and GB kinematics. A fully coupled theory was recently proposed in [7] for small deformations, combining Cosserat crystal plasticity with a phase-field model due to [42,74]. The Kobayashi-Warren-Carter (KWC) phase-field approach considers the crystal orientation as a phase field with its own relaxational dynamics.…”

“…The main objective of the present work is, first, to extend the Cosserat-phase-field model proposed in [7] to the finite deformation framework and, second, to provide finite element simulation of dynamic recovery and GB migration, also not presented in the Ref. [7].…”

“…The main objective of the present work is, first, to extend the Cosserat-phase-field model proposed in [7] to the finite deformation framework and, second, to provide finite element simulation of dynamic recovery and GB migration, also not presented in the Ref. [7]. The free energy density function of the model contains contributions from geometrically necessary dislocations in the form of the torsion-curvature tensor and comprises terms coming from the KWC model.…”

Mathematical analysis of a solution method for finite-strain holonomic plasticity of Cosserat materials

“…(cf. [13,14,15] for an overview). Particularly interesting is the Cosserat modeling of chiral honeycomb lattices with bending-dominated behavior whose mechanical response cannot be accurately described by classical continuum theories due to large size effects, [3].…”