Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-25T02:14:52.041Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  01 January 2006

Dejun Ma ,
Taihua Zhang  and
Chung Wo Ong
Dejun Ma
Affiliation:
Department of Mechanical Engineering, The Academy of Armored Forces Engineering,Beijing 100072, People's Republic of China
Taihua Zhang
Affiliation:
State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, People's Republic of China
Chung Wo Ong*
Affiliation:
Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People's Republic of China
*
a)Address all correspondence to this author. e-mail: apacwong@inet.polyu.edu.hk
Get access

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.

Keywords

HardnessIndentation
Type
Articles
Information
Journal of Materials Research , Volume 21 , Issue 1 , January 2006 , pp. 225 - 233
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.Cheng, Y-T. and Cheng, C.M.: Scaling, dimension analysis, and indentation measurements. Mater. Sci. Eng. R 44, 91 (2004).Google Scholar
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).Google Scholar
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).CrossRefGoogle Scholar
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).Google Scholar
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).Google Scholar
6.Cheng, Y-T. and Cheng, C-M.: Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73, 614 (1998).Google Scholar
7.Cheng, Y-T. and Li, Z.: Scaling relationships for indentation measurements. Philos. Mag. A 82, 1893 (2002).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
9.Cheng, Y-T. and Li, Z.: Scaling relationships in conical indentation of elastic-perfectly plastic solids. Int. J. Solids Struct. 36, 1231 (1999).Google Scholar
10.Cheng, Y-T. and Li, Z.: What is indentation hardness? Surf. Coat. Technol. 133–134, 417 (2000).CrossRefGoogle Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
15.Version, ABAQUS 6.2 (Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI, 2001).Google Scholar
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).Google Scholar
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).Google Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).Google Scholar
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).CrossRefGoogle Scholar
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).Google Scholar
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).CrossRefGoogle Scholar
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).Google Scholar