Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T15:56:03.616Z Has data issue: false hasContentIssue false
  • English
  • Français

A critical examination of the relationship between plastic deformation zone size and Young's modulus to hardness ratio in indentation testing

Published online by Cambridge University Press:  03 March 2011

J. Chen  and
S.J. Bull
J. Chen
Affiliation:
Department of Chemical Engineering and Advanced Materials, University of Newcastle, Newcastle Upon Tyne NE1 7RU, United Kingdom
S.J. Bull*
Affiliation:
Department of Chemical Engineering and Advanced Materials, University of Newcastle, Newcastle Upon Tyne NE1 7RU, United Kingdom
*
a) Address all correspondence to this author. e-mail: s.j.bull@ncl.ac.uk
Get access

Abstract

Existing indentation models (both analytical models and numerical analysis) show a linear relationship between δr/δm and H/Er, where δr and δm are the residual and maximum indentation depth, and Er and H are the reduced Young's modulus and hardness of the test material. Based on the analysis of Oliver and Pharr, a new relationship between δr/δm and H/Er has been derived in a different way without any additional assumptions, which is nonlinear, and this has been verified by finite element analysis for a range of bulk materials. Furthermore, this new relationship for residual depth is used to derive an analytical relationship for the radius of the plastic deformation zone Rp in terms of the residual depth, Young’s modulus, and hardness, which has also been verified by finite element simulations for elastic perfectly plastic materials with different work hardening behavior. The analytical model and finite element simulation confirms that the conventional relationship used to determine Rp developed by Lawn et al. overestimates the plastic deformation, especially for those materials with high E/H ratio. The model and finite element analysis demonstrate that Rp scales with δr, which is sensible given the self-similarity of the indentations at different scales, and that the ratio of Rp/δr is nearly constant for materials with different E/H, which contradicts the conventional view.

Keywords

Hardness
Type
Articles
Information
Journal of Materials Research , Volume 21 , Issue 10 , October 2006 , pp. 2617 - 2627
Copyright
Copyright © Materials Research Society 2006

