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ONLINE ISSN: 1347-5460
PRINT ISSN: 0915-1559

ISIJ International Vol. 54 (2014), No. 2

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

    Keiji Nakajima

    pp. 253-253

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    DOI:10.2355/isijinternational.54.253

    Recommended Articles: Growth of Secondary Dendrite Arms of Fe–C Alloy during Transient Directional Solidification by Phase-field Method [ View more ]

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    2. Phase-field Modeling and Simulations of Dendrite Growth ISIJ International Vol.54(2014), No.2
    3. Water Analog Experimental Method for the Diffusion and Distribution of Alloy Elements in Liquid Steel during Ingot Filling Process ISIJ International Vol.54(2014), No.2

  • Numerical Simulation for Optimizing Temperature Gradients during Single Crystal Casting Process

    Aleksandr Aleksandrovich Inozemtsev, Aleksandra Sergeevna Dubrovskaya, Konstantin Aleksandrovich Dongauzer, Nikolay Aleksandrovich Trufanov

    pp. 254-258

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    DOI:10.2355/isijinternational.54.254

    Abstract

    This article describes application of computational simulation for manufacturing of castings using investment casting technique. A mathematical model was created describing the process of melted metal pouring into the ceramic shell with its further solidification. Using this model the process of manufacturing single-crystal patterns from heat-resistant nickel superalloy was simulated. The obtained computational model was verified by the temperature measuring of the real-life production experiment. Using mathematical simulation the speed of the patterns moving out was optimized to increase temperature gradient on the casting.

    Recommended Articles: Simulation of Horizontal Centrifugal Casting: Mold Filling and Solidification [ View more ]

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    1. Simulation of Horizontal Centrifugal Casting: Mold Filling and Solidification ISIJ International Vol.54(2014), No.2

  • Closed Chain Simulations of a Cast Aluminium Component - Incorporating Casting Process Simulation and Local Material Characterization into Stress-strain Simulations

    Jakob Olofsson, Ingvar L. Svensson

    pp. 259-265

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    DOI:10.2355/isijinternational.54.259

    Abstract

    The coupling between simulations of solidification, microstructure and local mechanical behaviour and simulation of stress-strain behaviour is studied by applying a recently developed simulation strategy to a high pressure die cast aluminium component. In the simulation strategy, named a closed chain of simulations for cast components, the mechanical behaviour throughout the component is determined locally by a casting process simulation. The entire casting process, including mould filling and solidification, is simulated to predict the formation of microstructure and residual stresses throughout the component, and material characterization models are applied to relate microstructural features to local elastic and plastic mechanical material behaviour. The local material behaviour is incorporated into a finite element method (FEM) stress-strain simulation of a realistic load case of the component in service.
    In the current contribution the influences of local variations in mechanical behaviour and residual stresses on the component behaviour are investigated. The simulation results for local microstructure and mechanical behaviour are compared to experimental results, and the predicted local mechanical behaviour is incorporated on an element level into the FEM simulation. The numerical effect of the variations in mechanical behaviour is quantified by comparing the results achieved using local behaviour and homogeneous behaviour. The influence of residual stresses predicted by the casting process simulation on the component behaviour is also studied.
    The casting process simulation is found to accurately predict the local variations in microstructure throughout the component, and the local variations in mechanical behaviour are well described. The numerical results show that casting process simulation and modelling of microstructure formation, material behaviour and residual stresses are important contributions to correctly predict the behaviour of a cast aluminium component in service. This motivates the use of the proposed simulation strategy, and show the importance of incorporating materials science and casting process simulations into structural analyses of cast components. It is discussed that integration of these areas, e.g. using the closed chain of simulations, is important in order to increase the accuracy of FEM simulations and the product development efficiency in the future.

  • Simulation of Horizontal Centrifugal Casting: Mold Filling and Solidification

    Jan Bohacek, Abdellah Kharicha, Andreas Ludwig, Menghuai Wu

    pp. 266-274

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    DOI:10.2355/isijinternational.54.266

    Abstract

    In order to simulate the mold filling and solidification of the outer shell of large work rolls being cast by horizontal centrifugal casting, the shallow water equations were adopted to solve the 2D average flow dynamics of the melt spreading inside the cylindrical mold. The model accounts for centrifugal force, Coriolis force, shear force, gravity and convective and diffusive energy transport. The solidification front was tracked by fulfilling the Stefan condition. Radiative and convective heat losses were included from both, the free surface and the outer wall of the mold. By introducing a stochastic factor to account for the irregular filling jet behavior an uneven spreading of liquid from the center of the mold towards the extremities was predicted. Thus, the formation of the first solid layer also happens unevenly. However, when the mold is covered everywhere with a solid layer, the solidification rate decreases and further filling increases the height of the liquid layer. With increase liquid height the amplitude of the free surface waves also increases.

