Introduction Polycrystalline aggregates in pure shear dynamic recrystallisation Grain shape and preferred orientation changes Grain shape and preferred orientation changes Fabric Evolution of glacial ice during deformation Movies References List of figures Acknowledgements Home
Polycrystalline Aggregates Deformation in Pure Shear
The simplest deformation that we can consider is a pure shear (see fig. 1.2.1) where there is no rotation of the principal strain axes.
Figure 1. 2. 1
Figure 1.2.1. A Pure shear deformation
Figure 1. 2. 2
Figure 1.2.2. Two dimensional representation of four undeformed polygonal grains (A, B, C and D) with basal planes (0001) indicated by broken lines being deformed in a pure shear regime. These basal planes are oriented at high-angle to the viewing plane.
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 (see 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.

 
Movie 2 Image
Movie 2 - Pure shear deformation over About 6 days. Click on the image to see the movie. It may take a few minutes to download. So please be patient.
 
Figure 1. 2. 3
Figure 1.2.3. A pure-shear deformation with 20% bulk shortening
and showing the relationship to the finite strain ellipse.
Grains in easy-glide orientations (see 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.
 
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.
Movie 3 Image
Movie 3 - A pure shear deformation of four ice grains over About 2.5 days. Click on the image to see the movie. It takes a few minutes to download. So please be patient.

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 occuring 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.
Grains in hard-glide orientations in combination with nearest neighbour interactions produces a local rotation of the crystal lattice to form kink bands.
 
Figure 1. 2. 4
Figure 1.2.4. Numerically generated principal-stress distribution in sample shown in
Fig. 1.2.2 and shortened 20% in Fig. 1.2.3 (after Wilson & Zhang 1994).
 

The Numerical specimen generated in Figure 1.2.4 is from a FLAC (Fast Lagrangian Analysis of Continua) model described by Wilson & Zhang (1994, 1996) and reproduces portion of the coarser-grained ice sample shown in Movie 2. Grains with easy-glide lattice orientations or with lattice orientations favourable for kinking usually show large strains and small stresses (see fig. 1.2.4). Furthermore, grain boundaries, in particular triple junctions, are generally the places where strain and stress are locally strengthened or sharply changed. This is because these areas involve the strongest grain interaction arising from the need to achieve strain compatibility and are the regions where new grain nucleation occurs.

Polycrystalline materials tend to develop a bulk crystallographic preferred orientation in response to its stress, strain rate and temperature history. In the movie below we consider a two-dimensional hexagonal-grain model with grains with variable slip-plane traces that is subjected to axial shortening.

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.
 
Movie 4 Image
Movie 4 - Polycrystalline ice aggregate deformed in pure shear over About 5 days. Click on the image to see the movie. It takes a few minutes to download. So please be patient.

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.
 
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Created: August 23, 1999
Last modified: March 15, 2004
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