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A systematic study of the validation of Oliver and Pharr’s method

Published online by Cambridge University Press:  31 January 2011

Siqi Shu ,
Jian Lu  and
Dongfeng Li
Siqi Shu
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
Jian Lu*
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
Dongfeng Li
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
*
a)Address all correspondence to this author. e-mail: Jian.Lu@inet.polyu.edu.hk
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Abstract

Oliver and Pharr’s method (O&P’s method) is an efficient and popular way of measuring the hardness and Young’s modulus of many classes of solid materials. However, there exists a range of errors between the real values and the calculated values when O&P’s method is applied to materials not included in the basic assumption proposed initially. In this article, the dimensional analysis theorem and the finite element method are applied to evaluate errors for high elastic (E/σY → 5) to full plastic (E/σY→ 1000) materials with different strain-hardening exponents from 0 to 0.5. A new method is proposed to correct errors obtained using O&P’s method. The numerical simulation results show that the errors obtained using O&P’s method, given in the form of charts, are mainly dependent on the ratio of the reduced Young’s modulus to the yield stress (i.e., Er/σY) and the strain-hardening exponent, n, for an indenter with a fixed included angle. The two mechanical properties, which can be extracted from the load–depth curves of two indenters with different included angles, are used to correct the errors in the hardness and Young’s modulus of the indented materials produced by O&P’s method.

Keywords

HardnessElastic propertiesStress/strain relationship
Type
Articles
Information
Journal of Materials Research , Volume 22 , Issue 12 , December 2007 , pp. 3385 - 3396
Copyright
Copyright © Materials Research Society 2007

