Discrepancy between results of flow law modelling and microstructural analysis

The results from flow law modelling using the modified grain size sensitive composite flow law from Goldsby and Kohlstedt (2001) predicts that GBS-limited creep is the main strain producing mechanism along almost the entire length of the NEEM ice core (Chapter 4 and 5). Only for the coarsest grained regions in the Eemian-glacial facies it is predicted that dislocation creep and GBS-limited creep have roughly the same strain rate (Figure 5.4).

However, slip system analysis from SGBs (Chapter 2 and 3) suggests that considerable amounts of non-basal slip are activated along the entire length of the NEEM ice core.

Furthermore, dominant GBS-limited creep is not consistent with the microstructures in the Holocene ice (Section 6.5.2.1) and the coarse grained regions in the Eemian-glacial facies (Section 6.5.2.3). It is therefore likely that the modified composite flow law underestimates the rate of dislocation creep, as was also pointed out in Chapter 4. In Chapter 4, the absence

of SIBM during the deformation experiments of Goldsby and Kohlstedt (1997, 2001) was proposed as an explanation for the low strain rates predicted for dislocation creep.

A related explanation for the low strain rate calculated for dislocation creep was provided by Stern et al. (1997) and is shown in Figure 6.7. These authors showed, using constant temperature and constant strain rate deformation tests, that the fine grained ice (grain size 1-3 µm) did not go through a peak stress, while the standard ice (grain size 300

± 50 µm) did go through a peak stress at about one percent of strain. The temperature, stress and grain size conditions in both the fine and coarse grained deformation tests during the experiments of Goldsby and Kohlstedt (1997, 2001) were roughly similar to the temperature, stress and grain size conditions of Stern et al. (1997). Goldsby and Kohlstedt (1997, 2001) took their stress-strain rate data points during secondary creep at a few percent strain. Figure 6.7 shows that the fine grained ice is relatively soft at 1-2% strain, while the standard ice is relatively hard at 1-2% strain. Therefore, the flow law parameters derived from Goldsby and Kohlstedt’s experimental results could describes ice that is relatively soft in the grain size sensitive regime (GBS-limited creep), while the flow law parameters describe ice that is relatively hard in the grain size insensitive regime (dislocation creep).

Dynamic recovery and recrystallization processes that are activated after secondary creep at 1-2% strain (e.g. Jacka, 1984; Montagnat et al., 2009; Schulson and Duval, 2009) results in the enhancement of dislocation creep rates, which is not included in the composite flow law of Goldsby and Kohlstedt (2001). The enhancement factor for higher strain in tertiary creep depends on deformation mode and stress (e.g. Budd and Jacka, 1989; Treverrow et al., 2012) and can have a value of up to 10 for high stress and simple shear deformation experiments (Treverrow et al., 2012).

Figure 6.7: Schematic stress-strain curves of deformation tests at constant temperature and constant strain rate for fine grained ice (1-3 µm) and standard ice (300 ± 50 µm). Standard ice samples go through peak stress at about 1% strain, while fine grained samples are much weaker and do not go through a peak stress at about 1% strain. Figure after Stern et al. (1997).

6.6 Conclusions

On the basis of (polarized) LM techniques, cryo-EBSD, flow law modelling and earlier work on ice microstructure in the NEEM ice core, the following conclusions were made.

The Holocene ice likely deforms by basal slip accommodated by recovery via SIBM and non-basal slip. In the middle and lower part of the Holocene ice, non-basal slip is less often activated compared to the shallow part of the Holocene ice. Here, SIBM controls the amount of non-basal slip that is activated by reducing strain incompatibilities that activate non-basal slip. The dominant recrystallization mechanisms and processes in the Holocene ice are grain dissection, bulging recrystallization, SIBM and normal grain growth which is limited to the upper 250 meters. Rotation recrystallization is expected to be relatively unimportant in the Holocene ice.

In the glacial ice a process resembling microstructural shear was identified in fine grained sub-horizontal bands. This process includes GBS and the formation of SGBs in grains that are blocking sliding along aligned grain boundaries. Microstructures suggest that these SGBs might contribute to sliding when a misorientation angle of 5.0°-6.0° is reached.

