Modified Cellular Automaton Model Research Articles

Constitutive Model and Cellular Automaton Simulation of the Dynamic Recrystallization of Railway EA4T‐Grade Steel

Herein, isothermal compression experiments are conducted on EA4T steel at 970–1170 °C, with strain rates of 0.01–1.0 s−1 and a strain of 0.2–0.8 s−1. Based on the experimental data, a high‐temperature constitutive model is developed for EA4T steel. The activation energy of dynamic recrystallization (DRX) is calculated to be 383 666 J mol−1, and the correlation coefficient and root mean square error between the results of the constitutive model and experimental results are 0.9943 and 4.6823, respectively. The average grain size for each deformation condition is determined using the linear‐intercept method. The grain growth model widely used in cellular automaton (CA) simulations is found unsuitable for EA4T steel. Therefore, a modified CA model of DRX behavior suitable for EA4T steel is developed. The nucleation rates and solute drag effect coefficients under different deformation conditions are determined. Furthermore, simulations are performed under other deformation conditions using the CA model. The simulated results for the average grain size, microstructure morphology, and DRX fraction agree well with the experimental results. The reason for the deviation between the observed and simulated DRX fractions is also explored.

Study of microstructure evolution of magnesium alloy cylindrical part with longitudinal inner ribs during hot flow forming by coupling ANN-modified CA and FEA

Hot flow forming (HFF) is a promising forming technology to manufacture thin-walled cylindrical part with longitudinal inner ribs (CPLIRs) made of magnesium (Mg) alloys, which has wide applications in the aerospace field. However, due to the thermo-mechanical coupling effect and the existence of stiffened structure, complex microstructure evolution and uneven microstructure occur easily at the cylindrical wall (CW) and inner rib (IR) of Mg alloy thin-walled CPLIRs during the HFF. In this paper, a modified cellular automaton (CA) model of Mg alloy considering the effects of deformation conditions on material parameters was developed using the artificial neural network (ANN) method. It is found that the ANN-modified CA model exhibits better predictability for the microstructure of hot deformation than the conventional CA model. Furthermore, the microstructure evolution of ZK61 alloy CPLIRs during the HFF was analyzed by coupling the modified CA model and finite element analysis (FEA). The results show that compared with the microstructure at the same layer of the IR, more refined grains and less sufficient DRX resulted from larger strain and strain rate occur at that of the CW; various differences of strain and strain rate in the wall-thickness exist between the CW and IR, which leads to the inhomogeneity of microstructure rising firstly and declining from the inside layer to outside layer; the obtained Hall-Petch relationship between the measured microhardness and predicted grain sizes at the CW and the IR indicates the reliability of the coupled FEA-CA simulation results.

Coupled CA-FE simulation for dynamic recrystallization of magnesium alloy during hot extrusion

In the present research, the dynamic recrystallization (DRX) behavior of a newly-developed Mg–Al–Zn–RE alloy with abundant second-phase particles during hot extrusion is investigated by coupling finite element (FE) and cellular automaton (CA) models. A two-dimensional CA model is developed to quantitatively and topologically evaluate the DRX process during deformation with constant forming conditions. Considering the fact that second-phase particles with various sizes extensively exist in the studied Mg–Al–Zn–RE magnesium alloy, models of DRX nucleation and grain growth velocity are modified. The coefficients of the modified CA model are calibrated by isothermal compression experiments of the magnesium alloy. Subsequently, the CA model is coupled with FE analysis to investigate the DRX behavior during the hot extrusions of the Mg–Al–Zn–RE alloy. The DRX behavior of the magnesium alloy at different stages and positions of extruded plates is simulated by the established model. Finer grains near the edge than in the inner of the plates result from higher strain and strain rate. The influence of extrusion conditions on microstructural evolution is explored. Under the employed forming conditions, average grain size decreases 28–62 times from as-cast and solution-treated to as-extruded state due to grain refinement by DRX. With increasing initial billet temperature or extrusion speed, average grain size increases. The finest grains are obtained at the initial billet temperature of 623 K and the extrusion speed of 7.83 mm/s. Low initial billet temperature or high extrusion speed benefits homogeneous grain distribution. The simulated results are in good agreement with experimental ones.

