Influence of anisotropic grain boundary properties on the evolution of grain boundary character distribution during grain growth—a 2D level set study

Abstract

The present study elaborates on a 2D level set model of polycrystal microstructures that was recently established by adding the influence of anisotropic grain boundary energy and mobility on microstructure evolution. The new model is used to trace the evolution of grain boundary character distribution during grain growth. The employed level set formulation conveniently allows the grain boundary characteristics to be quantified in terms of coincidence site lattice (CSL) type per unit of grain boundary length, providing a measure of the distribution of such boundaries. In the model, both the mobility and energy of the grain boundaries are allowed to vary with misorientation. In addition, the influence of initial polycrystal texture is studied by comparing results obtained from a polycrystal with random initial texture against results from a polycrystal that initially has a cube texture. It is shown that the proposed level set formulation can readily incorporate anisotropic grain boundary properties and the simulation results further show that anisotropic grain boundary properties only have a minor influence on the evolution of CSL boundary distribution during grain growth. As anisotropic boundary properties are considered, the most prominent changes in the CSL distributions are an increase of general low-angle Σ1 boundaries as well as a more stable presence of Σ3 boundaries. The observations also hold for the case of an initially cube-textured polycrystal. The presence of this kind of texture has little influence over the evolution of the CSL distribution. Although considering the anisotropy of grain boundary properties, grain growth alone does not seem to be sufficient to promote any significantly increased overall presence of CSL boundaries.

Grain Growth in Large-Scale Molecular Dynamics Simulation: Linkage between Atomic Configuration and von Neumann-Mullins Relation

“…For example, Monte Carlo (MD) simulations based on the Potts model 5) are often used to study the grain growth kinetics. [6][7][8][9][10] Moreover, cellular automata (CA), [11][12][13][14] front tracking method, [15][16][17] level-set model, 18) vertex model, 19) surface-evolver model, 20) phasefield model [21][22][23][24][25][26][27] have been widely employed to discuss the grain growth kinetics from the mesoscale point of view. Especially, the multi-phase-field simulation 28,29) is a powerful tool to investigate microstructure evolution since it is not necessary to explicitly track the position of grain boundaries in the polycrystalline microstructure.…”

A kinetic approach to modeling general-texture evolution in two-dimensional polycrystalline grain growth

“…where r 1 , r 2 , r 3 are independent random numbers generated according to the uniform distribution on the interval [0, 1]; see, for instance, [13,14,23,24].…”

“…In this situation, the further reduction in the interface energy can be reached only by decreasing the total measure of grain boundaries; see, for instance, [8,9]. Important statistical descriptors of grain boundary networks are misorientation distribution functions (often referred to as grain boundary character distributions), which show relative measures of interfaces with given misorientation parameters; see [1,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In order to investigate how the structure and time evolution of misorientation distribution functions depend on the grain boundary energy anisotropy and set of laws governing the dynamics at a microscopic scale, it is possible to conduct numerical experiments via well-known large-scale simulation approaches.…”

“…In order to investigate how the structure and time evolution of misorientation distribution functions depend on the grain boundary energy anisotropy and set of laws governing the dynamics at a microscopic scale, it is possible to conduct numerical experiments via well-known large-scale simulation approaches. In particular, these are Monte Carlo methods [10][11][12][13][14], phase field models [12,17,18,25], curvature-driven grain growth models [19][20][21], level set methods [23,24], vertex models [26][27][28], etc. An alternative way is to develop kinetic models which are based on differential equations and, therefore, can be more computationally efficient, while focusing only on a restricted amount of essential characteristics.…”

“…The disorientation of a grain boundary is defined as the smallest rotation angle from all the corresponding symmetrically equivalent misorientations. Although the misorientation of a grain boundary is characterized by three degrees of freedom, such reduction to disorientations is a commonly adopted and reasonable technique; see, for instance, [10,13,14,23,24]. Besides, the two additional variables specifying the orientation of a grain boundary plane are not included in our two-dimensional model, since they are related mainly to three-dimensional grain growth (where a full crystallographic characterization of a grain boundary requires not three but already five degrees of freedom); see [9].…”