A coupled crystal plasticity - phase field formulation to describe microstructural evolution in polycrystalline aggregates during recrystallisation

During thermo-mechanical processing, the strain energy stored in the microstucture of an FCC polycrystalline aggregate is generally reduced by physical mechanisms which rely, at least partially, on mechanisms such as dislocation cell or grain boundary motion which occur during recovery, recrystallisation or grain growth. The aim of this work is to develop a constitutive framework capable of describing the microstructural evolution driven by grain boundary curvature and/or stored energy during recrystallisation and grain growth. As recrystallisation processes depend primarily on the nature of the microstructural state, an accurate prediction of such phenomena requires that the microstructural heterogeneities which develop just before recrystallisation be properly described. These heterogeneities may consist of structures such as dislocation cells and pile-ups, shear and twin bands. The microstructural characteristics present in a polycrystal aggregate just before the onset of thermal recrystallisation are first reproduced numerically. The constitutive behaviour of each grain in the aggregate is described using a dislocation mechanics-based crystallographic formulation which accounts for non-local effects through the introduction of geometrically necessary dislocations. The single crystal model is implemented into the finite element method using a finite-strain kinematics framework. Different measures of stored internal strain energy are determined based on the dislocation density distribution in the aggregate. The minimisation of stored and grain boundary energies provides the driving force for grain boundary motion. To describe the interface motion, a phase field model taking into account the stored energy distribution is formulated and implemented within a continuum mechanics framework. A weak coupling between the grain boundary kinematics and the crystal plasticity model is made through the dislocation densities and the grain orientations. Furthermore, the parameters of the free energy are calibrated based on published Read-Shockley boundary energy data. To validate the proposed model, a polycrystalline aluminium aggregate is first cold deformed under plan strain conditions and then annealed. The predicted recrystallised material volume fraction evolution with respect to time was found to have the same dependence on deformation level and temperature as that reported in the literature. The implications of such findings for future developments are discussed.