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Pressure sensitive flow and constraint factor in amorphous materials below glass transition

Published online by Cambridge University Press:  31 January 2011

K. Eswar Prasad
Affiliation:
Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012, India
V. Keryvin
Affiliation:
Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012, India; and LARMAUR, EA 410, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes, France
U. Ramamurty*
Affiliation:
Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012, India
*
a) Address all correspondence to this author. e-mail: ramu@materials.iisc.ernet.in
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Abstract

The constraint factor, C (given by the hardness-yield strength ratio H/Y in the fully plastic regime of indentation), in metallic glasses, is greater than three, a reflection of the sensitivity of their plastic flow to pressure. Furthermore, C increases with increasing temperature. In this work, we examine if this is true in amorphous polymers as well, through experiments on amorphous poly(methyl methacrylate) (PMMA). Uniaxial compression as well as spherical indentation tests were conducted in the 248–348 K range to construct H/Y versus indentation strain plots at each temperature and obtain the C-values. Results show that C increases with temperature in PMMA as well. Good correlation between the loss factors, measured using a dynamic mechanical analyzer, and C, suggest that the enhanced sensitivity to pressure is possibly due to β-relaxation. We offer possible mechanistic reasons for the observed trends in amorphous materials in terms of relaxation processes.

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Articles
Copyright
Copyright © Materials Research Society 2009

