Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-18T10:54:20.846Z Has data issue: false hasContentIssue false
  • English
  • Français

Broadband nanoindentation of glassy polymers: Part I. Viscoelasticity

Published online by Cambridge University Press:  01 December 2011

Joseph E. Jakes ,
Rod S. Lakes  and
Don S. Stone
Joseph E. Jakes*
Affiliation:
Performance Enhanced Biopolymers, USDA Forest Service, Forest Products Laboratory, Madison, Wisconsin 53726; and Materials Science Program, University of Wisconsin—Madison, Madison, Wisconsin 53706
Rod S. Lakes
Affiliation:
Department of Engineering Physics, University of Wisconsin—Madison, Madison, Wisconsin 53706
Don S. Stone
Affiliation:
Materials Science Program, University of Wisconsin—Madison, Madison, Wisconsin 53706; and Department of Materials Science and Engineering, University of Wisconsin—Madison, Madison, Wisconsin 53706
*
a)Address all correspondence to this author. e-mail: jjakes@fs.fed.us
Get access

Abstract

Protocols are developed to assess viscoelastic moduli from unloading slopes in Berkovich nanoindentation across four orders of magnitude in time scale (0.01–100 s unloading time). Measured viscoelastic moduli of glassy polymers poly(methyl methacrylate), polystyrene, and polycarbonate follow the same trends with frequency (1/unloading time) as viscoelastic moduli generated from dynamic mechanical analysis and broadband viscoelastic spectroscopy but are 18–50% higher. Included in the developed protocols is an experimental method based on measured indent area to remove from consideration indents for which viscoplastic deformation takes place during unloading. Ancillary measurements of indent area and depth reveal no detectable (∼1%) change in area between 200 s and 4.9 days following removal of indenter.

