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Determination of plastic properties by instrumented spherical indentation: Expanding cavity model and similarity solution approach

Published online by Cambridge University Press:  31 January 2011

Peng Jiang ,
Taihua Zhang ,
Yihui Feng ,
Rong Yang  and
Naigang Liang
Peng Jiang
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Taihua Zhang*
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Yihui Feng
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Rong Yang
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Naigang Liang
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
*
a) Address all correspondence to this author. e-mail: zhangth@lnm.imech.ac.cn
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Abstract

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed on three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

Keywords

NanoindentationSimulationStress/strain relationship
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 1045 - 1053
Copyright
Copyright © Materials Research Society 2009

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References

REFERENCES

1.Cheng, Y.T. and Cheng, C.M.: Can stress-strain relationships be obtained from indentation curves using conical and pyramidal indenters? J. Mater. Res. 14(9), 3493 (1999).CrossRefGoogle Scholar
2.Chen, X., Ogasawara, N., Zhao, M.H., and Chiba, N.: On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials., J. Mech. Phys. Solids 55(8), 1618 (2007).CrossRefGoogle Scholar
3.Choppacoop, N., Dao, M., and Suresh, S.: Depth-sensing instrumented indentation with dual sharp indenters. Acta Mater. 51, 3713 (2003).CrossRefGoogle Scholar
4.Swaddiwudhipong, S., Tho, K.K., Liu, Z.S., and Zeng, K.: Material characterization based on dual indenters. Int. J. Solids Struct. 42, 69 (2005).CrossRefGoogle Scholar
5.Bucaille, J.L., Stauss, S., Felder, E., and Michler, J.: Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater. 51, 1663 (2003).CrossRefGoogle Scholar
6.Cao, Y.P., Qian, X.Q., Lu, J., and Yao, Z.H.: An energy-based method to extract plastic properties of metal materials from conical indentation tests. J. Mater. Res. 20(5), 1194 (2005).CrossRefGoogle Scholar
7.Ogasawara, N., Chiba, N., and Chen, X.: Representative strain of indentation analysis. J. Mater. Res. 20(8), 2225 (2005).CrossRefGoogle Scholar
8.Wang, L., Ganor, M., and Rokhlin, S.I.: Inverse scaling functions in nanoindentation with sharp indenters: Determination of material properties. J. Mater. Res. 20(4), 987 (2005).CrossRefGoogle Scholar
9.Tabor, D.: Hardness of Metals (Clarendon Press, Oxford, UK, 1951), pp. 73, 76.Google Scholar
10.Murty, K.L., Mathew, M.D., Wang, Y., Shah, V.N., and Haggag, F.M.: Nondestructive determination of tensile properties and fracture toughness of cold worked A36 steel. Int. J. Press. Vessels Pip. 75(11), 831 (1998).CrossRefGoogle Scholar
11.Ahn, J.H. and Kwon, D.: Derivation of plastic stress-strain relationship from ball indentation: Examination of strain definition and pileup effect. J. Mater. Res. 16, 3170 (2001).CrossRefGoogle Scholar
12.Kim, J.Y. and Lee, K.W.: Determination of tensile properties by instrumented indentation technique: Representative stress and strain approach. Surf. Coat. Technol. 201, 4278 (2006).CrossRefGoogle Scholar
13.Lee, H.: A numerical approach to spherical indentation techniques for material property evaluation. J. Mech. Phys. Solids 53, 203 (2005).CrossRefGoogle Scholar
14.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
15.Taljat, B., Zacharia, T., and Kosel, F.: New analytical procedure to determine stress-strain curve from spherical indentation data. Int. J. Solids Struct. 35(33), 4411 (1998).CrossRefGoogle Scholar
