Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-11T09:15:14.757Z Has data issue: false hasContentIssue false

Evaluating initial unloading stiffness from elastic work-of-indentation measured in a nanoindentation experiment

Published online by Cambridge University Press:  11 March 2013

Kaushal K. Jha
Affiliation:
Department of Civil and Environmental Engineering, Florida International University, Miami, Florida 33174
Nakin Suksawang*
Affiliation:
Department of Civil and Environmental Engineering, Florida International University, Miami, Florida 33174
Debrupa Lahiri
Affiliation:
Nanomechanics and Nanotribology Laboratory, Department of Mechanical and Materials Engineering, Florida International University, Miami, Florida 33174
Arvind Agarwal
Affiliation:
Nanomechanics and Nanotribology Laboratory, Department of Mechanical and Materials Engineering, Florida International University, Miami, Florida 33174
*
a)Address all correspondence to this author. e-mail: suksawan@fiu.edu
Get access

Abstract

Differentiation of the energy-based power function used to represent the nanoindentation unloading response at the peak indentation load generally overestimates the contact stiffness. This is mainly because of the larger curvature associated with this function and the proximity between the contact and maximum penetration depths. Using the nanoindentation data from ceramics and metals, we have shown that these two errors can be eliminated if the derivative is multiplied by the geometric and stiffness correction factors, respectively. The stiffness correction factor is found to be a function of the elastic energy constant and is independent of the peak indentation load. The contact stiffness evaluated by the proposed method is in excellent agreement with that obtained from the power law derivative for a wide range of elastoplastic materials and peak indentation loads. The relationship between the elastic recovery ratio and elastic energy constant developed in this study further simplifies the proposed procedure.

Type
Articles
Copyright
Copyright © Materials Research Society 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Pharr, G.M., Oliver, W.C., and Brotzen, F.R.: On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7, 613 (1992).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
Pharr, G.M. and Bolshakov, A.: Understanding nanoindentation loading curves. J. Mater. Res. 17, 2660 (2002).CrossRefGoogle Scholar
Marx, V. and Balke, H.: A critical investigation of the unloading behavior of sharp indentation. Acta Mater. 45, 3791 (1997).CrossRefGoogle Scholar
Sawa, T. and Tanaka, K.: Simplified method for analyzing nanoindentation data and evaluating performance of nanoindentation instruments. J. Mater. Res. 16, 3084 (2001).CrossRefGoogle Scholar
Gong, J., Miao, H., and Peng, Z.: Analysis of the nanoindentation data measured with a Berkovich indenter for brittle materials: Effect of the residual contact stress. Acta Mater. 52, 785 (2004).CrossRefGoogle Scholar
Giannakopoulos, A.E. and Suresh, S.: Determination of elastoplastic properties by instrumented sharp indentation. Scr. Mater. 40, 1191 (1999).CrossRefGoogle Scholar
Briscoe, B.J. and Sebastian, K.S.: The elastoplastic response of poly(methyl methacrylate) to indentation. Proc. R. Soc. London, Ser. A 452, 439 (1996).Google Scholar
Tranchida, D. and Piccarolo, S.: On the use of the nanoindentation unloading curve to measure Young’s modulus of polymers on nanometer scale. Macromol. Rapid Commun. 26, 1800 (2005).CrossRefGoogle Scholar
Jha, K.K., Suksawang, N., Lahiri, D., and Agarwal, A.: Energy-based analysis of nanoindentation curves for cementitious materials. ACI Mater. J. 109, 81 (2012).Google Scholar
VanLandingham, M.R., Villarrubia, J.S., Guthrie, W.F., and Meyers, G.F.: Nanoindentation of polymers: An overview. Macromol. Symp. 167, 15 (2001).3.0.CO;2-T>CrossRefGoogle Scholar
Sakai, M.: Energy principle of the indentation-induced inelastic surface deformation and hardness of brittle materials. Acta Metall. Mater. 41, 1751 (1993).CrossRefGoogle Scholar
Attaf, M.T.: New ceramics related investigation of the indentation energy concept. Mater. Lett. 57, 4684 (2003).CrossRefGoogle Scholar
Malzbender, J.: Comment on the determination of mechanical properties from the energy dissipated during indentation. J. Mater. Res. 20, 1090 (2005).CrossRefGoogle Scholar
Attaf, M.T.: A unified aspect of power-law correlations for Berkovich hardness testing of ceramics. Mater. Lett. 57, 4627 (2003).CrossRefGoogle Scholar
Attaf, M.T.: Step by step building of a model for the Berkovich indentation cycle. Mater. Lett. 58, 507 (2004).CrossRefGoogle Scholar
Attaf, M.T.: New formulation of the nanomechanical quantities using the β-material concept and the indentation function. Mater. Lett. 58, 889 (2004).CrossRefGoogle Scholar
Hainsworth, S.V., Chandler, H.W., and Page, T.F.: Analysis of nanoindentation load-displacement loading curves. J. Mater. Res. 11, 1987 (1996).CrossRefGoogle Scholar
Milman, Y.V.: Plasticity characteristic obtained by indentation. J. Phys. D: Appl. Phys. 41, 074013 (2008).CrossRefGoogle Scholar
Jha, K.K., Suksawang, N., and Agarwal, A.: Analytical approach for the determination of nanomechanical properties for metals, in MEMS and Nanotechnology, Vol. 4, edited by T. Proulx (Conference proceedings of the Society for Experimental Mechanics, Uncasville, CT, 2011).Google Scholar
Xiang, Z., Fenghui, W., Jianye, H., and Tiejun, L.: Determining the mechanical properties of solid oxide fuel cell by an improved work of indentation approach. J. Power Sources 201, 231 (2012).CrossRefGoogle Scholar
Lee, H., Ko, S., Han, J., Park, H., and Hwang, W.: Novel analysis for nanoindentation size effect using strain gradient plasticity. Scr. Mater. 53, 1135 (2005).CrossRefGoogle Scholar
Bakshi, S.R., Singh, V., Seal, S., and Agarwal, A.: Aluminum composite reinforced with multiwalled carbon nanotubes from plasma spraying of spray dried powders. Surf. Coat. Technol. 203, 1544 (2009).CrossRefGoogle Scholar
Jayaraman, S., Hahn, G.T., Oliver, W.C., Rubin, C.A., and Bastias, P.C.: Determination of monotonic stress-strain curve of hard materials from ultra-low-load indentation tests. Int. J. Solids Struct. 35, 365, (1998).CrossRefGoogle Scholar
Doerner, M.F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
Suresh, S. and Giannakopoulos, A.E.: A new method for estimating residual stresses by instrumented sharp indentation. Acta Mater. 46, 5755 (1998).CrossRefGoogle Scholar
Tuck, J.R., Korsunsky, A.M., Bull, S.J., and Davidson, R.I.: On the application of the work-of-indentation approach to depth-sensing indentation experiments in coated systems. Surf. Coat. Technol. 137, 217 (2001).CrossRefGoogle Scholar