Skip to main content
SpringerLink
Log in

Protocols for studying the time-dependent mechanical response of viscoelastic materials using spherical indentation stress-strain curves

  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

Spherical nanoindentation has been used successfully to extract meaningful indentation stress-strain curves in hard materials such as metals and ceramics. These methods have not yet been applied on viscoelastic-viscoplastic polymer samples. This study explores the potential of the current spherical nanoindentation analysis protocols in extracting indentation stress-strain curves and viscoelastic properties on samples exhibiting time-dependent material response at room temperature. These new protocols were tested on polymethyl methacrylate, polycarbonate, and low-density polyethylene. The properties extracted under different loading rates and indenter tip sizes conditions were observed to be consistent. It is further demonstrated that it is possible to recover the compression stress-strain curves for polymethyl methacrylate and low-density polyethylene from the measured indentation stress-strain curves. This study establishes some of the foundations needed for the development of protocols needed to reliably investigate the local time-dependent mechanical response of materials using spherical nanoindentation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Arruda, E.M., Boyce, M.C., Jayachandran, R.: Effects of strain rate, temperature and thermomechanical coupling on the finite strain deformation of glassy polymers. Mech. Mater. 19(2), 193–212 (1995)

    Google Scholar 

  • ASTM D695-10: Standard Test Method for Compressive Properties of Rigid Plastics. ASTM International (2010)

  • Bahr, D.F., Watkins, C.M., Kramer, D.E., Gerberich, W.W.: Yield point phenomena during indentation. In: Fundamentals of Nanoindentation and Nanotribology. Symposium, 13-17, vol. 522, pp. 83–88. Mater. Res. Soc., Warrendale, PA, USA (1998). 1998

    Google Scholar 

  • Bouzakis, K.D., Michailidis, N., Hadjiyiannis, S., Skordaris, G., Erkens, G.: Continuous FEM simulation of the nanoindentation: actual indenter tip geometries, material elastoplastic deformation laws and universal hardness. Z. Met.kd. 93(9), 862–869 (2002)

    Google Scholar 

  • Brinson, H., Brinson, C.: Polymer Engineering Science and Viscoelasticity: An Introduction. Springer, New York (2008)

    Google Scholar 

  • Briscoe, B.J., Fiori, L., Pelillo, E.: Nano-indentation of polymeric surfaces. J. Phys. D, Appl. Phys. 31(19), 2395 (1998)

    Google Scholar 

  • Caddell, R.M., Raghava, R.S., Atkins, A.G.: Pressure dependent yield criteria for polymers. Mater. Sci. Eng. 13(2), 113–120 (1974)

    Google Scholar 

  • Cheng, Y.T., Cheng, C.M.: Relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in linear viscoelastic solids. Mater. Sci. Eng.: A 409(1–2), 93–99 (2005a)

    Google Scholar 

  • Cheng, Y.T., Cheng, C.M.: Relationships between initial unloading slope, contact depth, and mechanical properties for conical indentation in linear viscoelastic solids. J. Mater. Res. 20(4), 1046–1053 (2005b)

    Google Scholar 

  • Cheng, L., Xia, X., Scriven, L.E., Gerberich, W.W.: Spherical-tip indentation of viscoelastic material. Mech. Mater. 37(1), 213–226 (2005)

    Google Scholar 

  • Cirnu, M.I.: Linear discrete convolution and its inverse. Part 2. Deconvolution. J. Inf. Syst. Oper. Manag. 4(2), 43–55 (2010)

    Google Scholar 

  • Dassault Systemes Simulia Corp.: ABAQUS. In: Providence, RI, USA, (2014)

  • Donohue, B.R., Ambrus, A., Kalidindi, S.R.: Critical evaluation of the indentation data analyses methods for the extraction of isotropic uniaxial mechanical properties using finite element models. Acta Mater. 60(9), 3943–3952 (2012)

    Google Scholar 

  • Fischer-Cripps, A.C.: A review of analysis methods for sub-micron indentation testing. Vacuum 58, 569–585 (2000)

    Google Scholar 

  • Fischer-Cripps, A.C.: Nanoindentation. Mechanical Engineering Series. Springer, New York (2002)

    Google Scholar 

  • Gauthier, M.M.: Engineered Materials Handbook. ASM International, Russel, Township, OH (1995)

    Google Scholar 

  • Graham, G.A.C.: The contact problem in the linear theory of viscoelasticity. Int. J. Eng. Sci. 3(1), 27–46 (1965)

