Time lapse photography Glaciers Dislocations Bernal-Fowler rule Generation of defect structures Crystal structures Crystal structures Ice Basal glide Strain rate for glide on basal systems Critical resolved shear stress Non-basal glide Non-basal glide Diffusional flow Plastic Deformation Primary creep Secondary creep Tertiary creep Deformation maps Grain growth and grain size reduction Anisotropic flow Index

Glide and diffusional processes also play significant roles in the plastic deformation of polycrystalline ice. Compression experiments show that polycrystalline ice deforms instantly when a stress is applied suddenly (Barnes et al. 1971; Kamb 1972). Initially the strain rate slows with increasing strain; this is known as primary creep (see fig. 2.9.2). This reduction in strain rate reflects work hardening similar to that observed in a single crystal of ice that is being deformed in a hard glide orientation (see Strain rate for glide on basal systems). Eventually the strain rate becomes constant; this is secondary creep, the minimum strain rate. Secondary creep is of principal interest as it gives rise to the steady state flow observed in glaciers. When the compressive stress exceeded a critical stress the strain rate increased significantly. This is known as tertiary creep and is due to recrystallisation of ice. Other complicating factors in the deformation of polycrystalline ice are grain boundary melting, pressure melting (Wilson et al. 1996) and the development of crystallographic fabrics which may enhance the flow of the ice.

In order that a polycrystalline solid can deform homogeneously into any arbitrary shape, with no volume change and maintain strain compatibility it must have at least five independent slip systems (Taylor 1938). If uniform strain is not pre-supposed then the polycrystals only require four independent systems (Hutchison 1976). The basal plane of ice crystals provides only two systems. The other two independent systems must be non-basal, but glide is 2 or 3 orders of magnitude more difficult to activate than for basal systems. The non-basal system therefore plays a major role in macroscopic behaviour making deformation of polycrystalline ice slower than that of a single ice crystal (see fig. 2.11.1). The additional non-basal system are most probably the prismatic systems {0110} <2110> and pyramidal {1122} <1123> slip systems (see fig. 1.1.2). The other possibility is that movement of dislocations on the two independent systems in the basal plane gives rise to dislocation climb normal to the basal plane; and provides a further two systems (Ashby & Duval 1985).
 
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When a load is initially applied to a polycrystalline aggregate, both grains in easy glide and hard glide orientations deform elastically (see fig. 2.14.1, AB). With increasing stress the easy glide grains begin to glide and plastically deform. As the easy glide grains relax, stress is redistributed onto the hard glide grains which are progressively rotated and begin to deform in an elastic-plastic manner. If the stress is removed at this point, some but not all of the strain is recoverable, as the easy glide grains have deformed permanently. If the stress is continued then, hard glide grains will eventually begin to fail by plastic deformation and contribute to the bulk deformation at which point secondary glide is achieved.
Figure 2. 14. 1
Figure 2.14.1. Schematic creep curve for polycrystalline ice under constant load.
The region of decelerating "primary creep" extends from B to the inflection point C, after which the creep accelerates and eventually reaches a constant rate DE. Early work on ice by Glen (1955) and Barnes et al. (1971) identified a region of steady-state or "secondary creep" around the point C. Later experiments show only a broad minimum in Strain Rate, but the minimum strain rate Minimum Strain Rate represents a very important quantity in the analysis of the creep data. Deformation beyond the minimum is called "tertiary creep". The final steady state Final Steady State marked DE in Fig. 2.14.1 is hard to attain in laboratory experiments, but this is the region of most significance in geology and glaciology.
 
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True steady-state secondary creep is not observed in ice. Figure 2.15.1 shows examples at -17.8°C from the many creep curves obtained by Jacka (1984), plotted here in the form of strain rate as a function of strain using logarithmic scales. These curves show well-developed minima, but note that to achieve the minimum at the lowest stress the deformation had to be followed for more than a year! Many early experiments did not reach the strain rate minimum, and secondary creep rates reported in the literature may be misleading. Nevertheless secondary creep rates, whether obtained at the true minimum or not, have been extensively used in making comparisons between experiments performed at different stresses and temperatures. The important thing about the point of inflection C on the creep curve (see fig. 2.14.1) is not the balance between decelerating primary creep and accelerating tertiary creep. It is that in this approximately steady-state situation plastic flow of the grains occurs at a rate that is in balance with the processes which relieve the internal stresses so produced. These processes, which may include dislocation climb and grain boundary sliding or migration, are the rate limiting factors for secondary creep in polycrystalline ice.
 

