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Licensed Unlicensed Requires Authentication Published by De Gruyter January 8, 2022

Continuous FEM simulation of the nanoindentation

Actual indenter tip geometries, material elastoplastic deformation laws and universal hardness

K.-D. Bouzakis, N. Michailidis, S. Hadjiyiannis, G. Skordaris and G. Erkens


The precise knowledge of materials mechanical properties is always a core issue in every technical application. Through a developed finite elements method (FEM) continuous simulation of the nanoindentation, the applied force course versus the penetration depth is adequately simulated during the loading and unloading phases of this test, and the corresponding material stress – strain curves, as well as the universal hardness, are stepwise defined. Furthermore, the actual tip geometries of various indenters are approached and through equivalent magnitudes described. The results show that the defined material elastoplastic deformation characteristics are independent of the indenter type, as Vickers or Berkovich, since the existing indenter tip form deviations from their ideal geometry are considered. Furthermore, using the developed FEM-based nanoindentation simulation, the influence of the indenter tip geometry on the defined constitutive laws and the universal hardness is sufficiently elucidated. Various materials stress – strain curves and universal hardness courses versus the indentation depth, determined by means of the developed procedure, are presented.

Prof. Dr.-Ing. habil. K.-D. Bouzakis Mechanical Engineering Department Aristoteles University of Thessaloniki GR-54124, Thessaloniki, Greece Tel.: +30 310 996 021 Fax: +30 310 996 059


1 Oliver, W.C.; Pharr, G.M.: J. Mater. Res. 7 (1992) 1564.Search in Google Scholar

2 Alcala, J.; Giannakopoulos, A.E.; Suresh, S.: J. Mater. Res. 13 (1998) 1390.Search in Google Scholar

3 Chudoba, T.; Schwarzer, N.; Richter, F.: Surf. Coat. Technol. 127 (2000) 9.Search in Google Scholar

4 Helmut Fischer GmbH + Co: Evaluation Manual of Indentation Procedure, Sindelfingen, Germany (2000).Search in Google Scholar

5 Bouzakis, K.-D.; Michailidis, N.; Erkens, G.: Surf. Coat. Technol. 142–144 (2001) 102.Search in Google Scholar

6 Herrmann, K.; Jennett, N.M.; Wegener, W.; Meneve, J.; Hasche, K.; Seemann, R: Thin Solid Films 377–378 (2000) 394.Search in Google Scholar

7 Jennett, N.M.; Meneve, J.: Proc. MRS Symp. 522 (1998) 239.Search in Google Scholar

8 Jennett, N.M.; Shafirstein, G.; Saunders, S.R.J.: Hardness Testing in Theory and Practice, VDI Berichte 1194, VDI-Verlag GmbH, Düsseldorf (1995) 201.Search in Google Scholar

9 Zarm, H.: Jahrbuch für Optik und Feinmechanik, Fachverlag Schiele & Schoen GmbH, Berlin (1991) 269.Search in Google Scholar

10 Doerner, M.F.; Nix, W.D.: J. Mater. Res. 1 (1986) 601.Search in Google Scholar

11 Bhushan, B.; Gupta, B.K.: Handbook of Hard Coatings, Deposition Technologies–Properties and Applications, Noyes Publications, Park Ridge, NJ (2001) 229.Search in Google Scholar

12 Swanson Analysis System, INC.: ANSYS User Manuals (1995).Search in Google Scholar

13 Loubet, J.L.; Georges, J.M.; Meille, G.: ASTM STP 889, Philadelphia, PA (1986) 72.Search in Google Scholar

14 Brookes, K.:Word Directory and Handbook of Hardmetals, International Carbide Data, 33 Oakhurst Av. East Barnet, Herts., UK (1987).Search in Google Scholar

Received: 2001-11-18
Published Online: 2022-01-08

© 2002 Carl Hanser Verlag, München