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  • Water Analog Experimental Method for the Diffusion and Distribution of Alloy Elements in Liquid Steel during Ingot Filling Process

    Jinwu Kang, Chao Dong, Xiaokun Hao, Gang Nie, Houfa Shen, Baicheng Liu

    pp. 275-280

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    DOI:10.2355/isijinternational.54.275

    Abstract

    To physically simulate the alloy elements transportation and diffusion in the liquid steel during the making of heavy ingots, a water analogy experimental method is presented. In this method, methylene blue dye is used as solute to simulate the alloy element carbon in the melt steel. And a measurement method is proposed to measure the concentration of the solute, in which the laser reflection intensity detection method is used. The water analogy experiment setup is constructed. The multi-concentration pouring of a 438 t ingot is investigated by this method. The concentration of the ladles decrease with the pouring consequence. The concentration variation curves with time at the tundish outlet and in the mold are acquired and analyzed. The tundish outlet concentration decreases gradually and no fluctuation occurs during the change of ladles. Negative concentration gradient is achieved at the end of pouring, which can be helpful for controlling of the macrosegration usually occurring in the heavy ingot.

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    3. Evaluation of Permeability for Columnar Dendritic Structures by Three-dimensional Numerical Flow Analysis ISIJ International Vol.54(2014), No.2

  • Ultrasonic Treatment of the 304 Stainless Steel Melt

    Jinwu Kang, Xiaopeng Zhang, Yisen Hu, Jiyu Ma, Yongyi Hu, Tianyou Huang

    pp. 281-287

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    DOI:10.2355/isijinternational.54.281

    Abstract

    Ultrasonic treatment of the melt metals is a hot research topic; however, it is hard to introduce ultrasound into liquid steel because of the requirement of resistance to high temperature and erosion in the melt. In this paper, the author proposed a new method to introduce ultrasound into liquid steel. The metal to be treated is cast together to the tip of the booster. During the test, the booster is placed upward with the metal to be treated connected on the top as a free end, which is melt by induction coils. The booster which generates ultrasound, by this way, acts on the melt pool. The determination of the length of the booster under this situation is given. The effect of ultrasonic treatment on the melt of 304 stainless steel is studied. The microstructure of the treated area is significantly refined and equi-axed grains are obtained; the fragmentation of inclusions occurs due to the ultrasonic treatment; the mechanism of the fragmentation of the dendrite and inclusions is discussed.

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    3. Turbulent Flow and Gas-Liquid Mass Transfer in Gas-injected System Tetsu-to-Hagané Vol.86(2000), No.4

  • Undercooling, Cooling Curves and Nodule Count for Near-eutectic Thin-walled Ductile Iron Castings

    Wojciech Kapturkiewicz, Andriy Burbelko, Marcin Górny

    pp. 288-293

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    DOI:10.2355/isijinternational.54.288

    Abstract

    A solidification model for ductile iron, including Weibull formula for nodule count, has been presented. The principal assumptions of the kinetic nature of growth, depending on undercooling in respect of the eutectic equilibrium temperature and austenite liquidus line, have been adopted, disregarding the diffusion processes, which was justified by the rapid course of the crystallization process in a thin-walled casting. From this model, the following parameters can be determined: cooling curves, kinetics of austenite and eutectic nucleation, austenite and eutectic growth velocity, and volume fraction.
    The correctness of the mathematical model has been experimentally verified by comparison with literature data in the range of the most significant factors, which include temperature field, the value of maximum undercooling, the value of minimum and maximum temperature on a cooling curve, maximum undercooling, the recalescence and graphite nodule count interrelated with the casting cross-section.

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  • Mathematical Modeling and Microstructure Analysis of Al–Mg–Sc–Zr Alloy Strips Produced by Horizontal Single Belt Casting (HSBC)

    Sa Ge, Mert Celikin, Mihaiela Isac, Roderick Ian Lawrence Guthrie

    pp. 294-303

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    DOI:10.2355/isijinternational.54.294

    Abstract

    Horizontal Single Belt Casting (HSBC) is a near net shape strip casting technology that will probably gain significant prominence in the coming years. Fluid mechanics and associated heat and mass transfer are important aspects of any continuous casting process, and the HSBC process is no exception.
    In this study, mathematical models have been developed, using ANSYS FLUENT 14, to assess various aspects of the HSBC process for the Al–Mg–Sc–Zr system. Specific emphasis is placed on a) the effects of substrate surface properties on strip quality, b) liquid metal-air two-phase interactions and meniscus behavior, c) heat fluxes between the metal and substrate, and d) solidification behavior during strip casting.
    These predictions are validated against experimental casting results. A 5000 series Al–Mg alloy, with added Sc and Zr, shows exceptional potential as a structural material for aerospace and transportation applications. It is also a suitable material to be produced via the HSBC process. Optical microscopy, SEM and EBSD analyses were conducted to compare the potential advantages of casting this alloy via the HSBC process versus conventionally produced Direct Chill Casting.

