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Evaluation of the effectiveness of representative methods for determining Young's modulus and hardness from instrumented indentation data

  • Dejun Ma (a1), Taihua Zhang (a2) and Chung Wo Ong (a3)

Abstract

The effectiveness of Oliver & Pharr's (O&P's) method, Cheng & Cheng's (C&C’s) method, and a new method developed by our group for estimating Young's modulus and hardness based on instrumented indentation was evaluated for the case of yield stress to reduced Young's modulus ratio (σy/Er) ≥ 4.55 × 10−4 and hardening coefficient (n) ≤ 0.45. Dimensional theorem and finite element simulations were applied to produce reference results for this purpose. Both O&P's and C&C's methods overestimated the Young's modulus under some conditions, whereas the error can be controlled within ±16% if the formulation was modified with appropriate correction functions. Similar modification was not introduced to our method for determining Young's modulus, while the maximum error of results was around ±13%. The errors of hardness values obtained from all the three methods could be even larger and were irreducible with any correction scheme. It is therefore suggested that when hardness values of different materials are concerned, relative comparison of the data obtained from a single standard measurement technique would be more practically useful. It is noted that the ranges of error derived from the analysis could be different if different ranges of material parameters σy/Er and n are considered.

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Corresponding author

a)Address all correspondence to this author. e-mail: apacwong@inet.polyu.edu.hk

References

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1.Cheng, Y-T. and Cheng, C.M.: Scaling, dimension analysis, and indentation measurements. Mater. Sci. Eng. R 44, 91 (2004).
2.Doerner, M.F. and Nix, W.D.: A method for interpretating the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).
3.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, 1564 (1992).
4.Pharr, G.M., Oliver, W.C. and 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).
5.Oliver, W.C. and Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).
6.Cheng, Y-T. and Cheng, C-M.: Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73, 614 (1998).
7.Cheng, Y-T. and Li, Z.: Scaling relationships for indentation measurements. Philos. Mag. A 82, 1893 (2002).
8.Cheng, Y-T. and Li, Z.: Can stress-strain relationship be obtained from indentation curves using conical and pyramidal indenters? J. Mater. Res. 14, 3493 (1999).
9.Cheng, Y-T. and Li, Z.: Scaling relationships in conical indentation of elastic-perfectly plastic solids. Int. J. Solids Struct. 36, 1231 (1999).
10.Cheng, Y-T. and Li, Z.: What is indentation hardness? Surf. Coat. Technol. 133–134, 417 (2000).
11.Ma, D., Ong, C.W. and Wong, S.F.: New relationship between Young's modulus and nonideally sharp indentation parameters. J. Mater. Res. 19, 2144 (2004).
12.Ma, D., Ong, C.W., Wong, S.F. and He, J.: New method for determining Young's modulus by non-ideally sharp indentation. J. Mater. Res. 20, 1498 (2005).
13.Ma, D., Ong, C.W., Lu, J. and He, J.: Determination of Young's modulus by nanoindentation. Sci. China Ser. E, Eng. Mater. Sci. 47, 398 (2004).
14.Sneddon, I.N.: The relationship between load and penetration in the axisymmetric Bousinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).
15.Version, ABAQUS 6.2 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI, 2001).
16.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).
17.Ma, D., Ong, C.W., Lu, J. and He, J.: Methodology for evaluation of yield strength and hardening behavior of metallic materials by indentation with spherical tip. J. Appl. Phys. 94, 288 (2003).
18.Ni, W. and Cheng, Y-T.: Modeling conical indentation in homogeneous materials and in hard films on soft substrates. J. Mater. Res. 20, 521 (2005).
19.Cheng, Y-T. and Cheng, C-M.: Effect of ‘sinking in’ and ‘piling up’ on estimating the contact area under load in indentation. Philos. Mag. Lett. 78, 115 (1998).
20.Bolshakov, A. and 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).
21.Hay, J.C., Bolshakov, A. and Pharr, G.M.: A critical examination of the fundamental relations used in the analysis of nanoindentation data. J. Mater. Res. 14, 2296 (1999).
22.Alkorta, J., Martinez-Esnaola, J.M. and Sevillano, J. Gil: Absence of one-to-one correspondence between elastoplastic properties and sharp-indentation load-penetration data. J. Mater. Res. 20, 432 (2005).
23.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).
24.Cao, Y., Qian, X., Lu, J. and Yao, Z.: An energy-based method to extract plastic properties of metal materials from conical indentation tests. J. Mater. Res. 20, 1194 (2005).

Keywords

Evaluation of the effectiveness of representative methods for determining Young's modulus and hardness from instrumented indentation data

  • Dejun Ma (a1), Taihua Zhang (a2) and Chung Wo Ong (a3)

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