2023 Volume 64 Issue 2 Pages 360-365
A digital twin for Aluminium billet DC-casting, a digital replica of the physical casting process, creates a living simulation platform that can analyse, update, and change the process to achieve the multi-objectives process optimization. In this work, we assess the possibility of integrating high throughput micro-macro scale computation, SQL database and an artificial neural network (ANN) to establish an analytical twin for the prediction of a typical Direct Chill casting defect of Al alloys, i.e., hot tearing. The high throughput computation consists of solidification path computation at the microscopic scale (dendrite arm scale with software Alstruc) and heat transfer, fluid flow and stress/strain computation at the macroscopic scale (the scale of billet/ingot dimensions with software Alsim). The two-scale computations are coupled via sharing with Alsim the compositional dependent solidification path (Solid fraction-Temperature curve), thermo-physical properties such as densities, thermal conductivities calculated by Alstruc. Then Alsim calculates all the field variables including thermal stress, volumetric strain, and predicts the locations of the most vulnerable position and its hot tearing susceptibility. We demonstrate that the proposed framework can efficiently predict sump depth and hot-tearing tendency in the center of billets for a range of industrial AA6xxx alloy composition, casting parameters including casting speed and casting temperature. The data generated by the multi-scale computation are used to build a SQL database for training and testing the neural network. The utilities of the trained neural network and established SQL database are discussed for their application to optimize DC casting recipes of 6xxx extrusion billets. Our conclusion is that the proposed high throughput multi-scale simulation, SQLite database and ANN parameterization are three essential pillars supporting the establishment of a digital casting twin, and such a twin can provide a quick screening and selection/adjustment of process parameters before casting or during casting to avoid hot-tears.
A digital twin for Aluminium billet DC-casting, a digital replica of the physical casting process, creates a living simulation platform that can analyse, update, and change the process to achieve a multi-objective process optimization. Digital twins can help, quickly or even in real time, aluminum cast houses to decide whether a specific combination or modification in the process parameters and alloy composition would give a quality and productivity within required specifications. It will significantly reduce the early phase exploration margins, minimize the risk of operator errors, increase safety and productivity, and improve scrap-rate in the cast house. It will also significantly reduce the qualification time of new alloys associated with the experimental trial-and-error methods.
Digital twin of a manufacturing system can help in monitoring physical processes, making smart decisions through real-time communication and cooperation with humans, machines, and sensors. It is valuable in coping with the challenges of producing increasingly individualized products with a short lead-time to market and higher quality.1) Research activities on establishing digital twin also have emerged on casting and solidification of metallic materials. In Ref. 2) digital twin has been applied to shorten time between design and production for 3D printing of metallic components, and concluded that a comprehensive digital twin of 3D printing machine can reduce the volume of trial and error testing, reduce defects and shorten time between the design and production. In Ref. 3), neural network has been employed to establish digital twin for gating system design in sand casting. The authors claimed that the digital twin approach is an effective solution to recognize the functional design parameters from the entire filling systems used during casting process. In Ref. 4) the authors demonstrated the viability of the through process simulation-based concept for set up a digital twin to predict and compensate distortion in a High Pressure Die Casting process chain. Nevertheless, no report has been found on establishing digital twin for DC casting of aluminum alloys.
In this paper, we report our practices to build such a digital twin by integrating High Throughput Computation (HTC) with our in-house software Alstruc and Alsim, sqlite relational database and Artificial Neural Network (ANN). We will focus on developing an efficient and autonomous algorithm to perform high throughput Alstruc-Alsim paired simulations (at the scale of 10000) to cover the full combination of all the potential variants in casting parameters and alloy compositions. SQL database will be used to store and index the large amount of data generated by the HTC simulations while ANN is employed for mining and parameterization of the data generated by the HTC.
The proposed digital twin is a data driven approach. Figure 1 illustrates the data flow within the digital twin. The high throughput computations generate data, which is to be managed/stored in a SQL database and further processed/analyzed/parameterized by a machine learning method – Artificial Neural Network. ANN parameterization provides an opportunity for the data to interact with Augmented Reality (AR), In-situ sensors, intelligent robotics, and even Management Information System. This would promote the deployment of the proposed digital twin and make it embedded/interactive with physical casting equipment. This paper is a part of our ongoing project in developing Intelligent Casting systems for Aluminium DC-casting, which aims to combine process know-how systematised in the form of a digital process twin delivered using visualization technologies for simplified and enhanced casthouse operations. It is also the aim of this article to demonstrate that the proposed framework can efficiently predict sump depth and hot-tearing tendency in the center of billets for a range of alloy composition, casting parameters including casting speed and casting temperature.
