Dynamic recrystallization during deformation of polycrystalline ice: insights from numerical simulations

Abstract

The flow of glaciers and polar ice sheets is controlled by the highly anisotropic rheology of ice crystals that have hexagonal symmetry (ice lh). To improve our knowledge of ice sheet dynamics, it is necessary to understand how dynamic recrystallization (DRX) controls ice microstructures and rheology at different boundary conditions that range from pure shear flattening at the top to simple shear near the base of the sheets. We present a series of two-dimensional numerical simulations that couple ice deformation with DRX of various intensities, paying special attention to the effect of boundary conditions. The simulations show how similar orientations of c-axis maxima with respect to the finite deformation direction develop regardless of the amount of DRX and applied boundary conditions. In pure shear this direction is parallel to the maximum compressional stress, while it rotates towards the shear direction in simple shear. This leads to strain hardening and increased activity of non-basal slip systems in pure shear and to strain softening in simple shear. Therefore, it is expected that ice is effectively weaker in the lower parts of the ice sheets than in the upper parts. Strain-rate localization occurs in all simulations, especially in simple shear cases. Recrystallization suppresses localization, which necessitates the activation of hard, non-basal slip systems.This article is part of the themed issue 'Microdynamics of ice'.

Keywords: dynamic recrystallization; ice microstructure; ice rheology; non-basal activity; strain hardening.

Figure 1.

Initial microstructures showing the ELLE data layers and program flow. The initial microstructure in simple shear simulations is a square model defined by a side of one-unit length (L) (a), while in pure shear simulations the initial size of the model is duplicated vertically (2L) (b) to allow better visualization of the deformed microstructure. (d) Detail of boundary nodes (bnodes) defining grains and (e) detail of unodes or Fourier points. (c) The microstructure goes through a loop of processes every time step: deformation by small increments of dextral simple shear or vertical shortening in pure shear simulations, reposition that brings the model back into the unit cell and a subloop of DRX processes (grain boundary migration, recovery and polygonization). (Online version in colour.)

Figure 2.

Example of the polygonization routine. (a) The initial microstructure has grains with homogeneous lattice orientations inside grains (no misorientation). (b) After one step of simple shear deformation LAGB (cyan, magenta and dark grey lines) and new HAGB (black lines) have developed. (c) The polygonization routine identifies the HAGB (more than 15°) and updates the grain boundary network. Red arrows indicate newly nucleated grains. (Online version in colour.)

Figure 3.

Comparison of the grain boundary network and local misorientation field at a natural strain of ε = 1.2 for simulations deformed in simple shear (a–d) and pure shear (e–h), with (a,e) no recrystallization, (b,f) 1 step, (c,g) 10 steps and (d,h) 25 steps of recrystallization per deformation step, respectively, indicated by the N_DRX suffix (or ratio DRX/VPFFT). The initial microstructure is shown in figure 1a,b. In pure shear simulations (e–h), the original image length is double that of the images shown. For better visibility, figures for experiments 0 and 1, both in simple (SSH) and pure shear (PSH), have been enlarged two times, only showing the upper left quarter of each model. (Online version in colour.)

Figure 4.

Lattice orientations relative to the y-direction (inverse poles) and pole figures of lattice orientation at natural strain of ε = 1.2 for simulations of ice deformed in simple shear (a–d) and pure shear (e–h), with (a,e) no recrystallization, (b,f) 1 step, (c,g) 10 steps and (d,h) 25 steps of recrystallization per deformation step, respectively. Initial random distribution of lattice orientations is shown in the upper part of the figure. In pure shear simulations (e–h), the original image length is double that of the images shown. In order to allow visualization of the microstructures, the figures of experiments 0 and 1, in both simple (SSH) and pure shear (PSH), have been enlarged two times, only showing the upper left quarter of each model. Lattice orientation figures include misorientation map and grain network. Pole figures show orientation of unodes. (Online version in colour.)

Figure 5.

Pole figures of c-axes {0001} orientation at natural strains of ε = 0.3, 0.6, 0.9 and the end of the simulations (ε = 1.2) for simulations of ice deformed in simple shear (a–d,i) and pure shear (e–h,j) boundary conditions, with (a,e) no recrystallization, (b,f) 1 step, (c,g) 10 steps and (d,h) 25 steps of recrystallization per deformation step, respectively. The angle α indicates the obliquity of the developed LPO with respect to the y-direction. The colour bar indicates the multiples of a uniform distribution. Pole figures of lattice orientation in high- and low-strain domains of simulations performed with no recrystallization in both pure and simple shear, respectively (i,j). Pole figures show orientation of unodes. (Online version in colour.)

Figure 6.

Evolution of the average relative slip system activity with progressive deformation for the simulations (a) without DRX (N_DRX = 0) and (b) including DRX (N_DRX = 25). (Online version in colour.)

Figure 7.

Maps of slip system activity for the last step of deformation (at ε = 1.2) are shown for (a,b) simple shear and (c,d) pure shear simulations with N_DRX = 0 and N_DRX = 25. In pure shear simulations (c,d) the original image length is double that of the images shown. Two examples of grains with subgrain boundaries developed by the activity of non-basal slip systems are marked in black squares in (b,d).

Figure 8.

(a) Differential stress versus natural strain for all simulations. The ratio between DRX and FFT (N_DRX) is indicated as 1, 10 or 25. A summary of the LPO and SPO developed with respect to the principal stresses is indicated in (b) for simple shear and (c) for pure shear numerical simulations. Differential stresses were normalized using the experimental values of [2]. (Online version in colour.)

Figure 9.

Localization factor (f) evolution (equation (3.1)) during deformation for simulations with N_DRX = 0, 1, 10 and 25 with (a) simple and (b) pure shear boundary conditions.

Figure 10.

Maps of the von Mises strain-rate field normalized to the bulk von Mises strain rate at the final step (natural strain ε = 1.2) are shown for (a,b) simple shear and (c,d) pure shear simulations with N_DRX = 0 and 25. Colour coding is for local strain rate normalized to bulk strain rate. In pure shear simulations (c,d) the original image length is double that of the images shown. (Online version in colour.)

Figure 11.

Lattice orientations relative to the y-direction (inverse poles) and pole figures of lattice orientation comparing the influence of incorporation of the polygonization process (indicated with suffix _N). Simple shear simulations (a–d) reach a final natural strain of ε = 1.2, while pure shear simulations (e,f) reach a final natural strain of ε = 0.75. The final LPO is not noticeably affected by polygonization, regardless of the amount of DRX: 1 (a,b), 10 (c,d) and 20 (e,f). In order to allow visualization of the microstructures, the figures of experiments SSH 1 and SSH 1_N, have been enlarged two times, only showing the upper left quarter of each model. Pole figures show orientation of unodes. (Online version in colour.)

Figure 12.

Comparison of the final grain area distribution normalized to the initial average grain area at the start of the simulation (a) and at the end of the simulations, performed without or with polygonization (indicated with suffix _N), for (b) 1 step or (c) 10 steps of DRX per deformation. Initial distribution in (a).

Figure 13.

Example of subgrain boundary types in EDML ice core. n, Normal to basal plane ‘Nakaya’ type; p, parallel to basal plane type; z, mixed type. Further details see [74,75].