Submit to Metals Review for Metals Propose a Special Issue

Journal Menu

Journal Browser

Numerical Simulation of Solidification Processes

Print Special Issue Flyer
Special Issue Editors
Special Issue Information
Keywords
Benefits of Publishing in a Special Issue
Published Papers

A special issue of Metals (ISSN 2075-4701). This special issue belongs to the section "Computation and Simulation on Metals".

Deadline for manuscript submissions: closed (30 September 2022) | Viewed by 29708

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special issue Numerical Simulation of Solidification Processes book cover image

Share This Special Issue

Special Issue Editor

Prof. Mohsen Eshraghi

E-Mail Website
Guest Editor

California State University, Los Angeles, CA, USA
Interests: Integrated Computational Materials Engineering; Solidification; Numerical Modeling of Microstructural Evolution and Phase Transformations; Additive Manufacturing

Special Issue Information

Dear Colleagues,

Solidification is a critical step for many manufacturing processes, including casting, welding, and additive manufacturing. While solidification happens during processing of all types of materials, solidification of metallic alloys has been of utmost importance to scientists and engineers. The importance comes from the fact that the solidification microstructure has a significant influence on the properties of the solidified materials. The kinetics of solidification also determines the distribution of solute atoms, which eventually leads to micro-segregation, secondary phases, and formation of various defects, which exert enormous influence on mechanical properties. By combining the bedrock computational physics and informatics with systematic experiments and advanced manufacturing, we can reduce the cost, risk, and cycle time for new product development. Numerical simulation of solidification processes can help scientists to gain a better understanding of the kinetics governing the macroscopic as well as microscopic features of the solidification process. From an industrial point of view, solidification modeling enables engineers to predict the properties of the material and subsequently modify the process parameters in order to produce materials of higher quality. However, several physical phenomena are involved during the solidification processes that in turn make the simulations very complex. In the wake of promising progress in the area of solidification modeling, this Special Issue embraces studies on numerical simulation of solidification processes ranging from atomistic models to micro-scale and macro-scale process models.

Prof. Mohsen Eshraghi
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Metals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Solidification
Numerical Simulation
Microstructural Evolution
Phase Transformations
Dendrite Growth
Atomistic Modeling
Phase Field
Cellular Automata
Integrated Computational Materials Engineering
Casting
Additive Manufacturing

Benefits of Publishing in a Special Issue

Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (12 papers)

Download All Papers

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Editorial

Jump to: Research, Review

2 pages, 162 KiB

Open AccessEditorial

Numerical Simulation of Solidification Processes

by Mohsen Eshraghi

Metals 2023, 13(7), 1303; https://doi.org/10.3390/met13071303 - 21 Jul 2023

Viewed by 1475

Abstract

Solidification is a critical step for many manufacturing processes, including casting, welding, and additive manufacturing [...] Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

Research

Jump to: Editorial, Review

17 pages, 7095 KiB

Open AccessArticle

Optimization of Heavy Reduction Process on Continuous-Casting Bloom

by Bao Yang, Minglin Wang, Hui Zhang, Shuai Liu, Guobin Wang and Xuebing Wang

Metals 2022, 12(11), 1873; https://doi.org/10.3390/met12111873 - 2 Nov 2022

Cited by 6 | Viewed by 2174

Abstract

Heavy reduction (HR) is an effective technique to control V segregation in continuous casting bloom, but the effect of segregation improvement is limited by the parameters such as reduction position and reduction amounts. In order to improve the macrosegregation of bloom, numerical simulation and plant experiments are adopted in this research. A heat transfer model and a reduction model with comprehensive thermo-physical parameters were established. The two models were verified by comparing the measured surface temperature and the theoretical strain at the solidification front. It is determined that the position of the HR of the bearing steel bloom is 20.82 m~24.97 m from the meniscus, and the solid fraction in the center of the bloom is 0.6~1. The total reduction of the HR is set to 30 mm, and the reduction of each roller in the reduction range is set to 4 mm, 5 mm, 9 mm, 7 mm, and 5 mm, respectively, to prevent the formation of internal cracks. Plant trials were conducted to verify the effect of the optimized HR. The results show that the carbon segregation degree on the V channel and non-channel of the bloom decreases from 1.2 to 1.16 and increases from 0.93 to 0.95, respectively, and the central carbon segregation degree decreases from 1.17 to 1.15. Meanwhile, the internal crack was not found in the bloom. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Figure 1

19 pages, 17433 KiB

Open AccessArticle

Effects of Alloying Elements on Solidification Structures and Macrosegregation in Slabs

by Pan Zhang, Minglin Wang, Pengzhao Shi and Lijun Xu

Metals 2022, 12(11), 1826; https://doi.org/10.3390/met12111826 - 27 Oct 2022

Cited by 6 | Viewed by 1860

Abstract

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. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Figure 1

