Fabric and flow

The effects of anisotropy on deformation are complex. One way to represent fabric is through a cone angle, where the cone angle goes from a = 0° for all crystals aligned, to a = 90° for isotropic ice. In general, stronger anisotropy (smaller cone angle) makes the ice softer in shear parallel to the basal planes, and stiffer in compression normal to the basal planes (think of a deck of cards), as shown in Fig. 61.2.

It has been a common practice to account for the effects of anisotropy with scalar 'enhancement' factors. Where there is one

Figure 61.1 Deformation in uniaxial compression where polygonization and migration recrystallization are active: (a) the fabric after 0.5 vertical strain, where the initial fabric was isotropic, and (b) normalized strain rate versus strain.

dominant stress component (shear or compression) it may be a reasonable approximation; however, in general, a scalar enhancement factor is inadequate, because the enhancement of strain rate due to fabric depends on both stress orientation and deformation direction. Accounting for anisotropy explains most of the 'enhanced' deformation in Greenland, about 75% at Dye 3 for instance (Thorsteinsson et al., 1999).

The vertically symmetric fabric commonly observed in icesheets makes horizontal shearing easier (Fig. 61.2). This facilitates folding, i.e. elements with smaller slopes can be overturned. The effects of anisotropy on folding are complicated by the fact that, for a range of cone angles, ice is also softer in compression (Figs 61.2 & 61.3a); this opposes folding (Thorsteinsson & Waddington, 2002). Figure 61.3 shows (a) the vertical strain rate and (b) shear strain rate in combined uniaxial compressive stress and simple shear stress (as when moving away from the centre of a dome). In layers with spatially variable and evolving fabric, the fabric causes localized flow variations, which could create layer disturbances.

Figure 61.2 Normalized strain rate for different levels of nearest neighbour interaction (NNI) in uniaxial compression and simple shear as a function of cone angle. Isotropic ice has a cone angle of 90° and ice with all crystals aligned has a cone angle of 0°.
Figure 61.3 Normalized strain rate in combined uniaxial compression (s) and simple shear (t) stress state as a function of stress ratio (t/s) and cone angle: (a) vertical strain rate and (b) shear strain rate (Thorsteinsson & Waddington, 2002).

Along most particle paths in polar ice sheets, ice experiences a slowly changing local deviatoric-stress pattern, and develops a fabric characteristic of its current stress state, in which there is generally a correspondence between non-zero strain-rate components and non-zero deviatoric-stress components. However, when the stress pattern changes more rapidly than the fabric can evolve, unusual or unexpected deformation patterns can result (Thorsteinsson et al., 2003). The degree to which fabric follows the local stress is determined by the characteristic time-scales for changes in stress, given by the transition-zone width and ice velocity, and for changes in crystal orientation, given, in the absence of recrystallization, by the inverse of the local strain rate due to the principal stress. Recrystallization can significantly reduce the time-scale for fabric adjustment. Stress and fabric tend to be misaligned in ice-stream margins (although recrystallization will also be active) and in flow through a saddle (Thorsteinsson et al., 2003). Non-intuitive deformation patterns can also result if the stress state applied to an ice sample in an experiment is markedly different from the in situ stress state in the ice sheet.

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