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

1.Oliver, W.C., 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
2.Pharr, G.M., Oliver, W.C., 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
3.Hainsworth, S.V., Chandler, H.W., Page, T.F.: Analysis of nanoindentation load-displacement loading curves. J. Mater. Res. 11, 1987 (1996).CrossRefGoogle Scholar
4.Li, X., Diao, D., Bhushan, B.: Fracture mechanisms of thin amorphous carbon films in nanoindentation. Acta Mater. 45, 4453 (1997).CrossRefGoogle Scholar
5.Malzbender, J., de With, G., Toonder, J. den: Elastic modulus, indentation pressure and fracture toughness of hybrid coatings on glass. Thin Solid Films 366, 139 (2000).CrossRefGoogle Scholar
6.Chen, J., Bull, S.J.: Assessment of the toughness of thin coatings using nanoindentation under displacement control. Thin Solid Films 494, 1 (2006).CrossRefGoogle Scholar
7.Cheng, Y-T., Cheng, C-M.: Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73, 614 (1998).CrossRefGoogle Scholar
8.Cheng, Y-T., Li, Z., Cheng, C-M.: Scaling relationships for indentation measurements. Philos. Mag. A 82, 1821 (2002).CrossRefGoogle Scholar
9.Malzbender, J., With, G. de.: Energy dissipation, fracture toughness and the indentation load–displacement curve of coated materials. Surf. Coat. Technol. 135, 60 (2000).CrossRefGoogle Scholar
10.Lawn, B.R., Evans, A.G., Marshall, D.B.: Elastic/plastic indentation damage in ceramics: The median/radial crack system. J. Am. Ceram. Soc. 63, 574 (1980).CrossRefGoogle Scholar
11.Burnett, P.J., Rickerby, D.S.: The mechanical properties of wear-resistant coatings. 1. Modeling of hardness behaviour. Thin Solid Films 148, 41 (1987).CrossRefGoogle Scholar
12.Giannakopoulos, A.E., Suresh, S.: Determination of elastoplastic properties by instrumented sharp indentation. Script Mater. 40, 1191 (1999).CrossRefGoogle Scholar
13.Harvey, S., Huang, H., Venkataraman, S., Gerberich, W.W.: Microscopy and microindentation mechanics of single-crystal Fe-3 wt% Si: Part I. Atomic force microscopy of a small indentation. J. Mater. Res. 8, 1291 (1993).CrossRefGoogle Scholar
14.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).CrossRefGoogle Scholar
15.Lawn, B.R., Howes, V.R.: Elastic recovery at hardness indentations. J. Mater. Sci. 16, 2745 (1981).CrossRefGoogle Scholar
16.Sakai, M.: Energy principle of the indentation-induced inelastic surface deformation and hardness of brittle materials. Acta Metall. Mater. 41, 1751 (1993).CrossRefGoogle Scholar
17.Sakai, M., Shimizu, S., Ishikawa, T.: The indentation load-depth curve of ceramics. J. Mater. Res. 14, 1471 (1999).CrossRefGoogle Scholar
18.Sakai, M.: Simultaneous estimate of elastic/plastic parameters in depth-sensing indentation tests. Scripta Mater. 51, 391 (2004).CrossRefGoogle Scholar
19.Bull, S.J.: Interface engineering and graded films: Structure and characterization. J. Vac. Sci. Technol., A 19, 1404 (2001).CrossRefGoogle Scholar
20.Bull, S.J., G-Berasetegui, E., Page, T. F.: Modelling of the indentation response of coatings and surface treatments. Wear 256, 857 (2004).CrossRefGoogle Scholar
21.Pharr, G.M., Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002).CrossRefGoogle Scholar
22.Malzbender, J., de With, G.: The use of the loading curve to assess soft coatings. Surf. Coat. Technol. 127, 265 (2000).CrossRefGoogle Scholar
23.Oliver, W.C.: Alternative technique for analyzing instrumented indentation data. J. Mater. Res. 16, 3202 (2001).CrossRefGoogle Scholar
24.Malzbender, J., de With, G., Toonder, J. den: The P-h 2 relationship in indentation. J. Mater. Res. 15, 1209 (2000).CrossRefGoogle Scholar
25.Bao, Y., Liu, L., Zhou, Y.: Assessing the elastic parameters and energy-dissipation capacity of solid materials: A residual indent may tell all. Acta Mater. 53, 4857 (2005).CrossRefGoogle Scholar
26.Malzbender, J.: Comment on the determination of mechanical properties from the energy dissipated during indentation. J. Mater. Res. 20, 1090 (2005).CrossRefGoogle Scholar
27.Alkorta, J., Martinez-Esnaola, J.M., Sevillano, J.G.: Comments on “Comment on the determination of mechanical properties from the energy dissipated during indentation” by J. Malzbender [J. Mater. Res. 20, 1090 (2005)]. J. Mater. Res. 21, 302 (2006).CrossRefGoogle Scholar
28.Menčik, J., Swain, M.V.: Microindentation tests with pointed indenters. Mater. Forum 18, 277 (1994).Google Scholar
29.Liu, J., Mwanza, M.C., Reed, P.A.S., Syngellakis, S.: ANSYS Application Note. (ANSYS Inc., Canonsburg, PA, 2002).Google Scholar
30. ANSYS 8.0 Documentation, ANSYS Inc., Canonsburg, PA.Google Scholar
31.Soare, S. Design of a rotating sensor for stress measurement in metallisation. Ph.D. Thesis, University of Newcastle Upon Tyne (2004).Google Scholar
32.Bolshakov, A., 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).CrossRefGoogle Scholar
33.Johnson, K.L.: The correlation of indentation experiments. J. Mech. Phys. Solids 18, 115 (1970).CrossRefGoogle Scholar
34.Li, M., Chen, W., Liang, N., Wang, L.: A numerical study of indentation using indenters of different geometry. J. Mater. Res. 19, 73 (2004).Google Scholar
35.Cheng, Y.T., Cheng, C.M.: Scaling approach to conical indentation in elastic-plastic solids with work hardening. J. Appl. Phys. 84, 1284 (1998).CrossRefGoogle Scholar
36.Marsh, D.B.: Plastic flow in glass. Proc. R. Soc. Lond. A 279, 420 (1963).Google Scholar
37.Vandeperre, L.J., Giuliani, F., Clegg, W.J.: Effect of elastic surface deformation on the relation between hardness and yield strength. J. Mater. Res. 19, 3704 (2004).CrossRefGoogle Scholar
38.Yu, W., Blanchard, J.P.: An elastic-plastic indentation model and its solutions. J. Mater. Res. 11, 2358 (1996).CrossRefGoogle Scholar
39.Tabor, D.: Hardness of Metals. (Clarendon Press, Oxford, 1951).Google Scholar
40.Chen, J. and Bull, S.J.: (in preparation).Google Scholar
41.Hay, J.C., Bolshakov, A., Pharr, G.M.: A critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 (1999).CrossRefGoogle Scholar
42.Troyon, M., Huang, L.: About the correction factor for contact area in nanoindentation measurements. J. Mater. Res. 20, 610 (2005).CrossRefGoogle Scholar