Glacial ice shows a strong single maximum CPO. The a-axes in the glacial ice were also aligned. This suggests that GBS and basal slip are operating simultaneously where basal slip is accommodated by GBS. This deformation mechanism does not destroy, but strengthens CPO. The high percentage of SGBs indicative of non-basal slip in the glacial ice shows that GBS is not the only accommodating mechanism for basal slip, but

significant amounts of basal slip are also accommodated by non-basal slip. In the glacial ice rotation recrystallization is more important and SIBM is less important compared to the Holocene ice.

Deformation of ice in the Eemian-glacial facies is expected to be strongly dependent on grain size, grain shape and CPO, all of which vary strongly with depth. The fine grained impurity-rich regions with a strong single maximum CPO likely to deform by simple shear at relatively high strain rates, whereas the coarse grained impurity-poor regions are likely to deform by coaxial deformation at relatively low strain rates. The extensive SIBM, which is likely enhanced by premelting along the grain boundaries, results in a relatively low stored strain energy in the Eemian-glacial facies compared to the other part of the NEEM ice core and in low activity of dislocation glide along the non-basal planes.

The results from flow law modelling and analysis of ice microstructures in the Holocene and the coarse grained layers in the Eemian-glacial facies suggests that the modified composite flow law of Goldsby and Kohlstedt (1997, 2001) underestimates the strain rate produced by dislocation creep. The underestimation of dislocation creep can be explained by dynamic recovery and recrystallization mechanisms not being active during the deformation experiments used to calibrate the composite flow law, while these mechanisms enhance dislocation creep at the high strains that are relevant for polar ice sheets.

References

Alley, R. B. (1992) Flow-law hypotheses for ice-sheet modeling. Journal of Glaciology, 38, 129, 245-256.

Ashby, M. F. (1970) The deformation of plastically non-homogeneous materials. The Philosophical Magazine, 21, 170, 399-424, doi: 10.1080/14786437008238426.

Azuma, N. (1994) A flow law for anisotropic ice and its application to ice sheets. Earth and Planetary Science Letters, 128, 601-614, doi: 10.1016/0012-821X(94)90173-2.

Azuma, N., Higashi, A. (1985) Formation processes of ice fabric pattern in ice sheets.

Annals of Glaciology, 6, 120, 130-134.

Barnes, P., Tabor, D., Walker, J. C. F. (1971) The friction and creep of polycrystalline ice. Proceedings of the Royal Society London A., 324, 1557, 127-155.

Bestmann, M., Prior, D. J. (2003) Intragranular dynamic recrystallization in naturally deformed calcite marble: diffusion accommodated grain boundary sliding as a result of subgrain rotation recrystallization. Journal of Structural Geology, 25, 10, 1597-1613, doi:

10.1016/S0191-8141(03)00006-3.

Binder, T., Weikusat, I., Freitag, J., Garbe, C. S., Wagenbach, D., Kipfstuhl, S. (2013) Microstructure through an ice sheet. Materials Science Forum, 753, 481-484, doi:

10.4028/www.scientific.net/MSF.753.481.

Binder, T. (2014) Measurements of grain boundary networks in deep polar ice cores – A digital image processing approach. PhD dissertation, University of Heidelberg, Germany, 141 pages.

Bons, P. D., Jessell, M. W. (1999) Micro-shear zones in experimentally deformed octachloropropane. Journal of Structural Geology, 21, 3, 323-334, doi: 10.1016/50191-8141(98)90116-X.

Breton, D. J., Baker, I., Cole, D. M. (2016) Microstructural evolution of polycrystalline ice during confined creep testing. Cold Regions Science and Technology, 127, 25-36, doi:

10.1016/j.coldregions.2016.03.009.

Budd, W. F., Jacka, T. H. (1989) A review of ice rheology for ice sheet modelling. Cold Regions Science and Technology, 16, 107-144, doi: 10.1016/0165-232X(89)90014-1.

Chauve, T., Montagnat, M., Barou, F., Hidas, K., Tommasi, A., Mainprice, D. (2017) Investigation of nucleation processes during dynamic recrystallization of ice using cryo-EBSD. Philosophical Transactions of the Royal Society A, 375, 20150345, doi:

10.1098/rsta.2015.0345.

Cuffey, K. M., Thorsteinsson, T., Waddington, E. D. (2000a) A renewed argument for crystal size control of ice sheet strain rates. Journal of Geophysical Research, 105, B12, 27889-27894, doi: 10.1029/1000JB900270.

