Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- 1 Introduction
- 2 Structure of ice
- 3 Microstructure of natural ice features
- 4 Physical properties: elasticity, friction and diffusivity
- 5 Plastic deformation of the ice single crystal
- 6 Ductile behavior of polycrystalline ice: experimental data and physical processes
- 7 Modeling the ductile behavior of isotropic and anisotropic polycrystalline ice
- 8 Rheology of high-pressure and planetary ices
- 9 Fracture toughness of ice
- 10 Brittle failure of ice under tension
- 11 Brittle compressive failure of unconfined ice
- 12 Brittle compressive failure of confined ice
- 13 Ductile-to-brittle transition under compression
- 14 Indentation fracture and ice forces on structures
- 15 Fracture of the ice cover on the Arctic Ocean
- Index
- References
7 - Modeling the ductile behavior of isotropic and anisotropic polycrystalline ice
Published online by Cambridge University Press: 01 February 2010
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- 1 Introduction
- 2 Structure of ice
- 3 Microstructure of natural ice features
- 4 Physical properties: elasticity, friction and diffusivity
- 5 Plastic deformation of the ice single crystal
- 6 Ductile behavior of polycrystalline ice: experimental data and physical processes
- 7 Modeling the ductile behavior of isotropic and anisotropic polycrystalline ice
- 8 Rheology of high-pressure and planetary ices
- 9 Fracture toughness of ice
- 10 Brittle failure of ice under tension
- 11 Brittle compressive failure of unconfined ice
- 12 Brittle compressive failure of confined ice
- 13 Ductile-to-brittle transition under compression
- 14 Indentation fracture and ice forces on structures
- 15 Fracture of the ice cover on the Arctic Ocean
- Index
- References
Summary
Introduction
During the gravity-driven flow of glaciers and ice sheets, isotropic ice at the surface progressively becomes anisotropic with the development of textures. Strain-induced textures, combined with the strong anisotropy of the ice crystal, make the polycrystal anisotropic. A polycrystal of ice with most of its c-axes oriented in the same direction deforms at least ten times faster than an isotropic polycrystal, when it is sheared parallel to the basal planes. Depending on the flow conditions, this anisotropy varies from place to place. To construct ice-sheet flow models for the dating of deep ice cores, this evolving viscoplastic anisotropy must be taken into account. Computation with isotropic and anisotropic flow models predicts at depth an age of ice that can differ by several thousand years. From Mangeney et al. (1997), anisotropic ice could be more than 10% younger above the bumps of the bedrock and could be older by more than 100% within hollows. An adequate constitutive relationship must be also incorporated within large-scale flow models to simulate the variation of polar ice sheets with climate.
Various models have been proposed to simulate the evolution of the anisotropy and the behavior of such ices. The increasing numerical capability of computers and the advances in theories that link materials' microstructures and properties have enabled the development of new concepts and algorithms that constitute the so-called multiscale approach for the modeling of material behavior. In this chapter, we restrict our analysis to physically based micro-macro models using a self-consistent approach.
