Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-29T05:24:19.322Z Has data issue: false hasContentIssue false
  • English
  • Français

Broadband nanoindentation of glassy polymers: Part II. Viscoplasticity

Published online by Cambridge University Press:  18 November 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: [email protected]
Get access

Abstract

The relationship between hardness and flow stress in glassy polymers is examined. Materials studied include poly(methylmethacrylate), polystyrene, and polycarbonate. Properties are strongly rate dependent, so broadband nanoindentation creep (BNC) is used to measure hardness across a broad range of indentation strain rates (10−4 to 10 s−1). Molybdenum (Mo) is also studied to serve as a “control” whose rate-dependent hardness properties have been measured previously and whose flow stress, unlike the polymers, is pressure insensitive. The BNC hardness data are converted to uniaxial flow stress using two methods based on the usual Tabor–Marsh–Johnson correlation. With both methods the resulting BNC-derived uniaxial flow stress data agree closely with literature compression uniaxial flow stress data for all materials. For the polymers, the BNC hardness data depend on initial rate of loading, indicating that the measured properties are path dependent. Path dependence is not detected in Mo.

Keywords

PolymerHardnessViscoelasticity
Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 2 , 28 January 2012 , pp. 475 - 484
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.Boyer, R.F.: Dependence of mechanical properties on molecular motion in polymers. Polym. Eng. Sci. 8(3), 161 (1968).CrossRefGoogle Scholar
2.Argon, A.S.: A theory for the low-temperature plastic deformation of glassy polymers. Philos. Mag. 28(4), 839 (1973).CrossRefGoogle Scholar
3.Mayr, A.E., Cook, W.D., and Edward, G.H.: Yielding behaviour in model epoxy thermosets—I. Effect of strain rate and composition. Polymer 39, 3719 (1998).CrossRefGoogle Scholar
4.Rana, D., Sauvant, V., and Halary, J.L.: Molecular analysis of yielding in pure and antiplasticized epoxy-amine thermosets. J. Mater. Sci. 37(24), 5267 (2002).CrossRefGoogle Scholar
5.Lin, L. and Argon, A.S.: Rate mechanism of plasticity in the crystalline component of semicrystalline nylon 6. Macromolecules 27(23), 6903 (1994).CrossRefGoogle Scholar
6.Brooks, N.W.J., Duckett, R.A., and Ward, I.M.: Temperature and strain-rate dependence of yield stress of polyethylene. J. Polym. Sci., Part B: Polym. Phys. 36(12), 2177 (1998).3.0.CO;2-X>CrossRefGoogle Scholar
7.Kazmierczak, T., Galeski, A., and Argon, A.S.: Plastic deformation of polyethylene crystals as a function of crystal thickness and compression rate. Polymer 46(21), 8926 (2005).CrossRefGoogle Scholar
8.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).CrossRefGoogle Scholar
9.Warren, O.L. and Wyrobek, T.J.: Nanomechanical property screening of combinatorial thin-film libraries by nanoindentation. Meas. Sci. Technol. 16(1), 100 (2005).CrossRefGoogle Scholar
10.Ebenstein, D.M. and Pruitt, L.A.: Nanoindentation of biological materials. Nano Today 1(3), 26 (2006).CrossRefGoogle Scholar
11.Jakes, J.E., Frihart, C.R., and Stone, D.S.: Creep properties of micron-size domains in ethylene glycol modified wood across 4½ decades in strain rate, in Mechanics of Biological and Biomedical Materials, edited by Katti, K., Hellmich, C., Wegst, U.G.K., and Narayan, R. (Mater. Res. Soc. Symp. Proc. 1132, Warrendale, PA, 2009), 1132-Z07-21.Google Scholar
12.Rostoker, W. and Galante, J.O.: Indentation creep of polymers for human joint applications. J. Biomed. Mater. Res. 13(5), 825 (1979).CrossRefGoogle ScholarPubMed
13.Takahashi, M., Shen, M.C., Taylor, R.B., and Tobolsky, A.V.: Master curves for some amorphous polymers. J. Appl. Polym. Sci. 8(4), 1548 (1964).CrossRefGoogle Scholar
14.Chu, S.N.G. and Li, J.C.M.: Impression creep; a new creep test. J. Mater. Sci. 12(11), 2200 (1977).CrossRefGoogle Scholar
