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ISIJ International Vol. 50 (2010), No. 12

ISIJ International
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ONLINE ISSN: 1347-5460
PRINT ISSN: 0915-1559
Publisher: The Iron and Steel Institute of Japan

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  1. Vol. 64 (2024)

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ISIJ International Vol. 50 (2010), No. 12

Preface to the Special Issue on “Cutting Edge of Computer Simulation of Solidification and Casting”

Keiji Nakajima

pp. 1723-1723

DOI:

10.2355/isijinternational.50.1723

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Preface to the Special Issue on “Cutting Edge of Computer Simulation of Solidification and Casting”

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Methodological Progress for Computer Simulation of Solidification and Casting

Keiji Nakajima, Hongwei Zhang, Katsunari Oikawa, Munekazu Ohno, Pär G. Jönsson

pp. 1724-1734

DOI:

10.2355/isijinternational.50.1724

Abstract

The dramatic progress made over the last 10 to 15 years in the field of “computer simulation of solidification and casting” is greatly due to the supports by academic as well as industrial research. The driving force behind this undertaking was the promise of predictive capabilities that will allow process and material developments. Here, the recent works on modeling were summarized, for the macrosegregation in the macro-scale simulation, and the Cellular Automaton, the solidification path combined with the microsegregation, the phase-field model in the meso-scale and micro-scale simulation.

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Methodological Progress for Computer Simulation of Solidification and Casting

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Mathematical Model for Nucleation, Ostwald Ripening and Growth of Inclusion in Molten Steel

Hong Lei, Keiji Nakajima, Ji-Cheng He

pp. 1735-1745

DOI:

10.2355/isijinternational.50.1735

Abstract

Numerical simulation is a powerful tool to investigate inclusion behavior in the molten steel. Although many mathematical models have been developed to predict inclusion collision-growth behavior in different metallurgical reactors, the inclusion size distribution had to be obtained by experiment or assumption. Thus, a general nucleation-growth model, which involves in chemical reaction, homogeneous nucleation and growth kinetics, is developed to investigate the inclusion nucleation, Ostwald ripening, Brownian collision-growth, Stokes collision-growth and turbulent collision-growth. In order to speed up the calculation, the deoxidation products are divided into two parts. The first part only consists of embryos, and directly numerical simulation is used to solve the differential equations. The second part only consists of inclusion particles, and particle-size-grouping method is introduced to solve the related equations. Numerical results showed that the predicted inclusion size distributions are consistent with previous experimental data. With the increasing diffusion coefficient, the peak-value diameter keeps unchanged and the maximum number density decreases. With the increasing turbulent energy dissipation rate, the peak-value diameter and the maximum number density decrease under the assumption on floating-out of larger inclusions.

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Mathematical Model for Nucleation, Ostwald Ripening and Growth of Inclusion in Molten Steel

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Simulation of the Steel Sampling Process

Zhi Zhang, Anders Tilliander, Andrey Karasev, Pär G. Jönsson

pp. 1746-1755

DOI:

10.2355/isijinternational.50.1746

Abstract

This work presents a theoretical study of the liquid steel sampling process in the iron and steel industry. As a continuous research with the previous work, the initial solidification during the sampler filling was taken into account. The liquid steel sampling procedure, which is mainly used to monitor whether the steel is at the correct composition during the steelmaking, can also be applied to examine the inclusion size characteristics. Focus was on the influence of the initial solidification on the inclusion concentrations. The whole sampling system was modeled in order to obtain a simulation result which is realistic from an industrial perspective. Argon-protected sampling was the focus in the simulations. A discrete phase model was used to simulate the movement of inclusions in the liquid steel. Inclusions were injected from the inlet pin of the lollipop-shaped sampler. Some selected different sized primary inclusions that exist in the ladles during a steelmaking process were simulated. The conclusion from this work is that turbulent flow patterns within the sampler mold will change because of the space shrinkage due to the solidification. This, in turn, will also affect the inclusion dispersions. It concludes that the preferred position for detecting inclusions is the bottom region, except the bottom surface. It estimates that the mean deviation between the calculated result and the initial concentration for all inclusions in these regions is within 10%.

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Simulation of the Steel Sampling Process

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A Numerical Study of Swirl Blade Effects in Uphill Teeming Casting

Zhi Zhang, Shinichiro Yokoya, Anders Tilliander, Pär G. Jönsson

pp. 1756-1762

DOI:

10.2355/isijinternational.50.1756

Abstract

The initial filling period during ingot casting was studied theoretically. The motivation was that it is crucial to achieve a preferred flow pattern which can lead to a smooth filling condition, particularly during the initial teeming stage. In this study, a twist-tape swirl blade was applied in a mathematical model to create a swirl flow in the inlet of the mold. The swirl blade was set vertically just beneath the inlet, which was made of a gradually divergent cross section area. The results showed that combinations of the inlet swirl flow and mold with gradually divergent bottom contributes to: i) Inlet flow passes along the wall of the mold, ii) the formation of a very uniform velocity distribution within only 6 s after the molten steel filled into the mold and iii) No formation of a hump on the free surface of the mold during the entire filling times. These phenomena will ensure that the mold flux is spread onto the surface of liquid steel evenly. Besides, the stable surface also prevents the mold flux from being dispersed into the molten steel.

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A Numerical Study of Swirl Blade Effects in Uphill Teeming Casting

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A First Attempt to Implement a Swirl Blade in Production of Ingots

Liue Hallgren, Anders Tilliander, Shinichiro Yokoya, Pär G. Jönsson, Sölve Hagman

pp. 1763-1769

DOI:

10.2355/isijinternational.50.1763

Abstract

Plant trials were carried out to test if it would be possible to place a ceramic swirl blade in the runner channel during filling of ingots. The initial experiments showed that no production disturbances were found. More specifically, no problems with unusual refractory wear or cracks in the refractory were found. Thus, it was concluded that the use of swirl blade has a potential in the future to be used to influence the initial filling conditions. Also, mathematical modeling was done in order to illustrate how it was possible to improve the layout of the runner system in order to increase the potential for use of swirl for the current plant conditions. The results showed that the meniscus was not dampened as much when the swirl blade is positioned in a horizontal direction in the runner channel compared to the results of a previous physical modeling study where the swirl blade was placed in a vertical direction just before the steel entered the mold. However, if a horizontally positioned swirl blade is used in combination with an inlet with an angle of 15 degrees the hump height at the initial filling stage can be lowered from 100 to 58 mm compared to a case without a swirl blade. This illustrates the potential to apply mold powder closer to the bottom, without risking reoxidation due to reactions with steel and mold powder.

