Decoupling between strain localisation and the microstructural record revealed by in-situ strain measurements in polycrystalline ice

We explore the links between strain localisation and microstructural evolution in ice Ih deformed by dislocation creep. Using digital image correlation (DIC), we monitored the evolution of the strain field in two coarse-grained columnar ice samples deformed by creep (uniaxial compression at constant load) at − 7 ° C and 0.5 MPa up to 9.5% bulk shortening. After a brief transient (<0.2% bulk strain), in which strain localises nearby grain boundaries, viscoplastic strain concentrates in a few narrow intracrystalline shear bands that eventually extend over multiple grains. A comparison of pre- and post-deformation crystal orientation maps shows that strain localisation in shear bands is mainly accommodated by basal slip without producing significant dislocation-related substructures. Severe dynamic recrystallization develops locally at grain boundaries that act as barriers to dislocation motion, particularly where basal shear transfer is ineffective. These observations are compared to full-field simulations reproducing the initial microstructure and experimental setup, which predict the stress and strain rate fields for deformation entirely accommodated by dislocation slip on the known slip systems in ice. The present data indicate that during the deformation of coarse-grained ice Ih at high homologous temperatures: (1) recrystallization does not drive strain localisation but accommodates strain incompatibility, and (2) large strains can be accommodated by unimpeded basal slip with no formation of dislocation substructures. Observation (2) implies that intragranular orientation gradients are unreliable gauges of viscoplastic strain intensity at the grain scale and that the proportion of dislocation types in subgrains does not measure the relative contribution of different slip systems to deformation. Finally, we discuss the implications of this study for the interpretation and modelling of deformation by dislocation creep in rocks.


Introduction
Variations in crystal orientation and viscoplastic anisotropy result in highly heterogeneous stress and strain rate fields during the deformation of polycrystalline materials like ice, rocks, or metallic alloys. The heterogeneity in the stress and strain rate fields controls the evolution of the microstructure, which in turn modifies the mechanical response of the polycrystal at both local and larger scales. Understanding the complex feedbacks between the evolution of the microstructure and the stress and strain fields is thus essential to define accurate strain-dependent flow laws describing the mechanical behaviour of these materials. Deformation experiments that couple technologies to record (preferably in situ) the evolution of the strain field and microstructure at the polycrystal and grain scales are key to studying the links between these two variables. The evolution of the displacement and strain fields can be measured in situ by digital image correlation (DIC) of random speckle patterns deposited on the surface of the sample (Dong and Pan, 2017;Sutton et al., 2009), while the microstructure can be measured by optical or electron microscopy.
Due to its strong viscoplastic anisotropy, hexagonal (Ih) ice is an ideal model material for investigating the relationships between local strain, intragranular misorientation, and dynamic recrystallization. Viscoplastic deformation in Ice Ih crystals occurs essentially by the glide of dislocations with  Burger vectors on the basal plane (normal to the crystal [0001] or c-axis) since non-basal slip systems are at least 60 times harder to activate than the basal one (Duval et al., 1983;Weertman, 1983). Electron backscattered diffraction (EBSD) data on ice polycrystals show, however, that non-basal dislocations account for up to ~35% of the geometrically necessary dislocations delimiting subgrains (Chauve et al. 2017;Weikusat et al. 2017). The large shear stresses required to activate the non-basal slip systems imply local high-stress concentrations within the polycrystal.
Previous deformation studies using DIC on Ice Ih have shown that the strain field is heterogeneous at both crystal and polycrystal scales. Uniaxial compression creep tests at −12°C, 0.5 MPa on columnar ice polycrystals documented strain localisation already in the transient creep stage (bulk strains ≤ 1%) . Local strains five to ten times larger than the bulk strain were measured in shear bands oriented at 30 to 60° to compression, with the highest strains near grain boundaries and triple junctions. Moreover, the finite strain of each grain does not correlate with the intensity of the bulk stress projected on the basal plane (i.e., the Schmid factor). This lack of correlation suggests a strong influence of grain interactions on the stress and strain fields . DIC imaging of uniaxial compression creep tests in columnar ice at −7 and −10°C, 0.5 MPa to higher bulk strains showed that nucleation occurred mainly at triple junctions and along boundaries between grains with markedly different orientations, highlighting a relationship between local strain incompatibility and dynamic recrystallization (Chauve et al., 2015;Piazolo et al., 2015). Grain-scale strain incompatibility also played an essential role in strain localisation at the brittle-plastic transition, where dynamic recrystallization and fracturing are coupled (Chauve et al., 2017b).
The present study focuses on how grain interactions and the activation of different deformation mechanisms (intracrystalline slip, dynamic recrystallization and kink formation) affect strain localisation and microstructural evolution in coarse-grained polycrystalline materials deforming at high temperatures.
We performed compressional creep tests at high homologous temperatures at −7°C up to 9.3% bulk shortening on Ice Ih polycrystals composed of columnar centimetre-scale crystals. Using DIC, we tracked the evolution of the viscoplastic deformation field with a micrometric resolution over the entire surface normal to both the compression direction and the columnar structure of the ice. We monitored the changes in the microstructure ex-situ by mapping crystal orientations on thin sections cut parallel and as close as possible to the surface analysed by DIC before and after deformation. These two sets of observations are compared to the predictions of a full-field FFT-based model reproducing the experimental setup and initial microstructure of the samples, but in which deformation occurs only by dislocation slip. We then discuss the extrapolation of these results to other polycrystalline materials deforming by dislocation creep, focusing on their implications for the deformation of rocks.

