Skip to main content Accessibility help
×
Home
  • Print publication year: 2009
  • Online publication date: February 2010

4 - Physical properties: elasticity, friction and diffusivity

Summary

Introduction

In this chapter we review the elastic behavior of ice, friction of ice on ice and mass diffusion. In terms of creep, elastic properties allow the applied stress to be normalized and thus the behavior to be analyzed within the context of physical mechanisms (Chapters 5–8). The mass diffusion coefficient plays a similar role in creep under low stresses. It is important, as well, to the transformation from snow to ice (Chapter 3). In terms of fracture, elastic constants affect fracture toughness (Chapter 9) and, through that property, both the tensile (Chapter 10) and the compressive strength (Chapters 11, 12). Elasticity is also relevant to the ductile-to-brittle transition (Chapters 13) and to ice loads on structures (Chapter 14). Friction is a factor in the DB transition under compression and is a major consideration in brittle compressive failure, on scales small (Chapters 11, 12) and large (Chapter 15). Friction is also fundamental to tidally driven, strike-slip-like tectonic activity on a number of icy satellites within the outer Solar System, including Jupiter's moon Europa (Greenberg et al., 1998; Hoppa et al., 1999; Schulson, 2002; Kattenhorn, 2004), Neptune's Triton (Prockter et al., 2005) and Saturn's Enceladus (Nimmo et al., 2007; Smith-Konter and Pappalardo, 2008). Thermal properties play a less direct role, but we list them for completeness, Table 4.1.

Elastic properties of ice Ih single crystals

Elastic properties have been relatively well studied.

