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Inverse scaling functions in nanoindentation with sharp indenters: Determination of material properties

Published online by Cambridge University Press:  01 April 2005

Lugen Wang ,
M. Ganor  and
S.I. Rokhlin
Lugen Wang
Affiliation:
Laboratory for Multiscale Materials Processing and Characterization, Edison Joining Technology Center, The Ohio State University, Columbus, Ohio 43221
M. Ganor
Affiliation:
Laboratory for Multiscale Materials Processing and Characterization, Edison Joining Technology Center, The Ohio State University, Columbus, Ohio 43221
S.I. Rokhlin*
Affiliation:
Laboratory for Multiscale Materials Processing and Characterization, Edison Joining Technology Center, The Ohio State University, Columbus, Ohio 43221
*
a) Address all correspondence to this author. e-mail: [email protected]
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Abstract

This paper, based on extensive finite element simulations and scaling analysis, presents scaling functions for the inverse problem in nanoindentation with sharp indenters to determine material properties from nanoindentation response. All the inverse scaling functions were directly compared with results calculated using the large deformation finite element method and are valid from the elastic to the full plastic regimes. To relate the material properties to measurable indentation parameters a new nondimensional experimental parameter Λ=P/(DS) was introduced, where P is load, D is indentation depth, and S is contact stiffness. This parameter is monotonically related to the ratio of yield stress to modulus. The modulus, hardness and yield stress are presented as explicit functions of Λ and the strain hardening exponent. The error in the inverse modulus, hardness, and yield stress due to uncertainty of the strain hardening exponent was studied and is compared with that of the traditional Oliver–Pharr method. The method of determining the strain hardening exponent from measurement with an additional indenter with a different cone apex angle is described. For this, a scaling function with the strain hardening exponent as the only unknown was obtained. In this way, the modulus, hardness, yield stress and strain hardening exponent may be determined. Experimental results show the inversion method permits the modulus and hardness to be accurately determined irrespective of the effects of pileup or sink-in.

Keywords

Elastic propertiesHardnessNanoindentation
Type
Research Article
Information
Journal of Materials Research , Volume 20 , Issue 4 , April 2005 , pp. 987 - 1001
Copyright
Copyright © Materials Research Society 2005

