Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T21:07:46.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Determining the Instantaneous Modulus of Viscoelastic Solids Using Instrumented Indentation Measurements

Published online by Cambridge University Press:  03 March 2011

Yang-Tse Cheng ,
Wangyang Ni  and
Che-Min Cheng
Yang-Tse Cheng
Affiliation:
Materials and Processes Laboratory, General Motors Research and Development Center, Warren, Michigan 48090
Wangyang Ni
Affiliation:
Brown University, Providence, Rhode Island 02912
Che-Min Cheng
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Get access

Abstract

Instrumented indentation is often used in the study of small-scale mechanical behavior of “soft” matters that exhibit viscoelastic behavior. A number of techniques have recently been proposed to obtain the viscoelastic properties from indentation load–displacement curves. In this study, we examine the relationships between initial unloading slope, contact depth, and the instantaneous elastic modulus for instrumented indentation in linear viscoelastic solids using either conical or spherical indenters. In particular, we study the effects of “hold-at-the-peak-load” and “hold-at-the-maximum-displacement” on initial unloading slopes and contact depths. We then discuss the applicability of the Oliver–Pharr method (Refs. 29, 30) for determining contact depth that was originally proposed for indentation in elastic and elastic-plastic solids and recently modified by Ngan et al. (Refs. 20–23) for viscoelastic solids. The results of this study should help facilitate the analysis of instrumented indentation measurements in linear viscoelastic solids.

Keywords

IndentationMechanical properties
Type
Articles
Information
Journal of Materials Research , Volume 20 , Issue 11 , November 2005 , pp. 3061 - 3071
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