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References

REFERENCES

1.Tabor, D.: Hardness of Metals (Clarendon Press, Oxford, 1951).Google Scholar
2.Hill, R., Lee, E.H., and Tupper, S.J.: Theory of wedge indentation. Proc. R. Soc. A 188, 273 (1947).Google Scholar
3.Ramachandra, S., Sudheer Kumar, P., and Ramamurty, U.: Impact energy absorption in an Al foam at low velocities. Scr. Mater. 49, 741 (2003).CrossRefGoogle Scholar
4.Ramamurty, U. and Kumaran, M.C.: Mechanical property extraction through conical indentation of a closed-cell aluminum foam. Acta Mater. 52, 181 (2004).CrossRefGoogle Scholar
5.Hill, R.: The Mathematical Theory of Plasticity (Clarendon Press, Oxford, 1950).Google Scholar
6.Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, 1985).CrossRefGoogle Scholar
7.Marsh, D.: Plastic flow in glass. Proc. R. Soc. A 279, 420 (1964).Google Scholar
8.Shaw, M.C.: The fundamental basis of the hardness test, in The Science of Hardness Testing and Its Research Applications, edited by Westbrook, J.H. and Conrad, H. (American Society for Metals, Metals Park, OH, 1973), p. 1.Google Scholar
9.Sundararajan, G. and Tirupataiah, Y.: The localization of plastic flow under dynamic indentation conditions: I. Experimental results. Acta Mater. 54, 565 (2006).CrossRefGoogle Scholar
10.Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A., and Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).CrossRefGoogle Scholar
11.Sakai, M., Akatsu, T., Numata, S., and Matsuda, K.: Linear strain hardening in elastoplastic indentation contact. J. Mater. Res. 18, 2087 (2003).CrossRefGoogle Scholar
12.Narasimhan, R.: Analysis of indentation pf pressure sensitive plastic solids using expanding cavity model. Mech. Mater. 36, 633 (2004).CrossRefGoogle Scholar
13.Patnaik, M.N.M., Narasimhan, R., and Ramamurty, U.: Spherical indentation response of metallic glasses. Acta Mater. 52, 3335 (2004).CrossRefGoogle Scholar
14.Keryvin, V.: Indentation of bulk metallic glasses: Relationships between sharp bands observed around the prints and hardness. Acta Mater. 55, 2565 (2007).CrossRefGoogle Scholar
15.Eswar Prasad, K., Raghavan, R., and Ramamurty, U.: Temperature dependence of pressure sensitivity in a metallic glass. Scr. Mater. 57, 121 (2007).CrossRefGoogle Scholar
16.Keryvin, V., Prasad, K.E., Gueguen, Y., Sangleboeuf, J-C., and Ramamurty, U.: Temperature dependence of mechanical properties and pressure sensitivity in metallic glasses below glass transition. Philos. Mag. 88, 1773 (2008).CrossRefGoogle Scholar
17.Kumaraswamy, A. and Venkataraman, B.: Effect of temperature on constraint factor of Ti–6Al–4V under static indentation conditions. Scr. Mater. 54, 493 (2006).CrossRefGoogle Scholar
18.Bauwens-Crowet, C., Bauwens, J.C., and Homes, G.: The temperature dependence of yield of polycarbonate in uniaxial compression and tensile tests. J. Mater. Sci. 7, 172 (1972).CrossRefGoogle Scholar
19.Klompen, E.T.J., Engels, T.A.P., Govaert, L.E., and Meijer, H.E. H.: Modeling of the postyield response of glassy polymers: Influence of thermomechanical history. Macromolecules 38, 6997 (2005).CrossRefGoogle Scholar
20.Pelletier, C.: Mechanical characterization of glassy polymers using instrumented indentation. Ph.D. Thesis, Eindhoven University Technology (2008).Google Scholar
21.Stachurski, Z.: Review of deformation and computer simulations in amorphous glassy polymers. J. Indust. Eng. Chem. 11, 773 (2005).Google Scholar
22.Perez, J.: Physics and Mechanics of Amorphous Polymers (A.A. Balkema, Rotterdam, The Netherlands, 1998).Google Scholar
23.Puttick, K., Smith, L., and Miller, L.: Stress fields round indentation in polymethylmethacrylate. J. Phys. D: Appl. Phys. 10, 617 (1977).CrossRefGoogle Scholar
24.Bucaille, J.L., Gauthier, C., Felder, E., and Schirrer, R.: The influence of strain hardening of polymers on the piling-up phenomenon in scratch tests: Experiments and numerical modeling. Wear 260, 803 (2006).CrossRefGoogle Scholar
25.Ganneau, F.P., Constantinides, G., and Ulm, F-J.: Dual-indentation technique for the assessment of strength properties of cohesivefrictional materials. Int. J. Solid Struct. 43, 1727 (2006).CrossRefGoogle Scholar
26.Khan, A. and Huang, S.: Continuum Theory of Plasticity (John Wiley, New York, 1995).Google Scholar
27.Keryvin, V.: Indentation as a probe for pressure sensitivity. J. Phys. Condens. Matter 20, 114119 (2008).CrossRefGoogle ScholarPubMed
28.Quinson, R., Perez, J., Rink, M., and Pavan, A.: Yield criteria for amorphous glassy polymers. J. Mater. Sci. 32, 1371 (1997).CrossRefGoogle Scholar
