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Physically-Based and Power-Law Constitutive Relations for Higher Temperature Metal Processing and Creep-Type Deformations

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Abstract

There is continuing research interest in the development and use of constitutive relations for assistance with description and optimization of higher temperature metal and alloy processing conditions and desired mechanical property performances, particularly in the latter case for nanopolycrystalline materials under creep-type loading deformations. Here, we focus on the plastic flow stress dependence on strain rate, temperature, and especially, on material grain size. Connection is established between, on the one hand, relatively recent thermal-activation-based relations for dislocation motion and, on the other hand, comparative power law expressions.

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References

  1. H. Conrad, JOM 16 (7), 582 (1964).

    Article  Google Scholar 

  2. A. Seeger, Dislocations and the Mechanical Properties of Crystals, ed. J.C. Fisher, W.G. Johnston, R. Thomson, and T. Vreeland, Jr. (New York, NY: Wiley, 1957), p. 243.

    Google Scholar 

  3. E. Orowan, J. West Scotl. Iron Steel Inst. 54, 45 (1946).

    Google Scholar 

  4. R.W. Armstrong, J. Sci. Ind. Res. 32, 591 (1973).

    Google Scholar 

  5. R.W. Armstrong, (Jpn) Mater. Trans. 55, 2 (2014).

    Article  Google Scholar 

  6. J.C.M. Li, Dislocation Dynamics, ed. A.R. Rosenfield, G.T. Hahn, A.L. Bement, Jr, and R.I. Jaffee (New York: McGraw-Hill, 1968), p. 87.

    Google Scholar 

  7. R.W. Armstrong, in 14th International Conference on Fracture (ICF14), David Taplin Symposium, ed. A Saxena (Rhodes, GR, 2017).

  8. R.W. Armstrong and Q.Z. Li, Metall. Mater. Trans. A 46A, 4438 (2015).

    Article  Google Scholar 

  9. N. Balasubramanian and J.C.M. Li, J. Mater. Sci. 5, 434 (1970).

    Article  Google Scholar 

  10. F.J. Zerilli and R.W. Armstrong, J. Appl. Phys. 61, 1816 (1987).

    Article  Google Scholar 

  11. F.J. Zerilli, Metall. Mater. Trans. A 35A, 2547 (2004).

    Article  Google Scholar 

  12. R.W. Armstrong, Canad. Metall. Q. 13, 187 (1974).

    Article  Google Scholar 

  13. C. Zener and J.H. Hollomon, J. Appl. Phys. 15, 22 (1944).

    Article  Google Scholar 

  14. F.J. Zerilli, R.W. Armstrong, in Shock Compression of Condensed Matter1995, ed. S.C. Schmidt, W.C. Tao (American Institute of Physics, Woodbury, 1996), CP370, Part 1, p. 315.

  15. J. Weertman, Chapter 13.Mechanics and Materials; Fundamentals and Linkages, ed. M.A. Meyers, R.W. Armstrong, and H.O.K. Kirchner (New York: Wiley Interscience, 1999), p. 451.

    Google Scholar 

  16. M.A. Przystupa and A.J. Ardell, Metall. Mater. Trans. A 33A, 231 (2002).

    Article  Google Scholar 

  17. A.J. Ardell and M.A. Przystupa, Mech. Mater. 3, 319 (1984).

    Article  Google Scholar 

  18. R.W. Armstrong, H. Conrad, and F.R.N. Nabarro, Mechanical Properties of Nanostructured Materials and Nanocomposites, ed. I. Ovid’ko, C.S. Pande, R. Krishnamoorti, E. Lavernia, and G. Skandan (Warrendale: Material Research Society, 2004), p. 69.