18 pages, 5700 KiB

Open AccessArticle

Prediction of Thermal Distortion during Steel Solidification

by Ghavam Azizi, Brian. G. Thomas and Mohsen Asle Zaeem

Metals 2022, 12(11), 1807; https://doi.org/10.3390/met12111807 - 25 Oct 2022

Cited by 4 | Viewed by 1799

Abstract

Thermal distortion during the initial stages of solidification is an important cause of surface quality problems in cast products. In this work, a finite element model including non-linear temperature-, phase-, and carbon-content-dependent elastic–viscoplastic constitutive equations is applied to study the effect of steel grade and interfacial heat flux on thermal distortion of a solidifying steel droplet. Due to thermal contraction, the bottom surface of the droplet bends away from the chill plate and a gap forms. It is shown that, regardless of the nature of the heat flux, the gap forms and grows the most very early during solidification (~0.1 s) and remains almost unchanged afterward. Increasing the heat flux decreases the time for evolution of the gap and increases its depth. When the carbon content is less than 0.10%C, the gap depth is very sensitive to the heat flux, but for higher carbon contents, this sensitivity is much weaker. The highest gap depths are predicted in ultra-low carbon (0.003%C) and peritectic steels (0.12%C), and agree both qualitatively and quantitatively with the experimental measurements. Thus, the current thermal-mechanical model, including its phase-dependent properties, captures the mechanism responsible for nonuniform solidification, depression sensitivity and surface defects affecting these steels. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Figure 1

15 pages, 3991 KiB

Open AccessArticle

In Situ X-ray Radiography and Computational Modeling to Predict Grain Morphology in β-Titanium during Simulated Additive Manufacturing

by Chris Jasien, Alec Saville, Chandler Gus Becker, Jonah Klemm-Toole, Kamel Fezzaa, Tao Sun, Tresa Pollock and Amy J. Clarke

Metals 2022, 12(7), 1217; https://doi.org/10.3390/met12071217 - 19 Jul 2022

Cited by 4 | Viewed by 2464

Abstract

The continued development of metal additive manufacturing (AM) has expanded the engineering metallic alloys for which these processes may be applied, including beta-titanium alloys with desirable strength-to-density ratios. To understand the response of beta-titanium alloys to AM processing, solidification and microstructure evolution needs to be investigated. In particular, thermal gradients (Gs) and solidification velocities (Vs) experienced during AM are needed to link processing to microstructure development, including the columnar-to-equiaxed transition (CET). In this work, in situ synchrotron X-ray radiography of the beta-titanium alloy Ti-10V-2Fe-3Al (wt.%) (Ti-1023) during simulated laser-powder bed fusion (L-PBF) was performed at the Advanced Photon Source at Argonne National Laboratory, allowing for direct determination of Vs. Two different computational modeling tools, SYSWELD and FLOW-3D, were utilized to investigate the solidification conditions of spot and raster melt scenarios. The predicted Vs obtained from both pieces of computational software exhibited good agreement with those obtained from in situ synchrotron X-ray radiography measurements. The model that accounted for fluid flow also showed the ability to predict trends unobservable in the in situ synchrotron X-ray radiography, but are known to occur during rapid solidification. A CET model for Ti-1023 was also developed using the Kurz–Giovanola–Trivedi model, which allowed modeled Gs and Vs to be compared in the context of predicted grain morphologies. Both pieces of software were in agreement for morphology predictions of spot-melts, but drastically differed for raster predictions. The discrepancy is attributable to the difference in accounting for fluid flow, resulting in magnitude-different values of Gs for similar Vs. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Figure 1

16 pages, 1391 KiB

Open AccessArticle

A Two-Dimensional Phase-Field Investigation on Unidirectionally Solidified Tip-Splitting Microstructures

by V. Pavan Laxmipathy, Fei Wang, Michael Selzer and Britta Nestler

Metals 2022, 12(3), 376; https://doi.org/10.3390/met12030376 - 22 Feb 2022

Cited by 3 | Viewed by 1590

Abstract

The onset of morphological instabilities along a solidifying interface has a tendency to influence the microstructural characteristics of cast alloys. In the present study, the initiation as well as the mechanism of microstructural pattern formation is investigated by a quantitative phase-field approach. For energetically isotropic interfaces, we show that the presence of grain boundary grooves promotes the initiation of morphological instabilities, and with progressive solidification, they subsequently amplify into tip-splitting microstructures. We also demonstrate that the grain boundary groove shape influences the amplification of the ridge-shaped instability near the pit region. The structural transition of tip splitting to dendritic microstructures is showcased through the effect of interfacial anisotropy. In addition, the prediction of the tip-splitting position is discussed through an analytical criterion, wherein the sign of the surface Laplacian of interfacial curvature dictates the formation of crest and trough positions in a tip-splitting pattern. In complete agreement with the sharp-interface theory, our phase-field simulations validate the analytically obtained tip-splitting position and suggest that the two tips evolve symmetrically on either side of the hindered concave region. Furthermore, the role of lattice anisotropy on the tip-splitting phenomenon is also discussed in detail. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Graphical abstract