Cuffey, K. M., Conway, H., Gades, A., Hallet, B., Raymond, C. F., Whitlow, S. (2000b) Deformation properties of subfreezing glacial ice: Role of crystal size, chemical impurities, and rock particles inferred from in situ measurements. Journal of Geophysical Research, 105, B12, 27895-27915, doi: 10.1029/2001JB900014.

Dahl-Jensen, D. Gundestrup, N. S. (1987) Constitutive properties of ice at Dye 3, Greenland. The Physical Basis of Ice Sheet Modelling, 170, 31-43.

Dansgaard, W., Johnson, J. (1969) A flow model and time scale for the ice core from camp century, Greenland. Journal of Glaciology, 8, 53, 215-223.

Dash, J. G., Fu, H., Wettlaufer, J. S. (1995) The premelting of ice and its environmental consequences. Reports on Progress in Physics, 58, 1, 115-167, doi: 10.1088/0034-4885/58/1/003.

De La Chapelle, S., Milsch, H., Castelnau, O., Duval, P. (1999) Compressive creep of ice containing a liquid intergranular phase: rate-controlling processes in the dislocation creep regime. Geophysical Research Letters, 26, 2, 251-254, doi: 10.1029/1998GL900289.

Diprinzio, C. L., Wilen, L. A., Alley, R. B., Fitzpatrick, J. J., Spencer, M. K., Gow, A. J.

(2005) Fabric and texture at Siple Dome, Antarctica. Journal of Glaciology, 51, 173, 281-290, doi: 10.3189/172756505781829359.

Doake, S. S. M., Wolff, E. W. (1985) Flow law for ice in polar ice sheets. Nature, 314, 6008, 255-257.

Drury, M. R., Humphreys, F. J. (1986) The development of microstructure in Al-5% Mg during high temperature deformation. Acta Metallurgica, 34, 11, 2259-2271, doi:

10.1016/0001-6160(86)90171-9.

Drury, M. R., Humphreys, F. J. (1988) Microstructural shear criteria associated with grain-boundary sliding during ductile deformation. Journal of Structural Geology, 10, 1, 83-89, doi: 10.1016/0191-8141(88)90130-7.

Durand, G., Persson, A., Samyn, D., Svensson, A. (2008) Relation between neighbouring grains in the upper part of the NorthGRIP ice core – Implication for rotation

recrystallization. Earth and Planetary Science Letters, 265, 3-4, 666-671, doi:

10.1016/j.epsl.2007.11.002.

Durand, G., Svensson, A., Persson, A., Gagliardini, O., Gillet-Chaulet, F., Sjolte, J., Montagnat, M., Dahl-Jensen, D. (2009) Evolution of the texture along the EPICA Dome C ice core. Low Temperature Science, 68, 91-105.

Durham, W. B., Kirby, S. H., Stern, L. A. (1997) Creep of water ices at planetary conditions: A compilation. Journal of Geophysical Research, 102, E7, 16293-16302, doi:

10.1029/97JE00916.

Durham, W. B., Prieto-Ballesteros, O., Goldsby, D. L., Kargel, J. S. (2010) Rheological and Thermal Properties of Icy Materials. Space Science Reviews, 153, 273-298, doi:10.1007/s111214-009-9619-1.

Duval, P., Ashby, M. F., Anderman, I. (1983) Rate-Controlling Processes in the Creep of Polycrystalline Ice. Journal of Physical Chemistry, 87, C1, 4066-4074, doi:

10.1021/j100244a014.

Duval, P., Arnaud, L., Brissaud, O., Montagnat, M., De La Chapelle, S. (2000) Deformation and recrystallization processes of ice from polar ice sheets. Annals of Glaciology, 30, 83-87, doi: 10.3189/172756400781820688.

Duval, P. Castelnau, O. (1995) Dynamic Recrystallization of Ice in Polar Ice Sheets.

Journal de Physique III, 05, C3-197-C3-205, doi: 10.1051/jp4:1995317.

Duval, P., Montagnat, M. (2002) Comment on “Superplastic deformation of ice:

Experimental observations” by D. L. Goldsby and D. L. Kohlstedt. Journal of Geophysical Research, 107, B4, 1-2, doi: 10.1029/2001JB000946.