Cellular Automaton Finite Element Research Articles

Porosity-grain growth relationships in the laser beam deep penetration welding of 6061 aluminum alloy

Porosity is one of the significant defects existing in the weld seam of aluminum alloy by laser. In the current research, the evolution of porosity and grain coupling growth in the weld seam is realized via a Cellular Automaton-Finite Element simulation method. A detailed calculating method of three phases was proposed by taking into account the liquid/solid phase transformation on the nucleation and growth of porosity. The results show that the porosity nuclei with larger size can grow preferentially, while the small porosity nuclei's development is inhibited. Because of the effect of gas/liquid surface tension, porosity increases spherically when it is enveloped by liquid. After touching with grain, the porosity's growth space is restricted by the complex dendrite network, and thus its shape becomes irregular. The coupling of grain and micro-porosities predicted by the simulation method is in good agreement with the results obtained by the experiments.

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 New Cooling Strategy in Curved Continuous Casting Process of Vanadium Micro-alloyed YQ450NQR1 Steel Bloom Combining Experimental and Modeling Approach

In the continuous casting process of steel, the bloom surfaces would experience intensive cooling from the water-cooled copper mold to secondary cooling water spray. If the cooling process is not controlled properly, hot ductility of the bloom surface microstructures would deteriorate, and bloom surface cracks would form easily under straightening deformation in a curved caster. Considering the above facts, the cooling scheme for the continuous casting of YQ450NQR1 steel bloom, a kind of vanadium-containing micro-alloyed steel, is studied with both experimental investigation and mathematical modeling in this work. The authors first investigate the hot ductility of bloom surface microstructures at various cooling rates using a Gleeble thermal simulator. Then, the precipitation of V(C, N) particles and its influence on ferrite formation during continuous cooling are studied and characterized using High-Temperature Laser Scanning Confocal Microscopy. Based on these, the preferred cooling rate for surface microstructures at the straightening position in the caster is obtained. To further reduce the solute macro-segregation through enlargement of the equiaxed crystal zone, a cellular automaton-finite element model is used to calculate heat transfer and solidification structure evolution during the continuous casting process. After calibration with industrial trials, the model is utilized to determine the critical position for columnar to equiaxed transition and to adjust the pouring temperature for the melt. Combining the above research, a new cooling strategy for YQ450NQR1 steel bloom is obtained, which can improve crack resistance of bloom surface microstructures and reduce solute macro-segregation at the same time.

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.

2-D Selector Simulation Studies on Grain Selection for Single Crystal Superalloy of CM247LC.

In the present work, the single crystal superalloy CM247LC was selected as the research material. By using directional experiments and the cellular automaton finite element (CAFE) model, the process of grain texture evolution in a two-dimensional grain selector was investigated to clarify the mechanism of grain selection in the two-dimensional passage during the process of directional solidification (DS). To optimize single crystal turbine blade production processes, the effects of grain selector geometries (i.e., selector diameter and pitch length, take-off angle) on the microstructure and stray grain were simulated and discussed.

Application of a nonlocal grid model for analysis of the creep damage of metals

The paper presents a model of creep damage development in polycrystalline material. The model operates at two scales: micro and macro. The microscale is appropriate for simulation of the damage development phenomenon. Engineering structures operate and experimental tests are performed at the macroscale. For a polycrystalline material, damage development is strictly dependent on the structure of the material. At the microscale, the model uses a tool called cellular automata that enables the description of this dependence. The macroscopic results, required for comparison with the experimental results and for the analysis of engineering structures, are achieved by means of the finite element method. The model connects the cellular automata damage model with the deformation model implemented in the finite element system to realize the multiscale cellular automata finite element model. This connection is made using a nonlocal approach to avoid a solution dependence on the finite element mesh. The nonlocal grid method is considered the most suitable for the discrete cellular automata model. The model has been verified with the experimental results of a uniaxial tension test for copper at elevated temperature. The effectiveness and different variants of the nonlocal grid method for creep crack growth problems have been examined.

Acquiring High-Quality Oil Casing Steel 26CrMoVTiB under Optimal Continuous Casting Process Conditions

While the solidification macrostructure of continuous cast billets is an important factor influencing the final performance and rolling yield of oil casing steel, the continuous casting process parameters have a direct influence on the solidification structure. This study simulated the solidification process of the continuous casting round billets of oil casing steel using a cellular automaton–finite element (CAFE) model. According to the simulation results, at a superheat degree of 20–35 K, a casting speed of 1.9–2.1 m/min, and a secondary cooling specific water flow of 0.34–0.45 L/Kg, the solidification structure had a relatively high equiaxed crystal ratio and small average grain radius. Guided by the simulation results, this paper establishes optimal process schemes for producing 26CrMoVTiB steel round billets, comparatively analyzes the equiaxed crystal ratio and central shrinkage of round billets produced according to these schemes, and defines the optimal continuous casting process conditions, which are: superheat degree = 25 K, casting speed = 2.1 m/min, and specific water flow = 0.35 L/Kg. When adopting these process parameters, the 26CrMoVTiB steel round billets demonstrate a tiny central shrinkage and an equiaxed crystal ratio of 45.2%.

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

Comparison of Transverse Uniform and Non-Uniform Secondary Cooling Strategies on Heat Transfer and Solidification Structure of Continuous-Casting Billet

Water flux distribution largely influences the heat transfer and solidification of continuously-cast steel billets. In this paper, a secondary cooling strategy of transverse non-uniform water flux (i.e., higher flux density on billet center), was established and compared with the uniform cooling strategy using mathematical modeling. Specifically, a heat transfer model and a cellular automaton finite element coupling model were established to simulate the continuous casting of C80D steel billet. The water flux was measured using different nozzle configurations to assist the modeling. The mathematical results were validated by comparing the surface temperature and the solidification structure. It is shown that the non-uniform cooling strategy enables the increase of corner temperature and reduction in surface temperature difference, while a higher reheating rate is found on the surface center of the billet. Moreover, the non-uniform cooling strategy can enhance the cooling effect and refine the solidification structure. Accordingly, the liquid pool length is shortened, and the equiaxed crystal density is increased along with the decreased equiaxed crystal ratio. The uniform cooling strategy contributes to reducing internal cracks of billet, and the non-uniform one is beneficial for surface quality and central segregation. For C80D steel, the non-uniform cooling strategy outperforms the uniform one.

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.

Identification of critical strains for the random cellular automata finite element failure model based on in-situ tensile test

The work is focused on the concept of identification of critical parameters of the random cellular automata finite element (RCAFE) fracture model. The investigated parameters are related to the fracture initiation criteria at the micro scale level for further simulation of the dual phase steel behaviour under deformation conditions. Parameters for brittle and ductile fractures initiation are identified based on the close combination of experimental and numerical in-situ tensile tests. Concept of the RCAFE model as well as details of proposed identification methodology with examples of obtained results are presented within the paper.

Numerical microstructure prediction by a coupled finite element cellular automaton model for selective electron beam melting

Selective Electron Beam Melting (SEBM) refers to an additive manufacturing process of building near net shaped components layer wise by iteratively melting of metal powder using an electron beam. Due to the preheating of the material and very high scan velocities of the electron beam, the process allows large processing windows defined by different process strategies. This variety enables the adjustment of part properties by, e.g., targeting certain microstructures. However, this variety has its disadvantage in the need for costly trial and error experiments. Therefore, numerical predictions are inevitable in locating promising process parameter combinations.We present the weak coupling of a Finite-Element (FE) model with a cellular automaton (CA) model to predict the microstructure evolution during SEBM. We use an FE model for the computation of the heat input, since the temperature history mainly influences the subsequent microstructure evolution. The FE model provides precomputed temperature fields for our sophisticated CA-based crystal growth model, which successfully predicts bulk material microstructures. The compound is validated by accurately reproducing the microstructure of an additively build cylinder from CMSX-4 powder, a nickel based superalloy. Special emphasize is laid on the accurate prediction of the microstructure both in the shell as well as the core of the cylinder.

Direct Macroscopic Modeling of Grain Structure and Macrosegregation with a Cellular Automaton–Finite Element Model

Grain structure and macrosegregation are two main factors determining mechanical properties of components and are strongly coupled during alloy solidification. A two-dimensional (2D) cellular automaton (CA)–finite element (FE) model is developed to achieve a direct macroscopic modeling of grain structure and macrosegregation during the solidification of binary alloys. With the conservation equations of mass, momentum, energy, and solute solved by a macroscopic FE model and the grain structure described by a microscopic CA model, a two-way coupling between the CA and FE models is applied. Furthermore, the effect of the fluid flow on the dendrite tip growth velocity is considered by modified dendrite tip growth kinetics. The CAFE model is applied to a quasi-2D benchmark solidification experiment of a Sn–3.0wt.%Pb alloy, and the grain structure and macrosegregation are predicted simultaneously. It is demonstrated that the model has a capacity to describe the undercooling ahead of the growth front. The growth directions of columnar grains, grain sizes, and columnar-to-equiaxed transition (CET) position are obviously modified by the fluid flow, and obvious segregated channels almost aligned with the orientations of the columnar grains are found. Qualitatively good agreement is obtained between the predicted segregation profiles and experimental measurements.