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  • Numerical Investigation of Unsteady Molten Steel Flow and Inclusion Behavior in the Tundish in the Ladle Change Period

    Koichi Takahashi, Makoto Ando, Toshio Ishii

    pp. 304-310

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    DOI:10.2355/isijinternational.54.304

    Abstract

    Prevention of defects caused by inclusions is an important technical issue in the production of high-grade steel products. In particular, inclusion removal in the continuous casting tundish is an essential technology for production of high-grade steels. It is well known that inclusion removal in the ladle change period is more difficult than during steady state casting. However, the unsteady phenomena of molten steel flow and inclusion motion in the ladle change period have not been studied in detail. To clarify these phenomena, unsteady molten steel flow and inclusion particle motion in the tundish in the ladle change period were investigated by numerical approaches. First, a numerical simulation of the unsteady molten steel flow and unsteady inclusion particle motion was carried out. As a result, it is found that the outflow rate of inclusions to the mold increases sharply immediately after the start of pouring from the new ladle. Second, flow characterization of the molten steel flow in the tundish in the ladle change period was carried out. A new method using a combined model was proposed to evaluate the flow characteristics of unsteady state tundishes in the ladle change period. The method was applied to the numerical simulation results, and showed that sharp increases in the well-mixed volume and dead volume occur simultaneously with inclusion outflow. This result indicates that flow control at the start of pouring from a new ladle is an effective approach to improve the inclusion removal performance of tundishes.

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  • Modeling of a Thermo-Electromagneto-Hydrodynamic Problem in Continuous Casting Tundish with Channel Type Induction Heating

    Qiang Wang, Baokuan Li, Fumitaka Tsukihashi

    pp. 311-320

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    DOI:10.2355/isijinternational.54.311

    Abstract

    A mathematical model has been developed to understand the electromagnetic phenomena, heat transfer and molten steel flow in a continuous casting tundish with channel-type induction heating. Maxwell equations are first solved using the finite element method to determine the electromagnetic force and joule heating. Then, the Navier-Stokes equations and energy conservation equation are also solved with the electromagnetic force and joule heating as a source term, respectively. The two-equation RNG k-ε model is used to represent the turbulent mixing. Additionally, the tracer distribution is determined by solving a scale transport equation. The coupled flow field, temperature distribution and concentration distribution are solved by the finite volume method. A non-isothermal water model experiment is performed to observe significantly buoyancy driven flow in the tundish with induction heating. The results indicate that a current loop would be formed by the induced current through the two channels. The electromagnetic force points to the center of the channel generating a pinch effect on molten steel. As skin effect and proximity effect, the electromagnetic force as well as the joule heating in the region closer to the induction coil is greater than that in another region. Therefore, spiral recirculation would occur in the channels when molten steel flows through. After flows through the channels, the molten steel lifts upward under the effect of buoyancy. The heat loss of molten steel can be compensated effectively by the joule heating, and the temperature distribution become more uniform in the continuous casting tundish with induction heating.

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  • Effect of Coil Design on the Temperature and Velocity Fields during Solidification in Electromagnetic Stirring Processes

    Gregory Poole, Nagy El-kaddah

    pp. 321-327

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    DOI:10.2355/isijinternational.54.321

    Abstract

    This paper examines the role of induction coil design on stirring of molten metal in electromagnetic (EM) solidification processes. A model is presented to describe the EM, heat transfer, and fluid flow phenomena in these processes. It is based on a dual-zone description of the mushy region, and accounts for damping of turbulence by the solidified crystallites. The electromagnetic field equations were solved using the mutual inductance technique, while the temperature and turbulent flow fields were calculated using the control volume method. Calculations were performed for solidification of an Al–Cu alloy placed in a stationary magnetic field generated by an induction coil. The effect of coil design on the flow structure was investigated for three different coil positions. It was found that changing the coil position significantly alters the flow pattern from four recirculating loops when the coil is above the midsection of the melt to two loops, typical of a travelling magnetic field, when the coil is at the base of the melt. This significantly modifies the rate of solidification across the ingot, as well as the temperature gradient, in the mushy region. The decay of the velocity and turbulent fields in the mushy region was found to be exponential, with the maximum rate of decay at the solidification front. These results indicate that through changes in coil design, it is possible to control the flow characteristics and solidification behavior in the molten metal.

  • Real-time Heat Transfer Model Based on Variable Non-uniform Grid for Dynamic Control of Continuous Casting Billets

    Jian Yang, Zhi Xie, Zhenping Ji, Hongji Meng

    pp. 328-335

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    DOI:10.2355/isijinternational.54.328

    Abstract

    A real-time heat transfer model has been developed for dynamic control of continuous casting billets. In order to fulfill the real-time requirements for efficiency and accuracy, finite volume method (FVM) and alternating direction implicit algorithm (ADI) have been selected as the efficient numerical solution algorithm. And most important of all, variable non-uniform grid and variable time step have been adopted in the algorithm, accelerating the calculation of heat transfer model by 20–40 times. Further, the algorithm’s discretization parameters including the grid, time step and slice distance have been optimized by error control (< 3°C), improving the relative calculation time to 0.57. The real-time model has been calibrated by surface temperature measurements using a thermal infrared imager, and its online performance has been tested, within ±13°C of the measurements. After the calibration, the model has been applied to the dynamic control of secondary cooling and the dynamic control of the electric current of final electromagnetic stirring (FEMS), providing the surface temperatures and mushy zone radius at the installation position of FEMS. The latter has been validated by shell-thickness measurements using nail-shooting (relative error< 2.3%). The model-based dynamic control systems controlled the surface temperatures and the flow in mushy zone precisely with changing casting conditions, and have improved the billet quality obviously and reduced the fractures of rolling line during wire-drawing to 1/6 times per month in average from 2–3 times before.

  • Thermo-mechanical Modeling in Continuous Slab Casting Mould and Its Application

    Daojie Zhang, Song Lei, Shan Zeng, Houfa Shen

    pp. 336-341

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    DOI:10.2355/isijinternational.54.336

    Abstract

    In order to understand the thermal and mechanical behavior during solidification of the strand in the slab casting mould, a two-dimensional coupled thermo-mechanical finite element model was built and the corresponding FEM program was developed. The model simulates a quarter of the transverse section of the strand as it moves down in the mould at the casting speed. The heat transfer in the mould and the strand is analyzed with the steady model and the transient model, respectively. A thermo-elastoplastic plane stress model is used for analyzing the strand deformation. The heat transfer and the deformation are coupled through the interfacial thermal resistance between the strand and the mould. The model was used to investigate the effects of mould corner configuration and mould taper on the crack formation tendency of strand. The results show that employing a chamfered mould with proper corner size could modify the 2D heat transfer conditions at slab corners, hence reducing the risk of transverse corner cracks. Likewise, employing an optimized parabolic mould taper could remarkably achieve better uniformity of the strand temperature and stress, and simultaneously reduce the peak value of the stress, thus resulting in less crack occurrence, which favorably coincides with the theoretical expectation. The successful application of the coupled thermo-mechanical model demonstrates its tremendous potentialities for further understanding of the internal crack formation and for the optimization of operation parameters and the mould configuration.

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  • Recent Developments of a Numerical Model for Continuous Casting of Steel: Model Theory, Setup and Comparison to Physical Modelling with Liquid Metal

    Pavel Ernesto Ramirez Lopez, Pooria Nazem Jalali, Johan Björkvall, Ulf Sjöström, Christer Nilsson

    pp. 342-350

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    DOI:10.2355/isijinternational.54.342

    Abstract

    Recent developments of an advanced numerical model for Continuous Casting of steel unveiled at the previous 2010 CSSCR Conference in Sapporo, Japan are presented. These include coupling of the existing multiphase, heat transfer and solidification model to argon injection for tracking bubble trajectories in the SEN, metal bulk and across the slag bed after passing through the metal surface. Hence, description of a method for adding gas injection in combination with a multiphase model for tracking metal/slag interfaces (Discrete Phase Model + Volume Of Fluid, DPM+VOF) is given.
    Validation is supported by tests on a revamped Continuous Casting Simulator (CCS-1) based on a low melting point alloy, which can realistically replicate the flow conditions in the caster. Metal-slag-argon flow predictions were compared to observations in the physical model showing good agreement on features such as discharging jets, rolls, standing waves and argon distribution measured through a variety of techniques such as ultrasound, electromagnetic probes and video sequences.
    Ultimately, the model makes possible the prediction of stable or unstable flows within the mould as a function of different argon flow-rates and bubble sizes. Application to industrial practice is an ongoing task and preliminary results are illustrated. The robustness of the model combined with direct observations in CCS-1 make possible the description of phenomena difficult to observe in the caster (e.g. argon injection and metal flow), but critical for the stability of the process and the quality of cast products.

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  • Two-Phase Modeling of Macrosegregation in a 231 t Steel Ingot

    Wutao Tu, Houfa Shen, Baicheng Liu

    pp. 351-355

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    DOI:10.2355/isijinternational.54.351

    Abstract

    The formation of macrosegregation in the steel ingots is a multiphase/multiscale flow phenomenon inherently. It still remains a challenge to simulate the macrosegregation in the large steel ingots. The objective of this work is to validate a two phase model by measuring the macrosegregation in a 231 t steel ingot. The model incorporates the descriptions of heat transfer, melt convection, solute transport, and the solid movement on the system scale with microscopic relations for grain nucleation and growth. The model simulates the solidification process by solving the conservation equations of mass, momentum, energy and species for both the liquid and solid phases. Besides, simulations are performed to investigate the influence of the critical solid volume fraction (gsc) on the final macrosegregation pattern which was characterized by experimental measurements. It is indicated that the typical macrosegregation patterns encountered in a large steel ingot, including a positively segregated zone in the hot top and a negatively segregated zone in the bottom part of the ingot, are well reproduced with the current two phase model. Comparison of the simulation results and the measurements is made. It is demonstrated that the critical solid volume fraction gsc is an important factor for the final macrosegregation pattern.

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  • Macrosegregation and Its Formation Mechanism in Steel Ingot with Designed Local Thermal Control

    Xiaoping Ma, Dianzhong Li

    pp. 356-358

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    DOI:10.2355/isijinternational.54.356

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  • Simulation of the Center-Line Segregation Generated by the Formation of Bridging

    Takemasa Murao, Toshiyuki Kajitani, Hideaki Yamamura, Koichi Anzai, Katsunari Oikawa, Tomoki Sawada

    pp. 359-365

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    DOI:10.2355/isijinternational.54.359

    Abstract

    The macrosegregation model that heat transfer, solidification, liquid flow and solute movement were considered was developed to simulate the generation of the center-line segregation in the casting of steel. The classical model which considers only the liquid flow caused by solidification shrinkage leads the negative segregation which contradicts the fact. In order to explain the contradiction, the bulging of the cast slab has been claimed to be important factor to form the positive segregation at the center of the cast. However, some experimental data show that the bulging has not been necessarily formed during the generation of center-line segregation. In this case, the bridging with the solidification shrinkage has been found to be formed instead of the bulging. In this paper, the macrosegregation model is developed considering, thus, three driving forces of fluid flow; solute concentration, thermal expansion and solidification shrinkage. This simulation results show that the primary driving force which results in the center-line segregation is the solidification shrinkage with the bridge. In addition to that, the mechanism of generating the center-line segregation is discussed based on the simulation results.

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  • Evaluation of Permeability for Columnar Dendritic Structures by Three-dimensional Numerical Flow Analysis

    Yukinobu Natsume, Daiki Takahashi, Kasumi Kawashima, Eiji Tanigawa, Kenichi Ohsasa

    pp. 366-373

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    DOI:10.2355/isijinternational.54.366

    Abstract

    In order to evaluate the permeability of columnar dendritic structures, three-dimensional (3-D) flow simulations of interdendritic liquid were carried out. The 3-D columnar dendrite morphologies, created by means of a computer-aided design (CAD) software, were based on two-dimensional dendrite morphologies calculated by a phase-field method. The artificial 3-D columnar dendrites were regularly arranged, and six kinds of 3-D columnar dendritic structures were observed, each with different liquid volume fractions between 0.56 and 0.95. For these 3-D columnar dendritic structures, the flow parallel and normal to the primary arms were calculated using FLUENT, and the permeability of six 3-D columnar dendritic structures for both flow directions were determined using the Darcy law. The values of our simulated permeability were compared with those values of permeability obtained experimentally [K. Murakami, A. Shiraishi and T. Okamoto: Acta Metall., 31 (1983), p. 1417, 32 (1984), p. 1423, C. Y. Liu, K. Murakami and T. Okamoto: Mater. Sci. Tech., 5 (1989), p. 1148]. For both flow directions, our simulated permeability for high liquid volume fractions complemented their experimental permeability for low liquid volume fractions. Therefore, we confirmed the consistency of simulated reading with extrapolations of experimental values of low volume fractions to high volume fractions. In addition, we discussed the limitation of flow within the mushy region, and found that defining the limiting permeability of interdendritic flow, in order to evaluate the relationship between dendritic morphology and the solid volume fraction where interdendritic liquid flow ceases, was effective.

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    3. Growth of Secondary Dendrite Arms of Fe–C Alloy during Transient Directional Solidification by Phase-field Method ISIJ International Vol.54(2014), No.2

  • Partial Equilibrium Prediction of Solidification and Carbide Precipitation in Ti-added High Cr Cast Irons

    Hongwei Zhang, Qiang Liu, Hiroyuki Shibata, Qiang Wang, Pär Jönsson, Jicheng He, Keiji Nakajima

    pp. 374-383

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    DOI:10.2355/isijinternational.54.374

    Abstract

    Carbide precipitation and eutectic phase transformation during solidification of Fe–C–Cr–Ti–Mn–Mo–Ni–Si Ti–added high-chromium cast irons (HCCIs) were studied numerically and experimentally by the help of Partial Equilibrium approximation, DSC thermal analyses and EDX analyses. The main carbides formed during the solidification are distinguished as MC, primary M7C3 and eutectic M7C3 from their distinguished constitution, while other researchers didn’t distinguish the primary and eutectic M7C3 carbide. Through comparing the prediction of Partial Equilibrium approximation with DSC thermal analysis measurement, the precipitation sequence of the eutectic structure in HCCIs is clarified to follow the sequence of FCC prior to the eutectic M7C3, although they were usually expected to precipitate simultaneously. The hardness index of the HCCIs is evaluated quantatively by summation of the contributions of the Vickers hardness of MC, primary M7C3 and eutectic M7C3 carbides with predicted precipitation amount and composition / constitution. The effects of C, Ti and Cr contents on the precipitation sequence, the amount and the composition of carbides as well as the hardness of the HCCIs are discussed deeply. Finally, the validity of Partial Equilibrium approximation is shown in prediction of the solidification in multicomponent system with large amount of precipitated carbides.

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  • Cellular Automaton Modeling of Microporosity Formation during Solidification of Aluminum Alloys

    Mingfang Zhu, Zhengyang Li, Dong An, Qingyu Zhang, Ting Dai

    pp. 384-391

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    DOI:10.2355/isijinternational.54.384

    Abstract

    A two-dimensional (2D) cellular automaton (CA)-finite difference method (FDM) model is proposed to simulate the dendrite growth and microporosity formation during solidification of aluminum alloys. The model involves a three-phase system of liquid, gas, and solid. The growth of both dendrite and gas pore is simulated using a CA approach. The diffusion of solute and hydrogen is calculated using the FDM. The model is applied to simulate the formation and interactions of dendrites and micropores in an Al-7wt.%Si alloy. The effects of initial hydrogen concentration and cooling rate on microporosity formation are investigated. It is found that the porosity nuclei with larger size grow preferentially, while the growth of the small porosity nuclei is restrained. The competitive growth between porosities and dendrites is also observed. With the increase of initial hydrogen concentration, the incubation time of porosity nucleation and growth decreases, and the percentage of porosity increases, while porosity density does not increase apparently. With the decrease of cooling rate, porosity nucleates and starts to grow at higher temperatures, and the percentage of porosity increases, but the porosity density displays a decreasing trend. In addition, at a slower cooling rate, the competitive growth between porosities and dendrites becomes more evident, leading to a more non-uniform distribution of porosity size, and an increased maximum porosity size. The simulation results agree reasonably with the experimental data in the literature.

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    2. Three-dimensional Cellular Automaton Model for the Prediction of Microsegregation in Solidification Grain Structures ISIJ International Vol.54(2014), No.2
    3. Modeling of Ferrite-Austenite Phase Transformation Using a Cellular Automaton Model ISIJ International Vol.54(2014), No.2

  • Coupled Cellular Automaton (CA) – Finite Element (FE) Modeling of Directional Solidification of Al-3.5 wt% Ni Alloy: A Comparison with X-ray Synchrotron Observations

    Dong Rong Liu, Guillaume Reinhart, Nathalie Mangelinck‑Noel, Charles-André Gandin, Henri Nguyen-Thi, Bernard Billia

    pp. 392-400

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    DOI:10.2355/isijinternational.54.392

    Abstract

    Development of dendritic grain structure and meso‑segregation leading to localized intergranular eutectic is simulated during directional solidification of an Al ‑ 3.5 wt% Ni alloy with two pulling velocities (4 μm s–1 and 8 μm s–1) using a two‑dimensional (2D) Cellular Automaton – Finite Element (CAFE) model. 2D CAFE simulations are compared with in situ and real-time experiments characterized by means of X-ray radiography at the European Synchrotron Radiation Facility (Grenoble, France). Two nucleation models are used. The first model is established by listing all measured positions and orientations of experimentally-observed nucleation events. The undetermined value of the nucleation undercooling is then set to 0°C for all nucleation sites. The other model considers a stochastic model with a Gaussian distribution of the nucleation site as a function of the undercooling. It is derived from series of experiments. The influences of the nucleation models and liquid convection on the grain structure characteristics are numerically investigated. A good agreement with experimental observations is achieved concerning the evolutions of both the dendritic and the eutectic growth fronts (i.e., the size of the mushy zone). The predicted grain size and elongation are compared with measurements for the two nucleation laws. Simulations using the list of nucleation events reach better agreement with the longitudinal profiles of the grain equivalent diameter and elongation factor compared to the stochastic nucleation model. Direct tracking of the eutectic growth front as well as three‑dimensional analyses are found to be required for improvement of the predictions.

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    3. 3D Coupled Cellular Automaton (CA)–Finite Element (FE) Modeling for Solidification Grain Structures in Gas Tungsten Arc Welding (GTAW) ISIJ International Vol.54(2014), No.2

  • 3D Coupled Cellular Automaton (CA)–Finite Element (FE) Modeling for Solidification Grain Structures in Gas Tungsten Arc Welding (GTAW)

    Shijia Chen, Gildas Guillemot, Charles-André Gandin

    pp. 401-407

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    DOI:10.2355/isijinternational.54.401

    Abstract

    A coupled Cellular Automaton (CA) – Finite Element (FE) model is proposed to predict the grain structure formation during Gas Tungsten Arc Welding (GTAW). The FE model solves the heat flow problem based on an adaptive meshing. This is done on a first FE mesh. The CA model simulates the development of the envelope of the grains in the liquid. For that purpose, a second FE mesh, referred to as CA mesh, is used. Fields can be interpolated between the adaptive FE mesh and the CA mesh. A CA grid made of a regular lattice of cubic cells is defined and superimposed onto the CA mesh. A new dynamic strategy for the allocation/deallocation of the CA grid is proposed to reduce the computation and memory costs. This CAFE model is applied to partial melting of an initial grain structure and epitaxial growth in the undercooled zone of a liquid pool, thus simulating the formation of solidification structure during the GTAW process. Examples of single linear passes simulations for various processing conditions and a multiple pass simulation are presented.

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  • Numerical Simulation of Microstructure Evolution of Heavy Steel Casting in Casting and Heat Treatment Processes

    Bin Su, Zhiqiang Han, Yongrang Zhao, Bingzhen Shen, Enxian Xu, Shujun Huang, Baicheng Liu

    pp. 408-414

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    DOI:10.2355/isijinternational.54.408

    Abstract

    The microstructure evolution of hypoeutectoid steel during casting and heat treatment processes was simulated by using cellular automaton method. In the simulation, the peritectic solidification, α phase precipitation and pearlite transformation during casting process were considered, and the austenite formation, grain coarsening and decomposition during heat treatment were simulated. The final microstructure, including the average grain size and fraction of α phase as well as the average interlamellar spacing of pearlite, was obtained. The use of through-process simulation as well as a comparison with experiments was demonstrated using a hollow shaft casting as an example. By using the model, the microstructure evolution at different locations in the hollow shaft was simulated, in which the thermal history data obtained by simulating the casting and heat treatment processes were adopted. Metallographic samples taken from the test bar were examined and corresponding mechanical properties tests were conducted. The simulated results were compared with the experimental results to validate the model.

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  • Three-dimensional Cellular Automaton Model for the Prediction of Microsegregation in Solidification Grain Structures

    Yukinobu Natsume, Kenichi Ohsasa

    pp. 415-421

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    DOI:10.2355/isijinternational.54.415

    Abstract

    A 3-D cellular automaton finite difference (3-D CAFD) model to predict the solidification grain structure and the microsegregation was developed. In the present model, a new approach to calculate the solute concentration distribution was developed. Moreover, the CA cell including the grain boundary was newly defined. The probabilistic approach was adopted as the nucleation model, and the decentered octahedron growth algorithm was adopted as the grain growth model. The growth kinetics of the dendrite tip to calculate the growth of the dendrite envelope was calculated by a 3-D Kurz-Giovanola-Trivedi (KGT) model. In the 3-D KGT model, the local undercooling estimated by the local temperature and local solute concentration was used. To evaluate the validity of the present model, we carried out simulations of the solidification grain structure under directional solidification. The different solidification grain structures were obtained by the different solute concentration distributions. In addition, we compared our model with the microsegregation predicted by Scheil’s equation. The simulated results of microsegregation by the present model were in fairly good agreement with those by Scheil’s equation. From these results, we confirmed that the calculation of solute concentrations has to be considered and that the present model can simultaneously simulate microstructure and microsegregation.

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  • Modeling of Ferrite-Austenite Phase Transformation Using a Cellular Automaton Model

    Dong An, Shiyan Pan, Li Huang, Ting Dai, Bruce Krakauer, Mingfang Zhu

    pp. 422-429

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    DOI:10.2355/isijinternational.54.422

    Abstract

    A two-dimensional (2D) cellular automaton (CA) model is proposed to simulate the ferrite-austenite transformation in binary low-carbon steels. In the model, the preferential nucleation sites of austenite, the driving force of phase transformation coupled with thermodynamic parameters, solute partition at the ferrite/austenite interface, and carbon diffusion in both the ferrite and austenite phases are taken into consideration. The proposed model is applied to simulate the ferrite-to-austenite transformation during isothermal heating at 760°C that is in the ferrite and austenite two-phase range, the austenite-to-ferrite transformation during continuous cooling, and carbon diffusion during tempering at different temperatures for an Fe-0.2969 mol.% C alloy. The results show that during the isothermal heating, austenite nucleates and grows. The austenite grains are mostly located at the boundaries of ferrite grains. The carbon concentration in austenite is higher than that in ferrite. The simulated microstructure agrees reasonably well with the experimental observation. During the continuous cooling process, the austenite-to-ferrite transformation occurs accompanied with carbon diffusion. After cooling from the heating temperature of 760°C to room temperature with a cooling rate of 2°C/s, the carbon concentration field is nearly uniform, while a higher cooling rate of 5°C/s results in a non-uniform carbon concentration field. After tempering at different temperatures for 20 min, the uniformity of carbon distribution increases with increasing tempering temperature. The simulation results are used to understand the mechanisms of the observed experimental phenomena that a cold-rolled low-carbon enameling steel presents different yield strengths after different heat treatment processes.

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  • Growth of Secondary Dendrite Arms of Fe–C Alloy during Transient Directional Solidification by Phase-field Method

    Yu Xie, Hongbiao Dong, Jonathan Dantzig

    pp. 430-436

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    DOI:10.2355/isijinternational.54.430

    Abstract

    Due to the variations in the local solidification conditions in typical industrial casting processes, dendrites grow under transient rather than steady-state conditions. In this study, the phase-field method was used to study the evolution of secondary dendrite arms of Fe-0.3 wt.% C alloy during transient directional solidification imposed by decreasing the pulling velocity. We find that the dendrite under transient growth conditions is different from the steady-state dendrite, with smaller selection parameter σ* and the dendrite envelope inside the parabola scaled by the tip radius. The secondary arms undergo a ripening process in which other secondary arms remelt by shrinking from their tips, rather than by detachment from the primary stalk. The surviving arms are finer than those found under steady-state growth conditions, and the size of the surviving arms decreases with decreasing growth velocity.

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    2. Phase-field Modeling and Simulations of Dendrite Growth ISIJ International Vol.54(2014), No.2
    3. Evaluation of Permeability for Columnar Dendritic Structures by Three-dimensional Numerical Flow Analysis ISIJ International Vol.54(2014), No.2

  • Phase-field Modeling and Simulations of Dendrite Growth

    Tomohiro Takaki

    pp. 437-444

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    DOI:10.2355/isijinternational.54.437

    Abstract

    The phase-field method has recently emerged as the most powerful computational tool for simulating complicated dendrite growth. However, these simulations are still limited to two-dimensional or small three-dimensional spaces; therefore, to realistic and practical dendritic structures, it is crucial to develop a large-scale phase-field simulation technique. This review discusses the phase-field modeling and simulations of dendrite growth from the fundamental model to cutting-edge very-large-scale simulations. First, phase-field models for the dendrite growth of pure materials and binary alloys and their histories are summarized. Then, models and studies of interface anisotropy, polycrystalline solidification, and solidification with convection, which are very important in dendritic solidification, are reviewed. Finally, by introducing very-large-scale phase-field simulations performed recently using a graphics processing unit supercomputer, the power, potential and importance of the very-large-scale phase-field simulation are emphasized.

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    2. Growth of Secondary Dendrite Arms of Fe–C Alloy during Transient Directional Solidification by Phase-field Method ISIJ International Vol.54(2014), No.2
    3. Evaluation of Permeability for Columnar Dendritic Structures by Three-dimensional Numerical Flow Analysis ISIJ International Vol.54(2014), No.2

  • Quantitative Phase-field Simulation of Dendritic Equiaxed Growth and Comparison with in Situ Observation on Al – 4 wt.% Cu Alloy by Means of Synchrotron X-ray Radiography

    Yun Chen, Dian Zhong Li, Bernard Billia, Henri Nguyen-Thi, Xin Bo Qi, Na Min Xiao

    pp. 445-451

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    DOI:10.2355/isijinternational.54.445

    Abstract

    Dendritic equiaxed growth from the melt by continuous cooling-down is investigated by quantitative 2D phase-field simulations. The results are compared with detailed data from solidification experiments on Al–4 wt.% Cu alloy with in situ X-ray monitoring. In a first step, the simulation of an isolated equiaxed alloy dendrite growing freely in <100>-direction in the melt is performed. Then, the impingement between two grains is considered by simulating two dendritic crystals growing towards each other in <100>-direction. From the phase-field simulations, the time evolution of the equiaxed crystals is characterized by measuring the lengths and tip velocities of the primary dendrite arms in free growth and in the presence of neighbor interaction, which enables the analysis of growth dynamics. In a second part, the results of the phase-field simulations are compared to data extracted from an experiment on Al – 4 wt.% Cu alloys carried out at the European Synchrotron Radiation Facility (ESRF), with in situ and real-time characterization by means of X-ray radiography, and to analytical relationship for dendrite tip growth. The limitations of 2D-phase-field simulations to fully describe the dynamic formation and interaction of dendritic equiaxed grains are briefly discussed.

  • Multiscale Hot-working Simulations Using Multi-phase-field and Finite Element Dynamic Recrystallization Model

    Chihiro Yoshimoto, Tomohiro Takaki

    pp. 452-459

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    DOI:10.2355/isijinternational.54.452

    Abstract

    In this study, we simulated non-uniform compression of a cylinder under various temperatures and deformation rates using a multi-phase-field and finite element dynamic recrystallization (MPFFE-DRX) model, which couples the multi-phase-field dynamic recrystallization (MPF-DRX) model with a large-deformation elastic-plastic finite element (FE) method using J2 flow theory for DRX microstructure evolution and macroscopic mechanical behavior, respectively. Detailed examination of the results confirmed that microstructure evolution and macroscopic mechanical behavior were accurately coupled over a wide range of temperature and deformation rate conditions. We also concluded that the MPFFE-DRX model can be used with a wide variety of temperatures and deformation rates.

  • Determination of the Columnar to Equiaxed Transition in Hypoeutectic Lamellar Cast Iron

    Péter Svidró, Attila Diószegi

    pp. 460-465

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    DOI:10.2355/isijinternational.54.460

    Abstract

    Shrinkage porosity as a volume change related casting defect in lamellar cast iron was reported in the literature to form during solidification in connection to the dendrite coherency. The present work includes an experimental study on dendrite coherency – also called columnar-to-equiaxed transition in lamellar cast iron using thermal analysis and expansion force measurements. Investigation was carried out in order to study the mechanism of dendrite coherency formation. Cylindrical test bars were cast from the same alloy with different pouring temperature, amount of inoculant and time between the addition of inoculant and start of pouring the samples. Cooling rate and expansion force was recorded as a function of time. A numerical algorithm based on temperature differences measured under solidification was used to interpret the solidification process. Three different methods have been compared to determine the columnar to equiaxed transition. The compared methods were based on registered temperature differences, based on registered expansion forces during the volume change of the solidifying samples and based on the calculated released latent heat of crystallization. The obtained results indicate a considerable influence on the formation and progress of coherency due to variation of casting parameters. It has been shown that the coherency is not a single event at a defined time moment rather a process progressing during a time interval.

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  • Mechanism of the Peritectic Phase Transition in Fe–C and Fe–Ni Alloys under Conditions Close to Chemical and Thermal Equilibrium

    Stefan Griesser, Christian Bernhard, Rian Dippenaar

    pp. 466-473

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    DOI:10.2355/isijinternational.54.466

    Abstract

    In-situ studies of the peritectic phase transition were performed under conditions close to chemical and thermal equilibrium in order to investigate the governing mechanism of both the peritectic reaction and the subsequent peritectic transformation using high-temperature laser-scanning microscopy in combination with the concentric solidification technique. Experiments have been conducted in the Fe–C and Fe–Ni systems in order to determine the role of solute diffusion on the observed reaction and transformation kinetics. The peritectic reaction as such as well as the subsequent peritectic transformation can be explained by diffusion-controlled mechanisms. Observations of the triple point L/γ/δ revealed that the peritectic reaction can be described as the solidification of γ along the L/δ interface, and new insights have been gained on the localized re-melting of δ during the peritectic reaction.
  • © 2014 The Iron and Steel Institute of Japan

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