FLOW IN POLYCRYSTALLINE ICE

Part 1 - Examples of microscopic flow

By Chris Wilson and Brett Marmo

1.1 Introduction

Experimental modelling to illustrate the development of microstructures at high metamorphic grade is inherently difficult due to the paucity of information concerning the rheology of polyphase rocks in the Earth's crust. Conversely, the rheology of ice, even close to its melting point, is very well known and provides an excellent material to model a dynamic system.

A proper interpretation of the origins of microstructure and microstructural dynamics is fundamental to our understanding of the flow in rocks and in ice masses such as glaciers. Glacial ice and rock at high metamorphic grade deform according to the same non-linear flow laws. Ice is therefore an ideal analogue for the study of crustal deformation. Folds, faults, boudinage structures and shear zones can be observed in glaciers at both the mesoscale and macroscale. It is also possible to directly measure the strain rate associated with the development of structures in glaciers. The integration of strain rate measurements with constitutive flow laws and an understanding of material parameters allows us to interpret the flow of polycrystalline materials.

• This is a deforming ice mass, that is viewed under a microscope and photographed in plane polarised light using time lapse photography.
• The processes we see occur as solid state transformations and involve submicroscopic interactions between dislocations, and differently oriented grain boundaries in a variety of misoriented grains with respect to the applied stress axis.
• These are referred to as intracrystalline processes and involve the generation of defect structures in the crystal lattice as a result of the deformation.

The flow of rock and on the scale of a crystal is dominated by the anisotropic nature of the crystal structure; in hexagonal minerals such as quartz (Fig. 1.1.1) and ice (Fig. 1.1.2) the most commonly reported slip system is in the basal plane (0001). Basal glide will only occur if the critical resolved shear stress on the potential glide plane is sufficiently low to activate three-dimensional glide. Diffusional flow is another process that operates at high temperatures.

• It should be noted that not all slip systems will be activated as the critical resolved shear stress of many of these systems will be too high to prevent activation of the system.
• As the critical resolved shear-stress is very low on (0001) then deformation is dominated by slip on the basal plane.
• Additional independent glide can occur on non-basal systems and include various combinations parallel to an a-axis, c-axis or one of the vector sums c+a and these are particularly important in the higher temperature deformation of minerals such as quartz (Fig. 1.1.1).

Because of their low crystallographic symmetry and their limited glide systems it is possible to make comparisons between the microstructural behaviour of quartz (Fig. 1.1.1) and ice (Fig. 1.1.2) when undergoing plastic deformation. For instance if a single crystal is flattened it will shear by intracrystalline glide on its basal plane; this produces a shape transformation and a rotation of its c- axis (Fig. 1.1.3). A crystal can be considered as a matrix of elastic-plastic glide planes belonging to the one slip system, which will follow elastic-plastic behaviour and will only be activated if it reaches a critical value of resolved shear-stress.

1.2 Polycrystalline aggregates deformed in pure-shear

The simplest deformation that we can consider is a pure shear (Fig. 1.2.1) where there is no rotation of the principal strain axes.

• Rocks are composed of densely packed collections of single crystals that comprises a polycrystalline grain aggregate. Each crystal grain contains an infinite number of glide planes which will be activated for slip when the resolved shear stress on the glide plane is equal to the critical resolved shear stress.

To ensure homogeneous deformation of a polycrystalline material, in three-dimensions, 5 independent slip systems are necessary as specified by the Taylor-von Mises criteria (see Taylor, 1938). In ice the basal plane provides only 2 slip systems while the non-basal systems are at least 2-3 orders of magnitude harder to activate. Consequently, the stresses and strain rates for glide on basal systems are different in each grain. The deviation of local behaviour with respect to macroscopic behaviour depends on the directional viscoplastic properties of the grains and the whole polycrystal.

The glide planes that will be first activated upon deformation will occupy orientations that have high critical resolved shear-stresses on the basal planes (Fig. 1.2.2, grains B and C), these are the easy-glide planes, and have orientations at approximately 45° to the bulk compression axis.

Grains in easy-glide orientations (Fig. 1.2.3, grains B and C) will be activated first and then produce bending of the (0001) as they try to accommodate for the strain in their neighbouring grains. Grain A is in hard-glide orientation and would undergo flattening and extension. Whereas Grain D undergoes only limited glide, but as it lies parallel to the bulk compression direction it will kink.

• Grains in hard-glide orientations in combination with nearest neighbour interactions produces a local rotation of the crystal lattice to form kink bands.

• Slip-planes are activated and differently oriented in adjacent grains. As deformation proceeds the slip-planes are bent and this produces undulose extinction and differences in the birefringence colours.
• Intragranular microstructures are well developed, they include undulatory extinction (smooth slip-plane bending), subgrains, kink structures, elongate older grains and the nucleation of recrystallised grains.
• These processes are occurring under dynamic conditions to produce syn-tectonic (or dynamic) recrystallisation. New grain nucleation and grain growth occurs adjacent to and on the boundaries between neighbouring grains. As a result the original grains are reduced in size and preserved as relics between the unstrained new grains.

