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Quantifying plasticity-independent creep compliance and relaxation of viscoelastoplastic materials under contact loading

Published online by Cambridge University Press:  21 October 2011

Matthieu Vandamme ,
Catherine A. Tweedie ,
Georgios Constantinides ,
Franz-Josef Ulm  and
Krystyn J. Van Vliet
Matthieu Vandamme*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; and Laboratoire Navier (École des Ponts ParisTech; Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux; Centre National de la Recherche Scientifique), Université Paris-Est, 77455 Marne-la-Vallée, France
Catherine A. Tweedie
Affiliation:
Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Georgios Constantinides
Affiliation:
Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, 3603 Lemesos, Cyprus
Franz-Josef Ulm
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Krystyn J. Van Vliet*
Affiliation:
Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
*
a)Address all correspondence to these authors. e-mail: [email protected]
b)e-mail: [email protected]
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Abstract

Here we quantify the time-dependent mechanical properties of a linear viscoelastoplastic material under contact loading. For contact load relaxation, we showed that the relaxation modulus can be measured independently of concurrent plasticity exhibited during the loading phase. For indentation creep, we showed that the rate of change of the contact creep compliance can be measured independently of any plastic deformation exhibited during loading through , where a(t) is the contact radius, h(t) is the displacement of the contact probe, and Pmax is the constant applied load during the creep phase. These analytical relations were compared with numerical simulations of conical indentation creep for a viscoelastoplastic material and validated against sharp indentation creep experiments conducted on polystyrene. The derived relations enable extraction of viscoelastic material characteristics, even if sharp probes confer concurrent plasticity, applicable for a general axisymmetric contact probe geometry and a general time-independent plasticity.

Keywords

NanoindentationPolymerElastic properties
Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 1: Focus Issue: Instrumented Indentation , 14 January 2012 , pp. 302 - 312
Copyright
Copyright © Materials Research Society 2011

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References

REFERENCES

1.Galin, L.A.: Contact Problems in the Theory of Elasticity (Gostekhizdat, Moscow, Russia, 1953).Google Scholar
2.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
3.Lee, E.H. and Radok, J.R.M.: The contact problem for viscoelastic bodies. J. Appl. Mech. 27, 438 (1960).CrossRefGoogle Scholar
4.Vandamme, M. and Ulm, F-J.: Viscoelastic solutions for conical indentation. Int. J. Solids Struct. 43, 3142 (2006).CrossRefGoogle Scholar
5.Tweedie, C.A. and Van Vliet, K.J.: Contact creep compliance of viscoelastic materials via nanoindentation. J. Mater. Res. 21, 1576 (2006).CrossRefGoogle Scholar
6.Christensen, R.M.: Theory of Viscoelasticity: An Introduction (Academic Press, NY, 1982).Google Scholar
7.Cheng, Y-T. and Yang, F.: Obtaining shear relaxation modulus and creep compliance of linear viscoelastic materials from instrumented indentation using axisymmetric indenters of power-law profiles. J. Mater. Res. 24, 3013 (2009).CrossRefGoogle Scholar
8.Shimizu, S., Yanagimoto, T., and Sakai, M.: Pyramidal indentation load-depth curve of viscoelastic materials. J. Mater. Res. 14, 4075 (1999).CrossRefGoogle Scholar
9.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
10.Oyen, M.L., Cook, R.F., Emerson, J.A., and Moody, N.R.: Indentation responses of time-dependent films on stiff substrates. J. Mater. Res. 19, 2487 (2004).CrossRefGoogle Scholar
11.Cook, R.F. and Oyen, M.L.: Nanoindentation behavior and mechanical properties measurement of polymeric materials. Int. J. Mater. Res. 98, 370 (2007).CrossRefGoogle Scholar
12.Olesiak, S.E., Oyen, M.L., and Ferguson, V.L.: Viscous-elastic-plastic behavior of bone using Berkovich nanoindentation. Mech. Time-Depend. Mater. 14, 111 (2010).CrossRefGoogle Scholar
13.Zhang, C.Y., Zhang, Y.W., Zeng, K.Y., and Shen, L.: Nanoindentation of polymers with a sharp indenter. J. Mater. Res. 20, 1597 (2005).CrossRefGoogle Scholar
14.Zhang, C.Y., Zhang, Y.W., Zeng, K.Y., and Shen, L.: Characterization of mechanical properties of polymers by nanoindentation tests. Philos. Mag. 86, 4487 (2006).CrossRefGoogle Scholar
15.Pharr, G.M. and Bolshakov, A.: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002).CrossRefGoogle Scholar
16.Zhang, C.Y., Zhang, Y.W., Zeng, K.Y., Shen, L., and Wang, Y.Y.: Extracting the elastic and viscoelastic properties of a polymeric film using a sharp indentation relaxation test. J. Mater. Res. 21, 2991 (2006).CrossRefGoogle Scholar
17.Seltzer, R. and Mai, Y-W.: Depth-sensing indentation of linear viscoelastic-plastic solids: A simple method to determine creep compliance. Eng. Fract. Mech. 75, 4852 (2008).CrossRefGoogle Scholar
18.Anand, L. and Ames, N.M.: On modeling the micro-indentation response of an amorphous polymer. Int. J. Plast. 22, 1123 (2006).CrossRefGoogle Scholar
19.Hartmann, S., Gibmeier, J., and Scholtes, B.: Experiments and material parameter identification using finite elements. Uniaxial tests and validation using instrumented indentation tests. Exp. Mech. 46, 5 (2006).CrossRefGoogle Scholar
20.Tyulyukovskiy, E. and Huber, N.: Identification of viscoplastic material parameters from spherical indentation data: Part I. Neural networks. J. Mater. Res. 21, 664 (2006).CrossRefGoogle Scholar
21.Rauchs, G. and Bardon, J.: Identification of elasto-viscoplastic material parameters by indentation testing and combined finite element modelling and numerical optimization. Finite Elem. Anal. Des. 47, 653 (2011).CrossRefGoogle Scholar
22.Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, United Kingdom, 1985).CrossRefGoogle Scholar
23.Larsson, P.L., Giannakopoulos, A.E., Soderlund, E., Rowcliffe, D.J., and Vestergaard, R.: Analysis of Berkovich indentation. Int. J. Solids Struct. 33, 221 (1996).CrossRefGoogle Scholar
24.Ashby, M.: Materials Selection in Mechanical Design, 3rd ed. (Butterworth-Heinemann, Oxford, United Kingdom, 2004), p. 58.Google Scholar
25.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
26.Cheng, Y-T. and Cheng, C-M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 (2004).CrossRefGoogle Scholar
27.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
28.Bulychev, S.I., Alekhin, V., Shorshorov, M.K., Ternovskii, A., and Shnyrev, G.: Determination of Young’s modulus according to indentation diagram. Ind. Lab. (Transl: Zavodskaya Laboratoria) 41, 1137 (1975).Google Scholar
29.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
30.Tweedie, C.A. and Van Vliet, K.J.: On the indentation recovery and fleeting hardness of polymers. J. Mater. Res. 21, 3029 (2006).CrossRefGoogle Scholar