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Journal = Metals
Section = Computation and Simulation on Metals

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15 pages, 1858 KB  
Article
Comparison of FE Modeling Approaches for the Prediction of Cutting Forces and Chip Morphology During Turning of Ti-6Al-4V ELI Alloy
by Nikolaos E. Karkalos, Nikolaos A. Fountas and Nikolaos M. Vaxevanidis
Metals 2026, 16(6), 677; https://doi.org/10.3390/met16060677 (registering DOI) - 19 Jun 2026
Viewed by 79
Abstract
The significant challenges of machining hard-to-cut materials pose an important problem for the manufacturing industries, as it can lead to increased tool wear, higher machining costs, and reduced productivity. Apart from experimental investigations, which are rather expensive and cannot always provide a comprehensive [...] Read more.
The significant challenges of machining hard-to-cut materials pose an important problem for the manufacturing industries, as it can lead to increased tool wear, higher machining costs, and reduced productivity. Apart from experimental investigations, which are rather expensive and cannot always provide a comprehensive view of the process outcome due to limitations in measurement techniques, it is possible to use validated models to predict the temperature and stress state of the workpieces or test the effect of different process conditions. Although many Finite Element (FE) models have been developed for the turning process, usually accurate representation of the machining setup with a realistic 3D geometry for both cutting tool and workpiece is not taken into account. Thus, in this work, two different representations of the machining setup, including curved workpiece geometry, which is more rarely studied, are compared for the case of Ti-6Al-4V ELI turning under various conditions, and their effect on the accuracy of the prediction of the cutting force and chip morphology is investigated. It was found that the model with the straight workpiece overpredicts the cutting force to a higher extent compared to the model with the curved workpiece and also predicts a much higher workpiece temperature, whereas chip morphology was mainly affected by feed rate. No noticeable differences were observed between the two models. These results indicate that in most cases, the use of geometry with curved workpiece is more suitable for better prediction of the cutting forces. Full article
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19 pages, 2414 KB  
Article
Optimization of Copper-Embedded Cathode Collector Bars for Reducing Cathode Voltage Drop and Horizontal Current in Aluminum Electrolysis
by Jinfeng Han, Chunchun Dong, Yuran Chen, Yapeng Kong and Xuemin Liang
Metals 2026, 16(6), 639; https://doi.org/10.3390/met16060639 - 10 Jun 2026
Viewed by 205
Abstract
Aluminum electrolysis is an energy-intensive process in which the cathode voltage drop (CVD) and horizontal current in the molten aluminum layer directly affect energy consumption and cell stability. In this study, a three-dimensional electro-thermal model of a 400 kA prebaked aluminum electrolysis cell [...] Read more.
Aluminum electrolysis is an energy-intensive process in which the cathode voltage drop (CVD) and horizontal current in the molten aluminum layer directly affect energy consumption and cell stability. In this study, a three-dimensional electro-thermal model of a 400 kA prebaked aluminum electrolysis cell was established to optimize copper-embedded cathode collector bars. Using a staged parameter-screening and integrated optimization strategy, the effects of copper rod longitudinal position, diameter, and embedded length on CVD, horizontal current density, cathode surface current uniformity, and thermal response were systematically evaluated. Under the present modeling conditions, the configuration with a longitudinal position of 1.0 m, diameter of 0.05 m, and embedded length of 1.0 m provided a favorable balance between electrical performance and copper consumption. This design reduced the equivalent voltage drop by 142.7 mV and decreased the average horizontal current density in the molten aluminum layer to approximately 4900 A/m2. The peak cathode surface current density was also reduced, corresponding to a predicted cathode service-life increase of approximately 13.2% based on a relative wear model. A preliminary economic analysis indicated that an initial investment of CNY 424,000 could yield conservative annual electricity cost savings of approximately CNY 114,000, with a simple payback period of about 3.7 years. These results provide quantitative guidance for the structural design and industrial evaluation of copper-embedded cathode collector bars. Full article
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17 pages, 1626 KB  
Article
Modeling of Gibbsite Solubility in Na+-K+-OH-Al(OH)4-SO42−-CO32− System Applied to Precipitation at Sintering Alumina Refineries
by Tatiana E. Litvinova and Nickolai V. Tuleshov
Metals 2026, 16(6), 633; https://doi.org/10.3390/met16060633 - 9 Jun 2026
Viewed by 228
Abstract
The quantitative prediction of the equilibrium gibbsite content in alkaline liquors of alumina production is a key parameter for controlling precipitation kinetics and ensuring product quality. Unlike Bayer alumina refineries, sintering alumina refineries use different alkali and impurity content ranges; moreover, they are [...] Read more.
