Generalized phase-field model for computer simulation of grain growth in anisotropic systems

Abstract

We study the dynamics and morphology of grain growth with anisotropic energy and mobility of grain boundaries using a generalized phase field model. In contrast to previous studies, both inclination and misorientation of the boundaries are considered. The model is first validated against exact analytical solutions for the classical problem of an island grain embedded in an infinite matrix. It is found that grain boundary energy anisotropy has a much stronger effect on grain shape than that of mobility anisotropy. In a polycrystalline system with mobility anisotropy, we find that the system evolves in a non-self-similar manner and grain shape anisotropy develops. However, the average area of the grains grows linearly with time, as in an isotropic system. The effect of anisotropy in energy and mobility of grain boundaries on the kinetics of grain growth and morphological evolution is a relatively unexplored problem. Studies have shown that energy and mobility of a grain boundary depend on the misorientation between the two crystals and the inclination of the grain boundary [1]. In addition, phenomena as segregation of impurities [2] or presence of a liquid phase [3] at the grain boundaries may also result in anisotropy of both energy and mobility.Although most computer simulations of grain growth have been performed for isotropic cases [4][5][6][7][8], anisotropy in grain boundary properties has been introduced in a number of simulations, mainly by the Monte Carlo method [9][10][11][12][13][14][15]. For example in the study of texture development during grain growth [9][10][11], grains are divided into two types and the contacts between them form three kinds of grain boundaries of either small or large misorientations. To take into account the full range of grain orientations, more general approaches have been proposed [12][13][14][15]. However, all these models consider either misorientation or inclination dependence of grain boundary properties. A simple dislocation model of the grain boundary shows that both energy and mobility of the boundary could depend strongly on both misorientation and inclination [16]. Furthermore, in the models that deal with inclination dependence [14,15] only a few inclinations are considered and the use of only first neighbors for the calculation of boundary inclination results in an intrinsic energy and mobility anisotropy associated with the discrete lattice used in the simulations [17].In this paper, to study the kinetics and morphology of grain growth in anisotropic systems, we extend the phase field approach to take into account both inclination and misorientation dependence of grain boundary energy and mobility. The phase field method has been successfully applied for computer simulation of isotropic grain growth [7,8], phase transformations [18], and solidification [19]. In this model, the polycrystalline microstructure is described by a set of non-conserved order parameter fields (η 1 , η 2 , . . . , η p ), each representing grains of a given crystallographic orientation. Mic...

An integrated full-field model of concurrent plastic deformation and microstructure evolution: Application to 3D simulation of dynamic recrystallization in polycrystalline copper

“…In principle, GB energy and mobility should depend on the misorientation and inclination, which leads to grain growth in anisotropic systems and has been considered by previous PF models (Kazaryan et al, 2000;Suwa et al, 2007;Moelans et al, 2008a). Nevertheless, the experiment (Wusatowska-Sarnek et al, 2002) to be simulated and compared shows mostly equiaxed DRX grains, unlike what was predicted by PF grain growth in anisotropic system (Kazaryan et al, 2002); the essentially random texture found in the experiment (Wusatowska-Sarnek et al, 2002) also frees us from considering the high anisotropy in GB mobility that manifests only in highly textured polycrystals Suwa et al, 2007).…”

On the incorporation of cubic and hexagonal interfacial energy anisotropy in phase field models using higher order tensor terms

“…The origins of anisotropy could be energetic (such as anisotropies in interfacial, elastic or magnetic energies) and/or kinetic (such as anisotropies in the attachment kinetics). Hence, a large number of phase field models have been developed to account for these anisotropies: even though it is not possible to list all the phase field studies that deal with anisotropies within the purview of this article, the following listing is fairly representative: see, for interfacial anisotropy [6][7][8][9][10][11][12][13][14][15][16][17][18][19] ; for elastic anisotropy [20][21][22][23][24][25] , for magnetocrystalline anisotropy 26 , and, for anisotropy in attachment kinetics 27 . In a typical phase field model, the microstructure is described by order parameters and the thermodynamic quantities (free energy or entropy) are represented as functionals in these order parameters.…”

Microstructural Evolution Based on Fundamental Interfacial Properties

“…Recently, the diffuse-interface phase field model of grain growth has been generalized to account for anisotropy in grain boundary properties such as energy and mobility (Kazaryan, Wang et al 2000). The model allows for quantitative characterization of the kinetics and morphological evolution of grain growth with both inclination and misorientation dependence Bragard et al 2003).…”