Keywords

ViscoelasticityPolymerHardness
Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 2 , 28 January 2012 , pp. 463 - 474
Copyright
Copyright © Materials Research Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Lakes, R.: Viscoelastic Materials. (Cambridge University Press, Cambridge, UK, 2009), pp. 1–110.Google Scholar
2.Cheng, Y-T. and Cheng, C-M.: Scaling, dimensional analysis, and indentation measurements. Mat. Sci. Eng. R 44, 91 (2004).Google Scholar
3.Vandamme, M. and Ulm, F-J.: Viscoelastic solutions for conical indentation. Int. J. Solids Struct. 43, 3142 (2006).Google Scholar
4.Giannakopoulos, A.E.: Elastic and viscoelastic indentation of flat surfaces by pyramid indentors. J. Mech. Phys. Solids. 54, 1305 (2006).CrossRefGoogle Scholar
5.Lee, E.H. and Radok, J.R.M.: Contact problem for viscoelastic bodies. J. Appl. Mech. 27, 438 (1960).Google Scholar
6.Hunter, S.C.: The Hertz problem for a rigid spherical indenter and a viscoelastic half-space. J. Mech. Phys. Solids. 8, 219 (1960).CrossRefGoogle Scholar
7.Lee, E.H.: Stress analysis for linear viscoelastic materials. Rheol. Acta. 1, 426 (1961).CrossRefGoogle Scholar
8.Graham, G.A.C.: The contact problem in the linear theory of viscoelasticity. Int. J. Eng. Sci. 3, 27 (1965).CrossRefGoogle Scholar
9.Ting, T.C.T.: Contact stresses between rigid indenter and viscoelastic half-space. J. Appl. Mech. 33, 845 (1966).CrossRefGoogle Scholar
10.Graham, G.A.C.: The contact problem in the linear theory of viscoelasticity when the time dependent contact area has any number of maxima and minima. Int. J. Eng. Sci. 5, 495 (1967).CrossRefGoogle Scholar
11.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).CrossRefGoogle Scholar
12.Loubet, J.L., Oliver, W.C., and Lucas, B.N.: Measurement of the loss tangent of low-density polyethylene with a nanoindentation technique. J. Mater. Res. 15, 1195 (2000).Google Scholar
13.Asif, S.A.S., Wahl, K.J., Colton, R.J., and Warren, O.L.: Quantitative imaging of nanoscale mechanical properties using hybrid nanoindentation and force modulation. J. Appl. Phys. 90, 5838 (2001).Google Scholar
14.White, C.C., Vanlandingham, M.R., Drzal, P.L., Chang, N.K., and Chang, S.H.: Viscoelastic characterization of polymers using instrumented indentation. II. Dynamic testing. J. Polym. Sci. Part B: Polym. Phys. 43, 1812 (2005).CrossRefGoogle Scholar
15.Jäger, A., Lackner, R., and Eberhardsteiner, J.: Identification of viscoelastic properties by means of nanoindentation taking the real tip geometry into account. Meccanica 42, 293 (2007).Google Scholar
16.Oyen, M.L.: Relating viscoelastic nanoindentation creep and load relaxation experiments. Int. J. Mater. Res. 99, 823 (2008).CrossRefGoogle Scholar
17.Oyen, M.L. and Cook, R.F.: Load-displacement behavior during sharp indentation of viscous-elastic-plastic materials. J. Mater. Res. 18, 139 (2003).CrossRefGoogle Scholar
18.Beake, B.: Modelling indentation creep of polymers: A phenomenological approach. J. Phys. D: Appl. Phys. 39, 4478 (2006).CrossRefGoogle Scholar
19.Lu, H., Wang, B., Ma, J., Huang, G., and Viswanathan, H.: Measurement of creep compliance of solid polymers by nanoindentation. Mech. Time-Depend. Mater. 7, 189 (2003).Google Scholar
20.Tweedie, C.A. and Van Vliet, K.J.: Contact creep compliance of viscoelastic materials via nanoindentation. J. Mater. Res. 21, 1576 (2006).CrossRefGoogle Scholar
21.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
22.Odegard, G.M., Gates, T.S., and Herring, H.M.: Characterization of viscoelastic properties of polymeric materials through nanoindentation, in Proceedings of the Society for Experimental Mechanics, Inc 52, 130 (2005).Google Scholar
23.King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 (1987).Google Scholar
24.Bolshakov, A. and Pharr, G.M.: Inaccuracies in Sneddon’s solution for elastic indentation by a rigid cone and their implications for nanoindentation data analysis, in Thin Films: Stresses and Mechanical Properties VI, edited by Gerberich, W.W., Gao, H., Sundgren, J-E., and Baker, S.P. (Mater. Res. Soc. Symp. Proc. 436, Pittsburgh, PA, 1997), p. 189.Google Scholar
25.Chudoba, T. and Jennett, N.M.: Higher accuracy analysis of instrumented indentation data obtained with pointed indenters. J. Phys. D: Appl. Phys. 41, 215407 (2008).Google Scholar
26.Strader, J.H., Shim, S., Bei, H., Oliver, W.C., and Pharr, G.M.: An experimental evaluation of the constant β relating the contact stiffness to the contact area in nanoindentation. Philos. Mag. 86, 5285 (2006).Google Scholar
27.Jakes, J.E., Frihart, C.R., Beecher, J.F., Moon, R.J., and Stone, D.S.: Experimental method to account for structural compliance in nanoindentation measurements. J. Mater. Res. 23, 1113 (2008).Google Scholar
28.Oliver, W.C. and Pharr, G.M.: Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).Google Scholar
29.Cheng, Y-T. and 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).Google Scholar
30.Cheng, Y-T. and 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, 93 (2005).Google Scholar
31.Cheng, Y-T., Cheng, C-M., and Wangyang, N.: Methods of obtaining instantaneous modulus of viscoelastic solids using displacement-controlled instrumented indentation with axisymmetric indenters of arbitrary smooth profiles. Mater. Sci. Eng., A 423, 2 (2006).Google Scholar