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- Chapter
- Information
- Creep and Fracture of Ice , pp. 153 - 178Publisher: Cambridge University PressPrint publication year: 2009
References
and (1985). The creep of polycrystalline ice. Cold Reg. Sci. Technol., 11, 285–300.CrossRefGoogle Scholar
(1994). A flow law for anisotropic ice and its application to ice sheets. Earth Planet. Sci. Lett., 128, 601–614.CrossRefGoogle Scholar
(1995). A flow law for anisotropic polycrystalline ice under uniaxial compressive deformation. Cold Reg. Sci. Technol., 23, 137–147.CrossRefGoogle Scholar
and (1985). Formation processes of ice fabric pattern in ice sheets. Ann. Glaciol., 6, 130–134.CrossRefGoogle Scholar
(1987). Representations for isotropic and anisotropic non-polynomial tensor functions. In Applications of Tensor Functions in Solid Mechanics, ed. . Berlin: Springer-Verlag, pp. 31–53.CrossRefGoogle Scholar
and (1989). A review of ice rheology for ice sheet modelling. Cold Reg. Sci. Technol., 16, 107–144.CrossRefGoogle Scholar
, , and (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.CrossRefGoogle Scholar
, , , and (1996b). Modelling fabric development along the GRIP ice core, central Greenland. Ann. Glaciol., 23, 194–201.CrossRefGoogle Scholar
, , and (1997). Modelling viscoplastic behavior of anisotropic polycrystalline ice with a self-consistent approach. Acta Mater., 45, 4823–4834.CrossRefGoogle Scholar
, , and (2008). Elastoviscoplastic micromechanical modelling of the transient creep of ice. J. Geophys. Res., 113, B11203.CrossRefGoogle Scholar
, , and (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.CrossRefGoogle Scholar
and 10 others (2006). Effect of impurities on grain growth in cold ice sheets. J. Geophys. Res., 111, FO1015, 1–18.CrossRefGoogle Scholar
(1976). Lois de fluage transitoire ou permanent de la glace polycristalline pour divers états de contrainte. Ann. Geophys., 32, 335–350.Google Scholar
(2006). Creep and recrystallization of large polycrystalline masses. I. General continuum theory. Proc. R. Soc. A, 462, 1493–1514.CrossRefGoogle Scholar
and (1999). Analytical derivations for the behaviour and fabric evolution of a linear orthotropic ice polycrystal. J. Geophys. Res., 104 (B8), 17,797–17,809.CrossRefGoogle Scholar
, and (in press). A review of anisotropic polar ice models: from crystal to ice-sheet flow models. In Physics of Ice Core Records 11, ed. . Sapporo: Hokkaido University Press.
(2006). Modélisation de l'écoulement de la glace polaire anisotrope et premières applications au forage de Dôme C. Thèse de l'Université Joseph Fourier, Grenoble, France.
, , , and (2005). A user-friendly anisotropic flow law for ice-sheet modelling. J. Glaciol., 51, 1–14.CrossRefGoogle Scholar
, , , and (2006). Flow-induced anisotropy in polar ice and related ice-sheet flow modeling. J. Non-Newtonian Fluid Mech., 134, 33–43.CrossRefGoogle Scholar
and (1998). Induced anisotropy in large ice shields: theory and its homogenization. Continuum Mech. Thermodyn., 10, 293–318.Google Scholar
and (1984). Bore-hole survey at Dye 3, South Greenland. J. Glaciol., 30, 282–288.CrossRefGoogle Scholar
and (2002). Performance and applications of an automated c-axis fabric analyser. J. Glaciol., 48, 159–170.CrossRefGoogle Scholar
(1976). Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lond. A, 348, 101–127.CrossRefGoogle Scholar
(1977). Creep and plasticity of hexagonal polycrystals as related to single crystal slip. Metall. Trans. 8A (9), 1465–1469.CrossRefGoogle Scholar
(2001). N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform. Acta Mater., 49, 2723–2737.CrossRefGoogle Scholar
and (1993). A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall., 41, 2611–2624.CrossRefGoogle Scholar
, and (2004a). On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations. Acta Mater., 52, 5347–5361.CrossRefGoogle Scholar
, and (2004b). Macroscopic properties and field fluctuations in model power-law polycrystals: full-field solutions versus self-consistent estimates. Proc. R. Soc. Lond. A, 460, 1381–1405.CrossRefGoogle Scholar
, and (2007). Self-consistent modeling of the mechanical behavior of viscoplastic polycrystals incorporating intragranular field fluctuations. Phil. Mag., 87, 4287–4322.CrossRefGoogle Scholar
, , et al. (2009). Modeling viscoplastic behavior and heterogeneous intracrystalline deformation of columnar ice polycrystals, Acta Mater. (in press).CrossRefGoogle Scholar
, , and (1989). Crystalline structure of the 2083 m ice core at Vostok Station, Antarctica. J. Glaciol., 35, 392–398.CrossRefGoogle Scholar
, and (1997). Bubbly-ice densification in ice sheets: applications. J. Glaciol., 43, 397–407.CrossRefGoogle Scholar
and (2004). Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals. J. Mech. Phys. Solids, 52, 467–495.CrossRefGoogle Scholar
(1993). Anisotropic, transversely isotropic nonlinear viscosity of rock ice and rheological parameters inferred from homogenization. Int. J. Plast., 9, 619–632.CrossRefGoogle Scholar
, and (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.CrossRefGoogle Scholar
and (1997). Kinks bands and cracks in S1 ice under across-column compression. Phil. Mag., 75, 83–90.Google Scholar
(2001). Contribution à l'étude du comportement viscoplastique d'un multicristal de glace: hétérogénéité de la déformation et localisation, expériences et modèles. Thèse de l'Université Joseph Fourier, Grenoble, France.
