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Contact creep compliance of viscoelastic materials via nanoindentation

Published online by Cambridge University Press:  01 June 2006

Catherine A. Tweedie  and
Krystyn J. Van Vliet
Catherine A. Tweedie
Affiliation:
Department of Materials Science and 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 this author. e-mail: [email protected]
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Abstract

The creep compliance of viscoelastic materials such as synthetic polymers is an established metric of the rate at which strain increases for a constant applied stress and can, in principle, be implemented at the nanoscale to compare quantitatively bulk or thin film polymers of different structures or processing histories. Here, we outline the evolution of contact creep compliance analysis and application for both conical and spherical indenter geometries. Through systematic experiments on four amorphous (glassy) polymers, two semi-crystalline polymers and two epoxies, we show that assumptions of linear viscoelasticity are not maintained for any of these polymers when creep compliance is measured via conical indentation at the nanoscale, regardless of the rate of stress application (step or ramp). Further, we show that these assumptions can be maintained to evaluate the contact creep compliance Jc(t) of these bulk polymers, regardless of the rate of stress application, provided that the contact strains are reduced sufficiently through spherical indentation. Finally, we consider the structural and physical properties of these polymers in relation to Jc(t), and demonstrate that Jc(t) correlates positively with molecular weight between entanglements or crosslinks of bulk, glassy polymers.

Keywords

AmorphousPolymerStructural
Type
Articles
Information
Journal of Materials Research , Volume 21 , Issue 6 , June 2006 , pp. 1576 - 1589
Copyright
Copyright © Materials Research Society 2006