The quantitative prediction of the equilibrium gibbsite content in alkaline liquors of alumina production is a key parameter for controlling precipitation kinetics and ensuring product quality. Unlike Bayer alumina refineries, sintering alumina refineries use different alkali and impurity content ranges; moreover, they are characterized by the presence of significant amounts of potassium in aluminate liquors that are not considered in the existing gibbsite equilibrium models. This paper presents an extended mathematical model, which is based on the Rosenberg–Healey methodology and incorporates sodium (Na2O) and potassium (K2O) components into the total alkaline system. Model coefficients were optimized using 18 tests designed by the D-optimal method at temperatures of 50–85 °C and a total alkali content of [R2Ok] = 40–80 g/L, which contains up to 30% of potassium alkali K2O, as well as the impurities in the form of soda [Na2CO3] = 0–58 g/L and sodium sulfate [Na2SO4 ]= 0–25 g/L. The fine-tuned model was verified using the composition of actual refinery liquors and provides RMSE = 0.71 g/L Al2O3, thus demonstrating satisfactory solubility prediction accuracy. The presented model can be used to calculate aluminate liquor productivity at existing sintering refineries with a sodium–potassium system. Full article
(This article belongs to the Section Computation and Simulation on Metals)
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28 pages, 140968 KB  
Article
CNN-Based Classification of Structural Steel Microstructures for the Prediction of the Outcome of the Welded Bead Bending Test
by Fritz Backofen, Matthias Hockauf, Kristin Hockauf and Thorsten Halle
Metals 2026, 16(6), 625; https://doi.org/10.3390/met16060625 - 7 Jun 2026
Viewed by 266
Abstract
The Welded Bead Bending Test (WBBT), used in Germany to assess the crack-arrest capacity of structural steels, is conducted in accordance with ZTV-ING Part 4 or Deutsche Bahn Standard 918 002-02 and specified in Stahl-Eisen-Prüfblatt 1390. Three possible test outcomes are distinguished: passed [...] Read more.
The Welded Bead Bending Test (WBBT), used in Germany to assess the crack-arrest capacity of structural steels, is conducted in accordance with ZTV-ING Part 4 or Deutsche Bahn Standard 918 002-02 and specified in Stahl-Eisen-Prüfblatt 1390. Three possible test outcomes are distinguished: passed if a bending angle of α60° is reached without fracture but with visible cracks in the base material, not passed if fracture occurs beforehand, and invalid if no crack propagates into the base material despite bending to α60°. This study proposes a novel data-driven approach for predicting WBBT outcomes using a Convolutional Neural Network (CNN) applied to patch-wise classification of Light Optical Microscopy images (LOMs) taken from WBB-tested samples. A dataset comprising 800 LOMs from 40 steel samples originating from various manufacturers was acquired in collaboration with Chemnitzer Werkstoff- und Oberflächentechnik GmbH. Five CNN architectures are evaluated in terms of Accuracy, Recall and Specificity: MicroNet-pretrained DenseNet-121 and EfficientNet-B0, ResNet-34 pretrained on both ImageNet (I-ResNet-34) and MicroNet (M-ResNet-34), and a light CNN trained from scratch. The models were subjected to training in accordance with three different methods, which varied by patch size and number of LOMs utilised for training. Two validation strategies, patch-level and sample-level splitting, were employed to analyse potential data leakage effects. The I-ResNet-34 model demonstrates the best performance in this comparison, achieving a patch-level Accuracy of 79.58% ± 6.82% and an image- and sample-level Specificity of 100% under sample-level splitting. This performance is confirmed via leave-one-sample-out cross-validation, yielding a comparable patch-level Accuracy of 79.36% and a Specificity of 86.26%. The corresponding WBBT sample-level results under this validation scheme are approximately 86% Accuracy and 91% Specificity. Full article
(This article belongs to the Special Issue Machine Learning Models in Metals (2nd Edition))
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22 pages, 20012 KB  
Article
A Detail-Preserving Multi-Scale Cascaded Network for Infrared Rotary Kiln Shell Temperature Recognition and Refractory Lining Assessment
by Jie Li, Jianxin He, Hao Liu, Yunhan Hou, Zhiming Dong and Qian Zhang
Metals 2026, 16(6), 597; https://doi.org/10.3390/met16060597 - 29 May 2026
Viewed by 164
Abstract
Rotary kiln shell temperature monitoring is essential for metallic shell protection and refractory lining maintenance in high-temperature industrial processes, while smoke, dust, thermal diffusion and non-kiln heat sources make valid shell temperature extraction difficult. This study develops a multi-scale cascaded network with low-resolution [...] Read more.
