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Modeling the Effect of Finite-Rate Hydrogen Diffusion on Porosity Formation in Aluminum Alloys

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Abstract

A volume-averaged model for finite-rate diffusion of hydrogen in the melt is developed to predict pore formation during the solidification of aluminum alloys. The calculation of the micro-/macro-scale gas species transport in the melt is coupled with a model for the feeding flow and pressure field. The rate of pore growth is shown to be proportional to the local level of gas supersaturation in the melt, as well as various microstructural parameters. Parametric studies of one-dimensional solidification under an imposed temperature gradient and cooling rate illustrate that the model captures important phenomena observed in porosity formation in aluminum alloys. The transition from gas to shrinkage dominated porosity and the effects of different solubilities of hydrogen in the eutectic solid, capillary pressures at pore nucleation, and pore number densities are investigated in detail. Comparisons between predicted porosity percentages and previous experimental measurements show good correspondence, although some uncertainties remain regarding the extent of impingement of solid on the pores.

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References

  1. T.S. Piwonka, M.C. Flemings: Trans. AIME, 1966, vol. 236, pp. 1157–65

    Google Scholar 

  2. K. Kubo, R.D. Pehlke: Metall. Trans. B, 1985, vol. 16B, pp. 359–66

    Article  Google Scholar 

  3. P.D. Lee, A. Chirazi, D. See: J. Light Met., 2001, vol. 1, pp. 15–30

    Article  Google Scholar 

  4. A.S. Sabau, S. Viswanathan: Metall. Mater. Trans. B, 2002, vol. 33B, pp. 243–55

    Article  Google Scholar 

  5. C. Pequet, M. Gremaud, M. Rappaz: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2095–2106

    Article  Google Scholar 

  6. P.D. Lee, J.D. Hunt: in M. Cross, J. Campbell, eds., Modeling of Casting, Welding and Advanced Solidification Processes VII, TMS, Warrendale, PA, 1995, pp. 585–92

  7. P.D. Lee, J.D. Hunt: Acta Mater., 1997, vol. 45, pp. 4155–69

    Article  Google Scholar 

  8. R.C. Atwood, S. Sridhar, W. Zhang, P.D. Lee: Acta Mater., 2000, vol. 48, pp. 405–17

    Article  Google Scholar 

  9. R.C. Atwood, P.D. Lee: Metall. Mater. Trans. B, 2002, vol. 33B, pp. 209–21

    Article  Google Scholar 

  10. R.W. Hamilton, D. See, S. Butler, P.D. Lee: Mater. Sci. Eng. A, 2003, vol. A343, pp. 290–300

    Google Scholar 

  11. K. Tynelius, J.F. Major, D. Apelian: AFS Trans., 1993, vol. 101, pp. 401–13

    Google Scholar 

  12. R. Fuoco, H. Goldenstein, J.E. Gruzleski: AFS Trans., 1994, vol. 102, pp. 297–306

    Google Scholar 

  13. D. Emadi, J.E. Gruzleski: AFS Trans., 1994, vol. 102, pp. 307–11

    Google Scholar 

  14. Q.T. Fang, D.A. Granger: AFS Trans., 1989, vol. 97, pp. 989–1000

    Google Scholar 

  15. E. Underwood: Quantitative Stereology, Addison-Wesley Publishing Co., Reading, MA, 1970, 27, 96, and 103

    Google Scholar 

  16. E. Niyama, T. Uchida, M. Morikawa, S. Saito: Am. Foundrymen’s Soc. Int. Cast Met. J., 1982, vol. 7 (3), pp. 52–63

    Google Scholar 

  17. K.D. Carlson, S. Ou, R.A. Hardin, C. Beckermann: Metall. Mater. Trans. B, 2002, vol. 33B, pp. 731–40

    Article  Google Scholar 

  18. K.D. Carlson, Z. Lin, R.A. Hardin, C. Beckermann, G. Mazurkevich, M.C. Schneider: in D.M. Stefanesu, J.A. Warren, M.R. Jolly, and M.J.M. Krane, eds., Modeling of Casting, Welding and Advanced Solidification Processes X, TMS, Warrendale, PA, 2003, pp. 295–302

  19. S. Shivkumar, D. Apelian, J. Zou: AFS Trans., 1990, vol. 98, pp. 897–904

    Google Scholar 

  20. J.D. Zhu, S.L. Cockcroft, D.M. Maijer, R. Ding: Int. J. Cast Met. Res., 2005, vol. 18(4), pp. 229–35

    Article  Google Scholar 

  21. D. Emadi, J.E. Gruzleski, J.M. Toguri: Metall. Trans. B, 1993, vol. 24B, pp. 1055–63

    Article  Google Scholar 

  22. M.J. Moran, H.N. Shapiro: Fundamentals of Engineering Thermodynamics, 5th ed., John Wiley & Sons, Inc., New York, NY, 2004, 102 and 759

    Google Scholar 

  23. W. Eichenauer, J. Markopoulos: Z. Metallkd., 1974, vol. 65 (10), pp. 649–52

    Google Scholar 

  24. P.N. Anyalebechi: Scripta Metall. Mater., 1995, vol. 33 (8), pp. 1209–26

    Article  Google Scholar 

  25. J. Ni, C. Beckermann: Metall. Trans. B, 1991, vol. 22B, pp. 349–61

    Article  Google Scholar 

  26. JMatPro, Sente Software Ltd., Surrey Technology Centre, Surrey GU2 7YG, United Kingdom

  27. S. Thompson, S.L. Cockcroft, M.A. Wells: Mater. Sci. Technol., 2004, vol. 20, pp. 194–200

    Article  Google Scholar 

  28. D.R. Poirier, P.K. Sung: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 3874–76

    Article  Google Scholar 

  29. M. Ichimura, Y. Sasajima: J. Jpn. Inst. Light Met., 1993, vol. 43 (7), pp. 385–91

    Google Scholar 

  30. P.N. Anyalebechi: in B. Welch, ed., Light Metals 1998, TMS, Warrendale, PA, 1998, pp. 827–42

  31. R.C. Newman: J. Phys.: Condens. Matter, 2000, vol. 12, pp. R335–R365

  32. MAGMASOFT, MAGMA GmbH, 52072 Aachen, Germany

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Acknowledgments

This work was supported, in part, by the United States National Science Foundation under Grant No. DMR-0132225 and by Magma Foundry Technologies.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, IA, 52242, United States

    Kent D. Carlson (Research Engineer), Zhiping Lin (Graduate Research Assistant) & Christoph Beckermann (Professor)

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  1. Kent D. Carlson
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  2. Zhiping Lin
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  3. Christoph Beckermann
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Correspondence to Christoph Beckermann.

Additional information

This article is based on a presentation made in the symposium “Simulation of Aluminium Shape Casting Processing: From Design to Mechnacial Properties” which occured March 12–16, 2006, during the TMS Spring meeting in San Antonio, Texas, under the auspices of the Computational Materials Science and Engineering Committee, the Process Modelling, Analysis and Control Committee, the Solidification Committee, the Mechanical Behavior of Materials Committee, and the Light Metal Division/Aluminium Committee.

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Carlson, K.D., Lin, Z. & Beckermann, C. Modeling the Effect of Finite-Rate Hydrogen Diffusion on Porosity Formation in Aluminum Alloys. Metall Mater Trans B 38, 541–555 (2007). https://doi.org/10.1007/s11663-006-9013-2

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