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Investigating the Effects of Dendrite Evolution on Microsegregation in Al–Cu Alloys by Coupling Experiments, Micro-modeling, and Phase-Field Simulations

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Abstract

The microsegregation that occurs in Al–Cu alloys during solidification processes was quantitatively characterized using Electron Probe Micro-Analysis (EPMA) and examined by analytical micro-models of microsegregation as well as phase-field simulations. The analysis of EPMA data showed a pronounced increase in microsegregation of Cu solute at low and intermediate solid fractions during directional solidification. This initial increase of solute concentration in the solid cannot be readily explained by any conventional analytical models. In this study, the effect of dendritic evolution on microsegregation was systematically investigated, and the observed increase in Cu solute can be predicted by a comprehensive micro-model developed in this study. This micro-model considers constitutional undercooling, back diffusion, and the dendrite remelting that can occur during solidification. A semi-empirical prefactor that accounts for dendrite remelting was mathematically derived and was determined to be key to capturing the initial increase of solute concentration. The model further indicates that the influence of dendrite remelting continually increases until solid fractions of approximately 50 pct are reached after which the influence of dendrite remelting declines. The comprehensive micro-model is analytical and straightforward to implement. It is able to accurately predict the solute microsegregation behavior observed under a variety of solidification conditions. In addition, the microsegregation and dendrite morphology evolution were simulated using a quantitative phase-field model for binary alloy solidification, implemented as a new application within the open-source PRISMS-PF phase-field framework. This application was used to simulate solidification of Al–Cu alloys in 2D and 3D. The combined experimental and theoretical study demonstrated that microsegregation can be significantly influenced by dendritic evolution, especially at low cooling rates under conditions that promote columnar growth.

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Data Availability

The experimental data supporting this publication are available on the Materials Commons at https://doi.org/10.13011/m3-068f-a233.

Code Availability

PRISMS-PF is an open-source computer code available for download at https://github.com/prisms-center/phaseField. A written tutorial is available in the GitHub repository.

Abbreviations

\(X_{{\text{s}}}\) :

Size of the solid phase

\(C_{{\text{l}}}^{*}\) :

Solute concentration at the liquid side of solid/liquid interface

\(C_{0}\) :

Bulk composition of the sample

\(A\) :

Degree of constitutional undercooling at dendrite tip

\(\Omega\) :

Degree of back diffusion in solid

\(k_{{\text{v}}}\) :

Velocity-dependent partition coefficient

\(f_{{\text{s}}}\) :

Solid fraction

\(\lambda\) :

Secondary dendrite arm spacing (SDAS)

\(\lambda_{{\text{f}}}\) :

Finial SDAS

\(\lambda_{0}\) :

Initial SDAS

\(L\) :

Product of cooling rate and liquidus slope

\(K\) :

Growth rate coefficient for the average SDAS

\(n\) :

Exponent for the coarsening of the average SDAS

\({\text{Pe}}\) :

Péclet number

\(R\) :

Tip radius

\(v\) :

Solidification front velocity

\(D_{{\text{l}}}\) :

Solute diffusion coefficient in liquid

\({\text{Iv}}\) :

Ivantsov integration

\(G\) :

Thermal gradient

\(x\) :

Position in the x-direction in the simulation

\(V_{{\text{p}}}\) :

Pulling velocity

\(t\) :

System solidification time

\(\widetilde{{V_{{\text{p}}} }}\) :

Dimensionless velocity

\(\widetilde{{l_{{\text{T}}} }}\) :

Dimensionless thermal length

\(\tilde{t}\) :

Dimensionless time

\(\tilde{y}\) :

Dimensionless position in the y-direction

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Acknowledgments

The authors acknowledge with appreciation helpful discussions with and suggestions of Professor Katsuyo Thornton from University of Michigan. ZY and JA acknowledge financial assistance from Ford Motor Co. We are grateful for the assistance of Yang Huo and Larry Godlewski in preparing the cast plates and Mei Li (Ford Motor Co) for helpful discussions. DM was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award #DE-SC0008637 as part of the Center for PRedictive Integrated Structural Materials Science (PRISMS Center) at University of Michigan. Computational resources and services were provided by the Extreme Science and Engineering Discovery Environment (XSEDE) through allocations TG-DMR110007 and TG-MSS160003.

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  1. Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Zhenjie Yao, David Montiel & John Allison

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  1. Zhenjie Yao
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Correspondence to Zhenjie Yao.

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Yao, Z., Montiel, D. & Allison, J. Investigating the Effects of Dendrite Evolution on Microsegregation in Al–Cu Alloys by Coupling Experiments, Micro-modeling, and Phase-Field Simulations. Metall Mater Trans A 53, 3341–3356 (2022). https://doi.org/10.1007/s11661-022-06748-5

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