Advertisement

Analysis of Nanoindentation Test Data

  • Anthony C. Fischer-CrippsEmail author
Chapter
Part of the Mechanical Engineering Series book series (MES)

Abstract

As described in Chap. 2, estimations of both elastic modulus and hardness of the specimen material in a nanoindentation test are obtained from load versus penetration measurements. Rather than a direct measurement of the size of residual impressions, contact areas are instead calculated from depth measurements together with a knowledge of the actual shape of the indenter. For this reason, nanoindentation testing is sometimes referred to as depth-sensing indentation testing. In this chapter, methods of the analysis of load-displacement data that are used to compute hardness and modulus of test specimens are presented in detail. It is an appropriate introduction to first consider the case of a cylindrical punch indenter —even though this type of indenter is rarely used for this type of testing, its response illustrates and introduces the theory for the more complicated cases of spherical and pyramidal indenters.

Keywords

Contact Stiffness Elastic Recovery Specimen Material Elastic Displacement Spherical Indenter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    A.C. Fischer-Cripps, Introduction to Contact Mechanics, 2nd Ed. Springer-Verlag, New York, 2007.CrossRefzbMATHGoogle Scholar
  2. 2.
    G.M. Pharr, W.C. Oliver, and F.R. Brotzen, “On the generality of the relationship among contact stiffness, contact area, and the elastic modulus during indentation,” J. Mater. Res. 7 3, 1992, pp. 613–617.CrossRefGoogle Scholar
  3. 3.
    M.F. Doerner and W.D. Nix, “A method for interpreting the data from depth-sensing indentation instruments,” J. Mater. Res. 1 4, 1986, pp. 601–609.CrossRefGoogle Scholar
  4. 4.
    W.C. Oliver and G.M. Pharr, “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments,” J. Mater. Res. 7 4, 1992, pp. 1564–1583.CrossRefGoogle Scholar
  5. 5.
    J.S. Field and M.V. Swain, “A simple predictive model for spherical indentation,” J. Mater. Res. 8 2, 1993, pp. 297–306.CrossRefGoogle Scholar
  6. 6.
    E.S. Berkovich, “Three-faceted diamond pyramid for micro-hardness testing,” Ind. Diamond Rev. 11 127, 1951, pp. 129–133.Google Scholar
  7. 7.
    I.N. Sneddon, “Boussinesq’s problem for a rigid cone,” Proc. Cambridge Philos. Soc. 44, 1948, pp. 492–507.CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    J.Woirgard and J-C. Dargenton, “An alternative method for penetration depth determination in nanoindentation measurements,” J. Mater. Res. 12 9, 1997, pp. 2455–2458.CrossRefGoogle Scholar
  9. 9.
    T. Sawa and K. Tanaka, “Simplified method for analyzing nanoindentation data and evaluating performance of nanoindentation instruments,” J. Mater. Res. 16 11, 2001, pp. 3084–3096.CrossRefGoogle Scholar
  10. 10.
    G.M.Pharr and A. Bolshakov, “Understanding nanoindentation unloading curves,” J. Mater. Res. 17 10, 2002, pp. 2660–2671.CrossRefGoogle Scholar
  11. 11.
    R.B. King, “Elastic analysis of some punch problems for a layered medium,” Int. J. Solids Struct. 23 12, 1987, pp. 1657–1664.CrossRefzbMATHGoogle Scholar
  12. 12.
    Y.-T. Cheng and C.-M. Cheng, “Scaling approach to conical indentation in elastic-plastic solids with work hardening,” J. App. Physics, 84 3, 1998, pp. 1284–1291.CrossRefGoogle Scholar
  13. 13.
    J.C. Hay, A. Bolshakov and G.M. Pharr, “A critical examination of the fundamental relations used in the analysis of nanoindentation data,” J. Mater. Res. 14 6, 1999, pp. 2296–2305.CrossRefGoogle Scholar
  14. 14.
    M. Martin and M. Troyon, “Fundamental relations used in nanoindentation: Critical examination based on experimental measurements,” J. Mater. Res. 17 9, 2002, pp. 2227–2234.CrossRefGoogle Scholar
  15. 15.
    M. Dao, N. Chollacoop, K. J. Van Vliet, T. A. Venkatesh and S. Suresh, “Computational modeling of the forward and reverse problems in instrumented sharp indentation,” Acta Mater. 49, 2001, pp.3899–3918.CrossRefGoogle Scholar
  16. 16.
