Simulations of anisotropic grain growth: Efficient algorithms and misorientation distributions

Abstract

An accurate and efficient algorithm, closely related to the level set method, is presented for the simulation of Mullins’s model of grain growth with arbitrarily prescribed surface energies. The implicit representation of interfaces allows for seamless transitions through topo-logical changes. Well-resolved large-scale simulations are presented, beginning with over 650,000 grains in two dimensions and 64,000 grains in three dimensions. The evolution of the misorientation distribution function (MDF) is computed, starting from random and fiber crystallographic textures with Read–Shockley surface energies. Prior work had established that with random texture the MDF shows little change as the grain network coarsened whereas with fiber texture the MDF concentrates near zero misorientation. The lack of concentration about zero of the MDF in the random texture case has not been satisfactorily explained previously since this concen-tration would decrease the energy of the system. In this study, very-large-scale simulations confirm these previous studies. However, com-putations with a larger cut-off for the Read–Shockley energies and an affine surface energy show a greater tendency for the MDF to concentrate near small misorientations. This suggests that the reason the previous studies had observed little change in the MDF is kinetic in nature. In addition, patterns of similarly oriented grains are observed to form as the MDF concentrates