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A numerical approach to evaluation of elastic modulus using conical indenter with finite tip radius

Published online by Cambridge University Press:  31 January 2011

Jin Haeng Lee ,
Hyungyil Lee  and
Deok Hoon Kim
Jin Haeng Lee*
Affiliation:
Department of Mechanical Engineering, Sogang University, Seoul 121-742, Republic of Korea
Hyungyil Lee
Affiliation:
Department of Mechanical Engineering, Sogang University, Seoul 121-742, Republic of Korea
Deok Hoon Kim
Affiliation:
Department of Mechanical Engineering, Sogang University, Seoul 121-742, Republic of Korea
*
a)Address all correspondence to this author. e-mail: jinhaeng@sogang.ac.kr Present address: Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996.
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Abstract

Geometrical self-similarity is a feature of mathematically sharp indenters such as conical and Berkovich indenters. However, self-similarity is considered inappropriate for practical use because of inevitable indenter tip blunting. In this study, we analyze the load–depth curves of conical indenters with various tip radii via finite element analyses. Based on the numerical data, we propose a method of restoring the Kick’s law coefficient C of finite tip-radius indenter to that of zero tip-radius indenter, thereby retaining the self-similarity of the sharp indenter. We then regress the unloading slope for the evaluation of elastic modulus in several ways. Finally, we establish a method to evaluate elastic modulus, which successfully provides the value of the elastic modulus with a maximum error of less than 5%, regardless of tip radius and material properties of both indenter and specimen.

Keywords

Elastic propertiesMetalNanoscale
Type
Articles
Information
Journal of Materials Research , Volume 23 , Issue 9 , September 2008 , pp. 2528 - 2537
Copyright
Copyright © Materials Research Society 2008

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References

REFERENCES

1Sneddon, I.N.: The relaxation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 1965CrossRefGoogle Scholar
2Doerner, M.F.Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 1986CrossRefGoogle Scholar
3Oliver, 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
4Field, J.S.Swain, M.V.: Determining the mechanical properties of small volumes of material from submicrometer spherical indentations. J. Mater. Res. 10, 101 1995CrossRefGoogle Scholar
5Giannakopoulos, A.E.Suresh, S.: Determination of elastoplastic properties by instrumented sharp indentation. Scr. Mater. 40, 1191 1999CrossRefGoogle Scholar
6Chollacoop, N., Dao, M.Suresh, S.: Depth-sensing instrumented indentation with dual sharp indenters. Acta Mater. 51, 3713 2003CrossRefGoogle Scholar
7Bucaille, J.L., Stauss, S., Schwaller, P.Michler, J.: A new technique to determine the elastoplastic properties of thin metallic films using sharp indenters. Thin Solid Films 447–448, 239 2004CrossRefGoogle Scholar
8Lee, H., Lee, J.H.Pharr, G.M.: A numerical approach to spherical indentation techniques for material property evaluation. J. Mech. Phys. Solids 53, 2037 2005CrossRefGoogle Scholar
9Beghini, M., L, , Bertini, , and Fontanari, V.: Evaluation of the stress–strain curve of metallic materials by spherical indentation. Int. J. Solids Struct. 43, 2441 2006CrossRefGoogle Scholar
10Chen, X., Ogasawara, N., Zhao, M.Chiba, N.: On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials. J. Mech. Phys. Solids 55, 1618 2007CrossRefGoogle Scholar
11Suresh, S.Giannakopoulos, A.E.: A new method for estimating residual stresses by instrumented sharp indentation. Acta Mater. 46, 5755 1998CrossRefGoogle Scholar
12Lee, Y.H.Kwon, D.: Estimation of biaxial surface stress by instrumented indentation with sharp indenters. Acta Mater. 52, 1555 2004CrossRefGoogle Scholar
13Xu, Z.H.Li, X.: Influence of equi-biaxial residual stress on unloading behaviour of nanoindentation. Acta Mater. 53, 1913 2005CrossRefGoogle Scholar
14Lee, J.H.Lee, H.: An indentation method based on FEA for equi-biaxial residual stress evaluation. Trans. KSME 30, 42 2006CrossRefGoogle Scholar
15Bower, A.F., Fleck, N.A., Needleman, A.Ogbonna, N.: Indentation of a power law creeping solid. Proc. R. Soc. London Ser. A 441, 97 1993CrossRefGoogle Scholar
16LaManna, J.A.: A study of the relationship between indentation creep and uniaxial creep. Ph.D. Dissertation, University of Tennessee, TN,2006Google Scholar
17Lawn, 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 1980CrossRefGoogle Scholar
18Pharr, G.M.: Measurement of mechanical properties by ultra-low-load indentation. Mater. Sci. Eng., A 253, 151 1998CrossRefGoogle Scholar
19Menčík, J.Swain, M.V.: Error associated with depth-sensing microindentation tests. J. Mater. Res. 10, 1491 1995CrossRefGoogle Scholar
20Cheng, Y-T.Cheng, C-M.: Further analysis of indentation loading curves: Effects of tip rounding on mechanical property measurements. J. Mater. Res. 13, 1059 1998CrossRefGoogle Scholar
21Herrmann, K., Jennett, N.M., Wegener, W., Meneve, J., Hasche, K.Seemann, R.: Progress in determination of the area function of indenters used for nanoindentation. Thin Solid Films 377–378, 394 2000CrossRefGoogle Scholar
22Xue, Z., Huang, Y., Hwang, K.C.Li, M.: The influence of indenter tip radius on the micro-indentation hardness. J. Eng. Mater. Technol. 124, 371 2002CrossRefGoogle Scholar
23Troyon, M.Huang, L.: Correction factor for contact area in nanoindentation measurements. J. Mater. Res. 20, 610 2005CrossRefGoogle Scholar
24ABAQUS User’s Manual, Version 6.5 Hibbitt, Karlsson and Sorensen, Inc. PawtucketRI, 2004Google Scholar
25Pharr, 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 1992CrossRefGoogle Scholar
26Cheng, C-M.Cheng, Y-T.: On the initial unloading slope in indentation of elastic-plastic solids by an indenter with an axisymmetric smooth profile. Appl. Phys. Lett. 71, 2623 1997CrossRefGoogle Scholar
27Fischer-Cripps, A.C.: Critical review of analysis and interpretation of nanoindentation test data. Surf. Coat. Technol. 200, 4153 2006CrossRefGoogle Scholar
28 ISO 14577, Metallic materials-instrumented indentation test for hardness and materials parameters, ISO Central Secreariat, 1 rue de Varembé, 1211 Geneva, 20 SwitzerlandGoogle Scholar
29Rice, J.R.Rosengren, G.F.: Plane strain deformation near a crack-tip in a power law hardening material. J. Mech. Phys. Solids 16, 1 1968CrossRefGoogle Scholar
30Shim, S., Oliver, W.C.Pharr, G.M.: A comparison of 3D finite element simulations for Berkovich and conical indentation of fused silica. Int. J. Surf. Sci. Eng. 1, 259 2007CrossRefGoogle Scholar
31Xu, Z-H.Li, X.: Effects of indenter geometry and material properties on the correction factor of Sneddon’s relationship for nanoindentation of elastic and elastic-plastic materials. Acta Mater. 56, 1399 2008CrossRefGoogle Scholar
32Lee, J.H.: A numerical approach and experimental verification of the indentation techniques for material property and residual stress evaluation. Ph.D. Dissertation, Sogang University, Seoul, Korea,2006Google Scholar
33Dao, M., Chollacoop, N., Vliet, J.V., Venkatesh, T.A.Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 2001CrossRefGoogle Scholar