Schematic of a digital twin for DC casting of Al alloys and data flow.
The Alstruc microstructure modelling software is built on solidification theory with embedded phase diagram and kinetic data for multi-component industrial Al alloys. With the input of alloy composition and cooling rate, Alstruc predict the temperature vs. fraction solid relation, the solid-state concentration profiles, the type, volume fraction, and size of the intermetallic particles, and the temperature-dependent thermal conductivity, density, specific heat, and heat of fusion for use in Alsim (to be introduced below) simulation. This in-house software is developed and maintained by SINTEF with the funding support by Norwegian Research Council and aluminum companies Hydro and Alcoa. Please refer to Ref. 5) for more details about the software. The Alsim casting process modelling software is an FEM model for transient simulations of heat, fluid flow, macrosegreation, stresses and deformation for continuous casting processes. For direct-chill casting the model includes detailed boundary conditions regarding contact zones, air gap sizes and water hit points, and also takes into account the effect of stresses and deformation on the ingot/mould and ingot/bottom block contact during casting. Several cracking indicators are implemented for evaluation of hot-tearing sensitivities and cold-cracking tendencies. This in-house software is developed and maintained by IFE with the funding support by Norwegian Research Council and aluminum companies Hydro, Alcoa, Arconic, Speira and Novelis. Please refer to Ref. 6) for more details about the software.
A tight coupling between these two softwares are described in Ref. 7) for realistic predictions of macrosegregation formation during casting of industrial aluminium alloys. In this work, the models have a looser coupling as thethermophysical properties of the alloys, e.g., solidification paths, heat of fusion as well as temperature dependent densities, thermal conductivity and heat capacity are first calculated by the Alstruc software using the alloy composition cooling rate (e.g. 5 K/s) as input and then automatically added to the Alsim software database for use in the subsequent process simulations. These two in-house softwares are the essential components of the to-be-built digital twin.
2.2 High throughput and autonomous Alstruc-Alsim simulation and results analysisIndustrial aluminum alloys contains up to five alloying components, and all of them have impact on cracking tendency. The casting parameters to be varied include casting speed and casting temperature. To cover the potential compositional and process parameter window, we assume that each component has 4 different compositions while the feasible casting parameters includes 3 different casting speed and casting temperature. The full combination of these varying parameters gives 4 × 4 × 4 × 4 × 4 × 3 × 3 = 9216 simulations. This is the scale to be dealt with our high-throughput simulations.
By taking the advantages of open-source python libraries such as subprocess, threading, Pandas, matplotlib and pario, high throughput and autonomous Alstruc-Alsim simulation and results analysis have been implemented in our in-house software PyMat. PyMat can set up the input files of many user-designated Alstruc-Alsim simulations, manage the execution of the simulations in parallel, and collect and analyze the simulation results.
The basic structure of a PyMat input file is shown on the right of Fig. 2. It consists of three blocks: configuration, App’s keywords, results analysis and visualization. Please note “App” in Fig. 2 is the abbreviation of “Application” while “Software APP” is to highlight that Application represent software within this context.
Illustration of PyMat and software input files structures and their connections.
An exemplary App’s input file can be found on the left of Fig. 2. The connections between PyMat input file and the application’s input file are also illustrated in the figure. The first connection is that a template APP input file name is provided with the keyword of app_case_list:
| \begin{align*} \textbf{app_case_list} &= [[\text{“.$\backslash$template$\backslash$APP1_input_file.txt”,}\\ &\quad \text{ “.$\backslash$template$\backslash$APP2_input_file.txt, ${\ldots}$.}]] \end{align*} |
PyMat schedules the executions of all the simulations in parallel, and monitors the status of each run. It is possible to take some actions when an error is identified and recorded to restart the failed simulation with some recommended numerical input parameters. When all the cases have been executed, PyMat reports their termination status, and analyzes the cases with normal termination status. The input parameters, the main output results and some descriptors are exacted from each simulation and stored in a text file. The HTC simulations generate a large amount of data, and their management/storage are described in the next subsection.
