ALBERT

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 increasing catalogue of high-quality ice-penetrating radar data provides a unique insight in the internal layering architecture of the Greenland ice sheet. The stratigraphy, an indicator of past deformation, highlights irregularities in ice flow and reveals large perturbations without obvious links to bedrock shape. In this work, to establish a new conceptual model for the formation process, we analysed the radar data at the onset of the Petermann Glacier, North Greenland, and created a three-dimensional model of several distinct stratigraphic layers. We demonstrate that the dominant structures are cylindrical folds sub-parallel to the ice flow. By numerical modelling, we show that these folds can be formed by lateral compression of mechanically anisotropic ice, while a general viscosity contrast between layers would not lead to folding for the same boundary conditions. We conclude that the folds primarily form by converging flow as the mechanically anisotropic ice is channelled towards the glacier.

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: The flow of ice depends on the properties of the aggregate of individual ice crystals, such as grain size or lattice orientation distributions. Therefore, an understanding of the processes controlling ice micro-dynamics is needed to ultimately develop a physically based macroscopic ice flow law. We investigated the relevance of the process of grain dissection as a grain-size-modifying process in natural ice. For that purpose, we performed numerical multi-process microstructure modelling and analysed microstructure and crystallographic orientation maps from natural deep ice-core samples from the North Greenland Eemian Ice Drilling (NEEM) project. Full crystallographic orientations measured by electron backscatter diffraction (EBSD) have been used together with c-axis orientations using an optical technique (Fabric Analyser). Grain dissection is a feature of strain-induced grain boundary migration. During grain dissection, grain boundaries bulge into a neighbouring grain in an area of high dislocation energy and merge with the opposite grain boundary. This splits the high dislocation-energy grain into two parts, effectively decreasing the local grain size. Currently, grain size reduction in ice is thought to be achieved by either the progressive transformation from dislocation walls into new high-angle grain boundaries, called subgrain rotation or polygonisation, or bulging nucleation that is assisted by subgrain rotation. Both our time-resolved numerical modelling and NEEM ice core samples show that grain dissection is a common mechanism during ice deformation and can provide an efficient process to reduce grain sizes and counter-act dynamic grain-growth in addition to polygonisation or bulging nucleation. Thus, our results show that solely strain-induced boundary migration, in absence of subgrain rotation, can reduce grain sizes in polar ice, in particular if strain energy gradients are high. We describe the microstructural characteristics that can be used to identify grain dissection in natural microstructures.

Description: Although ice sheets are valuable paleo-climate archives, they can loose their integrity by ice flow (Faria et al. 2010). Consequently, understanding the dynamic processes that control the flow of ice is essential when investigating the past and future climate. While recent research successfully modelled the microdynamics of pure ice (e.g. Montagnat et al., 2014; Llorens et al., 2015), work taking into account second phases is scarce. Only a few studies also show the microstructural influence of air inclusions (Azuma et al., 2012, Roessiger et al., 2014). Therefore, modelling was performed focussing on the implications of the presence of bubbles on the microdynamical mechanisms and microstructure evolution. 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. The models further incorporate surface- and stored strain energy driven grain boundary migration (GBM) and intracrystalline recovery simulating annihilation and rearrangement of dislocations by reduction of internal misorientations. GBM was refined for polyphase materials following Becker et al. (2008) and Roessiger et al. (2014). Additionally, the formation of new high angle grain boundaries by nucleation and polygonisation based on critical internal misorientations has been implemented. Successively running the codes for different processes in very short numerical timesteps effectively enables multi-process modelling of deformation and concurrent recrystallisation. Results show how air inclusions control and increase strain localisation, leading to locally enhanced dynamic recrystallisation. This is in compliance with Faria et al. (2014), who theoretically predicted these localizations based on firn data from EPICA Dronning Maud Land (EDML) ice core. We propose that strain localisation has a strong control on the dominating recrystallisation mechanisms and can account for microstructural observations from alpine and polar ice cores. Our results confirm dynamic recrystallisation occurring in the uppermost levels of ice sheets as observed by Kipfstuhl et al. (2009) and Weikusat et al. (2009) in EDML core. Azuma, N., et al. (2012) Journal of Structural Geology, 42, 184-193 Becker, J.K., et al. (2008) Computers & Geosciences, 34, 201-212 Bons, P.D., et al. (2008) Lecture Notes in Earth Sciences, 106 Faria, S.H., et al. (2010) Quaternary Science Reviews, 29, 338-351 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) Journal of Glaciology, in press, doi:10.1017/jog.2016.28 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: Disturbances on the centimetre scale in the stratigraphy of the North Greenland Eemian Ice Drilling (NEEM) ice core (North Greenland) can be mapped by an optical line scanner as long as the ice has visual layering, such as, for example, cloudy bands. Different focal depths allow, to a certain extent, a three-dimensional view of the structures. In this study we present a detailed analysis of the visible folds, discuss their characteristics and frequency, and present examples of typical fold structures. We also analyse the structures with regard to the deformation boundary conditions under which they formed. The structures evolve from gentle waves at about 1500 m to overturned z folds with increasing depth. Occasionally, the folding causes significant thickening of layers. Their similar fold shape indicates that they are passive features and are probably not initiated by rheology differences between alternating layers. Layering is heavily disturbed and tracing of single layers is no longer possible below a depth of 2160 m. C axes orientation distributions for the corresponding core sections were analysed, where available, in addition to visual stratigraphy. The data show axial-plane parallel strings of grains with c axis orientations that deviate from that of the matrix, which shows a single maximum fabric at the depth where the folding occurs. Numerical modelling of crystal viscoplastic deformation and dynamic recrystallisation was used to improve the understanding of the formation of the observed structures during deformation. The modelling reproduces the development of bands of grains with a tilted-lattice orientation relative to the single maximum fabric of the matrix, and also the associated local deformation. We conclude from these results that the observed folding can be explained by formation of these tilted-lattice bands.

