Present Cellular Automaton Model Research Articles

Modeling of Abnormal Grain Growth That Considers Anisotropic Grain Boundary Energies by Cellular Automaton Model

A new cellular automaton (CA) model of abnormal grain growth (AGG) that considers anisotropic grain boundary energies was developed in this paper. The anisotropic grain boundary energy was expressed based on two types of grains, which correspond to two components of different crystallographic orientation in textured materials. The CA model was established by assigning different grain boundary energies and grain-growth-driven mechanisms to four types of grain boundaries formed by two types of grains. The grain boundaries formed by different kinds of grains adopted the lowest energy principle, while the grain boundaries formed by the same kind of grains adopted the curvature-driven mechanism. The morphology calculated by the CA model shows the characteristics of AGG. Then, the Johnson–Mehl–Avrami (JMA) model was fitted to predict the growth kinetics. By analyzing the fitting results, the JMA model is capable of predicting the growth kinetics of AGG. The Avrami exponent p decreases from about 1.5 to 1 with the initial number of Type II grains increasing. The investigation of the Hillert model and grain size distribution further indicates that the microstructure evolution is consistent with AGG. Therefore, the analysis of morphology and kinetics indicates that AGG can be fairly well-simulated by the present CA model.

Simulation of the Peritectic Phase Transition in Fe-C Alloys.

In this work, a multi-phase cellular automaton (CA) model is extended for the quantitative simulation of peritectic phase transition. First, the effects of cooling rate/supersaturation and temperature on the peritectic transformation kinetics in Fe-C alloys are investigated by utilizing the present CA model. The CA simulations show that supersaturations in the parent phases (liquid and δ-ferrite) increase the L/γ interface growth velocity remarkably, but tinily for the δ/γ interface migration velocity. There exists a transition supersaturation for isothermal transformations, at which the growth rates of the two interfaces are equal. The transition supersaturation is found to increase with decreasing temperature. Microstructural evolution at different cooling rates during peritectic transformation is simulated using the experimental conditions. At low cooling rates, the δ/γ interface propagates at a higher velocity than the L/γ interface. At high cooling rates, however, the γ-phase grows more into the L-phase with a cellular morphology. Then, the proposed CA model is applied to simulate the microstructural evolution during peritectic reaction. It is observed that the γ-phase propagates along the L/δ interface and finally encircles the δ-phase. Meanwhile, the intervenient γ-phase grows in thickness through peritectic transformation. The CA simulations are compared reasonably well with the experimental data and analytical calculations.

Numerical simulations of solidification microstructure evolution process for commercial-purity aluminum alloys inoculated by Al-Ti-B refiner

Solidification microstructure of aluminum alloy has a great influence on the properties of the casting. An aluminum alloy with the structure of fine equiaxed grains has low casting defects and presents excellent mechanical properties. Recently, chemical inoculation by adding grain refiner is the technique most extensively used to achieve a fine, equiaxed grain structure of Al alloy in the industrial production. In order to investigate the detailed solidification microstructure evolution of the alloy, many numerical models have been proposed. Cellular automaton method is one of the powerful tools for simulating the morphology evolution of detailed grains in the solidification process of alloy. However, the present cellular automata model has a shortcoming, that is, its calculation of the nucleation rate is based on the experimental number density of grains. In this work, a population dynamics-cellular automaton model is developed for describing the solidification microstructure evolution of the inoculated aluminum alloy. The model takes account of the heterogeneous nucleation of α-Al nucleus, the initial spherical growth of <i>α</i>-Al grains and the dendritic growth process. The model is used for simulating the solidification microstructure evolution of the commercial-purity aluminum (CP-Al) inoculated by Al-5Ti-1B master alloy. The results indicate that the heterogeneous nucleation process of α-Al can be divided into the two stages. In the early stage of nucleation, there are enough effective particles in the melt. The nucleation rate of <i>α</i>-Al increases with the increase of the undercooling of the melt. After a short time, the nucleation of α-Al is dominated by the number density of the effective particles in the melt. Nucleation process stops when the recalescence takes place. The effects of the additive amount of Al-5Ti-1B master alloy and the cooling rate of the melt on the solidification microstructure of the CP-Al are investigated by using the established model. The final solidification structures of CP-Al are predicted. And a comparison between the predicted results and the experimental ones shows that they are in good agreement with each other.

