Skip to main content

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

Metallurgical and Materials Transactions A volume 49, pages 4424–4428 (2018)Cite this article

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3

References

  1. E.J. Payton, G. Wang, M. J. Mills, Y. Wang: Acta Mater., 2013, vol. 61, pp. 1316-1326.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  3. S.L. Semiatin, B.C. Kirby, G.A. Salishchev: Metall. Trans. A., 2004, vol. 35A, pp. 2809-2819.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  5. S.L. Semiatin, V. Seetharaman, D.M. Dimiduk, K.H.G. Ashbee: Metall. Trans. A., 1998, vol. 29, pp. 7-18.

    Article  Google Scholar 

  6. A.L. Pilchak, G.A. Sargent, S.L. Semiatin: Metall. Mater. Trans. A., 2017, 49(3), pp 908-919.

    Google Scholar 

  7. J.E. Hillard, L.R. Lawson: Stereology and Stochastic Geometry. Kluwer, Dordrecht, 2010.

    Google Scholar 

  8. E.E. Underwood: J. Microsc., 1969, vol. 89, pp 161-180.

    Article  Google Scholar 

  9. E.J. Payton: J. Miner. Mater. Charact. Eng., 2012, vol. 11 No. 3, pp. 221-242.

    Google Scholar 

  10. T. Hatch, S.P. Choate: J. Franklin Inst., 1929 vol. 207, pp. 369-97.

    Article  Google Scholar 

  11. M.I. Mendelson: J. Am. Ceram. Soc, 1967, vol. 52, No. 8 pp 443-446.

    Article  Google Scholar 

  12. S.A. Saltikov: Stereology, ed. H. Elias, Springer, Berlin, Heidelberg, 1970.

  13. P. Feltham: Acta Met., 1957, vol. 5, pp. 97-105.

    Article  Google Scholar 

  14. M. Hillert, Acta Met., 1965, vol. 13, pp. 227-238.

    Article  Google Scholar 

  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. H.B. Aaron, R.D. Smith, and E.E Underwood: Proceedings from the 1st International Congress on Stereology, Vienna, paper 16, 1963.

  17. G. Liu, H Yu: Image analysis Stereology, 2000, vol19, pp 91-97.

    Article  Google Scholar 

  18. S.S. Shapiro, M.B. Wilk, Biometrika, 1965, vol. 52, pp 591-611.

    Article  Google Scholar 

  19. P. Louis, A. Gokhale: Metall. Mater. Trans. A., 1995, vol. 26, pp 1741-1744.

    Article  Google Scholar 

  20. Y.A. Coutinho, S.C.K. Rooney, E.J. Payton: Metall. Mater Trans. A., 2017, 48(5), pp 2375-2395.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, OH, 45433, USA

    A. R. C. Gerlt, R. S. Picard, A. E. Saurber, A. K. Criner, S. L. Semiatin & E. J. Payton

Authors
  1. A. R. C. Gerlt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. S. Picard
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. E. Saurber
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. K. Criner
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. S. L. Semiatin
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. E. J. Payton
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. J. Payton.

Additional information

Manuscript submitted May 3, 2018.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 15 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gerlt, A.R.C., Picard, R.S., Saurber, A.E. et al. A Transfer Function for Relating Mean 2D Cross-Section Measurements to Mean 3D Particle Sizes. Metall Mater Trans A 49, 4424–4428 (2018). https://doi.org/10.1007/s11661-018-4808-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11661-018-4808-8