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Constitutive behavior of tantalum and tantalum-tungsten alloys

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Abstract

The effects of strain rate, temperature, and tungsten alloying on the yield stress and the strainhardening behavior of tantalum were investigated. The yield and flow stresses of unalloyed Ta and tantalum-tungsten alloys were found to exhibit very high rate sensitivities, while the hardening rates in Ta and Ta-W alloys were found to be insensitive to strain rate and temperature at lower temperatures or at higher strain rates. This behavior is consistent with the observation that overcoming the intrinsic Peierls stress is shown to be the rate-controlling mechanism in these materials at low temperatures. The dependence of yield stress on temperature and strain rate was found to decrease, while the strain-hardening rate increased with tungsten alloying content. The mechanical threshold stress (MTS) model was adopted to model the stress-strain behavior of unalloyed Ta and the Ta-W alloys. Parameters for the constitutive relations for Ta and the Ta-W alloys were derived for the MTS model, the Johnson—Cook (JC), and the Zerilli-Armstrong (ZA) models. The results of this study substantiate the applicability of these models for describing the high strain-rate deformation of Ta and Ta-W alloys. The JC and ZA models, however, due to their use of a power strain-hardening law, were found to yield constitutive relations for Ta and Ta-W alloys that are strongly dependent on the range of strains for which the models were optimized.

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References

  1. W. Kock and P. Paschen:J. Met., 1989, vol. 41, pp. 33–39.

    Google Scholar 

  2. R.J. Arsenault and A. Lawley:Work Hardening, J.P. Hirth and J. Weertman, eds., Gordon and Breach, New York, NY, 1968, pp. 283–309.

    Google Scholar 

  3. G.T. Gray III and A.D. Rollett:High Strain Rate Behavior of Refractory Metals and Alloys, R. Asfhani, E. Chen, and A. Crowson, eds., TMS, Warrendale, PA, 1992, pp. 303–15.

    Google Scholar 

  4. J.B. Clark, R.K. Garrett, Jr.,T.L. Jungling, and R.I. Asfahani:Metall. Trans. A, 1991, vol. 22A, pp. 2959–68.

    CAS  Google Scholar 

  5. J.B. Clark, R.K. Garrett, Jr., T.L. Jungling, and R.I. Asfahani:Metall. Trans. A, 1992, vol. 23A, pp. 2183–91.

    CAS  Google Scholar 

  6. A. Gilbert, D. Hull, W.S. Owen, and C.N. Reid:J. Less-Common Met, 1962, vol. 4, pp. 399–408.

    Article  CAS  Google Scholar 

  7. J.W. Christian:Metall. Trans. A, 1983, vol. 14A, pp. 1237–56.

    CAS  Google Scholar 

  8. W.H. Gourdin, D.H. Lassila, M.M. LeBlanc, and A.L. Shields:J. Phys. IV, 1994, pp. C8–207~C8–212.

    Google Scholar 

  9. K.G. Hoge and A.K. Mukherjee:J. Mater. Sci., 1977, vol. 12, pp. 1666–72.

    Article  CAS  Google Scholar 

  10. R.A. Foxall and CD. Statham:Acta Metall, 1970, vol. 18, pp. 1147–58.

    Article  CAS  Google Scholar 

  11. P.J. Maudlin, R.F. Davidson, and R.J. Henninger: Report No. LA-11895-MS, Los Alamos National Laboratory, Los Alamos, NM, 1990.

  12. M.N. Raftenberg: Report No. BRL-TR-3363, United States Army Ballistic Research Laboratory, Maryland, 1992.

  13. A.M. Rajendran and P. Woolsey: Report No. ARL-TR-216, United States Army Research Laboratory, Maryland, 1993.

  14. P.S. Follansbee and U.F. Kocks:Acta Metall, 1988, vol. 36, pp. 81–93.

    Article  Google Scholar 

  15. G.R. Johnson and W.H. Cook:Proc. 7th Int. Symp. on Ballistic, The Hague, The Netherlands, 1983, pp. 541–47.

    Google Scholar 

  16. F.J. Zerilli and R.W. Armstrong:J. Appl. Phys., 1987, vol. 61, pp. 1816–25.

    Article  CAS  Google Scholar 

  17. G.R. Johnson and Stryk: Report No. AFATL-TR-86-51, Air Force Armament Laboratory, Eglin Air Force Base, Florida, 1986.

  18. D.J. Caliostro, D.A. Mandell, and L.A. Schwalbe:Int. J. Impact Eng., 1990, vol. 10, pp. 81–92.

    Article  Google Scholar 

  19. J.O. Hallquist: Report No. UCID-19592, Rev. 4, Lawrence Livermore National Laboratory, Livermore, CA, 1988.

  20. G.T. Gray III, S.R. Bingert, S.I. Wright, and S.R. Chen:High Temperature Silicides and Refractory Alloys, C.L. Briant, J.J. Petrovic, B.P. Bewlay, A.K. Vasudevan, and H.A. Lipsitt, eds., Materials Research Society, Pittsburgh, PA, 1994, vol. 322, pp. 407–12.

    Google Scholar 

  21. P.S. Follansbee:High Strain Rate Compression Testing—The Hopkinson Bar, 9th ed., ASM, Metals Park, OH, 1985, vol. 8, pp. 198–203.

    Google Scholar 

  22. G. Simmons and H. Wang:Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook, 2nd ed., The MIT Press, Boston, MA, 1991.

    Google Scholar 

  23. Y.P. Varshni:Phys. Rev. B, 1970, vol. 2, pp. 3952–58.

    Article  Google Scholar 

  24. S.R. Chen and G.T. Gray III:2nd Int. Conf. on Tungsten and Refractory Metals, A. Bose and R.J. Dowding, eds., Oct. 17–19, McLean, VA, Metal Powder Industries Federation, Princeton, NJ, 1995, pp. 489–98.

    Google Scholar 

  25. P.S. Follansbee and G.T. Gray III:Metall. Trans. A, 1989, vol. 20A, pp. 863–74.

    CAS  Google Scholar 

  26. P.S. Follansbee, J.C. Huang, and G.T. Gray III:Acta Metall, 1990, vol. 38, pp. 1241–54.

    Article  CAS  Google Scholar 

  27. U.F. Kocks, A.S. Argon, and M.F. Ashby:Thermodynamics and Kinetics of Slip, Progress in Materials Science, Pergamon Press, New York, NY, 1975, vol. 19.

    Google Scholar 

  28. U.F. Kocks:J. Eng. Mater. Technol, Trans. ASME, 1976, vol. 98, pp. 76–85.

    CAS  Google Scholar 

  29. P. Hassen:Phil. Mag., 1958, vol. 3, pp. 384–418.

    Article  Google Scholar 

  30. G. Schoeck and A. Seeger:Defects in Crystalline Solids, Physical Society, London, 1955.

    Google Scholar 

  31. B.L. Mordike, K.D. Rogausch, and A.A. Braithwaite:Met. Sci. J., 1970, vol. 4, pp. 37–40.

    CAS  Google Scholar 

  32. F.J. Zerilli and R.W. Armstrong:J. Appl. Phys., 1990, vol. 68, pp. 1580–91.

    Article  CAS  Google Scholar 

  33. Thermodynamic Properties of the Elements, D.R. Stall and G.C. Sinke, eds., American Chemical Society, Washington, DC, 1956.

    Google Scholar 

  34. S.R. Chen and G.T. Gray III: to be submitted.

  35. G.T. Gray III, S.R. Chen, W. Wright, and M.F. Lopez: Report No. LA-12669-MS, Los Alamos National Laboratory, Los Alamos, NM, 1994.

  36. H. Conrad:J. Met, 1964, vol. 16, pp. 582–88.

    CAS  Google Scholar 

  37. A.H. Cottrell:Dislocation and Plastic Flow in Crystals, Clarendon Press, Oxford, United Kingdom, 1953.

    Google Scholar 

  38. P. Ludwik:Elemente der Technologischen Mechanik, Springer, Berlin, 1909.

    Google Scholar 

  39. D.A. Hughes and W.D. Nix:Metall. Trans. A, 1988, vol. 19A, pp. 3013–24.

    CAS  Google Scholar 

  40. A.D. Rollett: Ph.D. Thesis, Drexel University, Philadelphia, PA, 1988.

    Google Scholar 

  41. P.J. Maudlin: Report No. LA-12960-PR: The Joint DoD/DOE Munitions Technology Development Program Progress Report for 1994—“Unconventionally Processed High-Density Materials,” Los Alamos National Laboratory, Los Alamos, NM, 1995.

    Google Scholar 

  42. G.T. Gray III, S.R. Chen, and K.S. Vecchio: 1996, to be submitted.

  43. G.T. Gray III and K.S. Vecchio:Metall. Trans. A, 1995, vol. 26A, pp. 2555–62.

    CAS  Google Scholar 

  44. G.T. Gray III, S.R. Chen, S.R. Bingert, S.I. Wright, and P.J. Maudlin: The Joint DoD/DOE Munitions Technology Development Program, Los Alamos National Laboratory, Los Alamos, NM, 1996.

  45. T.J. Holmquist and G.R. Johnson:J. Phys. IV, 1991, pp. C3–853~C3–860.

    Google Scholar 

  46. C.L. Wittman and CM. Lopatin:Tungsten & Tungsten Alloys—1992, A. Bose and R.J. Dowding, eds., Metal Powder Industries Federation, Princeton, NJ, 1992, pp. 357–64.

    Google Scholar 

  47. F.J. Zerilli and R.W. Armstrong:Symp. on High Strain Rate Effects, San Francisco, CA, 1995.

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Authors and Affiliations

  1. Los Alamos National Laboratory, 87545, Los Alamos, NM

    Shuh Rong Chen (Staff Member) & George T. Gray (Staff Member)

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  1. Shuh Rong Chen
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Chen, S.R., Gray, G.T. Constitutive behavior of tantalum and tantalum-tungsten alloys. Metall Mater Trans A 27, 2994–3006 (1996). https://doi.org/10.1007/BF02663849

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