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' model of grain growth with arbitrarily prescribed surface energies. The implicit representation of interfaces allows for seamless transitions through topological 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 concentration would decrease the energy of the system. In this study, very large-scale simulations confirm these previous studies. However, computations with a larger cutoff 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.

Microstructural and mechanical analysis on Cu–Sn intermetallic micro-joints under isothermal condition

“…Obviously, the low-misorientation grains boundaries are predominant within Cu 3 Sn IMC for the samples with dwell time of 50 mins and 70mins. Based on the analysis in reference [27], the misorientation distribution is primarily concentrated on small misorientation, so the grains tend to be clustered. Therefore, the Cu 3 Sn IMC grains have a great tendency to grow along the vertical direction on copper substrates with the increasing of dwell time.…”

Phase-Field Simulations of Large-Scale Microstructures by Integrated Parallel Algorithms

“…The brute force method is employed to simulate grain structure evolution and to recover the relations of neighboring grains proposed by Elsey et al and Kazaryan et al [5,13]. In the following, the growth rate distributions for the Read-Shockley surface energy model in two dimensions (2D) with regular 3-to 8-sided grains are computed.…”

An advanced level set approach to grain growth – Accounting for grain boundary anisotropy and finite triple junction mobility

“…Additionally, grain boundary motion can also be affected by their possibly distinct mobilities [8][9][10]. This interplay is reflected in the way microstructure evolution proceeds concomitantly with a change in the misorientation distribution function (MODF) [7]. Furthermore, as shown recently in several investigations [13,11,12,8,14], the properties of triple junctions (TJ) can decisively influence microstructure evolution especially in ultra-fine grained or nanocrystalline materials and lead normally to different grain growth kinetics [15,16].…”

“…They can be roughly separated into two classes based on their deterministic or probabilistic approach to represent microstructure evolution. Vertex models (VM) [13,17,20,[24][25][26][27], phase field models (PFM) [28][29][30][31] and level-set models (LSM) [4,5,7] are examples of deterministic algorithms, whereas in the class of probabilistic approaches the Monte Carlo Potts models (MCP) [18,19,32] are widely used.…”

“…This evolution is often described as a motion by mean curvature of the GBs [1][2][3][4][5][6][7]. In an anisotropic scenario, the evolution of the GB network obeys to different rules of energy dissipation.…”