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Journal of Materials Science

, Volume 54, Issue 13, pp 9907–9920 | Cite as

Predicting primary dendrite arm spacing in Al–Si–Mg alloys: effect of Mg alloying

  • Colin D. Ridgeway
  • Cheng Gu
  • Alan A. LuoEmail author
Metals
  • 26 Downloads

Abstract

Directional solidification experiments were performed on Al–Si–Mg alloys to examine the effect of compositional variation on dendritic growth and to develop a novel growth model for the prediction of primary dendrite arm spacing in solidification microstructures. Instead of relying on the growth restriction factor or inoculant particle efficacy, this model examines solute effects to describe the final primary dendritic arm spacing. Increased Mg concentration was shown to decrease the dendritic growth velocity by decreasing constitutional undercooling. Solute enrichment at the solid/liquid interface was shown to limit lateral coarsening of primary dendrite arms and create a region of local solute depletion. This phenomenon allowed increased nucleation due to an increase in the resulting local liquidus temperature, and ultimately produced a refined primary dendrite arm spacing. Primary and secondary dendrites were measured and quantitatively analyzed in validation of the model. The model, which shows increased accuracy compared to existing models, was developed with aid of the three-dimensional cellular automaton method and experimentally verified.

List of symbols

\( C_{0} \)

Nominal composition

\( C_{x}^{0} \)

Composition of ‘x

\( C_{x}^{{{\mathrm{L}}*}} \)

Composition of element ‘x’ at the S/L interface

\( C_{i}^{E} \)

Solute concentration of element (i) in state of matter of (E)

\( D \)

Diffusion coefficient

\( d_{\mathrm{gs}} \)

Grain size

\( D_{ij}^{\mathrm{L}} \)

Solute diffusion coefficient in liquid aluminum

\( f \)

Fraction of particles that successfully nucleate a grain

\( \Delta f_{\mathrm{s}} \)

Fraction solid

\( G \)

Thermal gradient

\( \Gamma \)

Gibbs–Thomson coefficient

\( k \)

Partition coefficient

\( \kappa \)

Curvature of S/L interface

λ

PDAS

\( m \)

Liquidus slope

\( \rho \)

Number density of inoculant particles added to the melt

\( Q \)

Growth restriction factor

s

Time required to reach final dendritic spacing (completion of competitive growth process)

\( \sigma_{\mathrm{DAS}} \)

Primary and secondary dendrite arm strengthening

\( \sigma_{\mathrm{eutectic}} \)

Eutectic modification strengthening

\( \sigma_{\mathrm{GB}} \)

Grain boundary strengthening

\( \sigma_{i} \)

Intrinsic strength of a material

\( \sigma_{\mathrm{PPT}} \)

Precipitate strengthening

\( \sigma_{\mathrm{SS}} \)

Solid solution strengthening

\( \sigma_{\mathrm{YS}} \)

Yield strength of a material

\( \frac{\partial T}{{\partial C_{x}^{\mathrm{L}} }} \)

Slope of liquidus surface with respect to solute element x

\( T_{0} - T_{\mathrm{local}} \)

Thermal undercooling

\( \Delta T_{n} \)

Undercooling required for nucleation

\( \Delta t \)

Time step for CA

\( \mu_{\mathrm{k}} \)

Dendritic growth kinetic coefficient

\( v \)

Normal dendritic growth velocity

\( \Delta x \)

Mesh size used in CA

Notes

Acknowledgements

The authors would like to acknowledge the National Science Foundation for supporting this work (Award CMMI-1432688). The authors would also like to thank the members of OSU Light Metals and Manufacturing Research Lab for discussions and design assistance.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringThe Ohio State UniversityColumbusUSA
  2. 2.Department of Integrated Systems EngineeringThe Ohio State UniversityColumbusUSA

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