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A First Attempt to Implement a Swirl Blade in Production of Ingots

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Analysis of an Automatic Steel-teeming Method Using Electromagnetic Induction Heating in Slide Gate System

Ao Gao, Dejun Li, Qiang Wang, Kai Wang, Baigang Jin, Katsukiyo Marukawa, Jicheng He

pp. 1770-1776

DOI:

10.2355/isijinternational.50.1770

Abstract

A new method (electromagnetic steel-teeming method) using electromagnetic induction heating in slide gate system was proposed to overcome the pollution of traditional nozzle sand on the molten steel and achieve 100% automatic steel teeming. By Joule heat, this new process is to melt part or the whole of a new ladle well-packing materials (i.e. Fe–C alloy particles with similar composition as the molten steel), which is the substitute for traditional nozzle sand. A numerical simulation method based on the integration of both electromagnetic and thermal analysis modules of ANSYS was employed to investigate the outside surface temperature change of the Fe–C alloy. In addition, the effects of the coil structural parameters (the distance between the molten steel and the coil, the length and the diameter of the coil) and electric current parameters (ampere-turns, frequency) on teeming time were investigated. Under the condition of the optimal parameters found according to simulation, the smoothly steel-teeming using induction heating was achieved. The safety of the steel shell under the action of electromagnetic induction heating with the optimal parameters was also checked via the distribution of temperature field on the shell.

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Analysis of an Automatic Steel-teeming Method Using Electromagnetic Induction Heating in Slide Gate System

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Transient Fluid Flow Phenomena during Continuous Casting: Part I—Cast Start

Yufeng Wang, Lifeng Zhang

pp. 1777-1782

DOI:

10.2355/isijinternational.50.1777

Abstract

This work presents a three-dimensional numerical simulation of transient fluid flow phenomena during continuous casting of steel. In the Part I, the process of cast start was investigated. Cast start involved the filling process and the caster start process. In the filling process, molten steel was continuously filled into the mold cavity with surrounding mold walls and a dummy bar head at the bottom. To simulate the interface between the molten steel and the air, an algorithm of volume of fluid has been employed. In the cast start process, the dummy bar was gradually dragged out with a low casting speed. The movement of dummy bar was represented using dynamic mesh, and the moving speed of the boundary was controlled by a subroutine. The shape of the air/steel surface was tracked over the time, and the speed variation at a series of points close to the surface was monitored to reflect the fluctuation at top surface during cast start.

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Transient Fluid Flow Phenomena during Continuous Casting: Part I—Cast Start

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Transient Fluid Flow Phenomena during Continuous Casting: Part II—Cast Speed Change, Temperature Fluctuation, and Steel Grade Mixing

Yufeng Wang, Lifeng Zhang

pp. 1783-1791

DOI:

10.2355/isijinternational.50.1783

Abstract

Many complicated phenomena are associated with transient stages during the continuous casting process, especially inside the casting mold cavity. A deep understanding of the phenomena and optimized control over the process ensure the high quality product and low costs. This work presents a three-dimensional numerical simulation of transient fluid flow phenomena during steel continuous casting. In the Part II, the process of casting speed change (increase or decrease), temperature fluctuation, and steel grade mixing in a slab mold were investigated. The phenomena, such as flow pattern, inclusion removal fraction, temperature variation, top surface profile, and steel transportation, were addressed to evaluate the process and enhance product quality.

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Transient Fluid Flow Phenomena during Continuous Casting: Part II—Cast Speed Change, Temperature Fluctuation, and Steel Grade Mixing

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A Simple Model to Calculate Dendrite Growth Rate during Steel Continuous Casting Process

Mujun Long, Lifeng Zhang, Fei Lu

pp. 1792-1796

DOI:

10.2355/isijinternational.50.1792

Abstract

In the current paper, the relationship between the casting speed and the dendrite growth during steel continuous casting process was studied; and a simple mathematical model to calculate the primary dendrite growth rate according to the casting speed was developed. The model was used to predict the distribution of the dendrite growth rate along width direction and casting direction during a continuous casting process, indicating a dendrite growth rate of 0.1–3.0 mm/s, which is much higher than that in regular ingot casting. The dendrite growth rate fluctuates along casting direction because of the different cooling intensity in each zone of the continuous caster; and the distribution of the dendrite growth rate along width direction was non-uniform due to the uneven transverse distribution of cooling intensity. The predicted results agree well with the measurements.

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A Simple Model to Calculate Dendrite Growth Rate during Steel Continuous Casting Process

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A New Approach for Modelling Slag Infiltration and Solidification in a Continuous Casting Mould

Pavel E. Ramirez-Lopez, Peter D. Lee, Kenneth C. Mills, Begoña Santillana

pp. 1797-1804

DOI:

10.2355/isijinternational.50.1797

Abstract

A mathematical model of the continuous casting process has been developed which couples metal, slag and gas flow with heat flux and solidification. An extensive sensitivity study has been carried out with this model, studying the influence of changing casting conditions upon a number of quantifiable model predictions (i.e. responses). The casting conditions studied were: casting speed, mould flux properties (viscosity, break temperature), mould oscillation frequency and stroke, and superheat. The model was then applied to determine the influence of each of these parameters on the variations in: powder consumption (lubrication), heat flux (solidification) and oscillation mark formation (defects). It is shown that all three responses vary in a consistent manner through the cycle. Equations are derived for the powder consumption and heat flux, showing good agreement with prior experimental data.

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A New Approach for Modelling Slag Infiltration and Solidification in a Continuous Casting Mould

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Ab-initio Predictions of Interfacial Heat Fluxes in Horizontal Single Belt Casting (HSBC), Incorporating Surface Texture and Air Gap Evolution

Roderick I. L. Guthrie, Mihaiela Isac, Donghui Li

pp. 1805-1813

DOI:

10.2355/isijinternational.50.1805

Abstract

The purpose of this study was to develop ab-initio mathematical and computational models, aimed at predicting instantaneous heat fluxes when a liquid metal or alloy first comes into contact with a colder substrate during near net shape casting processes. Fully computational models were developed to determine whether the measured instantaneous heat fluxes associated with the strip casting of aluminum alloys on copper substrates could be inferred from first principles. For this, strip cast aluminum surfaces were physically analyzed using a 3-D Profilometer, so as to provide the detailed surface textural information needed for the mathematical modeling. It was shown that the modeled mould surface characteristics, such as pyramid height and number of contact points per mm2, are critical in determining the peak heat fluxes achieved during metal/mould contact. Reducing pyramid heights and/or increasing the number of contact points are beneficial in enhancing interfacial heat fluxes.
The mechanism of air pocket formation was also explored through mathematical modeling. The volume expansion of entrapped air was deduced to be the main reason for “air pockets” forming on the strip's bottom surface. A new method for predicting air gap evolution was proposed in which a fixed grid system and an anisotropic thermal conductivity model were used. The computational models allow for various scenarios to be effectively studied, and for experimental curves to be matched against “predicted” curves. Finally, copper moulds with macroscopically textured surfaces were tested, and it was found that these surfaces were effective in expelling entrapped air to adjacent grooves, and in enhancing overall interfacial heat fluxes.

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Ab-initio Predictions of Interfacial Heat Fluxes in Horizontal Single Belt Casting (HSBC), Incorporating Surface Texture and Air Gap Evolution

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Microstructural Simulations of the Influence of Solidification Velocity on Freckle Initiation during Directional Solidification

Lang Yuan, Peter D. Lee

pp. 1814-1818

DOI:

10.2355/isijinternational.50.1814

Abstract

The initiation of freckles by thermosolutal convection during the directional solidification of Pb–Sn alloys was studied numerically at the microstructural level. The model predicts the detailed dendritic structures, microsegregation and interdendritic convection in three dimensions. The onset and sustained growth of solutal channel (freckles) was simulated as a function of casting speed. The predictions were compared with experimental measurements via the introduction of a Rayleigh number. Good agreement was achieved, suggesting that such models might be used to predict the critical Rayleigh number for more complex alloy systems with further development. It was found that the large density variation of Pb–Sn alloys induces strong upward convection of segregated liquid and promotes the formation of solutal channels. However, the competition between upward solute transport and dendritic growth determines both the initiation and sustained growth of these channels. These open solute channels become the defect structure known as a freckle upon final solidification.

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Microstructural Simulations of the Influence of Solidification Velocity on Freckle Initiation during Directional Solidification

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Design Methods for Solidification Structures in Micro Continuous Casting

Nobuaki Ito, Koichi Anzai

pp. 1819-1828

DOI:

10.2355/isijinternational.50.1819

Abstract

Micro continuous casting, which includes, for example, single-roll casting, twin-roll casting, and EFG, is a comprehensive casting method concept for high-performance material produced with rapid solidification. When a new material functionalized through micro continuous casting is industrially developed, the caster type generally differs between design (experimental) phases because of the discrepancy of the purpose in each design phase. In the present design method, experimental data is arranged as ‘solidification structure map’ with local field properties, solidification rates, and temperature gradients, as the dominant general parameters is assisted with the casting simulation of temperature and flow field without microstructure prediction. The present method could reduce the design steps necessary for conventional design, in which the fully empirical method has been adopted, because no solidification microstructure model can determine the structure for industrial accuracy for untested material composition or casting conditions.
The present design method requires high accuracy for solidification models because the shape of the ‘solidification structure map’ changes significantly by the model accuracy in a casting simulation.

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Design Methods for Solidification Structures in Micro Continuous Casting

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CFD Modeling of Macro-segregation and Shrinkage During Solidification of Superalloy Castings

Laurentiu Nastac

pp. 1829-1834

DOI:

10.2355/isijinternational.50.1829

Abstract

Minimizing macro-segregation during static casting of segregation prone alloys has always been a challenge. Over the years, alloy manufacturers have optimized the processing techniques for these alloys by balancing the total heat input of a casting and the rate of heat extraction from the casting surface. In this study, a computational fluid dynamics (CFD) code was used to develop a generic framework for studying macro-segregation and shrinkage in various casting processes. The code developed the framework by solving for the solid fraction evolution, micro-scale characteristics, temperature, flow and solute balance in multi-component alloy systems.
Experiments were previously designed to measure solidification parameters using micro-probe compositional analysis. The thermo-physical properties of alloy 718 that were used in the simulations strongly depend on temperature. The partition coefficients of Nb, Ti, Al, and Mo in alloy 718 are also a strong function of temperature. They were determined based on quenching experiments during solidification of alloy 718.
The model predictions were validated against measured macro-shrinkage and shrinkage porosities and against macro-segregation measured from pieces cut from both laboratory scale and industrials scale castings. A special segregation index was developed and then applied to properly assess the influence of material and process parameters on macro-segregation. The effect of Nb content and processing parameters such as super-heat, mold taper, mold type, and mold diameter on macro-segregation was also studied.
Additional validation of the segregation model was performed using the literature analytical solution and experiments. Additional experimental validation of the model for prediction of macro-shrinkage and shrinkage porosities was performed using A356 plates cast in furan-silica sand molds.

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CFD Modeling of Macro-segregation and Shrinkage During Solidification of Superalloy Castings

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Restrictions of Physical Properties on Solidification Microstructures of Al-based Binary Alloys by Cellular Automaton

Hongwei Zhang, Keiji Nakajima, Hong Lei, Jicheng He

pp. 1835-1842

DOI:

10.2355/isijinternational.50.1835

Abstract

The solidification microstructure evolution and the Columnar to Equiaxed Transition (CET) during Al–Si and Al–Cu binary alloy solidification processes are analyzed by the help of Cellular Automaton-Finite Difference (CA-FD) model. The effects of the physical properties, except the effects of the nucleation parameters and the operation parameters, on the cooling curves, the dendrite growth, the solidification morphologies and the CET of the Al–Si and Al–Cu binary alloys are emphatically discussed. Results show that the solidification morphologies are internally influenced by the physical properties related to the dendrite tip growth kinetics. Besides the solute diffusivity in liquid DL and the growth restriction parameter Q=mC0(kS/L−1), the Gibbs–Thomson coefficient Γ shows a great effect on dendrite tip growth rate. Their effects on the dendrite tip kinetics are ordered as m(kS/L−1)>Γ>DL. The growth rate can be predicted efficiently by the present simplified expression based on GGAN model combining several physical parameters and the local undercooling, which clearly shows the physical meaning of the constant coefficients in the simplified expression based on KGT model. The equiaxed ratio related to the solidification morphologies can also be evaluated as a function of those physical properties.