References
Anderson, D. L. and Benson, C. S. (1963). The densification and diagenesis of snow. In Ice and Snow, ed. Kingery, W. D.. Cambridge, Mass.: MIT Press, pp. 391–411.
Arakawa, M. and Maeno, N. (1997). Mechanical strength of polycrystalline ice under uniaxial compression. Cold Reg. Sci. Technol., 26, 215–229
Baer, B. J., Brown, J. M., Zaug, J. M., Schiferl, D. and Chronister, E. L. (1998). Impulsive stimulated scattering on ice VI and ice VII. J. Chem. Phys., 108, 4540–4544.
Barnes, P., Tabor, D., Walker, F. R. S. and Walker, J. F. C. (1971). The friction and creep of polycrystalline ice. Proc. R. Soc. Lond. A, 324, 127–155.
Bender, M. L. (2002). Orbital tuning chronology for the Vostok climate record supported by trapped gas composition. Earth Planet. Sci. Lett., 204, 275–289.
Brown, D. E. and George, S. M. (1996). Surface and bulk diffusion of H218O on single-crystal H216O ice multilayers. J. Phys. Chem., 100, 15460–15469.
Budiansky, B. and O'Connell, R. J. (1976). Elastic-moduli of a cracked solid. Int. J. Solids Struct., 12, 81–97.
Cox, G. F. N. and Weeks, W. F. (1983). Equations for determining the gas and brine volumes in sea-ice samples. J. Glaciol., 29, 306–316.
Cox, G. F. N. and Weeks, W. F. (1986). Changes in the salinity and porosity of sea-ice samples during shipping and storage. J. Glaciol., 32, 371–375.
Dantl, G. (1968). Die elastischen Moduln von Eis-Einkristallen. Phys. Kondens. Mater., 7, 390–397.
Dantl, G. (1969). Elastic moduli of ice. In Physics of Ice: Proceedings of the International Symposium on Physics of Ice, Munich, Germany, September 9–14, 1968, eds. Riechl, N., Bullemer, B. and Engelhardt, H.. New York: Plenum Press, 223–230.
Dash, J. G., Fu, H. and Wettlaufer, J. S. (1995). The pre-melting of ice and its environmental consequences. Rep. Prog. Phys., 58, 115–167.
Domine, F. and Xueref, I. (2001). Evaluation of depth profiling using laser resonant desorption as a method to measure diffusion coefficients in ice. Anal. Chem., 73, 4348–4353.
Eisenberg, D. and Kauzmann, W. (1969). The Structure and Properties of Water. New York: Oxford University Press.
Elvin, A. A. (1996). Number of grains required to homogenize elastic properties of polycrystalline ice. Mech. Mater., 22, 51–64.
Fletcher, N. H. (1970). The Chemical Physics of Ice. Cambridge: Cambridge University Press.
Fortt, A. (2006). The resistance to sliding along coulombic shear faults in columnar S2 ice. Ph.D. thesis, Thayer School of Engineering, Dartmouth College.
Furukawa, Y. and Nada, H. (1997). Anisotropic surface melting of an ice crystal and its relationship to growth forms. J. Phys. Chem. B., 101, 6167–6170.
Gagnon, R. E., Kiefte, H., Clouter, M. J. and Whalley, E. (1988). Pressure dependence of the elastic constants of ice Ih to 2.8 kbar by Brillouin spectroscopy. J. Chem. Phys., 89, 4522–4528.
Gagnon, R. E., Kiefte, H., Clouter, M. J. and Whalley, E. (1990). Acoustic velocities and densities of polycrystalline ice-Ih, Ice-II, Ice-III, Ice-V, and Ice-VI by Brillouin spectroscopy. J. Chem. Phys., 92, 1909–1914.
Gammon, P. H., Kiefte, H. and Clouter, M. J. (1980). Elastic-constants of ice by Brillouin spectroscopy. J. Glaciol., 25, 159–167.
Gammon, P. H., Kiefte, H., Clouter, M. J. and Denner, W. W. (1983). Elastic constants of artificial ice and natural ice samples by Brillouin spectroscopy. J. Glaciol., 29, 433–460.
Gibson, L. G. and Ashby, M. F. (1988). Cellular Solids: Structure and Properties, 1st edn. Oxford: Pergamon Press.
Gold, L. W. (1958). Some observations on the dependence of strain on stress for ice. Can. J. Phys., 36, 1265–1275.
Gold, L. W. (1988). On the elasticity of ice plates. Can. J. Civil Eng., 15, 1080–1084.
Gold, L. W. (1994). The elastic modulus of columnar-grain fresh-water ice. Ann. Glaciol., 19, 13–18.
