Accuracy Evaluation of Phase-field Models for Grain Growth Simulation with Anisotropic Grain Boundary Properties

Abstract

The phase-field method has been widely employed recently for simulating grain growth. Phase-field grain growth models are classified into two types according to their conservation constraints for phase-field variables: the multi-phase-field model and the continuum-field model. In addition, within the multi-phase-field model framework, three models with different formulations exist. These models are reported to accurately simulate grain growth under conditions of isotropic or weakly anisotropic grain boundary energy and mobility. However, for cases of strongly anisotropic grain boundary properties, the accuracy of these models has not yet been examined in detail. In this study, using the continuum-field model and three different multi-phase-field models, systematic grain growth simulations with anisotropic grain boundary energies and mobilities are performed. Through the detailed investigation of the accuracy of the simulated results, the suitability of each model for anisotropic grain growth simulations is revealed. Furthermore, based on the higher-order terms, accuracy improvement of the phase-field models is attempted.

Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth

“…The level of anisotropy defined here is high ( ), and this order of value has also been discussed in the literature [ 26 , 30 , 51 ] and remains necessary to discuss realistic polycrystal aggregates (coherent twin energy, for example). In Figure 10 , the effect of the anisotropy level ( value) on the top dihedral angle and the triple junction velocity is illustrated.…”

“…Hence, the models have evolved in order to reproduce more complex microstructures or local heterogeneities, such as twin boundaries. Heterogeneous models were proposed, in which each boundary has its own energy and mobility [10,18,19,[24][25][26][27][28][29][30][31]. For instance, every grain could be related with an orientation, thus the mobility and energy can be computed in terms of the disorientation [7,19], but the mis-orientation axis and inclination dependence are frequently not taken into account.…”

A novel level-set finite element formulation for grain growth with heterogeneous grain boundary energies

“…where G is a (2, 0)-tensor field of C whose only component G θθ ∈ R is actually a constant in this chart. As such, using equations (26) and (21)…”

“…While being able to reproduce mean value evolutions, such as mean grain size or even grain size distributions, rather efficiently, local heterogeneities in microstructures, such as the twin boundary, can not be modeled correctly [4,5,6,7,8]. Heterogeneous models may employ homogenized intrinsic properties along each grain boundary but differentiate different boundaries between each other [18,19,20,21,22,23,24,25,26,27,28]. As such, in a polycrystalline setting, the misorientation dependence of boundary properties can be modeled by these methods but not the inclination dependence.…”

Comparative study and limits of different level-set formulations for the modeling of anisotropic grain growth

“…Hence, the models have evolved in order to reproduce more complex microstructures or local heterogeneities, such as twin boundaries. Heterogeneous models were proposed, in which each boundary has its own energy and mobility [23,24,10,25,26,27,28,29,17,18,30]. For instance, every grain could be related with an orientation, thus the mobility and energy can be computed in terms of the disorientation [7,18] but the misorientation axis and inclination dependence are frequently not taken into account.…”