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Restrictions of Physical Properties on Solidification Microstructures of Al-based Binary Alloys by Cellular Automaton

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Mathematical Modeling of Solidification Microstructure of Pure Copper by Vacuum Continuous Casting and Its Experimental Verification

De-Chang Tsai, Man-Shan Hsu, Weng-Sing Hwang, Cheng-Syue Jiang

pp. 1843-1850

DOI:

10.2355/isijinternational.50.1843

Abstract

The purpose of this study is to predict the solidification microstructure of pure copper rod by vacuum continuous casting (VCC) process and verify its accuracy by experimental observation. This study was extended from previous study (using 2D-CA model). A three dimensional cellular automaton (3D-CA) model and the finite difference method were utilized to simulate the macro-temperature field, nucleation, and grain growth of a pure copper rod based on the actual casting operations. The simulated solidification microstructures obtained from the 3D-CA model were found in good agreement with the results of actual casting experiments. Both numerical simulations and experimental observations show that the microstructure of a copper rod changes with casting speed and that the S/L interface moves closer to the orifice of the mould with increasing drawing speed.

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Mathematical Modeling of Solidification Microstructure of Pure Copper by Vacuum Continuous Casting and Its Experimental Verification

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Numerical Simulation of Microstructure Evolution During Alloy Solidification by Using Cellular Automaton Method

Mingfang Zhu, Shiyan Pan, Dongke Sun, Honglei Zhao

pp. 1851-1858

DOI:

10.2355/isijinternational.50.1851

Abstract

This paper presents two and three dimensional cellular automaton (CA) based models and derived coupling models to simulate micro-scale microstructure evolution during alloy solidification. The models adopt a local solutal equilibrium approach to calculate the kinetics of the solid/liquid (SL) interface evolution, which allows the reasonable calculation of crystal growth from the initial unstable stage to the steady-state stage without the need of a kinetic parameter. Dendrite morphologies with various crystallographic orientations and well developed side branches in two and three dimensions can be successfully simulated by the proposed models. In conjunction with the lattice Boltzmann method (LBM), adopted for numerically solving fluid flow and solutal transport, a coupling model was derived to simulate the solutal dendrite growth in the presence of melt convection. The 2D model was extended to the multiphase system for the simulation of divorced eutectic solidification of spheroidal graphite (SG) cast iron. The quantitative capabilities of the models are addressed by comparing simulations to analytical predictions and experimental data.

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Numerical Simulation of Microstructure Evolution During Alloy Solidification by Using Cellular Automaton Method

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Prediction of Solidification Paths for Fe–C–Cr Alloys by a Multiphase Segregation Model Coupled to Thermodynamic Equilibrium Calculations

Hongwei Zhang, Charles-André Gandin, Haithem Ben Hamouda, Damien Tourret, Keiji Nakajima, Jicheng He

pp. 1859-1866

DOI:

10.2355/isijinternational.50.1859

Abstract

A microsegregation model for the solidification of multicomponent alloys is developed. It couples the volume-averaged conservation equations for total mass, solute mass and energy assuming a uniform temperature. The diffusion in the liquid and solid phases, the growth kinetics of the solidifying microstructures and the velocity of the solid/liquid and solid/solid phase interfaces are considered in the model. Equilibrium between phases is taken into account and computed using dedicated thermodynamic software. The thermodynamic properties and their evolutions during solidification are directly retrieved from a database. Illustration is provided by the solidification of a Fe–C–Cr alloy. The occurrence of the recalescence due to the growth of the microstructure and the progress of solidification are predicted. The solidification behavior near to recalescence is evaluated. By adjusting the cooling intensity and the solute diffusivities, extreme approximations are retrieved. The model shows potentials to be coupled with a macrosegregation model for application to the solidification of multicomponent alloys.

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Prediction of Solidification Paths for Fe–C–Cr Alloys by a Multiphase Segregation Model Coupled to Thermodynamic Equilibrium Calculations

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Numerical Modeling of Microsegregation for Fe-base Multicomponent Alloys with Peritectic Transformation Coupled with Thermodynamic Calculations

Yukinobu Natsume, Masaki Shimamoto, Hitoshi Ishida

pp. 1867-1874

DOI:

10.2355/isijinternational.50.1867

Abstract

Numerical model was developed to simulate the microsegregation and phase transformation for an Fe-based multicomponent alloy with peritectic transformation. The present model was based on the simplest one-dimensional free boundary problem and assumed the local equilibrium condition at the interface. In addition, the model was coupled with thermodynamic calculation software (ChemAPP) in order to calculate equilibrium concentration at an interface. As the calculation region, the transverse and longitudinal cross section of columnar dendrite was approximated by a star shape, assuming dendrite envelope. The validity of the present model was evaluated by comparing with the analytical models and experimental data. In the comparison with the analytical models, which are lever rule, Gulliver–Scheil model and Clyne–Kurz model, the calculated results were close to the curve of lever rule for Fe–C binary alloy, and were close to the curve of Gulliver–Scheil model for Fe–Mn binary alloy. For both alloys, the calculated results were in good agreement with the curves of Clyne–Kurz model. The relationship between peritectic temperature range and carbon content was calculated for Fe–C binary alloy and compared with the result of a model by Fredriksson et al. [H. Fredriksson et al.: Metal Science, 16 (1982), 575]. The calculated result was in great agreement with their one. Also, the peritectic temperature range for peritectic content was not always the maximum, and the carbon content slightly shifted to hyper-peritectic side as the cooling rate became higher. For Fe–C–Mn–Si–P–Mo alloy, we calculated microsegregation and peritectic transformation, and compared with the experimental data reported by Ueshima et al. [Y. Ueshima et al.: Tetsu-to-Hagané, 73 (1987), 1551]. Temperatures of δ/γ transformation and γ-solidification decreased by adding to molybdenum, and these results were close to those of Ueshima et al. Also, the distributions of manganese, phosphorus and molybdenum calculated by the present model were in essential agreement with those of their experimental data.

