Advertisement

Properties and Mechanical Behaviour of Ice

  • Ryszard StaroszczykEmail author
Chapter
Part of the GeoPlanet: Earth and Planetary Sciences book series (GEPS)

Abstract

The properties of ice and its mechanical behaviour are discussed. First, the basic facts concerning various forms of ice are presented, and relevant physical parameters are given. Then, the crystalline microstructure of ice is described, with an emphasis on the anisotropic properties of a single ice crystal and their effect on various types of its microscopic deformation. This is followed by the presentation of the macroscopic properties of polycrystalline ice and its behaviour in various stress and deformation regimes. Thus, the elastic, viscoelastic, viscous creep and brittle behaviour of the material is discussed, and examples of constitutive equations describing all these types of the response of ice to stress are given.

References

  1. Alley RB (1992) Flow-law hypotheses for ice-sheet modelling. J Glaciol 38(129):245–256CrossRefGoogle Scholar
  2. Ashby MF, Duval P (1985) The creep of polycrystalline ice. Cold Reg Sci Technol 11(3):285–300CrossRefGoogle Scholar
  3. Ashby MF, Hallam SD (1986) The failure of brittle solids containing small cracks under compressive stress-states. Acta Metall 34(3):497–510CrossRefGoogle Scholar
  4. Atkinson BK (ed) (1987) Fracture mechanics of rock. Academic Press, LondonGoogle Scholar
  5. Baral DR, Hutter K, Greve R (2001) Asymptotic theories of large-scale motion, temperature, and moisture distribution in land-based polythermal ice sheets: a critical review and new developments. Appl Mech Rev 54(3):215–256CrossRefGoogle Scholar
  6. Barnes P, Tabor D, Walker JCF (1971) The friction and creep of polycrystalline ice. Proc R Soc Lond A 324(1557):127–155CrossRefGoogle Scholar
  7. Budd WF, Jacka TH (1989) A review of ice rheology for ice sheet modelling. Cold Reg Sci Technol 16(2):107–144.  https://doi.org/10.1016/0165-232X(89)90014-1CrossRefGoogle Scholar
  8. Colbeck SC, Evans RJ (1973) A flow law for temperate glacier ice. J Glaciol 12(64):71–86CrossRefGoogle Scholar
  9. Cole DM (1988) Crack nucleation in polycrystalline ice. Cold Reg Sci Technol 15(1):79–87CrossRefGoogle Scholar
  10. Dantl G (1969) Elastic moduli of ice. In: Riehl N, Bullemer B, Engelhardt H (eds) Physics of ice. Plenum Press, New York, pp 223–230CrossRefGoogle Scholar
  11. Doake CSM, Wolff EW (1985) Flow law for ice in polar ice sheets. Nature 314(6008):255–257CrossRefGoogle Scholar
  12. Duval P (1981) Creep and fabric of polycrystalline ice under shear and compression. J Glaciol 27(95):129–140CrossRefGoogle Scholar
  13. Duval P, Ashby MF, Anderman I (1983) Rate-controlling processes in the creep of polycrystalline ice. J Phys Chem 87(21):4066–4074CrossRefGoogle Scholar
  14. Duval P, Lorius C (1980) Crystal size and climatic record down to the last ice age from Antarctic ice. Earth Planet Sci Lett 48:59–64CrossRefGoogle Scholar
  15. Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond A 241:376–396CrossRefGoogle Scholar
  16. Findley WN, Lai JS, Onaran K (1976) Creep and relaxation of nonlinear viscoelastic materials. North-Holland, AmsterdamGoogle Scholar
  17. Flügge W (1967) Viscoelasticity. Blaisdell, TorontoGoogle Scholar
  18. Gammon PH, Kiefte H, Clouter MJ, Denner WW (1983) Elastic constants of artificial and natural ice samples by Brillouin spectroscopy. J Glaciol 29(103):433–460CrossRefGoogle Scholar
  19. Glen JW (1955) The creep of polycrystalline ice. Proc R Soc Lond A 228(1175):519–538CrossRefGoogle Scholar
  20. Gold LW, Sinha NK (1980) The rheological behaviour of ice at small strains. In: Tryde P (ed) Physics and mechanics of ice, proceedings of the IUTAM Symposium, Copenhagen 1979. Springer, Berlin, pp 117–128CrossRefGoogle Scholar
  21. Goodman DJ, Frost HJ, Ashby MF (1981) The plasticity of polycrystalline ice. Philos Mag A 43(3):665–695CrossRefGoogle Scholar
  22. Gow AJ, Meese DA, Alley RB, Fitzpatrick JJ, Anandakrishnan S, Woods GA, Elder BC (1997) Physical and structural properties of the Greenland Ice Sheet Project 2 ice core: a review. J Geophys Res 102(C12):26559–26575.  https://doi.org/10.1029/97JC00165CrossRefGoogle Scholar
  23. Green AE, Zerna W (1992) Theoretical elasticity. Dover, Mineola, New YorkGoogle Scholar
  24. Hawkes I, Mellor M (1972) Deformation and fracture of ice under uniaxial stress. J Glaciol 11(61):103–131CrossRefGoogle Scholar
  25. Hill R (1952) The elastic behaviour of a crystalline aggregate. Proc Phys Soc A 65(389):349–354CrossRefGoogle Scholar
  26. Hill R (1965) Continuum micro-mechanics of elastoplastic polycrystals. J Mech Phys Solids 13(2):89–101CrossRefGoogle Scholar
  27. Hobbs PV (2010) Ice physics. Oxford University Press, OxfordGoogle Scholar
  28. Hutter K (1975) Floating sea ice plates and the significance of the dependence of the Poisson ratio on brine content. Proc R Soc Lond A 343(1632):85–108CrossRefGoogle Scholar
  29. Hutter K (1983) Theoretical glaciology. Material science of ice and the mechanics of glaciers and ice sheets. Reidel, DordrechtGoogle Scholar
  30. Jacka TH (1984) The time and strain required for development of minimum strain rates in ice. Cold Reg Sci Technol 8(3):261–268.  https://doi.org/10.1016/0165-232X(84)90057-0CrossRefGoogle Scholar
  31. Kamb WB (1961) The glide direction in ice. J Glaciol 3(30):1097–1106CrossRefGoogle Scholar
  32. Le Gac H, Duval P (1980) Constitutive relations for the non-elastic deformation of polycrystalline ice. In: Tryde P (ed) Physics and mechanics of ice, proceedings of the IUTAM symposium, Copenhagen 1979. Springer, Berlin, pp 51–59Google Scholar
  33. Lliboutry L (1969) The dynamics of temperate glaciers from the detailed viewpoint. J Glaciol 8(53):185–205CrossRefGoogle Scholar
  34. Lliboutry L, Duval P (1985) Various isotropic and anisotropic ices found in glaciers and polar ice caps and their corresponding rheologies. Ann Gheophys 3(2):207–224Google Scholar
  35. Mellor M (1980) Mechanical properties of polycrystalline ice. In: Tryde P (ed) Physics and mechanics of ice, proceedings of the IUTAM symposium, Copenhagen 1979. Springer, Berlin, pp 217–245CrossRefGoogle Scholar
  36. Mellor M, Cole DM (1982) Deformation and failure of ice under constant stress or constant strain-rate. Cold Reg Sci Technol 5(3):201–219CrossRefGoogle Scholar
  37. Mellor M, Cole DM (1983) Stress/strain/time relations for ice under uniaxial compression. Cold Reg Sci Technol 6(3):207–230CrossRefGoogle Scholar
  38. Mellor M, Testa R (1969a) Creep of ice under low stress. J Glaciol 8(52):147–152CrossRefGoogle Scholar
  39. Mellor M, Testa R (1969b) Effect of temperature on the creep of ice. J Glaciol 8(52):131–145CrossRefGoogle Scholar
  40. Morland LW (1993) The flow of ice sheets and ice shelves. In: Hutter K (ed) Continuum mechanics in environmental sciences and geophysics. Springer, Wien, pp 403–466CrossRefGoogle Scholar
  41. Morland LW (1996) Dynamic impact between a viscoelastic ice floe and a rigid structure. Cold Reg Sci Technol 24(1):7–28CrossRefGoogle Scholar
  42. Morland LW (2001) Influence of bed topography on steady plane ice sheet flow. In: Straughan B, Greve R, Ehrentraut H, Wang Y (eds) Continuum mechanics and applications in geophysics and the environment. Springer, Berlin, pp 276–304CrossRefGoogle Scholar
  43. Nakawo M, Sinha NK (1981) Growth rate and salinity profile of first-year ice in the high Arctic. J Glaciol 27(96):315–330CrossRefGoogle Scholar
  44. Nanthikesan S, Shyam Sunder S (1994) Anisotropic elasticity of polycrystalline ice Ih. Cold Reg Sci Technol 22(2):149–169CrossRefGoogle Scholar
  45. Nixon WA (1996) Wing crack models of the brittle compressive failure of ice. Cold Reg Sci Technol 24(1):41–55CrossRefGoogle Scholar
  46. Paterson WSB (1994) The physics of glaciers, 3rd edn. Butterworth-Heinemann, OxfordGoogle Scholar
  47. Rist MA, Sammonds PR, Oerter H, Doake CSM (2002) Fracture of Antartctic shelf ice. J Geophys Res 107(B1):ECV 2–1–ECV 2–13.  https://doi.org/10.1029/2000JB000058CrossRefGoogle Scholar
  48. Sanderson TJO (1988) Ice mechanics. Risks to offshore structures, Graham and Trotman, LondonGoogle Scholar
