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Theoretical and experimental analysis of indentation relaxation test

Published online by Cambridge University Press:  09 June 2017

Paul Baral*
Affiliation:
Université de Lyon, Ecole Centrale de Lyon, LTDS UMR CNRS 5513, Ecully, France
Gaylord Guillonneau
Affiliation:
Université de Lyon, Ecole Centrale de Lyon, LTDS UMR CNRS 5513, Ecully, France
Guillaume Kermouche
Affiliation:
Ecole des Mines de Saint Etienne, Centre SMS, Laboratoire LGF UMR 5307, Saint Etienne, France
Jean-Michel Bergheau
Affiliation:
Université de Lyon, Ecole Nationale d'Ingénieurs de Saint Etienne, LTDS UMR CNRS 5513, Saint Etienne, France
Jean-Luc Loubet
Affiliation:
Université de Lyon, Ecole Centrale de Lyon, LTDS UMR CNRS 5513, Ecully, France
*
a)Address all correspondence to this author. e-mail: paul.baral@doctorant.ec-lyon.fr
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Abstract

Indentation relaxation test is investigated from theoretical and experimental points of view. Analytical expressions are derived based on the conical indentation of a homogeneous linear viscoelastic half space. Two loading kinetics prior to the hold displacement segment are studied—i.e., constant displacement rate and constant strain rate. Effects of loading procedure on measured relaxation behavior are considered. It is pointed out that a constant strain rate loading is required to perform depth-independent relaxation measurements and the strain rate affects the relaxation spectrum up to a critical time constant. Few experiments on poly(methyl methacrylate) are then performed to check the consistency of the analytical results. Some experimental limitations are also discussed. Good agreement is found between analytical calculations and experimental measurement trends, especially for the constant strain rate loading effect on the measured relaxation behavior.

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Articles
Copyright
Copyright © Materials Research Society 2017 

