Skip to main content Accessibility help
×
Home
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 1
  • Print publication year: 2009
  • Online publication date: February 2010

6 - Ductile behavior of polycrystalline ice: experimental data and physical processes

Summary

Introduction

Understanding how polar ice sheets interact with the climatic system is of the highest importance to predict sea-level changes. Ice sheets contain information on the climate and the atmospheric composition over the last 800 000 years (EPICA Community Members, 2004). Interpretation of ice core data is directly dependent on the accuracy of ice sheet flow models used for ice core dating. Knowledge of the rheological properties of ice in the low stress conditions of glaciers and polar ice sheets is therefore needed to improve the constitutive laws that are incorporated in flow models. Due to very high viscoplastic anisotropy of the crystal (Chapter 5), ice is considered as a model material to validate micro-macro polycrystal models used to simulate the behavior of anisotropic viscoplastic materials (Gilormini et al., 2001; Lebensohn et al., 2007).

Ice displays a wide range of mechanical properties, including elasticity, visco-elasticity, viscoplasticity, creep rupture and brittle failure (Schulson, 2001). In glaciers and ice sheets, ice is generally treated as a heat-conducting non-linear viscous fluid.

Ice is assumed here to be incompressible. It will be shown that the main effect of hydrostatic pressure on the ductile behavior of ice is to modify the melting temperature of pure ice Tf with dTf /dP ≈ 0.074 ℃/MPa (Lliboutry, 1971).

In this chapter, we focus the analysis on the mechanical behavior of granular glacier ice. We assume that the behavior is ductile without the formation of cracks.

Related content

Powered by UNSILO
References
Acharya, A. (2001). A model of crystal plasticity based on the theory of continuously distributed dislocations. J. Mech. Phys. Sol., 49, 761–784.
Alley, R. B. (1988). Fabrics in polar ice sheets: development and prediction. Science, 240, 493–495.
Alley, R. B. (1992). Flow-law hypotheses for ice-sheet modeling. J. Glaciol., 38, 245–256.
Alley, R. B. and Woods, G. A. (1996). Impurity influence on normal grain growth in the GISP2 ice core, Greenland. J. Glaciol., 42, 255–260.
Alley, R. B., Perepezko, J. H. and Bentley, C. R. (1986a). Grain growth in polar ice: I. Theory. J. Glaciol., 32, 415–424.
Alley, R. B., Perepezko, J. H. and Bentley, C. R. (1986b). Grain growth in polar ice: II. Application. J. Glaciol., 32, 425–433.
Alley, R. B., Gow, A. J. and Meese, D. A. (1995). Mapping c-axis fabrics to study physical processes in ice. J. Glaciol., 41, 197–203.
Andrade, E. N.da, C. (1914). The flow of metals under large constant stresses. Proc. R. Soc. London A, 90, 329–340.
Ashby, M. F. (1966). Work hardening of dispersion-hardened crystals. Phil. Mag., 14, 1157–1178.
Ashby, M. F. (1970). The deformation of plastically non-homogeneous materials. Phil. Mag., 21, 399–424.
Ashby, M. F. and Duval, P. (1985). The creep of polycrystalline ice. Cold Reg. Sci. Technol., 11, 285–300.
Azuma, N. and Higashi, A. (1985). Formation processes of ice fabric pattern in ice sheets. Ann. Glaciol., 6, 130–134.
Azuma, N., Wang, Y., Mori, K.et al. (2000). Textures and fabrics in the Dome F (Antarctica) ice core. Ann. Glaciol., 29, 163–168.
Baker, R. W. and Gerberich, W. W. (1979). The effect of crystal size and dispersed-solid inclusions on the activation energy for creep of ice. J. Glaciol., 24, 179–194.
Barnes, P., Tabor, D. and Walker, J. C. F. (1971). The friction and creep of polycrystalline ice. Proc. R. Soc. London A, 324, 127–155.
Barrette, P. D. and Jordaan, I. J. (2003). Pressure-temperature effects on the compressive behavior of laboratory-grown and iceberg ice. Cold Reg. Sci. Technol., 36, 25–36.
Blum, W. and Maier, W. (1999). Harper-Dorn creep – a myth?Phys. Stat. Sol. A, 171, 467–474.
Bouchez, J. L. and Duval, P. (1982). The fabric of polycrystalline ice deformed in simple shear: experiments in torsion, natural deformation and geometrical interpretation. Textures Microstruct., 5, 171–190.
Budd, W. F. and Jacka, T. H. (1989). A review of ice rheology for ice sheet modelling. Cold Reg. Sci. Technol., 16, 107–144.
Castelnau, O., Duval, P., Lebensohn, R. A. and Canova, G. R. (1996a). Viscoplastic modelling of texture development in polycrystalline ice with a self-consistent approach: comparison with bound estimates. J. Geophys. Res., 101 (B6), 13,851–13,868.
Castelnau, O., Thorsteinsson, Th., Kipfstuhl, J., Duval, P. and Canova, G. R. (1996b). Modelling fabric development along the GRIP ice core, central Greenland. Ann. Glaciol., 23, 194–201.
Cohen, D. (2000). Rheology of ice at the bed of Engabreen, Norway. J. Glaciol., 46, 611–621.
Colbeck, S. C. and Evans, R. J. (1973). A flow law for temperate glacier ice. J. Glaciol., 12, 71–86.
Cole, D. M. (1991). Anelastic straining in polycrystalline ice. In Proceedings of the 6th International Specialty Conference on Cold Regions Engineering, ed. Sodhi, D.. Lebanon, N.H.: American Society of Civil Engineers, pp. 504–518.
Cole, D. M. (1995). A model for the anelastic straining of saline ice subjected to cyclic loading. Phil. Mag. A, 72 (1), 231–248.
Cole, D. M. (2003). A dislocation-based analysis of the creep of granular ice: preliminary experiments and modeling. Ann. Glaciol., 37, 18–22.
Cole, D. M. (2004). A dislocation-based model for creep recovery in ice. Phil. Mag., 84, 3217–3234.
Cole, D. M. and Durell, G. D. (1995). The cyclic loading of saline ice. Phil. Mag., 72, 209–229.
Cole, D. M. and Durell, G. D. (2001). A dislocation-based analysis of strain history effects in ice. Phil. Mag. A, 81, 1849–1872.
Cuffey, K. M., Conway, H., Hallet, B., Gades, A. M. and Raymond, C. F. (1999). Interfacial water in polar glaciers and glacier sliding at −17 ℃. Geophys. Res. Lett., 26, 751–754.
Cuffey, K. M., Thorsteinsson, T. and Waddington, E. D. (2000a). A renewed argument for crystal size control of ice sheet strain rates. J. Geophys. Res., 105 (B12), 27,889–27,894.
Cuffey, K. M., Conway, H., Gades, A.et al. (2000b). Deformation properties of subfreezing glacier ice: role of crystal size, chemical impurities, and rock particles inferred from in situ measurements. J. Geophys. Res., 105 (B12), 27,895–27,915.
Dahl-Jensen, D. and Gundestrup, N. S. (1987). Constitutive properties of ice at Dye 3, Greenland. In The Physical Basis of Ice Sheet Modeling, eds. Waddington, E. D. and Walder, J. S.. Vancouver: IAHS Publication 170, pp. 31–43.
Angelis, M., Steffensen, J. P., Legrand, M., Clausen, H. and Hammer, C. (1997). Primary aerosol (sea salt and soil dust) deposited in Greenland ice during the last climatic cycle: comparison with east Antarctic records, J. Geophys. Res., 102 (C12), 26,681–26,698.
Chapelle, S., Castelnau, O., Lipenkov, V. and Duval, P. (1998). Dynamic recrystallization and texture development in ice as revealed by the study of deep ice cores in Antarctica and Greenland. J. Geophys. Res., 103 (B3), 5091–5105.
Chapelle, S., Milsch, H., Castelnau, O. and Duval, P. (1999). Compressive creep of ice containing a liquid intergranular phase: ratecontrolling processes in the dislocation creep regime. Geophys. Res. Lett., 26, 251–254.
Delmonte, B., Petit, J. R. and Maggi, V. (2002). Glacial to Holocene implications of the new 27 000-year dust record from the EPICA Dome C (East Antarctica) ice core. Climate Dynamics, 18, 647–660.
Derby, B. (1991). The dependence of grain size on stress during dynamic recrystallization. Acta Metall. Mater., 39, 955–962.
