On the Size Effect in Hardness by Nanoindentation Method


Article Preview

A model describing nanoindentation as plastic deformation resulting from a strain gradient is investigated. Using a simplified axisymmetric nanoindentation, the effective strain gradient for indentation depth is derived. The proposed indentation model is a modification of Nix and Gao’s model (1998) . To validate this approach for nanoindentation, solutions for depth-dependent hardness of single various materials such as Cu, Al, Ni are compared with experiments. Results show that the proposed model agrees well with the hardness experiments.



Key Engineering Materials (Volumes 306-308)

Edited by:

Ichsan Setya Putra and Djoko Suharto




H. K. Lee et al., "On the Size Effect in Hardness by Nanoindentation Method", Key Engineering Materials, Vols. 306-308, pp. 911-916, 2006

Online since:

March 2006




[1] Nix, W. D.: Metall. Trans , Vol. 20A (1989), p.2217.

[2] De Guzman, M. S., Newbauer, G.: Mater. Res. Sym. Proc. Vol. 308 (1993), p.613.

[3] Stelmashenko, N. A., Walls, M. G., Brown, L. M., Milman, Y. V.: Acta Materialia Vol. 41 (1993), p.2855.

[4] Ma, Q., Clarke, D. R.: J. Materials Research Vol 10 (1995), p.853.

[5] McElhaney, K. W., Vlassak, J. J. and Nix, W. D.: J. Mater. Res. Vol. 13 (1997), p.1300.

[6] Fleck, N. A., Muller, G. M., Ashby, M. F., Hutchinson, J. W.: Acta Metallurigica et Materialia Vol. 42 (1994), p.475.

[7] Stolken, J. S., Evans, A. G.: Acta Materialia Vol. 46 (1998), p.509.

[8] Elssner, G., Korn, D., Ruehle. M.: Scripta Metall. Mater. Vol. 31 (1994), p.1037.

[9] Fleck, N. A., Hutchinson, J. W.: Advances in applied mechanics Vol. 33 (1997), p.295.

[10] Gao, H., Huang, Y., Nix, W. D., Hutchinson, J. W.: J. Mech. Phys. Solids Vol. 47 (1999), p.1239.

[11] Gao, H., Huang, Y., Nix, W. D., Hutchinson, J. W.:J. Mech. Phys. Solids Vol. 48 (2000), p.99.

[12] Zhao, M., Slaughter, W. S., Li, M., Mao, S. X.: Acta Materialia Vol. 51 (2003), p.4461.

[13] Kriese M, Robach J, Nelson J, Wright A, Bahr D, Kramer D et al.: Acta Materialia. Vol. 7 (1999), p.333.

[14] Grunran JC, Gerberich WW, Tymiak NI, Kramer DE, Gerberich WW.: J. Appl. Mech Vol. 69 (2002), p.433.

[15] Nix, W. D., Gao, H.: J. Mech. Phys. Solids Vol. 46 (1998), p.411.

[16] Meyers MA, Chawla KK: Mechanical behavior of materials (Prentice-Hall 1999).

Fetching data from Crossref.
This may take some time to load.