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References

REFERENCES

1Tabor, D.: Hardness of Metal Clarendon Press Oxford 1951Google Scholar
2Johnson, K.L.: Contact Mechanics Cambridge University Press Cambridge 1985CrossRefGoogle Scholar
3Cheng, Y.T.Cheng, C.M.: Scaling relationships in conical indentation of elastic-perfectly plastic solids. Int. J. Solids Struct. 36, 1231 1997CrossRefGoogle Scholar
4Cheng, Y.T.Cheng, C.M.: Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73, 614 1998CrossRefGoogle Scholar
5Cheng, Y.T.Cheng, C.M.: Scaling relationships in conical indentation of elastic-perfectly plastic solids. Int. J. Solids Struct. 36, 1231 1998CrossRefGoogle Scholar
6Cheng, Y.T.Cheng, C.M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 2004CrossRefGoogle Scholar
7Cao, Y.P., Qian, X.Q.Lu, J.: On the determination of reduced Young’s modulus and hardness of elastoplastic materials using a single sharp indenter. J. Mater. Res. 21, 215 2006CrossRefGoogle Scholar
8Doerner, M.F.Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 1986CrossRefGoogle Scholar
9Oliver, 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 1992CrossRefGoogle Scholar
10Loubet, J.L., Georges, J.M., Marchesini, O.Meille, G.: Vickers indentation curves of magnesium-oxide (MGO). Tribology 106, 43 1984CrossRefGoogle Scholar
11Oliver, W.C.Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 2004CrossRefGoogle Scholar
12Bolshakov, A.Pharr, G.M.: Influences of pile up on the measurement of mechanical properties by load and depth-sensing indentation techniques. J. Mater. Res. 13, 1049 1998CrossRefGoogle Scholar
13Gorokhovsky, V., Bowman, C., Gannon, P., VanVorous, D., Voevodin, A.A., Rutkowski, A., Muratore, C., Smith, R.J., Kayani, A., Gelles, D., Shutthanandan, V.Trusov, B.G.: Tribological performance of hybrid filtered arc-magnetron coatings, Part 1: Coating deposition process and basic coating basic coating properties characterization. Surf. Coat. Technol. 201, 3732 2006CrossRefGoogle Scholar
14ISI http://portal.isiknowledge.com 2007Google Scholar
15Ma, D.J., Zhang, T.H.Ong, C.W.: Evaluation of the effectiveness of representative method for determining Young’s modulus and hardness from instrumented indentation data. J. Mater. Res. 21, 225 2006CrossRefGoogle Scholar
16Aksel, C.Riley, F.L.: Young’s modulus measurements of magnesia-spinel composites using load-deflection curves, sonic modulus, strain gauges and Rayleigh waves. J. Eur. Ceram. Soc. 23, 3089 2003CrossRefGoogle Scholar
17Aldrich-Smith, G., Jennett, N.M.Hangen, U.: Direct measurement of nanoindentation area function by metrological AFM. Z. Metallkd. 96, 1267 2005CrossRefGoogle Scholar
18Ashby, M.F.Materials Selection in Mechanical Design 3rd ed.Pergamon Press Oxford 1985Google Scholar
19King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 1987CrossRefGoogle Scholar
20Vlassak, J.J.Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42, 1223 1994CrossRefGoogle Scholar
21Hay, J.C., Bolshakov, A.Pharr, M.M.: A critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 1999CrossRefGoogle Scholar
22Cao, Y.P., Dao, M.Lu, J.: A precise correction method for the study the superhard materials using the nanoindentation. J. Mater. Res. 22, 1255 2007CrossRefGoogle Scholar
23Tho, K.K., Swaddiwudhipong, S., Liu, Z.S.Hua, J.: Artificial neural network model for material characterization by indentation. Modell. Simul. Mater. Sci. Eng. 12, 1055 2004CrossRefGoogle Scholar
24Wei, Y.G., Shu, S.Q., Du, Y.Zhu, C.: Size geometry and nonuniformity effects of surface-nanocrystalline aluminum in nanoindentation test. Int. J. Plast. 11, 2089 2005CrossRefGoogle Scholar
25Mata, M.Alcala, J.: The role of friction on sharp indentation. J. Mech. Phys. Solids 52, 145 2004CrossRefGoogle Scholar
26Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A.Suresh, S.: Computational modelling of the forward and reverse problems in instrumented sharp Indentation. Acta Mater. 49, 3899 2001Google Scholar
27Tho, K.K., Swaddiwudhipong, S., Liu, Z.S., Zeng, K.Hua, J.: Uniqueness of reverse analysis from conical indentation tests. J. Mater. Res. 19, 2498 2004CrossRefGoogle Scholar
28Alkorta, J., Martinez-Esnaola, J.M.Sevillana, J. Gil: Absence of one-to-one correspondence between elastoplastic properties and sharp-indentation load-penetration data. J. Mater. Res. 20, 432 2005CrossRefGoogle Scholar
29Fischer-Cripps, A.C.Nonoindentation 2nd ed.Springer Press New York 2004CrossRefGoogle Scholar
30ABAQUS Theory Manual Version 6.2 Hibbitt, Karlsson and Sorensen, Inc. Pawtucket, RI 2006Google Scholar
31Jayaraman, S., Hahn, G.T., Oliver, W.C.Bastias, P.C.: Determination of monotonic stress-strain curve of hard materials from ultra-low-load indentation tests. Int. J. Solids Struct. 35, 365 1998CrossRefGoogle Scholar
32Ashby, M.F., Cebon, D.Lee-Shothaman, L.: Cambridge Engineering Selector V3.1 Granta Design Limited Cambridge 2001Google Scholar
33Cheng, Y.T.Cheng, C.M.: Can stress-strain relationships be obtained from indentation curves using conical or pyramidal indenters? J. Mater. Res. 14, 3494 1999CrossRefGoogle Scholar
34Capehart, T.W.Cheng, Y.T.: Determination constitutive models from conical indentation: Sensitivity analysis. J. Mater. Res. 18, 827 2003CrossRefGoogle Scholar
35Cao, Y.P.Lu, J.: A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve. Acta Mater. 52, 4023 2004CrossRefGoogle Scholar
36Bucaille, J.L., Stauss, S., Felder, E.Michler, J.: Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater. 51, 1663 2003CrossRefGoogle Scholar
37Chollacoop, N., Dao, M.Suresh, S.: Depth-sensing instrumented indentation with dual sharp indenters. Acta Mater. 51, 3713 2003CrossRefGoogle Scholar
38Cao, Y.P., Qian, X.Q., Lu, J.Yao, Z.H.: An energy-based method to extract plastic properties of metal materials from conical indentation tests. J. Mater. Res. 20, 1194 2005CrossRefGoogle Scholar
39Shu, S.Q.Lu, J.: Principles for choosing indenters during the materials properties determined with indentation. J. Mater. Res., (2007, to be submitted)Google Scholar
40Hysitron Incorporated Triboscratch User Manual, Software Version 7.0 Hysitron Inc. Minneapolis, MN 2001Google Scholar
41Fisher-Cripps, C.A.Brian, R.L.: Stress analysis of contact deformation in quasi-plastic ceramics. J. Am. Ceram.Soc. 19, 2609 1996CrossRefGoogle Scholar
42Estibaliz, S.G.: Application of Hertzian tests to measure stress-strain characteristics of ceramics at elevated temperatures. J. Am. Ceram. Soc. 90, 149 2007Google Scholar
43Kim, K.T., Cha, S.Hong, S.Y.: Microstructure and tensile behavior of carbon nanotube reinforced Cu matrix nanocomposites. Mater. Sci. Eng., A 430, 27 2007CrossRefGoogle Scholar
44Zhou, Y.X., Yang, W., Xia, Y.M.Mallick, P.K.: An experimental study on the tensile behavior of a unirectional carbon fiber reinforced aluminum composite at different strain rates. Mater. Sci. Eng., A 362, 112 2003CrossRefGoogle Scholar
45Boehlert, C.J., Majumdar, B.S.Miracle, D.B.: Application of the cruciform specimen geometry to obtain transverse interface-property data in a high-fiber-volume–fraction SiC/Titanium alloy composite. Metall. Mater. Trans. A 32, 3143 2001CrossRefGoogle Scholar
46Rupnowski, P., Gentz, M.Kumosa, M.: Mechanical response of a unidirectional graphite fiber/polyimide composite as a function of temperature. Compos. Sci. Technol. 66, 1045 2006CrossRefGoogle Scholar