2.3 SQLite database for the storage, management and indexing of HTC simulation resultsSQLite has been selected to manage and store the massive data generated by the HTC simulations. SQLite is a database engine, not a standalone application. As such, it belongs to the family of embedded databases. Its binding to Python language has been used for the implementation of the digital twin. In PyMat, the SQLite database engine is called to record all the input parameters, simulation status and the links (full paths) to the simulations results.
As shown in Fig. 3, the database saves all the input parameters such as the alloys compositions as well as the output related to hot tearing susceptibility such as accumulated volumetric strain. The database enables easy access, indexing and searching of the huge amount data generated from the HTC computations. It also allows the combination and comparison of the database established by different users.
SQLite database for simulation results management and storage.
With the high-throughput computation and simulation result analysis procedure described in the previous section, various descriptors can be generated to reveal the dependency of cracking sensibility on composition and casting parameters. These data will be further parameterized with artificial neural network. The parameterization procedure has been employed in our previous study to parameterize phase diagram data, and detailed description can be found in Ref. 8). Below only a brief description is given.
A fully connected three-layer ANN is shown in Fig. 4, including one input layer, one hidden layer, and one output layer. The number of input and output nodes are defined by the problem to be solved while the number of hidden nodes is arbitrary. Please note the implemented ANN parameterization procedure is not restricted to only three layers.
Input layer, hidden layer and output layer of an artificial neural network.
Assuming there are N input nodes, J hidden nodes, and K output nodes, the non-linear regression function is expressed as
| \begin{equation} y_{k} = \theta_{k} + \sum_{j = 1}^{J}W_{jk} \textit{sigmoid} \left(\theta_{j} + \sum_{n = 1}^{N}\omega_{nj}x_{n}\right) \end{equation} | (1) |
| \begin{equation} \textit{sigmoid}(x) = 1/(1 + \exp(- x)) \end{equation} | (2) |
After making the ANN regression, a parameterization dataset is generated, and combined with eq. (1) these datasets can reproduce the discrete tabulated data points.
In this section, the case study with the established twin for AA 6xxx alloys is reported to avoid hot tearing, i.e., find the casting recipe giving the least hot tearing susceptibility, with the constrains of high productivities. The alloys contain the alloying components of Cu, Mg, Mn and Si. In addition, casting temperature and speed are the other two parameters to be optimized. As to be shown in Section 3.1, the full combination of these varying composition and parameters gives 5 × 7 × 6 × 5 × 2 × 2 = 4200 simulations. It is worthy of estimating the total CPU times required to complete all these simulations in a serial and manual running mode. Each Alsim simulation takes average 5 hours on a PC. Roughly takes total of 21000 hours ≈ 2.4 years in serial running mode (without any delays between each run). Each Alstruc simulation takes about 4 seconds. However, setting up a simulation requires 5 minutes. Roughly takes total of 21000 minutes ≈ 15 days in serial running mode. In addition, it is very tedious job to perform manually as it involves many editing/labelling/checking the calculation status. The method proposed in this article can automate the execution of this large number of simulations and the analysis of the simulation results demonstrating the power of such a digital twin.
3.1 Autonomous high throughput simulations set-up and overall resultsTable 1 list the casting parameter window including the alloy composition and casting temperature and casting speed. The number of full combinations of all the casting parameters variants is 4200.
The casting process is Low Pressure Direct Casting of an extrusion billet with a diameter of 203 mm. 2D axi-symmetric model is used. The meshing of the billet and mould is shown in Fig. 5. Water amount pr mould is set at 7.5 m3/hour while casting temperature is either 680°C or 710°C. The casting speed is set at either 1.4 mm/s or 3 mm/s. The Alsim simulation takes into the coupling of thermal, flow and mechanics (stress and strain), and run until a steady state is reached.
The meshing of the AA6xxx extrusion billet and the LPC mould used in the Alsim simulations.
