Cellular Automaton Finite Element Research Articles

Solidification Structure and Compactness Degree of Central Equiaxed Grain Zone in Continuous Casting Billet Using Cellular Automaton-Finite Element Method

Solidification Structure and Compactness Degree of Central Equiaxed Grain Zone in Continuous Casting Billet Using Cellular Automaton-Finite Element Method

Simulation of stray grain formation during unidirectional solidification of IN738LC superalloy

The influence of casting parameters on stray grain formation of a unidirectionally solidified superalloy IN738LC casting with three platforms was investigated by using a 3D cellular automaton-finite element (CAFE) model in CALCOSOFT package. The model was first validated by comparison of the reported grain structure of Al-7%Si (mass fraction) alloy. Then, the influence of pouring temperature, heat flux of the lateral surface, convection heat coefficient of the cooled chill and mean undercooling of the bulk nucleation on the stray grain formation was studied during the unidirectional solidification. The predictions show that the stray grain formation is obviously sensitive to the pouring temperature, heat flux and mean undercooling of the bulk nucleation. However, increasing the heat convection coefficient has little influence on the stray grain formation.

Influence of inclusion on nucleation of silicon casting for photovoltaic (PV) application

The photovoltaic (PV) industry has grown rapidly in recent years. The predominant PV material, multicrystalline silicon (mc-Si), is manufactured by relatively low-cost casting methods, especially directional solidification. One factor affecting the quality of cast silicon and the resultant mc-Si solar cells is Si3N4 and SiC precipitates and inclusions. These inclusions cause crystal defects, distorted grain structure, decreased wafer yield and quality and even electrical shunts. A Computational Fluid Dynamic (CFD) Simulation tool has been applied to simulate temperatures and flow fields during growth and how they will affect the grain structure under the influence of inclusions. The Cellular Automata Finite Element (CAFE) modeling technique is used to simulate silicon grain growth.

Effect of Pulling Velocity on the Unidirectional Solidification Phenomenon of DZ417G Superalloy

In this study, the influence of pulling velocity on temperature field, fluid field and grain structure of a unidirectionally solidified superalloy DZ417G cylindrical casting was investigated by using a 3D cellular automaton finite element (CAFE) model within commercial software CALCOSOFT. The predictions show that temperature distribution in the casting is well in accordance with the experiment result. The solidification front and fluid field are sensitive to changes in pulling velocity. And the pulling velocity should be controlled less than 0.5 mm/s in our experiment so as to effectively decrease the grain number and mean grain deviation.

Effect of Simulation Conditions on Grain Selection during Solidification of Single Crystal Casting

A macro-scale ProCAST and a meso-scale Cellular Automaton Finite Element model (CAFE) are used to simulate the grain selection during solidification with different simulation conditions. To improve the efficiency of the spiral grain selector, the effects of spiral geometries, boundary conditions and nucleation parameters on the grain selection are investigated. Simulation results reveal that the spiral geometries affect the height where the single crystal occurs in the spiral selector when volume nucleation is neglected. The average orientation deviation and grain number is relatively insensitive to volume nucleation and thermal boundary conditions around grain selector, and the thermal boundary conditions in the top of grain selector being of lesser importance.

CAFE Modeling of Segregation and Structure in Levitated Droplets

The coupled two dimensional (2D) Cellular Automaton (CA) Finite Element (FE) model has been extended based on the recent work by Guillemot et al. [1]. Extensions concern i microsegregation at the scale of the CA cells ii macrosegregation at the scale of the FE mesh based on a remeshing technique. The model is applied to segregation taking place upon single grain nucleation and growth from the centre of a spherical domain. The simulation retrieves the prediction of Heringer et al. [2]. Application to solidification of a spherical Al-4wt%Cu droplet demonstrates its capability to deal with mass exchange by diffusion outside the grain envelope defined by the mushy zone together with back diffusion in the solid [3].

Numerical simulation of 3D-microstructures in solidification processes based on the CAFE method

It was analyzed that the finite element-cellular automaton (CAFE) method was used to simulate 3D-microstructures in solidification processes. Based on this method, the 3D-microstructure of 9SMn28 free-cutting steel was simulated in solidification processes and the simulation results are consistent with the experimental ones. In addition, the effects of Gaussian distribution parameters were also studied. The simulation results show that the higher the mean undercooling, the larger the columnar dendrite zones, and the larger the maximum nucleation density, the smaller the size of grains. The larger the standard deviation, the less the number of minimum grains is. However, the uniformity degree decreases first, and then increases gradually.

Internal Variable and Cellular Automata-Finite Element Models of Heat Treatment

Heat treatment is one of the most important process es in advanced steel products manufacturing. While production processes are still being optimised, numerical modelling of heat treatment is very useful. Finite Elements Method (FEM) is widely used in these cases, due to its proved potential fo r modelling of continuous, macroscopic phenomena. However, its capability to simulate microscale and noncontinuous processes is very limited. Introducing e mpirical model of phase changes into FEM, usually based on Internal Variable Method (IVM) is useful when the information about volume fraction of the phases in the domain a nd stresses due to phase change satisfies the requirements. Notwithstanding, it is difficult to obtain information in-depth about microstructure during heat treatment, because it requires more sophisticated description of phase change process. Those problems can be resolved with multiscale modelling. One of the current approaches in this fi eld employs FEM for computing of temperature, stress and strain fields, while non-co ntinuous, microscale model is based on Cellular Automata (CA) method [1]. Recently, several CA models concerning phase transformation have been proposed, e.g. [2]. In th is paper Cellular Automata ‐ Finite Elements (CAFE) is applied for modelling of both macroscopic and microscopic influence of heat treatment. It also takes into acc ount a stochastic character of processes, which is hard to obtain in typical FEM or IVM solut ion. The advantage of CAFE model ensues from direct representation of microstructure. Although the current microstructural CA model is two-dimensional, it reproduces topological and morphological relations between components of microstructure. The state of CA cells is updated synchronically in cons ecutive time steps. Every cell includes state vector representing fractions of all phases. Thermodynamics of phase transition is a base for a rule-based knowledge rep resentation in the CA model. However, the nondeterministic definition of neighbo urhood and probabilistic energy

Simulation of 3D-Microstructure in Free-cutting Steel 9SMn28 under Water Cooling Condition with Convection and Porosity

The 3D-microstructure in 9SMn28 free-cutting steel under water cooling condition was simulated based on the finite element–cellular automaton method with convection and porosity, and the simulated results are consistent with that of the experiment. The casting of 9SMn28 alloy is a stepwise solidification mode under water cooling condition. Convection is mainly made of buoyancy-driven flows and feeding flows in perpendicular direction of the solid–liquid interface. Convection is the reason of shaggy on free surface; it can decrease pipe shrinkage and columnar grain zone. Flow field plays an importance role in even temperature field and irregulation porosity morphology. The simulated result of pipe shrinkage is consistent with that of this experiment; the simulated result of porosity is identical with that of this experiment basically.

Effect of spiral shape on grain selection during casting of single crystal turbine blades

In the development of turbine blades, solidification structures have progressed from equiaxed to directionally solidified (DS) and then to single crystal (SX). The transition from DS to SX was achieved by introducing a grain selector which consists of two parts: a starter block referring to the grain orientation optimisation and a spiral part to ensure that only one grain can eventually survive and grow into the blade. With emphasis on the spiral selector, the microstructure evolution and grain competitive growth is visualised using a coupled macroscale ProCAST and mesoscale cellular automaton finite element (CAFE) model in this study. To improve the efficiency of the spiral grain selector and to save cost in casting, the effects of spiral geometries on the grain selection are investigated. Simulation results reveal that the spiral becomes more efficient in grain number selection with a smaller spiral thickness (dT) and a larger spiral diameter (dS).

The Influence of Geometrical and Operational Factors on Supercooling Capacity in Strawberries: A Simulation Study

Supercooling is still today one of the most challenging physical phenomena to be modelled in food bioprocess engineering. In this study, we evaluate the capacity of a finite-element-cellular automata (FEM-CA) approach to model the propagation of nucleation inside supercooled strawberries with five different morphologies (higher and lower volumes of vascular tissue, pulp, and central air void) frozen inside an air blast freezer under different operational conditions: initial temperature (0 to +20 °C), air temperature (−45 to −20 °C), and velocity (1 to 10 m s − 1). Results show that nucleation is highly affected by the initial temperature and heat transfer rate during phase change. The stochastic nature of nucleation only allowed us to consider it a random variable inside the model temperature restriction interval, it not yet being possible to know what triggers nucleation. However, this study allowed us to conclude that: (1) the structure of liquid water in the supercooled region plays a very significant role during the supercooling effect, (2) nucleation temperatures increase in the supercooled region due to the release of latent heat, and (3) strawberry morphology and operational variables have a profound effect on the supercooling capacity. In our opinion, supercooling is still an open subject, and only a deeper understanding of the structuring of water and dynamics of nucleation at the molecular level may lead to significant advances in the quality of frozen foods and cryopreservation.