A cellular automaton model integrated with CALPHAD-based thermodynamic calculations for ferrite-austenite phase transformations in multicomponent alloys

A cellular automaton (CA) model, which is directly coupled with thermodynamic calculations based on the CALPHAD method, is developed for the simulation of ferrite (α)-austenite (γ) phase transformations involving the partitioning and long-range diffusion of both interstitial and substitutional elements in multicomponent alloys. A data management scheme is proposed, which renders the efficient coupling between the kinetic simulation using the CA approach and thermodynamic calculations. The present CA model is applied to simulate the cyclic phase transformations between the α- and γ-phases for a quaternary Fe-0.02C-0.2Mn-0.1Si (wt%) alloy in both one- and two-dimensions. The simulated curves of α-volume fraction varying with temperature clearly illustrate the different α-γ transformation stages. The transformation kinetics and concentration profiles of Mn and Si obtained by the 1-D CA simulation agree well with DICTRA predictions. The 2-D simulation of a single circular grain is found to have shorter stagnant stages and faster transformation kinetics than that of the 1-D planar case. This can be attributed to the different growth geometries of 1-D planar and 2-D circular, and the effect of substitutional element Mn on the migrating interface. The non-uniform distribution of C and residual spikes of Mn and Si can be clearly delineated in the 2-D multi-grain simulation. It is shown that the data management scheme proposed in the present work significantly reduces the simulation time for the required thermodynamic data by two orders of magnitude approximately, which makes it feasible to perform valid simulations of microstructural evolution and solute distributions during α-γ phase transformations in steels with more than three components.

Recalescence and Segregation Phenomena During Equiaxed Dendritic Solidification of Fe-C Alloy

Recalescence and segregation are two characteristic phenomena for the equiaxed dendritic solidification of alloys. The present work developed a two-dimensional dendritic model with cellular automaton (CA) method to investigate influence mechanisms of thermal conditions on recalescence and segregation behaviors of Fe-0.82wt pct C alloy. The released latent heat reduces the undercooling around the equiaxed dendrite, and thus eases its growth velocity. The predicted steady growth velocity agrees well with the analytical results as the melt undercooling is 9 K. Additionally, the present CA model can ensure the growth consistence of equiaxed dendrites in the undercooled melt. With improving the convective heat transfer coefficients applied around the domain boundaries, the temperature recalescence in the domain center becomes more significant, and the corresponding solid fractions enhance. It is because that the stronger cooling promotes the solidification, resulting in more latent heat released. Accordingly, the heat dissipation can be neutralized. Moreover, a deeper undercooling for the temperature recalescence is needed under a stronger cooling condition. With the increase of both the cooling rate and the convection coefficient, secondary arms of the equiaxed dendrite become more developed. At the lower cooling rate range, the segregation ratio in the domain enlarges with the improvement of the cooling rate. However, it gets weaker under the condition with super cooling intensity due to the expansion of the low concentration region. As the convection coefficient is enhanced, the solute segregation in the domain gets less pronounced.

Study of dynamic recrystallization behavior of T2 copper in hot working conditions by experiments and cellular automaton method

The dynamic recrystallization (DRX) behavior of T2 copper was studied by experiments and cellular automaton (CA) simulation during hot compression. The hot compression deformation of T2 copper was performed by isothermal hot compression tests over a wide range of temperatures (400–900 °C) and strain rates (0.001–10 s−1). The experimental results show that the deformation temperatures and strain rates have a profound influence on the DRX behavior. The characteristic parameters for the DRX behavior of T2 copper were obtained and a DRX kinetics model based on the modified Avrami equation was proposed to describe the DRX behavior of T2 copper. The average DRX grain size of the copper was estimated on the basis of metallography observation, and a power law function of Zener-Hollomon parameter was established to predict the grain size under different deformation conditions. A mesoscopic cellular automaton model was established to simulate the DRX behavior of T2 copper. The comparison between experimental and simulation results indicates that the recrystallization fraction and the average DRX grain size can be accurately predicted by the present CA model. It suggests that the developed CA model can be used to take control of the DRX process for the copper during hot working.

