Cellular Automata Finite Element Method Research Articles

A multiscale model for efficiently simulating laser powder bed fusion process with detailed microstructure and mechanical performance results

Numerical simulation is regarded as an important method for studying the mechanisms of additive manufacturing (AM), especially in building a multiscale simulation model. However, the conversion of physical phenomena and parameters across scales is complex, and the number of simulation elements often changes extremely, leading to an inherent conflict between simulation accuracy and efficiency. Therefore, this work introduces a model that balances the need for detailed grain morphology and overall simulation efficiency, to investigate the relationship between process parameters, microstructure, and mechanical performance during Inconel 718 laser powder bed fusion (L-PBF) process. The cellular automata - finite element method (CA-FEM) was used to simulate the melt pool forming and predict the microstructure evolution. Based on the CA result, the tensile process was simulated through crystal plasticity-finite element method (CP-FEM). Specially, the CA-FEM model was simplified and sliced layer-by-layer to reduce simulation time and data storage, supporting parallel computation. The prediction time for the microstructure growth of millions of elements was less than 1.5 h. The CP-FEM model was simplified by reasonably reducing elements in the representative volume element (RVE) model, improving the simulation efficiency by 73 %. The simulation results were validated through EBSD observation and tensile tests, showing good agreement with experimental results, with the final simulation error for mechanical performance not exceeding 10 %. The effects of process parameters on microstructure and mechanical performance were comprehensively discussed. This model supports the optimization of L-PBF process parameters for Ni-based alloys and provides a reference for improving the efficiency of multiscale simulations for other AM processes and materials.

Simulation and Study of Influencing Factors on the Solidification Microstructure of Hazelett Continuous Casting Slabs Using CAFE Model.

The Hazelett continuous casting and rolling process represents a leading-edge production method for cold-rolled aluminum sheet and strip billets in the world. Its solidification microstructure significantly influences the quality of billets produced for cold rolling of aluminum sheets and strips. In this study, employing the CAFE (Cellular Automaton-Finite Element) method, we developed a coupled computational model to simulate the solidification microstructure in the Hazelett continuous casting process. We investigated the impact of nucleation parameters, casting temperature, and continuous casting speed on the microstructural evolution of the continuous casting billet. Through integrated metallographic analyses, we aimed to elucidate the controlling mechanisms underlying the Hazelett continuous casting process and its resultant microstructure. The results demonstrate that the equiaxed rate of grains increases with an increase in nucleation density, and the grain size decreases under constant cooling strength. With other nucleation parameters held constant, the grain size decreases as undercooling increases, and the columnar crystal zone expands. The nucleation density of the Hazelett continuous casting aluminum alloy has been determined to range between 1011 m-3 and 1013 m-3, and the undercooling ranges between 1 °C and 2.5 °C. The solidified grain structure can be controlled between 35 μm and 72 μm. The grain size of the continuous casting billet increases with an increase in pouring temperature and decreases as the casting speed increases. Elevating the pouring temperature positively impacts the fraction of high-angle grain boundaries and promotes the dendritic to equiaxed grain transition. Moreover, there exists potential for further optimization of continuous casting process parameters.

Numerical Investigation of Grain Structure Under the Rotating Arc Based on Cellular Automata-Finite Element Method During Vacuum Arc Remelting Process

Numerical Investigation of Grain Structure Under the Rotating Arc Based on Cellular Automata-Finite Element Method During Vacuum Arc Remelting Process

Prediction of grain structure in direct-chill cast Al–Zn–Mg–Cu billets using cellular automaton-finite element method

A cellular automaton-finite element (CA-FE) model was used to predict the solidification grain structure of permanent mold cast A7086 alloy. In this model, a Gaussian distribution of nucleation sites was adopted, and the Kurz-Giovanola-Trivedi model was extended to a multicomponent Al–Zn–Mg–Cu alloy system to determine the growth kinetics of the dendrite tip. For describing the Gaussian distribution of nucleation sites on the mold surface, an empirical relationship between the initial cooling rate of the melt and the nucleation density was proposed. Under various casting conditions, the calculated grain structures agreed well with the experimental results. Subsequently, the model was applied to the direct-chill (DC) cast billets, and the simulated grain structures reproduced well the experimental results. This confirmed that the current CA-FE model can be used practically and effectively in DC casting processes.

