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Relationships between initial unloading slope, contact depth, and mechanical properties for conical indentation in linear viscoelastic solids

Published online by Cambridge University Press:  01 April 2005

Yang-Tse Cheng  and
Che-Min Cheng
Yang-Tse Cheng*
Affiliation:
Materials and Processes Laboratory, General Motors Research and Development Center, Warren, Michigan 48090
Che-Min Cheng
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, People's Republic of China
*
a) Address all correspondence to this author. e-mail: yang.t.cheng@gm.com This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/publications/jmr/policy.html.
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Abstract

Using analytical and finite element modeling, we studied conical indentation in linear viscoelastic solids with either displacement or load as the independent variable. We examine the relationships between initial unloading slope, contact depth, and viscoelastic properties for various loading conditions such as constant displacement rate, constant loading rate, and constant indentation strain rate. We then discuss whether the Oliver–Pharr method for determining contact depth, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to indentation in viscoelastic solids. We conclude with a few comments about two commonly used experimental procedures for indentation measurements in viscoelastic solids: the “hold-at-peak-load” technique and the constant indentation strain-rate method.

Keywords

IndentationMechanical propertiesItheory
Type
Research Article
Information
Journal of Materials Research , Volume 20 , Issue 4 , April 2005 , pp. 1046 - 1053
Copyright
Copyright © Materials Research Society 2005

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References

REFERENCES

1. Lee, E.H.: Stress analysis in visco-elastic bodies. Quarterly Appl. Math. 13, 183 (1955).CrossRefGoogle Scholar
2. Radok, J.R.M.: Visco-elastic stress analysis. Quarterly Appl. Math. 15, 198 (1957).CrossRefGoogle Scholar
3. Lee, E.H. and Radok, J.R.M.: The contact problem for viscoelastic bodies. J. Appl. Mech. 27, 438 (1960).CrossRefGoogle Scholar
4. Hunter, S.C.: The Hertz problem for a rigid spherical indenter and a viscoelastic half-space. J. Mech. Phys. Solids 8, 219 (1960).CrossRefGoogle Scholar
5. Graham, G.A.C.: The contact problem in the linear theory of viscoelasticity. Int. J. Eng. Sci. 3, 27 (1965).CrossRefGoogle Scholar
6. Graham, 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
7. Yang, W.H.: Contact problem for viscoelastic bodies. J. Appl. Mech. 33, 395 (1966).CrossRefGoogle Scholar
8. Ting, T.C.T.: Contact stresses between a rigid indenter and a viscoelastic half-space. J. Appl. Mech. 33, 845 (1966).CrossRefGoogle Scholar
9. Ting, T.C.T.: Contact problems in linear theory of viscoelasticity. J. Appl. Mech. 35, 248 (1968).CrossRefGoogle Scholar
10. Cheng, L., Xia, X., Yu, W., Scriven, L.E. and Gerberich, W.W.: Flat-punch indentation of viscoelastic material. J. Polym. Sci. Part B: Polym. Phys. 38, 10 (2000).3.0.CO;2-6>CrossRefGoogle Scholar
11. Larrson, P-L. and Carlsson, S.: On microindentation of viscoelastic polymers. Polym. Test. 17, 49 (1998).CrossRefGoogle Scholar
12. Shimizu, S., Yanagimoto, T. and Sakai, M.: Pyramidal indentation load-depth curve of viscoelastic materials. J. Mater. Res. 14, 4075 (1999).CrossRefGoogle Scholar
13. Sakai, M. and Shimizu, S.: Indentation rheometry for glass-forming materials. J. Non-Cryst. Solids 282, 236 (2001).CrossRefGoogle Scholar
14. Sakai, M.: Time-dependent viscoelastic relation between load and penetration for an axisymmetric indenter. Philos. Mag. A82, 1841 (2002).CrossRefGoogle Scholar
15. Oyen, 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
16. 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
17. 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).CrossRefGoogle Scholar
18. Findley, W.N., Lai, J.S. and Onaran, K.: Creep and Relaxation of Nonlinear Viscoelastic Materials (Dover, NY, 1976).Google Scholar
19. Mase, G.T. and Mase, G.E.: Continuum Mechanics for Engineers, 2nd Ed. (CRC, Boca Raton, FL, 1999).CrossRefGoogle Scholar
20. Cheng, Y-T. and Cheng, C-M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. R44, 91 (2004).CrossRefGoogle Scholar
21. Sneddon, 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
22. Van Landingham, M.R.: Review of instrumented indentation. J. Res. Nat. Inst. Stand. Tech. 108, 249 (2003).CrossRefGoogle Scholar
23. Briscoe, B.J., Fiori, L. and Pelillo, E.: Nano-indentation of polymeric surfaces. J. Phys. D: Appl. Phys. 31, 2395 (1998).CrossRefGoogle Scholar
24. Ni, 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
25. Hochstetter, G., Jimenez, A. and Loubet, J.L.: Strain-rate effects on hardness of glassy polymers in the nanoscale range. Comparison between quasi-static and continuous stiffness measurements. J. Macromol. Sci. Phys. B38, 681 (1999).CrossRefGoogle Scholar
26. Chudoba, T. and Richter, F.: Investigation of creep behaviour under load during indentation experiments and its influence on hardness and modulus results. Surf. Coat. Tech. 148, 191 (2001).CrossRefGoogle Scholar
27. Feng, 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
28. Ngan, A.H.W. and Tang, B.: Viscoelastic effects during unloading in depth-sensing indentation. J. Mater. Res. 17, 2604 (2002).CrossRefGoogle Scholar
29. Tang, 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
30. Ngan, 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
31. Lucas, B.N. and Oliver, W.C.: Indentation power-law creep of high-purity indium. Metall. Mater. Trans. A 30, 601 (1999).CrossRefGoogle Scholar
32. Cheng, 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
33. Cheng, Y-T. and Cheng, C-M.: Relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in linear viscoelastic solids. GM R&D Publication R&D. 10,059 (Feb. 21, 2005).Google Scholar