Viscous behaviour of ice at low stresses application to polar ice sheets Deformation modes

For conditions prevailing in ice sheets (equivalent stress lower than 0.2MPa), the stress exponent is slightly lower than 2, a value close to that found in isolated single crystals (Fig. 59.1). This result is supported by densification measurements of bubbly ice at Vostok (Lipenkov etal., 1997). The high difference in strain rate between crystals oriented for basal slip and isotropic ice (Fig. 59.1) cannot be explained by a geometric effect related to the random orientation of grains. As at high stresses, basal slip is the dominant deformation mode, but other deformation modes are required to assure the compatibility of deformation. However, the internal stress field induced by the mismatch of slip at grain boundaries is reduced under the low stress conditions of ice sheets by grain-boundary migration. By sweeping away dislocations located in front of moving grain boundaries, grain-boundary migration associated with grain growth and recrystallization prevents kinematic hardening caused by the incompatibility of deformation between grains. Accommodation of slip by grain-boundary migration in polar ice must be taken into account to explain the low stress exponent observed at low stresses.

A physical deformation model, considering dislocation density within an average grain as an internal variable, was developed by Montagnat & Duval (2000). The increase of dislocation density by work hardening is balanced by grain-boundary migration and by the formation of new grain boundaries. This model accounts for the transition between grain growth and recrystallization in several locations in the Greenland and Antarctic ice sheets. However, the low stress exponent of the flow law cannot be deduced from such a model. It is also difficult to assume that the same value of stress exponent for single crystals and polycrystalline ice at low stresses (Fig. 59.1) implies the same ratecontrolling processes.

Grain-boundary sliding (GBS) is also suggested to accommodate basal slip, but the occurrence of such a process in the flow conditions of ice sheets has not been proven. This deformation mode was put forward by Goldsby & Kohlstedt (2001,2002), who consider polar ice as a superplastic material. It is worth noting that the dominant deformation mode corresponding to the n = 1.8 regime in superplastic materials is GBS (Langdon, 1994; Goldsby & Kohlstedt, 1997). The observed microstructures and the development of preferential orientations of ice crystals in ice sheets, associated with easy basal slip, are clearly not compatible with GBS as the dominant deformation mode in polar ice sheets (Duval & Montagnat, 2002). Dynamic recrystallization in glaciers and ice sheets

The evolution of texture in ice sheets is achieved via three recrys-tallization processes, which are termed: normal grain growth, rotation recrystallization and migration recrystallization (Alley, 1992; Duval & Castelnau, 1995; De La Chapelle et al, 1998). In the upper layers of ice sheets (several hundred metres), the mean grain size increases with depth (Gow, 1969; Gow & Williamson, 1976). The driving force for the normal grain growth results from the decrease in free energy that accompanies reduction in grain-boundary area. The driving force 3 ggb/D is less than 100Jm-3 because grain size D is larger than 1 mm and the grain-boundary free energy ggb = 0.065Jm-2. The boundary migration velocity is typically 10-15ms-1 at -50°C and can reach a value higher than 10-6ms-1 at the melting point. Grain growth appears to be inhibited by soluble and (or) insoluble impurities (Alley etal., 1986b,c; Fisher & Koerner, 1986; Alley & Woods, 1996; Li et al, 1998). Particles deposited during the Last Glacial Maximum (LGM) and located on grain boundaries seem to reduce the rate of grain growth (Weiss et al., 2002). The pinning pressure due to particles randomly distributed within the ice volume is shown to be too low to explain fine-grained ice in LGM (Alley et al., 1986c).

High-angle boundaries form by the progressive misorientation of sub-boundaries (De La Chapelle et al., 1998). This recrystallization mechanism is termed rotation recrystallization (Poirier, 1985). It counteracts further grain-size increase due to grain growth from 400 m depth in the Byrd ice core (Alley et al., 1995) and 650m in the GRIP ice core (Thorsteinsson et al., 1997). In this recrystallization regime, grain boundaries migrate in the same low-velocity regime as the one associated with normal grain growth (Duval & Castelnau, 1995).

In the last hundred metres of ice sheets, just above the bedrock, temperature can be higher than -10°C, reaching the melting point at the interface between ice and rock. In this zone, rapid migration of grain boundaries can occur between dislocation-free nuclei and deformed grains. This recrystallization regime, referred to as migration recrystallization, produces coarse and interlocking grains (Gow & Williamson, 1976). The velocity of grain-boundary migration is more than 100 times higher than that associated with rotation recrystallization (Duval & Castelnau, 1995). It is worth noting that migration recrystal-lization is very active in temperate glaciers and is associated with tertiary creep. Rate-controlling processes in the creep of polar ice; effect of crystal size

The deformation of polar ice is essentially produced by dislocation slip on basal planes. The mismatch of slip at grain boundaries induces lattice distortion and strain gradients.

Grain-boundary migration associated with grain growth and recrystallization reduces the dislocation density and the internal stress field. As a consequence, strain rate is higher than that extrapolated from high stress conditions with a stress exponent n = 3. The large difference between the basal slip of single crystals and the creep behaviour of polycrystalline ice (Fig. 59.1) shows that the incompatibility of deformation between grains is significant even at low stresses. The amount of non-basal slip or climb of dislocations required for compatibility reasons, however, should be reduced in the flow conditions of ice sheets. With regard to non-basal slip, the bending of basal planes observed by hard X-ray diffraction (Montagnat etal., 2003) must be taken into account when considering deformation along the c-axis. Mechanisms that give the value of the stress exponent n = 2 at low stresses cannot be determined on the basis of this analysis alone. The slowest deformation mechanism could control strain rate if it occurs in series with basal slip. It is probably the case at high stresses where non-basal slip or climb of dislocations is the likely rate-controlling process. At low stresses, the amount of these hard deformation systems is reduced by several processes such as the formation of strain heterogeneities within grains and recovery by recrystallization.

The influence of grain size on strain rate has been the subject of discussions during the past few decades. The lack of significant grain-size effect on the minimum creep rate as shown by laboratory tests under deformation conditions corresponding to n = 3 (Duval & LeGac, 1980; Jacka, 1984a, 1994) is in accordance with the deformation modes discussed above. Owing to the difficulty of obtaining good laboratory data at low stresses, it is not possible to prove a grain size effect in the deformation conditions of ice sheets on the basis of laboratory experiments alone. The value of the stress exponent lower than 2, unambiguously deduced from in situ measurements in polar ice sheets, cannot prove the occurrence of grain-boundary sliding or other mode of deformation. A convincing analysis of deformation measurement data on Meserve Glacier (Antarctica) by Cuffey et al. (2000a) suggests a direct dependence of strain rate on grain size. A multi-term flow law with grain-size dependence was adopted by Pettit & Waddington (2003) to simulate the surface morphology of ice divides. A grain-size effect at low stresses, if not yet proven, is likely. It is in accordance with intracrystalline slip accommodated with grain-boundary migration (Montagnat etal., 2003).

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