Acta Mechanica Sinica

, Volume 20, Issue 4, pp 383–392 | Cite as

Nanoindentation of thin-film-substrate system: Determination of film hardness and Young's modulus

  • Chen Shaohua
  • Liu Lei
  • Wang Tzuchiang


In the present paper, the hardness and Young's modulus of film-substrate systems are determined by means of nanoindentation experiments and modified models. Aluminum film and two kinds of substrates, i.e. glass and silicon, are studied. Nanoindentation XP II and continuous stiffness mode are used during the experiments. In order to avoid the influence of the Oliver and Pharr method used in the experiments, the experiment data are analyzed with the constant Young's modulus assumption and the equal hardness assumption. The volume fraction model (CZ model) proposed by Fabes et al. (1992) is used and modified to analyze the measured hardness. The method proposed by Doerner and Nix (DN formula) (1986) is modified to analyze the measured Young's modulus. Two kinds of modified empirical formula are used to predict the present experiment results and those in the literature, which include the results of two kinds of systems, i.e., a soft film on a hard substrate and a hard film on a soft substrate. In the modified CZ model, the indentation influence angle, φ, is considered as a relevant physical parameter, which embodies the effects of the indenter tip radius, pile-up or sink-in phenomena and deformation of film and substrate.

Key Words

nanoindentation hardness Young's modulus film-substrate system 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Burnett PJ, Rickerby DS. The mechanical properties of wear-resistant coatings. II: Experimental studies and interpretation of hardness.Thin Solid Films, 1987, 148: 51–65CrossRefGoogle Scholar
  2. 2.
    Burnett PJ, Rickerby DS. The mechanical properties of wear-resistant coatings I: Modelling of hardness behaviour.Thin Solid Films, 1987, 148: 41–50CrossRefGoogle Scholar
  3. 3.
    Bhattacharya AK, Nix WD. Finite element simulation of indentation experiment.Int J Solids Struct, 1988, 24: 881–891CrossRefGoogle Scholar
  4. 4.
    Laursen TA, Simo JC. A study of the mechanics of microindentation using finite elements.J Mater Res, 1992, 7: 618–626Google Scholar
  5. 5.
    Jonsson B, Hogmark S. Hardness measurements of thin films.Thin Solid Films 1984, 114: 257–269CrossRefGoogle Scholar
  6. 6.
    Burnett PJ, Page TF. Surface softening in silicon by ion implantation.J Mater Sci, 1984, 19: 845–860CrossRefGoogle Scholar
  7. 7.
    Fabes BD, Oliver WC, McKee RA, et al. The determination of hardness from the composite response of film and substrate to nanometer scale indentation.J Mater Res, 1992, 7: 3056–3064Google Scholar
  8. 8.
    Chechenin N, Bottiger GJ, Krog JP. Nanoindentation of amorphous aluminum oxide films II. Critical parameters for the breakthrough and a membrane effect in thin hard films on soft substrates.Thin Solid Films, 1995, 261: 227–235Google Scholar
  9. 9.
    Gao H, Cheng-Hsin C, Jin L. Elastic contact versus indentation modeling of multi-layered materials.Int J Solids Struct, 1992, 29: 2471–2492CrossRefGoogle Scholar
  10. 10.
    Doerner MF, Nix WD. A method for interpreting the data from depth-sensing indentation instruments,J Mater Res, 1986, 1: 601–609Google Scholar
  11. 11.
    King RB. Elastic analysis of some punch problems for a layered medium.Int J Solids Struct, 1987, 23: 1657–1664zbMATHCrossRefGoogle Scholar
  12. 12.
    Schweitz JA. Mechanical characterization of thin films by micromechanical techniques.MRS Bulletin, 1992, 17: 33–45Google Scholar
  13. 13.
    Pharr GM, Oliver WC. Measurement of thin film mechanical properties using nanoindentation.MRS Bulletin, 1992, 17: 28–33Google Scholar
  14. 14.
    Field JS, Swain MV. A simple predictive model for spherical indentation.J Mater Res, 1993, 8: 297–306Google Scholar
  15. 15.
    Oliver WC, Pharr GM. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiment.J Mater Res, 1992, 7: 1564–1583Google Scholar
  16. 16.
    Joslin DL, Oliver WC. A new method for analyzing data from continuous depth-sensing microindentation test.J Mater Res, 1990, 5: 123–126Google Scholar
  17. 17.
    Saha R, Nix WD. Effects of the substrate on the determination of thin film mechanical properties by nanoindentation.Acta Mater, 2002, 50: 23–38CrossRefGoogle Scholar
  18. 18.
    Jager IL. Comment on: “Effects of the substrate on the determination of thin films mechanical properties by nanoindentation”.Scripta Mater, 2002, 47: 429–432CrossRefGoogle Scholar
  19. 19.
    Saha R, Xue Z, Huang Y, et al. Indentation of a soft metal film on a hard substrate: strain gradient hardening effects.J Mech Phys Solids, 2001, 49: 1997–2014zbMATHCrossRefGoogle Scholar
  20. 20.
    Chen SH, Liu L, Wang TC. Size dependent nanoindentation of a soft film on a hard substrate.Acta Mater, 2004, 52: 1089–1095MathSciNetCrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2004

Authors and Affiliations

  • Chen Shaohua
    • 1
  • Liu Lei
    • 1
  • Wang Tzuchiang
    • 1
  1. 1.LNM, Institute of MechanicsChinese Academy of SciencesBeijingChina

Personalised recommendations