Doake, C. S. M. and Wolff, E. W. (1985). Flow law for ice in polar ice sheets. Nature, 314, 255–257.
Drouin, M. and Michel, B. (1971). Les poussées d'origine thermique exercées par les couverts de glace sur les structures hydrauliques. Rapport S-23, Laboratoire de Mécanique des Glaces, Université Laval, Canada.
Durand, G. and 10 others (2006). Effect of impurities on grain growth in cold ice sheets. J. Geophys. Res., 111, FO1015, 1–18.
Durham, W. B. and Stern, L. A. (2001). Rheological properties of water ice – Applications to satellites of the outer planets. Ann. Rev. Earth Planet. Sci., 29, 295–330.
Durham, W. B., Kirby, S. H. and Stern, L. A. (1992). Effect of dispersed particulates on the rheology of water ice at planetary conditions. J. Geophys. Res., 97 (E12), 20,883–20,897.
Durham, W. B., Kirby, S. H. and Stern, L. A. (1997). Creep of water ices at planetary conditions: a compilation. J. Geophys. Res., 102 (E7), 16,293–16,302.
Durham, W. B., Stern, L. A. and Kirby, S. H. (2001). Rheology of ice I at low stresses and elevated confining pressure. J. Geophys. Res., 106, 11,031–11,042.
Duval, P. (1973). Fluage de la glace polycrystalline pour les faibles contraintes. C.R. Acad. Sci. Paris, 277, 703–706.
Duval, P. (1976). Lois de fluage transitoire ou permanent de la glace polycristalline pour divers états de contrainte. Ann. Géophys., IV, 32, 335–350.
Duval, P. (1977). The role of the water content on the creep rate of polycrystalline ice. In Isotopes and Impurities in Snow and Ice. IAHS Publication, 118, 29–33.
Duval, P. (1978). Anelastic behavior of polycrystalline ice. J. Glaciol., 21, 621–628.
Duval, P. (1981). Creep and fabrics of polycrystalline ice under shear and compression. J. Glaciol., 27, 129–140.
Duval, P. and Castelnau, O. (1995). Dynamic recrystallization of ice in polar ice sheets. J. Phys. IV, 5 (Colloque N°3), C3-197–C3-205.
Duval, P. and Gac, H. (1980). Does the permanent creep-rate of polycrystalline ice increase with crystal size?J. Glaciol., 25, 151–157.
Duval, P. and Lorius, C. (1980). Crystal size and climatic record down to the last ice age from Antarctic ice. Earth Planet. Sci. Lett., 48, 59–64.
Duval, P. and Montagnat, M. (2002). Comments on “Superplastic deformation of ice: experimental observations” by Goldsby, D. L. and Kohlstedt, D. L.. J. Geophys. Res., 107B, ECV4, 1–2.
Duval, P., Ashby, M. F. and Anderman, I. (1983). Rate-controlling processes in the creep of polycrystalline ice. J. Phys. Chem., 87, 4066–4074.
Dysthe, D. K., Podladchikov, Y., Renard, F., Feder, J. and Jamtveit, G. (2002). Universal scaling in transient creep. Phys. Rev. Lett., 89, 246102-1–246102-4.
Echelmeyer, K. and Zhongxiang, W. (1987). Direct observation of basal sliding and deformation of basal drift at sub-freezing temperatures. J. Glaciol., 33, 83–98.
,EPICA Community Members (2004). Eight glacial cycles from an Antarctic ice core. Nature, 429, 623–628.
Fischer, D. A. and Koerner, R. M. (1986). On the special rheological properties of ancient microparticles-laden Northern Hemisphere ice as derived from bore-hole and core measurements. J. Glaciol., 32, 501–510.
Fitzsimons, S. J., Lorrain, R. and McManus, K. J. (1999). Structure and strength of basal ice and substrate of a dry-based glacier: evidence for substrate deformation at sub-freezing temperatures. Ann. Glaciol., 28, 236–240.
Friedel, J. (1964). Dislocations. Oxford: Pergamon Press.
Frost, H. J. and Ashby, M. F. (1982). Deformation-Mechanism Maps for Metals and Alloys. Oxford: Pergamon Press.
Gagliardini, O. and Meyssonnier, J. (1999). Analytical derivations for the behavior and fabric evolution of a linear orthotropic ice polycrystal. J. Geophys. Res., 104 (B8), 17,797–17,809.
