Phase field modeling of stressed grain growth: Effect of inclination and misorientation dependence of grain boundary energy

The effect of anisotropic grain boundary energy on the kinetics of stressed grain growth is investigated by two-dimensional phase field simulations. The simulations are performed for a two-dimensional representative volume element of polycrystalline copper with elastic cubic symmetry under both uniaxial elongation and shear loading with elastic strains in the order of a few thousandths. The Read-Shockley relation for the misorientation–dependence and the cubic symmetry for the inclination–dependence of grain boundary energy are assumed. The simulation results have generally shown that the misorientation–dependent anisotropy, compared to the inclination–dependent anisotropy, significantly affects the evolution of microstructure and texture during stressed grain growth. Particularly, the misorientation–dependent anisotropy of grain boundary energy results in (i) the elongated morphology of grains in the evolved microstructure; (ii) the aggregation of grains with similar orientations in the evolved microstructure; (iii) the strengthening of lower–misorientation angle grain boundary segments; and hence (iv) decelerating the overall rate of stressed grain growth and texture evolution and (v) decelerating stress relaxation under constant–strain loading. These results are based on the assumption that the isotropic grain boundary energy is equal to the high angle grain boundary energy of the misorientation–dependent grain boundary energy and the inclination–dependent grain boundary energy varies sinusoidally around the isotropic grain boundary energy.