Lattice Boltzmann Models And Simulations For The Grain Growth In Polycrystalline Systems

Polycrystalline materials are widely used in engineering practices and their mechanical properties are strongly affected by their microstructure, such as the average grain size and the grain size distribution. In recent years, many studies have shown that when the average grain size is reduced to a very small scale, the polycrystalline materials will get better physical and mechanical performance. For example, nanocrystalline metal materials show higher strength and hardness than their corresponding coarse grained materials. Therefore, in the process of manufacturing advanced nanomaterials, it is of great importance to fully understand the grain growth behaviors for controlling material microstructures.Over the past few decades, a variety of theoretical models have been proposed to predict the grain growth behavior. However, these theoretical models can only give the time dependence of the average grain size and some simple microstructural evolution rules in polycrystalline materials. These models are generally too simple to involve the complex topologies, grain boundary interactions and microstructural evolutions during real grain growth process. Recently, computer simulations become indispensable in exploring the details of grain growth and microstructural evolutions. Simulation models for this purpose include the Potts model, the vertex model, the phase field model, etc. However, these models still have some shortcomings to predict the complicated grain growth. For example, the Potts model has difficulties in scaling the Monte Carlo time to the physical time, the vertex model is very difficult to extend from two to three dimensions and the phase field model has difficulties to deal with the coupling problem of grain growth with other physical fields. Recently, lattice Boltzmann models have been proposed and drawn much attention due to their clear physical concept, ease for implementation, parallel computation and handling of complex boundary conditions. The lattice Boltzmann method shows great potentials to model the grain growth. However, this method has only been applied to simulate the dendritic growth problems such as dendritic growth of a crystal into an undercooled melt and the dendritic growth in a forced melt convection. This method has been rarely applied to model the grain growth behavior in single-and multi- phase polycrystalline systems.In the present work, lattice Boltzmann models have been proposed for the computer simulations of curvature-driven grain growth behaviors, the grain growth in the two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models. Numerical results show that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The lattice Boltzmann method becomes a promising candidate to model the grain growth behavior in single-and multiphase systems involving heat transfer and melt convection, and provide effective tools to guide the experiments such as laser selective melting and selective laser sintering. Moreover, the proposed models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.