Skip to main content Accesibility Help

Representative Strain of Indentation Analysis

  • Nagahisa Ogasawara (a1), Norimasa Chiba (a2) and Xi Chen (a3)

Indentation analysis based on the concept of representative strain offers an effective way of obtaining mechanical properties, especially work-hardening behavior of metals, from reverse analysis of indentation load–displacement data, and does not require measuring of the projected contact area. The definition of representative strain adopted in previous studies [e.g., Dao et al., Acta Mater.49, 3899 (2001)] has a weak physical basis, and it works only for a limited range in some sense of engineering materials. A new indentation stress-state based formulation of representation is proposed in this study, which is defined as the plastic strain during equi-biaxial loading. Extensive numerical analysis based on the finite element method has shown that with the new formulation of representative strain and representative stress, the critical normalized relationship between load and material parameters is essentially independent of the work-hardening exponent for all engineering materials, and the results also hold for three distinct indenter angles. The new technique is used for four materials with mechanical properties outside the applicable regime of previous studies, and the reverse analysis has validated the present analysis. The new formulation based on indentation stress-state based definition of representative strain has the potential to quickly and effectively measure the mechanical properties of essentially all engineering materials as long as their constitutive behavior can be approximated into a power-law form.

Corresponding author
a)Address all correspondence to this author. e-mail:
Hide All
1Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).
2Doerner, F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).
3Pharr, G.M.: Measurement of mechanical properties by ultra-low-load indentation. Mater. Sci. Eng. A 253, 151 (1998).
4Pharr, G.M. and Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002).
5Vlassak, J.J. and Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42, 1223 (1994).
6Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, U.K., 1985).
7Chen, X. and Vlassak, J.J.: Numerical study on the measurement of thin film mechanical properties by means of nanoindentation. J. Mater. Res. 16, 2974 (2001).
8King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 (1987).
9Hay, J.C., Bolshakov, A. and Pharr, G.M.: A critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 (1999).
10Fleck, N.A. and Hutchinson, J.W.: Strain gradient plasticity. Adv. Appl. Mech. 33, 295 (1997).
11Cheng, Y.T. and Cheng, C.M.: Scaling approach to conical indentation in elastic-plastic solids with work hardening. J. Appl. Phys. 84, 1284 (1998).
12Cheng, Y.T. and Cheng, C.M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng R44, 91 (2004).
13Mesarovic, S.D. and Fleck, N.A.: Spherical indentation of elastic-plastic solids. Proc. R. Soc. London A455, 2707 (1999).
14Wang, L. and Rokhlin, S.I.: Universal scaling functions for continuous stiffness nanoindentation with sharp indenters. Int. J. Solids Struct. 42, 3807 (2005).
15Wang, L., Ganor, M. and Rokhlin, S.I.: Inverse scaling function in nanoindentation with sharp indenters: Determination of material properties. J. Mater. Res. 20, 987 (2005).
16Atkins, A.G. and Tabor, D.: Plastic indentation in metals with cones. J. Mech. Phys. Solids 13, 149 (1965).
17Dao, M., Chollacoop, N., VanVliet, K.J., Venkatesh, T.A. and Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).
18Ogasawara, N., Makiguchi, W. and Chiba, N.: Plastic properties determination method using triangular pyramid indenters based on elastic solution and rigid/perfectly plastic solution. Trans. Jpn. Soc. Mech. Eng (2005, in press).
19Sneddon, I.N.: The relationship between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).
20Lockett, F.J.: Indentation of a rigid/plastic material by a conical indenter. J. Mech. Phys. Solids 11, 345 (1963).
21Ogasawara, N., Makiguchi, W. and Chiba, N.: Plastic properties determination method for power-law hardening material using plural triangular pyramid indenters. Trans. Jpn. Soc. Mech. Eng 70, 1529 (2004).
22Bucaille, J.L., Stauss, S., Felder, E. and Michler, J.: Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater. 51, 1663 (2003).
23Chollacoop, N., Dao, M. and Suresh, S.: Depth-sensing instrumented indentation with dual sharp indenters. Acta Mater 51, 3713 (2003).
24Cao, Y.P. and Lu, J.: A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve. Acta Mater. 52, 4023 (2004).
25Ashby, M.F. and Jones, D.R.H.: Engineering Materials I (Butterworth Heinemann, Boston, MA, 1996).
26Ashby, M.F.: Material Selection in Mechanical Design (Butterworth Heinemann, Boston, MA, 1999).
27 ANSYS, Ansys Release 8.0 Documentation. (ANSYS Inc., Canonsburg, PA 2003).
28 ABAQUS, ABAQUS 6.4 User’s Manual. (ABAQUS Inc., Pawtucket, RI, 2004).
29Bowden, F.P. and Tabor, D., The Friction and Lubrications of Solids (Oxford University Press, Oxford, U.K., 1950).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
  • URL: /core/journals/journal-of-materials-research
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed