Cellular Automaton Finite Element Research Articles

Towards a Direct Consideration of Microstructure Deformation during Dynamic Recrystallisation Simulations with the Use of Coupled Random Cellular Automata-Finite Element Model.

Dynamic recrystallisation (DRX) is one of the fundamental phenomena in materials science, significantly impacting the microstructure and mechanical properties of components subjected to large plastic deformations. Experimental research on that topic carried out for a wide range of new metallic materials is often supported by computational materials science. A direct consideration and detailed understanding of this phenomenon are possible with a class of full-field numerical models based on the cellular automata (CA) method. However, the classical CA approach is based on a regular, fixed computational space and has limitations in capturing large deformations of the computational domain. Therefore, the main goal of the work is to develop and implement an alternative solution to overcome this limitation. The proposed solution is based on coupling the finite element (FE) method with the random cellular automata (RCA) approach. Such a model can directly consider the influence of geometrical changes in microstructure during large plastic deformation on recrystallisation progress. Details of the developed RCA DRX model assumptions and coupling issues with FE mesh are discussed. Particular attention is also paid to increasing model efficiency and robustness studies.

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.

Parametric Modelling of Rousselier ́s Damage Model Parameters with Instrumented Charpy Tests

This work presents Rousselier´s damage model parameters effect and their physical meaning on Charpy fracture propagation curves. Therefore, instrumented Charpy tests were performed at room test temperature to measure the load-displacement curve. The parameters were measured from a Grade A ship plate steel, employed for the construction of merchant ships. The effect of Rousselier´s model parameter was done by performing cellular automata finite element (CAFE) modelling, where Rousselier’s damage model was coded, and therefore Rousselier´s model parameters were incorporated using random number generators in the ductile arrays of cells, using Weibull distributions. Consequently, in each CAFE simulation, the model evaluates random values of Rousselier´s damage model parameters performing a more physically based modelling. The results showed that the present CAFE modelling was able to reproduce the hardening and fracture propagation regions of instrumented Charpy data. Furthermore, the present work showed a suitable Rousselier´s damage model parameters calibration procedure with Charpy data, and how each Rousselier´s model parameter can affect the hardening and fracture propagations regions when they are not properly calibrated, producing unrealistic results. Additionally, it can be observed that the present results can be used as a template for a better calibration of Rousselier´s damage model parameters in CAFE modelling.

A framework for predicting residual mechanical response fields for laser powder bed fusion at the polycrystalline length scale

A framework is developed to directly model the effect of processing parameters utilized during laser powder bed fusion additive manufacturing (LPBF AM) on material thermomechanical response during solidification in order to predict residual stress and strain development at the microstructure-resolved polycrystalline length scale. Specifically, a workflow is established where the processing parameters serve as input to a cellular automata finite element (CAFE) model that simulates the microstructure solidification evolution via a thermally driven empirical solidification law. The CAFE’s output microstructures serve as representative volume elements which are input to a Multiphysics finite element solver, which solves the thermally driven mechanical response during solidification based on the crystal plasticity finite element formulation. A model validation study is presented, which demonstrates that the modeling framework accurately predicts various features of intragrain misorientation when compared to electron backscatter diffraction data of an LBPF 316L thin wall part built using a GE/Concept Laser M2 SLM system. Following model validation, four variations of processing parameters are chosen to investigate the influence of scan strategy and laser scan velocity on the manufacturing of an LPBF 316L thin wall. Also included is an analogous simulation that treats the microstructure as isotropic and homogeneous, which allows for quantifying the contribution of microstructural heterogeneity on residual stress and strain distribution and magnitudes. Correlations between processing parameters, temperature fields, texture and grain morphology, and the resulting as-built mechanical response are determined and discussed. The current research has the potential to provide valuable insights and guidance for designing AM build conditions to optimize residual mechanical response together with grain structures and textures.

Evaluation of Dynamic Recrystallization Phenomenon in Friction Stir Welding of AA5083-O by Cellular Automata Finite Element Approach

Evaluation of Dynamic Recrystallization Phenomenon in Friction Stir Welding of AA5083-O by Cellular Automata Finite Element Approach

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

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 %.