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Numerical Modeling of Microsegregation for Fe-base Multicomponent Alloys with Peritectic Transformation Coupled with Thermodynamic Calculations

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A Modified Method of Latent Heat Release during Al–Si Alloy Solidification

Yucheng Sun, Hongliang Zheng, Ning Zhang, Xuelei Tian

pp. 1875-1878

DOI:

10.2355/isijinternational.50.1875

Abstract

The treatment of latent heat plays a significant role in the solidification simulation process. Many methods have been developed to make the simulation results much closer to reality. In this study, in order to process the latent heat release of Al–Si alloy, the apparent heat capacity method and the heat integration method are applied to deal with the latent heat release of the primary phase and the eutectic phase, respectively. The latent heat of each phase of Al–Si alloy is acquired according to Differential Scanning Calorimetry experiment. The solidification simulation software named TMCast based on Finite Difference Method employs this modified latent heat treatment method. Applying the DSC results, the temperature field is calculated for a step casting. The casting experiment is carried out to validate the method by comparing the actual cooling curves with the simulated ones. It indicates that the computed cooling curves are close to the actual ones at the phase transformation stage so that the solidification simulation will be improved by using the modified latent heat method.

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A Modified Method of Latent Heat Release during Al–Si Alloy Solidification

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Motion and Morphology of Triple Junction in Peritectic Reaction Analyzed by Quantitative Phase-field Model

Munekazu Ohno, Kiyotaka Matsuura

pp. 1879-1885

DOI:

10.2355/isijinternational.50.1879

Abstract

Motion and morphology of triple junction during peritectic reaction process is analyzed for a model alloy system based on a quantitative-phase-field simulation for two-phase solidification involving diffusion in the solid. It is demonstrated that the dominative process controlling the motion of the reaction front gradually changes from the solid–solid transformation to the secondary solid solidification as the moving velocity of solid–solid interface decreases. On the other hand, the local shape of the triple junction is mainly determined by the balance between the interfacial energies regardless of the difference in the moving velocity of solid–solid interface.

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Motion and Morphology of Triple Junction in Peritectic Reaction Analyzed by Quantitative Phase-field Model

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Mesoscopic Simulation of Dendritic Growth Observed in X-ray Video Microscopy During Directional Solidification of Al–Cu Alloys

Pierre Delaleau, Christoph Beckermann, Ragnvald H. Mathiesen, Lars Arnberg

pp. 1886-1894

DOI:

10.2355/isijinternational.50.1886

Abstract

A mesoscopic model is developed to simulate microstructures observed in situ by X-ray video microscopy during directional solidification of Al–Cu alloys in a Hele–Shaw cell. In the model, a volume-averaged species conservation equation is solved to obtain the solute concentration and solid fraction fields, and an analytical stagnant film model is used to predict the motion of the dendrite envelopes. The model is carefully validated in several test cases. Then, the model is applied to simulate the columnar dendritic microstructures observed in the X-ray video microscopy experiments for two different alloy compositions. Reasonable agreement is found between the measured and predicted dendrite envelope shapes, solid fractions, and solute concentration fields. The predicted size of the mushy zone and the extent of the undercooled melt region ahead of the columnar front agree well with the in situ experimental observations. The simulation results show quantitative agreement with the internal solid fraction variations measured from the radiographs. The present model is also able to realistically simulate a primary dendrite trunk spacing adjustment that was observed in one of the experiments. Overall, the present study represents the first successful validation of a solidification model using real time, in situ data from an experiment with a metallic alloy. Considerable additional research is needed to account in the model for the effect of gravity driven melt convection.

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Mesoscopic Simulation of Dendritic Growth Observed in X-ray Video Microscopy During Directional Solidification of Al–Cu Alloys

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Phase-field Modeling of the Initial Transient in Directional Solidification of Al–4wt%Cu Alloy

Yun Chen, Abdoul-Aziz Bogno, Bernard Billia, Xiu Hong Kang, Henri Nguyen-Thi, Dian Zhong Li, Xing Hong Luo, Jean-Marc Debierre

pp. 1895-1900

DOI:

10.2355/isijinternational.50.1895

Abstract

The initial transient in directional solidification of Al–4wt%Cu alloy by cooling-down is investigated by numerical simulation using the phase-field model proposed by Karma (Phys. Rev. Lett., 87 (2001) 115701), which includes solute antitrapping in mass conservation relation and is solved by the adaptive finite element method. The simulated velocity of the unsteady planar solidification interface and the solute profile in the liquid are always close to the predictions of the Warren–Langer analytical model of initial solidification transient (Phys. Rev. E, 47 (1993) 2702) but only in the very beginning of growth in fair quantitative agreement with the experimental data obtained by means of in situ and real-time X-ray radiography at the European Synchrotron Radiation Facility (ESRF). Then, the influence of gravity-driven fluid flow becomes significant in experiments, and increases with time. In the phase-field simulations, once the smooth solidification front has lost morphological stability in the initial solidification transient, the evolution of the non-planar solid–liquid interface microstructure varies with the processing control parameters. It is found that the solid–liquid interface shape changes through transitions from flat to cellular, cellular to dendritic, cellular or dendritic to seaweed depending on the values of the applied cooling rate and temperature gradient.

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Phase-field Modeling of the Initial Transient in Directional Solidification of Al–4wt%Cu Alloy

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Three-dimensional Phase Field Modeling of the Faceted Cellular Growth

Jincheng Wang, Yuko Inatomi

pp. 1901-1907

DOI:

10.2355/isijinternational.50.1901

Abstract

The new phase field model for strongly anisotropic systems proposed by Torabi et al. was employed to simulate the faceted cellular growth in three dimensions. Simulation reveals the whole formation process of the faceted cellular clearly. Simulation results also show that a linear relation of undercooling and growth velocity when the shape selection is completed at the late stage of the evolution, but a nonlinear relation holds during the shape selection stage. During the facet cellular formation, the crystal–melt interface is kept isothermal although the interface is sawtooth, and areas with negative temperature gradient appear in the melts, particularly at the ravine bottom of the sawtooth interface.