Coupling fuzzy clustering and cellular automata based on local maxima of development potential to model urban emergence and expansion in economic development zones

ABSTRACT Modeling urban growth in Economic development zones (EDZs) can help planners determine appropriate land policies for these regions. However, sometimes EDZs are established in remote areas outside of central cities that have no historical urban areas. Existing models are unable to simulate the emergence of urban areas without historical urban land in EDZs. In this study, a cellular automaton (CA) model based on fuzzy clustering is developed to address this issue. This model is implemented by coupling an unsupervised classification method and a modified CA model with an urban emergence mechanism based on local maxima. Through an analysis of the planning policies and existing infrastructure, the proposed model can detect the potential start zones and simulate the trajectory of urban growth independent of the historical urban land use. The method is validated in the urban emergence simulation of the Taiping Bay development zone in Dalian, China from 2013 to 2019. The proposed model is applied to future simulation in 2019–2030. The results demonstrate that the proposed model can be used to predict urban emergence and generate the possible future urban form, which will assist planners in determining the urban layout and controlling urban growth in EDZs.

Investigation on the influences of δ phase on the dynamic recrystallization of Inconel 718 through a modified cellular automaton model

The dynamic recrystallization (DRX) behavior of Inconel 718 containing δ phase was investigated through the isothermal compression experiments and cellular automaton (CA). The compression experiments were conducted under the deformation temperature of 980Co and strain rates of 0.01, 0.1, 1s−1. A modified CA model was established to investigate the DRX for Inconel 718 alloy with δ phase, by which the influences of size, volume fraction and shape of δ phase on DRX behavior of the alloy were investigated. One commercial Ni-based superalloy with 5.40% Nb and the other with 5.27% Nb were used to investigate the influences of δ phase content on DRX, and the various pre-treatments were carried out to investigate the influences of δ phase size and morphology on DRX. The results obtained by the developed CA model show a great agreement with the physical results, which indicates that the modified CA model could be used to describe the DRX phenomenon with δ phase. The results show the smaller size and rod-like δ phase make the DRX fraction increase faster. Little difference for the studied alloy with the various particle fractions in DRX curves at early stage and faster DRX fraction rising for the alloy with higher particle fraction at later stage are shown. Compared with the alloy with rod-like δ phase, the strain reaching entire DRX fraction is larger for the alloy with needle-like δ phase. The finer grain size can be obtained for the studied alloy with smaller δ phase size after the deformation stage.

Cellular Automaton Modeling of Dynamic Recrystallization of Nimonic 80A Superalloy Based on Inhomogeneous Distribution of Dislocations Inside Grains

A modified cellular automaton (CA) model in the time and space scale is developed to simulate the dynamic recrystallization (DRX) mechanism of Nimonic 80A nickel-base superalloy during hot deformation. Some necessary thermo-mechanical parameters used as input data in CA approach such as work hardening and softening coefficient are fitted according to the previous hot compression experiments. Based on the experimental results, nucleation kinetics is modified as a function of Zener-Holloman parameter. A dislocation density model at transient recrystallization boundary is proposed, in which the dislocation density is a function of temperature, strain rate and annealed dislocation density. The simulated results are in good agreement with experimental results, proving that the modified CA model is capable of predicting both flow behavior and microstructural evolution of Nimonic 80A during hot deformation. According to the experimental and simulated results, the DRX behavior is discussed in detail. It demonstrates that the flow stress and microstructural evolution of DRX have a relationship with the deformation temperature and strain rate.

Cellular automaton modeling for dendritic growth during laser beam welding solidification process

A modified non-equilibrium cellular automaton (CA) model is proposed to simulate the dendrite growth along the fusion boundary under transient conditions during the solidification process of laser beam welding (LBW) pool. The main non-equilibrium solidification effects, including solute trapping, deviation of the liquidus line slope, and kinetic undercooling, are taken into consideration in this modified CA model. The evolution of dendrite morphology, concentration field, and velocity field was investigated. Four growth periods, i.e., the initial stable period, the instability period, the competitive growth period, and the short-term stable period, were observed during the solidification process of LBW pool. The dendrite growth patterns were different in these periods due to the transient solidification conditions. The solute distribution predicted by this modified CA model showed similar trends to that predicted by the previous phase field model. The dendrite tip velocity was significantly influenced by the thermal undercooling and constitutional undercooling in the LBW pool, and the tip velocity field can be divided into three stages, i.e., the planar growth stage, competitive stage, and short-term steady growth stage. In addition, further comparison between the simulated dendrite morphology and experimental dendrite morphology was performed. Results showed that the simulated morphology of dendrites agreed well with the experimental results. In particular, the primary dendrite arm spacing predicted by this model was in good agreement with that obtained from experiments.