15.Chen, J., Bell, G.A., Hanshan, D., Smith, J.F., and Beake, B.D.: A study of low temperature mechanical properties and creep behaviour of polypropylene using a new sub-ambient temperature nanoindentation test platform. J. Phys. D: Appl. Phys. 43(42), 425404 (2010).CrossRefGoogle Scholar
16.Oyen, M.L.: Sensitivity of polymer nanoindentation creep measurements to experimental variables. Acta Mater. 55(11), 3633 (2007).CrossRefGoogle Scholar
17.Fischer-Cripps, A.C.: A simple phenomenological approach to nanoindentation creep. Mater. Sci. Eng., A 385(1–2), 74 (2004).CrossRefGoogle Scholar
18.Li, H. and Ngan, A.H.W.: Size effects of nanoindentation creep. J. Mater. Res. 19(2), 513 (2004).CrossRefGoogle Scholar
19.Constantinides, G., Tweedie, C.A., Holbrook, D.M., Barragan, P., Smith, J.F., and Van Vliet, K.J.: Quantifying deformation and energy dissipation of polymeric surfaces under localized impact. Mater. Sci. Eng., A 489, 403 (2008).Google Scholar
20.Jager, A. and Lackner, R.: Identification of viscoelastic model parameters by means of cyclic nanoindentation testing. Int. J. Mater. Res. 99, 829 (2008).CrossRefGoogle Scholar
21.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).CrossRefGoogle Scholar
22.Oyen, M.L.: Spherical indentation creep following ramp loading. J. Mater. Res. 20(8), 2094 (2005).CrossRefGoogle Scholar
23.Oyen, M.L.: Relating viscoelastic nanoindentation creep and load relaxation experiments. Int. J. Mater. Res. 99, 823 (2008).CrossRefGoogle Scholar
24.Tweedie, C.A. and Van Vliet, K.J.: Contact creep compliance of viscoelastic materials via nanoindentation. J. Mater. Res. 21(6), 1576 (2006).CrossRefGoogle Scholar
25.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).CrossRefGoogle Scholar
26.Beake, B.: Modelling indentation creep of polymers: A phenomenological approach. J. Phys. D: Appl. Phys. 39, 4478 (2006).CrossRefGoogle Scholar
27.Zhang, C.Y., Zhang, Y.W., Zeng, K.Y., and Shen, L.: Characterization of mechanical properties of polymers by nanoindentation tests. Philos. Mag. 86, 4487 (2006).CrossRefGoogle Scholar
28.Jakes, J.E., Lakes, R.S., and Stone, D.S.: Broadband nanoindentation of glassy polymers: Part I. Viscoelasticity. J. Mater. Res. 27(2), 463 (2011).CrossRefGoogle Scholar
29.Elmustafa, A.A., Kose, S., and Stone, D.S.: The strain-rate sensitivity of the hardness in indentation creep. J. Mater. Res. 22(4), 926 (2007).CrossRefGoogle Scholar
30.Puthoff, J.B., Jakes, J.E., Cao, H., and Stone, D.S.: Investigation of thermally activated deformation in amorphous PMMA and Zr-Cu-Al bulk metallic glasses with broadband nanoindentation creep. J. Mater. Res. 24(3), 1279 (2009).CrossRefGoogle Scholar
31.Stone, D.S. and Yoder, K.B.: Division of the hardness of molybdenum into rate-dependent and rate-independent components. J. Mater. Res. 9(10), 2524 (1994).CrossRefGoogle Scholar
32.Yoder, K.B., Elmustafa, A.A., Lin, J.C., Hoffman, R.A., and Stone, D.S.: Activation analysis of deformation in evaporated molybdenum thin films. J. Phys. D: Appl. Phys. 36, 884 (2003).CrossRefGoogle Scholar
33.Doerner, M.F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1(4), 601 (1986).CrossRefGoogle Scholar
34.Stone, D.S., Jakes, J.E., Puthoff, J.B., and Elmustafa, A.A.: Analysis of indentation creep. J. Mater. Res. 25(4), 611 (2010).CrossRefGoogle Scholar
35.Jakes, J.E., Frihart, C.R., Beecher, J.F., Moon, R.J., Resto, P.J., Melgarejo, Z.H., Surez, O.M., Baumgart, H., Elmustafa, A.A., and Stone, D.S.: Nanoindentation near the edge. J. Mater. Res. 24(3), 1016 (2009).CrossRefGoogle Scholar
36.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(4), 1113 (2008).CrossRefGoogle Scholar
37.Ma, Q. and Clarke, D.R.: Size dependent hardness of silver single crystals. J. Mater. Res. 10(4), 853 (1995).CrossRefGoogle Scholar
38.Nix, W.D. and Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46(3), 411 (1998).CrossRefGoogle Scholar
39.Tweedie, C.A., Constantinides, G., Lehman, K.E., Brill, D.J., Blackman, G.S., and Van Vliet, K.J.: Enhanced stiffness of amorphous polymer surfaces under confinement of localized contact loads. Adv. Mater. 19(18), 2540 (2007).CrossRefGoogle Scholar