Upon deformation, intragranular slip accommodates most of the deformation and the initial equi-axed grain geometry has been deformed into non-equi-axed shapes. The grains showing high strain are mostly those with deformation-favourable easy-glide orientations. Such deformation can also be represented on deformation maps.

• In the pure shear deformation that is seen in movie 4, the sample is shortened 30%.
• Adjacent grains in the initial aggregate have a random distribution of their c-axes, when plotted on the lower hemisphere of a stereographic net.
• Slip-lines are developed at different times in adjacent grains.
• As deformation proceeds the slip lines and hence the crystal structure is bent and this produces undulose extinction, as seen in the change in the birefringence colour.
• Grains in a hard glide orientation also develop distinct kink bands.

1.3 Dynamic recrystallisation

• With the movement of dislocations on glide planes and the development of the kink bands there is also dynamic recrystallisation.
• Recrystallisation involves new grain nucleation and grain growth.
• Recrystallisation can also reduce the original average grain size leaving behind a few relict deformed old grains (Grain size reduction).

• New recrystallised grains are nucleated as small equiaxed grains and grain boundaries then begin to bulge and migrate as they undergo grain growth.
• These new grains are themselves deformed with the continuing deformation.

1.4 Grain shape and preferred orientation change

• The pure shear deformation seen in the movies produces a sub-horizontal foliation defined by an alignment of grain shapes.
• Many of the original grains, both in the movies and in the FLAC model below that displayed higher order birefringence colours have disappeared. This reflects the development of a more permissive preferred-orientation within the sample and the evolution of a new fabric.

• A two-dimensional view of Undeformed grains in a polycrystalline aggregate and slip-plane traces and initial random orientation of slip-plane normal (c-axes).
• Deformed aggregate shows grain-shape alignment parallel to the extension direction and the c-axes are concentrated in a bi-symmetrical pattern about the shortening axis.

• Three-dimensional change from randomly oriented c-axes in undeformed aggregate (Fig. 1.4.2) to a distribution containing two concentrations of c-axes symmetrically distributed about the foliation plane.
• These concentrations are symmetrically related to the shortening axis and the plane of flattening defined by the grain-shape distribution.
• In this pure-shear environment we have the situation where the principal axes of the strain ellipsoid do not rotate.
• The plane of flattening in the corresponding strain ellipsoid will coincide with the alignment of grain-shapes.
• The c-axis fabric development is symmetrically related to the shortening direction.

1.5 Fabric

When a stress is applied to a polycrystalline aggregate of ice with a random distribution of c-axes, greater than 90% of the deformation is accommodated by glide on basal planes (Castelnau et al. 1996). The deformation of any individual grains is restricted by the glide in neighbouring grains (Fig. 1.2.4). Grains rotate relative to each other and the applied stress so that deformation can proceed. The rotation may be accommodated by grain boundary sliding (Goldsby & Kohlstedt 1997) at the same time as internal glide proceeds. Grains tend to rotate such that their c-axes move towards a compressive stress and away from a tensile stress. Thus, ice which has undergone prolonged compression will have c-axes oriented in a solid cone about the compression direction (Fig. 1.4.2), while ice that has experienced prolonged tension will have c-axes oriented in a girdle orthogonal to the tensile direction. The rotation of grains relative to an applied stress, combined with elongation of grains parallel to their basal planes, produces a mechanical anisotropy and in simple shear this is a strong concentration symmetrically related to the new grain shape fabric (Fig. 1.4.3).

Recrystallisation also contributes to fabric development. If strain is sufficiently high then recrystallisation tends to replace grains at 45° to the compressive direction. Wilson & Russell-Head (1982) and Castelnau et al. (1996) suggest that recrystallisation begins with less than 1% shortening. Once new grains are formed their c-axes continuously rotate towards the compression direction leading to a smaller diameter girdle around the compressive axis. If recrystallisation occurs at lower strain then the girdle is thinner and the diameter larger (Van der Veen & Whillans 1994).

• Ice deforming at -10°C. This is at a lower temperature than the preceding movies where deformation occurred at -1°C.
• It can be seen that the older grains are progressively flattened and rotated during deformation and are part of a foliation forming element.
• Recrystallisation and nucleation during the deformation produces strain-free grains which are not foliation-forming elements until they are deformed.

• The new grain nucleation has the function of destroying, in part, any grain alignment produced during the rotation of the earlier grain population.
• The grain shape is controlled by the rate of boundary migration in a specific direction, that is before grain growth is arrested by interaction with neighbouring grains with stable crystallographic preferred orientations.

Temperature variation in an ice mass has direct ramifications on strain rate as diffusion flow, basal glide controlled creep and the importance of grain boundary melting and grain growth are temperature dependent. Similarly deformation can be partitioned into two competing regions: (1) those where strain softening processes occur by dynamic recrystallisation and (2) hard spots or older grains that are undergoing little deformation. Hence as the stress regime and magnitude varies in a glacier, the relative pervasiveness and style of fabrics also varies spatially and temporally. The development of fabric controls strain rate, producing a feed-back loop which further complicates ice flow models and our understanding of plastic deformation.