    MathSciNet  MATH  Google Scholar 

  • Gutierrez-Lemini, D.: Engineering Viscoelasticity. Springer, New York (2014)

    MATH  Google Scholar 

  • Hemker, K.J., Sharpe, W.N.: Microscale characterization of mechanical properties. In: Annual Review of Materials Research, vol. 37, pp. 93–126. Annual Reviews, Palo Alto (2007)

    Google Scholar 

  • Huang, G., Lu, H.: Measurement of Young’s relaxation modulus using nanoindentation. Mech. Time-Depend. Mater. 10(3), 229–243 (2006)

    Google Scholar 

  • Huang, G., Lu, H.: Measurements of two independent viscoelastic functions by nanoindentation. Exp. Mech. 47(1), 87–98 (2007)

    Google Scholar 

  • Huang, G., Wang, B., Lu, H.: Measurements of viscoelastic functions of polymers in the frequency-domain using nanoindentation. Mech. Time-Depend. Mater. 8(4), 345–364 (2004)

    Google Scholar 

  • Hunter, S.C.: The Hertz problem for a rigid spherical indenter and a viscoelastic half-space. J. Mech. Phys. Solids 8(4), 219–234 (1960)

    MathSciNet  MATH  Google Scholar 

  • Jäger, A., Lackner, R.: Identification of viscoelastic model parameters by means of cyclic nanoindentation testing. Int. J. Mater. Res. 99(8), 829–835 (2008)

    Google Scholar 

  • Jakes, J.E., Lakes, R.S., Stone, D.S.: Broadband nanoindentation of glassy polymers: Part I. Viscoelasticity. J. Mater. Res. 27(2), 463–474 (2012)

    Google Scholar 

  • Jaya, N.B., Alam, M.Z.: Small-scale mechanical testing of materials Curr. Sci. 105(8), 1073–1099 (2013)

    Google Scholar 

  • Kalidindi, S.R., Pathak, S.: Determination of the effective zero-point and the extraction of spherical nanoindentation stress–strain curves. Acta Mater. 56(14), 3523–3532 (2008)

    Google Scholar 

  • Kalidindi, S.R., Mohan, S., Rossi, A.: Mechanical characterization of mesoscale interfaces using indentation techniques. JOM 69(1), 22–29 (2017)

    Google Scholar 

  • Khosravani, A., Caliendo, C.M., Kalidindi, S.R.: New insights into the microstructural changes during the processing of dual-phase steels from multiresolution spherical indentation stress-strain protocols. Metals 10(1), 18 (2020)

    Google Scholar 

  • Knauss, W.G., Emri, I., Lu, H.: Mechanics of polymers: viscoelasticity. In: Sharpe, W.N. (ed.) Springer Handbook of Experimental Solid Mechanics, pp. 49–95. Springer, Boston (2008)

    Google Scholar 

  • Kreyszig, E.: Advanced Engineering Mathematics. Wiley, Hoboken (2010)

    MATH  Google Scholar 

  • Lakes, R.: Viscoelastic Materials. Cambridge University Press, Cambridge (2009)

    MATH  Google Scholar 

  • Lakes, R.S., Wineman, A.: On Poisson’s ratio in linearly viscoelastic solids. J. Elast. 85(1), 45–63 (2006)

    MathSciNet  MATH  Google Scholar 

  • Lee, E.H.: Stress analysis in viscoelastic materials. J. Appl. Phys. 27(7), 665–672 (1956)

    MathSciNet  Google Scholar 

  • Lee, E.H., Radok, J.R.M.: The contact problem for viscoelastic bodies. J. Appl. Mech. 27(3), 438–444 (1960)

    MathSciNet  MATH  Google Scholar 

  • Li, X., Bhushan, B.: A review of nanoindentation continuous stiffness measurement technique and its applications. Mater. Charact. 48(1), 11–36 (2002)

    Google Scholar 

  • Martynova, E.: Determination of the properties of viscoelastic materials using spherical nanoindentation. Mech. Time-Depend. Mater. 20(1), 85–93 (2016)

    Google Scholar 

  • Mase, G.: Schaum’s Outline of Continuum Mechanics. McGraw-Hill Education, New York (1970)

    Google Scholar 

  • Moseson, A.J., Basu, S., Barsoum, M.W.: Determination of the effective zero point of contact for spherical nanoindentation. J. Mater. Res. 23(1), 204–209 (2008)

