Corrosion Science and Technology

The Corrosion Science Society of Korea (한국부식방식학회)
권호 표지
DOI QR코드

DOI QR Code

Phase-Field Modelling of Zinc Dendrite Growth in ZnAlMg Coatings

  • Received : 2024.01.12
  • Accepted : 2024.02.08
  • Published : 2024.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

In the present work, a phase-field model for dendritic solidification is applied to hot-dip ZnAlMg coatings to elucidate the morphology of zinc dendrites and the solute segregation leading to the formation of eutectics. These aspects define the microstructure that conditions the corrosion resistance and the mechanical behaviour of the coating. Along with modelling phase transformation and solute diffusion, the implemented model is partially coupled with the tracking of crystal orientation in solid grains, thus allowing the effects of surface tension anisotropy to be considered in multi-dendrite simulations. For this purpose, the composition of a hot-dip ZnAlMg coating is assimilated to a dilute pseudo-binary system. 1D and 2D simulations of isothermal solidification are performed in a finite element solver by introducing nuclei as initial conditions. The results are qualitatively consistent with existing analytical solutions for growth velocity and concentration profiles, but the spatial domain of the simulations is limited by the required mesh refinement.

Keywords

References

  1. H. E. Chaieb, V. Maurel, K. Ammar, S. Forest, A. Tanguy, E. Heripre, F. Nozahic, J. -M. Mataigne, J. D. Strycker, In-situ localization of damage in a Zn-Al-Mg coating deposited on steel by continuous hot-dip galvanizing, Scripta Materialia, 243, 115960 (2024). Doi: https://doi.org/10.1016/j.scriptamat.2023.115960
  2. M. Ahmadi, B. Salgin, B. J. Kooi, and Y. Pei, Genesis and mechanism of microstructural scale deformation and cracking in ZnAlMg coationgs, Materials & Design, 186, 108364 (2020). Doi: https://doi.org/10.1016/j.matdes.2019.108364
  3. E. De Bruycker, Z. Zermout, and B. C. De Cooman, Zn-Al-Mg Coatings: Thermodynamic Analysis and Microstructure Related Properties, Materials Science Forum, 539-543, 1276 (2007). Doi: https://doi.org/10.4028/www.scientific.net/MSF.539-543.1276
  4. E. Baril and G. L'Esperance, Studies of the morphology of the Al-rich interfacial layer formed during the hot dip galvanazing of steel sheet, Metallurgical and Materials Transactions A, 30, 681 (1999). Doi: https://doi.org/10.1007/s11661-999-1000-1
  5. A. R. Marder, The metallurgy of zinc-coated steel, Progress in Materials Science, 45, 191 (2000). Doi: https://doi.org/10.1016/S0079-6425(98)00006-1
  6. W. R. Osorio, C. M. Freire, and A. Garcia, The effect of the dendritic microstructure on the corrosion resistance of Zn-Al alloys, Journal of Alloys and Compounds, 397, 179 (2005). Doi: https://doi.org/10.1016/j.jallcom.2005.01.035
  7. C. Yaom, H. Teng, G. Jiang, Y. Li, M. Li, and G. Liu, The Solidification and Corrosion Behavior Determination of the Ti/B Added Zn-Al-Mg Alloys, Journal of Alloys and Compounds, 670, 239 (2016). Doi: https://doi.org/10.1007/s11595-022-2585-0
  8. T. Prosek, J. Hagstrom, D. Persson, N. Fuertes, F. Lindberg, O. Chocholaty, C. Taxen, J. Serak, D. Thierry, Corrosion Science, 110, 71 (2016). Doi: https://doi.org/10.1016/j.corsci.2016.04.022
  9. W. R. Osorio, C. M. Freire, and A. Garcia, The role of macrostructural morphology and grain size on the corrosion resistance of Zn and Al castings, Materials Science and Engineering A, 402, 22 (2005). Doi: https://doi.org/10.1016/j.msea.2005.02.09