Methods
We made polycrystalline columnar ice samples of 10×10×1.5 cm consisting of ~65 to 75 columnar grains elongated normal to the square face of the sample, hereafter referred to as the sample surface. The samples have thus an approximate 2D microstructure. The elaboration process is detailed in Grennerat et al. (2012). The area of the grain sections on the sample surface varies both within and between samples, but most grains are centimetric (Figs 1 and 2). Grain boundaries lie nearly perpendicular to the sample surface in most cases. The large grain size favours dislocation creep relative to diffusion creep and grain boundary sliding. The columnar microstructure facilitates the study of interactions between grains with different orientations and the detection of dynamically recrystallized grains. However, due to the limited number of grains, the samples are not representative volume elements, and their mechanical response can be strongly influenced by a few coarse grains in key positions in the aggregate, such as the coarse grain that occupies more than half of the central part of sample A (Fig. 1).
We performed uniaxial creep tests (initial stress of 0.5 MPa) under unconfined conditions (room pressure) where the load is applied perpendicular to the columnar structure of the grains using an in-house deadweight rig at −7 ºC (0.97 Tm, where Tm is the melting temperature). Axial stress decreased slightly over time from 0.5 MPa to 0.49 MPa (for sample A deformed to a total bulk shortening of 3.1%) or 0.48 MPa (for sample B deformed to a total bulk shortening of 9.5%, Fig. 3a) due to a slight increase in the cross-sectional area of the samples. Instantaneous strain rates during the experiments ranged from 3×10 -7 to 9×10 -7 s -1 (Fig. 3b, c). Bulk strain ( ) at a given time was calculated by two different methods: (1) measuring the change in sample length ( − 0 ) in the shortening direction directly on the image sequence based on the displacement of the press trays and using (%) = 100 × |( − 0 ) ÷ 0 | and (2) averaging (median) the component, where y is the compression direction, over the full strain field estimated from digital image correlation.
For digital image correlation, a random speckle pattern was created on the sample surface by scratchingabrading the surface with sandpaper and then applying shoe polish with a brush to create high-contrast grey intensity gradients (for details on the procedure see Grennerat et al., 2012). The evolution of the displacement and the strain field during the experiments were measured using the free open-source Digital Image Correlation Engine (DICe) tool (https://github.com/dicengine/dice ) v2.0 from Sandia National Laboratories (Turner, 2015). Details on the methods and parameters used are provided in Table 1, Appendix A, and as metadata in the Supplementary material. Raw image resolutions were 17.26 μm/pixel (sample A) and 17.98 μm/pixel (sample B); detailed image acquisition setup and procedures are described in the Supplementary material. The optimal subset size was set at 35 × 35 pixels using the autocorrelation approach (Sutton et al., 2009). For an optimal result, step and virtual strain gauge (VSG) sizes were set at 12 (~1/3 of the subset size) and 24 pixels, respectively (International Digital Image Correlation Society et al., 2018). The step size is physically equivalent to ~210 μm (VSG ~420 μm) and the maximum displacement resolution was estimated to be ±6-7 μm for the x-direction (horizontal) and ±12-15 μm for the y-direction (vertical). The evolution of the strain field is presented as the Von Mises 2D equivalent strain field = � 2 3 � 2 + 2 + 2 2 � (1) The maximum equivalent strain resolution expected is ±5.7×10 -4 (sample B) and ±7.3×10 -4 (sample A), respectively. Strain field maps are presented as (1) incremental equivalent strain