Quantitative cellular automaton model and simulations of dendritic and anomalous eutectic growth

A quantitative cellular automaton (CA) model for dendritic and anomalous eutectic growth has been developed. Solid/liquid(SL) interface curvature plays an important role on the dendritic and eutectic growth kinetics. In order to improve the accuracy of calculated interface curvature, a height function method was used in this research. Simulation results showed that the precision of the interface curvature has been significantly improved. And the quantitative ability of present CA model has also been improved through the simulations of equilibrium shapes. Using the quantitative CA model, directional solidification of dendritic and eutectic growth has been investigated, as well as the anomalous eutectic growth during laser remelting process. For anomalous eutectic, it is found that the very fine lamellar eutectic growing at much smaller cooling rate is the reason to observe the lamellar to anomalous transition.

Simulation of Dynamic Recrystallization Behavior under Hot Isothermal Compressions for as-extruded 3Cr20Ni10W2 Heat-Resistant Alloy by Cellular Automaton Model

AbstractIn order to study dynamic recrystallization behavior of the as-extruded 3Cr20Ni10W2 under isothermal compression conditions, a cellular automaton (CA) model was applied to simulate hot compression. Analysis on the strain–stress curves indicates that dynamic recrystallization is the main softening mechanism for the 3Cr20Ni10W2 when the deformation occurred in the temperature range of 1203–1303 K with an interval of 50 K and strain rate range of 0.01–10 s−1. The deformation temperature and strain rate have a significant influence on the dynamically recrystallized grain size. Subsequently, a CA model is established to simulate the dynamic recrystallization behaviors of the studied alloy. The simulated results show that the mean grain size increases with the increased deformation temperature and decreases with the increased strain rate, which is consistent with the experimental result. In addition, the average absolute relative error, which is 13.14%, indicates that the process of the dynamic recrystallization and the dynamically recrystallized grain size can be well predicted by the present CA model.

Microstructural evolution during temperature gradient zone melting: Cellular automaton simulation and experiment

The microstructural evolution in mushy zones of alloys due to temperature gradient zone melting (TGZM) is studied by simulations using a two-dimensional quantitative cellular automaton (CA) model and in situ observations of directional solidification with a transparent organic SCN-ACE alloy. The present model is an extension of a previous CA model by involving the mechanisms of both solidification and melting. The present CA model is adopted to simulate the temporal evolution of the position and velocity of a liquid pool migrating in the solid matrix of a SCN–0.3 wt% ACE alloy under conditions that the pulling velocity is either lower or higher than the critical pulling velocity. The CA simulated position and velocity curves agree well with analytical solutions. Simulations are also performed for the microstructural evolution of columnar dendrites in a SCN–2.0 wt% ACE alloy held in a stationary temperature gradient using the present CA model and a previous CA model that does not include the melting mechanism under otherwise identical conditions for comparison. The results show how melting is essential to dendrite arm migration in a temperature gradient. The time-averaged velocities of arm migration obtained from the present CA simulations increase with increasing temperature gradient and with decreasing the length between the initial arm position and the liquidus. This agrees reasonably well with experimental measurements and analytical predictions. The mechanisms of dendrite arm migration are investigated in detail by comparing the local equilibrium and actual liquid compositions at solid/liquid interfaces. The simulations render visualizing the complex interactions among local temperature, solute distribution/diffusion, and solidification/melting during the TGZM process.

A cellular automaton simulation of W–Ni alloy solidification in laser solid forming process

An alloy cellular automaton (CA) model is developed for the microstructure simulation in directional solidification and laser solid forming (LSF) process. The CA model's capture rule was modified by a limited neighbor solid fraction (LNSF) method. A multiscale two-dimensional model is presented for simulating laser remelting process, which is the same as LSF without the addition of metallic powders into melt pool. The metallurgy process in melt pool was simulated, including temperature distribution, pool shape and solidification of microstructure. The microstructure evolution of tungsten–nickel alloy (W–Ni) during LSF is also simulated by present CA model.

