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Comparison of the Young’s moduli of polymers measured from nanoindentation and bending experiments

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Abstract

Spherical and conical nanoindentation experiments were performed for the same polymer specimens to compare Young’s moduli measured from the elastic loading and unloading curves, and bending experiments. Finite-element simulation was employed to ensure pure elastic deformation during spherical nanoindentation. The moduli measured from the elastic loading curves using Hertz’s contact law are very close to the bending moduli, because both measurements were conducted under the same elastic deformation. However, the moduli measured from the elastic unloading curves are up to 60% higher than the bending moduli owing to plastic deformation close to the sharp conical indenter tip.

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References

  1. P. Wang and L.R. Xu: Dynamic interfacial debonding initiation induced by an incident crack. Int. J. Solids Struct. 43, 6535 (2006).

    Article  Google Scholar 

  2. X. Wei and J.W. Kysar: Experimental validation of multiscale modeling of indentation of suspended circular graphene membranes. Int. J. Solids Struct. 49, 3201 (2012).

    Article  CAS  Google Scholar 

  3. L.R. Xu, L. Li, C.M. Lukehart, and H. Kuai: Mechanical property characterization nanofiber-reinforced composite adhesives. J. Nanosci. Nanotechnol. 7, 2546 (2007).

    Article  CAS  Google Scholar 

  4. B. Anasori and M.W. Barsoum: reversible dislocation motion and micro-cracking in plastically anisotropic solids under cyclic spherical nanoin-dentation. MRS Communications, available on CJO September 2013. doi:10.1557/mrc.2013.39.

    Google Scholar 

  5. G.M. Odegard, T.S. Gate, and H.M. Herring: Characterization of visco-elastic properties of polymeric materials through nanoindentation. Exp. Mech. 45, 130 (2005).

    Article  Google Scholar 

  6. Y.C. Lu, D.C. Jones, G.P. Tandon, S. Putthanarat, and G.A. Schoeppner: High temperature nanoindentation of PMR-15 polyimide. Exp. Mech. 50, 491 (2010).

    Article  CAS  Google Scholar 

  7. M.I. Oyen and R.F. Cook: Load-displacement behavior during sharp indentation of viscous elastic-plastic materials. J. Mater. Res. 18, 139 (2002).

    Article  Google Scholar 

  8. A. Delafrague and F.J. Ulm: Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters. Int. J. Solids Struct. 41, 7351 (2004).

    Article  Google Scholar 

  9. W. Li and T. Siegmund: A numerical study of indentation delamination of weakly bonded ductile films on elastic substrates. Acta Mater. 52, 2989 (2004).

    Article  CAS  Google Scholar 

  10. Y.F. Gao and G.M. Pharr: Multidimensional contact moduli of elastically anisotropic solids. Scr. Mater. 57, 13 (2007).

    Article  CAS  Google Scholar 

  11. G. Cao, X. Chen, Z.H. Xu and X.D. Li: Measuring mechanical properties of micro- and nano-fibers embedded in an elastic substrate: theoretical framework and experiment. Composites 6 41, 33 (2010).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  14. C. Feng, J.M. Tannenbaum, B.S. King, and M.A. Alvin: A load-based multiple-partial unloading micro-indentation technique for mechanical property evaluation. Exp. Mech. 50, 737 (2009).

    Article  Google Scholar 

  15. D. Ghosh, G. Subhash, T.S. Sudarshan, R. Radhakrishnan,and X-L. Gao: Dynamic indentation response of fine-grained boron carbide. J. Am. Ceram. Soc. 90, 1850 (2007).

    Article  CAS  Google Scholar 

  16. W.W. Gerberich, W.Y. Kramer, D. Bahr, A. Stronjy, E. Lilleodden, and J. Nelson: Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations. J. Mater. Res. 13, 421 (1997).

    Article  Google Scholar 

  17. A-Y. Jee and M. Lee: Comparative analysis on the nanoindentation of polymers using atomic force microscopy. Polym. Test. 20, 95 (2009).

    Google Scholar 

  18. K.K. Jha, N. Suksawang, D. Lahiri, and A. Agarwal: Evaluating initial unloading stiffness from elastic work-of-indentation measured in a nanoindentation experiment. J. Mater. Res. 28, 789 (2013).

    Article  CAS  Google Scholar 

  19. C.T. McKee, J.A. Last, P. Russell, and C.J. Murphy: Indentation versus tensile measurements of Young’s modulus for soft biological tissues. Tissue Eng. 617, 155 (2011).

    Article  Google Scholar 

  20. T. Nakamura and Y. Gu: Identification of elastic-plastic anisotropic parameters using instrumented indentation and inverse analysis. Mech. Mater. 39, 340 (2007).

    Article  Google Scholar 

  21. W.C. Oliver and G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).

    Article  CAS  Google Scholar 

  22. B.P. Rittel and G. Ravichandran: An analysis of nanoindentation in linearly elastic solids. Int. J. Solids Struct. 45, 6018 (2008).

    Article  Google Scholar 

  23. D. Tranchida, S. Piccarolo, J. Loos, and A. Alexeev: Accurately evaluating Young’s modulus of polymers through nanoindentations: a phenomenological correction factor to the Oliver and Pharr procedure. Appl. Phys. Lett. 89, 171905 (2006).

    Article  Google Scholar 

  24. C.Y. Zhang, Y.W. Zhang, K.Y. Zeng,and L. Shen: Nanoindentation of polymers with sharp indenters. J. Mater. Res. 20, 1597 (2005).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  26. E.R. Olivas, J.G. Swadener, and Y-L. Shen: Nanoindentation measurement of surface residual stresses in particle-reinforced metal matrix composites. Scr. Mater. 54, 263 (2006).

    Article  CAS  Google Scholar 

  27. A.C. Fischer-Cripps: Nanoindentation, 2nd ed. (Springer Publisher, New South Wales, Australia, 2011), p. 163.

    Book  Google Scholar 

  28. Y.F. Wu, H.Y. Yu,and W.Q. Chen: Mechanics of indentation for piezoelectric thin films on elastic substrate. Int. J. Solids Struct. 49, 95 (2012).

    Article  Google Scholar 

  29. A. Krishnan and L.R. Xu: Experimental studies on the interaction among cracks, notches and interfaces of bonded polymers. Int. J. Solids Struct. 50, 1583 (2014).

    Article  Google Scholar 

  30. R. Martinez and L.R. Xu: Approximate measurements of the though-thickness Young’s moduli of fibrous composite laminates using nanoindentation. Submitted for publication (2014).

    Google Scholar 

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Acknowledgments

The authors acknowledge the support from the Office of Naval Research (Polymer Composites Program) and the National Science Foundation (Surface Engineering and Materials Design Program). Valuable discussion with Professor Yu-Lin Sheng is appreciated.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Texas at El Paso, El Paso, Texas, 79968, USA

    Ricardo Martinez

  2. Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruses, New Mexico, 88003, USA

    L. Roy Xu

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  1. Ricardo Martinez
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  2. L. Roy Xu
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Correspondence to L. Roy Xu.

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For supplementary material for this article, please visit http://dx.doi.org/10.1557/mrc.2014.19

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Martinez, R., Xu, L.R. Comparison of the Young’s moduli of polymers measured from nanoindentation and bending experiments. MRS Communications 4, 89–93 (2014). https://doi.org/10.1557/mrc.2014.19

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  • DOI: https://doi.org/10.1557/mrc.2014.19

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