Description: Results of numerical simulations of co-axial deformation of pure ice up to high-strain, combining full-field modelling with recrystallisation are presented. Grain size and lattice preferred orientation analysis and comparisons between simulations at different strain-rates show how recrystallisation has a major effect on the microstructure, developing larger and equi-dimensional grains, but a relatively minor effect on the development of a preferred orientation of c-axes. Although c-axis distributions do not vary much, recrystallisation appears to have a distinct effect on the relative activities of slip systems, activating the pyramidal slip system and affecting the distribution of a-axes. The simulations reveal that the survival probability of individual grains is strongly related to the initial grain size, but only weakly dependent on hard or soft orientations with respect to the flow field. Dynamic recrystallisation reduces initial hardening, which is followed by a steady state characteristic of pure-shear deformation.

Description: We performed numerical simulations on the micro-dynamics of ice with air inclusions as a second phase. This provides first results of a numerical approach to model dynamic recrystallisation in polyphase crystalline aggregates. Our aim was to investigate the rheological effects of air inclusions and explain the onset of dynamic recrystallisation in the permeable firn. The simulations employ a full field theory crystal plasticity code coupled to codes simulating dynamic recrystallisation processes and predict time-resolved microstructure evolution in terms of lattice orientations, strain distribution, grain sizes and grain boundary network. Results show heterogeneous deformation throughout the simulations and indicate the importance of strain localisation controlled by air inclusions. This strain localisation gives rise to locally increased energies that drive dynamic recrystallisation and induce heterogeneous microstructures that are coherent with natural firn microstructures from EPICA Dronning Maud Land ice coring site in Antarctica. We conclude that although overall strains and stresses in firn are low, strain localisation associated with locally increased strain energies can explain the occurrence of dynamic recrystallisation.

Description: We performed numerical simulations on the microdynamics of ice with air inclusions as a second phase. Our aim was to investigate the rheological effects of air inclusions and explain the onset of dynamic recrystallization in the permeable firn. The simulations employ a full-field theory crystal plasticity code coupled to codes simulating dynamic recrystallization processes and predict time-resolved microstructure evolution in terms of lattice orientations, strain distribution, grain sizes and grain-boundary network. Results show heterogeneous deformation throughout the simulations and indicate the importance of strain localization controlled by air inclusions. This strain localization gives rise to locally increased energies that drive dynamic recrystallization and induce heterogeneous microstructures that are coherent with natural firn microstructures from EPICA Dronning Maud Land ice coring site in Antarctica. We conclude that although overall strains and stresses in firn are low, strain localization associated with locally increased strain energies can explain the occurrence of dynamic recrystallization.

Description: 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 {\textquoteleft}Microdynamics of ice{\textquoteright}.

Description: The Antarctic and Greenland ice sheets store a significant amount of air within their upper, approximately thousand meters. Research shows how the presence of air inclusions can influence the microdynamical processes that affect the flow of ice (Azuma et al., 2012, Roessiger et al., 2014). The microdynamics of pure ice were successfully modelled by e.g. Montagnat et al. (2014) or Llorens et al. (2015), but studies taking into account second phases are scarce. Therefore, polyphase modelling was performed to focus on the implications of bubbles on recrystallisation and deformation. The full-field theory crystal plasticity code (FFT) of Lebensohn (2001), was coupled to the 2D multi-process modelling platform Elle (Bons et al., 2008), following the approach by Griera et al. (2013). FFT calculates the viscoplastic response of polycrystalline materials deforming by dislocation glide, taking into account mechanical anisotropy. Our models further incorporate surface- and strain-energy driven grain boundary migration and intracrystalline recovery. Sequential operation of each process for small time steps enables multi-process modelling of deformation and concurrent recrystallisation. Results show that air inclusions lead to increased strain localization and hence locally enhanced dynamic recrystallisation. This is in accordance with Faria et al. (2014), who theoretically predicted such localization, based on firn data from the EPICA Dronning Maud Land (EDML) deep ice core. Our results confirm that strain-induced grain boundary migration already occurs in the uppermost levels of ice sheets, as observed by Kipfstuhl et al. (2009) and Weikusat et al. (2009) in the EDML core. References Azuma, N., et al. (2012) Journal of Structural Geology, 42, 184-193 Bons, P.D., et al. (2008) Lecture Notes in Earth Sciences, 106 Faria, S.H., et al. (2014) Journal of Structural Geology, 61, 21-49 Griera, A., et al. (2013) Tectonophysics, 587, 4-29 Kipfstuhl, S., et al. (2009) Journal of Geophysical Research, 114, B05204 Lebensohn, R.A. (2001) Acta Materialia, 49, 2723-2737 Llorens, M.G., et al. (2015) submitted to Journal of Glaciology Montagnat, M., et al. (2014) Journal of Structural Geology, 61, 78-108 Roessiger, J., et al. (2014) Journal of Structural Geology, 61, 123-132 Weikusat, I., et al. (2009) Journal of Glaciology, 55, 461-472

Description: Static (or ‘normal’) grain growth, i.e. grain boundary migration driven solely by grain boundary energy, is considered to be an important process in polar ice. Many ice-core studies report a continual increase in average grain size with depth in the upper hundreds of metres of ice sheets, while at deeper levels grain size appears to reach a steady state as a consequence of a balance between grain growth and grain-size reduction by dynamic recrystallization. The growth factor k in the normal grain growth law is important for any process where grain growth plays a role, and it is normally assumed to be a temperature-dependent material property. Here we show, using numerical simulations with the program Elle, that the factor k also incorporates the effect of the microstructure on grain growth. For example, a change in grain-size distribution from normal to log-normal in a thin section is found to correspond to an increase in k by a factor of 3.5.

