Deformation mechanism maps

Our discussion so far has focused on the type of creep most commonly observed in glaciers, called power-law creep because the creep rate is proportional to the stress raised to some power > 1 (Equation (4.4)). The dominant processes in power-law creep are dislocation glide and climb. For completeness, some other types of creep should be mentioned.

In recent years, scientists working on ice deformation mechanisms have found it useful to plot "maps" showing the deformation mechanisms operating at different temperatures and stresses (Figure 4.16). The temperature is usually normalized by dividing by the melting temperature in Kelvin, 0Km. This is called the homologous temperature. Similarly, the stress is normalized by dividing by Young's modulus. In Figure 4.16 the stress used is V3ae. Note that the equivalent octahedral stress is shown on the right ordinate.

The heavy lines in Figure 4.16 divide the diagram into fields in which a single deformation mechanism is dominant. Power-law creep occupies much of the right side of the diagram. Below and to the left of the power-law creep field is the field of diffusional flow. In this type of flow, atoms move from crystal boundaries that are under compression to ones that are

Temperature, oC

10-1

-250

-200

-150

-100

10-3

Plasticity (Under confining pressure)

Dynamic recrystallization and grain-boundary mobility -

-250

-200

-150

-100

Plasticity (Under confining pressure)

Dynamic recrystallization and grain-boundary mobility -

10-3

Figure 4.16. Deformation mechanism map for ice with a grain size of 1 mm. (Adapted with permission from Duval et al., 1983, Figure 1. Copyright 1983 American Chemical Society.)

Homologous temperature, 0/0Km

Figure 4.16. Deformation mechanism map for ice with a grain size of 1 mm. (Adapted with permission from Duval et al., 1983, Figure 1. Copyright 1983 American Chemical Society.)

under tension. At low temperatures, atoms are believed to move along grain boundaries (grain-boundary or Coble creep) whereas at higher temperatures they probably move through the crystal lattice (lattice diffusion or Nabarro-Herring creep). These two diffusional creep fields are separated by a vertical dashed line at about 0.8 0/0Km. The shading along the heavy lines separating these two diffusional creep fields from each other and from the power-law field represents the zone of overlap of the fields. On the right edge of the shaded zone, power-law creep contributes 90% of the deformation and on the left edge, diffusional creep contributes 90%.

At octahedral stresses between 2 and 10 MPa, fracture also contributes to the deformation. The onset of fracturing occurs at lower stresses in tension than in compression, so this field has an appreciable width. Under sufficiently large confining pressures, fracture is suppressed, and the upper part of the diagram is then accessible.

Another field shown on the diagram is that labeled "dynamic recrystallization and grain-boundary mobility". At temperatures above about -10 °C, the increase in creep rate with temperature is more rapid than predicted by an activation energy of 79 kJ mol-1. In addition, there is a rapid increase in the electrical conductivity of ice (Mellor and Testa, 1969), and a less striking but still significant increase in the heat capacity (Harrison, 1972). Finally, multiple-maximum fabrics are common in glacier ice deformed at temperatures above -10 °C, but rare or absent in ice below -10 °C (Hooke and Hudleston, 1980). The first three of these phenomena can be explained if grain-boundary melting begins at about -10 °C. Grain-boundary melting involves the formation of a widened zone with a liquidlike structure at grain boundaries and particularly at multiple grain junctions (Duval et al., 1983; de La Chapelle et al., 1995). This liquidlike layer is, in part, a consequence of impurities that become concentrated at grain boundaries, lowering the melting point (Equation (2.1)). In addition, molecules on such a surface are not well bonded to adjacent molecules on all sides, and thus form a liquidlike layer even in the absence of impurities. This layer can explain the increase in creep rate (as the liquid phase reduces grain interactions and thus attenuates the internal stress field), the increase in electrical conductivity (as impure water has a much higher conductivity than pure ice), and the increase in heat capacity (as some heat is absorbed by melting). Whether it can explain the development of multiple-maximum fabrics is uncertain, but attempts to develop a theory explaining these fabrics should take it into consideration.

In glaciers, stresses rarely exceed 0.2 MPa, and temperatures are rarely below -50 °C, so for our purposes only the lower right-hand corner of the deformation mechanism map is of interest. It appears from this part of the diagram that both diffusional and power-law creep should occur, as long as the grain size of the ice is about 1 mm. However, this is actually a lower limit for the grain size in glacier ice. Grain sizes of 10-30 mm are common in polar and polythermal glaciers (Figure 4.12), and much larger crystals can be found deep in polar glaciers and in temperate glaciers. As grain size increases, the power-law creep field increases at the expense of the diffusional creep field. This is intuitively reasonable as larger grain sizes imply longer diffusion paths.

In diffusional creep, the strain rate is linearly proportional to stress, in contrast to the situation with power-law creep. At present, there seems to be no unequivocal field evidence suggesting that pure diffusional creep is important in glaciers. However, Alley (1992) and Montagnat and Duval (2000) have suggested that during grain growth (p. 58), migration of grain boundaries can annihilate dislocations and thus reduce the dislocation density below that predicted by Equation (4.3). In this case, n is likely to be less than 3. Thus, diffusive processes associated with grain-boundary migration may be important, in combination with dislocation glide, to depths of a few hundred meters in colder parts of the Antarctic and Greenland ice sheets. On the other hand, in a study of floating ice shelves bordering the Antarctic ice sheet, Thomas (1973b) and Jezek et al. (1985) found that power-law creep with n « 3 seemed to prevail at temperatures of —-15 °C and stresses of only 0.04-0.06 MPa.

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