estimated over a 10 min creep interval normalized to the interval median equivalent strain, or as (2) finite (cumulative) equivalent strain. For reference, the bulk (longitudinal) shortening (%) is indicated in all strain field maps. To characterize the evolution of the microstructure, we mapped the orientation of c-axes (azimuth and colatitude ) before and after deformation on thin sections (~0.4 mm thick) cut parallel and as close as possible to the observation surface using the Automatic Ice Texture Analyser (AITA), which provides an angular resolution of ~3° (Peternell et al., 2011;Wilson et al., 2003). Pre-and post-deformation maps have spatial resolutions of 50 and 20 µm, respectively. Orientation data treatment, maps, and pole figures were made using the AITAToolbox (https://shorturl.at/krGS9).
As Ice Ih deforms essentially by dislocation slip on the basal plane, the theoretical deformation capacity of a grain under axial compression can be approximated by the Schmid factor of the basal slip system using: A Schmid factor of 0.5 characterises grains with c-axes at 45° from the compression direction, resulting in maximum resolved shear stresses on the basal plane, while a value of zero implies c-axes parallel or perpendicular to the compression direction, leading to null resolved shear stresses on the basal plane. However, in strongly anisotropic polycrystals such as ice, the Schmid factor calculated using the macroscopic imposed stress is an unreliable measure of a crystal's ability to deform because grain interactions can generate local stresses that differ greatly in intensity and orientation from the macroscopic imposed stress . Comparison of the "macroscopic" Schmid factor with the actual strain of the grain, therefore, provides an estimate of the deviation of the local stresses relative to the macroscopic one.
Lastly, we performed full-field micro-macro simulations based on the pre-deformed microstructure of the samples using the CraFT code (Moulinec and Suquet, 1998). CraFT models crystal plasticity using an algorithm based on the discrete Fast Fourier Transform (FFT). It predicts the evolution of strain and stress fields in response to an imposed deformation for a given crystal plasticity constitutive law and an initial microstructure by minimising the average local work rate under strain compatibility and stress equilibrium constraints. To simulate the deformation of Ice Ih, we used the elasto-viscoplastic law described in Suquet et al. (2012), which considers three slip systems: basal, prismatic, and pyramidal, strongly favouring basal slip. This constitutive law has been validated by comparison with experimental data at low strain Piazolo et al., 2015). Since the simulation ignores changes in the microstructure (i.e., recrystallization) it can only reliably predict stress and strain fields before the development of recrystallization, i.e., below 1% bulk shortening (Chauve et al., 2015). Grain boundaries represent only contrasts in crystallographic orientation between crystals with no specific physical properties or behaviour, and thus no possibility of sliding or opening. The predicted strain and stress fields will therefore be used as likely predictors of the occurrence of recrystallization through work (the product of strain and stress). The initial microstructure of the sample surface was discretized with a step size of 0.15 mm·pixel -1 resulting in 533 × 600 (Sample A) and 571 × 578 (Sample B) Fourier points, respectively.
Creep conditions equivalent to the experimental ones were applied up to a 1% bulk shortening, but the simulations have periodic boundary conditions that differ from the stress-free lateral surfaces in the experimental setup. The effect of such an approximation was estimated by Grennerat et al. (2012) to be negligible except at the very edges of the sample.