1.6 Evolution of glacial ice during deformation

Numerical stress maps derived from deformation experiments (Fig. 1.2.4), and the use of such relations to plot deformation mechanism maps, assume that ice is homogeneous and mechanically isotropic. However, an initially isotropic polycrystalline aggregate will develop a fabric after prolonged deformations. In addition to basal glide, deformation is generally accompanied by grain boundary migration, recrystallisation and rotation of crystals (Fig. 1.1.3). All these contribute to a dynamic recrystallisation processes where there is a change in the mechanical properties of a deforming polycrystalline aggregate with time. These processes produce strong mechanical anisotropies in polycrystalline ice and result in the foliation we see in glaciers.

In an ice sheet gravity forces induce internal stresses which drive deformation and glacial flow. Nye (1952) demonstrated that flow is driven by a shear stress acting down the glacier and is related primarily to the surface slope at any point on the sheet and the depth of a column of ice directly below that point according to:

----------------------------------------equation (10)

where is the surface slope measured from the horizontal, g is acceleration due to gravity, h is the depth and is the density of ice. At the base of the glacier the shear stress is assumed to be balanced by friction acting in the opposite direction such that there is no basal sliding. This assumption is true for much of the east Antarctic ice sheet where the ice is generally frozen to its base. Nye (1952) also showed that the shear stress at the base was independent of the slope of the base, so long as the difference in slope between the base and the surface was not large.

Within real ice sheets, the shear stress produced by surface slope is not the only differential stress acting on the ice mass. Changes is surface slope, rapid changes in the bed-rock topography and variations in the accumulation and ablation rates, all produce longitudinal and transverse differential stresses. However, equation 10 can be used to derive a first order estimate of stress conditions in an ice body. For example the surface slope of the section of outlet glacier in the Framnes Mountains, east Antartica investigated by Marmo & Wilson (1998) is ~0.02 Rad and depth of over 800m (Fig. 1.6.1). If equation 10 is applied to this generalised column of ice within this outlet glacier, then the shear stress increases linearly with depth from zero at the surface to 0.17 MPa at a depth of 800m (Fig. 1.6.2).

Figure 1.6.1: Flow lines in an outlet glacier in the Framnes Mountains, Antarctica (Marmo & Wilson 1998).

Figure 1.6.2: Longitudinal section parallel to the flow lines in the Framnes Mountains glaciers. The flow lines transect strain grids at Rumdoodle and Fern Hill area where the maximum velocity and bed-rock topography data have been collected.

In a glacier, the orientation and tightness of c-axis maxima become dependent on the flow regime (Azuma 1994). In general, the upper part of ice sheets experiences pure shear due to vertical compression and longitudinal extension. If the region is in a parallel flow regime, or a divergent flow regime, the ice experiences progressive uniaxial compression or pure shearing and the c-axes rotate to form a broad maximum around the vertical (Fig. 1.6.3). The maximum increases with depth and cumulative strain. If the region is in a convergent flow regime, then longitudinal stresses become important producing progressive uniaxial tension or pure shearing in tension, and a girdle distribution of c-axes orthogonal to the flow direction. The basal ice, and ice close to the margins on the stream, have a strong single maximum due to simple shearing. In outlet glaciers the strain rate is sufficiently high that recovery via dynamic recrystallisation becomes an important process. Recrystallisation tends preferentially to produce new grains at 45° to the compression direction. With continued deformation the c-axes of ice crystals rotate towards the compression direction to form a tight girdle in ice at depth. The strong girdle fabric in outlet glaciers tends to produce deformation closer to steady state flow than is observed in other parts of large ice sheets. The flow parameter n=3 (see equation 1) is consistent for most outlet glaciers, except for the uppermost parts where grain growth may still occur reducing n to between 1 and 3 (Alley 1992).

Figure 1.6.3 Divergent, parallel and convergent flow regimes and observed c-axes fabric associated with each. (After Azuma, 1994)

The development of fabrics can reduce the resistance of the polycrystals to creep for a given applied stress promoting an increase in strain rate. This presents a feedback loop as a strain-rate increase leads to polycrystalline aggregates accumulating more strain, leading to stronger fabrics. It is possible that this process results in bifurcation, as strain is localised into thin layers that are less resistant to glide. Hudleston (1980) noted the development of thin shear zones in the margins of glaciers. The shear zones initially developed as lenses tens of millimeters thick and attained shear strains greater than . Higher strains were accommodated by the growth and coalescence of these thin shear zones to distribute strain more uniformly through the ice. The continuous development of fabrics and strain localisation adds further complexity to the deformation processes occuring in glaciers and many natural bodies of rock.

Click here for 1.7 REFERENCES

Click here for 1.8 ACKNOWLEDGMENTS

Further information can be obtained from:

C.J.L. Wilson

School of Earth Sciences

The University of Melbourne

Victoria 3010, Australia

Phone: (61) 3 8344 6538

Fax: (61) 3 8344 7761

Email: c.wilson@earthsci.unimelb.edu.au