Optimizing Grain Selection Design in the Single‐Crystal Solidification of Ni‐Based Superalloys

AbstractAn attempt is made to model the design of grain selection during single‐crystal solidification of an Ni‐based superalloy by the Bridgman method. Various geometrical designs of the starter block and spiral grain selector are chosen and their effects on crystal orientation of the single‐crystal part are studied. The competitive grain selection is simulated utilizing the cellular automaton finite element module of the ProCAST software. The simulated results are validated against the experimental observation of grain structure along with the crystal orientation measured by the electron backscatter diffraction (EBSD) and rotational orientation X‐ray diffraction (RO‐XRD) techniques. The results show that in order to obtain the single crystal with a minimum deviation from longitudinal axis, the height and diameter of the starter block as well as the height and the take‐off angle of the spiral should be optimized. It is found that the diameter/height ratio of the starter block should be less than 0.6 to obtain a well‐oriented single crystal prior to entrance of solidification front into the spiral. The height of starter block is found to be more influential than its diameter in selecting the suitable single grain.

Modeling of dynamic recrystallization in white layer in dry hard cutting by finite element—cellular automaton method

White layer formed in hard cutting process has great influence on surface quality of the workpiece, simulation of the white layer has great significance. Dynamic recrystallization critical temperature model is derived to calculate the critical temperature of the dynamic recrystallization in the white layer. A finite element model was developed to simulate the hard cutting process based on the Johnson-Cook constitutive equation. The dynamic recrystallization critical temperature was derived based on the true stress-strain curves obtained by the split Hopkinson pressure bar experiments. The cellular automaton model which aims to simulate the white layer grains formed by the dynamic recrystallization process in hard cutting is established. The temperature and strain data extracted from the finite element model are used in the cellular automaton model. The contrast between the simulation and experimental results demonstrates that the cellular automaton model can simulate the dynamic recrystallization process in the white layer accurately. The dynamic recrystallization processes in the white layer under different cutting speed and flank wear are simulated based on the finite element - cellular automaton model. The results show that the dynamic recrystallization grain size of the white layer decreases with the increase in cutting speed and tool wear.

A two-dimensional simulation of grain structure growth within the substrate and the fusion zone during direct metal deposition

In this paper, a predictive multi-scale model based on a cellular automaton (CA)-finite element (FE) method has been developed to simulate thermal history and microstructure evolution during metal solidification for the Direct Metal Deposition (DMD) process. The macroscopic FE calculation that is validated by thermocouple experiment is developed to simulate the transient temperature field and cooling rate of single layer and multiple layers. In order to integrate the different scales, a CA–FE coupled model is developed to combine with thermal history and simulate grain growth. In the mesoscopic CA model, heterogeneous nucleation sites, grain growth orientation and rate, epitaxial growth, re-melting of pre-existing grains, metal addition, grain competitive growth, and columnar to equiaxed phenomena are simulated. The CA model is able to show the entrapment of neighboring cells and the relationship between undercooling and the grain growth rate. The model predicts the grain size, and the morphological evolution during the solidification phase of the deposition process. The developed “decentered polygon” growth algorithm is appropriate for the non-uniform temperature field. Finally, the single and multiple-layer DMD experiment is conducted to validate the characteristics of grain features in the simulation.

Effect of Nb Addition on Dendrite Growth and Equiaxed Grain Ratio of Fe-20 Pct Cr High-Purity Ferritic Stainless Steel

The acquisition of a high equiaxed zone ratio (EZR) is crucial for ferritic stainless steel (FSS). The main method of achieving this is to use effective particles to promote heterogeneous nucleation. In this study, an increased EZR was obtained owing to dendritic growth kinetics influenced by Nb addition. The EZR increased from 12 to 44 pct when 0.7 wt pct Nb was added to the FSS. The mechanism of increase of the EZR was analyzed by modified dendritic growth kinetics using the Kurz–Giovanola–Trivedi model coupled with thermodynamic data from ThermoCalc. The dendritic growth kinetics for Fe-20 pct Cr and Fe-20 pct Cr-0.7 pct Nb can be expressed as $$ V = 2.258 \times 10^{ - 5} \cdot \Delta T^{3.617} $$ and $$ V = 5.755 \times 10^{ - 7} \cdot \Delta T^{3.248} $$ , respectively, which means that undercooling (ΔT) of Fe-20 pct Cr-0.7 pct Nb was larger than that of Fe-20 pct Cr under the same solidification velocity (V). The undercooling enlarged at the dendrite tip then provided favorable nucleation conditions for FSS and increased the EZR. The as-cast structure, simulated by the cellular automaton–finite element model combined with modified dendritic growth kinetics, compared well with an actual ingot.

