Solidification Of Ternary Alloys Research Articles

Role of microstructure and composition on natural convection during ternary alloy solidification

Solidifying ternary systems can exhibit complex natural convection phenomena, particularly due to the presence of two porous zones (cotectic and primary mush), and the rejection of two differently dense solutes. The primary objectives of this study are to investigate the following: (i) the natural convection patterns in various compositional regimes of a typical ternary system, and (ii) the role of the combined existence of the microstructure (facets and dendrites) in the porous zone on natural convection, with a motivation to enhance the current understanding of the microstructure–convection relationships. A ternary mixture is chosen such that different compositions of the three primary solidifying components lead to the formation of distinct ice, dendritic and faceted solid structures that cover the complete span of microstructure–convection relationships. The observations of flow in different compositional regimes show convection occurring in the form of plumes, random mixing and double-diffusive layering, as well as combinations of these, which are governed by the type of coexisting microstructures. The study reveals the occurrence of Rayleigh–Taylor instability with varying amounts of the heavier component. The bulk liquid composition showed a tendency to cross the cotectic line, and thus also change the nature of primary solidifying structure from faceted to dendritic in cases where facets and dendrites were present in cotectic mush, and facets in primary mush. These insights are believed to elucidate the complex mechanisms of ternary solidification, as well as provide important real-time data for direct numerical simulations.

Modelling the evolution of MnS inclusions and macrosegregation during solidification using a three-phase model

Manganese sulphide (MnS) is one of the major non-metallic inclusion in steel which greatly impacts the properties of steels. Previous models have been developed to simulate the dynamics of MnS during solidification without considering the effects of macrosegregation formation. A comprehensive model incorporating the formation kinetics of MnS with a ternary macrosegregation model is presented to investigate the evolution of MnS inclusions and its effects on C and Mn macrosegregation. Classical nucleation theory and a diffusion-controlled growth model are applied to describe the evolution of MnS, which is fully coupled with a two-phase ternary alloy solidification model. The model considers the growth of columnar dendrite trunks, thermosolutal convection of the melt, solute transport by convection and inclusion floatation. It has been applied to a benchmark case, and reasonable results are obtained with a good agreement with the reported experimental ones. The effects of MnS behaviours on the segregation of different solute elements are discussed.

Cellular automaton modelling of M7C3 carbide growth during solidification of Fe-C-Cr alloy

A microscopic cellular automaton combined with macroscopic heat and solute transport was developed to simulate the mutual growth and evolution of austenite and M7C3 carbide grains during Fe-C-Cr ternary alloy solidification process. The diffusion of solute C and Cr are contributed together to the constitutional undercooling, together with curvature undercooling, for obtaining the grain growth rate of austenite and M7C3 carbide. Results show that, the absorption of solute C and Cr by M7C3 grain and rejection by austenite grain promote the two grains’ cooperative growth. Once they approach to each other, the austenite grain quickly overgrows towards the M7C3 grain till finally envelops it. The simulated solidification morphology of the Fe-4wt%C-17wt%Cr alloy, predicted averaged grain size of M7C3 carbides and C and Cr concentration in austenite grains agree with the experimental measurements and solidification path prediction. The predicted average liquid concentration curve fits with the LR, GS and PE prediction at the initial M7C3 precipitation regime and after austenite grains fully enveloping towards the M7C3 grains, returns to overlap the LR, GS and PE prediction curves.

Three-dimensional natural heat convection and ternary alloy solidification problems by finite volume geometric multigrid method

Natural heat convection of air and water and transient free convection with conduction and solidification of a ternary high temperature alloy inside square cavities are described by a three levels V cycle geometric multigrid and the finite volume method. The efficiency of the calculation procedure to characterize three-dimensional natural convection inside cubical cavities with and without liquid-solid phase change by the geometric multigrid is evaluated against the computation time required to solve each one of the three problems by a single staggered grid. The numerical simulations shows that the performance of the finite volume method increased when a geometric multigrid with a V cycle of three levels was used. Reductions in the computation time obtained by the multigrid scheme accounted to 35% for steady natural convection of air with a Rayleigh number Ra = 106 and of water with Ra = 2.2 × 105, and by a 15% for unsteady natural convection with heat diffusion in liquid to solid phase transformation at high temperature of an aluminum ternary alloy (Ra = 104). The accuracy of the numerical results obtained for velocity and temperature distributions by the multigrid technique was verified with reliable numerical results reported for each problem.

Application of alloy solidification theory to cellular automata modeling of near-rapid constrained solidification

To utilize the full potential of additive manufacturing routes for metallic part production, understanding how microstructure and texture develop as functions of alloying additions and process conditions is critical. Use of cellular automata (CA) with alloy solidification theory can provide a useful augmentation to experimental microstructure observations, as it can accurately and efficiently reproduce nucleation and growth of cubic crystal structures common to binary and ternary alloy solidification. We apply CA to model constrained solidification under thermal gradient magnitudes and solidification velocities representative of those commonly encountered along the melt pool boundary in Laser Engineered Net Shaping (LENS®), a specific alloy-based additive process. Various sets of alloying elements, quantities, and nucleation parameters are used to show the model’s ability to predict realistic trends in nucleation and growth of single phase β-Ti alloys. 2D and 3D model implementations are qualitatively and quantitatively compared, and alloy composition (element and quantity) is shown to play a critical role on the columnar to equiaxed transition (CET) through changes to the interfacial response function. Simulation results are further used to define a parameter that correlates with the CET over a range of imposed conditions, linking alloy solidification theory to the CA prediction of microstructure. This CA model can serve as a useful tool when designing sets of alloying additions that would produce given microstructures, while coupled application of this CA to process scale simulations of additive process temperature fields will facilitate design of both specific alloy compositions and sets of process conditions for microstructure control.

Numerical Modelling of Transport Phenomena and Macrosegregation during Ternary Alloy Solidification: Solutal Undercooling Effects

In this paper, a macroscopic mathematical model is developed for simulation of transport phenomena during ternary alloy solidification processes, taking into account non-equilibrium effects due to solutal undercooling. The model is based on a fixed-grid, enthalpy-based, control volume approach. Microscopic features pertaining to non-equilibrium effects on account of solutal undercooling are incorporated through a novel formulation of a modified partition coefficient. The effective partition coefficient is numerically modeled by means of macroscopic parameters related to the solidifying domain. Numerical simulations are performed for ternary steel alloy by employing the present model and the resulting convection and macrosegregation patterns are analyzed. It is observed that the consideration of non-equilibrium solidification in the present mathematical approach is able to capture the thermo-solutal convection and leads to prediction of accurate value of macrosegregation. The results from the present model matches well with the experimental observations published in the literature.

Examination of Dendritic Growth During Solidification of Ternary Alloys via a Novel Quantitative 3D Cellular Automaton Model

A three-dimensional (3D) quantitative cellular automaton (CA) model was developed to simulate dendritic growth during solidification processing of ternary alloys. A detailed method was proposed to solve solute diffusion and calculate the solid fraction for ternary alloys during solidification. The present model has been shown to accurately predict dendrite morphologies and solute distributions of both single equiaxed dendrite and columnar dendrites during solidification. The model was also used to study the influence of the concentration of a third component (Mg in the Al-Si-Mg system) on dendritic growth. With increasing Mg concentration, the steady-state dendrite tip growth velocity was shown to decrease, resulting in a shorter primary dendrite length. The 3D CA simulation results agree well with the prediction of the LGK theoretical model. Multi-columnar dendrite growth was simulated with different cooling rates. Primary and secondary dendrite morphology was shown to have little variation at low cooling rates (1.0 to 2.0 K/s) and a constant undercooling. The average secondary dendrite arm spacing was shown to decrease with the increase of cooling rate within this range. The 3D CA simulation results are in good agreement with the experimental directional solidification experiments of a commercial A356 (Al-7 wt pct Si-0.3 wt pct Mg).

A lattice Boltzmann–cellular automaton study on dendrite growth with melt convection in solidification of ternary alloys**Project supported by the National Natural Science Foundation of China (Grant Nos. 51728601 and 51771118).

A lattice Boltzmann (LB)–cellular automaton (CA) model is employed to study the dendrite growth of Al-4.0 wt%Cu–1.0 wt%Mg alloy. The effects of melt convection, solute diffusion, interface curvature, and preferred growth orientation are incorporated into the coupled model by coupling the LB–CA model and the CALPHAD-based phase equilibrium solver, PanEngine. The dendrite growth with single and multiple initial seeds was numerically studied under the conditions of pure diffusion and melt convection. Effects of initial seed number and melt convection strength were characterized by new-defined solidification and concentration entropies. The numerical result shows that the growth behavior of dendrites, the final microstructure, and the micro-segregation are significantly influenced by melt convection during solidification of the ternary alloys. The proposed solidification and concentration entropies are useful characteristics bridging the solidification behavior and the microstructure evolution of alloys.

Susceptibility of ternary aluminum alloys to cracking during solidification

The crack susceptibility map of a ternary Al alloy system provides useful information about which alloy compositions are most susceptible to cracking and thus should be avoided by using a filler metal with a significantly different composition. In the present study the crack susceptibility maps of ternary Al alloy systems were calculated based on the maximum |dT/d(fS)1/2| as an index for the crack susceptibility, where T is temperature and fS fraction solid. Due to the complexity associated with ternary alloy solidification, commercial thermodynamic software Pandat and Al database PanAluminum, instead of analytical equations, were used to calculate fS as a function of T and hence the maximum |dT/d(fS)1/2| for ternary Al-Mg-Si, Al-Cu-Mg and Al-Cu-Si alloy systems. A crack susceptibility map covering 121 alloy compositions was constructed for each of the three ternary alloy systems at each of the following three levels of back diffusion: no back diffusion, back diffusion under a 100 °C/s cooling rate, and back diffusion under 20° C/s. The location of the region of high crack susceptibility, which is the most important part of the map, was shown in each of the nine calculated maps. These locations were compared with those observed in crack susceptibility tests by previous investigators. With back diffusion considered, either under 20 or 100 °C/s, the agreement between the calculated and observed maps was good especially for Al-Mg-Si and Al-Cu-Mg. Thus, the maximum |dT/d(fS)1/2| can be used as a crack susceptibility index to construct crack susceptibility maps for ternary Al alloys and to evaluate the effect of back diffusion on their crack susceptibility.

Simulation of Dendritic Growth with Melt Convection in Solidification of Ternary Alloys**Supported by the National Natural Science Foundation of China under Grant Nos 51306037 and 51371051.

A cellular automaton-lattice Boltzmann coupled model is extended to study the dendritic growth with melt convection in the solidification of ternary alloys. With a CALPHAD-based phase equilibrium engine, the effects of melt convection, solutal diffusion, interface curvature and preferred growth orientation are incorporated into the coupled model. After model validation, the multi dendritic growth of the Al-4.0 wt%Cu-1.0 wt%Mg alloy is simulated under the conditions of pure diffusion and melt convection. The result shows that the dendritic growth behavior, the final microstructure and microsegregation are significantly influenced by melt convection in the solidification.

Modeling diffusion-governed solidification of ternary alloys – Part 2: Macroscopic transport phenomena and macrosegregation

Part 1 of this two-part investigation presented a multiphase solidification model incorporating the finite diffusion kinetics and ternary phase diagram with the macroscopic transport phenomena (Wu et al., 2013). In Part 2, the importance of proper treatment of the finite diffusion kinetics in the calculation of macrosegregation is addressed. Calculations for a two-dimensional (2D) square casting (50×50mm2) of Fe–0.45wt.%C–1.06wt.%Mn considering thermo-solutal convection and crystal sedimentation are performed. The modeling result indicates that the infinite liquid mixing kinetics as assumed by classical models (e.g., the Gulliver–Scheil or lever rule), which cannot properly consider the solute enrichment of the interdendritic or inter-granular melt at the early stage of solidification, might lead to an erroneous estimation of the macrosegregation. To confirm this statement, further theoretical and experimental evaluations are desired. The pattern and intensity of the flow and crystal sedimentation are dependent on the crystal morphologies (columnar or equiaxed); hence, the potential error of the calculated macrosegregation caused by the assumed growth kinetics depends on the crystal morphology. Finally, an illustrative simulation of an engineering 2.45-ton steel ingot is performed, and the results are compared with experimental results. This example demonstrates the model applicability for engineering castings regarding both the calculation efficiency and functionality.

Scaling Theory of Two-Phase Dendritic Growth in Undercooled Ternary Melts

Two-phase dendrites are needlelike crystals with a eutectic internal structure growing during solidification of ternary alloys. We present a scaling theory of these objects based on Ivantsov's theory of dendritic growth and the Jackson-Hunt theory of eutectic growth. The additional introduction of the relationship ρ∼λ (ρ: dendrite tip radius; λ: eutectic interphase spacing) suggested by recent experimental results [S. Akamatsu et al., Phys. Rev. Lett. 104, 056101 (2010)] leads to a complete solution of theselection problem and to the scaling rule ρ∼λ -1/2 (v: dendrite tip growth rate).

Modeling diffusion-governed solidification of ternary alloys – Part 1: Coupling solidification kinetics with thermodynamics

A method incorporating the full diffusion-governed solidification kinetics and the ternary phase diagram into a multiphase volume average solidification model is presented. The motivation to develop such a model is to predict macrosegregation in castings. A key feature of this model, different from most previous ones which usually assume an infinite solute mixing in liquid (e.g. lever rule, Gulliver–Scheil), is that diffusions in both liquid and solid phases are considered. It is known that models with assumption of an infinite liquid mixing lead to erroneous estimation of the solidification path at the initial stage. Here solidification of a ternary alloy (Fe–0.45wt.%C–1.06wt.%Mn) is examined. As the two chosen alloy elements (C and Mn) have large differences in the solute partition coefficient, liquidus slope and liquid diffusion coefficient, the solidification path shows differently from those predicted by infinite liquid mixing models. The first part of this two-part investigation evaluates the full diffusion-governed kinetics and its influence on solidification path and microsegregation. Applications of the model for the calculation of solidification and macrosegregation are presented in the accompanying paper [Part 2].

A Generalized Approach for Macroscopic Modelling of Solidification of Ternary Alloys with Dendritic Arm Coarsening

A Generalized Approach for Macroscopic Modelling of Solidification of Ternary Alloys with Dendritic Arm Coarsening

Numerical computations for temperature, fraction of solid phase and composition couplings in ternary alloy solidification with three different thermodynamic data-acquisition methods

In this paper, a previously proposed numerical model for binary alloy solidification, and the corresponding algorithm for solving the strong coupling among the solidification temperature, solid fraction, and liquid composition (T–fS–CL), are extended to ternary alloys. The feasibility of the extended numerical method is demonstrated by sample simulations for the directional solidification of blade-like castings of Al–Cu–Si alloys using three different thermodynamic data-acquisition methods: direct coupling with the CALPHAD software Thermo-Calc via the TQ6-Interface, using the “mapping technique” and regression functions. The computational efficiency and the accuracy of the calculation results of the three different methods are compared. The present numerical simulations confirm that thermodynamic data-acquisition method of using regression functions and the “mapping technique” are much more efficient than that of direct coupling with Thermo-Calc.

Modelling of dendritic growth in ternary alloy solidification with melt convection

A two-dimensional lattice Boltzmann-cellular automaton model is coupled with the CALPHAD (Calculation of Phase Diagrams) method for simulating dendritic growth during ternary alloy solidification with convection. In the model, the kinetics of dendritic growth is determined by the difference between the equilibrium liquidus temperature and the actual temperature at the solid/liquid interface, incorporating the effects of the interface curvature and the preferred dendritic growth orientation. The lattice Boltzmann method is used for evaluating the local liquid compositions of the two solutes impacted by diffusion and convection. Based on the local liquid compositions, the equilibrium liquidus temperature and the solid concentrations of the two solutes are obtained by the CALPHAD method. The model is applied to simulate dendritic growth of an Al–4·0 wt-%Cu–1·0 wt-%Mg ternary alloy with melt convection. The results demonstrate the high numerical convergence and stability, as well as computational efficiency, of the proposed model. Melt convection is found to influence the dendritic morphologies and microsegregation patterns in the solidification of ternary alloys.

Modeling and experimental analysis of macrosegregation during transient solidification of a ternary Al–6wt%Cu–1wt%Si alloy

The aim of this article is to provide a numerical tool, which is able to predict macrosegregation profiles during the solidification of ternary alloys. The solute profiles during the transient directional solidification of an Al–6wt%Cu–1wt%Si alloy were calculated taking into account secondary phase transformations, which occur along the corresponding solidification path. The simulations were compared with experimental segregation profiles determined along the length of a directionally solidified casting through X-ray fluorescence spectrometry measurements. A very good agreement between predictions and experiments has been observed.

Simulação de microestruturas de ligas ternarias pelo método do Campo de Fase

Um modelo do Campo de Fase para a solidificação de ligas ternárias Fe-C-P é proposto. Neste trabalho a relação entre as propriedades do material e os parâmetros do modelo é apresentada. No desenvolvimento do trabalho foi aplicado o modelo para a solidificação de ligas ternárias para a análise da difusividade dos solutos. Para os cálculos bidimensionais, o crescimento dendrítico é simulado para ligas ternárias de Fe-C-P. As alterações na concentração de fósforo afetam a velocidade da interface sólido/líquido. Essas alterações na velocidade da interface sólido/líquido se devem à baixa difusividade do fósforo durante o processo de solidificação.

Modeling of Microstructure and Microsegregation in Solidification of Multi-Component Alloys

Driven by industrial demand, extensive efforts have been made to investigate microstructure evolution and microsegregation development during solidification of multicomponent alloys. This paper briefly reviews the recent progress in modeling of microstructures and microsegregation in solidification of multicomponent alloys using various models including micromodel, phase field, front tracking, and cellular automaton approaches. A two-dimensional modified cellular automaton (MCA) model coupled with phase diagram software PanEngine is presented for the prediction of microstructures and microsegregation in the solidification of ternary alloys. The model adopts MCA technique to simulate dendritic growth. The thermodynamic data needed for determining the dynamics of dendritic growth are calculated with PanEngine. After validating the model by comparing the simulated values with the prediction of the Scheil model for solute profiles in the primary dendrites as a function of solid fraction, the model was applied to simulate the microstructure and microsegregation in the solidification of Al-rich ternary alloys. The simulation results demonstrate the capabilities of the present model not only to simulate realistic dendrite morphologies, but also to predict quantitatively the microsegregation profiles in the solidification of multi-component alloys.

A Generalized Enthalpy-based Macro Model for Ternary Alloy Solidification Simulations

In this article, a generalized macroscopic mathematical model is developed to simulate the transport phenomena occurring during the solidification of ternary alloy systems. The model is essentially based on a fixed-grid, enthalpy-based control-volume approach. Microscopic features pertaining to complex thermosolutal transport mechanisms are incorporated through a novel formulation of latent enthalpy evolution, consistent with the phase-change morphology of general multicomponent alloy systems. Numerical simulations are performed for two different ternary steel alloys of apparently contrasting thermosolutal transport characteristics, and the resulting convection and macrosegregation patterns are analyzed in detail. The mathematical model is also tested by comparing the present numerical results with benchmark analytical solutions and experimental data reported in the literature for ternary alloy solidification systems, and excellent agreement is found in this regard.