Characterization of homogenous and plastically graded materials with spherical indentation and inverse analysis

Abstract

This study investigates spherical indentation of plastically graded materials (PGMs). The hardness of these materials decreases with depth due to microstructural or compositional changes. To predict the behavior of PGM, the knowledge of the plastic properties of the surface and the substrate is necessary. In this work, the spherical indentation technique is applied on carbonitrided steels to obtain their mechanical properties. First, spherical indentation was applied to characterize homogenous materials using inverse analysis. The comparison with tensile test’s results shows that the inverse analysis using spherical indentation data is a reliable method to determine the plastic properties of homogeneous materials. In the second part spherical indentation was used to characterize carbonitrided steels using inverse analysis to obtain plastic properties of the surface. The results show that spherical indentation using inverse analysis has a real potential for evaluating mechanical properties of PGM.

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References

  1. 1.

    Y.P. Cao and J. Lu: A new scheme for computational modeling of conical indentation in plastically graded materials. J. Mater. Res. 19(6), 1703 (2004).

    CAS  Article  Google Scholar 

  2. 2.

    V. Garnier and G. Corneloup: Determining of the evolution of the elasticity modulus by surface wave according to the depth in a nitrided layer. Ultrasonics 34(2–5), 401 (1996).

    CAS  Article  Google Scholar 

  3. 3.

    A.E. Giannakopoulos: Indentation of plastically graded substrates by sharp indentors. Int. J. Solids Struct. 39, 2495 (2002).

    Article  Google Scholar 

  4. 4.

    A. Nayebi, R. El Abdi, O. Bartier, and G. Mauvoisin: New procedure to determine steel mechanical parameters from the spherical indentation technique. Mech. Mater. 34, 243 (2002).

    Article  Google Scholar 

  5. 5.

    J.M. Collin, G. Mauvoisin, O. Bartier, R. El Abdi, and P. Pilvin: Use of spherical indentation data changes to materials characterization based on a new multiple cyclic loading protocol. Mater. Sci. Eng., A 501, 608 (2009).

    Article  Google Scholar 

  6. 6.

    H. Lee, J.H. Lee, and G.M. Pharr: A numerical approach to spherical indentation techniques for material property evaluation. J. Mech. Phys. Solids 53, 2037 (2005).

    CAS  Article  Google Scholar 

  7. 7.

    Y.P. Cao and J. Lu: A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve. Acta Mater. 52, 4023 (2004).

    CAS  Article  Google Scholar 

  8. 8.

    N. Ogasawara, N. Chiba, and X. Chen: Measuring the plastic properties of bulk materials by indentation test. Scr. Mater. 54, 65 (2006).

    CAS  Article  Google Scholar 

  9. 9.

    M. Zhao, N. Ogasawara, N. Chiba, and X. Chen: A new approach to measure the elastic–plastic properties of bulk materials using spherical indentation. Acta Mater. 54, 23 (2006).

    CAS  Article  Google Scholar 

  10. 10.

    J.H. Lee, T. Kim, and H. Lee: A study on robust indentation techniques to evaluate elastic–plastic properties of metals. Int. J. Solids Struct. 47, 647 (2010).

    Article  Google Scholar 

  11. 11.

    P. Jiang, T. Zhang, Y. Feng, R. Yang, and N. Liang: Determination of plastic properties by instrumented spherical indentation: Expanding cavity model and similarity solution approach. J. Mater. Res. 24(3), 1045 (2009).

    CAS  Article  Google Scholar 

  12. 12.

    N. Ogasawara, N. Chiba, and X. Chen: A simple framework of spherical indentation for measuring elastoplastic properties. Mech. Mater. 41, 1025 (2009).

    Article  Google Scholar 

  13. 13.

    T. Zhang, P. Jiang, Y. Feng, and R. Yang: Numerical verification for instrumented spherical indentation techniques in determining the plastic properties of materials. J. Mater. Res. 24(12), 3653 (2009).

    CAS  Article  Google Scholar 

  14. 14.

    N.A. Branch, G. Subhash, N.K. Arakere, and M.A. Klecka: A new reverse analysis to determine the constitutive response of plastically graded case hardened bearing steels. Int. J. Solids Struct. 48, 584 (2011).

    CAS  Article  Google Scholar 

  15. 15.

    I.S. Choi, M. Dao, and S. Suresh: Mechanics of indentation of plastically graded materials—I: Analysis. J. Mech. Phys. Solids 56, 157 (2008).

    CAS  Article  Google Scholar 

  16. 16.