8 pages, 3628 KiB

Open AccessArticle

3D Modeling of the Solidification Structure Evolution of Superalloys in Powder Bed Fusion Additive Manufacturing Processes

by Laurentiu Nastac

Metals 2021, 11(12), 1995; https://doi.org/10.3390/met11121995 - 10 Dec 2021

Cited by 6 | Viewed by 2493

Abstract

Recently, a few computational methodologies and algorithms have been developed to simulate the microstructure evolution in powder bed fusion (PBF) additive manufacturing (AM) processes. However, none of these have attempted to simulate the grain structure evolution in multitrack, multilayer AM components in a fully 3D transient mode and for the entire AM geometry. In this work, a multiscale model, which consists of coupling a transient, discrete-source 3D AM process model with a 3D stochastic solidification structure model, was applied to quickly, efficiently, and accurately predict the grain structure evolution of IN625 alloys during Laser Powder Bed Fusion (LPBF). The capabilities of this model include studying the effects of process parameters and part geometry on solidification conditions and their impact on the grain structure formation within multicomponent alloy parts processed via AM. Validation was accomplished based on single-layer LPBF IN625 benchmark experiments, previously performed and analyzed at the National Institute of Standards and Technology (NIST), USA. This modeling approach can also be used to quantitatively predict the solidification structure of Ti-6Al-4V alloys in electron beam AM processes. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Figure 1

11 pages, 1654 KiB

Open AccessArticle

Permeability Measurements of 3D Microstructures Generated by Phase Field Simulation of the Solidification of an Al-Si Alloy during Chill Casting

by Ralf Berger, Markus Apel, Gottfried Laschet, Wilhelm Jessen, Wolfgang Schröder, Jens Wipperfürth, Johannes Austermann and Christian Hopmann

Metals 2021, 11(12), 1895; https://doi.org/10.3390/met11121895 - 25 Nov 2021

Cited by 5 | Viewed by 1986

Abstract

The permeability of the semi-solid state is important for the compensation of volume shrinkage during solidification, since insufficient melt feeding can cause casting defects such as hot cracks or pores. Direct measurement of permeability during the dynamical evolution of solidification structures is almost impossible, and numerical simulations are the best way to obtain quantitative values. Equiaxed solidification of the Al-Si-Mg alloy A356 was simulated on the microscopic scale using the phase field method. Simulated 3D solidification structures for different stages along the solidification path were digitally processed and scaled up to generate 3D models by additive manufacturing via fused filament fabrication (FFF). The Darcy permeability of these models was determined by measuring the flow rate and the pressure drop using glycerol as a model fluid. The main focus of this work is a comparison of the measured permeability to results from computational fluid flow simulations in the phase field framework. In particular, the effect of the geometrical constraint due to isolated domain walls in a unit cell with a periodic microstructure is discussed. A novel method to minimize this effect is presented. For permeability values varying by more than two orders of magnitude, the largest deviation between measured and simulated permeabilities is less than a factor of two. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Figure 1

10 pages, 3426 KiB

Open AccessArticle

Analysis of Micro-Segregation of Solute Elements on the Central Cracking of Continuously Cast Bloom

by Qiang Zeng, Chao Xiao and Jianli Li

Metals 2021, 11(3), 382; https://doi.org/10.3390/met11030382 - 25 Feb 2021

Cited by 5 | Viewed by 2261

Abstract

On the basis of the Brody–Flemings model and modified Voller–Beckermann model, an analytical model of micro-segregation is established by considering the actual solidification cooling conditions of bloom. According to the developed model, the interdendritic solute distribution at the origin of the cracking gap is obtained. It is found that both phosphorus and sulfur have quite severe segregation, but both carbon and manganese have slight segregation; these results agree well with the semiquantitative analysis results of the scanning electron microscope (SEM). At the same time, the interdendritic segregation leads to an enhanced increase in the temperature range of crack formation; correspondingly, the possibility of cracking significantly increases and, thus, element segregation is the internal cause of crack formation. On the other hand, taking into account heat transfer, phase transformation, and metallurgical pressure, the strain of the solid shell is revealed through finite element software. When the solid shell thickness is equal to the distance of 90 mm between the opening point of the crack and the inner arc side, the tensile strain of the solid front is much bigger than the critical strain, which meets the external cause of crack formation; therefore, reasons for the cracking of blooms are successfully found. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Figure 1