Modeling studies on divorced eutectic formation of high pressure die cast magnesium alloy

The morphology and content of the divorced eutectic in the microstructure of high pressure die casting (HPDC) magnesium alloy have a great influence on the final performance of castings. Based on the previous work concerning simulation of the nucleation and dendritic growth of primary α-Mg during the solidification of magnesium alloy under HPDC process, an extension was made to the formerly established CA (Cellular Automaton) model with the purpose of modeling the nucleation and growth of Mg-Al eutectic. With a temperature field and solute field obtained during simulation of the primary α-Mg dendrites as the initial condition of the modified CA model, modeling of the Mg-Al eutectic with a divorced morphology was achieved. Moreover, the simulated results were in accordance with the experimental ones regarding the distribution and content of the divorced eutectic. Taking a cover-plate die casting with AM60 magnesium alloy as an example, the rapid solidification with a high cooling rate at the surface layer of the casting led to a fine and uniform grain size of primary α-Mg, while the divorced eutectic at the grain boundary revealed a more dispersed and granular morphology. Islands of divorced eutectic were observed at the central region of the casting, due to the existence of ESCs (Externally Solidified Crystals) which contributed to a coarse and non-uniform grain size of primary α-Mg. The volume percentage of the eutectic β-Mg17Al12 phase is about 2%-6% in the die casting as a whole. The numerical model established in this study is of great significance to the study of the divorced eutectic in the microstructure of die cast magnesium alloy.

Analysis of the effect of older drivers’ driving behaviors on traffic flow based on a modified CA model

As the global population ages, there are more and more older drivers on the road. The decline in driving performance of older drivers may influence the properties of traffic flow and safety. The purpose of this paper is to investigate the effect of older drivers’ driving behaviors on traffic flow. A modified cellular automaton (CA) model which takes driving behaviors of older drivers into account is proposed. The simulation results indicate that older drivers’ driving behaviors induce a reduction in traffic flow especially when the density is higher than 15 vehicles per km per lane and an increase in Lane-changing frequency. The analysis of stability shows that a number of disturbances could frequently emerge, be propagated and eventually dissipate in this modified model. The results also reflect that with the increase of older drivers on the road, the probability of the occurrence of rear-end collisions increases greatly and obviously. Furthermore, the value of acceleration influences the traffic flow and safety significantly. These results provide the theoretical basis and reference for the traffic management departments to develop traffic management measure in the aging society.

A Modified Cellular Automaton Approach for Mixed Bicycle Traffic Flow Modeling

Several previous studies have used the Cellular Automaton (CA) for the modeling of bicycle traffic flow. However, previous CA models have several limitations, resulting in differences between the simulated and the observed traffic flow features. The primary objective of this study is to propose a modified CA model for simulating the characteristics of mixed bicycle traffic flow. Field data were collected on physically separated bicycle path in Shanghai, China, and were used to calibrate the CA model using the genetic algorithm. Traffic flow features between simulations of several CA models and field observations were compared. The results showed that our modified CA model produced more accurate simulation for the fundamental diagram and the passing events in mixed bicycle traffic flow. Based on our model, the bicycle traffic flow features, including the fundamental diagram, the number of passing events, and the number of lane changes, were analyzed. We also analyzed the traffic flow features with different traffic densities, traffic components on different travel lanes. Results of the study can provide important information for understanding and simulating the operations of mixed bicycle traffic flow.

Simulation of Grain Growth during Solidification of Twin-Roll Continuously Cast Pure Aluminum with a Modified CA Model

Abstract A new mathematic model for the nucleation and the dendrite growth of twin-roll-continuously cast pure aluminum thin strip during solidification process was developed based on cellular automaton(CA)-finite element(FE) method and the classical transfer equations during dendrite growth. The model coupled the temperature field calculation and microstructure simulation. The solute diffusion, the curvature undercooling and the latent heat releasing were also considered in the model, all of which have significant influence on the dendrite evolution. So the dendrite growth morphology can be modeled. The applications of the model in equiaxed dendrite growth, multiple equiaxed dendrite growth, columnar grain growth, and columnar dendrite transformation to equiaxed dendrite in twin-roll-continuously cast aluminum thin strip solidification were presented. The microstructure simulation results were compared with the experimental results and they were in good agreement in dendrite morphology.