    Google Scholar 

  • Moseson, A.J., Basu, S., Barsoum, M.W.: (2009). U.S. Patent Application No. 12/184,711

  • Odegard, G., Gates, T., Herring, H.: Characterization of viscoelastic properties of polymeric materials through nanoindentation. Exp. Mech. 45(2), 130–136 (2005)

    Google Scholar 

  • Oyen, M.L.: Spherical indentation creep following ramp loading. J. Mater. Res. 20(8), 2094–2100 (2005)

    Google Scholar 

  • Patel, D.K., Kalidindi, S.R.: Correlation of spherical nanoindentation stress-strain curves to simple compression stress-strain curves for elastic-plastic isotropic materials using finite element models. Acta Mater. 112, 295–302 (2016)

    Google Scholar 

  • Patel, D.K., Kalidindi, S.R.: Estimating the slip resistance from spherical nanoindentation and orientation measurements in polycrystalline samples of cubic metals. Int. J. Plast. 92, 19–30 (2017)

    Google Scholar 

  • Pathak, S., Kalidindi, S.R.: Spherical nanoindentation stress–strain curves. Mater. Sci. Eng. R 91, 1–36 (2015)

    Google Scholar 

  • Pathak, S., Kalidindi, S.R., Klemenz, C., Orlovskaya, N.: Analyzing indentation stress–strain response of LaGaO3 single crystals using spherical indenters. J. Eur. Ceram. Soc. 28(11), 2213–2220 (2008)

    Google Scholar 

  • Pathak, S., Stojakovic, D., Doherty, R., Kalidindi, S.R.: Importance of surface preparation on the nano-indentation stress-strain curves measured in metals. J. Mater. Res. 24(3), 1142–1155 (2009a)

    Google Scholar 

  • Pathak, S., Stojakovic, D., Kalidindi, S.R.: Measurement of the local mechanical properties in polycrystalline samples using spherical nanoindentation and orientation imaging microscopy. Acta Mater. 57(10), 3020–3028 (2009b)

    Google Scholar 

  • Pharr, G.M., Strader, J.H., Oliver, W.C.: Critical issues in making small-depth mechanical property measurements by nanoindentation with continuous stiffness measurement. J. Mater. Res. 24(3), 653–666 (2009)

    Google Scholar 

  • Spitzig, W., Richmond, O.: Effect of hydrostatic pressure on the deformation behavior of polyethylene and polycarbonate in tension and in compression. Polym. Eng. Sci. 19(16), 1129–1139 (1979)

    Google Scholar 

  • Srikar, V.T., Spearing, S.M.: A critical review of microscale mechanical testing methods used in the design of microelectromechanical systems. Exp. Mech. 43(3), 238–247 (2003)

    Google Scholar 

  • Ting, T.C.T.: The contact stresses between a rigid indenter and a viscoelastic half-space. J. Appl. Mech. 33(4), 845–854 (1966)

    MATH  Google Scholar 

  • Vachhani, S.J., Doherty, R.D., Kalidindi, S.R.: Effect of the continuous stiffness measurement on the mechanical properties extracted using spherical nanoindentation. Acta Mater. 61(10), 3744–3751 (2013)

    Google Scholar 

  • Vachhani, S.J., Doherty, R.D., Kalidindi, S.R.: Studies of grain boundary regions in deformed polycrystalline aluminum using spherical nanoindentation. Int. J. Plast. 81, 87–101 (2016)

    Google Scholar 

  • Weaver, J.S., Kalidindi, S.R.: Mechanical characterization of Ti-6Al-4V titanium alloy at multiple length scales using spherical indentation stress-strain measurements. Mater. Des. 111, 463–472 (2016)

    Google Scholar 

  • Zhou, Z., Lu, H.: On the measurements of viscoelastic functions of a sphere by nanoindentation. Mech. Time-Depend. Mater. 14(1), 1–24 (2010)

    Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge support from the National Science Foundation (Grant# NSF 1761406).

Author information

Authors and Affiliations

  1. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0405, USA

    M. T. Abba & S. R. Kalidindi

Authors
  1. M. T. Abba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. R. Kalidindi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. R. Kalidindi.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abba, M.T., Kalidindi, S.R. Protocols for studying the time-dependent mechanical response of viscoelastic materials using spherical indentation stress-strain curves. Mech Time-Depend Mater 26, 1–20 (2022). https://doi.org/10.1007/s11043-020-09472-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11043-020-09472-y

Keywords

Search

Navigation