Simulation Of Normal Grain Growth Research Articles

Effect of Different Initial Structures on the Simulation of Microstructure Evolution During Normal Grain Growth via Phase-Field Modeling

The effect of different initial structures on the simulation of microstructure evolution during normal grain growth was comparatively studied by using a two-dimensional phase-field model. Three methods, standard Voronoi construction, weighted Voronoi construction, and hand drawing, were used to generate the initial structures. For the hand-drawn initial structure, different boundary conditions, including periodic and gradient boundary conditions, were also applied. The phase-field simulation of normal grain growth in the succinonitrile–coumarin152 system was chosen as the benchmark, and compared with the experimental microstructure evolution. The phase-field simulated results generally conformed to Hillert’s theory, Von Neumann–Mullins law, and the experimental results. Different initial structures with similar initial grain size distribution showed similar grain size evolution. The simulation results for the “experimental” initial structure constructed by hand drawing showed best agreement with the experimental results during the early stage of grain growth process. With the increased time, the accuracy of simulation appeared strongly dependent on the grain numbers, and thus the gradient boundary condition is more suitable for long-time grain growth simulation than the periodic boundary condition. Overall, the combination of phase-field simulation and “experimental” initial microstructures allows the study of the grain growth in arbitrary polycrystalline materials, as demonstrated here for comprehensive study of austenite grain growth in two commercial high-strength steels.

Lattice Boltzmann models for the grain growth in polycrystalline systems

In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in 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 based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found 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 grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these 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.

Extreme value analysis of tail departure from log-normality in experimental and simulated grain size distributions

Grain size data were taken from four three- and two-dimensional microstructures, including simulated grain growth, thin film and superalloy data sets. Probability plots revealed approximately log-normal distributions for experimental grain size data sets, but with systematic differences in the upper tails. A simulated grain size data set obtained from Potts model growth exhibited strong deviation from log-normality. A peaks-over-threshold analysis was applied to quantify the differences in the upper tails. Potts model simulation of normal grain growth shows the shortest tail, whereas the thin film data showed the longest tail (i.e. closest to log-normal), with an intermediate tail shape in the superalloy.

Large-scale simulation of normal grain growth via diffusion-generated motion

Diffusion-generated motion is used to perform a very large-scale simulation of normal grain growth in three dimensions with high accuracy. The method is based on the diffusion of signed distance functions and shares similarities with level-set methods. The Herring-angle condition at junctions and topological transitions are naturally captured with this formulation. This approach offers significant advantages over existing numerical methods and allows for accurate computations on scales not previously possible. A fully resolved simulation of normal grain growth, initially containing over 130 000 grains in three dimensions, is presented and analysed. It is shown that the average grain radius grows as the square root of time and the grain-size distribution is self-similar. Good agreement with other theoretical predictions, experimental results and simulation results via other techniques is also demonstrated.

Phase-field simulations of partial melts in geological materials

A diffuse interface description based on a multi-phase-field model for geological grain microstructures is introduced, especially useful in the treatment of partially molten structures. Each grain as well as different phases are represented by individual non-conserved order parameters, the phase fields φ α , which are defined on the complete simulation domain. The derivation of the model from a Ginzburg–Landau type free energy density functional is briefly shown and all occurring energy contributions are discussed. Also, the nondimensionalisation necessary to relate the simulation to real experiments and a brief overview of the numerical methods used in the simulations is given. To illustrate the applicability of the method to large grain systems a simulation of normal grain growth was carried out. The results on the dynamics of the process are in close agreement with theory. The extension of the phase-field model to incorporate phases with conserved volume is described next. This capacity is exploited for the liquid phase in a partially molten structure, where melt and a solid mineral phase are in equilibrium. Simulations with isolated melt inclusions within a grain structure in 2D and 3D are presented, resulting in the formation of the correct dihedral angles corresponding to the solid/solid and solid/liquid interface energies γ SS and γ SL . The case of complete wetting of the grain boundaries, if γ SL / γ SS < 0.5 is shown. Taking the structure of an analogue experiment as initial data, a simulation of a grain structure with a melt fraction of 3.6% and a dihedral angle of 10 ∘ were performed using the phase-field model. The comparison with a sharp interface front-tracking model for this case results in a highly comparable microstructure evolution.

Three-dimensional grain growth: Analytical approaches and computer simulations

A three-dimensional vertex model has been developed and applied to the simulation of normal grain growth. Several configurations, from single grains to polycrystals, were considered. The results were compared with the predictions of analytical models for the growth of grains with time. The models of Mullins, Hilgensfeldt, Glicksman–Rios, Cahn, and MacPherson–Srolovitz for the prediction of the volume rate of change of grains were used for this comparison. In all cases, the simulations show good agreement with the different considered models.