Goto, K., Hondoh, T. and Higashi, A. (1986). Determination of diffusion coefficients of self-interstitials in ice with a new method of observing climb of dislocations by X-ray topography. Jpn. J. Appl. Phys., 25, 351–357.
Greenberg, R., Geissler, P., Hoppa, G.et al. (1998). Tectonic processes on Europa: tidal stresses, mechnaical response and visible features. Icarus, 135, 64–78.
Haas, J., Bullemer, B. and Kahane, A. (1971). Diffusion of helium in monocrystalline ice. Solid State Commun., 9, 2033–2035.
Hearmon, R. F. S. (1961). Introduction to Applied Anisotropic Elasticity. Oxford: Oxford University Press.
Hill, R. (1952). The elastic behavior of a polycrystalline aggregate. Proc. Phys. Soc. Lond. A, 65, 349–354.
Hobbs, P. V. (1974). Ice Physics. Oxford: Clarendon Press.
Hoenig, A. (1979). Elastic-moduli of a non-randomly cracked body. Int. J. Solids Struct., 15, 137–154.
Hoppa, G., Tufts, B. R., Greenberg, R. and Geissler, P. (1999). Strike-slip faults on Europa: global shear patterns driven by tidal stress. Icarus, 141, 287–298.
Hori, A. and Hondoh, T. (2003). Theoretical study on the diffusion of gases in hexagonal ice by the molecular orbital method. Can. J. Phys., 81, 251–259.
Ikeda, T., Fukazawa, H., Mae, S.et al. (1999). Extreme fractionation of gases caused by formation of clathrate hydrates in Vostok Antarctic ice. Geophys. Res. Lett., 26, 91–94.
Kattenhorn, S. A. (2004). Strike-slip fault evolution on Europa: evidence from tailcrack geometries. Icarus, 172, 582–602.
Kennedy, F. E., Schulson, E. M. and Jones, D. (2000). Friction of ice on ice at low sliding velocities. Phil. Mag. A, 80, 1093–1110.
Kirchner, H. O. K., Michot, G., Narita, N. and Suzuki, T. (2001). Snow as a foam of ice: plasticity, fracture and the brittle-to-ductile transition. Phil. Mag. A, 81, 2161–2181.
Langleben, M. P. and Pounder, E. R. (1963). Elastic parameters of sea ice. In Ice and Snow Processes, Properties and Application, ed. Kingery, W. E.. Cambridge, Mass.: MIT Press, pp. 69–78.
Livingston, F. E. and George, S. M. (2001). Diffusion kinetics of HCl hydrates in ice measured using infrared laser resonant desorption depth-profiling. J. Phys. Chem. A, 105, 5155–5164.
Livingston, F. E., Whipple, G. C. and George, S. M. (1997). Diffusion of HDO into single-crystal H216O ice multilayers: Comparison with H218O. J. Phys. Chem. B., 101, 6127–6131.
Livingston, F. E., Whipple, G. C. and George, S. M. (1998). Surface and bulk diffusion of HDO on ultrathin single-crystal ice multilayers on Ru (001). J. Chem. Phys., 108, 2197–2207.
Livingston, F. E., Smith, J. A. and George, S. M. (2002). General trends for bulk diffusion in ice and surface diffusion on ice. J. Phys. Chem. A, 106, 6309–6318.
Mellor, M. (1975). A review of basic snow mechanics. In International Association of Hydrological Sciences Publication 114, pp. 251–291.
Mellor, M. (1977). Engineering properties of snow. J. Glaciol., 19, 15–66.
Mellor, M. (1983). Mechanical behavior of sea ice. US Army Cold Regions Research and Engineering Laboratory (CRREL) Report, M 83-1.
Michel, B. (1978). Ice Mechanics. Laval, Quebec: Laval University Press.
Michel, B. and Ramseier, R. O. (1971). Classification of river and lake ice. Can. Geotech. J., 8(36), 36–45.
Montagnat, M. and Schulson, E. M. (2003). On friction and surface cracking during sliding. J. Glaciol., 49, 391–396.
Nanthikesan, S. and Sunder, S. S. (1994). Anisotropic elasticity of polycrystalline ice IH. Cold Reg. Sci. Technol., 22, 149–169.
Nasello, O. B., Navarro de Juarez, S. and Prinzio, C. L. Di (2007). Measurement of self-diffusion on ice surface. Scr. Mater., 56, 1071–1073.
Nemat-Nasser, S. and Horii, M. (1993). Micromechanics: Overall Properties of Heterogeneous Materials. Amsterdam, The Netherlands: Elsevier Science Publishers.
Nimmo, F., Spencer, J. R., Pappalardo, R. T. and Mullen, M. E. (2007). Shear heating as the origin of the plumes and heat flux on Enceladus. Nature, 447, 289–291.