  10. J. Elvins, J. A. Spittle, J. H. Sullivan, and D. A. Worsley, The effect of magnesium additions on the microstructure and cut edge corrosion resistance of zinc aluminium alloy galvanised steel, Corrosion Science, 50, 1650 (2008). Doi: https://doi.org/10.1016/j.corsci.2008.02.005
  11. G. Jiang, L. Chen, H. Wang, and G. Liu, Microstructure and Corrosion Resistance Property of a Zn-Al-Mg Alloy with Different Solidification Processes, MATEC Web of Conferences, 109, 01004 (2017). Doi: https://doi.org/10.1051/matecconf/201710901004
  12. S. Li, B. Gao, G. Tu, Y. Hao, L. Hu, and S. Yin, Study on the Corrosion Mechanism of Zn-5Al-0.5Mg-0.08Si Coating, Journal of Metallurgy, 2011, 917469 (2011). Doi: https://doi.org/10.1155/2011/917469
  13. J. Tanaka, K. Ono, S. Hayashi, K. Ohsasa, and T. Narita, Effect of Mg and Si on the Microstructure and Corrosion Behavior of Zn-Al Hot Dip Coatings on Low Carbon Steel, ISIJ International, 42, 80 (2002). Doi: https://doi.org/10.2355/isijinternational.42.80
  14. N. Provatas and K. Elder, Phase-Field Methods in Materials Science and Engineering, John Wiley & Sons (2011). Doi: https://doi.org/10.1002/9783527631520
  15. A. Karma and W.-J. Rappel, Phase-field method for computationally efficient modelling of solidification with arbitrary interface kinetics, Physical Review E, 53, R3017 (1996). Doi: https://doi.org/10.1103/PhysRevE.53.R3017
  16. B. Echebarria, R. Folch, A. Karma, and M. Plapp, Quantitative phase-field model of alloy solidification, Physical Review E, 70, 061604 (2004). Doi: https://doi.org/10.1103/PhysRevE.70.061604
  17. J. C. Ramirez, C. Beckermann, A. Karma, and H.-J. Diepers, Phase-field modelling of binary alloy solidification with coupled heat and solute diffusion, Physical Review E, 69, 051607 (2004). Doi: https://doi.org/10.1103/PhysRevE.69.051607
  18. H. Wang, X. Zhang, C. Lai, W. Kuang, and F. Liu, Thermodynamic principles principles for phase-field modelling of alloy solidification, Current Opinion in Chemical Engineering, 7, 6 (2015). Doi: https://doi.org/10.1016/j.coche.2014.09.004
  19. T. Pinomaa, M. Lindroos, P. Jreidini, M. Haapalehto, K. Ammar, L. Wang, S. Forest, N. Provatas, and A. Laukkanen, Philosophical Transactions of the Royal Society A, 380, 20200319 (2022). Doi: https://doi.org/10.1098/rsta.2020.0319
  20. C. Sarkis, 'Phase-field modeling of dendritic solidification for an Al-4.5wt%Cu atomized droplet using an anisotropic adaptive mesh', PhD. thesis, PSL University (2016). https://theses.hal.science/tel-01649221/
  21. S. G. Kim, H.-S. Hwang, and J.-Y. Huh, Phase-field simulations of dendritic morphologies in hot-dip galvanized Zn-Al coatings, Computational Materials Science, 186, 110060 (2021). Doi: https://doi.org/10.1016/j.commatsci.2020.110060
  22. E. De Bruycker, B. C. De Cooman, and M. De Meyer, Experimental study and microstructure Simulation of ZnAl-Mg coationgs, Revue de Metallurgie Paris, 102, 543 (2005). Doi: https://doi.org/10.1051/metal:2005157
  23. J. P. Mogeritsch, A. Ludwig, B. Bottger, G. Angeli, C. K. Riener, R. Ebner, Proc. VII International Conference on Computational Methods for Coupled Problems in Science and Engineering (Coupled Problems 2017) Conf., pp. 1171 - 1182, (2017). https://smmp.unileoben.ac.at/fileadmin/shares/unileoben/smmp/docs/C161_Coupled_Problems_in_Science_and_Engineering_VII.pdf
  24. Z. Guo and S. M. Xiong, On solving the 3-D phase field equations by employing a parallel-adaptive mesh refinement (Para-AMR) algorithm, Computer Physics Communications, 190, 89 (2015). Doi: https://doi.org/10.1016/j.cpc.2015.01.016
  25. T. Z. Gong, Y. Chen, Y. F. Cao, X. H. Kang, and D. Z. Li, Fast simulations of a large number of crystals growth in centimeter-scale during alloy solidification via nonlinearly preconditioned quantitative phase-field formula, Computational Materials Science, 147, 338 (2018). Doi:https://doi.org/10.1016/j.commatsci.2018.02.003