Model-based simulation of normal grain growth in a two-phase nanostructured system

To systematically study normal grain growth in a two-phase volume-conserved system, a modified Potts model is proposed, in which the driving forces for grain boundary migration are the interfacial energy between two phases and the boundary energy inside each phase. Model-based simulation results show that the grain growth kinetics follows a power law with a temperature-independent exponent and that the normalized grain size distribution is lognormal and time invariant. Also, a simple theoretical model is used to predict the potential microstructure in a two-phase system due to the competition between interfacial and grain boundary energies. A critical ratio (~2.6) of the grain boundary energy to the interfacial energy is found for a common two-phase system.

Scalable, continuous variable, cellular automaton model for grain growth during homogenisation of vacuum arc remelted Inconel* 718

A scalable, continuous variable, cellular automaton (CA) model for the quantitative simulation of normal grain growth is presented. The CA model is based on a discrete solution of the classical Turnbull rate equation for grain boundary motion on a mesoscopic scale. The domain is discretised using a regular cubic lattice considering the first and second nearest neighbourhoods. CA rules were usedto determine the state of each cellbased on the local driving force. The effects of both the boundary curvature and the misorientation of grains were incorporated. The driving force was used to determine the direction of the movement of each boundary cell, forming the basis of a continuous variable cell transition rule. The use of experimental grain boundary characteristics (e.g. energy and mobility) allows one to make predictions on industrially applicable spatial and temporal scales. The model was applied to quantitatively predict grain growth during the homogenisation heat treatment of vacuum arc remelted Inconel 718.

Computer simulation of normal grain growth in polycrystalline thin films

A modified Monte Carlo method is proposed to simulate the two-dimensional normal grain growth in polycrystalline thin films. With the newly modified method, not only the simulation efficiency is improved but also the simulated time exponent of grain growth attained n = 0.49 ± 0.01, which is very close to the theoretical value for steady grain growth n = 0.5. Simulation of the complete process of normal grain growth including the steady state is made possible by means of the present method. The grain size distribution in the simulated thin films was found to vary continuously and slowly with time, the gamma and the Hillert functions may be two of the expression forms during its transition, and the latter corresponds to quasi steady grain growth. The so called “self-similarity” of the grain size distribution during the normal grain growth in two-dimensions is also discussed according to the simulation results.

A vertex dynamics simulation of grain growth in two dimensions

Abstract A vertex model including real and virtual vertices is presented. Equations for the dynamics are derived and applied in their complete form. Details of the implementation in two dimensions are discussed. It is shown that the mobility and the energy of grain boundaries, and consequently the simulation time, are the usual real quantities. The model is then applied to the simulation of normal grain growth and compared with the Potts model and the Kawasaki et al. vertex models. The present model proved to be successful in reproducing classical laws related to static and dynamic features. In particular, it provides a value of the pre-factor constant in the law describing the evolution of the mean grain size against time.

Monte Carlo simulation of normal grain growth in 2- and 3-dimensions: the lattice-model-independent grain size distribution

The phenomenon of normal grain growth in pure single phase systems is modeled with the Monte Carlo technique and a series of simulations are performed in 2- and 3-dimensions. The results are compared with natural and experimental monomineralic rock samples. In these simulations various lattice models with different anisotropic features in grain boundary energy are examined in order to check the universality of the simulation results. The obtained microstructure varies with the artificial parameter T ′ in each lattice model, where T ′ means scaled temperature and controls thermal fluctuation on grain boundary motion. As T ′ (thermal fluctuation) increases, the boundary energy anisotropy characterizing each lattice model becomes less important for the evolution of the microstructure. As a result the difference in the grain size distribution among the lattice models, which is significantly large for low T ′, is reduced with increasing T ′. The distribution independent of both the lattice model and the dimension is obtained at sufficiently high T ′ and is very close to the normal distribution when carrying out the weighting procedure with a weight of the square of each grain radius. A comparison of the planar grain size distribution of the natural and experimental rock samples with the 3-D simulation results reveals that the simulations reproduce very well the distributions observed in the real rock samples. Although various factors such as the presence of secondary minerals and a fluid phase, which are not included in the simulation modeling, are generally considered to influence the real grain growth behavior, the good agreement of the distribution indicates that the overall grain growth behavior in real rocks may still be described by the simplified model used in the present simulations. Thus the grain size distribution obtained from the present simulations is possessed of the universal form characterizing real normal grain growth of which the driving force is essentially grain boundary energy reduction through grain boundary migration.