Description: Results of numerical simulations of co-axial deformation of pure ice up to high-strain, combining full-field modelling with recrystallisation are presented. Grain size and lattice preferred orientation analysis and comparisons between simulations at different strain-rates show how recrystallisation has a major effect on the microstructure, developing larger and equi-dimensional grains, but a relatively minor effect on the development of a preferred orientation of c-axes. Although c-axis distributions do not vary much, recrystallisation appears to have a distinct effect on the relative activities of slip systems, activating the pyramidal slip system and affecting the distribution of a-axes. The simulations reveal that the survival probability of individual grains is strongly related to the initial grain size, but only weakly dependent on hard or soft orientations with respect to the flow field. Dynamic recrystallisation reduces initial hardening, which is followed by a steady state characteristic of pure-shear deformation.

Description: Within their upper approximately thousand meters, ice sheets on Earth contain a significant amount of air and air hydrates below. In the permeable firn, this air is still exchanging with the atmosphere and is under atmospheric pressure, whereas the air bubbles are entrapped at the firn-ice transition 60 – 120 m depth. As recent research showed, the presence of air bubbles can significantly influence microdynamical processes such as grain growth and grain boundary migration (Azuma et al., 2012, Roessiger et al., 2014). Understanding the dominant deformation mechanisms has essential implications on paleo-atmosphere research and allows more realistic modelling of ice sheet dynamics. Therefore, numerical models were set up and performed focussing on the implications of the presence of bubbles on recrystallisation and the mechanical properties of ice with air inclusions. The 2D numerical microstructural modelling platform Elle was coupled to the full-field crystal plasticity code of Lebensohn (2001), which is using a Fast Fourier Transform (FFT) following the approach by Griera et al. (2013). Taking into account the mechanical anisotropy of ice, FFT calculates the viscoplastic response of polycrystalline and polyphase materials that deform by dislocation glide, predicts lattice re-orientation and using the local gradient of the strain-rate field, dislocation densities are calculated. FFT was used for the simulation of dynamic recrystallization of pure ice by Montagnat et al. (2013). Polyphase grain boundary migration driven by surface energy and internal strain energy reduction was incorporated in the code and now also enables us to model deformation of ice with air bubbles. The approach is based on the methodology of Becker et al. (2008) and Roessiger et al. (2014). During Deformation, spherical to elliptical bubble shapes are only maintained, when surface energy based recrystallisation is activated, whereas they quickly collapse at low strains in the absence of recrystallisation. The presence of bubbles leads to increased localization of stress, strain and dislocation densities, a reduction of the bulk strength of the bubbly ice is observed. Furthermore, strain-induced grain boundary migration already occuring in the uppermost levels of ice sheets (Kipfstuhl et al. 2009, Weikusat et al. 2009) is confirmed by our modelling. References Azuma, N., Miyakoshi, T., Yokoyama, S., Takata, M., 2012. Journal of Structural Geology 42, 184- 193. Becker, J.K., Bons, P.D., Jessell, M.W., 2008. Computers & Geosciences 34, 201-212. Bons, P.D., Koehn, D., Jessell, M.W. (Eds.), 2008. Microdynamic Simulation. Springer, Berlin. Kipfstuhl, S., Faria, S.H., Azuma, N., Freitag, J., Hamann, I., Kaufmann, P., Miller, H., Weiler, K., Wilhelms, F., 2009. Journal of Geophysical Research 114, B05204. Lebensohn, R.A., 2001. Acta Mater 49 (14), 2723e2737. Montagnat, M., Castelnau, O., Bons, P.D., Faria, S.H., Gagliardini, O., Gillet-Chaulet, F., Grennerat, F., Griera, A., Lebensohn, R.A., Moulinec, H., Roessiger, J., Suquet, P., 2014. Journal of Structural Geology 61, 78-108 Rößiger, J., Bons, P.D., Faria, S.H., 2014. Journal of Structural Geology 61, 123-132 Weikusat, I., Kipfstuhl, S., Faria, S.H., Azuma, N., Miyamoto, A., 2009. Journal of Glaciology 55, 461-472.

Description: Research on ice flow is a key to understand how climate changes affect polar ice. Numerical modelling provides a better insight into the mechanics of ice from the microstructure to the ice sheet scale. The mechanics of polar ice are very sensitive to temperature changes mainly due to active recrystallization processes, as the material is very close to its melting point. We present numerical simulations that predict the microstructural evolution of ice polycrystals during deformation and dynamic recrystallization at large strain, using a full-field approach. The crystal plasticity code (Lebensohn, 2001) is used to calculate the response of a polycrystalline aggregate that deforms by dislocation glide, applying a Fast Fourier Transform (FFT). The coupling between FFT and the ELLE microstructural evolution platform allows us to include recrystallization in the aggregate, which is simulated by means of two main processes: (1) recovery and subgrain rotation, which locally reduces the crystal misorientation, and (2) grain boundary migration, which is driven by grain boundary curvature and intra-grain strain energies. This contribution presents a comparison of numerical simulations under pure and simple shear conditions up to high strain at different strain rates. The results show a strong effect of the recrystallization on the final microstructure. Dynamic recrystallization masks the strain rate and finite strain heterogeneity resulting from the strong slip anisotropy of ice. However, this strong effect does not significantly modify the single-maximum pattern of c-axes that are distributed at a low angle to the shortening direction in both pure and simple shear. In both cases, recrystallization produces larger and more equidimensional grains, with smooth boundaries. References: R. A. Lebensohn. N-site modelling of a 3D viscoplastic polycrystal using Fast Fourier Transform. 2001. Acta Materialia 49, pp 2723-2737.