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Three-dimensional Phase Field Modeling of the Faceted Cellular Growth

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Numerical Analyses of Effectiveness of Magnetic Field on Variant Selection in FePd by Phase Field Modeling

Nobufumi Ueshima, Masato Yoshiya, Hideyuki Yasuda

pp. 1908-1913

DOI:

10.2355/isijinternational.50.1908

Abstract

The effect of magnetic field on variant selection in FePd has been investigated by phase field modeling. In this study, multi phase field modeling [Physica D, 94 (1996), 135] was used for calculations. Chemical free energy, interface energy and magnetic energy were incorporated in our calculation. As for magnetic energy, magnetic crystalline anisotropy energy was taken into account. Disordered FePd at 50 K below the transition temperature is selected as the initial state. Then, calculations have been performed with the presence or absence of the external magnetic field as a variable. First of all, calculations under no magnetic field showed that the volume fractions of three variants were almost equal to each other. Secondly, calculations under magnetic field of 5 T showed that the volume fraction of magnetically favorable variant was much more than other variants. Finally, the timing to apply magnetic field was intentionally changed with fixing the length of time for application, in computational experiments to examine at what stage the magnetic field is most effective. It is found that applying magnetic field from the beginning of order–disorder transition results in the slightly more volume fraction of the favorable variant, and, in turn, the less interface energy per unit volume, than others, which leads to the dominance of the favorable variant at the end after variant coarsening driven by interface energy, resulting in successful grain alignment, although applying the magnetic field at later stage shows little effect.

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Numerical Analyses of Effectiveness of Magnetic Field on Variant Selection in FePd by Phase Field Modeling

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Microstructure Simulation for Solidification of Magnesium–Zinc–Yttrium Alloy by Multi-phase-field Method Coupled with CALPHAD Database

Satoshi Minamoto, Sukeharu Nomoto, Atsushi Hamaya, Toshiaki Horiuchi, Seiji Miura

pp. 1914-1919

DOI:

10.2355/isijinternational.50.1914

Abstract

The Mg–Zn–Y alloys show a good mechanical strength which can be achieved with the precipitation hardening by intermediate phases (X, W and I phase) in Mg solid solution (α phase). However, an accurate control of the microstructure formation is required in order to obtain good mechanical properties. In this study, experimental observations of microstructures of the Mg–Zn–Y system have been performed. Then we have focused on developing CALPHAD (CALculation of PHAse Diagrams) thermodynamic database to obtain the Gibbs free energy to draw phase diagram of the system and to understand the precipitation behavior of the intermediate phases. In order to understand the formation of microstructures, we have performed simulations of solidification of the alloy with use of multi-phase-field method. At the beginning the solidification process has been calculated for a large area, then the zoomed in region of the lamellar structures of the α phase and the W phase have been analyzed. Resulting optimum lamellar spacing reproduce experimental one well.

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Microstructure Simulation for Solidification of Magnesium–Zinc–Yttrium Alloy by Multi-phase-field Method Coupled with CALPHAD Database

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Simulations of Solidification in Sn–3Ag–0.5Cu Alloys by the Multi-phase-field Method

Yuko Nomura, Satoshi Minamoto, Sukeharu Nomoto

pp. 1920-1924

DOI:

10.2355/isijinternational.50.1920

Abstract

The microstructural evolutions in a Sn–3Ag–0.5Cu system of lead free alloys were predicted by the multi-phase field simulation coupled with CALPHAD thermodynamic database. In this simulation, the growth of Cu6Sn5 at 250°C and the precipitations of Cu3Sn and Ag3Sn at 150°C were calculated. These calculated micrographs were in good agreement with the experimental measurements. It was confirmed that this calculation method can be applied to the simulation of microstructures in the solidification of lead-free solder system including a Cu-substrate.

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Simulations of Solidification in Sn–3Ag–0.5Cu Alloys by the Multi-phase-field Method

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Excimer Laser Crystallization Processes of Amorphous Silicon Thin Films by Using Molecular-dynamics Simulations

Shinji Munetoh, Xiao Yan Ping, Tomohiko Ogata, Teruaki Motooka, Ryo Teranishi

pp. 1925-1928

DOI:

10.2355/isijinternational.50.1925

Abstract

Crystallization processes of amorphous Si during the excimer laser annealing in the complete-melting and near-complete-melting conditions have been investigated by using molecular-dynamics simulations. The initial amorphous Si MD cell was prepared by quenching a liquid Si layer with 18666 atoms. KrF excimer laser annealing processes of amorphous Si were calculated by taking account of the change in the optical constant upon melting during a Gaussian-shape laser pulse shot with full width at half maximum (FWHM) of 25 ns. The simulated results well reproduced the observed melting rate and the near-complete-melting and complete-melting conditions were obtained for 160 and 180 mJ/cm2 fluence, respectively. It was found that larger grains were obtained in the near-complete-melting condition. Our MD simulations also suggest that the nucleation occur from unmelted amorphous Si region during laser irradiation and crystal growth proceeds toward supercooled l-Si region in the near-complete-melting condition.

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Excimer Laser Crystallization Processes of Amorphous Silicon Thin Films by Using Molecular-dynamics Simulations

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In Situ Synchrotron X-ray Characterization of Microstructure Formation in Solidification Processing of Al-based Metallic Alloys

Bernard Billia, Henri Nguyen-Thi, Nathalie Mangelinck-Noel, Nathalie Bergeon, Hyejin Jung, Guillaume Reinhart, Aziz Bogno, Adeline Buffet, Jürgen Hartwig, Jose Baruchel, Thomas Schenk

pp. 1929-1935

DOI:

10.2355/isijinternational.50.1929

Abstract

The microstructure formed during the solidification step has a major influence on the properties of materials processed by major techniques (casting, welding ...). In situ and real-time characterization by synchrotron X-ray imaging is the method of choice to unveil the dynamical formation of the solidification microstructure in metallic alloys, and thus provide precise data for the critical validation of the theoretical predictions that is needed for sound advancement of modeling and numerical simulation. After a description of the experimental procedure used at the European Synchrotron Radiation Facility (ESRF), dynamical phenomena in the formation of the grain structure and dendritic or equiaxed solidification microstructure in Al-based alloys are presented. Beyond fluid flow interaction, earth gravity induces stresses, deformation and fragmentation in the dendritic mush. Settling of dendrite arms and equiaxed grains thus occurs, in particular in the columnar to equiaxed transition. Other types of stresses and strains are caused by the mere formation of the solidification microstructure itself. In white-beam X-ray topography, stresses and strains are manifested by specific contrasts and breaking of the Laue images into several pieces. Finally, quantitative analysis of the grey level in radiographs enables the analysis of solute segregation, which noticeably results in solutal poisoning of growth when equiaxed grains are interacting.