Rotary kiln shell temperature monitoring is essential for metallic shell protection and refractory lining maintenance in high-temperature industrial processes, while smoke, dust, thermal diffusion and non-kiln heat sources make valid shell temperature extraction difficult. This study develops a multi-scale cascaded network with low-resolution space-to-depth downsampling (MSC-LSTD) for infrared kiln shell segmentation and temperature recognition. Global infrared thermal images and local laser temperature measurements are used to construct a calibrated rotary kiln infrared dataset, and predicted kiln shell masks are mapped to temperature matrices for valid shell temperature analysis. MSC-LSTD achieves 99.82% aAcc, 99.14% mAcc and 97.03% mIoU on the rotary kiln infrared dataset, showing robust segmentation performance under complex thermal interference. The proposed framework provides a practical image-based solution for kiln shell overheating warning and refractory lining degradation assessment. Full article
(This article belongs to the Section Computation and Simulation on Metals)
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30 pages, 3196 KB  
Article
Analysis of EAF Energy Efficiency Characteristics Based on Industrial Data and Energy Balance
by Hongjin Zhang, Guangsheng Wei, Fuhai Liu, Shenghai Han, Xiaodan Zhong, Jianzhong Wang and Xiaoyun Luo
Metals 2026, 16(6), 594; https://doi.org/10.3390/met16060594 - 29 May 2026
Viewed by 314
Abstract
Improving energy efficiency of electric arc furnace (EAF) steelmaking is a key pathway for the iron and steel industry to achieve carbon neutrality. Based on statistical data from 56 industrial EAFs, this study established and validated a comprehensive mass and energy balance model [...] Read more.
Improving energy efficiency of electric arc furnace (EAF) steelmaking is a key pathway for the iron and steel industry to achieve carbon neutrality. Based on statistical data from 56 industrial EAFs, this study established and validated a comprehensive mass and energy balance model with a verification error of less than 5% and systematically quantified the effects of furnace type, furnace capacity, hot metal charging ratio, and scrap preheating on EAF energy efficiency through statistical analysis and scenario simulation. The results show that furnace type is the decisive factor for energy efficiency; Consteel and shaft furnace EAFs with scrap preheating are significantly more efficient than conventional EAFs, with the shaft furnace exhibiting the highest preheating efficiency and best stability. The scale effect of furnace capacity on energy efficiency is weak and fully overshadowed by furnace type. Each 10% increase in hot metal ratio reduces specific power consumption by about 50 kWh/t in conventional furnaces, and the optimal hot metal ratio is 40–50% to balance power consumption and total energy consumption. Scrap preheating saves electricity by recovering physical heat, with each 100 °C temperature increase reducing power consumption by 25 kWh/t; compared with the Consteel process, the shaft furnace process reduces total energy consumption by approximately 14% and increases energy efficiency by 9%. This study provides theoretical support and practical guidance for process optimization in the low-carbon transformation of EAF short-flow steelmaking. Full article
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20 pages, 17595 KB  
Article
Finite Element Simulation and Experimental Validation of Induction Heating Coil Design for TiAl Blade
by Yunchuan Zhang, Puwei Dang and Huiyu Xu
Metals 2026, 16(6), 585; https://doi.org/10.3390/met16060585 - 26 May 2026
Viewed by 193
Abstract
To improve temperature uniformity and reduce thermal stress-induced cracking during laser directed energy deposition (laser DED) repair of TiAl blades, this study proposes a refined induction heating coil design based on coupled electromagnetic-thermal finite element simulation. A temperature-dependent model of the induction heating [...] Read more.