The 4200 Alsim simulations have been performed parallelly on a workstation with 20 CPU cores and 32 GB Memory. All the simulations are finished in one month, among which 4083 simulations are completed successfully. The failed simulations are mainly due to some oscillations in the solid fraction-temperature relation curve produced by Alstruc. This numerical issue is planned to be resolved in our future study. The size of the total data generated is 323 GB. Figure 6 shows the RDG criterion index10) collected automatically by PyMat from all the successful paired Alstruc-Alsim simulations providing an overview of the simulation results. The RDG index, proved to be applicable to DC casting process,11) is calculated with the liquid pressure drop from the estimated thickness of the mushy zone and the strain rate at a selected solid fraction.
The final RDG criterion index collected from all 4083 successful paired Alstruc-Alsim simulations.
The paired Alstruc-Alsim simulation can describe in detail the casting process. Figure 7, which consists of the casting mould presented in Fig. 5 and the whole length of the billet, shows how the Mn composition affect the sump profile while the Mg/Si ratio is fixed at 1.2. PyMat can be used to automate this comparing process.
The sump profile for the two alloys with different Mn contents (a) 0.55 wt%Mn (b) 0.0 wt%Mn while the Mg/Si ratio is fixed at 1.2.
To predict hot tearing susceptibility, RDG criterion and accumulated Volumetric Strain at the central line in the casting with the designated solid fraction of 0.98 are calculated by Alsim and collected by PyMat from each simulation. These two are going to be used as a hot tearing index. Figure 8 shows the dependency of RDG criterion on Cu and Mg contents while the other alloying component contents and casting temperature and speed are fixed.
The dependency of RDG criterion on Cu and Mg contents while the other alloying component contents and casting temperature/speed are fixed.
One of the big advantages of the proposed HTC, database, and ANN analysis strategy is to enable scanning the full combination of all the possible variants of casting parameters. With the massive brute-force calculations, one could identify the casting recipe that gives least cracking susceptibility with some arbitrary constrains. Figure 9 gives such an example by searching for the effects of alloying component Si on Al–0.5 wt%Cu–0.5 wt%Mg–0.275 wt%Mn.
The effects of varying alloying component Si on the RDG index of Al–0.5 wt%Cu–0.5 wt%Mg–0.275 wt%Mn.
PyMat has collected the predicted cracking criterions from each simulation and assembled them into a separate datasheet together with simulation ID and the varying casting parameters. This datasheet has been fed as training data into the artificial neural network described in Section 2.4 for parameterization. PyMat allows the user to set the ranges of two key ANN parameters: number of network layers and number of neutrons per layer. For this case study, the form is set in the range list of (1, 2, 3, 4) while the later in the range list of (20, 30, 40, 100). The full combination of these two input parameters generates 16 different neural networks and leads to the parameterization with different accuracy. The ANN parameterization with the highest training accuracy (99.3%) is the one with 4 layers and 30 neutrons per layer. Its prediction for the RDG criterion is plotted against the training data in Fig. 10 demonstrating that the parameterization procedure has produced accurate fitting to the input data. The comparison of these numerical simulation results with experimental measurements is still in progress, and will be reported later.
The RDG criterions fed into the artificial network work (number of layers = 4 and number of neutrons = 30) vs. the prediction by the network.
It is worthy of noting that the trained ANN can be used not only to predict the hot tearing susceptibility within the ranges covered by the training data, but also outside the range after the verification with some key experimental results on cracking susceptibility.
In this work, we assess the possibility of integrating high throughput micro-macro scale computation, SQL database and an artificial neural network (ANN) to establish an analytical twin for the prediction of a typical Direct Chill casting defect of Al alloys, i.e., hot tearing. With an industrial case study for AA6xxx alloys, we demonstrate that the proposed framework can efficiently predict sump depth and hot-tearing tendency in the center of billets for a range of industrial AA6xxx alloy composition, casting parameters including casting speed and casting temperature. Our conclusion is that the proposed high throughput multi-scale simulation, SQLite database and ANN parameterization are three essential pillars supporting the establishing of a digital casting twin, and such a twin can provide a quick screening and selection of process parameters before casting or adjustments during casting to avoid hot-tears. In our further study we will explore the linkage of the ANN parametrization results with sensors and the control units of a casting equipment. An industrial demonstration is also planned to reveal further the potentials of the proposed data driven digital twin.
This research work is funded under the grant name “Digital technologies for Intelligent Aluminium Casting Systems” with support from the Research Council of Norway and Norsk Hydro and Hycast.
