FLOW IN POLYCRYSTALLINE ICE

Part 2 - Background information

By Chris Wilson and Brett Marmo

2.15 Secondary Creep

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 (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.

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).

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)

where A is a constant and 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 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.

For the creep curves in Fig. 2.15.1 all the minima occur at the same strain (equivalent to 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 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.

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).