Simulation of dynamic recrystallization in AZ80 magnesium alloy using cellular automaton

The deformation behaviors of AZ80 magnesium alloy were systematically investigated by the combination of simulations and experiments. Specifically, the isothermal hot compression test of AZ80 magnesium alloy was performed on Gleeble-3500 thermo-simulation machine in the temperature range of 573–723K with strain rates from 0.001 to 1s−1. It is found that the flow stress is very sensitive to deformation temperatures and strain rates. On the basis of microstructure evolution, a DRX kinetics model was proposed by using regression analysis in microstructural evolution of AZ80 alloy with a consideration of effects of dislocation density and nucleation rate on the DRX. The developed DRX model was coupled into the finite element software, DEFORM-3D, along with cellular automaton (CA) based on physical model, to simulate the microstructural evolution in the deformation zone. The developed CA model with DRX is able to predict the nucleation and growth of DRX grains (R-grains) of the testing material in hot working process. Microstructural evolution and the distribution of average grain size in final microstructure show a good agreement between the simulated results and experimental ones. It suggests that the present CA model with DRX is feasible in studying the DRX process of AZ80 alloy.

Characteristics of Traffic Flow at Nonsignalized T-Shaped Intersection with U-Turn Movements

Most nonsignalized T-shaped intersections permit U-turn movements, which make the traffic conditions of intersection complex. In this paper, a new cellular automaton (CA) model is proposed to characterize the traffic flow at the intersection of this type. In present CA model, new rules are designed to avoid the conflicts among different directional vehicles and eliminate the gridlock. Two kinds of performance measures (i.e., flux and average control delay) for intersection are compared. The impacts of U-turn movements are analyzed under different initial conditions. Simulation results demonstrate that (i) the average control delay is more practical than flux in measuring the performance of intersection, (ii) U-turn movements increase the range and degree of high congestion, and (iii) U-turn movements on the different direction of main road have asymmetrical influences on the traffic conditions of intersection.

Modeling of microstructure evolution of magnesium alloy during the high pressure die casting process

Two important microstructure characteristics of high pressure die cast magnesium alloy are the externally solidified crystals (ESCs) and the fully divorced eutectic which form at the filling stage of the shot sleeve and at the last stage of solidification in the die cavity, respectively. Both of them have a significant influence on the mechanical properties and performance of magnesium alloy die castings. In the present paper, a numerical model based on the cellular automaton (CA) method was developed to simulate the microstructure evolution of magnesium alloy during cold-chamber high pressure die casting (HPDC) process. Modeling of dendritic growth of magnesium alloy with six-fold symmetry was achieved by defining a special neighbourhood configuration and calculating of the growth kinetics from complete solution of the transport equations. Special attention was paid to establish a nucleation model considering both of the nucleation of externally solidified crystals in the shot sleeve and the massive nucleation in the die cavity. Meanwhile, simulation of the formation of fully divorced eutectic was also taken into account in the present CA model. Validation was performed and the capability of the present model was addressed by comparing the simulated results with those obtained by experiments.

Orientation selection of equiaxed dendritic growth by three-dimensional cellular automaton model

A three-dimensional (3-D) adaptive mesh refinement (AMR) cellular automata (CA) model is developed to simulate the equiaxed dendritic growth of pure substance. In order to reduce the mesh induced anisotropy by CA capture rules, a limited neighbor solid fraction (LNSF) method is presented. It is shown that the LNSF method reduced the mesh induced anisotropy based on the simulated morphologies for isotropic interface free energy. An expansion description using two interface free energy anisotropy parameters (ε1, ε2) is used in the present 3-D CA model. It is illustrated by present 3-D CA model that the positive ε1 favors the dendritic growth with the 〈100〉 preferred directions, and negative ε2 favors dendritic growth with the 〈110〉 preferred directions, which has a good agreement with the prediction of the spherical plot of the inverse of the interfacial stiffness. The dendritic growths with the orientation selection between 〈100〉 and 〈110〉 are also discussed using the different ε1 with ε2=−0.02. It is found that the simulated morphologies by present CA model are as expected from the minimum stiffness criterion.

Cellular automaton model with MeshTV interface reconstruction technique for alloy dendrite growth

In this paper, cellular automata (CA) model for free dendritic growth of alloy is presented, in which the interface cell is refined by MeshTV interface reconstruction algorithm. In the present CA model, the growth kinetic for both pure material and alloy is used. The effect of interfacial energy anisotropy parameter is validated in the CA model. The dendrite tip growth velocity and tip radius are compared with those of the LGK theoretical model, when =0.02.