Modelling fracture in heterogeneous materials on HPC systems using a hybrid MPI/Fortran coarray multi-scale CAFE framework

A 3D multi-scale cellular automata finite element (CAFE) framework for modelling fracture in heterogeneous materials is described. The framework is implemented in a hybrid MPI/Fortran coarray code for efficient parallel execution on HPC platforms. Two open source BSD licensed libraries developed by the authors in modern Fortran were used: CGPACK, implementing cellular automata (CA) using Fortran coarrays, and ParaFEM, implementing finite elements (FE) using MPI. The framework implements a two-way concurrent hierarchical information exchange between the structural level (FE) and the microstructure (CA). MPI to coarrays interface and data structures are described. The CAFE framework is used to predict transgranular cleavage propagation in a polycrystalline iron round bar under tension. Novel results enabled by this CAFE framework include simulation of progressive cleavage propagation through individual grains and across grain boundaries, and emergence of a macro-crack from merging of cracks on preferentially oriented cleavage planes in individual crystals. Nearly ideal strong scaling up to at least tens of thousands of cores was demonstrated by CGPACK and by ParaFEM in isolation in prior work on Cray XE6. Cray XC30 and XC40 platforms and CrayPAT profiling were used in this work. Initially the strong scaling limit of hybrid CGPACK/ParaFEM CAFE model was 2000 cores. After replacing all-to-all communication patterns with the nearest neighbour algorithms the strong scaling limit on Cray XC30 was increased to 7000 cores. TAU profiling on non-Cray systems identified deficiencies in Intel Fortran 16 optimisation of remote coarray operations. Finally, coarray synchronisation challenges and opportunities for thread parallelisation in CA are discussed.

Development and evaluation of data transfer protocols in the fully coupled random cellular automata finite element model of dynamic recrystallization

Development and application of the hybrid fully coupled, random cellular automata finite element (RCAFE) approach to modelling dynamic recrystallization phenomenon, during a high temperature deformation is the overall goal of the paper. The finite element (FE) solver provides information on equivalent stress, equivalent strain, temperature fields as well as on geometry of deformed computational domain after each time step. These data are transferred to the developed random cellular automata (RCA) model, which is responsible for evaluation of corresponding microstructure morphology evolution and dislocation density changes under dynamic recrystallization (DRX) conditions. Finally, a set of data from the RCA part is send back to the FE solver and used as an input for the next time step. As a result, the fully coupled RCAFE model for simulation of a DRX progress is established. Crucial developments of the RCA model related to the space deformation and efficient neighbors selection are presented within the paper. However, particular attention is put on the development of efficient communication algorithms and methods for input/output data transfer between the FE and RCA modules. The communication protocols based on text files and sockets have different levels of complexity but both are based on the Abaqus VUMAT subroutine. Their capabilities and limitations are evaluated within the paper. Finally, an application of the proposed RCAFE method to simulation of a dynamic recrystallization progress at the level of single grains is presented and discussed to highlight capabilities of the model.

Predicting the Effect of Tool Configuration during Friction Stir Welding by Cellular Automata Finite Element (CAFE) Analyses

The present work aims at selecting the pin geometry for single-sided friction stir welding of steel, and modelling the double-sided FSW process, both through cellular automata finite element analyses. Cellular automata cells are used to hold initial grain size of the base sheets. The stirring action during the process is not modelled physically. Instead the heat flux and strain-rate attained are incorporated by models. In the first objective, by developing heat flux models, strain-rate and strain models for different pin profiles, and the final grain size distribution across the weld zone is predicted. The final pin profile predicted from the present work is not the same used by authors in the existing literature, as observed from grain size prediction. In the second objective, during double-sided friction stir welding, the grain size predictions are agreeing well with the existing data. The efficiency of the approach for tool selection has been demonstrated successfully. [Submitted 8 December 2016; Accepted 5 December 2017]