and (1999). Self-consistent estimates for the rate-dependent elasto-plastic behaviour of polycrystalline materials. J. Mech. Phys. Sol., 47, 1543–1568.CrossRefGoogle Scholar
, , and (2001). Constitutive modeling and flow simulation of anisotropic polar ice. In Continuum Mechanics and Applications in Geophysics and the Environment. Berlin: Springer-Verlag.Google Scholar
, and (1987). A self-consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall., 35, 2983–2994.CrossRefGoogle Scholar
, , , and (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.CrossRefGoogle Scholar
, , et al. (2006). The heterogeneous nature of slip in ice single crystals deformed under torsion. Phil. Mag., 86, 4259–4270.CrossRefGoogle Scholar
and (1998). Viscous response of polar ice with evolving fabric. Continuum Mech. Thermodyn., 10, 135–152.CrossRefGoogle Scholar
and (1999). Dynamic analysis and two types of kink bands in quartz veins deformed under subgreenschist conditions. Tectonophysics, 301, 21–34.CrossRefGoogle Scholar
, and (1987). Mechanical behavior of anisotropic polar ice. In The Physical Basis of Ice Sheet Modeling, eds. and . Vancouver: IAHS Publication 170, pp. 57–66.Google Scholar
, and (2006). A critical review of the mechanics of polycrystalline polar ice. GAMM-Mitteilungen, 29, 80–117.CrossRefGoogle Scholar
(1951). Crystal fabric studies on Emmons Glacier, Mount Rainier, Washington. J. Geol., 59, 590–598.CrossRefGoogle Scholar
and (1979). Ice-flow properties derived from bore-hole shear measurement combined with ice-core studies. J. Glaciol., 24, 117–130.CrossRefGoogle Scholar
and (2001). Automated fabric analyzer system for quartz and ice. Geol. Soc. Austral. Abstr., 64, 159.Google Scholar
and . (1988). Flow-law parameters of the Dye 3, Greenland, deep ice core. Ann. Glaciol., 10, 146–150.CrossRefGoogle Scholar
and (2000). Plane ice-sheet flow with evolving orthotropic fabric. Ann. Glaciol., 30, 93–101.CrossRefGoogle Scholar
and (1996). A continuum approach for modeling induced anisotropy in glaciers and ice sheets. Ann. Glaciol., 23, 262–269.CrossRefGoogle Scholar
(2001). An analytical approach to deformation of anisotropic ice-crystal aggregates. J. Glaciol., 47, 507–516.CrossRefGoogle Scholar
(2002). Fabric development with nearest-neighbor interaction and dynamic recrystallization. J. Geophys. Res., 107 (B1), 1–13.CrossRefGoogle Scholar
, and (1997). Textures and fabrics in the GRIP ice core. J. Geophys. Res., 102 (C12), 26,583–26,599.CrossRefGoogle Scholar
, , , and (1999). Strain-rate enhancement at Dye 3, Greenland. J. Glaciol., 45, 338–345.CrossRefGoogle Scholar
and (1994). Development of fabric in ice. Cold Reg. Sci. Technol., 22, 171–195.CrossRefGoogle Scholar
, and (1986). The origin of kinks in polycrystalline ice. Tectonophysics, 127, 27–48.CrossRefGoogle Scholar
, and (2008). Kinking nonlinear elasticity, damping and microyielding of hexagonal close-packed metals. Acta Mater., 56, 60–67.CrossRefGoogle Scholar