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In Situ Synchrotron X-ray Characterization of Microstructure Formation in Solidification Processing of Al-based Metallic Alloys

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X-Ray Video Microscopy Studies of Irregular Eutectic Solidification Microstructures in Al–Si–Cu Alloys

Ragnvald H. Mathiesen, Lars Arnberg, Yanjun Li, Anatoly Snigirev, Irina Snigireva, Arne K. Dahle

pp. 1936-1940

DOI:

10.2355/isijinternational.50.1936

Abstract

In-situ studies of Al–Si eutectic growth has been carried out for the first time by X-ray video microscopy during directional solidification of Al–Si–Cu alloys with and without Sr-addtions. The unmodified eutectics showed distinctive non-isothermal growth dynamics, where Si-crystals attained needle-like tip morphologies and progressed under significantly higher undercooling than Al, leading to formation of an irregular eutectic with Si as the leading phase and subsequent nucleation of Al on the Si-surfaces. In the Sr-modified alloys, the eutectic reaction was found to be strongly suppressed, occurring with low nucleation frequencies at undercoolings in the range 10–18 K. In the Cu-enriched melt, the eutectic front was found to attain meso-scale interface perturbations, sometimes evolving into equiaxed cellular rosettes in order to accommodate to the long-range redistribution of Cu from the composite eutectic interface. The eutectic front also attained short-range microscale interface perturbations consistent with characteristics of a fibrous Si growth. However, further improvements in spatial resolution are required in order to study the microscale structure formation in greater detail. Evidence was found in support of Si-nucleation occurring on potent particles suspended in the melt. Yet, both with Sr-modified and unmodified alloys Si precipitation alone was not sufficient to facilitate the eutectic reaction, which apparently required additional undercooling for Al to form on the Si-particles. To what extent nucleation mechanisms in the Cu-enriched systems are transferable to binary or commercial Al–Si alloys remains uncertain.

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X-Ray Video Microscopy Studies of Irregular Eutectic Solidification Microstructures in Al–Si–Cu Alloys

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Solidified Structure Control of Metallic Materials by Static High Magnetic Fields

Qiang Wang, Tie Liu, Kai Wang, Changjiu Wang, Keiji Nakajima, Jicheng He

pp. 1941-1946

DOI:

10.2355/isijinternational.50.1941

Abstract

Recently, the studies on the effects of high magnetic fields on solidification processes have been paid much attention both from the fundamental and applied points of view. With the aid of the enhanced Lorentz force and magnetization effect caused by the remarkably increased magnetic field intensity, several interesting phenomena, such as the control of fluid flow and particle migration in a melt, crystal orientation, and phase alignment, have been obtained. Moreover, the magnetic force induced by the interaction of magnetization and high magnetic field gradient has been evidenced to show significant effects on the microstructure evolution of alloys. In this paper, the recent development of the control of the solidification process by high magnetic fields is reviewed from the view point of uniform magnetic fields and magnetic field gradients.

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Solidified Structure Control of Metallic Materials by Static High Magnetic Fields

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In-Situ Fabrication of Bi/BiMn–BiMn–Mn Graded Materials by High Magnetic Field Gradients

Tie Liu, Qiang Wang, Chunjiang Wang, Zhigang Liu, Yi Yuan, Jicheng He

pp. 1947-1949

DOI:

10.2355/isijinternational.50.1947

Abstract

In order to develop a new method for in situ fabricating multilayer functionally graded materials (FGMs), high magnetic field gradients are proposed to control the solidification behaviors of peritectic alloys. Solidification experiments of Bi–11.8wt%Mn alloys under various magnetic field gradient conditions have been conducted and the macro- and microstructures of the magnetic field-treated specimens were examined. The primary Mn and βBiMn crystals can successively precipitate during the solidification process. Bi/BiMn–BiMn–Mn FGMs with various gradients have been successfully fabricated during solidification process. The results indicate that the gradient distribution of precipitates could be adjusted by controlling the solidification strategy and the magnetic parameters such as the product of the magnetic flux density and its gradient BdB/dz.

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In-Situ Fabrication of Bi/BiMn–BiMn–Mn Graded Materials by High Magnetic Field Gradients

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Crystal Alignment of Bi–Sn Alloy by Simultaneous Imposition of a Static Magnetic Field and an Alternating Current during Solidification

Kazuhiko Iwai, Manabu Usui

pp. 1950-1954

DOI:

10.2355/isijinternational.50.1950

Abstract

Crystal alignment of a Bi–10mass%Sn alloy solidified under different electromagnetic field imposing condition has been experimentally investigated in this study. Simultaneous imposition of a static magnetic field and an alternating current excited an electromagnetic vibration and it promoted nucleation, and resulted in decrease of undercooling, though imposition of the static magnetic field alone did not affect the undercooling. Furthermore, grain size of the solidified structure under the simultaneous imposition of the static magnetic field and the alternating current was smaller than that solidified with the magnetic field alone or solidified without the electromagnetic field imposition. XRD pattern of the sample solidified without the electromagnetic field imposition was similar to that of bismuth powder. On the contrary, only specific crystal plane peaks were observed when the electromagnetic field was imposed on the sample during the solidification. That is, crystal alignment of bismuth rich primary phase was achieved not only by the static magnetic field imposition alone but also the simultaneous imposition of the static magnetic field and the alternating current. However, degree of the crystal alignment solidified under the latter electromagnetic condition was slightly higher than that solidified under the former electromagnetic condition.