Gagliardini, O. and Meyssonnier, J. (2000). Simulation of anisotropic ice flow and fabric evolution along the GRIP-GISP2 flowline, Central Greenland. Ann. Glaciol., 30, 503–509.
Gao, X. Q. and Jacka, T. H., (1987). The approach to similar tertiary creep rates for Antarctic core ice and laboratory prepared ice. J. Physique Coll., 48, C1-289–C1-296.
Gillet-Chaulet, F., Gagliardini, O., Meyssonnier, J., Zwinger, T. and Ruokolainen, J. (2006). Flow-induced anisotropy in polar ice and related ice-sheet flow modeling. J. Non-Newtonian Fluid Mech., 134, 33–43.
Gilormini, P., Nebozhyn, M. V. and Castaneda, P. Ponte (2001). Accurate estimates for the creep behavior of hexagonal polycrystals. Acta Mater., 49, 329–337.
Ginter, T. J., Chaudhury, P. K. and Mohamed, F. A. (2001). An investigation of Harper-Dorn creep at large strains. Acta Mater., 49, 263–272.
Glen, J. W. (1955). The creep of polycrystalline ice. Proc. R. Soc. London A, 228, 519–538.
Glen, J. W. and Perutz, M. F. (1954). The growth and deformation of ice crystals. J. Glaciol., 2, 397–403.
Gold, L. W. (1972). The Failure Process in Columnar-Grained Ice. Tech. Paper No. 369 of the Division of Building Research. Ottawa: National Research Council of Canada.
Goldsby, D. L. and Kohlstedt, D. L. (1997). Grain boundary sliding in fine-grained ice I. Scr. Mater., 37, 1399–1406.
Goldsby, D. L. and Kohlstedt, D. L. (2001). Superplastic deformation of ice: experimental observations. J. Geophys. Res. 106 (B6), 11,017–11,030.
Goodman, D. J., Frost, H. J. and Ashby, M. F. (1981). The plasticity of polycrystalline ice. Phil. Mag., 43, 665–695.
Gow, A. J. (1968). Bubbles and bubble pressure in Antarctic glacier ice. J. Glaciol., 7, 167–182.
Gow, A. J. (1969). On the rates of growth of grains and crystals in south polar firn. J. Glaciol., 8, 241–252.
Gow, A. J. (1974). Time-temperature dependence of sintering in perennial isothermal snowpacks. In Snow Mechanics Symposium. IAHS Publication 114, pp. 25–41.
Gow, A. J. and Williamson, T. (1976). Rheological implications of the internal structure and crystal fabrics of the West Antarctic ice sheet as revealed by deep ice core drilling at Byrd Station. CRREL Report, 76-35.
Gow, A. J., Meese, D. A., Alley, R. B.et al. (1997). Physical and structural properties of the Greeland Ice Sheet Project: A review. J. Geophys. Res., 102 (C12), 26,559–26,575.
Gundestrup, N. S. and Hansen, B. L. (1984). Bore-hole survey at Dye 3, South Greenland, J. Glaciol., 30, 282–288.
Hamann, I., Kipfstuhl, S., Faria, S.et al. (2009) Subgrain boundaries and related microstructural features in EPICA–Dronning Maud Land (EDML) deep ice core, J. Glaciol. (in press).
Hill, R. (1950). The Mathematic Theory of Plasticity. New York: Oxford University Press.
Hillert, M. (1965). On the theory of normal and abnormal grain growth. Acta Metall., 13, 227–238.
Hobbs, P. V. (1974). Ice Physics. Oxford: Clarendon Press.
Homer, D. R. and Glen, J. W. (1978). The creep activation energies of ice. J. Glaciol., 21, 429–444.
Hondoh, T. (2000). Nature and behavior of dislocations in ice. In Physics of Ice Core Records, ed. Hondoh, T.. Sapporo: Hokkaido University Press, pp. 3–24.
Hooke, R. LeB.Dahlin, B. B. and Kauper, M. T. (1972). Creep of ice containing dispersed fine sand. J. Glaciol., 11, 327–336.
Hooke, R. LeB. (1981). Flow law for polycrystalline ice in glaciers: comparison of theoretical predictions, laboratory data and field measurements. Rev. Geophys. Space Phys., 19, 664–672.