To improve temperature uniformity and reduce thermal stress-induced cracking during laser directed energy deposition (laser DED) repair of TiAl blades, this study proposes a refined induction heating coil design based on coupled electromagnetic-thermal finite element simulation. A temperature-dependent model of the induction heating process for a cast 45XD TiAl blade was established and used to compare circular and elliptical coil cross-sectional shapes. The elliptical coil reduced the magnetic field concentration at the leading and trailing edges and decreased the maximum temperature difference across the blade cross-section to below 100 K, thereby improving transverse temperature uniformity. To further improve the temperature distribution along the blade length, a variable-pitch solenoid coil with sparse turns in the middle and dense turns near both ends was designed. This arrangement improved the balance between local heat generation and heat dissipation and reduced the temperature variation within the central 10 cm region of the blade to about 10 K. Experimental validation showed engineering-level agreement with the simulation results, and the blade body was stably maintained at 1020–1030 K, satisfying the preheating requirement for laser DED repair of TiAl blades within the tested design set. Full article
(This article belongs to the Section Computation and Simulation on Metals)
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17 pages, 4888 KB  
Article
Investigation of Bubble Size and Spatial Distribution in a Continuous Casting Mold Considering Coalescence and Breakup
by Qingrui Lai, Zhiguo Luo, Yongjie Zhang and Zongshu Zou
Metals 2026, 16(6), 583; https://doi.org/10.3390/met16060583 - 26 May 2026
Viewed by 340
Abstract
In a steel continuous casting mold, argon bubbles injected through the submerged entry nozzle undergo transport, coalescence, and turbulent breakup, producing a polydisperse bubble swarm that affects flow stability and defect formation. In this study, an Euler–Lagrange model coupled with bubble collision coalescence [...] Read more.
In a steel continuous casting mold, argon bubbles injected through the submerged entry nozzle undergo transport, coalescence, and turbulent breakup, producing a polydisperse bubble swarm that affects flow stability and defect formation. In this study, an Euler–Lagrange model coupled with bubble collision coalescence and turbulence-induced breakup sub-models was established and validated using water model observations. Three daughter-bubble volume distribution models were compared in terms of bubble-cloud morphology, number-fraction distribution, and median-diameter evolution at different gas flow rates. For the median bubble diameter at different gas flow rates, the M-type model gives the lowest mean absolute error of 0.0349 mm. Large bubbles with diameters greater than 2.5 mm accounted for about 4% of the total number and were mainly concentrated near the SEN, whereas small bubbles with diameters of 1.0–1.5 mm accounted for about 60% and were dispersed throughout the upper recirculation region. Mechanism analysis further shows that bubble transport is drag-dominated in the high-velocity jet region, while buoyancy becomes more important in weaker flow regions; turbulent breakup is localized mainly in high-dissipation regions. Full article
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12 pages, 20109 KB  
Article
A Numerical Assessment on the Textural Stability of {112}<111> After Asymmetric Accumulative Roll-Bonding (AARB)
by Rui Wang, Xuhui Bai, Lihong Su, Guangyang Jiang, Yu Sun, Yu Liu, Yu Zhu and Xi Huang
Metals 2026, 16(6), 576; https://doi.org/10.3390/met16060576 - 25 May 2026
Viewed by 188
Abstract
In this study, the stability of the {112}<111> rolling texture component during asymmetric accumulative roll-bonding (AARB) was systematically investigated using a crystal plasticity finite element method (CPFEM) model. The CPFEM predictions showed that the plastic deformation was inhomogeneous along the thickness for all [...] Read more.