A cellular automaton model for a pure substance solidification with interface reconstruction method

A cellular automaton (CA) model with material interface reconstruction (MIR) technique for pure substance dendritic growth is developed. The present CA model used random zigzag capture rules and MIR technique to reduce the mesh induced anisotropy. MIR technique could reconstruct a smooth and accurate solid–liquid (S/L) interface shape inside the cell of interest, based on the solid fractions of the cell of interest and its neighbors. The temperature field was also interpolated, in order to calculate the growth of the S/L interface inside that cell. The CA model with MIR technique was validated by the comparison with experiment data and theoretical model. It is found that the CA model with MIR technique could use larger mesh size (no larger than 5 μm) and it is able for the CA model to reflect the effects of interfacial energy anisotropy on the simulated dendritic morphology. The mesh induced anisotropy in three-dimensional (3-D) CA model is also discussed.

A Study of Size Segregation of Particles Using Cellular Automata

This paper deals with the study of size segregation of particles where the difference in size causes characteristic movement of particles inner granular media according to the induced vibration. In this study, segregation of particles due to the difference in size is simulated using Cellular Automata. A connected lattice automaton is introduced in the model, so that the variation of particle sizes as well as geometrical arrangement between particles can be represented. The present Cellular Automata model can produce various patterns such as segregation, the heaping and convective pattern of particles which are observed in physical experiments. Furthermore, completion time of segregation is measured in each simulation which depends on the magnitude and frequency of excitation. Experimental investigations depicted that segregation time is reduced according to the increment of excitation amplitude, which correspond well with numerical results by Cellular Automata model.

Cellular automata simulation of grain growth in three dimensions based on the lowest-energy principle

The microstructure and morphology evolution of grain growth were studied by 3D simulation using the cellular automata (CA) model based on the lowest-energy principle. In the present CA model, the transition of cells during the grain growth has a typical physical meaning due to the application of the lowest-energy principle. The results show that the kinetics of grain growth follows Burke equation with the growth exponent as 2. The average number of grain faces is 13.6 and the highest frequency of grain faces is 10 faces. The grain size distribution follows Weibull function. The relationship between the number of faces of a grain and the average number of faces of its adjacent grains follows the Aboav–Weaire law. There is a correlation between the topologies of the simulated 2D and 3D grain growth. The average number of sides per face for all grains is 5.65 and the average number of sides per face is about equal to 6 when the grain aces is larger than 35.

Computer simulation of 2D grain growth using a cellular automata model based on the lowest energy principle

The morphology, topology and kinetics of normal grain growth in two-dimension were studied by computer simulation using a cellular automata (CA) model based on the lowest energy principle. The thermodynamic energy that follows Maxwell–Boltzmann statistics has been introduced into this model for the calculation of energy change. The transition that can reduce the system energy to the lowest level is chosen to occur when there is more than one possible transition direction. The simulation results show that the kinetics of normal grain growth follows the Burke equation with the growth exponent m = 2. The analysis of topology further indicates that normal grain growth can be simulated fairly well by the present CA model. The vanishing of grains with different number of sides is discussed in the simulation.

Modeling of Granular Damper Using Cellular Automata

The present paper deals with flow simulations of granular materials moving inside container using Cellular Automata (CA). CA is a class of computer modeling techniques, which consists of discrete unit elements arranged uniformly on spaces, each of which can vary within a finite set of values to express the physical state of the components of the system. The time of evolution of the element state is performed synchronously according to local neighbor rules, instead of governing equations, taking into account the state of the element itself and its nearby elements. Compared with the conventional method such as DEM, it is addressed that the modeling techniques with CA provide advantages on the point of computation efficiency and numerical stability due to the discrete treatment of time and space. In this study, the damping characteristics of a granular damper is investigated numerically by Cellular Automata model and also by DEM, where a container which incorporates granular materials is attached to the mass of one-DOF vibrating system. The container is treated two-dimensionally with thickness identical to a diameter of particle. The simulated particle motions and the damping effects obtained by CA model is compared with DEM solution as well as experimental results, and the present CA model is evaluated in qualitative aspects.