16.Field, J.S. and Swain, M.V.: Determining the mechanical properties of small volumes of material from submicron spherical indentations. J. Mater. Res. 10(1), 101 (1995).CrossRefGoogle Scholar
17.Kucharski, S. and Mroz, Z.: Identification of plastic hardening parameters of metals from spherical indentation tests. Mater. Sci. Eng., A 318, 65 (2001).CrossRefGoogle Scholar
18.Herbert, E.G., Pharr, G.M., and Oliver, W.C.: On the measurement of stress-strain curves by spherical indentation. Thin Solid Films 398–399, 331 (2001).CrossRefGoogle Scholar
19.Yu, W.P. and Blanchard, J.P.: An elastic-plastic indentation model and its solutions. J. Mater. Res. 11(9), 2358 (1996).CrossRefGoogle Scholar
20.Cao, Y.P. and Lu, J.: A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve. Acta Mater. 52(13), 4023 (2004).CrossRefGoogle Scholar
21.Zhao, M.H., Ogasawara, N., Chiba, N., and Chen, X.: A new approach to measure the elastic-plastic properties of bulk materials using spherical indentation. Acta Mater. 54, 23 (2006).CrossRefGoogle Scholar
22.Beghini, M., Bertini, L., and Fontanari, V.: Evaluation of the stress-strain curve of metallic materials by spherical indentation. Int. J. Solids Struct. 43, 2441 (2006).CrossRefGoogle Scholar
23.Huber, N. and Tsakmakis, Ch.: Determination of constitutive properties from spherical indentation data using neural networks. Part II: Plasticity with nonlinear isotropic and kinematic hardening. J. Mech. Phys. Solids 47, 1589 (1999).CrossRefGoogle Scholar
24.Nayebi, A., El Abdi, R., Bartier, O., and Mauvoisin, G.: New procedure to determine steel mechanical parameters from the spherical indentation technique. Mech. Mater. 34, 243 (2002).CrossRefGoogle Scholar
25.Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T. A., and Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).CrossRefGoogle Scholar
26.Herbert, E.G., Pharr, W.C., and Oliver, G.M.: On the measurements of yield strength by spherical indentation. Philos. Mag. 86(33–35), 5521 (2006).CrossRefGoogle Scholar
27.Ni, W., Cheng, Y.T., Cheng, Z.M., and Grummon, D.S.: An energy-based method for analyzing instrumented spherical indentation experiments. J. Mater. Res. 19, 149 (2004).CrossRefGoogle Scholar
28.Bishop, R.F., Hill, R., and Mott, N.F.: The theory of indentation and hardness tests. Proc. Phys. Soc. 57(3), 47 (1945).CrossRefGoogle Scholar
29.Johnson, K.L.: The correlation of indentation experiments. J. Mech. Phys. Solids 18, 115 (1970).CrossRefGoogle Scholar
30.Gao, X.L. and Jing, X.N.: Two new expanding cavity models for indentation deformations of elastic strain-hardening materials. Int. J. Solids Struct. 43, 2193 (2006).CrossRefGoogle Scholar
31.Hill, R., Storakers, B., and Zdunek, A.B.: A theoretical study of the Brinell hardness test. Proc. R. Soc. London, Ser. A 423, 301 (1989).Google Scholar
32.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(6), 1546 (1992).CrossRefGoogle Scholar
33.Hill, R.: The Mathematical Theory of Plasticity (Oxford University Press, Oxford, London, 1950), p. 97.Google Scholar
34.Mesarovic, S.D. and Fleck, N.A.: Spherical indentation of elastic-plastic solids. Proc. R. Soc. London, Ser. A 455, 2707 (1999).CrossRefGoogle Scholar
35.Yang, R., Zhang, T.H., Jiang, P., and Bai, Y.L.: Experimental verification and theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 92, 231906 (2008).CrossRefGoogle Scholar
36.Cheng, Y.T. and Cheng, C.M.: Scaling, dimensional analysis and indentation measurements. Mater. Sci. Eng. 44, 91 (2004).CrossRefGoogle Scholar
37.Meyer, E.: A study on the hardness test. Zeitchrift des Vereines Deutcher Ingenieure. 52, 645 (1908).Google Scholar