In this study, the stability of the {112}<111> rolling texture component during asymmetric accumulative roll-bonding (AARB) was systematically investigated using a crystal plasticity finite element method (CPFEM) model. The CPFEM predictions showed that the plastic deformation was inhomogeneous along the thickness for all five asymmetric ratios (1.0, 1.2, 1.5, 0.83, and 0.66). To characterize the plastic deformation and texture evolution, through-thickness shear strain, slip-system shear strain, crystal rotation behaviour, pole figures, and the retained area fraction of the {1 1 2}<1 1 1> texture component were analyzed. It was found that the asymmetric ratio, surface friction, and cutting-stacking pattern in AARB played a critical role in the preservation of initial {1 1 2}<1 1 1>. Full article
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16 pages, 2248 KB  
Article
Development and Application of the Operating Line for the CHORSF Process
by Jiangzilin Liu, Zhiguo Luo, Jiayu Luo and Xiaozhuang Liu
Metals 2026, 16(6), 562; https://doi.org/10.3390/met16060562 - 22 May 2026
Viewed by 444
Abstract
To achieve carbon emission reduction in the long ironmaking process with blast furnace-basic oxygen furnace (BF-BOF), the Hebei Iron & Steel Group and Northeastern University have jointly developed the Reduction Smelting Furnace with Carbon-Cycling, Hydrogen-Rich, and Pure-Oxygen (CHORSF) ironmaking process. This new process [...] Read more.
To achieve carbon emission reduction in the long ironmaking process with blast furnace-basic oxygen furnace (BF-BOF), the Hebei Iron & Steel Group and Northeastern University have jointly developed the Reduction Smelting Furnace with Carbon-Cycling, Hydrogen-Rich, and Pure-Oxygen (CHORSF) ironmaking process. This new process employs advanced technology to overcome the hydrogen enrichment limitation of traditional BFs and the problems of “hot at the lower part and cold at the upper part” in all-oxygen BFs. This paper establishes an operating line for the CHORSF ironmaking process, systematically analyzes the influence mechanisms of key smelting parameters on CHORSF, and provides guidance for optimizing the process. The results show that the slopes of the operating lines in the indirect reduction zone can characterize the reducing gas consumption under actual conditions; under the smelting conditions of this study, the reducing gas consumption falls within a specific range. The slope of the operating line in the softening–melting–dripping zone can be used to quantify the coke ratio. Furthermore, increasing the metallization ratio at the bottom of the indirect reduction zone leads to a slight increase in reducing gas consumption, while a 1% increase in the same metallization ratio results in a notable decrease in the coke ratio. Full article
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23 pages, 2057 KB  
Article
Defect Thermodynamics and the Intrinsic Stability Window of Mg3Sb2
by Madhuri Birare, Adam Dębski, Władysław Gąsior and Wojciech Gierlotka
Metals 2026, 16(5), 558; https://doi.org/10.3390/met16050558 - 20 May 2026
Viewed by 353
Abstract
Magnesium antimonide (Mg3Sb2) has emerged as a promising high-performance thermoelectric material, yet its efficiency is fundamentally determined by intrinsic point defects. In this study, we present a comprehensive investigation of defects in the intermetallic compound Mg3Sb2 [...] Read more.
Magnesium antimonide (Mg3Sb2) has emerged as a promising high-performance thermoelectric material, yet its efficiency is fundamentally determined by intrinsic point defects. In this study, we present a comprehensive investigation of defects in the intermetallic compound Mg3Sb2 using first laws of thermodynamics and density functional theory (DFT) within the generalized gradient approximation (GGA). By calculating the energy of defect formation and the charge transition energy between energy levels, it was determined how the change in chemical potential associated with phase synthesis affects the phase stability and carrier concentrations. Calculations show that donor defects dominate in Mg-rich alloys, primarily antimony vacancies and magnesium atoms in interstitial positions. This means that in a phase with a slight magnesium excess, e.g., Mg3.01Sb1.99 at 1400 K, n-type conductivity dominates. In the opposite case, i.e., in an Sb-rich alloy, magnesium vacancies spontaneously form in the Wyckoff 1a position. These ionized acceptors induce strong self-compensation, blocking the Fermi level about 0.38 eV above the valence band maximum. As a result of this process, the Mg3Sb2 phase, at elevated temperatures, becomes the non-stoichiometric Mg2.99Sb2.01 phase, which causes the material to retain p-type conductivity and actively block doping-induced n-type conductivity. The conducted studies demonstrate that the homogeneity range of the Mg-Sb system, although traditionally considered narrow, has a significant impact on the semiconducting properties of the material. Furthermore, they also point to the need for continued research on high temperature in the area of synthetic defect engineering, interface engineering, and optimization of the thermoelectric properties of materials based on Mg-Sb alloys. Full article
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26 pages, 4364 KB  
Article
Phase Transformation Characteristics of the Sn-Pb-Bi Ternary Alloy System Based on the DPMD Method
by Dexin Fan, Jiankang Huang, Chen Dong and Jiaojiao Xie
Metals 2026, 16(5), 532; https://doi.org/10.3390/met16050532 - 14 May 2026
Viewed by 314
Abstract
The phase transformation characteristics of Sn-Pb-Bi ternary alloys with four representative Bi/Pb mass fraction ratios (0, 0.14, 0.33, and 0.60) were systematically investigated using the deep potential molecular dynamics (DeePMD) method over a temperature range of 300–600 K. A high-precision machine-learned interatomic potential [...] Read more.
