ALBERT

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: Understanding the flow of ice on the microstructural scale is essential for improving our knowledge of large-scale ice dynamics, and thus our ability to predict future changes of ice sheets. Polar ice behaves anisotropically during flow, which can lead to strain localisation. In order to study how dynamic recrystallisation affects to strain localisation in deep levels of polar ice sheets, we present a series of numerical simulations of ice polycrystals deformed under simple-shear conditions. The models explicitly simulate the evolution of microstructures using a full-field approach, based on the coupling of a viscoplastic deformation code (VPFFT) with dynamic recrystallisation codes. The simulations provide new insights into the distribution of stress, strain rate and lattice orientation fields with progressive strain, up to a shear strain of three. Our simulations show how the recrystallisation processes have a strong influence on the resulting microstructure (grain size and shape), while the development of lattice preferred orientations (LPO) appears to be less affected. Activation of non-basal slip systems is enhanced by recrystallisation and induces a strain hardening behaviour up to the onset of strain localisation and strain weakening behaviour. Simulations demonstrate that the strong intrinsic anisotropy of ice crystals is transferred to the polycrystalline scale and results in the development of strain localisation bands than can be masked by grain boundary migration. Therefore, the finite-strain history is non-directly reflected by the final microstructure. Masked strain localisation can be recognised in ice cores, such as the EDML, from the presence of stepped boundaries, microshear and grains with zig-zag geometries.

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: This thesis contains 8 manuscripts for peer-reviewed journals (4 published, 2 submitted, 2 to be submitted within 4 weeks) that present studies of deformation microstructures and folds in polar ice and ductile anisotropic rocks by means of numerical simulations. It is organized in four different parts that focus: (1) Viscoplastic deformation of polycrystalline polar ice in simple and pure shear coupled with dynamic recrystallisation simulating microstructure evolution and formation of folds; (2) Folding and unfolding of single and multilayers in pure and simple shear; (3) Influence of anisotropy degree and type on rotation of rigid bodies (porphyroclasts and porphyroblasts); and (4) Analysis of the effects of dynamic recrystallisation on the rheology and microstructures of partially molten rocks. The first part (chapters 2, 3 and 4) contains three manuscripts analysing the influence of dynamic recrystallisation on deformation of pure polar ice. A full-field viscoplastic code (FFT) that fully reproduces the ice crystal’s mechanical anisotropy is coupled with dynamic recrystallisation processes to perform a series of numerical simulations in pure (chapter 2) and in simple shear (chapter 3 and 4). The results show that dynamic recrystallisation (DRX) has remarkable effects on the developed ice microstructures, producing larger and more equidimensional grains and masking strain heterogeneities. DRX has only a minor effect on the formation of lattice preferred orientations (LPOs), but it has a strong influence on the relative activity of the different slip systems of ice and, therefore, on its mechanical properties. The survival probability of ice grains during recrystallisation is mostly related to the initial grain size, while crystal orientation with respect to the deformation axes plays a minor role only. The last manuscript of this part analyses how folds form in polar ice (chapter 4) as a consequence of intrinsic anisotropy when a strong LPO has developed. This mechanism can explain the development of folds in ice, without needing to invoke unrealistic viscosity contrasts between folding layers. The second part of the thesis includes three manuscripts dedicated to the formation of folds in layered composite materials. The first of these manuscripts (chapter 5) investigates the development of folding of a single layer embedded in a softer matrix in linear and non-linear viscous media. Viscous deformation is simulated using a finite-element method (FEM) up to high strains. This study focuses on the influence of viscosity contrast, vorticity of deformation and the stress exponent on the resulting folding geometries. Folds forming in pure and simple shear do not develop distinctly different geometries, and are thus difficult to distinguish in the field. Folds formed under non-coaxial flow are slightly more irregular with more variable axial plane orientations than in pure shear. This study demonstrates that the best tool to distinguish simple shear folds is the asymmetry of associated axial plane cleavage. Chapter (6) presents an analysis of the instantaneous stress and strain fields of the simulations studied in the previous chapter to compare the mechanical behaviour of folding rocks under pure and simple shear. Most notably, the work required to fold a competent layer is lower in simple shear than in pure shear. Chapter 7 studies the response of a folded layer that goes into the extensional field with progressive non-coaxial deformation. This contribution contains observations and evidence that help to recognise in the field whether straight layers have been folded previously. Intrafolial and cusp-like folds adjacent to straight layers are indications of previous folding if layers experienced softening during or before stretching, or if the layers were influenced by adjacent layers with different rheologies. The third part of the thesis includes one manuscript (chapter 8) that addresses how the degree and type of anisotropy influence the rotation of rigid bodies embedded in a softer matrix (porphyroclasts and porphyroblasts) under non-coaxial flow. Viscoplastic full field numerical simulations were used to analyse systems with intrinsic anisotropies, and linear viscous FEM for the modelling of systems with composite anisotropies. The results demonstrate that a high degree of anisotropy can slow down or block the rotation of rigid objects. It thus reconciles the opposing positions in the decade-long controversy regarding the rotation of rigid objects, such as garnets, in rocks. The final part of this thesis (chapter 9) investigates the effect of viscosity contrast, linear viscous rheology, melt fraction and wetting angle on the effective weakening of rocks with melt pockets and polar ice with air bubbles. This study is based on the coupling of a linear viscous FEM with dynamic recrystallisation, simulating the evolution in simple shear of a composite based on a foam texture. The results indicate that dynamic recrystallisation and wetting angles have a first-order impact on the deformation of the aggregate, controlling the connection of melt pockets and bulk mechanical behaviour of the rock. Summarising, this thesis contains a number of studies that highlight how numerical simulations can give insight in structural and mechanical developments in ice and rocks, enabling better interpretation of the observed structures.

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: 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: Visual stratigraphy of ice cores from Greenland as well as Antarctica revealed folding on a cm scale, with fold amplitudes varying from less than 1 cm to a few decimetres. Stratigraphy bands are visualized by an indirect light source scattering on surfaces inside the ice, mainly particles and air bubbles / hydrates. Due to their potential influence on the integrity of the climatic record, folds have been subject to modelling studies, however, the initial formation of the disturbances is not fully understood. In this study we present a detailed analysis of the visible folds from the NEEM ice core from Greenland and the EDML ice core from Antarctica, 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. In case of the NEEM core 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. In case of the EDML ice cores the folding starts at a depth of about 1700 m and show very similar characteristics as found in the NEEM core. Numerical modelling of crystal viscoplasticity 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 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 is a consequence of localized deformation at the boundaries of kink bands.