Hooke, R. LeB. (1998). Principles of Glacier Mechanics. Upper Saddle River, N. J.: Prentice Hall.
Humphreys, F. J. and Hatherly, M. (1996). Recrystallization and Related Annealing Phenomena. Oxford: Pergamon Press.
Hutchinson, J. W. (1976). Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lond. A, 348, 101–127.
Hutchinson, J. W. (1977). Creep and plasticity of hexagonal polycrystals as related to single crystal slip. Metall. Trans., 8A, 9, 1465–1469.
Hutter, K. (1983). Theoretical Glaciology. Dordrecht: Reidel.
Iliescu, D., Baker, I. and Chang, Hui (2004). Determining the orientations of ice crystals using Electron Backscatter Patterns. Microsc. Res. Tech., 63, 183–187.
Jacka, T. H. (1984a). The time and strain required for development of minimum strain rates in ice. Cold Reg. Sci. Technol., 8, 261–268.
Jacka, T. H. (1984b). Laboratory studies on relationship between ice crystal size and flow rate. Cold Reg. Sci. Technol., 10, 31–42.
Jacka, T. H. (1994). Investigations of discrepancies between laboratory studies on the flow of ice: density, sample shape and size, and grain size. Ann. Glaciol., 19, 146–154.
Jacka, T. H. and Jun, Li (1994). The steady state crystal size of deforming ice. Ann. Glaciol., 20, 13–18.
Jacka, T. H. and Maccagnan, M. (1984). Ice crystallographic and strain rate changes with strain in compression and extension. Cold Reg. Sci. Technol., 8, 269–286.
Johnston, M. E., Croasdale, K. R. and Jordaan, I. J. (1998). Localized pressures during ice-structure interaction: relevance to design criteria. Cold Reg. Sci. Technol., 27, 105–117.
Jones, S. J. and Brunet, J. G. (1978). Deformation of ice single crystals close to the melting point. J. Glaciol., 21, 445–455.
Jones, S. J. and Chew, H. A. M. (1981). On the grain-size dependence of secondary creep. J. Glaciol., 27, 517–518.
Jones, S. J. and Chew, H. A. M. (1983a). Effect of sample and grain size on the compressive strength of ice. Ann. Glaciol., 4, 129–132.
Jones, S. J. and Chew, H. A. M. (1983b). Creep of ice as a function of hydrostatic pressure. J. Phys. Chem. 87, 4064–4066.
Jones, S. J., Gagnon, R. E., Derradji, A. and Bugden, A. (2003). Compressive strength of iceberg ice. Can. J. Phys., 81, 191–200.
Jordaan, I. J. (2001). Mechanics of ice-structure interaction. Eng. Fract. Mech., 68, 1923–1960.
Kalifa, P. (1988). Contribution à l'étude de la fissuration dans la glace polycristalline en compression. Thèse de l'Université Joseph Fourier, Grenoble, France.
Kamb, W. B. (1972). Experimental recrystallization of ice under stress. American Geophysical Union, Geophysical Monograph, 16, 211–241.
Kirby, S. H., Durham, W. B., Beeman, M. L., Heard, H. C. and Daley, M. A. (1987). Inelastic properties of ice Ih at low temperatures and high pressures. J. Physique Coll., 48, C1-227–C1-232.
Kohlstedt, D. L. and Zimmerman, M. E. (1996). Rheology of partially molten mantle rocks, Ann. Rev. Earth Planet. Sci., 24, 41–62.
Langdon, T. G. (1973). Creep mechanisms in Ice. In Physics and Chemistry of Ice, eds. Whalley, E., Jones, S. J. and Gold, L. W.. Ottawa: Royal Society of Canada, pp. 356–361.
Langdon, T. G. (1993). The role of grain boundaries in high temperature deformation. Mater. Sci. Eng., A166, 67–79.
Langdon, T. G. (1994). A unified approach to grain boundary sliding in creep and superplasticity. Acta Metal. Mater., 42, 2437–2443.
Langdon, M. and Yavari, P. (1982). An investigation of Harper-Dorn creep. II. The flow process. Acta Metall., 30, 881–887.
Lawson, W. (1996). The relative strength of debris-laden basal ice and clean glacier ice: some evidence from Taylor Glacier, Antarctica. Ann. Glaciol., 23, 270–276.
Lebensohn, R. A., Tomé, C. N. and Castaneda, P. Ponte (2007). Self-consistent modeling of the mechanical behavior of viscoplastic polycrystals incorporating intragranular field fluctuations. Phil. Mag., 7, 4287–4322.
Legrand, M. and Mayewski, P. (1997). Glaciochemistry of polar ice cores: a review. Rev. Geophys., 35, 219–243.
Jun, Li, Jacka, T. H. and Budd, W. F. (1996). Deformation rates in combined compression and shear for ice which is initially isotropic and after the development of strong anisotropy. Ann. Glaciol., 23, 247–252.
Jun, Li, Jacka, T. H. and Morgan, V. (1998). Crystal size and microparticle record in the ice core from Dome Summit South, Law Dome, East Antarctica. Ann. Glaciol., 27, 243–348.
Lipenkov, V., Barkov, N. I., Duval, P. and Pimienta, P. (1989). Crystalline structure of the 2083 m ice core at Vostok Station, Antarctica. J. Glaciol., 35, 392–398.
Lipenkov, V., Salamatin, A. and Duval, P. (1997). Bubbly-ice densification in ice sheets: applications. J. Glaciol., 43, 397–407.
Liu, F., Baker, I. and Dudley, M. (1995). Dislocation-grain boundary interactions in ice crystals. Phil. Mag., A71, 15–42.
Lliboutry, L. (1969). The dynamics of temperate glaciers from the detailed viewpoint. J. Glaciol., 8, 185–205.
Lliboutry, L. (1971). Permeability, brine content and temperature of a temperate glacier. J. Glaciol., 10, 15–29.
Lliboutry, L. and Duval, P. (1985). Various isotropic and anisotropic ices found in glaciers and polar ice caps and their corresponding rheologies. Ann. Geophys., 3, 207–224.
Louchet, F., Weiss, J. and Richeton, Th. (2006). Hall-Petch law revisited in terms of collective dislocation dynamics. Phys. Rev. Lett., 97, 075504-1–075504-4.
Mangeney, A., Califano, F. and Hutter, K. (1997). A numerical study of anisotropic, low Reynolds number, free surface flow of ice-sheet modeling. J. Geophys. Res., 102, B10, 22,749–22,764.
Mangold, N., Allemand, P., Duval, P., Geraud, Y. and Thomas, P. (2002). Experimental and theoretical deformation of ice-rock mixtures: implications on rheology and ice content of Martian permafrost. Planet. Space Sci., 50, 385–401.
Marshall, H. P., Harper, J. T., Pfeffer, W. T. and Humphrey, N. F. (2002). Depth-varying constitutive properties observed in an isothermal glacier. Geophys. Res. Lett., 29, doi: 10.1029/2002GL015412.
Mellor, M. (1980). Mechanical properties of polycrystalline ice. In Physics and Mechanics of Ice, ed. Tryde, P.. Berlin: Springer-Verlag.
Mellor, M. and Cole, D. M. (1982). Deformation and failure of ice under constant stress or constant strain-rate. Cold Reg. Sci. Technol., 5, 201–219.
Mellor, M. and Testa, R. (1969). Creep of ice under low stress. J. Glaciol., 8, 147–152.
Melton, J. S. and Schulson, E. M. (1998). Ductile compressive failure of columnar saline ice under triaxial loading. J. Geophys. Res., 103 (C10), 21,759–21,766.
Meyssonnier, J. and Goubert, A. (1994). Transient creep of polycrystalline ice under uniaxial compression: an assessment of internal state variables models. Ann. Glaciol., 19, 55–62.
Michel, B. (1978). Ice Mechanics. Québec: Laval University Press.
Mohamed, F. A. (2005). On the origin of superplastic flow at very low stresses. Mat. Sci. Eng., A410–411, 89–94.
Montagnat, M. and Duval, P. (2000). Rate controlling processes in the creep of polar ice: influence of grain boundary migration associated with recrystallization. Earth Planet. Sci. Lett., 183, 179–186.
Montagnat, M. and Duval, P. (2004). The viscoplastic behavior of ice in polar ice sheets: experimental results and modelling. C. R. Physique, 5, 699–708.