  26. Y. Chen, X. B. Qi, D. Z. Li, X. H. Kang, and N. M. Xiao, A quantitative phase-field model combining with front-tracking method for polycrystalline solidification of alloys, Computational Materials Science, 104, 155 (2015). Doi: https://doi.org/10.1016/j.commatsci.2015.04.003
  27. J. A. Warren, R. Kobayashi, A. E. Lobkovsky, and W. C. Carter, Extending phase field models of solidification to polycrystalline materials, Acta Materialia, 51, 6035 (2003). Doi: https://doi.org/10.1016/S1359-6454(03)00388-4
  28. R. Kobayashi and J. A. Warren, Modeling the formation and dynamics of polycrystals in 3D, Physica A: Statistical Mechanics and its Applications, 356, 127 (2005). Doi: https://doi.org/10.1016/j.physa.2005.05.024
  29. H. Henry, J. Mellenthin, and M. Plapp, Orientation-field model for polycrystalline solidification with a singular coupling between order and orientation, Physical Review B, 86, 054117 (2012). Doi: https://doi.org/10.1103/Phys-RevB.86.054117
  30. T. Pusztai, G. Bortel, and L. Granasy, Phase field theory of polycrystalline solidification in three dimensions, Europhysics Letters, 71, 131 (2005). Doi: https://doi.org/10.1209/epl/i2005-10081-7
  31. M. Ahmadi, B. Salgin, M. Ahmadi, B. J. Kooi, and Y. Pei, Unraveling dislocation mediated plasticity and strengthening in crack-resistant ZnAlMg coatings, International Journal of Plasticity, 144, 103041 (2021). Doi:https://doi.org/10.1016/j.ijplas.2021.103041
  32. S. Ghosh, 'Effects of solid-solid boundary anisotropy on directional solidification microstructures', PhD. thesis, Ecole Polytechnique (2015).
  33. I. Ansara, A. T. Dinsdale, and M. H. Rand, 'COST 507 Thermochemical database for light metal alloys', European Commission (1998). https://www.opencalphad.com/databases/CGNA18499ENC_001.pdf
  34. S. Yang, X. Su, J. Wang, F. Yin, N.-Y. Tang, Z. Li, X. Wang, Z. Zhu, H. Tu, and X. Li, Comprehensive Evaluation of Aluminum Diffusivity in Liquid Zinc, Metallurgical and Materials Transactions A, 42, 1785 (2011). Doi: https://doi.org/10.1007/s11661-010-0461-6
  35. T. Gancarz, W. Gasior, and H. Henein, Physicochemical Properties of Sb, Sn, Zn, and Sb-Sn System, International Journal of Thermophysics, 34, 250 (2013). Doi: https://doi.org/10.1007/s10765-013-1407-1
  36. K. Keslioglu and N. Marasli, Experimental determination of solid-liquid interfacial energy for Zn solid solution in equilibrium with the Zn-Al eutectic liquid, Metallurgical and Materials Transactions A, 35, 3665 (2004). Doi: https://doi.org/10.1007/s11661-004-0272-8
  37. M. Erol, K. Keslioglu, and N. Marasli, Measurement of Solid-Liquid Interfacial Energy for Solid Zn in Equilibrium with the ZnMg Eutectic Liquid, Metallurgical and Materials Transactions A, 38, 1539 (2007). Doi: https://doi.org/10.1007/s11661-007-9174-x
  38. H. B. Aaron, D. Fainstein, and G. R. Kotler, Diffusion-Limited Phase Transformations: A Comparison and Critical Evaluation of the Mathematical Approximations, Journal of Applied Physics, 41, 4404 (1970). Doi: https://doi.org/10.1063/1.1658474
  39. S. Kaboli, and J. R. McDermid, Effect of Process Variables on the Grain Size and Crystallographic Texture of Hot-Dip Galvanized Coatings, Metallurgical and Materials Transactions A, 45, 3938 (2014). Doi: https://doi.org/10.1007/s11661-014-2359-1
  40. S. Vakili, I. Steinbach, and F. Varnik, On the numerical evaluation of local curvature for diffuse interface models of microstructure evolution, Procedia Computer Science, 108, 1852 (2017). Doi: https://doi.org/10.1016/j.procs.2017.05.256