Modeling of grain growth under fully anisotropic grain boundary energy

Abstract

A level set formulation is proposed that can accurately trace the evolution of grain boundary networks in a polycrystalline aggregate while respecting grain boundary energy anisotropy. Commonly adopted simplifying assumptions related to the grain boundary energy variation with local microstructure conditions are avoided and the grain boundary energy dependence on both crystallographic misorientation and boundary plane inclination is respected. Key components in the formulation are discussed, such as an efficient and simple scheme for unequivocal identification of crystal neighbors at grain boundary junctions where an arbitrary number of crystals intersect. The method works without modifications in both two and three dimensions and is shown to provide grain boundary junction configurations that comply with classical equilibrium conditions as well as topological transforms of the grain boundary network that agree with theoretical predictions. Full grain boundary energy anisotropy is considered by adopting a parametrization of the five-parameter grain boundary energy space, as previously proposed by Bulatov et al 2014 Acta Mater. 65 161–75. Examples are provided to illustrate the relevance of the level set framework for simulations of microstructure evolution in polycrystalline solids. For example, it is clearly shown that the proposed modeling framework provides a grain boundary inclination dependence of the grain boundary energy that cannot be neglected in mesoscale simulations of grain growth.

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

“…The Iso, Het, and HetGrad are not presented here because they evolve in the wrong direction (the expected movement should reduce the length of the interface between grain and , depicted in yellow). The evolution of the interfaces shown in Figure 21 presents similar tendencies to the cases presented by Garcke in [ 75 ] and Hallberg in [ 34 ]. If both evolutions (without or with the inclination dependence) seem to promote similar triple junction evolution, the Aniso-GB5DOF case exhibits a much faster evolution, which illustrates the importance of accounting for the inclination in the reduced mobility description.…”

“…These special GBs play an important role on polycrystalline microstructures, and their modeling is not frequently discussed at the mesoscopic scale. The next example was firstly proposed by Brown and Ghoniem in [76] and also reproduced at the mesoscopic scale in [34]. It consists of two grains composed of two coherent twin boundaries (CTB) and one incoherent boundary (ICB).…”

“…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. Finally, general frameworks in which the five parameters, mis-orientation, and inclination are discussed have been proposed, and these models could be categorized as fully anisotropic [ 32 , 33 , 34 ].…”

“…For instance, in [ 7 , 12 , 29 , 31 , 35 ], heterogeneous GB energy and a constant GB mobility to model polycrystal evolution during GG are considered, and the models are categorized as anisotropic even if it is assumed that the GB energy does not depend on the GB normal direction and the GB mobility is not heterogeneous. In [ 34 ], the proposed LS formulation in the context of regular grids includes the effect of anisotropic GB energy into the driving force term ( ) using both the effect of the mis-orientation and the inclination in a GB energy gradient. However, the GB energy dependence on the normal direction is defined without inquiring if additional torque terms in the solved equations are negligible or not.…”

Survey of Modeling and Simulation Techniques for Advanced Manufacturing Technologies Volume I – Predicting Initial Microstructures

“…Other methods of modeling recrystallization include vertex or front tracking methods [337], and level set models [338]- [341]. The front tracking method has the advantage of including a physical time scale [342] but has been restricted mostly to two-dimensional investigations due to numerical and computational complexity.…”