Montagnat, M., Duval, P., Bastie, P., Hamelin, B. and Lipenkov, V. Ya. (2003). Lattice distortion in ice crystals from the Vostok core (Antarctica) revealed by hard X-ray diffraction: implication in the deformation of ice at low stresses. Earth Planet. Sci. Lett., 214, 369–378.
Morgan, V. I. (1991). High-temperature ice creep tests. Cold Reg. Sci. Technol., 19, 295–300.
Muguruma, J., Mae, S. and Higashi, A. (1966). Void formation by non-basal glide in ice single crystals. Phil. Mag., 13, 625–629.
Mukherjee, A. K. (2002). An examination of the constitutive equation for elevated temperature plasticity. Mater. Sci. Eng., A322, 1–22.
Nabarro, F. R. N. (2002). Creep at very low stresses. Metall. Mater. Trans., 33A, 213–218.
Obbard, R., Baker, I. and Sieg, K. (2006). Using electron backscatter diffraction patterns to examine recrystallization in polar ice sheets. J. Glaciol., 52, 546–557.
Paterson, W. S. B. (1991). Why is ice-age ice sometimes “soft”?Cold Reg. Sci. Technol., 20, 75–98.
Paterson, W. S. B. (1994). The Physics of Glaciers, 3rd edn. Oxford: Elsevier Science Ltd.
Peltier, W. R., Goldsby, D. L., Kohlstedt, D. L. and Tarasov, Lev (2000). Ice-age ice sheet rheology: constraints from the Last Glacial Maximum from the Laurentide ice sheet. Ann. Glaciol., 30, 163–176.
Petrenko, V. F. and Whitworth, R. W. (1999). Physics of Ice. Oxford: Oxford University Press.
Pettit, A. C. (2006). Ice flow at low deviatoric stresses: Siple Dome, West Antarctica. In Glacier Science and Environmental Change, ed. Knight, P. G.. Oxford: Blackwell Publishing, pp. 300–303.
Pettit, E. C. and Waddington, E. D. (2003). Ice flow at low deviatoric stress. J. Glaciol., 49, 359–369.
Pettit, E. C., Thorsteinsson, Th., Jacobson, H. P. and Waddington, E. D. (2007). The role of crystal fabric in flow near an ice divide. J. Glaciol., 53, 277–288.
Pimienta, P. and Duval, P. (1987). Rate controlling processes in the creep of polar glacier ice. J. Physique Coll., 48, C1-243–C1-248.
Plé, O. and Meyssonnier, J. (1997). Preparation and preliminary study of structure-controlled S2 columnar ice. J. Phys. Chem., 101, 6118–6122.
Poirier, J. P. (1985). Creep of Crystals: High Temperature Deformation Processes in Metals, Ceramics and Minerals. Cambridge: Cambridge University Press.
Raj, R. and Ashby, M. F. (1971). On grain boundary sliding and diffusional creep. Metall. Trans., 2, 1113–1128.
Ramseier, R. O. (1972). Growth and mechanical properties of river and lake ice. Ph.D. Thesis, Laval University, Canada.
Read, W. T. (1953). Dislocations in Crystals. New York: McGraw-Hill Book Company.
Richeton, Th., Weiss, J. and Louchet, F. (2005). Dislocation avalanches: role of temperature, grain size and strain hardening. Acta Mater., 53, 4463–4471.
Rigsby, G. P. (1951). Crystal fabric studies on Emmons Glacier, Mount Rainier, Washington. J. Geol., 59, 590–598.
Ruano, O. A., Wolfenstime, J., Wadsworth, J. and Sherby, O. D. (1991). Harper-Dorn and power law creep in uranium dioxide. Acta Metall. Mater., 39, 661–668.
Russell-Head, D. S. and Budd, W. F. (1979). Ice-flow properties derived from bore-hole shear measurements combined with ice-core studies. J. Glaciol., 24, 117–130.
Samyn, D., Svensson, A., Fitzsimons, S. J. and Lorrain, R. D. (2005). Ice crystal properties of amber ice and strain enhancement at the base of cold Antarctic glaciers. Ann. Glaciol., 40, 185–190.
Sanderson, T. J. O. (1988). Ice Mechanics: Risks to Offshore Structures. London: Graham and Trotman Limited.
Schmid, E. and Boas, W. (1936). Kristallplastizität. Berlin: Springer.
