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Representative Strain of Indentation Analysis

Published online by Cambridge University Press:  01 August 2005

Nagahisa Ogasawara ,
Norimasa Chiba  and
Xi Chen
Nagahisa Ogasawara
Affiliation:
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027-6699; and Department of Mechanical Engineering, National Defense Academy, Hashirimizu, Yokosuka 239, Japan
Norimasa Chiba
Affiliation:
Department of Mechanical Engineering, National Defense Academy, Hashirimizu, Yokosuka 239, Japan
Xi Chen*
Affiliation:
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027-6699
*
a)Address all correspondence to this author. e-mail: xichen@civil.columbia.edu
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Abstract

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.

Keywords

HardnessIndentationMechanical properties
Type
Articles
Information
Journal of Materials Research , Volume 20 , Issue 8 , August 2005 , pp. 2225 - 2234
Copyright
Copyright © Materials Research Society 2005

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References

REFERENCES

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).CrossRefGoogle Scholar
2Doerner, F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
3Pharr, G.M.: Measurement of mechanical properties by ultra-low-load indentation. Mater. Sci. Eng. A 253, 151 (1998).CrossRefGoogle Scholar
4Pharr, G.M. and Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
6Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, U.K., 1985).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
8King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 (1987).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
10Fleck, N.A. and Hutchinson, J.W.: Strain gradient plasticity. Adv. Appl. Mech. 33, 295 (1997).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
12Cheng, Y.T. and Cheng, C.M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng R44, 91 (2004).CrossRefGoogle Scholar
13Mesarovic, S.D. and Fleck, N.A.: Spherical indentation of elastic-plastic solids. Proc. R. Soc. London A455, 2707 (1999).CrossRefGoogle Scholar
14Wang, L. and Rokhlin, S.I.: Universal scaling functions for continuous stiffness nanoindentation with sharp indenters. Int. J. Solids Struct. 42, 3807 (2005).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
16Atkins, A.G. and Tabor, D.: Plastic indentation in metals with cones. J. Mech. Phys. Solids 13, 149 (1965).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
20Lockett, F.J.: Indentation of a rigid/plastic material by a conical indenter. J. Mech. Phys. Solids 11, 345 (1963).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
23Chollacoop, N., Dao, M. and Suresh, S.: Depth-sensing instrumented indentation with dual sharp indenters. Acta Mater 51, 3713 (2003).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
25Ashby, M.F. and Jones, D.R.H.: Engineering Materials I (Butterworth Heinemann, Boston, MA, 1996).Google Scholar
26Ashby, M.F.: Material Selection in Mechanical Design (Butterworth Heinemann, Boston, MA, 1999).Google Scholar
27 ANSYS, Ansys Release 8.0 Documentation. (ANSYS Inc., Canonsburg, PA 2003).Google Scholar
28 ABAQUS, ABAQUS 6.4 User’s Manual. (ABAQUS Inc., Pawtucket, RI, 2004).Google Scholar
29Bowden, F.P. and Tabor, D., The Friction and Lubrications of Solids (Oxford University Press, Oxford, U.K., 1950).Google Scholar