Grain structure and texture evolutions during single crystal casting of the Ni-base superalloy CMSX-4

The solidification grain structure and texture evolutions during single crystal (SX) casting of the advanced Ni-base superalloy CMSX-4 have been investigated. In order to understand the development of the solidification grain structure, SX casting experiments were carried out with a specially designed grain selector in a Bridgman directional solidification (DS) furnace. In addition to casting trials, the SX casting process was simulated by a 3-D cellular automaton-finite element (CAFE) model. The predicted solidification grain structure and the texture evolutions were validated by comparison with the microstructural observation and the electron back scattered diffraction (EBSD) results. It was shown that the overall grain structure, crystallographic texture evolution, and the location where the final selection of the single crystal occurs can be predicted well by the present CAFE model. The axial texture evolution of the single crystal was found to be significantly influenced by the grain density at the chill surface. The CAFE predictions also revealed that the geometry of the grain selector plays a significant role in the final selection of the single crystal.

Development of the Multi-scale Analysis Model to Simulate Strain Localization Occurring During Material Processing

A detailed description of possibilities given by the developed Cellular Automata—Finite Element (CAFE) multi scale model for prediction of the initiation and propagation of micro shear bands and shear bands in metallic materials subjected to plastic deformation is presented in the work. Particular emphasis in defining the criterion for initiation of micro shear and shear bands, as well as in defining the transition rules for the cellular automata, is put on accounting for the physical aspects of these phenomena occurring in two different scales in the material. The proposed approach led to the creation of the real multi scale model of strain localization phenomena. This model predicts material behavior in various thermo-mechanical processes. Selected examples of applications of the developed model to simulations of metal forming processes, which involve strain localization, are presented in the work. An approach based on the Smoothed Particle Hydrodynamic, which allows to overcome difficulties with remeshing in the traditional CAFE method, is a subject of this work as well. In the developed model remeshing becomes possible and difficulties limiting application of the CAFE method to simple deformation processes are solved. Obtained results of numerical simulations are compared with the experimental results of cold rolling process to show good predicative capabilities of the developed model.

Multi-scale Finite Element Cellular Automata Simulation of Multi-step Cold Forging Operations

Multi-scale Finite Element Cellular Automata Simulation of Multi-step Cold Forging Operations

The validation of a multiscale rheological model of discontinuous phenomena during metal rolling

The objective of the work is to incorporate stochastic and discontinuous phenomena, that occur at the microlevel, into macroscale models of forming processes. A Cellular Automata Finite Element (CAFE) multiscale model was developed to simulate the strain localization phenomena that occur during various plastometric test, as well real industrial processes. This flexibility of the CAFE model is one of the advantages of the developed solution. Application of the proposed CAFE model to simulate strain localization during cold rolling process is the subject of the work. OFHC (Oxygen Free High Conductivity) copper was selected for the numerical and experimental analysis and samples were subjected to rolling operations on the laboratory duo rolling mill. Experimental validation of the results obtained from the CAFE simulation confirmed the predictive capability of this model. The capabilities of the CAFE model and limitations of the conventional FE method in prediction of initiation and propagation of microshear and shear bands in metals subjected to plastic deformation, are presented and discussed.

Interaction between single grain solidification and macrosegregation: Application of a cellular automaton—Finite element model

A two-dimensional (2D) cellular automaton (CA)—finite element (FE) model developed for the prediction of grain structure formation during solidification processes is presented. While the FE method solves the macroscopic conservation equations for heat and mass transfers, the CA method is used at a mesoscopic scale to simulate the growth of a mushy zone domain. The limit between this mushy zone domain and the undercooled liquid melt in which it develops defines the envelope of a single grain. A verification is first performed to check that the CAFE model retrieves the solution of a purely FE simulation for a vanishing undercooling of the growth front. Since the present 2D CAFE model is relevant with respect to the solidification experiment developed by Yin and Koster [H. Yin, J. N. Koster, J. Crystal Growth 205 (1999) 590; H. Yin, J. N. Koster, J. Alloy Compd. 352 (2003) 197], comparison is then performed. In particular, the position of the growth front is considered as a time sequence. The effect of the growth undercooling is clearly revealed. The kinetics of the growth front used in the model assumes the development of a rough interfacial dendrite-like morphology. This assumption is discussed considering the value of the normalized entropy of fusion of gallium.