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Footnotes

Contributing Editor: Linda S. Schadler

References

REFERENCES

Wheeler, J.M., Armstrong, D.E.J., Heinz, W., and Schwaiger, R.: High temperature nanoindentation: The state of the art and future challenges. Curr. Opin. Solid State Mater. Sci. 19, 354 (2015).Google Scholar
Phani, P.S. and Oliver, W.C.: A direct comparison of high temperature nanoindentation creep and uniaxial creep measurements for commercial purity aluminum. Acta Mater. 111, 31 (2016).Google Scholar
Li, Y., Fang, X., Lu, S., Yu, Q., Hou, G., and Feng, X.: Effects of creep and oxidation on reduced modulus in high-temperature nanoindentation. Mater. Sci. Eng., A 678, 65 (2016).Google Scholar
Everitt, N.M., Davies, M.I., and Smith, J.F.: High temperature nanoindentation—The importance of isothermal contact. Philos. Mag. 91, 1221 (2011).Google Scholar
Sakai, M. and Shimizu, S.: Indentation rheometry for glass-forming materials. J. Non-Cryst. Solids 282, 236 (2001).CrossRefGoogle Scholar
Yang, S., Zhang, Y.W., and Zeng, K.: Analysis of nanoindentation creep for polymeric materials. J. Appl. Phys. 95, 3655 (2004).Google Scholar
Oyen, M.L.: Spherical indentation creep following ramp loading. J. Mater. Res. 20, 2094 (2005).Google Scholar
Oyen, M.L.: Analytical techniques for indentation of viscoelastic materials. Philos. Mag. 86, 5625 (2006).CrossRefGoogle Scholar
Tweedie, C.A. and Van Vliet, K.J.: Contact creep compliance of viscoelastic materials via nanoindentation. J. Mater. Res. 21, 1576 (2006).Google Scholar
Herbert, E.G., Oliver, W.C., Lumsdaine, A., and Pharr, G.M.: Measuring the constitutive behavior of viscoelastic solids in the time and frequency domain using flat punch nanoindentation. J. Mater. Res. 24, 626 (2009).Google Scholar
Mazeran, P.E., Beyaoui, M., Bigerelle, M., and Guigon, M.: Determination of mechanical properties by nanoindentation in the case of viscous materials. Int. J. Mater. Res. 103, 715 (2012).Google Scholar
Maier, V., Merle, B., Göken, M., and Durst, K.: An improved long-term nanoindentation creep testing approach for studying the local deformation processes in nanocrystalline metals at room and elevated temperatures. J. Mater. Res. 28, 1177 (2013).Google Scholar
Dean, J., Campbell, J., Aldrich-Smith, G., and Clyne, T.W.: A critical assessment of the “stable indenter velocity” method for obtaining the creep stress exponent from indentation data. Acta Mater. 80, 56 (2014).Google Scholar
Sakai, M., Sasaki, M., and Matsuda, A.: Indentation stress relaxation of sol–gel-derived organic/inorganic hybrid coating. Acta Mater. 53, 4455 (2005).Google Scholar
Mattice, J., Lau, A., Oyen, M., and Went, R.: Spherical indentation load-relaxation of soft biological tissues. J. Mater. Res. 21, 2003 (2006).CrossRefGoogle Scholar
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).Google Scholar
Andrews, J.W., Bowen, J., and Cheneler, D.: Optimised determination of viscoelastic properties using compliant measurement systems. Soft Matter 9, 5581 (2013).CrossRefGoogle Scholar
Peng, G., Ma, Y., Feng, Y., Huan, Y., Qin, C., and Zhang, T.: Nanoindentation creep of nonlinear viscoelastic polypropylene. Polym. Test. 43, 38 (2015).Google Scholar
Patel, N.G., Sreeram, A., Venkatanarayanan, R.I., Krishnan, S., and Yuya, P.A.: Elevated temperature nanoindentation characterization of poly(para-phenylene vinylene) conjugated polymer films. Polym. Test. 41, 17 (2015).Google Scholar
Goodall, R. and Clyne, T.W.: A critical appraisal of the extraction of creep parameters from nanoindentation data obtained at room temperature. Acta Mater. 54, 5489 (2006).Google Scholar
Vanlandingham, M.R., Chang, N.K., Drzal, P.L., White, C.C., and Chang, S.H.: Viscoelastic characterization of polymers using instrumented indentation. I. Quasi-static testing. J. Polym. Sci., Part B: Polym. Phys. 43, 1794 (2005).Google Scholar
Schiffmann, K.I.: Nanoindentation creep and stress relaxation tests of polycarbonate: Analysis of viscoelastic properties by different rheological models. Int. J. Mater. Res. 97, 1199 (2006).Google Scholar
Bucaille, J.L., Felder, E., and Hochstetter, G.: Identification of the viscoplastic behavior of a polycarbonate based on experiments and numerical modeling of the nano-indentation test. J. Mater. Sci. 37, 3999 (2002).Google Scholar
Kermouche, G., Loubet, J.L., and Bergheau, J.M.: Extraction of stress–strain curves of elastic-viscoplastic solids using conical/pyramidal indentation testing with application to polymers. Mech. Mater. 40, 271 (2008).Google Scholar
Findley, W.: Creep and Relaxation of Nonlinear Viscoelastic Materials (Dover Publication, Inc., New York 1978).Google Scholar
Tschoegl, N.W., Knauss, W.G., and Emri, I.: Poisson’s ratio in linear viscoelasticity—A critical review. Mech. Time-Depend. Mater. 6, 3 (2002).CrossRefGoogle Scholar
Ting, T.C.T.: The contact stresses between a rigid indenter and a viscoelastic half-space. J. Appl. Mech. 33, 845 (1966).Google Scholar
Graham, G.A.C.: The contact problem in the linear theory of viscoelasticity. Int. J. Eng. Sci. 3, 27 (1965).Google Scholar
Love, A.E.H.: Boussinesq’s problem for a rigid cone. Q. J. Math. os-10, 161 (1939).Google Scholar
Sneddon, I.N.: Boussinesq’s problem for a rigid cone. Math. Proc. Cambridge Philos. Soc. 44, 492 (1948).Google Scholar
Cheng, Y.T. and Cheng, C.M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 (2004).Google Scholar
Vandamme, M. and Ulm, F.J.: Viscoelastic solutions for conical indentation. Int. J. Solids Struct. 43, 3142 (2006).Google Scholar
Kermouche, G., Loubet, J.L., and Bergheau, J.M.: Cone indentation of time-dependent materials: The effects of the indentation strain rate. Mech. Mater. 39, 24 (2007).Google Scholar
Tschoegl, N.W.: The Phenomenological Theory of Linear Viscoelastic Behavior 3rd ed. (Springer Berlin Heidelberg, Berlin, Heidelberg, 1989). p. 134.Google Scholar
Ferry, J.D.: Viscoelastic Properties of Polymers (John Wiley and Sons, New York, 1980).Google Scholar
Schwarzl, F. and Staverman, A.J.: Higher approximations of relaxation spectra. Physica 18, 791 (1952).Google Scholar
Ferry, J.D. and Williams, M.L.: Second approximation methods for determining the relaxation time spectrum of a viscoelastic material. J. Colloid Sci. 7, 347 (1952).Google Scholar
Lucas, B.N., Oliver, W.C., Pharr, G.M., and Loubet, J-L.: Time dependent deformation during indentation testing. MRS Proc. 436, 233 (1997).Google Scholar
Guillonneau, G., Kermouche, G., Bec, S., and Loubet, J.L.: Extraction of mechanical properties with second harmonic detection for dynamic nanoindentation testing. Exp. Mech. 52, 933 (2012).Google Scholar
Loubet, J.L., Bauer, M., Tonck, A., Bec, S., and Gauthier-Manuel, B.: Nanoindentation with a surface force apparatus. In Mechanical Properties and Deformation Behavior of Materials Having Ultra-Fine Microstructures, Vol. 233 (1993); p. 429.Google Scholar
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
Guillonneau, G., Kermouche, G., Bergheau, J-M., and Loubet, J-L.: A new method to determine the true projected contact area using nanoindentation testing. C. R. Mec. 343, 410 (2015).CrossRefGoogle Scholar
Herbert, E.G., Sudharshan Phani, P., and Johanns, K.E.: Nanoindentation of viscoelastic solids: A critical assessment of experimental methods. Curr. Opin. Solid State Mater. Sci. 19, 334 (2015).Google Scholar
Yee, A.F. and Takemori, M.T.: Dynamic bulk and shear relaxation in glassy polymers. I. Experimental techniques and results on PMMA. J. Polym. Sci. Polym. Phys. Ed. 20, 205 (1982).Google Scholar
Tabor, D.: The hardness of solids. Rev. Phys. Technol. 1, 145 (1970).Google Scholar
Fernández, P., Rodríguez, D., Lamela, M.J., and Fernández-Canteli, A.: Study of the interconversion between viscoelastic behaviour functions of PMMA. Mech. Time-Depend. Mater. 15, 169 (2011).Google Scholar
Lu, H., Zhang, X., and Knauss, W.G.: Uniaxial, shear, and poisson relaxation and their conversion to bulk relaxation: Studies on poly(methyl methacrylate). Polym. Eng. Sci. 37, 1053 (1997).Google Scholar
Cruz Pinto, J.J.C. and André, J.R.S.: Toward the accurate modeling of amorphous nonlinear materials—Polymer stress relaxation (I). Polym. Eng. Sci. 56, 348 (2016).Google Scholar