32.Cheng, Y-T., Wangyang, N., and Cheng, C-M.: Determining the instantaneous modulus of viscoelastic solids using instrumented indentation measurements. J. Mater. Res. 20, 3061 (2005).Google Scholar
33.Fujisawa, N. and Swain, M.V.: Nanoindentation-derived elastic modulus of an amorphous polymer and its sensitivity to load-hold period and unloading strain rate. J. Mater. Res. 23, 637 (2008).CrossRefGoogle Scholar
34.Ngan, A.H.W., Wang, H.T., Tang, B., and Sze, K.Y.: Correcting power-law viscoelastic effects in elastic modulus measurement using depth-sensing indentation. Int. J. Solids Struct. 42, 1831 (2005).Google Scholar
35.Tang, B. and Ngan, A.H.W.: Accurate measurement of tip-sample contact size during nanoindentation of viscoelastic materials. J. Mater. Res. 18, 1141 (2003).Google Scholar
36.Fujisawa, N. and Swain, M.V.: Effect of unloading strain rate on the elastic modulus of a viscoelastic solid determined by nanoindentation. J. Mater. Res. 21, 708 (2006).CrossRefGoogle Scholar
37.Fujisawa, N. and Swain, M.V.: On the indentation contact area of a creeping solid during constant-strain-rate loading by a sharp indenter. J. Mater. Res. 22, 893 (2007).CrossRefGoogle Scholar
38.Tong, J., Sun, J., Chen, D., and Zhang, S.: Factors impacting nanoindentation testing results of the cuticle of dung beetle Copris ochus Motschulsky: J. Bionics Eng. 1, 221 (2004).Google Scholar
39.Chien-Kuo, L., Sanboh, L., Li-Piin, S., and Nguyen, T.: Load-displacement relations for nanoindentation of viscoelastic materials. J. Appl. Phys. 100, 33503 (2006).Google Scholar
40.Ebenstein, D.M. and Pruitt, L.A.: Nanoindentation of biological materials. Nano Today 1, 26 (2006).CrossRefGoogle Scholar
41.Feng, G. and Ngan, A.H.W.: Effects of creep and thermal drift on modulus measurement using depth-sensing indentation. J. Mater. Res. 17, 660 (2002).CrossRefGoogle Scholar
42.Ngan, A.H.W. and Tang, B.: Viscoelastic effects during unloading in depth-sensing indentation. J. Mater. Res. 17, 2604 (2002).Google Scholar
43.Briscoe, B.J., Fiori, L., and Pelillo, E.: Nano-indentation of polymeric surfaces. J. Phys. D: Appl. Phys. 31, 2395 (1998).Google Scholar
44.Tang, B., Ngan, A., and Lu, W.: An improved method for the measurement of mechanical properties of bone by nanoindentation. J. Mater. Sci. Mater. Med. 18, 1875 (2007).Google Scholar
45.Jakes, J.E., Lakes, R.S., and Stone, D.S.: Broadband nanoindentation of glassy polymers: Part II. Viscoplasticity. J. Mater. Res. Soc. 27(2), 475 (2011).Google Scholar
46.Stone, D.S., Yoder, K.B., and Sproul, W.D.: Hardness and elastic modulus of TiN based on continuous indentation technique and new correlation. J. Vac. Sci. Technol. A 9, 2543 (1991).Google Scholar
47.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
48.Afifi, H.A.: Ultrasonic pulse echo studies of the physical properties of PMMA, PS, and PVC. Polym. Plast. Technolo. and Eng. 42, 193 (2003).Google Scholar
49.Fukuhara, M. and Sampei, A.: Low-temperature elastic moduli and dilational and shear internal friction of polycarbonate. Jpn. J. Appl. Phys. 35, 3218 (1996).Google Scholar
50.Capodagli, J. and Lakes, R.: Isothermal viscoelastic properties of PMMA and LDPE over 11 decades of frequency and time: A test of time–temperature superposition. Rheologica Acta. 47, 777 (2008).Google Scholar
51.Tweedie, C.A. and Van Vliet, K.J.: On the indentation recovery and fleeting hardness of polymers. J. Mater. Res. 21, 3029 (2006).Google Scholar
52.Low, I.M., Paglia, G., and Shi, C.: Indentation responses of viscoelastic materials. J. Appl. Polym. Sci. 70, 2349 (1998).Google Scholar
53.VanLandingham, M.R., Villarrubia, J.S., Guthrie, W.F., and Meyers, G.F.: Nanoindentation of polymers: An overview. Macromol. Symp. 167, 15 (2001).Google Scholar
54.Briscoe, B.J. and Sebastian, K.S.: The elastoplastic response of poly(methyl methacrylate) to indentation. Proc. R. Soc. London, Ser. A 452, 439 (1996).Google Scholar
55.Anand, L. and Ames, N.M.: On modeling the micro-indentation response of an amorphous polymer. Int. J. Plast. 22, 1123 (2006).Google Scholar
56.Veprek, R.G., Parks, D.M., Argon, A.S., and Veprek, S.: Erratum to “Non-linear finite element constitutive modeling of mechanical properties of hard and superhard materials studied by indentation” [Mater. Sci. Eng. A 422 (2006) 205–217] (DOI:10.1016/j.msea.2006.02.020). Mater. Sci. Eng., A 448, 366 (2007).Google Scholar
57.Strojny, A., Xia, X., Tsou, A., and Gerberich, W.W.: Techniques and considerations for nanoindentation measurements of polymer thin film constitutive properties. J. Adhes. Sci. Technol. 12, 1299 (1998).Google Scholar
58.Mook, W.M. and Gerberich, W.W.: Effect of hydrostatic pressure on indentation modulus, in Fundamentals of Nanoindentation and Nanotribology IV, edited by Le Bourhis, E., Morris, D.J., Oyen, M.L., Schwaiger, R., and Staedler, T. (Mater. Res. Soc. Symp. Proc. 1049, Warrendale, PA, 2008) 1049-AA02-09, p. 21.Google Scholar
59.Wolf, B. and Goken, M.: On the pressure dependence of the indentation modulus. Z. Metallkd. 96, 1247 (2005).CrossRefGoogle Scholar