The points plotted in Fig. 2.11.1 are the secondary creep rates of polycrystalline ice deduced in various ways from various tensile and compressive tests at -10°C, and the figure shows that this creep rate is intermediate between those for basal and non-basal slip in single crystals. Over an intermediate range of the stresses shown on the figure the secondary creep of polycrystalline ice obeys the power law proposed by Glen (1955)

Power Law

where A is a constant and Value 11 The logarithmic plot of Fig. 2.14.2 includes a line with this slope. In the experiments of Barnes et al. (1971) there was evidence that n>3 at high stresses, and more recently Rist & Mureell (1994) obtained Value 12 from constant strain rate compression tests at high stress. Values of n greater than 3 have often been associated with the formation of microcracks in the ice. However, Manley and Schulson (1997) have produced experimental data suggesting that n is correlated with two-dimensional (glide) to three-dimensional (glide plus climb) of dislocations.

Figure 2. 15. 1
Figure 2.15.1. Plots of strain rate as a function of strain for creep of granular polycrystalline ice in uniaxial compression under various stresses. In this and the following three figures stresses and strains have been converted to octahedral values according to equations in Jacka (1984).
 
Figure 2. 15. 2
Figure 2.15.2. The minimum strain rate is uniaxial creep tests on granular polycrystalline ice as functions of stress at various temperatures (after Budd and Jacka, 1989).
For the creep curves in Fig. 2.15.1 all the minima occur at the same strain Value 13 (equivalent to Value 14 in compression). This strain for minimum strain rate is the same within experimental error for temperatures from -5 to -32.5°C in the experiments of Jacka (1984) and Mellor & Cole (1982). The dependence of the minimum strain rate Minimum Strain Rate on stress for various temperatures is shown in Fig. 2.15.2 (Budd and Jacka 1989). These stress dependencies all fit Glen's equation (equation 1) with n=3, and reports of smaller values of n at low stresses are probably consequences of failure to attain the true minimum rate.
 
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Duval et al. (1983) have demonstrated that the acceleration of creep in polycrystalline ice is at least partially due to the formation of microcracks within polycrystalline ice. The microcracks are about equal to the grain size and their density increase with strain. The initiation and movement across microcracks results in additional stresses on uncracked crystals which produces localised internal stress variations. Duval et al. (1983) also showed that a sample deformed at 1.86 MPa had a steady increase in microcrack initiation that resulted in a concurrent increase in strain rate, while a sample that was deformed under 1 MPa increased in strain rate without any observed cracking which indicates that microcracking is not the only process that produces tertiary creep.

Dynamic recrystallisation also contributes to tertiary creep. Recrystallisation induces the development of a preferential c-axis orientation in ice that deforms close to its melting point which results in strain softening and an increase in strain rate. Dynamic recrystallisation occurs as a discontinuous process. At a certain critical strain a wave of recrystallisation will occur and pass through the deforming ice. This is well documented in metals where it occurs at ~20%, whereas within ice it typically occurs at ~1% (Duval et al. 1983).

For a given kind of deformation the ratio of the strain rate for steady-state tertiary creep Tertiary Creep to the minimum strain rate Minimum Strain Rate is found to be a constant independent of both stress and temperature. In uniaxial compression Value 15, and for simple shear the ratio is About 8 (Budd and Jacka 1989). This shows that the flow processes are similar in both secondary and tertiary creep, with the difference between them arising from the more favourable fabric established in the tertiary stage. In the case of shear the preferred fabric has all grains with their c-axes, but in compression the c-axes are distributed over a cone, and this is how shear deformation can give a greater enhancement than compression. If ice deformed into the tertiary stage is subsequently tested in a different orientation it is much more resistant to deformation. Eventually recrystallisation re-orients the fabric to one appropriate to the new stress regime. It is very important to recognize that ice flowing in an ice sheet has highly anisotropic properties that are developed during its recent history.
 
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Created: August 23, 1999
Last modified: March 15, 2004
Authorised by: Head, School of Earth Sciences
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