Real time-temperature models for Monte Carlo simulations of normal grain growth

Two different models for the simulation of normal grain growth in metals and alloys are presented. These models demonstrate the application of real time-temperature based Monte Carlo (MC) simulation to materials processing. A Grain Boundary Migration model coupled the MC simulation to a first principle grain boundary migration model. The results of this simulation were shown to correlate well with the experimental results for isothermal grain growth in zone refined tin. An Experimental Data Based model coupled the MC simulation with experimental grain growth data. The results from this simulation were shown to correlate well with the grain growth during continuous heating of a beta titanium alloy.

Simulation of normal grain growth by cellular automata

Prediction of microstructure evolution and properties of ultrafine-grained materials is one of the most significant problems in materials science. Cellular automata (CA) method is able for proper simulation of the microstructure evolution and can be used for evaluation of mechanical properties. The paper presents a new original application of cellular automata for modeling of grain refinement. CA take into account deformation, evolution of dislocation density and dislocation structures; and simulate microstructure evolution as grain refinement. Deformation of grains in polycrystalline materials depends on their crystallographic orientation, which is unique for every grain. It causes anisotropy of deformation in micro-scale. Joining CA with other methods (finite element, discrete element, crystal plasticity, etc.) improves accuracy of coupled phenomena modeling in micro- and macro-scale. Finite element method and crystal plasticity theory provide information for CA calculations. Grain refinement occurs in two stages: a creation of low-angle boundaries and their evolution into high-angle boundaries. Three CA models of low-angle boundaries creation were developed. They are described and discussed in the paper. Developed models can be used for study of processes of grain refinement, as well as can be a part of the system for modeling of microstructure evolution in the processes of solidification, hot and cold deformation and phase transformation. Examples presented in the paper are model application for processes with severe plastic deformation (SPD). Results of simulations of grain refinement during the accumulative roll-bonding (ARB) process and MAXStrain® technology are presented in the paper.

Simulation of Normal Grain Growth by the 3-D Statistical Model

Simulation of Normal Grain Growth by the 3-D Statistical Model

Monte Carlo simulation of normal grain growth by consideration of the diffusion character of the processes

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Computer simulation of normal grain growth in three dimensions

Abstract Computer modelling has been carried out to study normal grain growth in three dimensions. The approach consists of digitizing the microstructure by dividing the polycrystalline material into small volume elements and storing the spatial location and crystallographic orientation of each element. An energy is assigned between each element and its neighbours, such that neighbours having unlike orientations provide weaker bonding than neighbours of like orientations. The annealing treatment during which grain growth occurs is simulated using a Monte Carlo technique in which elements are selected at random and thermally activated transitions to other orientations are attempted. With time, the system evolves so as to reduce the total grain interface area. The microstructures produced are in good correspondence to observations of pure metals and ceramics which have undergone grain growth. Power-law kinetics ([Rbar] = ct n) are observed, with a growth exponent in three dimensions of n = 0·48 ±0·04 in the...

Short-range order in the arrangement of grains in two-dimensional polycrystals

Abstract Experimental results for two-dimensional grain growth are compared with the results obtained from computer-generated random threefold vertex networks with a fixed one-particle distribution function. A considerable discrepancy in the two-particle distributions implies some kind of short-range order. New results in the computer simulation of normal grain growth are reported, demonstrating a similar kind of ordering. A simple relation is suggested for the quantity m n, introduced by Aboav and the second moment of the one-particle distribution μ2

Computer simulation of normal grain growth

The present theories of normal grain growth do not give an adequate description of the process as they fail to take into account the effects of retarding force and of the texture of material. In this paper we suggest the statistical approach to the problem of grain growth that has been used to study the process in material without texture. The investigation was made by computer simulation. It was found that equation D ̄ m − D ̄ 0 m = At describes the growth kinetics only in a limited number of cases. In material with an increased initial range of grain sizes the grain growth is decelerated. The limiting grain size in sheets should be larger than double sheet thickness. If grain growth kinetics can be described by equation D ̄ m − D ̄ 0 m = At the value of exponent m can be found from the slope n(m = 1 n ) of the straight line in coordinates lg D ̄ − lg t . The right value of n can be obtained from D ̄ which correspond to the relation D ̄ ⩾ α D ̄ 0 . The magnitude of α varies from 4.5 to 1.8 when m varies from 2.0 to 5.0.