40.Amitay-Sadovsky, E., Ward, B., Somorjai, G.A., and Komvopoulos, K.: Nanomechanical properties and morphology of thick polyurethane films under contact pressure and stretching. J. Appl. Phys. 91, 375 (2002).CrossRefGoogle Scholar
41.Fischer-Cripps, A.C.: Significance of a local temperature rise in nanoindentation testing. J. Mater. Sci. 39(18), 5849 (2004).CrossRefGoogle Scholar
42.Swallowe, G. and Lee, S.: Quasi-static and dynamic compressive behaviour of poly(methyl methacrylate) and polystyrene at temperatures from 293 K to 363 K. J. Mater. Sci. 41(19), 6280 (2006).Google Scholar
43.Fleck, N.A., Stronge, W.J., and Liu, J.H.: High strain-rate shear response of polycarbonate and polymethyl methacrylate. Proc. R. Soc. London, Ser. A. 429, 459 (1990).Google Scholar
44.Richeton, J., Ahzi, S., Vecchio, K.S., Jiang, F.C., and Adharapurapu, R.R.: Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: Characterization and modeling of the compressive yield stress. Int. J. Solids Struct. 43(7–8), 2318 (2006).CrossRefGoogle Scholar
45.Briggs, T.L. and Campbell, J.D.: The effect of strain rate and temperature on the yield and flow of polycrystalline niobium and molybdenum. Acta Metall. 20(5), 711 (1972).CrossRefGoogle Scholar
46.Lucas, B.N. and Oliver, W.C.: Indentation power-law creep of high-purity indium. Metall. Mater. Trans. A 30(3), 601 (1999).CrossRefGoogle Scholar
47.Tabor, D.: A simple theory of static and dynamic hardness. Proc. R. Soc. London, Ser. A 192, 247 (1948).Google Scholar
48.Tabor, D.: The hardness of solids. Rev. Phys. Technol. 1(3), 145 (1970).CrossRefGoogle Scholar
49.Marsh, D.M.: Plastic flow in glass. Proc. R. Soc. London, Ser. A 279(1378), 420 (1964).Google Scholar
50.Johnson, K.L.: Correlation of indentation experiments. J. Mech. Phys. Solids 18(2), 115 (1970).CrossRefGoogle Scholar
51.Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, United Kingdom, 1985), p. 452.CrossRefGoogle Scholar
52.Kermouche, G., Loubet, J.L., and Bergheau, J.M.: Cone indentation of time-dependent materials: The effects of the indentation strain rate. Mech. Mater. 39, 24 (2007).CrossRefGoogle Scholar
53.Kermouche, G., Loubet, J.L., and Bergheau, J.M.: A new index to estimate the strain rate sensitivity of glassy polymers using conical/pyramidal indentation. Philos. Mag. 86, 5667 (2006).CrossRefGoogle Scholar
54.Sneddon, I.N.: Relation between load and penetration in axisymmetric Boussinesq problem for punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
55.Davis, L.A. and Pampillo, C.A.: Deformation of polyethylene at high pressure. J. Appl. Phys. 42, 4659 (1971).CrossRefGoogle Scholar
56.Davis, L.A. and Pampillo, C.A.: Kinetics of deformation of PTFE at high pressure. J. Appl. Phys. 43, 4285 (1972).CrossRefGoogle Scholar
57.Pae, K.D., Sauer, J.A., and Silano, A.A.: Shear deformation under hydrostatic pressure of polytetrafluoroethylene and polycarbonate, in Proceedings of the Sixth International Conference on High-Pressure Science and Technology, Boulder, CO, edited by Timmerhaus, K.D. and Barber, M.S. (1979), pp. 512–518.Google Scholar
58.Chen, I.W.: Implications of transformation plasticity in ZrO2-containing ceramics: II. Elastic-plastic indentation. J. Am. Ceram. Soc. 69, 189 (1986).CrossRefGoogle Scholar
59.Bardia, P. and Narasimhan, R.: Characterisation of pressure-sensitive yielding in polymers. Strain 42, 187 (2006).CrossRefGoogle Scholar
60.Keryvin, V.: Indentation as a probe for pressure sensitivity of metallic glasses. J. Phys. Condens. Matter 20(11), 114119 (2008).CrossRefGoogle ScholarPubMed
61.Le, M-Q. and Kim, S-S.: Element analysis of instrumented sharp indentations into pressure-sensitive materials. J. Mater. Sci. Technol. 23(2), 277 (2007).Google Scholar
62.Narasimhan, R.: Analysis of indentation of pressure sensitive plastic solids using the expanding cavity model. Mech. Mater. 36(7), 633 (2004).CrossRefGoogle Scholar