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A Transfer Function for Relating Mean 2D Cross-Section Measurements to Mean 3D Particle Sizes

  • A. R. C. Gerlt
  • R. S. Picard
  • A. E. Saurber
  • A. K. Criner
  • S. L. Semiatin
  • E. J. Payton
Communication
  • 14 Downloads

Abstract

It is common practice to estimate mean 3D particle and grain size of polycrystalline materials by multiplying 2D cross-sectional measurements by a multiplication factor. However, the most frequently used multiplication factors apply only to uniform or specific dispersions of particles, and therefore can provide misleading results. In the present work, empirical equations are developed to more accurately predict the mean 3D grain size of a lognormal spherical particle dispersion, regardless of the dispersion’s width. The equations provide an improvement over scalar multiplier values by allowing the effects of particle size distribution to be accounted for using inputs that can be obtained by cross-sectional analysis.

Supplementary material

11661_2018_4808_MOESM1_ESM.docx (14 kb)
Supplementary material 1 (DOCX 15 kb)

References

  1. 1.
    E.J. Payton, G. Wang, M. J. Mills, Y. Wang: Acta Mater., 2013, vol. 61, pp. 1316-1326.CrossRefGoogle Scholar
  2. 2.
    G. Wang, D.S. Xu, N. Ma, N. Zhou, E.J. Payton, R. Yang, Y. Wang: Acta Mater., 2009, vol. 57, pp. 316-325.CrossRefGoogle Scholar
  3. 3.
    S.L. Semiatin, B.C. Kirby, G.A. Salishchev: Metall. Trans. A., 2004, vol. 35A, pp. 2809-2819.CrossRefGoogle Scholar
  4. 4.
    S.L. Semiatin, N.C. Levkulich, A.E. Saurber, D.W. Mahaffey, E.J. Payton, O.N. Senkov: Metall. Trans. A., 2017, vol. 48, pp. 5567-5578.CrossRefGoogle Scholar
  5. 5.
    S.L. Semiatin, V. Seetharaman, D.M. Dimiduk, K.H.G. Ashbee: Metall. Trans. A., 1998, vol. 29, pp. 7-18.CrossRefGoogle Scholar
  6. 6.
    A.L. Pilchak, G.A. Sargent, S.L. Semiatin: Metall. Mater. Trans. A., 2017, 49(3), pp 908-919.Google Scholar
  7. 7.
    J.E. Hillard, L.R. Lawson: Stereology and Stochastic Geometry. Kluwer, Dordrecht, 2010.Google Scholar
  8. 8.
    E.E. Underwood: J. Microsc., 1969, vol. 89, pp 161-180.CrossRefGoogle Scholar
  9. 9.
    E.J. Payton: J. Miner. Mater. Charact. Eng., 2012, vol. 11 No. 3, pp. 221-242.Google Scholar
  10. 10.
    T. Hatch, S.P. Choate: J. Franklin Inst., 1929 vol. 207, pp. 369-97.CrossRefGoogle Scholar
  11. 11.
    M.I. Mendelson: J. Am. Ceram. Soc, 1967, vol. 52, No. 8 pp 443-446.CrossRefGoogle Scholar
  12. 12.
    S.A. Saltikov: Stereology, ed. H. Elias, Springer, Berlin, Heidelberg, 1970.Google Scholar
  13. 13.
    P. Feltham: Acta Met., 1957, vol. 5, pp. 97-105.CrossRefGoogle Scholar
  14. 14.
    M. Hillert, Acta Met., 1965, vol. 13, pp. 227-238.CrossRefGoogle Scholar
  15. 15.
    ASTM Standard E112-2: “Standard Test Methods for Determining Average Grain Size”, ASTM International, West Conshohocken, PA, 2002,  https://doi.org/10.1520/e0112-12, www.astm.org.
  16. 16.
    H.B. Aaron, R.D. Smith, and E.E Underwood: Proceedings from the 1st International Congress on Stereology, Vienna, paper 16, 1963.Google Scholar
  17. 17.
    G. Liu, H Yu: Image analysis Stereology, 2000, vol19, pp 91-97.CrossRefGoogle Scholar
  18. 18.
    S.S. Shapiro, M.B. Wilk, Biometrika, 1965, vol. 52, pp 591-611.CrossRefGoogle Scholar
  19. 19.
    P. Louis, A. Gokhale: Metall. Mater. Trans. A., 1995, vol. 26, pp 1741-1744.CrossRefGoogle Scholar
  20. 20.
    Y.A. Coutinho, S.C.K. Rooney, E.J. Payton: Metall. Mater Trans. A., 2017, 48(5), pp 2375-2395.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2018

Authors and Affiliations

  • A. R. C. Gerlt
    • 1
  • R. S. Picard
    • 1
  • A. E. Saurber
    • 1
  • A. K. Criner
    • 1
  • S. L. Semiatin
    • 1
  • E. J. Payton
    • 1
  1. 1.Materials and Manufacturing DirectorateAir Force Research LaboratoryWright-Patterson Air Force BaseUSA

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