Abstract
This paper quantitatively describes the loading-unloading response in nanoindentation with sharp indenters using scaling analyses and finite element simulations. Explicit forward and inverse scaling functions for an indentation unloading have been obtained and related to those functions for the loading response [L. Wang et al., J. Material Res. 20(4), 987–1001 (2005)]. The scaling functions have been obtained by fitting the large deformation finite element simulations and are valid from the elastic to the full plastic indentation regimes. Using the explicit forward functions for loading and unloading, full indentation responses for a wide range of materials can be obtained without use of finite element calculations. The corresponding inverse scaling functions allow one to obtain material properties from the indentation measurements. The relation between the work of indentation and the ratio between hardness and modulus has also been studied. Using these scaling functions, the issue of nonuniqueness of the determination of material modulus, yield stress, and strain-hardening exponent from nanoindentation measurements with a single sharp indenter has been further investigated. It is shown that a limited material parameter range in the elastoplastic regime can be defined where the material modulus, yield stress, and strain-hardening exponent may be determined from only one full indentation response. The error of such property determination from scattering in experimental measurements is determined.
Similar content being viewed by others
References
M.F. Doerner, W.D. Nix: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).
W.C. Oliver, G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).
W.C. Oliver, G.M. Pharr: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).
Fischer-A.C. Cripps: Nanoindentation, Mechanical Engineering Series (Springer-Verlag, Berlin, 2002).
D. Tabor: Indentation hardness: Fifty years on—a personal view. Philos. Mag. A 74, 1207 (1996).
A.K. Bhattacharya, W.D. Nix: Finite element simulation of indentation experiments. Int. J. Solids Struct. 24, 881 (1988).
M. Dao, N. Chollacoop, Van K.J. Vliet, T.A. Venkatesh, S. Suresh: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).
A. Bolshakov, G.M. Pharr: Influences of pileup on the measurement of mechanical properties by load and depth-sensing indentation techniques. J. Mater. Res. 13, 1049 (1998).
J.A. Knapp, D.M. Follstaedt, S.M. Myers, J.C. Barbour, T.A. Friedmann: Finite-element modeling of nanoindentation. J. Appl. Phys. 85, 1460 (1999).
M. Sakai, T. Akatsu, S. Numata: Finite element analysis for conical indentation unloading of elastic plastic materials with strain hardening. Acta Mater. 52, 2359 (2004).
M. Mata, M. Anglada, J. Alcala: Contact deformation regimes around sharp indentations and the concept of the characteristic strain. J. Mater. Res. 17, 964 (2002).
Y.T. Cheng, C.M. Cheng: Scaling approach to conical indentation in elastic-plastic solids with work hardening. J. Appl. Phys. 84, 1284 (1998).
C.M. Cheng, Y.T. Cheng: Can stress-strain relationships be obtained from indentation curves using conical and pyramidal indenters? J. Mater. Res. 14, 3493 (1999).
Y.T. Cheng, C.M. Cheng: What is indentation hardness? Surf. Coat. Technol. 133, 417 (2000).
Y.T. Cheng, Z. Li, C.M. Cheng: Scaling relationships for indentation measurements. Philos. Mag. A 82, 1821 (2002).
L. Wang, S.I. Rokhlin: Universal scaling functions for continuous stiffness nanoindentation with sharp indenters. Int. J. Solids Struct. 42, 3807 (2005).
L. Wang, M. Ganor, S.I. Rokhlin: Inverse scaling functions in nanoindentation with sharp indenters: Determination of material properties. J. Mater. Res. 20, 987 (2005).
M. Mata, J. Alcalá: Mechanical properties evaluation through indentation experiments in elasto-plastic and fully plastic contact regimes. J. Mater. Res. 18, 1705 (2003).
Z.H. Xu, D. Rowcliffe: Method to determine the plastic properties of bulk materials by nanoindentation. Philos. Mag. A 82, 1893 (2002).
J.L. Bucaille, S. Stauss, E. Felder, J. Michler: Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater. 51, 1663 (2003).
N. Chollacoop, M. Dao, S. Suresh: Depth-sensing instrumented indentation with dual sharp indenters. Acta Mater. 51, 3713 (2003).
K.K. Tho, S. Swaddiwudhipond, Z.S. Liu, S. Hua: Uniqueness of reverse analysis from conical indentation tests. J. Mater. Res. 19, 2498 (2004).
K.K. Tho, S. Swaddiwudhipond, Z.S. Liu, K. Zeng: Simulation of instrumented indentation and material characterization. Mater. Sci. Eng. A 390(2005), 202–209.
J. Alkorta, J.M. Martinez-Esnaola, J.G. Sevillano: Absence of one-to-one correspondence between elastoplastic properties and sharp-indentation load-penetration data. J. Mater. Res. 20, 432 (2005).
O. Casals, J. Alcalá: The duality in mechanical property extraction from Vickers and Berkovich instrumented indentation experiments. Acta Mater. 53, 3545 (2005).
D.L. Joslin, W.C. Oliver: A new method for analyzing data from continuous depth-sensing microindentation tests. J. Mater. Res. 5, 123 (1990).
L. Wang, M. Ganor, S.I. Rokhlin, A. Grill: Mechanical properties of ultra-low dielectric constant SiCOH films: Nanoindentation measurements. J. Mater. Res. 20(8), 2080 (2005).
G.M. Pharr, A. Bolshakov: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, L., Rokhlin, S.I. On determination of material parameters from loading and unloading responses in nanoindentation with a single sharp indenter. Journal of Materials Research 21, 995–1011 (2006). https://doi.org/10.1557/jmr.2006.0130
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/jmr.2006.0130