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References

REFERENCES

1. Doerner, M.F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).10.1557/JMR.1986.0601CrossRefGoogle Scholar
2. Oliver, 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).10.1557/JMR.1992.1564CrossRefGoogle Scholar
3. Oliver, W.C. and Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).10.1557/jmr.2004.19.1.3CrossRefGoogle Scholar
4. Fischer-Cripps, A.C.: Nanoindentation (Mechanical Engineering Series, Springer-Verlag, New York, NY, 2002).CrossRefGoogle Scholar
5. Tabor, D.: Indentation hardness: Fifty years on—A personal view. Philos. Mag. A 74, 1207 (1996).CrossRefGoogle Scholar
6. Bhattacharya, A.K. and Nix, W.D.: Finite element simulation of indentation experiments. Int. J. Solids Struct. 24, 881 (1988).CrossRefGoogle Scholar
7. Dao, M., Chollacoop, N., Van Vliet, 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
8. Bolshakov, A. and Pharr, G.M.: Influences of pileup on the measurement of mechanical properties by load and depth-sensing indentation techniques. J. Mater. Res. 13, 1049 (1998).10.1557/JMR.1998.0146CrossRefGoogle Scholar
9. Knapp, J.A., Follstaedt, D.M., Myers, S.M., Barbour, J.C. and Friedmann, T.A.: Finite-element modeling of nanoindentation. J. Appl. Phys. 85, 1460 (1999).10.1063/1.369178CrossRefGoogle Scholar
10. Sakai, M., Akatsu, T. and Numata, S.: Finite element analysis for conical indentation unloading of elastic plastic materials with strain hardening. Acta Mater. 52, 2359 (2004).CrossRefGoogle Scholar
11. Mata, M., Anglada, M. and Alcala, J.: Contact deformation regimes around sharp indentations and the concept of the characteristic strain. J. Mater. Res. 17, 964 (2002).CrossRefGoogle Scholar
12. Cheng, Y.T. and Cheng, C.M.: Scaling approach to conical indentation in elastic-plastic solids with work hardening. J. Appl. Phys. 84, 1284 (1998).10.1063/1.368196CrossRefGoogle Scholar
13. Cheng, C.M. and Cheng, Y.T.: Can stress-strain relationships be obtained from indentation curves using conical and pyramidal indenters? J. Mater. Res. 14, 3493 (1999).10.1557/JMR.1999.0472CrossRefGoogle Scholar
14. Cheng, Y.T. and Cheng, C.M.: What is indentation hardness? Surf. Coat. Technol. 133, 417 (2000).10.1016/S0257-8972(00)00896-3CrossRefGoogle Scholar
15. Cheng, Y.T., Li, Z. and Cheng, C.M.: Scaling relationships for indentation measurements. Philos. Mag. A 82, 1821 (2002).10.1080/01418610208235693CrossRefGoogle Scholar
16. Cheng, Y.T. and Cheng, C.M.: Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73, 614 (1998).10.1063/1.121873CrossRefGoogle Scholar
17. Wang, L. and Rokhlin, S.I.: Universal scaling functions for continuous stiffness nanoindentation with sharp indenters. J. Solids Struct. 42, 3807 (2005).10.1016/j.ijsolstr.2004.11.012CrossRefGoogle Scholar
18. Sneddon, I.N.: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).10.1016/0020-7225(65)90019-4CrossRefGoogle Scholar
19. Constantinescu, A. and Tardieu, N.: On the identification of elastoviscoplastic constitutive laws from indentation tests. Inverse Problems Eng. 9, 19 (2001).10.1080/174159701088027751CrossRefGoogle Scholar
20. Mata, M. and Alcalá, J.: Mechanical properties evaluation through indentation experiments in elasto-plastic and fully plastic contact regimes. J. Mater. Res. 18, 1705 (2003).10.1557/JMR.2003.0234CrossRefGoogle Scholar
21. Xu, Z.H. and Rowcliffe, D.: Method to determine the plastic properties of bulk materials by nanoindentation. Philos. Mag. A 82, 1893 (2002).CrossRefGoogle Scholar
22. Bucaille, 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).10.1016/S1359-6454(02)00568-2CrossRefGoogle Scholar
23. Chollacoop, N., Dao, M. and Suresh, S.: Depth-sensing instrumented indentation with dual sharp indenters. Acta Mater. 51, 3713 (2003).CrossRefGoogle Scholar
24. Ma, D., Ong, C.W. and Wong, S.F.: New relationship between Young’s modulus and nonideally sharp indentation parameters. J. Mater. Res. 19, 2144 (2004).CrossRefGoogle Scholar
25. Nix, W.D. and Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411 (1998).10.1016/S0022-5096(97)00086-0CrossRefGoogle Scholar
26. Qu, S., Huang, Y., Nix, W.D., Jiang, H., Zhang, F. and Hwang, K.C.: Indenter tip radius effect on the Nix-Gao relation in micro- and nanoindentation hardness experiments. J. Mater. Res. 19, 3423 (2004).10.1557/JMR.2004.0441CrossRefGoogle Scholar
27. Stone, D.S.: Elastic rebound between an indenter and a layered specimen: Part I. Model. J. Mater. Res. 13, 3207 (1998).10.1557/JMR.1998.0435CrossRefGoogle Scholar
28. Joslin, D.L. and Oliver, W.C.: A new method for analyzing data from continuous depth-sensing microindentation tests. J. Mater. Res. 5, 123 (1990).CrossRefGoogle Scholar
29. Hay, J.C., Bolshakov, A. and Phar, G.M.: A critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 (1999).CrossRefGoogle Scholar
30. Cheng, C.M. and Cheng, Y.T.: On the initial unloading slope in indentation of elastic-plastic solids by an indenter with an axisymmetric smooth profile. Appl. Phys. Lett. 71, 2623 (1997).10.1063/1.120159CrossRefGoogle Scholar
31. Dennis, J.E. and Schnabel, R.B.: Numerical Methods for Uncontrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, NJ, 1983).Google Scholar