Multi-phase-field modeling of grain growth in polycrystalline titanium under magnetic field and elastic strain

A two-dimensional constitutive model was developed to simulate grain boundary motion in polycrystalline titanium exposed simultaneously to magnetic field and elastic strain based on the thermodynamic laws. The multi-scale coupled finite element and multi-phase-field simulations were used to investigate the simultaneous effects of the driving forces arising from the magnetic field and elastic strain energy on microstructure evolution of titanium bicrystalline and polycrystalline samples. The multi-phase-field approach was employed to implement the kinetic relations of grain boundary migration at the mesoscale level. On the other hand, the equilibrium equations were implemented on a macroscale level by the finite element method. Based on the simulation results, the magnetically induced driving force overrides the elastic strain driving force and causes texture evolution toward orientations that contain less magnetic stored energy when the microstructure is exposed to a magnetic field of sufficient strength. Additionally, applying an elastic strain before annealing reduces the time required for magnetic field annealing by accelerating the microstructure evolution. The mean grain size and desired texture grow rapidly when the magnetic field strength and elastic strain are simultaneously increased.