Microsegregation Model Research Articles

A coupled model of TiN inclusion growth in GCr15SiMn during solidification in the electroslag remelting process

TiN inclusions observed in an ingot produced by electroslag remelting (ESR) are extremely harmful to GCr15SiMn steel. Therefore, accurate predictions of the growth size of these inclusions during steel solidification are significant for clean ESR ingot production. On the basis of our previous work, a coupled model of solute microsegregation and TiN inclusion growth during solidification has been established. The results demonstrate that compared to a non-coupled model, the coupled model predictions of the size of TiN inclusions are in good agreement with experimental results using scanning electron microscopy with energy disperse spectroscopy (SEM-EDS). Because of high cooling rate, the sizes of TiN inclusions in the edge area of the ingots are relatively small compared to the sizes in the center area. During the ESR process, controlling the content of Ti in the steel is a feasible and effective method of decreasing the sizes of TiN inclusions.

Microsegregation Model with Local Equilibrium Partition Coefficients During Solidification of Steels

A microsegregation model with local partition coefficients and temperature‐dependent diffusion coefficients based on the model of Ohnaka (I. Ohnaka, Trans. Iron Steel Ins. Jpn. 1986, 26, 1045) is proposed. In this model, multicomponent alloy effects and precipitations are considered, and the peritectic reaction can be indicated using the thermodynamic library ChemApp. The proposed model is validated by comparing the results to other models from the literature and to measured data. Local partition coefficients are calculated, and their significant influence on microsegregation prediction is shown. The characteristic temperatures determined using the proposed model are in good agreement with measured values.

Analytical model for equiaxed globular solidification in multicomponent alloys

We present a solidification model for equiaxed globular microstructure based on an analytical solution of the diffusion fields in the liquid with cross-diffusion terms for multicomponent alloys. It is demonstrated that the solute profiles for any element can be defined after computation of the eigenvalues and the eigenvectors of the liquid diffusion matrix. The interface velocity and the solute profiles are compared and validated with a numerical solution developed with a front tracking approach. A comprehensive application to the Al–7wt.%Si–1wt.%Mg alloy shows the effect of interdiffusion phenomena on the solidification path. This application is developed with an integral approach for the computation of the liquid composition far from the interface. It appears to be the only relevant choice in order to compute the expected driving force. Analytical solutions of the diffusion profile can also be computed for planar and cylindrical geometries. Coupling of this microsegregation model with thermodynamic equilibrium calculations is finally proposed and discussed.

Modelling of micro- and macrosegregation for industrial multicomponent aluminium alloys

Realistic predictions of macrosegregation formation during casting of aluminium alloys requires an accurate modeling of solute microsegregation accounting for multicomponent phase diagrams and secondary phase formation. In the present work, the stand alone Alstruc model, a microsegregation model for industrial multicomponent aluminium alloys, is coupled with the continuum model ALSIM which calculates the macroscopic transport of mass, enthalpy, momentum, and solutes as well as stresses and deformation during solidification of aluminium. Alstruc deals with multicomponent alloys accounting for temperature dependent partition coefficients, liquidus slopes and the precipitation of secondary phases. The challenge associated with computation of microsegregation for multicomponent alloys is solved in Alstruc by approximating the phase diagram data by simple, analytical expressions which allows for a CPU-time efficient coupling with the macroscopic transport model. In the present work, the coupled model has been applied in a study of macrosegregation including thermal and solutal convection, solidification shrinkage and surface exudation on an industrial DC-cast billet.

A numerical benchmark test for continuous casting of steel III

This paper represents a continuation of numerical results regarding the recently proposed industrial benchmark test [1], obtained by a meshless method. A part of the benchmark test, involving turbulent fluid flow with solidification in two dimensions, was elaborated in [2]. A preliminary macrosegregation upgrade was presented in [3], and in [4], a first three dimensional test was performed. Previous tests were bound to calculations in mold and sub-moldregions only. In the present paper, reference calculations in two dimensions are presented for the entire strand. The physical model is established on a set of macroscopic equations for mass, energy, momentum, species, turbulent kinetic energy, and dissipation rate. The mixture continuum model is used to treat the solidification system. The mushy zone is modeled as a Darcy porous media with Kozeny-Karman permeability relation, where the morphology of the porous media is modeled by a constant value. The incompressible turbulent flow of the molten steel is described by the Low-Reynolds-Number k-ε turbulence model, closed by the Abe-Kondoh-Nagano closure coefficients and damping functions. Lever microsegregation model is used. The numerical method is established on explicit time-stepping, collocation with scaled multiquadrics radial basis functions with adaptive selection of its shape on non-uniform five-nodded influence domains. The velocity-pressure coupling of the incompressible flow is resolved by the explicit Chorin'sfractional step method. The advantages of the method are its simplicity and efficiency, since no polygonisation is involved, easy adaptation of the nodal points in areas with high gradients, almost the same formulation in two and three dimensions, high accuracy and low numerical diffusion.

Effect of Solute Elements and Cooling Rate on Strain in Brittle Temperature Range of Continuously Cast Strand

A micro-segregation model of solute elements in mushy zone with δ/γ transformation during solidification was established based on the regular hexagon transverse cross section of dendrite shape proposed by finite difference method under the non-equilibrium solidification condition. The model was used to calculate the non-equilibrium pseudo binary Fe-C phase diagram and the strain of steels induced by variation of temperature in brittle temperature range. On the basis of the phase diagram and the strain, the strain curve in brittle temperature range as a function of carbon content for continuously cast strand was introduced and obtained. Solute elements change the position of the strain curve. And cooling rate changes the position and the shape of the strain curve. The comprehensive formula of the strain as functions of solute elements and cooling rate in brittle temperature range has been obtained by nonlinear fitting program.

Effect of partition coefficient on microsegregation during solidification of aluminium alloys

In the modeling of microsegregation, the partition coefficient is usually calculated using data from the equilibrium phase diagrams. The aim of this study was to experimentally and theoretically analyze the partition coefficient in binary aluminum-copper alloys. The samples were analyzed by differential thermal analysis (DTA), which were melted and quenched from different temperatures during solidification. The mass fraction and composition of phases were measured by image processing and scanning electron microscopy (SEM) equipped with an energy-dispersive X-ray spectroscopy (EDS) unit. These data were used to calculate as the experimental partition coefficients with four different methods. The experimental and equilibrium partition coefficients were used to model the concentration profile in the primary phase. The modeling results show that the profiles calculated by the experimental partition coefficients are more consistent with the experimental profiles, compared to those calculated using the equilibrium partition coefficients.

Dynaphase: Online Calculation of Thermodynamic Properties during Continuous Casting

The Siemens VAI software model DynaPhase calculates thermodynamic properties depending on the chemical analysis of steel. It can be used online together with Siemens VAI’s secondary cooling model Dynacs 3D, which is a unique feature. Offline it can be used to investigate the thermodynamic properties of steel grades and therefore supports the development of new grades. The core of DynaPhase is a substitutional solution model for the Gibbs free energy for calculating multi-component phase diagrams. The parameters of this model are determined by employing the CALPHAD approach. This model is combined with a microsegregation model to account for the interdendritic solidification process. New differential scanning calometry measurements of the Department of Metallurgy at the Mining University of Leoben have been used to extend the DynaPhase database for high Al or Si concentrations. This paper shows how important correct thermodynamic properties calculations with DynaPhase are, for controlling the secondary cooling system in continuous casting.

Study on hot tearing tendency during continuous casting of steel by overall hot tearing susceptibility (OHTS)

In this work, a new criterion for estimating hot tear susceptibility called overall hot tearing susceptibility (OHTS) is proposed to determine hot tearing tendency in the mould region during continuous casting. The OHTS criterion takes into account the cooling rate, brittle temperature range, strain rate and thickness of the brittle region. For estimating these parameters, a solidification model along with a microsegregation model, was developed. Using OHTS, the effects of carbon content, casting speed, pouring temperature and mould level on the hot tearing tendency of steel bloom were evaluated; and it was concluded that, raising the cooling rate and reducing the thickness of the brittle region increase the tendency of hot tearing. Raising the brittle temperature range tends to decrease the critical strain, so an increase in OHTS occurs; and to decrease the strain rate causing an increase in critical strain and as a result the OHTS is reduced.

Understanding Channel Segregates in Numerical Models of Alloy Solidification: A Case of Converge First and Ask Questions Later

In static castings of multi-component alloys, visually observable bands of channels, with high solute concentration, can form in the final solidified product. The phenomenological explanation for these formations is that perturbations during the solidification process lead to preferred flow paths in the solid-liquid mushy region. Once these flow paths are initiated, the higher solute liquid that flows in them suppresses the solidification rate and thus provides a mechanism through which the preferred paths can evolve into high concentration channels. Models of solidification that couple heat transfer, fluid and flow and mass transport appear able to predict the formation of these channels. In many cases, however, the formation of these numerical channels is highly dependent on the nature of the numerical calculation. In particular, geometric attributes of the channels is a strong function of the size of the computational grid and in some cases the particular method (code) used. In this work, after discussing what might drive the observed discrepancies in predictions, a grid convergence study is undertaken. This study shows that for the case of a side cooled solidification of a binary (Al-4.5wt%Cu) in a square (40mm x 40mm) domain, it is possible to approach grid converged results of the solution of the standard mixture model for macrosegregation. Achieving this level of convergence requires the use of an explicit time stepping scheme to couple the thermal and solute fields along with a Carman-Kozeny permeability and lever rule microsegregation models. The results indicate that to reach grid convergence the size of a grid cell has to be on the order ~0.25-0.5 mm.

Design of hydrogen permeable Nb–Ni–Ti alloys by correlating the microstructures, solidification paths and hydrogen permeability

The compositional window in Nb–Ni–Ti alloys leading to the crystallization of primary α-Nb phase and the eutectic (α-Nb + NiTi) phase is of high technical relevance due to its favorable properties with respect to hydrogen permeation. The solidification behavior of Nb–Ni–Ti alloys in the primary α-Nb phase region is investigated to reveal the potential solidification paths. The study is based on the characterization of as-cast microstructures in combination with numerical calculations of solidification paths using the CALPHAD method coupled with a microsegregation model. Four different kinds of solidification paths depending on initial composition and cooling rate are found. Correspondingly, a new compositional window appropriate for hydrogen permeation is established in the primary α-Nb phase region. The variation of the hydrogen permeability of the alloys in this window is surprisingly high. High Nb content and Ni/Ti ratio lead to a high permeability. Nb55Ni20Ti25 shows the highest permeability at 673 K, particularly 2.9 × 10−8 mol H2 m−1 s−1 Pa−1/2. This is about 1.8 times higher than that of pure Pd.

Numerical simulation of AM1 microstructure

A modelling approach is developed for the description of microstructure formation in the industrial AM1 Ni-base superalloy. Solidification and homogenization simulations are first carried out using a microsegregation model, before using the local compositions as an input for precipitation calculations, in order to characterize the influence of segregation on precipitation. First, the precipitation model was validated by comparing simulated and measured evolutions of the average precipitate radius during isothermal heat treatments at 1100 ∘ C and 1210 ∘ C. The chained microsegregation and precipitation simulations indicate that the global sequences of precipitation events remains are qualitatively the same at the different locations in the microstructure, but the growth and dissolution kinetics are strongly influenced by the local compositions. Local supersaturations have a larger effect on the average radius of the precipitates than certain stages of the precipitation heat treatment.

Computation of Phase Transformation Paths in Steels by a Combination of the Partial- and Para-equilibrium Thermodynamic Approximations

A model combining the partial‑equilibrium and para‑equilibrium thermodynamic approximations is presented. It accounts for fast diffusion of interstitial elements, such as carbon, and low diffusion of substitutional elements in the solid phases, while complete mixing is assumed for all elements in the liquid phase. These considerations are turned into classical mathematical expressions for the chemical potentials and the u‑fractions, to which mass conservation equations are added. The combination of the two models permits application to steels, dealing with partial‑equilibrium for solidification and para‑equilibrium for both the δ‑BCC to γ‑FCC peritectic transformation and the γ‑FCC to α‑BCC solid state transformation. The numerical scheme makes use of calls to Thermo‑Calc and the TQ‑interface for calculating thermodynamic equilibrium and accessing data from the TCFE6 database. Applications are given for a commercial steel. The results are discussed based on comparison with classical microsegregation models and experimental data.

Numerical analysis of macrosegregation and shrinkage porosity in large steel ingot

A three-dimensional finite element model has been developed with heat, flow and solute transfer behaviour coupled calculation to predict shrinkage and macrosegregation defects in an as cast steel ingot. Solidification evolution and carbon segregation have been verified by previous investigations of a 3·3 t steel ingot. The heat transfer coefficient (HTC) at the ingot mould interface against temperature was researched by an inverse calculation method based on thermophysical parameters from microsegregation model and experimental temperatures. Good agreements were obtained both in range and variation trend of HTC compared with experimental results in references. Macrosegregation and shrinkage porosities were observed to accompany each other at the hot top of the rectangular ingot, which should be further investigated by numerical simulation. Applications of the model were extended to steel plants. The soundness and homogeneity of rolled blooms were both satisfied.

Prediction of the solidification path of Al-4.37Cu-27.02Mg ternary eutectic alloy with a unified microsegregation model coupled with Thermo-Calc

Abstract An extended unified microsegregation model with solid back diffusion effects and five different dendrite morphologies was used to investigate the solidification path of Al-4.37Cu-27.02Mg (wt.%) ternary eutectic alloy at different cooling rates and solid back diffusion coefficients, coupled with Thermo-Calc. It was indicated that the cooling rates (Rf ) had no obvious effect on the solidification path which was (L + α) → (L + α + T) → (L + α + β + T); but the solid back diffusion coefficient (Φ) had a great effect on the solidification path, which evolved gradually from (L + α) → (L + α + T) → (L + α + β + T) into (L + α) → (L + α + T) when Φ increased from 0 to 1. The volume fractions of primary α phase (V α), binary eutectic (V 2E) and ternary eutectic (V 3E) at each solidification path were calculated. It was shown that V 2E decreased with the increase of Rf whereas V 3E increased and V α was almost invariant. The dependence of V 2E, V 3E and Rf were determined by linear regression analysis given as: V 2E = −2.5lgRf + 47.5; V 3E = 6.4lgRf + 47. Increase in Φ lead to increases in V α and V 2E and decrease in V 3E. The predicted soldification paths and volume fractions of Al-4.37Cu-27.02Mg ternary eutectic alloy at different cooling rates were in good agreement with experimental results.

Multiphase Flow and Thermo-Mechanical Behaviors of Solidifying Shell in Continuous Casting Mold

The metallurgical phenomena occurring in the continuous casting mold have a significant influence on the performance and the quality of steel product. The multiphase flow phenomena of molten steel, steel/slag interface and gas bubbles in the slab continuous casting mold were described by numerical simulation, and the effect of electromagnetic brake (EMBR) and argon gas blowing on the process were investigated. The relationship between wavy fluctuation height near meniscus and the level fluctuation index F, which reflects the situation of mold flux entrapment, was clarified. Moreover, based on a microsegregation model of solute elements in mushy zone with δ/γ transformation and a thermo-mechanical coupling finite element model of shell solidification, the thermal and mechanical behaviors of solidifying shell including the dynamic distribution laws of air gap and mold flux, temperature and stress of shell in slab continuous casting mold were described.

A modified cellular automaton method for polydimensional modelling of dendritic growth and microsegregation in multicomponent alloys

Numerous numerical models for simulating solidification of metals on a microscopic scale have been proposed in the past, among them are most importantly the phase-field method and models based on cellular automata. Especially the models based on cellular automata (adopting the virtual front tracking (VFT) concept) published so far are often only suitable for the consideration of one alloying element. Since industrial alloys are usually constituted of multicomponent alloys, the possibility of applying cellular automata is rather limited. With the aim of enhancing this modelling technique, a new, modified VFT model, which allows for the treatment of several alloying elements, in the low Péclet number regime is presented. The model uses the physical fundamentals of solute and heat diffusion in two dimensions as a basis for determining the solidification progress. By a new and effective approach, based on a functional extrapolation of the concentration gradient, dendritic growth in multicomponent Fe-C-Si-Mn-P-S alloys could be studied. The model shows the typical behaviour of dendritic solidification, such as parabolic tip and secondary dendrite arm formation as well as selection of preferably aligned columnar dendrites. A validation of the model is performed by the evaluation of morphological parameters and comparing them to experimentally determined values. The results for free and constrained dendritic growth effectively demonstrate the capabilities of this new model. The model is especially attractive for bridging the gap between one-dimensional microsegregation models and multidimensional morphology models with regard to modelling the complex interrelations between segregation on a multidimensional level and morphology formation.

A multiphase segregation model for multicomponent alloys with a peritectic transformation

A multiphase microsegregation model for the solidification of multicomponent alloys that experience a peritectic transformation is developed. It is based on a volume averaging method. Coupling is achieved among the conservation equations for total mass, solute mass and energy. The diffusion in extradendritic and several interdendritic liquid and solid phases, the growth kinetics of the dendritic and peritectic solidifying microstructures, as well as the velocities of the solid/liquid and solid/solid phase interfaces are considered in the model. The model is applied to the dendritic and peritectic solidification of a Fe-C-Cr alloy. Equilibrium between phases at the interface is taken into account and computed using a thermodynamic software. The occurrence of several recalescences due to the growth of the microstructure and the peritectic transformation are predicted and the solidification behaviors near recalescence are evaluated. By adjusting the parameters, the lever rule (LR), Gulliver-Scheil (GS) and partial equilibrium (PE) approximations are retrieved.

Effect of the Non-Equilibrium Solidus Temperature on Length of Soft Reduction Zone

Solidus temperature is one of the important key parameters to describe the non-equilibrium solidification states. However, the study of the non-equilibrium solidus is not enough presently. In present work, the key Influence factors on solidus temperature have been discussed, and it can be calculated by a mathematical model for solute microsegregation during the solidification. The calculated solidus can be agree with the recommended values by some dynamic soft reduction model. It is shown clearly the thermal analysis with non-equilibrium solidus was consistent with the pin shooting experiments. And the effect of the non-equilibrium solidus temperature on solid fraction and the length of soft reduction zone at the solidifying front has been studied sufficiently. Dynamic soft reduction metallurgical effect with the non-equilibrium solidus has been agreed by carbon segregation index and Macroetched experiment.

A simple slice model for prediction of macrosegregation in continuously cast billets

Macrosegregation occurs in continuously cast products due to shrinkage, thermo-solutal natural and forced convection, floating of the solid grains and the deformation of the mushy zone, induced by the supporting rolls. A simple Lagrange-an traveling slice model has been successfully used in the past for prediction of the relations between the process parameters and the temperature field [1], grain structure [2], optimization of process parameters, and calculation of caster regulation coefficients. It is the purpose of this paper to demonstrate the applicability of this simple model for assessment of the macrosegregation. The main advantage of the slice model is its very fast calculation time in comparison with the complete 3D heat, solute and fluid flow model. The macroscopic model is based on continuum mixture theory by solving the enthalpy and concentration equations, while the microsegregation model is based on the Scheil rule. The fluid flow effects in the melt have been approximated by the increased solute diffusivity in the liquid phase of the slice. Ordinary, binary carbon steel is used for demonstration in this study. A sensitivity study of the approach on the recently introduced standard continuous casting configuration is performed with respect to inlet superheat, casting speed and cooling rates. The model surprisingly properly predicts the qualitative features of the macrosegregation pattern. Possible refinements of the model with respect to the additional physical mechanisms are discussed.