    I.S. Choi, A.J. Detor, R. Schwiger, M. Dao, C.A. Schuh, and S. Suresh: Mechanics of indentation of plastically graded materials—II: Experiments on nanocrystalline alloys with grain size gradients. J. Mech. Phys. Solids 56, 172 (2008).

    CAS  Article  Google Scholar 

  17. 17.

    M. Dao, N. Chollacoop, K.J. Van Vliet, T.A. Vankatesh, and S. Suresh: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49(19), 3899 (2001).

    CAS  Article  Google Scholar 

  18. 18.

    D. Chicot, L. Gil, K. Silva, F. Roudet, E.S. Puchi-Cabrera, M.H. Staia, and D.G. Teer: Thin film hardness determination using indentation loading curve modelling. Thin Solid Films 518, 5565 (2010).

    CAS  Article  Google Scholar 

  19. 19.

    F. Zhang, R. Saha, Y. Huang, W.D. Nix, K.C. Hwang, S. Ku, and M. Li: Indentation of a hard film on a soft substrate: Strain gradient hardening effects. Int. J. Plast. 23, 25 (2007).

    CAS  Article  Google Scholar 

  20. 20.

    M. Zhao, Y. Xiang, J. Xu, N. Ogasawara, N. Chiba, and X. Chen: Determining mechanical properties of thin films from the loading curve of nanoindentation testing. Thin Solid Films 516, 7571 (2008).

    CAS  Article  Google Scholar 

  21. 21.

    J.A. Knapp and J.F. Browning: Nanoindentation characterization of ErT2 thin films. J. Nucl. Mater. 350, 147 (2006).

    CAS  Article  Google Scholar 

  22. 22.

    A. Nayebi, R. El Abdi, O. Bartier, and G. Mauvoisin: Hardness profile analysis of elasto-plastic heat-treated steels with a gradient in yield strength. Mater. Sci. Eng., A 333, 160 (2002).

    Article  Google Scholar 

  23. 23.

    T. Nakamura, T. Wang, and S. Sampath: Determination of properties of graded materials by inverse analysis and instrumented indentation. Acta Mater. 18, 4293 (2000).

    Article  Google Scholar 

  24. 24.

    Y. Gu, T. Nakamura, L. Prchlik, S. Sampath, and J. Wallace: Micro-indentation and inverse analysis to characterize elastic/plastic graded materials. Mater. Sci. Eng., A 345, 233 (2003).

    Article  Google Scholar 

  25. 25.

    K.L. Johnson: Contact Mechanics (Cambridge University Press, London, 1985).

    Google Scholar 

  26. 26.

    A.C. Fischer-Cripps: Critical review of analysis and interpretation of nanoindentation test data. Surf. Coat. Tech. 200, 4153 (2006).

    CAS  Article  Google Scholar 

  27. 27.

    M.R. VanLandingham: Review of instrumented indentation. J. Res. Natl. Inst. Stand. Technol. 108, 249 (2003).

    Article  Google Scholar 

  28. 28.

    Y-T. Cheng and C-M. Cheng: Can stress strain relationship be obtained from indentation curves using conical and pyramidal indenters? J. Mater. Res. 14(9), 3493 (1999).

    CAS  Article  Google Scholar 

  29. 29.

    A.K. Bhattacharya and W.D. Nix: Analysis of elastic and plastic deformation associated with indentation testing of thin films on substrates. Int. J. Solids Struct. 24, 1287 (1988).

    Article  Google Scholar 

  30. 30.

    X.L. Gao, X.N. Jing, and G. Subhash: Two new expanding cavity models for indentation deformations of elastic strain-hardening materials. Int. J. Solids Struct. 43, 2193 (2006).

    Article  Google Scholar 

  31. 31.

    O. Bartier, X. Hernot, and G. Mauvoisin: Theoretical and experimental analysis of contact radius for spherical indentation. Mech. Mater. 42, 640 (2010).

    Article  Google Scholar 

  32. 32.

    P. Pilvin: Approaches multi-échelles pour la prévision du comportement anélastique des métaux. PhD Thesis (ENS Cachan, CRNS, Université Paris 6, France, 1990).

    Google Scholar 

  33. 33.

    V. Chean, E. Robin, R. El Abdi, J-C Sangleboeuf, and P. Houizot: Use of the mark-tracking method for optical fiber characterization. Optic Laser Technol. 43, 1172 (2011).

    CAS  Article  Google Scholar 

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Correspondence to Charbel Moussa.

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Moussa, C., Bartier, O., Mauvoisin, G. et al. Characterization of homogenous and plastically graded materials with spherical indentation and inverse analysis. Journal of Materials Research 27, 20–27 (2012). https://doi.org/10.1557/jmr.2011.303

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