  49. Schulson EM (2001) Brittle failure of ice. Eng Fract Mech 68(17–18):1839–1887CrossRefGoogle Scholar
  50. Schulson EM, Duval P (2009) Creep and fracture of ice. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  51. Schulson EM, Fortt AL, Iliescu D, Renshaw CE (2006) Failure envelope of first-year Arctic sea ice: the role of friction in compressive fracture. J Geophys Res 111:C11S25.  https://doi.org/10.1029/2005JC003234186
  52. Schulson EM, Lim PN, Lee RW (1984) A brittle to ductile transition in ice under tension. Philos Mag A 49(3):353–363CrossRefGoogle Scholar
  53. Schwarz J, Weeks WF (1977) Engineering properties of sea ice. J Glaciol 19(81):499–531CrossRefGoogle Scholar
  54. Shyam Sunder S, Wu MS (1989a) A differential flow model for polycrystalline ice. Cold Reg Sci Technol 16(1):45–62CrossRefGoogle Scholar
  55. Shyam Sunder S, Wu MS (1989b) A multiaxial differential model of flow in orthotropic polycrystalline ice. Cold Reg Sci Technol 16(3):223–235CrossRefGoogle Scholar
  56. Shyam Sunder S, Wu MS (1990a) Crack nucleation due to elastic anisotropy in polycrystalline ice. Cold Reg Sci Technol 18(1):29–47CrossRefGoogle Scholar
  57. Shyam Sunder S, Wu MS (1990b) On the constitutive modeling of transient creep in polycrystalline ice. Cold Reg Sci Technol 18(3):267–294CrossRefGoogle Scholar
  58. Sinha NK (1978a) Rheology of columnar-grained ice. Exp Mech 18(12):464–470CrossRefGoogle Scholar
  59. Sinha NK (1978b) Short-term rheology of polycrystalline ice. J Glaciol 21(85):457–473CrossRefGoogle Scholar
  60. Sinha NK (1979) Grain boundary sliding in polycrystalline materials. Philos Mag A 40(6):825–842CrossRefGoogle Scholar
  61. Sinha NK (1983) Creep model of ice for monotonically increasing stress. Cold Reg Sci Technol 8(1):25–33CrossRefGoogle Scholar
  62. Sinha NK (1989) Elasticity of natural types of polycrystalline ice. Cold Reg Sci Technol 17(2):127–135CrossRefGoogle Scholar
  63. Sjölind SG (1985) Viscoelastic buckling analysis of floating ice sheets. Cold Reg Sci Technol 11(3):241–246CrossRefGoogle Scholar
  64. Sjölind SG (1987) A constitutive model for ice as a damaging visco-elastic material. Cold Reg Sci Technol 14(3):247–262CrossRefGoogle Scholar
  65. Smith GD, Morland LW (1981) Viscous relations for the steady creep of polycrystalline ice. Cold Reg Sci Technol 5(2):141–150CrossRefGoogle Scholar
  66. Spring U, Morland LW (1983) Integral representations for the viscoelastic deformation of ice. Cold Reg Sci Technol 6(3):185–193CrossRefGoogle Scholar
  67. Thorsteinsson T, Kipfstuhl J, Miller H (1997) Textures and fabrics in the GRIP ice core. J Geophys Res 102(C12):26583–26599.  https://doi.org/10.1029/97JC00161CrossRefGoogle Scholar
  68. Timco GW, O’Brien S (1994) Flexural strength equation for sea ice. Cold Reg Sci Technol 22(3):285–298.  https://doi.org/10.1016/0165-232X(94)90006-XCrossRefGoogle Scholar
  69. Timco GW, Weeks WF (2010) A review of the engineering properties of sea ice. Cold Reg Sci Technol 60(2):107–129.  https://doi.org/10.1016/j.coldregions.2009.10.003CrossRefGoogle Scholar
  70. Treverrow A, Budd WF, Jacka TH, Warner RC (2012) The tertiary creep of polycrystalline ice: experimental evidence for stress-dependent levels of strain-rate enhancement. J Glaciol 58(208):301–314.  https://doi.org/10.3189/2012JoG11J149CrossRefGoogle Scholar
  71. Weeks WF (2010) On sea ice. University of Alaska Press, FairbanksGoogle Scholar
  72. Weeks WF, Assur A (1967) The mechanical properties of sea ice. USA, U.S, Army Cold Regions Research and Engineering Laboratory, Hanover, NHCrossRefGoogle Scholar
  73. Weertman J (1983) Creep deformation of ice. Annu Rev Earth Planet Sci 11:215–240CrossRefGoogle Scholar
  74. Zhan C, Evgin E, Sinha NK (1994) A three dimensional anisotropic constitutive model for ductile behaviour of columnar grained ice. Cold Reg Sci Technol 22(3):269–284CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Hydro-EngineeringPolish Academy of SciencesGdańskPoland

Personalised recommendations