Investigation on dynamic recrystallization using a modified cellular automaton

To predict and to control the microstructural evolution during dynamic recrystallization (DRX), a modified cellular automaton (CA) model based on mathematical statistics theory and physical metallurgical principles is developed. Initial microstructure and thermo-mechanical parameters are used as input data to the CA model. Dislocation density is used as a crucial internal state variable to link microstructural evolution with macroscopic flow stress. The latter two are output data, which can be compared with experimental one. In order to exhibit the effect of deformation stored energy on DRX, both the nucleation rate and the growth velocity of each recrystallizing grain (R-grain) are calculated from the dislocation density. The growth kinetics of R-grain is calculated from the metallurgical principles, and the nucleation kinetics is evaluated from a statistically based dislocation-related nucleation model. Model parameters are identified by a flow stress-based inverse analysis method, and then their variations with thermo-mechanical parameters (strain rate and temperature) are estimated and integrated into the CA model. The good agreement between the simulations and the experiments demonstrates the availability and predictability of the modified CA model.

Modeling and simulation of dendrite growth in solidification of Al-Si-Mg ternary alloys

Based on a previously cellular automaton (CA) model for Al-Si binary alloys, a modified cellular automaton (MCA) model is developed to numerically simulate the dendrite growth and microsegregation of Al-Si-Mg ternary alloys. By direct coupling PanEngine, the MCA model can obtain thermodynamic data for dendrite growth of ternary alloys in real time, such as equilibrium liquidus temperature, partition coefficient and liquidus slope of two solute elements. In the model, the normal velocity of the interface cell can not be derived only by solving the solute conservation equation, and must be simultaneously coupled with dimensionless solute supersaturation equation for each alloying element and local equilibrium temperature equation at the S/L interface. All the equations of the MCA model are solved by finite difference method on a uniform mesh. By considering local curvature and constitutional undercooling, solute diffusion and solute redistribution at the S/L interface, the MCA model can simulate the columnar dendrite growth and the solidification path of the equiaxed dendrite growth.

SIMULATION OF NH4Cl-H2O DENDRITIC GROWTH IN DIRECTIONAL SOLIDIFICATION

Studying the microstructure evolution mechanism of directional solidification by numerical simulation has the directive significance in the solidification theory and practical production. Taking account of constitutional undercooling,curvature undercooling,preferred growth orientation coefficient,temperature gradient and pulling velocity,a modified cellular automaton(MCA)model has been developed to simulate the influence of different temperature gradient directions,different preferred growth orientations and different pulling velocities on the morphologies of columnar dendrites. The simulation results well describe the influence of inclination angle between temperature gradient and growth direction on primary dendrite arm spacing(PDAS).Meanwhile the simulation results also reproduce the competitive growth of columnar dendrites with different preferred growth orientations and the splitting of the columnar dendritic tips.For the purpose of verifying this model,the relevant experiments have been carried out on an NH_4Cl-H_2O solution.The experimental results are compared critically with the simulation ones from the MCA model.

Computational Modeling of Microstructure Evolution in Solidification of Aluminum Alloys

In this article, a front tracking (FT) model and a modified cellular automaton (MCA) model are presented and their capabilities in modeling the microstructure evolution during solidification of aluminum alloys are demonstrated. The FT model is first validated by comparison with the predictions of the Lipton–Glicksman–Kurz (LGK) model. Calculations of the steady-state dendritic tip growth velocity and equilibrium liquid composition as a function of melt undercooling for an Al-4 wt pct Cu alloy exhibit good agreement between the FT simulations and the LGK predictions. The FT model is also used to simulate the secondary dendrite arm spacing as a function of local solidification time. The simulated results agree well with the experimental data. The MCA model is applied to simulate dendritic and nondendritic microstructure evolution in semisolid processing of an Al-Si alloy. The effect of fluid flow on dendritic growth is also examined. The solute profiles in equiaxed dendritic solidification of a ternary aluminum alloy are simulated as a function of cooling rate and compared with the prediction of the Scheil model. The MCA model is extended to the multiphase system for the simulation of eutectic solidification. A particular emphasis is made on the quantitative aspects of simulations.

