Phase field modelling of grain boundary motion driven by curvature and stored energy gradients. Part I: theory and numerical implementation

Abstract

During thermo-mechanical processing, the strain energy stored in the microstucture of an FCC polycrystalline aggregate is generally reduced by physical phenomena controlled, at least partially, by mechanisms involving dislocation cell or grain boundary motion such as recovery, recrystallisation and grain growth. This work presents a novel coupled phase field-single crystal constitutive framework capable of describing the microstructural evolution driven by grain boundary curvature and/or stored energy during recrystallisation and grain growth. Thus, the minimisation of stored and grain boundary energies provides the driving force for grain boundary motion. To describe interface motion, a phase field model taking into account the stored energy distribution is formulated and implemented within a continuum mechanics framework. The single crystal constitutive behaviour is described using a dislocation mechanics-based crystallographic formulation. The coupling between the grain boundary kinematics and the crystal plasticity formulation is made through the dislocation densities and the grain orientations. Furthermore, the free energy parameters are calibrated from existing Read–Shockley boundary energy data and those describing grain boundary mobilities from published experimental data.

Keywords:

• phase field
• grain boundary
• recrystallisation
• stored energy
• crystal plasticity
• finite elements

Acknowledgements

This research was supported by the European Commission, project DIGIMAT (contract number NMP3-CT-2006-017105). This support is gratefully acknowledged.