The phase transformation characteristics of Sn-Pb-Bi ternary alloys with four representative Bi/Pb mass fraction ratios (0, 0.14, 0.33, and 0.60) were systematically investigated using the deep potential molecular dynamics (DeePMD) method over a temperature range of 300–600 K. A high-precision machine-learned interatomic potential was achieved using large-scale ab initio molecular dynamics (AIMD) datasets, reaching chemical accuracy (energy error <5 meV/atom, force error <100 meV/Å). Complete solid–liquid–solid heating–cooling cycle simulations were performed to accurately determine the melting temperature Tm, solidification temperature Ts, and undercooling ΔT. The microscopic mechanisms through which Bi regulates phase transitions were revealed through radial distribution function (RDF), mean square displacement (MSD), self-diffusion coefficient, and viscosity analyses. Our results show that increasing the Bi/Pb ratio monotonically lowers Tm from 475 K to 450 K, while ΔT reaches a maximum of ~48 K at Bi/Pb = 0.14. Bi addition disrupts short-range order, enhances chemical homogeneity, suppresses atomic diffusion, and optimizes liquid viscosity, with the optimal composition found to be Bi/Pb ≈ 0.14, balancing a low melting point, controlled undercooling, and improved flowability. This study provides an atomic-scale theoretical foundation for the precise composition design of low-melting-point Sn-Pb-Bi solders for photovoltaic and electronic packaging applications. Full article
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11 pages, 984 KB  
Article
Hydrometallurgical Processing of Polymetallic Sublimates Containing Arsenic: Features of Leaching and Thermodynamic Analysis
by Aitbala Narembekova, Kalkaman Zhumashev, Pheruza Berdikulova, Yelena Zhinova and Anna Bogdanova
Metals 2026, 16(5), 512; https://doi.org/10.3390/met16050512 - 9 May 2026
Viewed by 249
Abstract
This article presents the results of developing a hydrometallurgical method for processing polymetallic sublimates containing arsenic, zinc, copper, and lead. Using sublimates from “BalkhashPolymetal” LLP (Kazakhstan) as an example, the optimal conditions for sulfuric acid leaching were determined as follows: t = 80–85 [...] Read more.
This article presents the results of developing a hydrometallurgical method for processing polymetallic sublimates containing arsenic, zinc, copper, and lead. Using sublimates from “BalkhashPolymetal” LLP (Kazakhstan) as an example, the optimal conditions for sulfuric acid leaching were determined as follows: t = 80–85 °C, H2SO4 = 25 g/dm3, τ = 60 min. Under these conditions, extraction of arsenic was 93%, zinc 80%, and copper 42% was achieved. Iron(II) hydroxide was used to remove arsenic from the solution, which made it possible to reduce the residual As content in the solution to 0.02 g/L and return approximately 97% of copper to the process cycle. Eh–pH analysis of the Fe–As–Cu–H2O system confirmed the thermodynamic stability of Fe(II/III) arsenates in the selected pH range 3–5. The obtained results can be used to develop safe and resource-saving technologies for processing technogenic raw materials. Full article
(This article belongs to the Section Computation and Simulation on Metals)
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25 pages, 6321 KB  
Article
A Physics-Guided Two-Stage Learning Framework for Constitutive Modeling of TC4 Titanium Alloy: Validation Through Temperature and Strain-Rate Extrapolation
by Lu Cheng, Chenxi Shao and Peng Cheng
Metals 2026, 16(5), 510; https://doi.org/10.3390/met16050510 - 9 May 2026
Viewed by 385
Abstract
Accurate constitutive modeling of TC4 titanium alloy at elevated temperatures is critical for process design and numerical simulation in aerospace manufacturing. However, purely data-driven deep neural networks (DNNs) often suffer from severe overfitting and may yield physically unreasonable predictions in data-sparse or strictly [...] Read more.