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References

REFERENCES

1.Oliver, W.C., 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
2.Asif, S.A.S., Wahl, K.J., Colton, R.J., Warren, O.L.: Quantitative imaging of nanoscale mechanical properties using hybrid nanoindentation and force modulation. J. Appl. Phys. 90, 1192 (2001).CrossRefGoogle Scholar
3.Loubet, J.L., Oliver, W.C., Lucas, B.N.: Measurement of the loss tangent of low-density polyethylene with a nanoindentation technique. J. Mater. Res. 15, 1195 (2000).CrossRefGoogle Scholar
4.Ngan, A.H.W., Tang, B.: Viscoelastic effects during unloading in depth-sensing indentation. J. Mater. Res. 17, 2604 (2002).CrossRefGoogle Scholar
5.Lu, H., Wang, B., Ma, J., Huang, G., Viswanathan, H.: Measurement of creep compliance of solid polymers by nanoindentation. Mech. Time-Depend. Mater. 7, 189 (2003).CrossRefGoogle Scholar
6.Fischer-Cripps, A.C.: A simple phenomenological approach to nanoindentation creep. Mater. Sci. Eng. A 385, 74 (2004).CrossRefGoogle Scholar
7.VanLandingham, M.R., Drzal, P.L., and White, C.C.: Indentation creep and relaxation measurements of polymers, in Fundamentals of Nanoindentation and Nanotribology III edited by Wahl, K.J., Huber, N., Mann, A.B., Bahr, D.F., and Cheng, Y-T. (Mater. Res. Soc. Symp. Proc. 841, Warrendale, PA, 2005), R5.5.Google Scholar
8.Lu, H., Huang, G., Wang, B., Mamedov, A., and Gupta, S.: Measurements of viscoelastic properties of SWNT/polymer composite films using nanoindentation, in Fundamentals of Nanoindentation and Nanotribology III edited by Wahl, K.J., Huber, N., Mann, A.B., Bahr, D.F., and Cheng, Y-T. (Mater. Res. Soc. Symp. Proc. 841, Warrendale, PA, 2005), R4.5.Google Scholar
9.Yang, S., Zhang, Y.W., Zeng, K.Y.: Analysis of nanoindentation creep for polymeric materials. J. Appl. Phys. 95, 3655 (2004).CrossRefGoogle Scholar
10.Oyen, M.L.: Spherical indentation creep following ramp loading. J. Mater. Res. 20, 2094 (2005).CrossRefGoogle Scholar
11.Tweedie, C.A. and Van Vliet, K.J.: Nanomechanical quantification of energy absorption, in Fundamentals of Nanoindentation and Nanotribology III edited by Wahl, K.J., Huber, N., Mann, A.B., Bahr, D.F., and Cheng, Y-T. (Mater. Res. Soc. Symp. Proc. 841, Warrendale, PA, 2005), R5.6.Google Scholar
12.Ting, T.C.T.: The contact stresses between a rigid indentor and a viscoelastic half-space. J. Appl. Mech. 88, 845 (1966).CrossRefGoogle Scholar
13.Lee, E.H., Radok, J.R.M.: The contact problem for viscoelastic bodies. J. Appl. Mech. 27, 438 (1960).CrossRefGoogle Scholar
14.Cheng, L., Xia, X., Scriven, L.E., Gerberich, W.W.: Spherical-tip indentation of viscoelastic material. Mech. Mater. 37, 213 (2005).CrossRefGoogle Scholar
15.VanLandingham, M.R., Chang, N-K., Drzal, P.L., White, C.C., Chang, S-H.: Viscoelastic characterization of polymers using instrumented indentation—I. Quasi-static testing. J. Polym. Sci. B: Polym. Phys. 43, 1794 (2005).CrossRefGoogle Scholar
16.Cheng, Y-T. and Cheng, C-M.: Modeling indentation in linear viscoelastic solids, in Fundamentals of Nanoindentation and Nanotribology III edited by Wahl, K.J., Huber, N., Mann, A.B., Bahr, D.F., and Cheng, Y-T. (Mater. Res. Soc. Symp. Proc. 841, Warrendale, PA, 2005), R11.2.Google Scholar
17.Briscoe, B.J., Fiori, L., Pelillo, E.: Nano-indentation of polymeric surfaces. J. Phys. D 31, 2395 (1998).CrossRefGoogle Scholar
18.Vandamme, M., Ulm, F. Viscoelastic solutions for conical indentation. (2005, unpublished).Google Scholar
19.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
20.Lesser, A.J., Calzia, K.J.: Molecular parameters governing the yield response of epoxy-based glassy networks. J. Polym. Sci. B: Polym. Phys. 42, 2050 (2004).CrossRefGoogle Scholar
21.Loo, L.S., Cohen, R.E., Gleason, K.K.: Chain mobility in the amorphous region of nylon 6 observed under active uniaxial deformation. Science 288, 116 (2000).CrossRefGoogle ScholarPubMed
22.Shimizu, S., Yanagimoto, T., Sakai, M.: The pyramidal indentation load-depth curve of viscoelastic materials. J. Mater. Res. 14, 4075 (1999).CrossRefGoogle Scholar
23.Sakai, M.: Indentation rheometry for glass-forming materials: J. Non-Cryst. Solids 282, 236 (2001).Google Scholar
24.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, 1046 (2005).CrossRefGoogle Scholar
25.Tweedie, C.A., Van Vliet, K.J. On the volumetric recovery and fleeting hardness of time-dependent materials (polymers). (2006, unpublished).CrossRefGoogle Scholar
26.Tabor, D.: The Hardness of Metals (Clarendon, London, UK, 1951).Google Scholar
27.Ferry, J.D.: Viscoelastic Properties of Polymers 3rd ed. (John Wiley & Sons, New York, 1980).Google Scholar
28.Brady, R.F.: Comprehensive Desk Reference of Polymer Characterization and Analysis (Oxford University Press, Washington, DC, 2003).Google Scholar
29.Young, R.J., Lovell, P.A.: Introduction to Polymers 2nd ed. (Chapman & Hall, New York, 1991).CrossRefGoogle Scholar
30.Dinelli, F., Leggett, G.J., Shipway, P.H.: Nanowear of polystyrene surfaces: Molecular entanglement and bundle formation. Nanotech. 16, 675 (2005).CrossRefGoogle Scholar
31.Priestly, R.D., Ellison, C.J., Broadbelt, L.J., Torkelson, J.M.: Structural relaxation of polymer glasses at surfaces, interfaces, and in between. Science 309, 456 (2005).CrossRefGoogle Scholar
32.Lee, E.H.: Stress analysis in visco-elastic bodies. Quart. Appl. Math. 13, 183 (1955).CrossRefGoogle Scholar
33.Hertz, H.R.: On the Contact of Two Elastic Solids (MacMillan, 1882).Google Scholar
34. See Eq. 25c of Ref. 12.Google Scholar