Schulson, E. M. (2001). Brittle failure of ice. Eng. Fract. Mech., 68, 1839–1887.
Schulson, E. M. and Buck, S. E. (1995). The ductile-to-brittle transition and ductile failure envelopes of orthotropic ice under biaxial compression. Acta Metall. Mater., 43, 3661–3668.
Schulson, E. M. and Nickolayev, O. Y. (1995). Failure of columnar saline ice under biaxial compression: failure envelopes and the brittle-to-ductile transition. J. Geophys. Res., 100 (B11), 22,383–22,400.
Sinha, N. K. (1978). Rheology of columnar-grained ice. Exp. Mech., 18, 464–470.
Smith, C. S. (1948). Grains, phases, and interfaces: an interpretation of microstructure. Trans. Metall. Soc. AIME, 175, 15–51.
Song, M., Cole, D. M. and Baker, I. (2005a). Creep of granular ice with and without dispersed particles. J. Glaciol., 51, 210–218.
Song, M., Baker, I. and Cole, D. M. (2005b). The effect of particles on dynamic recrystallization and fabric development of granular ice during creep. J. Glaciol., 51, 377–382.
Song, M., Cole, D. M. and Baker, I. (2006). Investigation of Newtonian creep in polycrystalline ice. Phil. Mag. Lett., 86, 763–771.
Steffensen, J. P. (1997). The size distribution of microparticles from selected segments of the GRIP ice core representing different climatic periods. J. Geophys. Res., 102 (C12), 26,755–26,763.
Steinemann, S. (1958). Experimentelle Untersuchungen Zur Plastizität von Eis. Beitr. Geol. Schweiz, Hydrologie, 10, 1–72.
Sunder, S. S. and Wu, M. S. (1990). On the constitutive modeling of transient creep of polycrystalline ice. Cold Reg. Sci. Technol., 18, 267–294.
Tatibouet, J., Perez, J. and Vassoille, R. (1986). High-temperature internal friction and dislocations in ice Ih. J. Physique, 47, 51–60.
Taupin, V., Varadhan, S., Chevy, J.et al. (2007). Effects of size on the dynamics of dislocations in ice single crystals. Phys. Rev. Lett., 99, 155507-1–155507-4.
Thorsteinsson, Th. (2002). Fabric development with nearest-neighbor interaction and dynamic recrystallization. J. Geophys. Res., 107 (B1), 1–13.
Thorsteinsson, Th., Kipfstuhl, J. and Miller, H. (1997). Textures and fabrics in the GRIP ice core. J. Geophys. Res., 102 (C12), 26,583–26,599.
Veen, C. J. and Whillans, I. M. (1990). Flow laws for glacier ice: comparison of numerical predictions and field measurements. J. Glaciol., 36, 324–339.
Veen, C. J. and Whillans, I. M. (1994). Development of fabric in ice. Cold Reg. Sci. Technol., 22, 171–195.
Wakahama, G. (1967). On the plastic deformation of single crystal of ice. In Physics of Snow and Ice, ed. Oura, H.. Sapporo: Hokkaido University Press, 291–311.
Weertman, J. (1973). Creep of ice. In Physics and Chemistry of ice, eds. Whalley, E., Jones, S. J. and Gold, L. W.. Ottawa: Royal Society of Canada.
Weertman, J. (1983). Creep deformation of ice. Ann. Rev. Earth Planet. Sci., 11, 215–240.
Weiss, J., Vidot, J., Gay, M.et al. (2002). Dome Concordia ice microstructure impurities effect on grain growth, Ann. Glaciol., 33, 552–558.
Wilson, C. J. L. (1986). Deformation induced recrystallization of ice: the application of in-situ experiments. American Geophysical Union, Geophysical Monograph, 36, 213–232.
Wilson, C. J. L. and Russell-Head, D. S. (1982). Steady state preferred orientation of ice deformed in plane strain at −1 ℃. J. Glaciol., 28, 145–159.
Wilson, C. J. L. and Zhang, Y. (1996). Development of microstructure in the high-temperature deformation of ice. Ann. Glaciol., 23, 293–302.
Wolff, E. W. and 27 co-authors (2006). Southern Ocean sea-ice extent, productivity and iron flux over the past eight glacial cycles. Nature, 440, 491–496.