Accurate constitutive modeling of TC4 titanium alloy at elevated temperatures is critical for process design and numerical simulation in aerospace manufacturing. However, purely data-driven deep neural networks (DNNs) often suffer from severe overfitting and may yield physically unreasonable predictions in data-sparse or strictly out-of-distribution (OOD) regions. To address this issue, this study proposes a physics-guided two-stage neural network framework, termed NN-PhysicsInit, for the constitutive modeling of TC4 alloy. In Stage I, a large synthetic dataset generated from a strain-compensated Arrhenius-type constitutive equation is used to pre-train the network, thereby introducing analytical prior knowledge into the initial topological space. In Stage II, the pre-trained model is fine-tuned using rigorously corrected experimental data obtained from isothermal compression tests conducted over 800–980 °C and 0.001–1 s−1 to improve material-specific predictive accuracy. To evaluate generalization capability, a rigorous dual-perspective extrapolation validation scheme is designed separately in the temperature (1010 °C) and strain-rate (10 s−1) dimensions. The results demonstrate that, compared with direct black-box training, the proposed framework successfully prevents non-physical divergence and better preserves macroscopic thermodynamic smoothness in unseen domains. Specifically, the extrapolation average absolute relative error (AARE) is significantly reduced from 34.21% to 14.34% in the temperature extrapolation task, and from 27.91% to 8.92% in the strain-rate extrapolation task. These findings confirm that physics-based initialization acts as a powerful implicit regularizer, effectively mitigating the extrapolation catastrophe while maintaining high fitting accuracy. The proposed framework provides a robust and practical strategy for the constitutive modeling of complex alloys under limited-data conditions. Full article
(This article belongs to the Section Computation and Simulation on Metals)
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37 pages, 7517 KB  
Article
Modeling Mold Heat Transfer Phenomena in Continuous Casting of Steel
by Ehsan Jebellat and Brian G. Thomas
Metals 2026, 16(5), 489; https://doi.org/10.3390/met16050489 - 30 Apr 2026
Viewed by 452
Abstract
Accurate thermal analysis of steel solidification and heat transfer in the continuous casting mold is essential for understanding and controlling solidification, shell thickness uniformity, interfacial gap phenomena, and defects such as cracks and breakouts. This study investigates heat transfer in a funnel mold [...] Read more.
Accurate thermal analysis of steel solidification and heat transfer in the continuous casting mold is essential for understanding and controlling solidification, shell thickness uniformity, interfacial gap phenomena, and defects such as cracks and breakouts. This study investigates heat transfer in a funnel mold slab caster using the in-house thermal model, Con1D. A new methodology is introduced to predict the slag layer roughness, and its effect on interface resistance. To account for the multidimensional thermal behavior near water channels and thermocouples, finite-element models are developed in Abaqus to calibrate Con1D to match three-dimensional calculations of mold heat transfer. After calibration to match plant measurements for one set of casting conditions, Con1D predictions are validated with plant measurements at different casting speeds and mold plate thicknesses. Key outputs analyzed include the heat flux profile, mold and shell temperatures, shell thickness, shell shrinkage, and interfacial parameters such as slag layer thickness. Increasing casting speed causes higher heat flux, higher shell surface and mold temperatures, and decreased shell and slag layer thicknesses. Decreasing mold plate thickness increases heat flux slightly due to reduced thermal resistance of both the mold and interfacial gap. The modeling approach presented here is a powerful methodology to gain quantitative fundamental understanding of mold heat transfer in continuous casting, especially including phenomena in the interfacial gap. Full article
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