1Lee, E.H.: Stress analysis in visco-elastic bodies. Quarterly Appl. Math. 13, 183 (1955).CrossRefGoogle Scholar
2Radok, J.R.M.: Visco-elastic stress analysis. Quarterly Appl. Math. 15, 198 (1957).CrossRefGoogle Scholar
3Lee, E.H. and Radok, J.R.M.: The contact problem for viscoelastic bodies. J. Appl. Mech. 27, 438 (1960).CrossRefGoogle Scholar
4Hunter, S.C.: The Hertz problem for a rigid spherical indenter and a viscoelastic half-space. J. Mech. Phys. Solids 8, 219 (1960).CrossRefGoogle Scholar
5Graham, G.A.C.: The contact problem in the linear theory of viscoelasticity. Int. J. Eng. Sci. 3, 27 (1965).CrossRefGoogle Scholar
6Graham, G.A.C.: Contact problem in linear theory of viscoelsticity when time dependent contact area has any number of maxima and minima. Int. J. Eng. Sci. 5, 495 (1967).CrossRefGoogle Scholar
7Yang, W.H.: Contact problem for viscoelastic bodies. J. Appl. Mech. 33, 395 (1966).CrossRefGoogle Scholar
8Ting, T.C.T.: Contact stresses between a rigid indenter and a viscoelastic half-space. J. Appl. Mech. 33, 845 (1966).CrossRefGoogle Scholar
9Ting, T.C.T.: Contact problems in linear theory of viscoelasticity. J. Appl. Mech. 35, 248 (1968).CrossRefGoogle Scholar
10Briscoe, B.J., Fiori, L. and Pelillo, E.: Nano-indentation of polymeric surfaces. J. Phys. D, Appl. Phys. 31, 2395 (1998).CrossRefGoogle Scholar
11Larrson, P-L. and Carlsson, S.: On microindentation of viscoelastic polymers. Polym. Testing 17, 49 (1998).CrossRefGoogle Scholar
12Cheng, L., Xia, X., Yu, W., Scriven, L.E. and Gerberich, W.W.: Flat-punch indentation of viscoelastic material. J. Polym. Sci. B, Polym. Phys 38, 10 (2001).3.0.CO;2-6>CrossRefGoogle Scholar
13Shimizu, S., Yanagimoto, T. and Sakai, M.: Pyramidal indentation load-depth curve of viscoelastic materials. J. Mater. Res. 14, 4075 (1999).CrossRefGoogle Scholar
14Sakai, M. and Shimizu, S.: Indentation rheometry for glass-forming materials. J. Non-Cryst. Solids 282, 236 (2001).CrossRefGoogle Scholar
15Sakai, M.: Time-dependent viscoelastic relation between load and penetration for an axisymmetric indenter. Philos. Mag. A82, 1841 (2002).CrossRefGoogle Scholar
16Oyen, M.L. and Cook, R.F.: Load-displacement behavior during sharp indentation of viscous-elastic-plastic materials. J. Mater. Res. 18, 139 (2003).CrossRefGoogle Scholar
17VanLandingham, M.R.: Review of instrumented indentation. J. Res. Nat. Inst. Stand. Technol. 108, 249 (2003).CrossRefGoogle ScholarPubMed
18Lu, H., Wang, B., Ma, J., Huang, G. and Viswanathan, H.: Measurement of creep compliance of solid polymers by nanoindentation. Mech. Time-Dependent Mater. 7, 189 (2003).CrossRefGoogle Scholar
19Kumar, M.V.R. and Narasimhan, R.: Analysis of spherical indentation of linear viscoelastic materials. Curr. Sci. 87, 1088 (2004).Google Scholar
20Feng, G. and Ngan, A.H.W.: Effects of creep and thermal drift on modulus measurement using depth-sensing indentation. J. Mater. Res. 17, 660 (2002).CrossRefGoogle Scholar
21Ngan, A.H.W. and Tang, B.: Viscoelastic effects during unloading in depth-sensing indentation. J. Mater. Res. 17, 2604 (2002).CrossRefGoogle Scholar
22Tang, B. and Ngan, A.H.W.: Accurate measurement of tip-sample contact size during nanoindentation of viscoelastic materials. J. Mater. Res. 18, 1141 (2003).CrossRefGoogle Scholar
23Ngan, A.H.W., Wang, H.T., Tang, B. and Sze, K.Y.: Correcting power-law viscoelastic effects in elastic modulus measurement using depth-sensing indentation. Int. J. Solids Struct. 42, 1831 (2005).CrossRefGoogle Scholar
24Cheng, Y-T. and Cheng, C-M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. R44, 91 (2004).Google Scholar
25Cheng, Y-T. and Cheng, C-M.: Relationships between initial unloading slope, contact depth, and mechanical properties for conical indentation in linear viscoelastic solids. J. Mater. Res. 20, 1046 (2005).CrossRefGoogle Scholar
26Cheng, Y-T. and Cheng, C-M.: Relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in linear viscoelastic solids. Mater. Sci. Eng., A (in press).Google Scholar
27Cheng, Y-T. and Cheng, C-M.: A general relationship between contact stiffness, contact depth, and mechanical properties for indentation in linear viscoelastic solids using axisymmetric indenters of arbitrary profiles. Appl. Phys. Lett. 87, 111914 (2005).CrossRefGoogle Scholar
28Doerner, M.F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
29Pharr, G.M., Oliver, W.C. and Brotzen, F.R.: On the generality of the relationship between contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7, 613 (1992).CrossRefGoogle Scholar
30Oliver, 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
31Timoshenko, S.P. and Goodier, J.N.: Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1970).Google Scholar
32Love, A.E.H.: Boussinesq’s problem for a rigid cone. Quart. J. Math. 10, 161 (1939).CrossRefGoogle Scholar
33Sneddon, I.N.: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
34Cheng, 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
35Findley, W.N., Lai, J.S. and Onaran, K.: Creep and Relaxation of Nonlinear Viscoelastic Materials (Dover, New York, 1976).Google Scholar
36Mase, G.T. and Mase, G.E.: Continuum Mechanics for Engineers , 2nd ed. (CRC, Boca Raton, FL, 1999).CrossRefGoogle Scholar
37Ni, W., Cheng, Y-T., Cheng, C-M. and Grummon, D.S.: An energy based method for analyzing instrumented spherical indentation experiments. J. Mater. Res. 19, 149 (2004).CrossRefGoogle Scholar