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Measurement of Creep Compliance of Solid Polymers by Nanoindentation

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Abstract

Methods to measure the local surface creep compliance of time-dependent materials are proposedand validated in the regime of linear viscoelasticity using nanoindentation. Two different bulkpolymers, Polymethyl Methacrylate (PMMA) and Polycarbonate (PC), were employed in thevalidation study; though it is expected that the methods developed herein can be applied for verysmall amounts of materials and heterogeneous materials. Both Berkovich and sphericalnanoindenters were used to indent into the material in nanoindentation tests. Two loading historieswere used: (1) a ramp loading history, in which the indentation load and displacement wererecorded; and (2) a step loading history, in which the indentation displacement was recorded as afunction of time. Analysis of the linearly viscoelastic material response was performed to measurethe creep compliance functions for the two materials under two different loading histories. The limitof linearly viscoelastic behavior for each of the two materials was determined through theobservation of the indent impression recovery after complete unloading; it is postulated that linearityis achieved if indentation impression is fully recovered after unloading. Results fromnanoindentation tests generally agree well with data from conventional tension and shear tests. It hasthus validated the techniques of measuring linear creep compliance in the glassy state usingnanoindentation with the Berkovich and spherical indenter tips.

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References

  • Bolshakov, A., Oliver, W.C. and Pharr, G.M., 'Influence of stress on the measurement of mechanical properties using nanoindentation: Part II. Finite element simulations', Journal of Materials Research 11(3), 1996, 760–768.

    Google Scholar 

  • Cheng, L., Xia, X., Yu, W., Scriven, L.E. and Gerberich, W.W., 'Flat-punch indentation of viscoelastic material', Journal of Polymer Science: Part B: Polymer Physics 38, 2000, 10–22.

    Google Scholar 

  • Fischer-Cripps, A.C., Nanoindentation, Mechanical Engineering Series, Springer-Verlag, Berlin, 2002, 1–6.

    Google Scholar 

  • Hunter, S.C., 'The Hertz problem for a rigid spherical indenter and a viscoelastic half-space', Journal of Mechanics, Physics and Solids 8, 1960, 219–234.

    Google Scholar 

  • Knauss, W.G. and Zhu, W., 'Nonlinearly viscoelastic behavior of polycarbonate. I. Response under pure shear', Mechanics of Time-Dependent Materials 6(3), 2002, 231–269.

    Google Scholar 

  • Lee, E.H. and Radok, J.R.M., 'The contact problem for viscoelastic bodies', Journal of Applied Mechanics 27, 1960, 438–444.

    Google Scholar 

  • Lee, S. and Knauss, W.G., 'A note on the determination of relaxation and creep data from ramp tests', Mechanics of Time-Dependent Materials 4, 2000, 1–7.

    Google Scholar 

  • Loubet, J.L., Lucas, B.N. and Oliver, W.C., 'Some measurements of viscoelastic properties with the help of nanoindentation', in International Workshop on Instrumental Indentation, San Diego, CA, April 1995, D.T. Smith (ed.), 1995, 31–34.

  • Lu, H., Zhang, X. and Knauss, W.G., 'Uniaxial, shear, and Poisson relaxation and their conversion to bulk relaxation: Studies on poly(methyl methacrylate)', Polymer Engineering and Science 37(6), 1997, 1053–1064.

    Google Scholar 

  • Nix, W.D., 'Elastic and plastic properties of thin films on substrates: Nanoindentation techniques', Materials Science and Engineering A 234–236, 1997, 37–44.

    Google Scholar 

  • Nix, W.D. and Gao, H., 'Indentation size effect in crystalline materials: A law for strain gradient plasticity', Journal of the Mechanics and Physics of Solids 46(3), 1998, 411–425.

    Google Scholar 

  • Oliver, W.C. and Pharr, G.M., 'An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments', Journal of Materials Research 7(6), 1992, 1564–1583.

    Google Scholar 

  • Oliver, W.C., Hutchings, R. and Pethica, J.B., 'Measurement of hardness at indentation depths as low as 20 nanometers', in Microindentation Techniques in Materials Science and Engineering, ASTM STP 889, American Society for Testing and Materials, Philadelphia, PA, 1986, 90–108.

    Google Scholar 

  • Pethica, J.B., Hutchings, R. and Oliver, W.C., 'Hardness measurement at penetration depths as small as 20 nm', Philosophical Magazine A 48, 1983, 593–606.

    Google Scholar 

  • Pharr, G.M., Oliver, W.C. and Brotzen, F.R., 'On the generality of the relationship between contact stiffness, contact area and elastic modulus during indentation', Journal of Materials Research 7(3), 1992, 613–617.

    Google Scholar 

  • Radok, J.R.M., 'Visco-elastic stress analysis', Quarterly of Applied Mathematics 15, 1957, 198–202.

    Google Scholar 

  • Riande, E., Diaz-calleja, R., Prolongo, M.G., Masegosa, R.M. and Salom, C., Polymer Viscoelasticity – Stress and Strain in Practice, Marcel Dekker, New York, 2000.

    Google Scholar 

  • Sneddon, I.N., 'The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile', International Journal of Engineering and Science 3, 1965, 47–57.

    Google Scholar 

  • Yang, W.H., 'The contact problem for viscoelastic bodies', Journal of Applied Mechanics 33, 1966, 395–401.

    Google Scholar 

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Lu, H., Wang, B., Ma, J. et al. Measurement of Creep Compliance of Solid Polymers by Nanoindentation. Mechanics of Time-Dependent Materials 7, 189–207 (2003). https://doi.org/10.1023/B:MTDM.0000007217.07156.9b

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  • DOI: https://doi.org/10.1023/B:MTDM.0000007217.07156.9b

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