Skip to main content
SpringerLink
Log in

A Methodology to Evaluate Continuum-Scale Yield Surfaces Based on the Spatial Distributions of Yielding at the Crystal Scale

  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

Using a correlation between local yielding and a multiaxial strength-to-stiffness parameter, the continuum-scale yield surface for a polyphase, polycrystalline solid is predicted. The predicted surface explicitly accounts for microstructure through the quantification of strength-to-stiffness based on a finite element model of a crystal-scale sample. The multiaxial strength-to-stiffness is evaluated from the elastic response of the sample and the restricted slip, single crystal yield surface. Macroscopic yielding is defined by the propagation of a yield band through the sample and is detected with the aid of a flood-fill algorithm. The methodology is demonstrated with the evaluation of a plane-stress yield surface for a dual-phase super-austenitic stainless steel.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Notes

  1. The relations are written in the current configuration for simplicity. Readers are referred to Reference 4 for more complete exposition of the associated deformation kinematics.

  2. The viscoplastic character of the equations for slip allows some level of plastic flow at any non-zero stress. However, the non-linearity of the relation implies that for stress levels below the strength the rates are small.

References

  1. A. C. Poshadel, P. R. Dawson, Metallurgical and Materials Transactions A, (2018), https://doi.org/10.1007/s11661-018-5013-5

    Google Scholar 

  2. A. C. Poshadel, M. Gharghouri, P. R. Dawson, Metall. Mater. Trans. A, (2018), https://doi.org/10.1007/s11661-018-5009-1

    Google Scholar 

  3. P.R. Dawson, S.R. MacEwen, P. D. Wu, Int. Mater. Rev., 48, 86–122. (2003)

    Article  Google Scholar 

  4. P.R. Dawson and D.E. Boyce: FEpX—Finite Element Polycrystals: Theory, Finite Element Formulation, Numerical Implementation and Illustrative Examples, 2015. arXiv:1504.03296 [cond-mat.mtrl-sci]

  5. W.A. Backofen: Deformation Processing, Addison-Wesley Publishing Company, Reading, 1972.

  6. U. F. Kocks, C. N. Tome, H.-R. Wenk, Texture and Anisotropy, Cambridge University Press, (1998)

    Google Scholar 

  7. H. Tresca, Comptes Rendus Acad. Sci. Paris, 59, 754–758 (1864)

    Google Scholar 

  8. M. T. Huber, , Lwow, 22, 38–81. (1904)

    Google Scholar 

  9. R. von Mises: Gottinger Nachrichten Math.-Phys. Klasse 4, pp. 582–592. (1913)

  10. H. Hencky, Zeits. ang. Math. Mech., 4, p. 323. (1924)

    Article  Google Scholar 

  11. M. Gurtin, An Introduction to Continuum Mechanics, Academic Press, New York, (1981)

    Google Scholar 

  12. R. Hill, Proc. R. Soc., A193, 281–297. (1948)

    Google Scholar 

  13. R. Hill, J. Mech. Phys. Solids, 38, 405–417. (1990)

    Article  Google Scholar 

  14. F. Barlat, Y. Maeda, K. Chung, M. Yanagawa, J. C. Brem, Y. Hayashida, D. J. Lege, K. Matsui, S. J. Murtha, S. Hattori, R. C. Becker, S. Makosey, J. Mech. Phys. Solids, 45, 1727–1763. (1997)

    Article  Google Scholar 

  15. W.F. Hosford: The Mechanics of Crystals and Textured Polycrystals. Oxford Science Publications, Oxford (1993)

    Google Scholar 

  16. P.J. Maudlin, S.I. Wright, I.G.T. Gray, and J.W. House: in Metallurgic and Materials Applications of Shock-Wave and High-Strain-Rate Phenomena, L.E. Murr, K.P. Staudhammer, and M.A. Meyers, eds., Elsevier Science B. V., 1995, pp. 877–884.

  17. P. R. Dawson, D. E. Boyce, R. Hale, J. P. Durkot, Int. J. Plasticity, 21, 251–283. (2005)

    Article  Google Scholar 

  18. S. Torbert, Applied Computer Science, , , 2d ed., (2016)

    Google Scholar 

  19. A. C. Poshadel, M. Gharghouri, P. R. Dawson, Metallurgical and Materials Transactions A, (2018), 10.1007/s11661-018-5085-2

    Google Scholar 

  20. D. W. A. Rees, Basic engineering plasticity : an introduction with engineering and manufacturing applications, Elsevier, Boston, MA, (2006)

    Google Scholar 

  21. K. Chatterjee, M. P. Echlin, M. Kasemer, P. G. Callahan, T. M. Pollock, P. Dawson, Acta Materialia, vol. 157, pp. 21–32. (2018)

    Article  Google Scholar 

Download references

Acknowledgment

Support was provided by the US Office of Naval Research (ONR) under contract N00014-09-1-0447.

Author information

Authors and Affiliations

  1. Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA, 14853

    Andrew C. Poshadel & Paul R. Dawson

Authors
  1. Andrew C. Poshadel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul R. Dawson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul R. Dawson.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Manuscript submitted June 9, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Poshadel, A.C., Dawson, P.R. A Methodology to Evaluate Continuum-Scale Yield Surfaces Based on the Spatial Distributions of Yielding at the Crystal Scale. Metall Mater Trans A 50, 2640–2654 (2019). https://doi.org/10.1007/s11661-019-05187-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11661-019-05187-z

Search

Navigation