A NEW CELLULAR AUTOMATON MODEL FOR TRAFFIC FLOW WITH DIFFERENT PROBABILITY FOR DRIVERS

Based on the Nagel–Schreckenberg (NaSch) model of traffic flow, a new cellular automaton (CA) traffic model is proposed to simulate microscopic traffic flow. The probability p is a variable which contains a randomly selected term for each individual driver and a density-dependent term which is the same for all drivers. When the rational probability p is obtained, the larger value of maximum flow which is close to the observed data can be reached compared with that obtained from the NaSch model. The fundamental diagram obtained by simulation shows the ability of this modified CA model to capture the essential features of traffic flow, e.g., the spontaneous formation of traffic jams and appearance of the metastable state. These indicate that the presented model is more reasonable and realistic.

Modified cellular automaton model for the prediction of dendritic growth with melt convection.

A modified cellular automaton (MCA) coupled with a momentum and species transport model has been developed in order to predict the evolution of dendritic morphology during solidification of alloys in the presence of melt convection. In the present model, the cellular automaton algorithm for dendritic growth is incorporated with the transport model, for calculating fluid flow and mass transfer by both convention and diffusion. The MCA model takes into account the effects of the constitutional undercooling and the curvature undercooling on the equilibrium interface temperature. It also considers the preferred growth orientation of crystals and solute redistribution during solidification. In the transport model, which is coupled with cellular automaton approach, the SIMPLE scheme is employed to solve the governing equations of momentum and species transfers. The present model was applied to model solutal dendritic growth of an Al-3mass%Cu alloy in a forced flow. The simulations reproduced the typical asymmetric growth features of convective dendrites with various preferred orientations. The effects of inlet flow velocity on the solute redistribution and the growth velocity of a dendritic tip were quantitatively investigated.

Modeling of irregular eutectic microstructures in solidification of Al-Si alloys

A modified cellular automaton (MCA) model was developed and applied to simulate the evolution of solidification microstructures of both eutectic and hypoeutectic Al-Si alloys. The present MCA model considers the equilibrium and metastable equilibrium solidification processes in a multiphase system. It accounts for the aspects including the nucleation of a new phase, the growth of primary α dendrites and two eutectic solid phases from a single liquid phase, as well as the coupling between the phase transformation and solute redistribution in liquid. The effects of alloy composition and eutectic undercooling on eutectic morphology and eutectic nucleation mode were investigated. The simulated results were compared with those obtained experimentally.

Modeling of eutectic structure formation by a modified cellular automaton model

In this paper, a modified cellular automaton (MCA) model was extended to the multi-phase solidification system for the eutectic structure simulation. The present model incorporates the effects of constitutional undercooling and curvature undercooling on the interface local undercooling and takes into account the solute redistribution during eutectic solidification. Different growth algorithms were employed for the growth of non-faceted and faceted crystals. This model was applied to simulate the eutectic structure formation in a transparent organic eutectic alloy, and eutectic and hypoeutectic Al-Si alloys. The effects of interface undercooling and growth velocity on the eutectic morphology, such as the lamellar spacing and interface shape, were investigated. It can be concluded that the present MCA model can successfully predict the eutectic growth morphology in both regular non-faceted / non-faceted and irregular non-faceted / faceted eutectic alloy systems.

Modeling of microstructure evolution in regular eutectic growth

The growth morphology of regular eutectics has been studied using a model eutectic alloy and a transparent ${\mathrm{CBr}}_{4}\ensuremath{-}{\mathrm{C}}_{2}{\mathrm{Cl}}_{6}$ eutectic alloy. A modified cellular automaton (MCA) model is developed to model the evolution of regular eutectic microstructures. Different from the classical cellular automata in which only the temperature field is involved, the present model also includes the solute redistribution and the curvature effect during eutectic solidification. The finite-volume method, which is coupled with the cellular automaton model, is used to calculate the solute field in the calculation domain. The growth velocities of both eutectic phases are evaluated according to the local undercooling, consisting of thermal, solutal, and curvature undercoolings. The cooperative and competitive growth mechanisms of two eutectic phases are embedded in the present MCA model. The effects of diffusion and growth velocity on eutectic growth morphology, such as lamellar spacing and interface shape, were systematically investigated. The simulation results reveal a wide range of realistic eutectic growth features, such as eutectic oscillatory growth, selection of eutectic lamellar spacing accomplished by lamellar branching or lamellar termination, as well as interaction between the solute redistribution and the adjustment of volume fractions.