17 pages, 5233 KiB

Open AccessArticle

Numerical Simulation of Macrosegregation Formation in a 2.45 ton Steel Ingot Using a Three-Phase Equiaxed Solidification Model

by Tao Wang, Engang Wang, Yves Delannoy, Yves Fautrelle and Olga Budenkova

Metals 2021, 11(2), 262; https://doi.org/10.3390/met11020262 - 4 Feb 2021

Cited by 5 | Viewed by 2598

Abstract

In the present work macrosegregation during solidification of a 2.45 ton steel ingot is simulated with a pure equiaxed model, which was tested previously via modeling of a benchmark experiment. While the columnar structure is not taken into account, a packed layer formed over inner walls of the mold at an early stage of solidification reproduces to some extent phenomena generally related to zones of columnar dendrites. Furthermore, it is demonstrated that interaction of free-floating equiaxed grains with ascending convective flow in the bulk liquid results in flow instabilities. This defines the irregular form of the negative segregation zone, the formation of which at the ingot bottom corresponds to experimental observation. Vertical channels reported in experimental measurements are reproduced in simulations. It is confirmed that intensification of ingot cooling may decrease segregation in the ingot. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Figure 1

21 pages, 8808 KiB

Open AccessArticle

The Interaction between Grains during Columnar-to-Equiaxed Transition in Laser Welding: A Phase-Field Study

by Lingda Xiong, Chunming Wang, Zhimin Wang and Ping Jiang

Metals 2020, 10(12), 1647; https://doi.org/10.3390/met10121647 - 7 Dec 2020

Cited by 7 | Viewed by 3729

Abstract

A phase-field model was applied to study CET (columnar-to-equiaxed transition) during laser welding of an Al-Cu model alloy. A parametric study was performed to investigate the effects of nucleation undercooling for the equiaxed grains, nucleation density and location of the first nucleation seed ahead of the columnar front on the microstructure of the fusion zone. The numerical results indicated that nucleation undercooling significantly influenced the occurrence and the time of CET. Nucleation density affected the occurrence of CET and the size of equiaxed grains. The dendrite growth behavior was analyzed to reveal the mechanism of the CET. The interactions between different grains were studied. Once the seeds ahead of the columnar dendrites nucleated and grew, the columnar dendrite tip velocity began to fluctuate around a value. It did not decrease until the columnar dendrite got rather close to the equiaxed grains. The undercooling and solute segregation profile evolutions of the columnar dendrite tip with the CET and without the CET had no significant difference before the CET occurred. Mechanical blocking was the major blocking mechanism for the CET. The equiaxed grains formed first were larger than the equiaxed grains formed later due to the decreasing of undercooling. The size of equiaxed grain decreased from fusion line to center line. The numerical results were basically consistent with the experimental results obtained by laser welding of a 2A12 Al-alloy. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Figure 1

Review

Jump to: Editorial, Research

40 pages, 13622 KiB

Open AccessReview

A Review of Large-Scale Simulations of Microstructural Evolution during Alloy Solidification

by Nicholas Cusato, Seyed Amin Nabavizadeh and Mohsen Eshraghi

Metals 2023, 13(7), 1169; https://doi.org/10.3390/met13071169 - 23 Jun 2023

Cited by 6 | Viewed by 3283

Abstract

During the past two decades, researchers have shown interest in large-scale simulations to analyze alloy solidification. Advances in in situ X-ray observations of the microstructural evolution of dendrites have shown defects that can be very costly for manufacturers. These simulations provide the basis for understanding applied meso-/macro-scale phenomena with microscale details using various numerical schemes to simulate the morphology and solve for transport phenomena. Methods for simulating methodologies include cellular automaton, phase field, direct interface tracking, level set, dendritic needle networks, and Monte Carlo while finite element, finite difference, finite volume, and lattice Boltzmann methods are commonly used to solve for transport phenomena. In this paper, these methodologies are explored in detail with respect to simulating the dendritic microstructure evolution and other solidification-related features. The current research, from innovations in algorithms for scaling to parallel processing details, is presented with a focus on understanding complex real-world phenomena. Topics include large-scale simulations of features with and without convection, columnar to equiaxed transition, dendrite interactions, competitive growth, microsegregation, permeability, and applications such as additive manufacturing. This review provides the framework and methodologies for achieving scalability while highlighting the areas of focus that need more attention. Full article

(This article belongs to the Special Issue Numerical Simulation of Solidification Processes)

► Show Figures

Journal Menu

Journal Browser

Numerical Simulation of Solidification Processes

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (12 papers)

Editorial

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI