Phase-field modeling of magnetic field-induced grain growth in polycrystalline metals

A constitutive model for diffuse interface description of magnetic field-induced grain boundary migration in polycrystalline metals is developed based on the laws of thermodynamics. Within this phase field modeling framework, simultaneous minimization of the total grain boundary energy and the stored magnetic energy within grains provides the driving force for grain growth in a polycrystal material exposure to a magnetic field. Using the available experimental data, phase field simulations of magnetic field induced grain growth in bicrystalline zinc and polycrystalline titanium with two-dimensional columnar microstructure are performed and the model is validated by demonstrating a qualitative and quantitative match with experimental data. Using the validated constitutive model, the effects of magnetic field intensity and direction on evolution of microstructure and polycrystalline texture in titanium are investigated. Quantitative simulation results show that under certain magnetic field directions and sufficient magnetic field intensity, the magnetic energy minimizing driving force can overcome the curvature driving force and cause texture evolution towards less magnetic energy grain orientations during annealing. However, magnetic fields with insufficient intensity or improper direction have negligible effect on grain coarsening by nearly normal grain growth. The desired magnetic field direction and intensity are quantitatively presented for cold-rolled and annealed sheet titanium samples.