29.Lu, J. and Ravichandran, G.: Pressure dependent flow behavior of Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 bulk metallic glass. J. Mater. Res. 18, 2039 (2003).CrossRefGoogle Scholar
30.Lewandowski, J.J. and Lowhaphandu, P.: Effect of hydrostatic pressure in the flow and fracture of a bulk amorphous metal. Philos. Mag. 82, 3427 (2002).CrossRefGoogle Scholar
31.Vaidyanathan, R., Dao, M., Ravichandran, G., and Suresh, S.: Study of mechanical deformation in bulk metallic glass through instrumented indentation. Acta Mater. 49, 3781 (2001).CrossRefGoogle Scholar
32.Donovan, P.E.: Plastic flow and fracture of Pd40Ni40P20 metallic glass under an indenter. J. Mater. Sci. 24, 523 (1989).CrossRefGoogle Scholar
33.Lund, A.C. and Schuh, C.A.: Yield surface of a simulated metallic glass. Acta Mater. 51, 5399 (2003).CrossRefGoogle Scholar
34.Rabinowitz, S., Ward, I.M., and Parry, J.S.C.: The effect of hydrostatic pressure on the shear yield behavior of polymers. J. Mater. Sci. 5, 29 (1970).CrossRefGoogle Scholar
35.Sternstein, S.S. and Ongchin, L.: Yield criteria for plastic deformation of glassy polymers in general stress fields. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 10, 1117 (1969).Google Scholar
36.Bowden, P.B. and Jukes, J.A.: The plastic flow of isotropic polymers. J. Mater. Sci. 7, 52 (1972).CrossRefGoogle Scholar
37.Nedderman, R.M.: Static and Kinematics of Granular Materials (Cambridge University Press, Cambridge, 1992).CrossRefGoogle Scholar
38.Baltá Calleja, F.J., Sanditov, D.S., and Privalko, V.P.: Review: The microhardness of non-crystalline materials. J. Mater. Sci. 37, 4507 (2002).CrossRefGoogle Scholar
39.Briscoe, B. and Sebastian, K.: The elastoplastic response of poly (methyl methacrylate) to indentation. Proc. R. Soc. A 439, 452 (1996).Google Scholar
40.Flichy, N., Kazarian, S., Lawrence, C., and Briscoe, B.: Indentation of polymethyl methacrylate under high pressure gasses. J. Polym. Sci., Part B: Polym. Phys. 39, 3020 (2001).CrossRefGoogle Scholar
41.Lafaye, S., Gauthier, C., and Schirrer, R.: Analysis of the apparent friction of polymeric surfaces. J. Mater. Sci. 41, 6441 (2006).CrossRefGoogle Scholar
42.Bridgman, P.W. and Simon, I.: Effects of very high pressures on glass. J. Appl. Phys. 24, 405 (1953).CrossRefGoogle Scholar
43.Ji, H., Keryvin, V., Rouxel, T., and Hammouda, T.: Densification of window glass under very high pressure and relevance to Vickers indentation. Scr. Mater. 55, 1159 (2006).CrossRefGoogle Scholar
44.Greaves, G.N. and Sen, S.: Inorganic glasses, glass-forming liquids and amorphizing solids. Adv. Phys. 56, 1 (2007).CrossRefGoogle Scholar
45.Schuh, C.A., Hufnagel, T.C., and Ramamurty, U.: Mechanical behavior of amorphous alloys. Acta Mater. 55, 4067 (2007).CrossRefGoogle Scholar
46.Ramamurty, U., Jana, S., Kawamura, Y., and Chattopadhyay, K.: Hardness and plastic deformation in a bulk metallic glass. Acta Mater. 53, 705 (2005).CrossRefGoogle Scholar
47.Jana, S., Ramamurty, U., Chattopadhyay, K., and Kawamura, Y.: Subsurface deformation during Vickers indentation of bulk metallic glasses. Mater. Sci. Eng., A 375, 1191 (2004).CrossRefGoogle Scholar
48.Tang, C., Li, Y., and Zeng, K.: Characterization of mechanical properties of a Zr-based metallic glass by indentation techniques. Mater. Sci. Eng., A 304, 215 (2004).CrossRefGoogle Scholar
49.Yu, G.S., Lin, J.G., Mo, M., Wang, X.F., Wang, F.H., and Wen, C.E.: Effect of relaxation on pressure sensitivity index in a Zr-based metallic glass. Mater. Sci. Eng., A 460, 58 (2007).CrossRefGoogle Scholar
50.Keryvin, V., Crosnier, R., Laniel, R., Hoang, V.H., and Sangleboeuf, J-C.: Indentation and scatching mechanisms of a ZrCuAlNi bulk metallic glass. J. Phys. D: Appl. Phys. 41, 074029 (2008).CrossRefGoogle Scholar
51.Murali, P. and Ramamurty, U.: Embrittlement of a bulk metallic glass due to sub-Tg annealing. Acta Mater. 53, 1467 (2005).CrossRefGoogle Scholar
52.Bhowmick, R., Raghavan, R., Chattopadhyay, K., and Ramamurty, U.: Plastic flow softening in a bulk metallic glass. Acta Mater. 54, 4221 (2006).CrossRefGoogle Scholar
53.Raghavan, R., Ayer, R., Jin, H.W., Marzinsky, C.N., and Ramamurty, U.: Effect of shot peening on the fatigue life of a Zr-based bulk metallic glass. Scr. Mater. 59, 167 (2008).CrossRefGoogle Scholar
54.Argon, A.S.: Plastic deformation in metallic glass. Acta Metall. 27, 47 (1979).CrossRefGoogle Scholar
55.Dalla Torre, F.H., Dubach, A., Schällibaum, J., and Löffler, J.F.: Shear striations and deformation kinetics in highly deformed Zr-based bulk metallic glasses. Acta Mater. 56, 4635 (2008).CrossRefGoogle Scholar