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The Influence of Indenter Tip Imperfection and Deformability on Analysing Instrumented Indentation Tests at Shallow Depths of Penetration on Stiff and Hard Materials

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We report on the difficulties of extracting plastic parameters from constitutive equations derived by instrumented indentation tests on hard and stiff materials at shallow depths of penetration. As a general rule, we refer here to materials with an elastic stiffness more than 10 % of that of the indenter and a yield strain higher than 1 %, as well as to penetration depths less than ∼ 5 times the characteristic tip defect length of the indenter. We experimentally tested such a material (an amorphous alloy) by nanoindentation. To describe the mechanical response of the test, namely the force-displacement curve, it is necessary to consider the combined effects of indenter tip imperfections and indenter deformability. For this purpose, an identification procedure has been carried out by performing numerical simulations (using Finite Element Analysis) with constitutive equations that are known to satisfactorily describe the behaviour of the tested material. We propose a straightforward procedure to address indenter tip imperfection and deformability, which consists of firstly taking account of a deformable indenter in the numerical simulations. This procedure also involves modifying the experimental curve by considering a truncated length to create artificially the material’s response to a perfectly sharp indentation. The truncated length is determined directly from the loading part of the force-displacement curve. We also show that ignoring one or both of these issues results in large errors in the plastic parameters extracted from the data.

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Fig. 5
Fig. 6


E :

Young’s modulus

ν :

Poisson’s ratio

Y c :

Compressive yield strength

\({\epsilon _{y}^{c}}\) :

Compressive yield strain

φ :

Friction angle (Drucker-Prager yield criterion)

P :

Indentation force

δ :

Indentation depth

C :

Indentation loading pre-factor

Δδ :

Indenter truncated length

R :

Indenter tip radius

β :

Indenter equivalent complementary angle

\(\mathcal {L}\) :

Residual of the identification procedure


  1. 1.

    Fischer-Cripps AC (2006) Introduction to Contact MEchanics. Mechanical Engineering Series, Berlin Heidelberg: Springer Berlin Heidelberg

  2. 2.

    Oliver W, Pharr G (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583

  3. 3.

    Andrade-Campos A, Thuillier S, Pilvin P, Teixeira-Dias F (2007) On the determination of material parameters for internal variable thermoelastic-viscoplastic constitutive models. Int J Plast 23(8):1349–1379

  4. 4.

    Fischer-Cripps AC (2011) Nanoindentation. Springer, Berlin, Heidelberg

  5. 5.

    Giannakopoulos A, Suresh S (1999) Determination of elastoplastic properties by instrumented sharp indentation, vol 40

  6. 6.

    Dao M, Chollacoop N, Van Vliet KJ, Venkatesh TA, Suresh S (2001) Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater 49(19):3899–3918

  7. 7.

    Casals O, Alcalá J (2005) The duality in mechanical property extractions from Vickers and Berkovich instrumented indentation experiments. Acta Mater 53:3545–3561

  8. 8.

    Lee J, Lee C, Kim B (2009) Reverse analysis of nano-indentation using different representative strains and residual indentation profiles. Mater Des 30:3395–3404

  9. 9.

    Warren AW, Guo YB (2006) Machined surface properties determined by nanoindentation: Experimental and FEA studies on the effects of surface integrity and tip geometry. Surf Coatings Technol 201(1-2):423–433

  10. 10.

    Oliver W, Pharr G (2004) Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology, vol 19

  11. 11.

    Hochstetter G, Jimenez A, Loubet J (2006) Strain-rate effects on hardness of glassy polymers in the nanoscale range. Comparison between quasi-static and continuous stiffness measurements. J Macromol Sci part B 38(5-6):681– 692

  12. 12.

    Poon B, Rittel D, Ravichandran G (2008) An analysis of nanoindentation in elasto-plastic solids. Int J Solids Struct 45:6399– 6415

  13. 13.

    Poon B, Rittel D, Ravichandran G (2008) An analysis of nanoindentation in linearly elastic solids. Int J Solids Struct 45(24):6018–6033

  14. 14.

    Wang TH, Fang TH, Lin YC (2007) A numerical study of factors affecting the characterization of nanoindentation on silicon. Mater Sci Eng A 447(1-2):244–253

  15. 15.

    Keryvin V, Vu X, Hoang V, Shen J (2010) On the deformation morphology of bulk metallic glasses underneath a Vickers indentation. J Alloys Compd 504:S41–S44

  16. 16.

    Keryvin V (2008) Indentation as a probe for pressure sensitivity of metallic glasses. J Phys Condens Matter 20:114119

  17. 17.

    Shen J, Chen Q, Sun J, Fan H, Wang G (2005) Exceptionally high glass-forming ability of an FeCoCrMoCBY alloy. Appl Phys Lett 86(15):151907

  18. 18.

    Keryvin V, Hoang VH, Shen J (2009) Hardness, toughness, brittleness and cracking systems of an iron-based bulk metallic glass by indentation. Intermetallics 17(4):211–217

  19. 19.

    VanLandingham MR, Juliano TF, Hagon MJ (2005) Measuring tip shape for instrumented indentation using atomic force microscopy. Meas Sci Technol 16(11):2173–2185

  20. 20.

    Charleux L, Keryvin V, Bizet L (2015) abapy: Abapy_v1.0

  21. 21.

    Chen W-F, Han D-J (2007) Plasticity for Structural Engineers. J. Ross Publishing Classics, Florida, USA

  22. 22.

    Donovan PE (1989) Plastic flow and fracture of Pd40Ni40P20 metallic glass under an indentor. J Mater Sci 24:523–535

  23. 23.

    Patnaik MNM, Narasimhan R, Ramamurty U (2004) Spherical indentation response of metallic glasses. Acta Mater 52(11):3335–3345

  24. 24.

    Keryvin V, Crosnier R, Laniel R, Hoang VH, Sangleboeuf J-C (2008) Indentation and scratching mechanisms of a ZrCuAlNi bulk metallic glass. J Phys D Appl Phys 41:074029

  25. 25.

    Brest J, Keryvin V, Longére P, Yokoyama Y (2014) Insight into plasticity mechanisms in metallic glasses by means of a Brazilian test and numerical simulation. J Alloys Compd 586:S236–S241

  26. 26.

    Cheng YT, Cheng CM (2004) Scaling, dimensional analysis, and indentation measurements. Mater Sci Eng R Reports 44(4-5):91–150

  27. 27.

    Tabor D (1956) The physical meaning of indentation and scratch hardness. Br J Appl Phys 7(5):159

  28. 28.

    Qu RT, Liu ZQ, Wang RF, Zhang ZF (2015) Yield strength and yield strain of metallic glasses and their correlations with glass transition temperature. J Alloys Compd 637:44–54

  29. 29.

    Keryvin V, Eswar Prasad K, Gueguen Y, Sanglebæuf J-C, Ramamurty U (2008) Temperature dependence of mechanical properties and pressure sensitivity in metallic glasses below glass transition. Philos Mag 88:1773–1790

  30. 30.

    Gadelrab K, Bonilla F, Chiesa M (2012) Densification modeling of fused silica under nanoindentation. J Non Cryst Solids 358:392–398

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We acknowledge financial support from the State-Region Plan Contract PRIN2TAN programme for acquisition of the Hysitron nanoindentation apparatus. We would like to thank Prof. Jun Shen (Harbin Institute of Technology, China) for providing the samples, Dr. J.-P. Guin (CNRS, France) for the AFM measurements and Prof. P. Pilvin for advice on the identification procedure. Dr M.S.N. Carpenter post-edited the English style and grammar.

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Correspondence to V. Keryvin.

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Keryvin, V., Charleux, L., Bernard, C. et al. The Influence of Indenter Tip Imperfection and Deformability on Analysing Instrumented Indentation Tests at Shallow Depths of Penetration on Stiff and Hard Materials. Exp Mech 57, 1107–1113 (2017). https://doi.org/10.1007/s11340-017-0267-1

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  • Nanoindentation
  • Indenter deformability
  • Tip defect
  • Hard material
  • Stiff Material