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Linear strain hardening in elastoplastic indentation contact

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Abstract

Finite-element analyses for elastoplastic cone indentations were conducted in which the effect of linear strain hardening on indentation behavior was intensively examined in relation to the influences of the frictional coefficient (μ) at the indenter/material contact interface and of the inclined face angle (β) of the cone indenter. A novel procedure of “graphical superposition” was proposed to determine the representative yield stress YR. It was confirmed that the concept of YR applied to elastic-perfectlyplastic solids is sufficient enough for describing the indentation behavior of strainhardening elastoplastic solids. The representative plastic strain of εR (plastic) ≈ 0.22 tan β, at which YR is prescribed, is applicable to the strain-hardening elastoplastic solids, affording a quantitative relationship of YR = Y + ε;R (plastic) × EP in terms of the strain-hardening modulus EP. The true hardness H as a measure for plasticity is estimated from the Meyer hardness HM and then successfully related to the yield stress Y as H = C(β,μ) × Y for elastic-perfectly-plastic solids and as H = C(β,μ) × YR for strain-hardening solids, by the use of a β- and μ-dependent constraint factor C(β,μ) ranging from 2.6 to 3.2.

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References

  1. D. Tabor, Hardness of Metals (Clarendon Press, Oxford, U.K., 1951), Chap. 4–7.

    Google Scholar 

  2. B.R. Lawn and V.R. Howes, J. Mater. Sci. 16, 2745 (1981).

    Article  CAS  Google Scholar 

  3. M. Sakai, Acta Metall. Mater. 41, 1751 (1993).

    Article  CAS  Google Scholar 

  4. M. Sakai, S. Shimizu, and T. Ishikawa, J. Mater. Res. 14, 1471 (1999).

    Article  CAS  Google Scholar 

  5. M. Sakai, J. Mater. Res. 14, 3630 (1999).

    Article  CAS  Google Scholar 

  6. M. Sakai and Y. Nakano, J. Mater. Res. 17, 2161 (2002).

    Article  CAS  Google Scholar 

  7. N.A. Stilwell and D. Tabor, Proc. Phys. Soc. London 78, 169 (1961).

    Article  Google Scholar 

  8. J.L. Loubet, J.M. Georges, and G. Meille, in Microindentation Techniques in Materials Science and Engineering, edited by P.J. Blay and B.R. Lawn (ASTM STP889, Philadelphia, PA, 1986), p. 72.

  9. M.F. Doerner and W.D. Nix, J. Mater. Res. 1, 601 (1986).

    Article  Google Scholar 

  10. W.C. Oliver and G.M. Pharr, J. Mater. Res. 7, 1564 (1992).

    Article  CAS  Google Scholar 

  11. G.M. Pharr, W.C. Oliver, and F.R. Brotzen, J. Mater. Res. 7, 613 (1992).

    Article  CAS  Google Scholar 

  12. J.S. Field and M.V. Swain, J. Mater. Res. 8, 297 (1993).

    Article  CAS  Google Scholar 

  13. E. Söderlund and D.J. Rowcliffe, J. Hard Mater. 5, 149 (1994).

    Google Scholar 

  14. R.F. Cook and G.M. Pharr, J. Hard Mater. 5, 179 (1994).

    CAS  Google Scholar 

  15. P.S. Follansbee and G.B. Sinclair, Int. J. Solids Struct. 20, 81 (1984).

    Article  Google Scholar 

  16. P.S. Follansbee, G.B. Sinclair, and K.L. Johnson, Int. J. Solids Struct. 21, 865 (1985).

    Article  Google Scholar 

  17. A.K. Bhattacharya and W.D. Nix, Int. J. Solids Struct. 27, 1047 (1991).

    Article  Google Scholar 

  18. T.A. Laursen and J.C. Simo, J. Mater. Res. 7, 618 (1992).

    Article  CAS  Google Scholar 

  19. Y. Murakami and K. Matsuda, J. App. Mech. 61, 822 (1994).

    Article  CAS  Google Scholar 

  20. A.E. Giannakopoulos, P.E. Larsson, and R. Vestergaard, Int. J. Solids Struct. 31, 2679 (1994).

    Article  Google Scholar 

  21. K. Matsuda and M. Kaneta, Philos. Mag. A 74, 1171 (1996).

    Article  CAS  Google Scholar 

  22. P.E. Larsson, A.E. Giannakopoulos, E. Söderlund, D.J. Rowcliffe, and R. Vestergaard, Int. J. Solids Struct. 33, 221 (1996).

    Article  Google Scholar 

  23. K. Zeng, E. Söderlund, A.E. Giannakopoulos, and D.J. Rowcliffe, Acta Mater. 44, 1127 (1996).

    Article  CAS  Google Scholar 

  24. Y. Murakami and M. Itokazu, Int. J. Solids Struct. 34, 4005 (1997).

    Article  Google Scholar 

  25. V. Marx and H. Balke, Acta Mater. 45, 3791 (1997).

    Article  CAS  Google Scholar 

  26. A.E. Giannakopoulos and S. Suresh, Int. J. Solids Struct. 34, 2357 (1997).

    Article  Google Scholar 

  27. Y.T. Cheng and C.M. Cheng, J. App. Phys. 84, 1284 (1998).

    Article  CAS  Google Scholar 

  28. X. Chen and J.J. Vlassak, J. Mater. Res. 16, 2974 (2001).

    Article  CAS  Google Scholar 

  29. K. Matsuda, Philos. Mag. A 82, 1941 (2002).

    Article  CAS  Google Scholar 

  30. K.L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, U.K., 1985), Chap. 3–6.

    Book  Google Scholar 

  31. R. Hill, Mathematical Theory of Plasticity (Clarendon Press, Oxford, U.K., 1951), Chap. 8.

    Google Scholar 

  32. R.T. Shield, Proc. Roy. Soc. A 233, 267 (1955).

    CAS  Google Scholar 

  33. F.J. Lockett, J. Mech. Phys. Solids 11, 345 (1963).

    Article  Google Scholar 

  34. I.N. Sneddon, Int. J. Eng. Sci. 3, 47 (1965).

    Article  Google Scholar 

  35. M. Mata, M. Anglada, and A. Alcala´, Philos. Mag. A 82, 1831 (2002).

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Materials Science, Toyohashi University of Technology, Tempaku-cho, 441–8580, Toyohashi, Japan

    M. Sakai

  2. Materials and Structures Laboratory, Tokyo Institute of Technology, 4259, Nagatsuta, Midori-ku, 226–8503, Yokohama, Japan

    T. Akatsu & S. Numata

  3. Department of Mechanical and Control Engineering, Kyushu Institute of Technology, 1–1 Sensui-cho, Tobata-ku, 804–8550, Kitakyushu, Japan

    K. Matsuda

Authors
  1. M. Sakai
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  2. T. Akatsu
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  3. S. Numata
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  4. K. Matsuda
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Correspondence to M. Sakai.

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Sakai, M., Akatsu, T., Numata, S. et al. Linear strain hardening in elastoplastic indentation contact. Journal of Materials Research 18, 2087–2096 (2003). https://doi.org/10.1557/JMR.2003.0293

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  • DOI: https://doi.org/10.1557/JMR.2003.0293

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