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: Disturbances on the centimeter scale in the layering of the NEEM ice core (North Greenland) can be mapped by means of visual stratigraphy as long as the ice does have a visual layering, such as, for example, cloudy bands. Different focal depths of the visual stratigraphy method allow, to a certain extent, a three dimensional view of the structures. In this study we present a structural analysis of the visible folds, discuss characteristics and frequency and present examples of typical fold structures. With this study we aim to quantify the potential impact of small scale folding on the integrity of climate proxy data. We also analyze the structures with regard to the stress environment under which they formed. The structures evolve from gentle waves at about 1700 m to overturned z-folds with increasing depth. Occasionally, the folding causes significant thickening of layers. Their shape indicates that they are passive features and are probably not initiated by rheology differences between layers. Layering is heavily disturbed and tracing of single layers is no longer possible below a depth of 2160 m. Lattice orientation distributions for the corresponding core sections were analyzed where available in addition to visual stratigraphy. The data show axial-plane parallel strings of grains with c.axis orientations that deviate from that of the matrix, which has more or less a single-maximum fabric at the depth where the folding occurs. We conclude from these data that folding is a consequence of deformation along localized shear planes and kink bands. The findings are compared with results from other deep ice cores. The observations presented are supplemented by micro-structural modeling using a crystal plasticity code that reproduces deformation, applying a Fast Fourier Transform (FFT), coupled with ELLE to include dynamic recrystallization processes. The model results reproduce the development of bands of grains with a tilted orientation relative to the single maximum fabric of the matrix and also the associated local deformation.

Description: The present study is based on a series of two-dimensional simple shear numerical simulations of two-phase non-linear viscous materials used to investigate the mechanical behaviour of two-phase aggregates representing partially molten rocks. These simulations couple viscoplastic deformation with dynamic recrystallisation (DRX). The aim of these simulations is to investigate the competition between deformation and recrystallisation, and how they affect the mechanical behaviour and resulting microstructures of the deforming material. We systematically vary the melt to solid rock ratio, the dihedral angle of melt and the ratio of DRX vs. deformation. The results show that the amount of DRX and the dihedral angle have a first-order impact on the bulk rheology and the melt distribution in the aggregate. The numerical results allow defining two regimes, depending on the relative contribution of deformation and DRX: (1) a deformation-dominated regime at high strain rates (i.e., with a low ratio of recrystallisation vs. viscoplastic deformation) and (2) a recrystallisation-dominated regime at low strain rates (i.e., with a high ratio of recrystallisation vs. viscoplastic deformation). The first case results in systems bearing large connected melt pockets whose viscous flow controls the deformation of the aggregate, while disconnected smaller melt pockets develop in models where dynamic recrystallisation dominates. The results of this study allow us to better understand the development of connected melt pockets, which may focus melt flow. The distribution of the melt phase plays a key role in the formation of larger-scale melt-enriched shear bands, which in turn has a direct influence on large-scale convective mantle flow.

Description: Ice sheets and glaciers flow under their own weight and their flow of ice is a major contributor to both global sea-level and climate changes. The macroscopic flow of ice is affected by the properties of the microstructure, which is formed by a small aggregate of individual ice crystals. The deformation of ice is accompanied by recrystallisation, a term which describes mechanisms causing re-orientations of the crystalline lattice, the formation of new crystals or the migration of their boundaries. The ice crystal is marked by a significant viscoplastic anisotropy, which causes a distinctly higher resistance to flow, if the crystalline lattice is unfavourably oriented. With deformation, the ice grains align and develop a crystallographic-preferred orientation within the ice-aggregate, which induces a macroscopic anisotropy. A knowledge of the micro-dynamic deformation and recrystallisation mechanisms and how they affect the properties of the ice aggregate is a key to understand ice sheet dynamics. The objective of this thesis to investigate the deformation and recrystallisation mechanisms in ice and the involved changes in the microstructures of ice- and ice-air aggregates. This is done by means of two-dimensional numerical simulations using the modelling platform Elle, which optimised for modelling interacting micro-dynamic processes. The simulations couple a numerical model for viscoplastic deformation of anisotropic polycrystalline aggregates to implementations of recrystallisation mechanisms in Elle. In particular, an explicit numerical approach to consider secondary phases such as air inclusions in the numerical setup is developed, implemented and used in this thesis for the first time. Additionally, the new approach allows grain-size-reducing mechanisms, which allows the achievement of stable-state microstructures with deformation. In each scientific publication presented in the thesis, qualitative comparisons to natural polar ice accompany the numerical simulations. The results of this thesis show that the deformation and microstructures of ice are generally more heterogeneous than previously thought. Strain localisation is common in ice and related to viscoplastic anisotropy and intensified by the presence of air inclusions. Probably, strain localisation is occurring over a range of scales and has implications for the large-scale flow of ice. The thesis further demonstrates that deformation-induced recrystallisation mechanisms are common in ice and discusses their relation to strain localisation. In particular, the study points out the importance of the dissection of grains by migrating grain boundaries as an additional grain-size-reducing process in polar ice, which was not studied previously. This thesis confirms that the activation of deformation and recrystallisation mechanisms is a function of the deformation conditions such as strain rate, temperature and likely the load of impurities and dust particles. The steady-state numerical-microstructures reflect the prescribed deformation conditions, but appear largely independent from the initial microstructures. These results of this study indicate a high rate of change in crystallographic-preferred orientation and other microstructural properties. Furthermore, the thesis confirms that the development of crystallographic-preferred orientation is a function of strain rather than time or stress.