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Crystal Alignment of Bi–Sn Alloy by Simultaneous Imposition of a Static Magnetic Field and an Alternating Current during Solidification

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Equilibrium Relationship between the Oxide Compounds in MgO–Al2O3–Ti2O3 and Molten Iron at 1 873 K

Hideki Ono, Keiji Nakajima, Toshio Ibuta, Tateo Usui

pp. 1955-1958

DOI:

10.2355/isijinternational.50.1955

Abstract

It is important to determine the equilibrium relationship between the oxide compounds in MgO–Al2O3–Ti2O3 and molten iron to avoid Al2O3 or MgO·Al2O3 formation and for inclusion control. In this study, we investigated the formation conditions of MgTi2O4 in preference to MgAl2O4 at 1873 K. The phase stability regions of MgTi2O4 and MgAl2O4 or Ti2O3 were determined at 1873 K in MgO–Al2O3–Ti2O3. At a low titanium content of less than 0.1 mass% and when [mass ppm Mg]=3, MgAl2O4 forms at more than [mass%Al]=0.08 and the region of MgAl2O4 formation widens as the titanium content of the molten iron decreases. Accordingly, it is necessary to lower the Al content and to adjust the Ti content to an appropriate concentration range to form MgTi2O4 instead of MgAl2O4.

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Equilibrium Relationship between the Oxide Compounds in MgO–Al2O3–Ti2O3 and Molten Iron at 1 873 K

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Effects of Cr Addition on Coarse Columnar Austenite Structure in As-Cast 0.2 mass% Carbon Steel

Shingo Tsuchiya, Munekazu Ohno, Kiyotaka Matsuura, Kohichi Isobe

pp. 1959-1964

DOI:

10.2355/isijinternational.50.1959

Abstract

Effects of Cr addition on as-cast Coarse Columnar austenite Grain (CCG) structure were investigated for 0.2 mass% carbon steel by means of rapid unidirectional solidification method which realizes cooling conditions similar to those in the vicinity of continuous cast slab surface. Although the as-cast structure of the unidirectionally solidified samples always consisted of the CCGs regardless of Cr addition, the aspect ratio of the CCGs was remarkably reduced by the Cr addition. During solidification, Fine Columnar austenite Grains (FCGs) existed at the growing front of the CCG region and the migration velocity of the FCG/CCG boundary was reduced by the Cr addition. EPMA analysis revealed that the Cr addition enhances P segregation at interdendritic positions, which lowers a temperature for completion of γ transformation, Tγ. This lowered Tγ reduces the migration velocity of the FCG/CCG boundary and, as a result, induces the formation of CCGs having shorter major axis diameters.

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Effects of Cr Addition on Coarse Columnar Austenite Structure in As-Cast 0.2 mass% Carbon Steel

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Effects of Al and P Additions on As-cast Austenite Grain Structure in 0.2 mass% Carbon Steel

Surya Kencana, Munekazu Ohno, Kiyotaka Matsuura, Kohichi Isobe

pp. 1965-1971

DOI:

10.2355/isijinternational.50.1965

Abstract

Effects of addition of P and simultaneous additions of Al and P on as-cast γ grain structures of 0.2 mass% C steel have been investigated by means of permanent mold casting. The as-cast γ grain structure consists of Coarse Columnar Grain (CCG), Fine Columnar Grain (FCG) and Coarse Equiaxed Grain (CEG) regions from the mold side to center of the ingot. The single addition of P increases the FCG region in which short axis diameter of the columnar γ grain is comparable to the primary dendrite arm spacing. The simultaneous additions of Al and P also lead to refinement of the structure and, importantly, the complete refinement of the as-cast γ grain structure, viz., the structure without CCG and CEG regions was obtained even with a small amount of P addition when Al was added. The EPMA analysis showed that the refinement is associated with P segregation at interdendritic regions which is enhanced by Al addition. From thermodynamic calculation, it was demonstrated that high P concentrations stabilize δ and liquid phases at lower temperatures and produce the pinning effect on the growth of γ grains at interdendritic regions.

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Effects of Al and P Additions on As-cast Austenite Grain Structure in 0.2 mass% Carbon Steel

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Effect of Mg Addition on Solidification Structure of Low Carbon Steel

Kohichi Isobe

pp. 1972-1980

DOI:

10.2355/isijinternational.50.1972

Abstract

Effect of Mg addition on the solidification structure of low carbon steel containing about 0.1 mass% carbon was investigated in order to improve internal quality of cast blooms of this steel by some experiments using small size ingot casting. Some kinds of thermodynamic analyses on the crystallization of oxides and nitrides were also conducted along with FE-SEM observation on inclusions formed in cast ingots.
The results in this study were summarized as follows.
Adding Mg to the steel allows the equi-axed crystallization to be facilitated. In particular, the promotion effect is significant in low-carbon steel containing approximately 0.2–0.25 mass% Ti which leads to crystallizations of TiN until the end of solidification. The facilitating effect of equi-axed crystallization due to Mg addition in the steel without Ti content was presumably attributable to the heterogeneous nucleation by MgO or MgO·Al2O3, however, the facilitating degree is less compared with that in the steel containing Ti. It is apparent that MgO is also effective for TiN crystallization as the agent resulting in the significant promotion of heterogeneous nucleation of δ-Fe and the equi-axed crystallization. Cooperative effect of MgO and TiN was confirmed in the low-carbon steel containing Ti by Mg addition. By Ca addition, the facilitating effect due to Mg addition is assumed to decrease to liquidize oxides and to reduce total oxygen, so that the crystallized amount of solid MgO or solid MgO·Al2O3 decreases. It was verified that planar disregistry is a useful index to evaluate the relative heterogeneous nucleation capacity.

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Effect of Mg Addition on Solidification Structure of Low Carbon Steel

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An Evaluation Model for the Nodule Count of Graphite Particles in Ductile Iron Castings

HongLiang Zheng, YuCheng Sun, Ning Zhang, XueLei Tian

pp. 1981-1984

DOI:

10.2355/isijinternational.50.1981

Abstract

An evaluation model on the nodule count of graphite particles in ductile iron castings was developed based on a series of orthogonal experiments. The model is proposed for evaluating the count of graphite particles in ductile iron castings with different carbon equivalent (CE), local solidification time (ts), and maximum undercooling. According to the nodule count spacial distribution theory, the graphite nodule density Nv equals nuclei density after solidification. The measurement of NA values were carried out on experimental ductile iron castings designed according to the orthogonal principles. Nv was calculated from area densities NA using Owadano rules. The results indicate that the count of graphite particles has a close relationship to CE, ts and instead of one of these three parameters.

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An Evaluation Model for the Nodule Count of Graphite Particles in Ductile Iron Castings

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