Numerical Calculation of the Concentration Distribution during the Solidification of Binary Alloys Allowing for Dendrite Arm Coarsening

Halder, E.; Roósz, András; Exner, Hans Eckart; Fischmeister, H. F.

doi:10.4028/www.scientific.net/msf.13-14.547

Cited by 8 publications

(5 citation statements)

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“…This model incorporates the effects of solid-state diffusion and dendrite arm coarsening on solute distribution, leading to predictions that closely match experimental observations. Particularly, [13] demonstrates excellent agreement between measured and predicted cooling curves and local solidification times for binary aluminum alloys containing up to 10 wt% Mg and 6 wt% Zn. C M.G.…”

Section: Introductionmentioning

confidence: 55%

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Modeling Dendrite Coarsening and Remelting during Directional Solidification of Al-06wt.%Cu Alloy

Sari,

Alrasheedi,

Ahmadein

et al. 2024

Materials

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Research efforts have been dedicated to predicting microstructural evolution during solidification processes. The main secondary arm spacing controls the mushy zone’s permeability. The aim of the current work was to build a simple sub-grid model that describes the growth and coarsening of secondary side dendrite arms. The idea was to reduce the complexity of the curvature distribution with only two adjacent side arms in concurrence. The model was built and applied to the directional solidification of Al-06wt%Cu alloy in a Bridgman experiment. The model showed its effectiveness in predicting coarsening phenomena during the solidification of Al-06wt%Cu alloy. The results showed a rapid growth of both arms at an earlier stage of solidification, followed by the remelting of the smaller arm. In addition, the results are in good agreement with an available time-dependent expression which covers the growth and coarsening. Such model can be implemented as a sub-grid model in volume average models for the prediction of the evolution of the main secondary arms spacing during macroscopic solidification processes.

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Section: Introductionmentioning

confidence: 55%

“…In ref. [13], the authors proposed a numerical model to evaluate the microstructural and compositional data of binary alloys during and after solidification. This model incorporates the effects of solid-state diffusion and dendrite arm coarsening on solute distribution, leading to predictions that closely match experimental observations.…”

Section: Introductionmentioning

confidence: 99%

Modeling Dendrite Coarsening and Remelting during Directional Solidification of Al-06wt.%Cu Alloy

Sari,

Alrasheedi,

Ahmadein

et al. 2024

Materials

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“…where G is a geometric factor. Using Equation ( 6), the SDAS vs. time was successfully first calculated in the case of a unidirectional solidified Al-Cu alloy [21], and then Cu-10Sn [22], Mg-Al [23], and Mg-Al-Zn [24], to simulate microsegregation. Battle and Pehlke [25] compared the experimental results of microsegregation in Al-Cu alloys with models that included empirical (Equation ( 7)) and dynamical coarsening equations (Equation ( 10)).…”

Section: Dynamical Simulation Methodsmentioning

confidence: 99%

Comparison of Dynamical and Empirical Simulation Methods of Secondary Dendrite Arm Coarsening

et al. 2022

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The physical and mechanical properties of an entirely (wrought alloys) or partly (cast alloys) dendritically solidified alloy strongly depend on the secondary dendrite arm spacing (SDAS). The casting practice and the simulation of solidification need a usable but simple method to calculate the SDAS during and at the end of solidification as a function of the cooling rate. Based on many solidification experiments, a simple equation to calculate the SDAS (empirical method) is known to use the local solidification time, which can be obtained from the measured cooling curves (equiaxed solidification), or can be calculated from the temperature gradient and front velocity (directional solidification). This equation is not usable for calculating the SDAS during solidification. Kirkwood developed a semi-empirical method based on the liquid phase’s diffusion, which contains only one geometric factor that seems constant for different alloys. This equation contains some physical parameters that depend on the temperature, so the equation cannot be integral in closed form. In the present work, first, we show the effect of the curvature of the solid/liquid interface on the equilibrium concentrations and then the different processes of SDA coarsening. In our earlier paper, we demonstrated that using the empirical method, the final SDAS can be calculated with acceptable correctness in the case of four unidirectional solidification experiments of Al-7wt%Si alloy. The present work shows that numerically integrated Kirkwood’s equations used the known cooling curve; the SDAS can be calculated at the end and during solidification in good agreement with these experimental results. Compared to the two calculation methods, we stated that the correctness of the methods is similar. Still, the results of the solidification simulation (the microsegregation) will be more correct using the dynamical method. It is also shown that with the dynamical method, the SDAS can be calculated from any type of cooling curve, and using the dynamical method, it is proved that some different SDASs could belong to the same local solidification time.

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“…Owing to the remelting and resolidification mechanism, dendrite arm coarsening contributes significantly to homogenization during solidification [23,27,29]. The evolution of the secondary dendrite arm spacing needs to be known since it sets the diffusion distances in the liquid and solid phase.…”

Section: Dendrite Arm Coarseningmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]) such as the limitation to binary alloys, unrealistic phase diagram approximations in the case of multicomponent alloys or omissions of undercooling or coarsening effects. Over many years the authors and other coworkers have developed numerical procedures to simulate microsegregation phenomena [21][22][23][24][25][26][27][28][29]. During the past decade various restrictions have been released stepwise improving the model to a state where it covers a large range of applications in technical problems and starts to gain commercial interest.…”

Section: Introductionmentioning

confidence: 99%

An extended numerical procedure for predicting microstructure and microsegregation of multicomponent alloys

Kraft

Rettenmayr

Exner

1996

Modelling Simul. Mater. Sci. Eng.

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A numerical model for the prediction of microstructure and microsegregation in multicomponent alloys during dendritic solidification using a finite difference scheme is presented. The main kinetic and thermodynamic effects that can influence microsegregation (solid state back diffusion, secondary dendrite arm coarsening, primary tip and eutectic undercooling and the thermodynamic correction of the interface concentrations) are accounted for. The liquid/solid phase equilibria in the thermodynamically stable and metastable range are calculated with thermodynamically formulated phase diagrams. For the calculation at high cooling rates non-equilibrium phase diagrams for multi-component alloys are assessed. The consideration of undercooling effects extends the applicability of the model to very low and very high cooling rates. The model thus covers the whole range of cooling conditions where dendritic solidification occurs. As compared with other models in the literature, the number of adjustable parameters is reduced to a minimum.

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Numerical Calculation of the Concentration Distribution during the Solidification of Binary Alloys Allowing for Dendrite Arm Coarsening

Cited by 8 publications

References 0 publications

Modeling Dendrite Coarsening and Remelting during Directional Solidification of Al-06wt.%Cu Alloy

Modeling Dendrite Coarsening and Remelting during Directional Solidification of Al-06wt.%Cu Alloy

Comparison of Dynamical and Empirical Simulation Methods of Secondary Dendrite Arm Coarsening

An extended numerical procedure for predicting microstructure and microsegregation of multicomponent alloys

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