Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-28T03:29:14.077Z Has data issue: false hasContentIssue false
  • English
  • Français

New Method for Determining Young’s Modulus by Non-ideally Sharp Indentation

Published online by Cambridge University Press:  01 June 2005

Dejun Ma ,
Chung Wo Ong ,
Sing Fai Wong  and
Jiawen He
Dejun Ma
Affiliation:
Surface Engineering Research Institute, Chinese Mechanical Engineering Society, Beijing 100072, People’s Republic of China
Chung Wo Ong*
Affiliation:
Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People’s Republic of China
Sing Fai Wong
Affiliation:
Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People’s Republic of China
Jiawen He
Affiliation:
State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
*
a) Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

In a previously developed method for estimating Young’s modulus E by depth-sensing indentation with spherical-tipped Berkovich indenter, the E value is deduced from several functional relationships (established by finite element analysis) relating nominal hardness/reduced elastic modulus ratio (Hn/Er) and elastic work/total work ratio (We/W). These relationships are specified for different absolute bluntness/maximum displacement ratios (Δh/hm). This paper reports the generalization of the method by proposing a function to replace all the above mentioned Hn/Er−We/W relationships. The function contains only a parameter Vr ≡ Videal/Vblunt instead of Δh/hm, where Videal is defined as the indented volume bounded by the cross-sectional areas measured at the maximum displacement hm for an ideally sharp indenter, and Vblunt is that of the real indenter. The use of Vr to replace Δh/hm is for the purpose of extending the application of the method for non-spherical tipped Berkovich indenters. The effectiveness of the method for materials of prominent plasticity was demonstrated by performing tests on carbon steel and aluminum alloy using three Berkovich indenters with different tip shapes.

Keywords

Elastic propertiesNanoindentation
Type
Articles
Information
Journal of Materials Research , Volume 20 , Issue 6 , June 2005 , pp. 1498 - 1506
Copyright
Copyright © Materials Research Society 2005

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

1Fischer-Cripps, A.C.: Nanoindentation (Springer-Verlag, New York, NY, 2004), p. 39.CrossRefGoogle Scholar
2Oliver, 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
3Pharr, 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).CrossRefGoogle Scholar
4Oliver, 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).CrossRefGoogle Scholar
5Cheng, Y-T., Li, Z. and Cheng, C-M. Scaling approach to modeling indentation measurements, in Fundamentals of Nanoindentation and Nanotribology II, edited by Baker, S.P., Cook, R.F., Corcoran, S.G., and Moody, N.R. (Mater. Res. Soc. Symp. Proc. 649, Warrendale, PA, 2001), p. Q1.1.Google Scholar
6Cheng, Y-T. and Cheng, C-M.: Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73, 614 (1998).CrossRefGoogle Scholar
7Cheng, C-M. and 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 (1997).CrossRefGoogle Scholar
8Ma, 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).CrossRefGoogle Scholar
9Vlassak, J.J. and Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42, 1223 (1994).CrossRefGoogle Scholar
10Vlassak, J.J. and Nix, W.D.: Indentation modulus of elastically anisotropic half spaces. J. Mech. Phys. Solids 67, 1045 (1993).Google Scholar
11Vlassak, J.J., Ciavarella, M., Barber, J.R. and Wang, X.: The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape. J. Mech. Phys. Solids 51, 1701 (2003).CrossRefGoogle Scholar
12Hirth, J.P. and Lothe, J. Elastic Constants, in Theory of Dislocations (Krieger Publishing Company, Malabar, FL, 1982), p. 837.Google Scholar
13Bolshakov, 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).CrossRefGoogle Scholar
14Cheng, Y-T. and Cheng, C-M.: Scaling relationships in indentation of power-law creep solids using self-similar indenters. Philos. Mag. Lett. 81, 9 (2001).CrossRefGoogle Scholar
15Chudoba, T. and Richter, F.: Investigation of creep behavior under load during indentation experiments and its influence on hardness and modulus results. Surf. Coat. Technol. 148, 191 (2001).CrossRefGoogle Scholar