Statistical modelling of fracture using cellular atomata finite element

Fracture is an inherently statistical phenomenon as it is a function of micro-structural heterogeneities such as distributed defects and inclusions. This is evidenced by scatter in the toughness of seemingly identical specimens. Therefore, deterministic approaches do not give full picture of scatter in fracture behaviour. More suitable probabilistic methods have been devised to describe the scatter associated with fracture. While the probabilistic approaches provide a sound scientific basis for capturing the scatter in the fracture data through assuming a probability for the presence of fracture initiators, their microstructurally agnostic assumptions can limit their predictive capability. This is because there is no information on the microstructure such as grain size and morphology, texture, and other important features considered in them. An alternative class of models which take into account the distribution of toughness is cellular automata finite element models (CAFE). CAFE models are stronger in simulating the scatter in the fracture data through their ability to represent the microstructure although so far, they have been limited to fully brittle or quasi-brittle materials. In addition, the CAFE models they are computationally expensive, and their running time can be prohibitive for their application to large scale engineering components thus reducing their appeal. In this study, a CAFE model was developed to take advantage of the microstructural fidelity of CAFE but presented within the context of a probabilistic fracture approach. The CAFE based model calculates the macroscopic strain from the continuum FE model. The strain is then used to load a model which is defined in the cellular automata space. The CAFE model then simulates the initiation and propagation of fracture in the microstructure to fully capture the heterogeneity of the material at the lower length scale. The critical stress acting normal to the cleavage plane of each grain is calculated in the CAFE model and used to decide the onset of cracking in a probabilistic manner; the stress depends on the orientation of the grain in which microcrack initiates as well as depending on the orientation of the surrounding grains. To evaluate its performance, the model was calibrated using a set of experimental fracture toughness data and the results of its prediction were compared with an intendent and separate set of warm prestress experiments of the same material. Good agreement between the prediction and the experiment of the second set was observed giving confidence in the model.

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.

Simulation study on temperature field and microstructure of Ti-6Al-4V alloy round ingot during EBCHM

The solidification structure of Ti-6Al-4V round ingot during the electron beam cold hearth melting (EBCHM) directly determines the quality of the ingot and the performance of the subsequent rolled coil. In this paper, the Cellular Automaton Finite Element (CAFE) method is used to numerically simulate the solidification structure of Ti-6Al-4V ingot. Firstly, the mathematical model is established with a numerical solution. Secondly, effects of process parameters including the pouring temperature and pulling speed on the solidification structure are revealed. The results show that the microstructures predicted by the numerical method match the experimental results. For the case of fixed pulling speed, a reduction in the pouring temperature leads to the grain refinement and the decreased volatilization of Al. With an increase of the pulling speed, the number of grains first increases and then decreases, but the average grain size first decreases and then increases. Furthermore, the maximum grain size monotonically increases with increasing the pulling speed. Thus, the fine solidified structure with fine grains can be obtained at the pouring temperature of 1700 °C and the pulling speed of 4 × 10−4 m s−1.

Ultrasonic Wave Propagation Analysis in Cast Stainless Steel With Solidification Grain Structure Predicted by Cellular Automaton Finite Element Approach

Abstract Several components of nuclear power plants are made of cast austenitic stainless steel (CASS) because of its high corrosion resistance and strength. The inservice inspection based on ultrasonic testing (UT) has to be conducted for CASS components in accordance with fitness-for-service codes such as the Japan Society of Mechanical Engineers Rules on Fitness-for-Service for Nuclear Power Plants. However, a high-accuracy evaluation of flaws in CASS components through UT is difficult because the ultrasonic waves are scattered and attenuated by coarse grains, and their beam is distorted by the anisotropy resulting from the grain orientations. Numerical simulations are useful and reasonable ways for better understanding the ultrasonic wave propagation behavior in CASS. To effectively achieve this, the simulation model should include a three-dimensional (3D) grain structure. If a casting simulation can predict the solidification structure in a CASS, the wave propagation could be simulated also for a more realistic situation. In this study, we predicted the solidification structure of statically CASS by using a cellular automaton (CA) coupled with the finite element method and fed this structure into an explicit finite element model (FEM) for simulating the propagation of waves emitted by angle beam probes. Afterward, these simulated wave propagations were compared with those measured by a 3D laser Doppler vibrometer (LDV), showing almost good agreement between predicted and experimental results.

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.