Cellular Automaton Finite Element Model Research Articles

Modelling the Charpy Impact Ductile-Brittle Transition of a Ship Plate Steel with CAFE Modelling

In the present work, a cellular automata finite element model (CAFE) was developed to model the ductile-brittle transition of a Grade A ship plate steel. Therefore, ductile and brittle cellular automata (CA) arrays of cells were created in the model to integrate material data at microstructural level, along with the ductile and brittle fracture processes. Microstructural data was analysed with Weibull distributions and incorporated in CAFE model using random number generators, along with ductile and brittle fracture parameters. Ductile fracture was modelled with Rousselier damage model; hence damage model parameters were calibrated with experimental data. Brittle fracture was modelled with Beremin model, and four different cleavage particles, found in a Grade A ship plate steel, were incorporated in CAFE model in order to model a competition of particles nucleating microcracks of critical size in the damage regions of Impact Charpy tests and four-point double-notch bend tests performed at low temperature. The mechanical properties the plate steel was measured in the transition region and incorporated in CAFE model, along with ductile-brittle transition rules. The present CAFE model was able to simulate distributions of microcracks in the notch region of four-point double-notch bend models (in the transition region), which correlated with experimental data. CAFE model was also able to simulate microvoids in the notch region of Charpy specimens along with the load-displacement Charpy curve for room test temperature, with very good agreement with experimental data. Once CAFE model was validated at micro and structural level, it was applied to model the typical scatter of impact Charpy energy values in the transition region of Grade A ship plate steel with good agreement with the measured ductile-brittle transition curved of the plate steel. Keywords: cellular automata, finite element modelling, ductile-brittle transition, damage modelling.

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.

Integrated vehicle chassis fabricated by wire and arc additive manufacturing: structure generation, printing radian optimisation, and performance prediction

ABSTRACT In the automotive industry, the extended design and iteration cycles for integrated chassis typically span 2–3 years, creating a misalignment with swiftly changing market demands. Wire arc additive manufacturing (WAAM) technology presents a viable alternative, overcoming the limitations of conventional chassis production. Our holistic framework significantly condenses the design, optimisation, and validation stages for automotive chassis. Initially, a ground structure method is utilised to outline and generate a skeleton chassis. We then utilise the OpenCV image processing method to select a hollow skeleton chassis with minimal material occupancy (0.476) and suspension printing. Subsequently, we assess the influence of printing radian variations by the robotic arm on the microstructure and stress, employing a cellular automaton-finite element (CA-FE) model at the 150th and 200th layer benchmarks. A Kalman filter (KF) is also implemented to fine-tune the printing radian in regions with coarse grain structures and elevated solute concentrations. The process concludes with collision and modal simulation verifications of the skeleton chassis, affirming the optimisation's success. This streamlined methodology allows the completion of the chassis design and manufacturing cycle within a remarkably condensed time frame of one week, accelerating the development process by a factor of 120.

Modeling the Evolution of Grain Texture during Solidification of Laser-Based Powder Bed Fusion Manufactured Alloy 625 Using a Cellular Automata Finite Element Model

The grain texture of the as-printed material evolves during the laser-based powder bed fusion (PBF-LB) process. The resulting mechanical properties are dependent on the obtained grain texture and the properties vary depending on the chosen process parameters such as scan velocity and laser power. A coupled 2D Cellular Automata and Finite Element model (2D CA-FE) is developed to predict the evolution of the grain texture during solidification of the nickel-based superalloy 625 produced by PBF-LB. The FE model predicts the temperature history of the build, and the CA model makes predictions of nucleation and grain growth based on the temperature history. The 2D CA-FE model captures the solidification behavior observed in PBF-LB such as competitive grain growth plus equiaxed and columnar grain growth. Three different nucleation densities for heterogeneous nucleation were studied, 1 × 1011, 3 × 1011, and 5 × 1011. It was found that the nucleation density 3 × 1011 gave the best result compared to existing EBSD data in the literature. With the selected nucleation density, the aspect ratio and grain size distribution of the simulated grain texture also agrees well with the observed textures from EBSD in the literature.