Nowick, A. S. and Berry, B. S. (1972). Anelastic Relaxation in Crystalline Solids. New York: Academic Press.
Nye, J. F. (1957). The distribution of stress and velocity in glaciers and ice-sheets. Proc. R. Soc. Lond. Ser. A, 239, 113–133.
Nye, J. F. (1985). Physical Properties of Crystals: Their Representation by Tensors and Matrices. Oxford: Oxford University Press.
Petrenko, V. F. and Whitworth, R. W. (1999). Physics of Ice. New York: Oxford University Press.
Prockter, L. M., Nimmo, F. and Pappalardo, R. T. (2005). A shear heating origin for ridges on Triton. Geophys. Res. Lett., 32, L14202, doi: 10.1029/2005GL022832.
Proctor, T. M. (1966). Low-temperature speed of sound in single-crystal ice. J. Acoust. Soc. Amer., 39, 972–977.
Ramseier, R. O. (1967). Self-diffusion of tritium in natural and synthetic ice monocrystals. J. Appl. Phys., 38, 2553–2556.
Reuss, A. Z. (1929). Berechnung der Fliessgrenze von Mischkristallen auf Grund der Pastizitatsbedingung fur Einkristalle. Z. Angew. Math. Mech., 9, 49.
Reyes-Morel, P. E. and Chen, I.-W. (1990). Stress-biased anisotropic microcracking in zirconia polycrystals. J. Am. Ceram. Soc., 73, 1026–1033.
Saeki, H., Ozaki, A. and Kubo, Y. (1981). Experimental study on flexural strength and elastic modulus of sea ice. In Proceedings of the 6th International Conference on Port and Ocean Engineering under Arctic Conditions. Quebec, Canada, Laval University, pp. 536–547.
Schulson, E. M. (2002). On the origin of a wedge crack within the icy crust of Europa. J. Geophys. Res., 107, doi:10.1029/2001JE001586.
Shapiro, L. H., Johnson, J. B., Sturm, M. and Blaisdell, G. L. (1997). Snow mechanics: review of the state of knowledge and applications. CRREL Report, 97-3, 1–43.
Shewmon, P. G. (1989). Diffusion in Solids. Warrendale, PA: Minerals, Metals and Materials Society.
Shimizu, H., Niabetani, T., Nishiba, T. and Sasaki, S. (1996). High-pressure elastic properties of the VI and VII phase of ice in dense H2O and D2O. Am. Phys. Soc., 53, 6107–6110.
Sinha, N. K. (1989a). Elasticity of natural types of polycrystalline ice. Cold Reg. Sci. Technol., 17, 127–135.
Sinha, N. K. (1989b). Experiments on anisotropic and rate-sensitive strain ratio and modulus of columnar-grained ice. Trans. ASME, 111, 354–560.
Smith-Konter, B. and Pappalardo, R. T. (2008). Tidally driven stress accumulation and shear failure of Enceladus's tiger stripes. Icarus (in press).
Thibert, E. and Domine, F. (1997). Thermodynamics and kinetics of the solid solution of HCl in ice. J. Phys. Chem. B., 101, 3554–3565.
Thibert, E. and Domine, F. (1998). Thermodynamics and kinetics of the solid solution of HNO3 in ice. J. Phys. Chem. B., 102, 4432–4439.
Traetteberg, A., Gold, L. and Frederking, R. (1975). The strain rate and temperature dependence of Young's modulus of ice. In 3rd International Symposium on Ice, Hanover, New Hampshire, International Association for Hydraulic Research.
Tulk, C. A., Gagnon, R. E., Kieffer, H. H. and Clouter, M. J. (1994). Elastic constants of ice III by Brillouin spectroscopy. J. Chem. Phys., 101, 2350–2354.
Tulk, C. A., Gagnon, R. E., Kieffer, H. H. and Clouter, M. J. (1996). Elastic constants of ice VI by Brillouin spectroscopy. J. Chem. Phys., 104, 7854–7859.
Tulk, C. A., Kieffer, H. H., Clouter, M. J. and Gagnon, R. E. (1997). Elastic constants of ice III, V, and VI by Brillouin spectroscopy. J. Phys. Chem. B., 101, 6154–6157.
Voigt, W. (1910). Lehrbuch der Kristallphysik, Berlin: B. G. Teubner.
Wang, Y. S. (1981). Uniaxial compression testing of Arctic sea ice. In 6th International Conference on Port and Ocean Engineering under Arctic Conditions. Quebec, Canada, Laval University.
Wegst, U. G. K., and Ashby, M. F. (2004). The mechanical efficiency of natural materials. Phil. Mag., 84, 2167–2181.