    J. Gong, H. Miao, and Z. Peng, “Analysis of the nanoindentation data measured with a Berkovich indenter for brittle materials: effect of residual contact stress,” Acta Materialia, 52, 2004, pp. 785–793.CrossRefGoogle Scholar
  17. 17.
    F.M. Borodich and L.M. Keer, “Evaluation of elastic modulus of materials by adhesive (no-slip) nano-indentation,” Proc. R. Soc. Lond. A460, 2004, pp. 507–514.CrossRefMathSciNetGoogle Scholar
  18. 18.
    D.B. Marshall and B.R. Lawn, “Indentation of Brittle Materials,” Microindentation Techniques in Materials Science and Engineering, ASTM STP 889, P.J. Blau and B.R. Lawn, Eds. American Society for Testing and Materials, Philadelphia, 1986, pp. 26–46.Google Scholar
  19. 19.
    L. Riester, T.J. Bell, and A.C. Fischer-Cripps, “Analysis of depth-sensing indentation tests with a Knoop indenter,” J. Mater. Res. 16 6, 2001, pp. 1660–1667.CrossRefGoogle Scholar
  20. 20.
    D.B. Marshall, T. Noma, and A.G. Evans, “A simple method for determining elastic-modulus-to-hardness ratios using Knoop indentation measurements,” J. Am. Ceram. Soc. 65, 1980, pp. C175–C176.CrossRefGoogle Scholar
  21. 21.
    I.N. Sneddon, “The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile”, Int. J. Eng. Sci. 3, 1965, pp. 47–57.CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Y.-T. Cheng, C.-M. Cheng, “Scaling, dimensional analysis, and indentation measurements,” Mat. Sci. Eng. R. 44, 2004, pp. 99–149.CrossRefGoogle Scholar
  23. 23.
    A.C. Fischer-Cripps, “Elastic recovery and reloading of hardness impressions with a conical indenter,” Mat. Res. Symp. Proc. 750, 2003, pp. Y6.9.1–Y6.9.6.Google Scholar
  24. 24.
    A.C. Fischer-Cripps, “Illustrative analysis of load-displacement curves in nanoindentation,” J. Mater. Res. 22 11, 2007, pp. 3075–3086.CrossRefGoogle Scholar
  25. 25.
    ISO 14577, “Metallic materials — Instrumented indentation test for hardness and materials parameters.” ISO Central Secretariat, 1 rue de Varembé, 1211 Geneva 20 Switzerland.Google Scholar
  26. 26.
    M.Kh. Shorshorov, S.I. Bulychev, and V.O. Alekhin, “Work of plastic and elastic deformation during indenter indentation,” Sov. Phys. Dokl. 26 8, 1981, pp. 769–771.Google Scholar
  27. 27.
    M. Sakai, “Energy principle of the indentation-induced inelastic surface deformation and hardness of brittle materials,” Acta. Metal. Mater. 41 6, 1993, pp. 1751–1758.CrossRefGoogle Scholar
  28. 28.
    J.B. Quinn and G.D. Quinn, “Indentation brittleness: a fresh approach,” J. Mat. Sci. 32, 1997, pp. 4331–4346.CrossRefMathSciNetGoogle Scholar
  29. 29.
    T.-Y. Zhang and W.-H. Xu, “Surface effects on nanoindentation,” J. Mater. Res. 17 7, 2002, pp. 1715–1720.CrossRefGoogle Scholar
  30. 30.
    Y.-T. Cheng, Z. Li, and C.-M. Cheng, “Scaling relationships for indentation measurements,” Phil. Mag. A 82, 2002, pp.1821–1829.CrossRefGoogle Scholar
  31. 31.
    K.K. Tho, S. Swaddiwudhipong, Z.S. Liu, K. Zeng, and J. Hua, “Uniqueness of reverse analysis from conical indentation tests,” J. Mater. Res. 19 8, 2004, pp. 2498–2502.CrossRefGoogle Scholar
  32. 32.
    W. Ni, Y.-T. Cheng, C.-M Cheng, and D.S. Grummon, “An energy-based method for analyzing instrumented spherical indentation experiments,” J. Mater. Res. 19 1, 2004, pp. 149–157.CrossRefGoogle Scholar
  33. 33.
    J. Alkorta, J.M. Martínez–Esnaola, and J. Gil Sevillano, “Comments on “Comment on the determination of mechanical properties from the energy dissipated during indentation” by J. Malzbender [J. Mater. Res. 20, 1090 (2005)],” J. Mater. Res. 21 1, 2006, pp. 302–306.CrossRefGoogle Scholar
  34. 34.
    Y.P. Cao, X.Q. Qian, J. Liu, Z.H. Yao, “An energy-based method to extract plastic properties of metal materials from conical indentation tests,” J.Mater.Res. 20 5, 2005, pp. 1194 – 1206.CrossRefGoogle Scholar
  35. 35.
    N. Ogasawara, N. Chiba, X. Chen, “Representative strain of indentation analysis,” J. Mater. Res. 20 8, 2005, pp. 2225 – 2234.CrossRefGoogle Scholar
  36. 36.
    D. Ma, T. Zhang, and C.W. Ong, “Revelation of a functional dependence of the sum of two uniaxial strengths/hardness on elastic work/total work of indentation,” J. Mater. Res., 21 4, 2006, pp. 895–903.CrossRefGoogle Scholar
  37. 37.
    B.N. Lucas, W.C. Oliver, and J.E. Swindeman, “The dynamics of frequency specific, depth sensing indentation testing,” Mat. Res. Soc. Symp. Proc. 522, 1998, pp. 3–14.CrossRefGoogle Scholar
  38. 38.
    D. Lorenz, W. Fränzel, M. Einax, P. Grau, and G. Berg, “Determination of the elastic properties of glasses and polymers exploiting the resonant characteristic of depth-sensing indentation tests,” J. Mater. Res. 16 6, 2001, pp. 1776–1783.CrossRefGoogle Scholar
  39. 39.
    D.L. Joslin and W.C. Oliver, “A new method for analyzing data from continuous depth-sensing microindentation tests,” J. Mater. Res. 5 1, 1990, pp. 123–126.CrossRefGoogle Scholar
  40. 40.
    S.V. Hainsworth, H.W. Chandler, and T.F. Page, “Analysis of nanoindentation load-displacement loading curves,” J. Mater. Res. 11 8, 1996, pp. 1987–1995.CrossRefGoogle Scholar
  41. 41.
    T.A. Venkatesh, K.J. Van Vliet, A.E. Giannakopolous, and S. Suresh, “Determination of elasto-plastic properties by instrumented sharp indentation: Guidelines for property extraction,” Scripta Mater. 42, 2000, pp. 833–839.CrossRefGoogle Scholar
  42. 42.
    E. Tyulyukovskiy and N. Huber, “Identification of viscoplastic material parameters from spherical indentation data: Part I. Neural networks,” J. Mater. Res. 21 3, 2006, pp. 664–676.CrossRefGoogle Scholar
  43. 43.
    D. Klötzer, Ch. Ullnera, E. Tyulyukovskiy and N. Huber, “Identification of viscoplastic material parameters from spherical indentation data: Part II. Experimental validation of the method,” J. Mater. Res. 21 3, 2006, pp. 677–684.CrossRefGoogle Scholar
  44. 44.
    W.W. Gerberich, W. Yu, D. Kramer, A. Strojny, D. Bahr, E. Lilleodden, and J. Nelson, “Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations,” J. Mater. Res. 13 2, 1998, pp. 421–439.CrossRefGoogle Scholar
  45. 45.
    T.F. Page, G.M. Pharr, J.C. Hay, W.C. Oliver, B.N. Lucas, E. Herbert, and L. Riester, “Nanoindentation characterization of coated systems: P:S2 – a new approach using the continuous stiffness technique,” Mat. Res. Symp. Proc. 522, 1998, pp. 53–64.CrossRefGoogle Scholar
  46. 46.
    D.S. Stone, “Elastic rebound between an indenter and a layered specimen: Part 1. Model,” J. Mater. Res. 13 11, 1998, pp. 3207–3213.CrossRefGoogle Scholar
  47. 47.
    K.B. Yoder, D.S. Stone, R.A. Hoffman, and J.C. Lin, “Elastic rebound between an indenter and a layered specimen: Part II. Using contact stiffness to help ensure reliability of nanoindentation measurements,” J. Mater. Res. 13 11, 1998, pp. 3214–3220.CrossRefGoogle Scholar
  48. 48.
    W.C. Oliver, “Alternative technique for analyzing instrumented indentation data,” J. Mater. Res. 16 11, 2001, pp. 3202–3206.CrossRefGoogle Scholar
  49. 49.
    J. Malzbender and G. de With, “Indentation load-displacement curve, plastic deformation, and energy,” J. Mater. Res. 17 2, 2002, pp. 502–511.CrossRefGoogle Scholar
  50. 50.
    M. Troyon and L. Huang, “Critical examination of the two-slope method in nanoindentation”, J. Mater. Res. 20 8, 2005, pp. 2194–2198.CrossRefGoogle Scholar
  51. 51.
    M. Sakai and Y, Nakano, “Elastoplastic load-depth hysteresis in pyramidal indentation,” J. Mater. Res. 17 8, 2002, pp. 2161–2173.CrossRefGoogle Scholar
  52. 52.
    K. Zeng and C.-h Chiu, “An analysis of load-penetration curves from instrumented indentation,” Acta Mater. 49, 2001, pp. 3539–3551.CrossRefGoogle Scholar
  53. 53.
    K. Zeng and L. Shen, “A new analysis of nanoindentation load-displacement curves,” Phil. Mag. A 82 10, 2002, pp. 2223–2229.CrossRefGoogle Scholar
  54. 54.
    N.X. Randall and C. Julia-Schmutz, “Evolution of contact area and pile-up during the nanoindentation of soft coatings on hard substrates,” Mat. Res. Symp. Proc. Vol. 522, 1998, pp. 21–26.CrossRefGoogle Scholar
  55. 55.
    N.X. Randall, “Direct measurement of residual contact area and volume during the nanoindentation of coated materials as an alternative method of calculating hardness,” Phil. Mag. A 82 10, 2002, pp. 1883–1892.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Fischer-Cripps Laboratories Pty Ltd.Killarney HeightsAustralia

Personalised recommendations