A multi-barrier model assisted CAFE method for predicting ductile-to-brittle transition with application to a low-carbon ultrahigh-strength steel

The conventional micromechanical approaches today are still not able to properly predict the ductile-to-brittle transition (DBT) of steels because of their inability to consider the co-operating ductile fracture and cleavage mechanisms in the transition region, and simultaneously to incorporate the inherent complexity of microstructures. In this study, a complete methodology with coupled cellular automata finite element method (CAFE) and multi-barrier microcrack propagation models is presented to advance the prediction of DBT. The methodology contains three key elements: (i) a multiscale CAFE modelling approach to realize the competition between ductile damage and cleavage fracture and embrace the probabilistic nature of microstructures, (ii) a continuum approach to estimate the effective surface energy for a microcrack to penetrate over particle/matrix interface, and (iii) a method to calculate the effective surface energy for the microcrack to propagate across grain boundaries. The prediction of DBT therefore needs only (1) the stress-strain curves tested at different temperatures, (2) the activation energy for DBT, (3) the ratio between the size of cleavage facets and cleavage-initiating defects, and (4) key statistical distributions of the given microstructures. The proposed methodology can accurately reproduce the experimental DBT curve of a low-carbon ultrahigh-strength steel.

Characterization of AZ91 magnesium alloy processed by cyclic contraction/expansion extrusion using the experimental and micromechanical cellular automaton finite element approach

The feasibility to fabricate ultra-fine-grained AZ91 Mg alloy is investigated with a newly presented severe plastic deformation method entitled cyclic contraction/expansion extrusion. In this method, an initial cylindrical AZ91 Mg billet is placed into a die and the moving punch causes the large deformations by extruding the material in two different regions entitled contraction and extrusion. The evolution of AZ91 microstructure and mechanical properties during cyclic contraction/expansion extrusion was studied through different experimental observations. The microstructure observations showed the ultra-fine-grained structure of AZ91 at the end of the third pass where the average grain size of 600 nm obtained from the initial value of 130 µm. The tensile tests showed that the ultimate tensile strength, yield strength, hardness, and elongation of AZ91 cyclic contraction/expansion extrusion-processed samples are increased significantly. Discontinuous dynamic recrystallization has a main role in the grain refinement of Mg alloys during hot deformations. The evolution of grains in microlevel is analyzed by the cellular automaton finite element method in the DEFORM software environment. The macroscopic flow parameters including effective plastic strain, stain rate, and temperature were calculated in finite element. By tracing these data in defined domain of cellular automaton, the discontinuous dynamic recrystallization of material is analyzed through a devised cellular automaton finite element post-processing step. The imposed plastic strain and variation of dislocation density are the two main driven forces in discontinuous dynamic recrystallization of AZ91 samples during cyclic contraction/expansion extrusion processing. The experimentally observed grains and the cellular automaton finite element predicted microstructure were reasonably in good agreement.

A Multi-Barrier Model Assisted CAFE Method for Predicting Ductile-to-Brittle Transition with Application to a Low-Carbon Ultrahigh-Strength Steel

The conventional micromechanical approaches today are still not able to properly predict the ductile-to-brittle transition (DBT) of steels because of their inability to consider the co-operating ductile fracture and cleavage mechanisms in the transition region, and simultaneously to incorporate the inherent complexity of microstructures. In this study, a complete methodology with coupled cellular automata finite element method (CAFE) and multi-barrier microcrack propagation models is presented to advance the prediction of DBT. The methodology contains three key elements: (i) a multiscale CAFE modelling approach to realize the competition between ductile damage and cleavage fracture and embrace the statistical nature of microstructures, (ii) a continuum approach to estimate the effective surface energy for a microcrack to penetrate over particle/matrix interface, and (iii) a method to calculate the effective surface energy for the microcrack to propagate across grain boundaries. The prediction of DBT therefore needs only (1) the stress-strain curves tested at different temperatures, (2) the activation energy for DBT, (3) the ratio between the size of cleavage facets and cleavage-initiating defects, and (4) key statistical distributions of the given microstructures. The proposed methodology can accurately reproduce the experimental DBT curve of a low-carbon ultrahigh-strength steel.

Cellular Automaton Finite Element Method Applied for Microstructure Prediction of Aluminium Casting Treated by Laser Beam

Cellular Automaton Finite Element Method Applied for Microstructure Prediction of Aluminium Casting Treated by Laser Beam

CAFE based multi-scale modelling of ductile-to-brittle transition of steel with a temperature dependent effective surface energy

It is still a challenge to numerically achieve the interactive competition between ductile damage and brittle fracture in ductile-to-brittle transition (DBT) region. In addition, since two types of fracture occur at two independent material length scales, it is difficult to process them with the same mesh size by using finite element method. In this study, a framework of modelling DBT of a thermal mechanical controlled-rolling (TMCR) steel is explored by using the cellular automata finite element (CAFE) method. The statistical feature of material's microstructure is incorporated in the modelling. It is found that DBT curve cannot be reproduced with only one temperature dependent flow property, for which another temperature dependent variable must be considered. A temperature dependent effective surface energy based on typical cleavage fracture stage is proposed and obtained through a continuum approach in present work. The DBT of TMCR steel is simulated by using CAFE method implemented with a temperature dependent effective surface energy. It is found that numerical simulation is able to produce a full transition curve, especially with scattered absorbed energies in the transition region represented. It is also observed that simulation results can reproduce a comparable DBT curve contrasting to the experimental results.