    Google Scholar 

  19. T.G. Langdon, J. Mater. Sci. 41, 597 (2006).

    Article  Google Scholar 

  20. W. Blum and X.H. Zeng, Acta Mater. 57, 1966 (2009).

    Article  Google Scholar 

  21. W. Blum, Y.J. Li, Y. Zhang, and J.T. Wang, Mater. Sci. Eng. A 528, 8621 (2011).

    Article  Google Scholar 

  22. W. Blum, J. Dvořák, P. Král, P. Eisenlohr, and V. Sklenička, Mater. Sci. Eng. A 590, 423 (2014).

    Article  Google Scholar 

  23. W. Blum, J. Dvořák, P. Král, M. Petranec, P. Eisenlohr, and V. Sklenička, Philos. Mag. 95, 3696 (2015).

    Article  Google Scholar 

  24. J.H. Schneibel, M. Heilmaier, W. Blum, G. Hasemann, and T. Shanmugasundaram, Acta Mater. 59, 1300 (2011).

    Article  Google Scholar 

  25. S.D. Antolovich and R.W. Armstrong, Prog. Mater. Sci. 59, 1 (2014).

    Article  Google Scholar 

  26. R.W. Armstrong, J.H. Bechtold, R.T. Begley, in Refractory Metals and Alloys II, TMS-AIME Metallurgical Society Conferences, 17, ed. by M. Semchyshen, I. Perlmutter (Interscience Publishers, New York, 1963), p. 159.

  27. Y.J. Li, J. Mueller, H.W. Höppel, M. Göken, and W. Blum, Acta Mater. 55, 5708 (2007).

    Article  Google Scholar 

  28. Q. Wei and L.J. Kecskes, Chapter 8.Mechanical Properties of Nanocrystalline Materials, ed. J.C.M. Li (Singapore: Pan Stanford Publishers, Ltd., 2011), p. 213.

    Google Scholar 

  29. L. Lu and K. Lu, Chapter 6.Mechanical Properties of Nanocrystalline Materials, ed. J.C.M. Li (New York: Pan Stanford Publishers Ltd, 2011), p. 163.

    Chapter  Google Scholar 

  30. N. Balasubramanian and T.G. Langdon, Metall. Mater. Trans. A 47A, 5827 (2016).

    Article  Google Scholar 

  31. M. Kawasaki and T.G. Langdon, J. Mater. Sci. 51, 19 (2016).

    Article  Google Scholar 

  32. M. Kawasaki, N. Balasubramanian, and T.G. Langdon, Mater. Sci. Eng. A 528, 6624 (2011).

    Article  Google Scholar 

  33. A.K. Mukherjee, Mater. Sci. Eng. A 322, 1 (2002).

    Article  Google Scholar 

  34. K.A. Padmanabhan, J. Leuthold, G. Wilde, and S.S. Bhattacharya, Mech. Mater. 91, 177 (2015).

    Article  Google Scholar 

  35. H. Conrad: J. Inst. Met., 87, 347 (1958–59).

  36. U.F. Kocks and H. Mecking, Prog. Mater. Sci. 48, 171 (2003).

    Article  Google Scholar 

  37. F.J. Zerilli and R.W. Armstrong, J. Appl. Phys. 68, 1580 (1990).

    Article  Google Scholar 

  38. G.R. Johnson, W.H. Cook, Proceedings of the 7th International Symposium on Ballistics (The Hague, TN, 1983), p. 541.

  39. H. Zhan, G. Wang, D. Kent, and M. Dargusch, Mater. Sci. Eng. A 612, 71 (2014).

    Article  Google Scholar 

  40. T. Mirzaie, H. Mirzadeh, and J.-M. Cabrera, Mech. Mater. 94, 38 (2016).

    Article  Google Scholar 

  41. A.H. Ammouri, G. Kridli, G. Ayoub, and R.F. Hamade, J. Mater. Process. Technol. 222, 301 (2015).

    Article  Google Scholar 

  42. R.W. Armstrong: in NanometalsStatus and Perspective, 33rd Risoe International Symposium on Materials Science, ed. by S. Faester, N. Hansen, X. Huang, D. Juul Jensen, B. Ralph (Technical University of Denmark, Roskilde, 2012), p. 181.

  43. A.H. Ammouri and R.F. Hamade, Mater. Des. 57, 673 (2014).

    Article  Google Scholar 

  44. C.J. Chang, C.J. Lee, and J.C. Huang, Scr. Mater. 51, 509 (2004).

    Article  Google Scholar 

  45. F.R. Larson and J. Miller, Trans. ASME 74, 765 (1952).

    Google Scholar 

  46. M. Tamura, F. Abe, K. Shiba, H. Sakasegawa, and H. Tanigawa, Metall. Mater. Trans. A 44A, 2645 (2013).

    Article  Google Scholar 

  47. F. Abe, Metall. Mater. Trans. A 46A, 5610 (2015).

    Article  Google Scholar 

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Armstrong, R.W., Balasubramanian, N. Physically-Based and Power-Law Constitutive Relations for Higher Temperature Metal Processing and Creep-Type Deformations. JOM 69, 822–829 (2017). https://doi.org/10.1007/s11837-017-2277-y

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