Grain structure prediction of Ni-base superalloy castings using the cellular automaton-finite element method

A three-dimensional cellular automaton (CA) model has been coupled with finite-element (FE) heat flow calculation to predict the solidification grain structures in a Ni-base superalloy. In the present CA–FE model, Gaussian distribution of nucleation sites was adopted and the Kurz–Giovanola–Trivedi model was extended to multi-component alloys to account for the growth kinetics of the dendrite tip. In particular, for describing the Gaussian distribution of nucleation sites at the mold surface, an empirical relationship between the nucleation density at the surface and the initial cooling time of the melt was proposed and applied to the input parameter in the model. The predicted grain structures were validated at various casting conditions by comparison with the experimental micrographs obtained with cylindrical shaped castings. The CA–FE model was also applied to the complex shaped turbine blade casting and the computed grain structure of turbine blade airfoil was compared with the experimental micrograph.

Multi-scale rheological model for discontinuous phenomena in materials under deformation conditions

A study of possibilities given by the developed Cellular Automata–Finite Element (CAFE) multi-scale model for prediction of the initiation and propagation of micro-shear bands and shear bands in metallic materials subjected to plastic deformation is described in the paper. Particular emphasis in defining the criterion for initiation of micro-shear and shear bands, as well as in defining the transition rules for the cellular automata, is put on accounting for the physical aspects of those phenomena occurring in two different scales in the material. The proposed approach led to the creation of the real multi-scale model of strain localization. This model predicts material behavior in various thermo-mechanical processes. Selected examples of applications of the developed model to simulations of metal forming processes, which involve strain localization, are presented in the paper. An approach based on the Smoothed Particle Hydrodynamic, which allows to overcome difficulties with remeshing in the traditional CAFE method, is presented in the paper as well. In this approach remeshing becomes possible and mesh distortion, which limits application of the CAFE method to simple deformation processes, is eliminated.

Modeling of Macrosegregation and Solidification Grain Structures with a Coupled Cellular Automaton-Finite Element Model

A coupled Cellular Automaton (CA)-Finite Element (FE) model is presented for the prediction of solidification grain structures coupled with the calculation of solid and liquid flow induced macrosegregation. The model is applied to simulate the solidification of a Pb-48wt%Sn alloy in a rectangular cavity cooled down from only one of its vertical boundaries. The algorithm and the numerical implementation of the coupling between the CA and FE methods are first validated by considering a single grain developing with no undercooling. Such a CAFE simulation is shown to retrieve the solution of a purely FE method simulation for which the grain structure is not accounted for. Several applications of the model are then presented to quantify the effects of the grain structure on the final macrosegregation map. In particular, the effect of the undercooling of the columnar front, the presence of equiaxed grains nucleated in the undercooled liquid, as well as the transport and sedimentation of equiaxed grains are investigated. Although good validation is reached when comparing computed and measured segregation profiles available in the literature for the chosen configuration, it is concluded that refined experimental data are required to further validate the predictions of a coupled CAFE model.

Modeling the ductile-brittle transition behavior in thermomechanically controlled rolled steels

The Charpy impact transition temperature (ITT) is well modeled for hot-rolled or normalized steels having uniform grain size using empirical equations. However, the ITT of nonhomogeneous steel microstructures, such as duplex (mixed fine and coarse) grain sizes, and the scatter in experimental Charpy energy values, observed in the transition region, are not accurately modeled. This article describes research on the microstructure-fracture property relationship and the prediction of the ITT using a cellular automata finite element (CAFE) model in thermomechanically controlled rolled (TMCR) Nb-microalloyed steels. The ferrite grain size distributions for two TMCR steel plates were analyzed and used for the prediction of the local fracture stress (σ F ) values based upon the Griffith model. It was found that the coarse grain size distribution could be used to predict the range of σ F values observed. The CAFE model was used to predict the ITT using the predicted σ F distribution for a TMCR steel. Results showed that the CAFE model realistically predicted the Charpy ITT; in particular, it was able to reproduce the scatter in values in the transition region. Within the model, the percentage of brittle failure and the upper shelf ductile energy were predicted well. However, the lower shelf brittle energy was overestimated due to computational limitations in the commercial FE software used with the current CAFE model.