Effects of Nucleus Density and Dendritic Growth Influenced by Ti and Nb on Solidification Structure of Fe-18 Pct Cr Ferritic Stainless Steel

The effects of nucleus density and dendritic growth influenced by Ti and Nb on the solidification structure of Fe-18 pct Cr ferritic stainless steel (FSS) ingots were investigated. The equiaxed zone ratios (EZR) were 8.5, 28.8, 67.5, and 57.3 pct in the blank, Nb-bearing, Ti-bearing, and Ti-Nb-bearing FSS ingots, respectively. The grain size was the smallest in the Ti-Nb-bearing ingot. Silicon oxide was present in the blank sample and Nb-bearing ingot, but the complex nuclei that were composed of TiOx-Ti(C, N) and TiOx-(Ti, Nb)x(C, N)y existed in the Ti-bearing and Ti-Nb-bearing ingots, respectively. The bulk density of the complex nucleus decreased by 70 pct when the Ti content decreased from 0.16 to 0.14 mass pct. Thermodynamic calculations indicate that the phase transformation from Ti3O5 to Ti2O3 was delayed in the ingot with a lower Ti content and that the Ti2O3 shows more potential for TiN nucleation compared with Ti3O5 according to the disregistry theory. The increased EZR mechanism was illustrated by a cellular-automaton–finite-element method with actual distribution statistics of the complex nucleus and dendritic-growth-kinetic analysis. The heterogeneous nucleation effect of the complex nucleus by Ti addition and the variations in dendritic-growth kinetics by Ti and Nb contribute to the EZR increase of FSS.

Effect of Solidification Pressure on Compactness Degree of 19Cr14Mn0.9N High Nitrogen Steel Using CAFE Method

The cellular automaton-finite element (CAFE) model is used to simulate solidification structures of 19Cr14Mn0.9N high nitrogen steel under different solidification pressures. The effect of solidification pressure on model parameters is firstly investigated. After validation, this model is used to clarify the effect of solidification pressure on compactness degree with number of grains and primary dendrite arm spacing (λ1). The results show that increasing solidification pressure from 0.5 to 1.2 MPa exhibits a significant increment (200 W m2 K−1)) on heat transfer coefficient and slight change for other model parameters. The model validation indicates CAFE model can accurately simulate solidification structure under higher solidification pressure. Under higher solidification pressure, the primary dendrite arm spacing (λ1) of central equiaxed grain becomes smaller and the number of grains of the whole ingot increases obviously, revealing a further improvement on the compactness degree of ingot. At a given pressure, the decrement in the number of grains is obvious away from the edge of ingot. With increasing solidification pressure, a more significant increment in the number of grains exists at columnar grain zone than that at central equiaxed grain zone, suggesting a greater increasing tendency of compactness degree at columnar grain zone.

Prediction of microstructure evolution during hot forging using grain aggregate model for dynamic recrystallization

In this study, dynamic recrystallization during nonisothermal hot compression test was numerically simulated by finite element analysis using new grain aggregate model for dynamic recrystallization. This model was developed based on mean field approach by assuming grain aggregate as representative element. For each grain aggregate, changes of state variables were calculated using three sub-models for work hardening, nucleation, and nucleus growth. A conventional single parameter dislocation density model was used to calculate change of dislocation density in grains. For modeling nucleation, constant nucleation rate and nucleation criterion developed by Roberts and Ahlblom were used. It was assumed that the nucleation occurs when the dislocation density of certain grain reaches a critical nucleation criterion. Conventional rate theory was used to model nucleus growth. The developed dynamic recrystallization model was validated by comparing with isothermal hot compression of pure copper. Then, the finite element analysis was conducted to predict the local changes of microstructure and average grain size by using the grain aggregate model. The predicted results were compared with nonisothermal hot compression results. The simulation results were in reasonably good agreement with experimentally obtained microstructures and the calculation time was much shorter than cellular automata-finite element method.

Microstructure Simulation of Al-Cu Alloy Based on Inverse Identified Interfacial Heat Transfer Coefficient

The interfacial heat transfer coefficient (IHTC) is taken as one of the most important factors affecting the accuracy of the simulation. In the present paper, the IHTC variation with temperature was obtained by an inverse heat conduction method. Then, a 3D cellular automaton-finite element method was adopted to predict the microstructure of an Al-Cu alloy based on the identified IHTC. It was found that the IHTC was of prime importance for the precise simulation of solidification microstructure, especially in the grains distribution. In addition, the simulated results using the IHTC variation with temperature were found to exhibit a better agreement with the experimental results than those using the constant value.

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

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.

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.