Skip to main content
SpringerLink
Log in

Further Analysis of Dynamic Strain Aging in Context of an Internal State Variable Constitutive Formalism

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

Abstract

Observations and analyses of dynamic strain aging in several metals are revisited. Common experimental trends are reviewed. A model of transport of solutes to a dislocation core is presented and predictions of the model are compared to experimental observations. A key element of the analysis is the influence of strain aging on the rate of structure evolution. The evidence presented here, based on strain-rate change measurements performed by Mulford and Kocks in Inconel 600, is that indeed the predominant effect of strain aging is to influence the rate of structure evolution. Estimates are presented for the rate of structure evolution and the extent of transport of solutes to the dislocation core in Inconel 600. While intriguing trends in hardening are observed, no fundamental insight is presented for the mechanism that contributes to the increased rate of structure evolution during strain aging.

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

Reprinted from Ref. [7]

Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Notes

  1. The units do cancel as specified. For instance, the units of T (K) and the energy units dynes in β canceled with the Boltzman constant shown in Eq. [20] which is now included in the constant 113.6.

References

  1. U.F. Kocks, R.E. Cook, and R.A. Mulford: Acta Metallurgica, 1985, vol. 33, pp. 623-638.

    Article  CAS  Google Scholar 

  2. R.A. Mulford and U.F. Kocks: Acta Metallurgica, 1979, vol. 27, pp. 1125-1134.

    Article  CAS  Google Scholar 

  3. L. P. Kubin and Y. Estrin: Journal de Physique III, 1991, vol. 1, pp. 929-943.

    CAS  Google Scholar 

  4. S. Nemat-Nasser and W. Guo: Materials Science and Engineering A, 2000, vol. 284, pp. 202-210.

    Article  Google Scholar 

  5. P.S. Follansbee: Fundamentals of Strength – Principles, Experiment, and Applications of an Internal State Variable Constitutive Formulation, Wiley, Hoboken, NJ, 2014.

    Book  Google Scholar 

  6. P.S. Follansbee: Trans. ASME J. Eng. Mater. Technol. 2014, 134, 41007

    Google Scholar 

  7. P.S. Follansbee: Materials Sciences and Applications, 2015, vol. 6, pp. 457-463.

    CAS  Google Scholar 

  8. P.S. Follansbee: Metallurgical and Materials Transactions A, 2016, vol. 47A, pp. 4455-4466.

    Article  Google Scholar 

  9. A. Stein and P.S. Follansbee: Mater. Sci. Appl. 8, 484–492 (2017)

    Google Scholar 

  10. S. Nemat and W. Guo: Mech. Mater. 2000, 32, 243-260.

    Article  Google Scholar 

  11. J. Cheng and S. Nemat-Nasser: Acta Materialia, 2000, vol. 48, pp. 3131-3144.

    Article  CAS  Google Scholar 

  12. M.A. Soare and W.A. Curtin: Acta Materialia, 2008, vol. 56, pp. 4091-4101.

    Article  CAS  Google Scholar 

  13. M.A. Soare and W.A. Curtin: Acta Materialia, 2008, vol. 56, pp. 4046-4061.

    Article  CAS  Google Scholar 

  14. F. Zhang, A.F. Bower, and W.A. Curtin: Acta Materialia, 2012, vol. 60, pp. 43-50.

    Article  CAS  Google Scholar 

  15. P. G. Shewmon: Diffusion in Solids, McGraw-Hill Series in Materials Science and Engineering, NY, 1963.

    Google Scholar 

  16. A. H. Cottrell: Dislocations and Plastic Flow in Solids, Clarendon Press, Oxford, 1953.

    Google Scholar 

  17. A. Van Den Beukel: (1975) Theory of the Effect of Dynamic Strain Aging on Mechanical Properties, Physica Status Solidi (a), 1975. vol. 30, pp. 197-206.

    Article  Google Scholar 

  18. J. B. Conway, R. H. Stentz, and J. T. Berling, Fatigue, Tensile, and Relaxation Behavior of Stainless Steels, U. S. Atomic Energy Commission, Division of Reactor Research and Development, NTIS, TID26135, 1974.

  19. . H. Hänninen, M. Ivanchenko, Y. Yagodzinskyy, V. Nevdacha, U. Ehrnstén, and P. Aaltonen, (2005) in T. R. Allen, P. J. King, and L. Nelson, eds., Proceedings of the 12th International Conference on Environmental Degradation of Materials in Nuclear Power System – Water Reactors, TMS, 2005, pp. 1423 – 1430.

  20. P. B. Hirsch and T. E. Mitchell: Canadian Journal of Physics, 1967, vol. 45, pp. 663-706.

    Article  CAS  Google Scholar 

  21. A. D. Rollett and U. F. Kocks: Solid State Phenomena, 1993, vols. 35-36, pp. 1-18.

    Article  Google Scholar 

  22. C. Albertini and M. Montagnani: Nuclear Engineering and Design, 1980, vol. 57, pp. 107-123.

    Article  CAS  Google Scholar 

  23. M. Bobadilla and A. Tschiptschin: Materials Research, 2015, vol. 18, pp. 390-394.

    Article  CAS  Google Scholar 

  24. L. H. Almeida, K. C. C. Pires, C. R. Grandini, O. Florencio: Mater. Res., 2005, 8, 239-243.

    Article  Google Scholar 

  25. J. J. Lander, H. E. Kern, A. L. Beach, J. Applied Physics, 1953, 23, 1305-1309.

    Article  Google Scholar 

  26. . P. S. Follansbee, J. C. Huang, and G. T. Gray: Acta Metallurgica,1990, vol. 38, pp. 1241-1254.

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The author is grateful for the support of Saint Vincent College in performance of this work.

Author information

Authors and Affiliations

  1. Saint Vincent College, Latrobe, PA, USA

    Paul S. Follansbee

Authors
  1. Paul S. Follansbee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul S. Follansbee.

Additional information

Publisher's Note

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

Manuscript submitted August 7, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Follansbee, P.S. Further Analysis of Dynamic Strain Aging in Context of an Internal State Variable Constitutive Formalism. Metall Mater Trans A 51, 1275–1285 (2020). https://doi.org/10.1007/s11661-019-05591-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11661-019-05591-5

Search

Navigation