Simulation of the solidification organization of X15CrNiSi20-12 alloy castings during investment casting based on the CAFE model

In this work, the CAFE (Cellular Automata Finite Element) model was used to simulate the grain growth of X15CrNiSi20-12 austenitic stainless steel during the investment casting process, and the effects of shell thickness, shell temperature, casting temperature, and cooling rate on the solidification organization were investigated by orthogonal tests. The results show that the cooling method has an important effect on the formation of equiaxed crystals. However, the shell temperature, shell thickness, and casting temperature have a smaller effect on the formation of equiaxed crystals. A more equiaxed fine grain structure can be obtained by using a shell thickness of 7 mm, shell temperature of 1143.15 K, casting temperature of 1913.15 K, and water-cooling conditions. In addition, a decrease in the shell thickness, shell temperature, and casting temperature can lead to an increase in the grain size, while an increase in the cooling rate will lead to smaller grain size and increase the number of equiaxed fine crystals, thus improving the mechanical properties of the material.

Effects of Alloying Elements on Solidification Structures and Macrosegregation in Slabs

A Cellular Automaton-Finite Element (CAFE) model and a secondary dendrite arm spacing (SDAS) model are established to study the evolutionary behavior of the macrostructure and the secondary dendrites on a 295 × 2270 mm2 slab cross-section of experimental steel, respectively. The relationship between the element content, SDAS, equiaxed crystal ratio (ECR) and macrosegregation in continuously cast experimental slabs was studied comprehensively. It is found that with the increase in carbon content, the ECR increases at first and then decreases, and the ECR reaches the maximum value when the carbon content is 0.3%. With the increase in carbon content, the SDAS and average grain size of the equiaxed crystal zone increase, whereas the Si and Al content evidently affects the SDAS and average grain size of the equiaxed crystal zone to a greater extent than the Mn content. In addition, the SDAS can be reduced by reducing the content of C and Si within the acceptable range of alloy composition.

Numerical simulation of solidification structures in continuous casting of a thin slab at high casting speed

ABSTRACT The solidification structure of a thin slab during the continuous casting process at high casting speed was simulated based on the cellular automaton-finite element (CAFE) model. The simulations were consistent with the solidification structures of actual steel samples, and the influence of the continuous casting process parameters and alloy elements were further studied in detail. The optimum process parameters obtained are as follows: the casting speed at 5.2–5.4 m min−1, the superheat at 20–25 °C, and the specific water flow at 1.62–1.64 L kg−1. Meanwhile, the Si content in the thin slab was appropriately increased to refine the grains and improve the production efficiency. This study provides important theoretical data for practical thin slab production, improvement of the continuous casting efficiency, thereby reducing accidents.

Structure and texture simulations in fusion welding processes – comparison with experimental data

The Cellular Automaton-Finite Element (CAFE) method is used to simulate grain structure evolution during gas tungsten arc welding of 316 L steel plates. The experimental configuration is designed for in-situ observations of the melt pool and liquid flow. It is complemented by electron back scattered diffraction analyses to reveal the texture resulting from melting and solidification. Simple configurations are used to facilitate comparisons with simulations, that consider no addition of metal (remelting process) and constant power for two welding speeds. It is found that the melt pool shape can be very well retrieved for the two welding speeds providing that the relation between the dendrite tip growth velocity and the undercooling is adjusted. As a result, the computed grain structure reaches good agreement with measurements in terms of morphology, orientation and texture. A standard growth kinetics model underestimates the melt pool shape and results in large deviation of the simulated grain structure with measurements. The plate subsidence after processing reaches a maximum deflection at the center of the weld seam. It is also measured and compared to the simulations that include free metal/gas boundaries, showing satisfying results despite a weaker calculated fluid flow. Finally, the chaining and coupling schemes of the CAFE model are both studied in order to quantitatively evaluate their roles on the predicted melt pool shape and grain structure. The coupling scheme reveals better coherency between macroscopic results and grain structure simulation.

Optimization of Shrinkage Porosity in Grinding Media Balls by Casting Design Modification and Simulation Technique

Shrinkage porosity or cavity are associated with the solidification of the metal either due to gas/air entrapment or when the shrinkage occurring during solidification is not entirely compensated by the riser. Shrinkage cavities occurring in the casting reduces its strength which leads to unfulfillment of the desired serviceability. In this paper, casting design has been modified using the DISA manual to achieve directional solidification which directly relates to improvement of casting quality. The running of metal from pouring basin into casting along with solidification has been analysed through PROCAST which is a casting simulation software based on Finite Element Method and CAFE (Cellular Automata Finite Element) Model. The feeding system of the casting has been modified in terms of shape and volume to minimize air aspiration effect and promote directional solidification. The model used is of grinding media balls casting of high chromium cast iron. The feeding pattern, feeding velocity and solidification with respect to pouring temperature, pouring rate, ambient temperature and film coefficient has been analysed. The final optimum range of all parameters with corresponding minimum shrinkage porosity in casting was obtained. Main aim was to minimize shrinkage porosity in the main casting, ignoring gating and feeding system. The actual minimization of shrinkage porosity comes out around 56 %.

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.

Optimizing the cellular automata finite element model for additive manufacturing to simulate large microstructures

This study proposes an implementation of the cellular automata finite element (CAFE) model in order to optimize its performance for simulating the solidification of additively manufactured (AM) materials. The translating melt pool in AM leads to a highly localized region of activity at any given time. The time scale associated with the evolving temperature field is much larger than the time scale associated with grain solidification. A separation of temporal scales is proposed such that solidification analysis is treated independently as sub-cycles within each discrete time step of the scanning laser. At each laser time step, all of the domain is idle except a small portion, which is the region where the material is undercooled but has yet to be solidified. This region is identified, and a second partition of the computational resources is established such that the solidification computations are evenly balanced. Numerical studies demonstrate that the proposed implementation achieves dramatic improvement in parallel scalability than previously reported and thus advances the state-of-the-art of CAFE modeling for AM in terms of computational efficiency. This improved computational performance is necessary to simulate the large 3D polycrystalline microstructures required to evaluate texture and grain morphology, and two of such simulations are presented. The model is validated for laser powder bed fusion 316L stainless steel, where the polycrystalline grain morphology and crystallographic texture of the simulated microstructure closely match experimental characterization data. A second simulation is performed for a different scan pattern in order to highlight and evaluate its effect on microstructural features.

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.

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.

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.

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.

Numerical Study on Solidification Behavior and Structure of Continuously Cast U71Mn Steel

The solidification behavior and structure of continuous casting high rail U71Mn bloom, under different secondary cooling conditions and superheat, were numerically investigated using the Cellular Automaton-Finite Element (CAFE) model implemented with ProCAST software. Nail shooting and macro etch experiments of the bloom samples under different cooling conditions were conducted to verify the model of macroscopic solidification and structure. The results showed that the simulated results of the solidified shell and solidification structure are basically consistent with experimental results. The secondary cooling condition has little effect on the grain size and distribution of the bloom, while both the bloom surface and corner temperatures are higher and the temperature rise at the beginning of the air-cooling zone is smaller under the super-slow cooling condition. The percentage of center-equiaxed grains decreases from 44.6% to 20.1% and the grain average radius increases from 1.025 to 1.128 mm when the superheat increases from 15 to 40 K, with little change in the grain size occurring between 15 and 20 K. Moreover, for a step increase in the superheat of 5 K, the solidification end is lengthened by about 0.19 m and the surface temperature is enhanced by 3 K. The super-slow secondary cooling condition with the superheat controlled within 20 K is suitable for big-bloom casting.

Columnar and Equiaxed Solidification of Al-7 wt.% Si Alloys in Reduced Gravity in the Framework of the CETSOL Project

During casting, often a dendritic microstructure is formed, resulting in a columnar or an equiaxed grain structure, or leading to a transition from columnar to equiaxed growth (CET). The detailed knowledge of the critical parameters for the CET is important because the microstructure affects materials properties. To provide unique data for testing of fundamental theories of grain and microstructure formation, solidification experiments in microgravity environment were performed within the European Space Agency Microgravity Application Promotion (ESA MAP) project Columnar-to-Equiaxed Transition in SOLidification Processing (CETSOL). Reduced gravity allows for purely diffusive solidification conditions, i.e., suppressing melt flow and sedimentation and floatation effects. On-board the International Space Station, Al-7 wt.% Si alloys with and without grain refiners were solidified in different temperature gradients and with different cooling conditions. Detailed analysis of the microstructure and the grain structure showed purely columnar growth for nonrefined alloys. The CET was detected only for refined alloys, either as a sharp CET in the case of a sudden increase in the solidification velocity or as a progressive CET in the case of a continuous decrease of the temperature gradient. The present experimental data were used for numerical modeling of the CET with three different approaches: (1) a front tracking model using an equiaxed growth model, (2) a three-dimensional (3D) cellular automaton–finite element model, and (3) a 3D dendrite needle network method. Each model allows for predicting the columnar dendrite tip undercooling and the growth rate with respect to time. Furthermore, the positions of CET and the spatial extent of the CET, being sharp or progressive, are in reasonably good quantitative agreement with experimental measurements.