Sample A
The evolution of the microstructure of sample A is well illustrated by the analysis of two coarse grains, denoted as grains #1 and #2 in figure 1, which accommodated most of the strain in this sample and had contrasted behaviours. Grain #1, in the centre of the sample, had a rather homogeneous orientation with its basal planes at ~78° to the bulk compression direction. Grain #2, in the lower-left part of the sample, shows well-defined subgrain boundaries delimiting domains with basal planes at 0° to 33° to the bulk compression direction prior to deformation. Both grains had low to moderate (<0.25) initial Schmid factors indicating unfavourable crystal orientations for triggering basal slip in response to the applied macroscopic stress (Fig 1d).
After a 3.1% bulk shortening, grain #1 preserved weak intragranular orientation gradients despite a marked change in shape. Grain #2 shows a less pronounced change in shape, but strong orientation gradients in the form of closely spaced kink bands and subgrain boundaries ( Fig. 1a, b, c). Many grain boundaries display millimetre-sized grains formed by dynamic recrystallization (Fig. 1b, c), but severe dynamic recrystallization is limited to the grain boundary between grains #1 and #2, and those to the right side of grain #1 (Fig. 1c, g).

Sample B
Sample B had a more homogeneous initial microstructure and a wider range of crystal orientations than Sample A (Fig. 2). The upper right corner of Sample B is composed of grains less than 1 cm wide, but more than 2/3 of the sample is composed of coarse columnar grains (grains #1 to #7 in figure 2a) of similar size (~3-6 grains across the sample height). Most of the coarse grains had their basal planes oblique to the imposed compression (Fig. 2a, e), resulting in moderate to high (>0.3) Schmid factors for basal slip (Fig.  2d). Sample B also had a few grains with basal planes parallel to the sample surface (dark hues in the orientation maps) and low Schmid factors (e.g., grain #2 in Fig. 2a). Low Schmid factors also predominated among the smaller grains in the upper right corner of the sample (Fig. 2d).
After a bulk shortening of 9.5%, most coarse grains display an increase in intragranular misorientation (Fig. 2b, c). As in sample A, the intragranular misorientation varies greatly between grains. For example, grains #1 and #6 show smooth orientation gradients, whereas grains #4 and #7 show sharp orientation gradients delimited by kink bands and closely-spaced subgrains. The higher bulk shortening resulted in more extensive dynamic recrystallization than in sample A. Dynamic recrystallization developed mainly: (i) within grain #2 and its neighbours, (ii) along the boundary segment between grains #4 and #5, and (iii) to the right of grains #5 and #7 (Fig 2b, c). Comparison of the crystal orientations before and after deformation reveals some dispersion of the original orientations due to intragranular distortion and recrystallization, but no major grain reorientations (Fig. 2e).    (b)). Due to the degradation of the speckle pattern quality with time, DIC-derived strain rates were estimated over the whole area only up to 2.4 %. For higher strains, DIC analysis was estimated on a region of interest (ROI, cf. figure 2d) where the speckle pattern preserved a good quality (hollow markers). After a short primary creep (~0.4%), sample B underwent an accelerated creep stage (weakening) up to ~2.9% and a deceleration creep stage (hardening) to completion at 9.5%. The different creep stages are highlighted by shaded areas. The equivalence between time and finite longitudinal strain is given at selected points for both samples at the top (in colour). The time at which the crack occurs in sample B is also indicated.

Macroscopic mechanical behaviour and the mean-field strain evolution from DIC
Sample A, shortened up to 3.1%, showed a primary creep stage characterized by a sharp decrease in the strain rate down to ~3×10 -7 s -1 at ~0.9 % bulk shortening. Then, the strain rate remained constant (steady state) until the end of the experiment (Fig. 3a, b). The evolution of the median strain rate (̇) estimated from DIC follows a similar trend (Fig. 3b), validating the DIC strain field measurements up to 3.1%.
The macroscopic mechanical evolution of sample B, shortened up to 9.5%, is markedly different (Fig. 3a,  c). Sample B displayed a faster primary creep stage with a decrease in strain rate down to ~2.5×10 -7 s -1 at ~0.4% of bulk shortening. However, primary creep was not followed by steady-state but by an increase in strain rate (softening) up to ~8×10 -7 s -1 at ~2.9% bulk shortening and then by a decrease in strain rate (hardening) to the end of the experiment down to a strain rate of ~4.6×10 -7 s -1 at 9.5% bulk shortening. The variation with time of the median strain rate (̇) estimated from DIC follows a similar trend than the bulk longitudinal strain even when the DIC strain is estimated over a small region that retained an acceptable quality speckle pattern (dashed box in Fig. 2d), thus validating the DIC data in this region up to 9.5%.

Strain field evolution from DIC
Both samples showed an initial transient stage where strain occurred nearby grain boundaries (e.g., Fig.  4). During this stage, incremental equivalent strains 5 to 10 times higher than the average occurred near virtually all grain boundaries (Figs. 5 and 6). In-plane rotation maps indicate that this strain localisation along grain boundaries has a simple shear component (Fig. 4). Analysis of the DIC data for this early stage also reveals intragranular shear bands propagating from triple junctions in sample B (arrows in Fig. 4). Strain localisation vanished along most grain boundaries at a longitudinal shortening of less than 0.2 % (i.e., at primary creep) in both samples (Figs. 5 and 6; see also Movies A2 and B2 in the supplementary material). The transient stage in sample B was followed by a short period of almost homogeneous deformation up to a bulk strain of ~0.4% ( Fig. 6 and movie B2 for a full sequence). For bulk strains >0.4%, strain localised in a few shear bands with apparent widths between 1 and 8 mm which grew until they coalesced into an almost continuous system crosscutting through the entire sample (Figs. 1, 2, 5 and 6).

Strain localisation: Sample A
As previously described, almost 1/3 of sample A consisted of two very coarse grains (#1 and #2) with low to moderate (<0.25) Schmid factors. DIC-derived strain maps indicate that these grains accommodated most of the imposed deformation. Strain localisation started early, at 0.1% bulk shortening, at two sites. The first site (grey arrows in Figure 5) is the lower segment of the grain boundary between grains #1 and #2, which was the only grain boundary preserving strain localisation at the end of the initial transient stage (Figs. 1f,g and 5). Strain continued to accumulate at this interface until the end of the experiment, but its intensity varied in time and space along the grain boundary, and the strain localisation along this grain boundary weakened with increasing bulk strain (Fig 5; see Movie A2 in the supplementary material). Most dynamic recrystallization in this sample occurred along this grain boundary (Fig. 1b, c). Strain localisation propagated from this grain boundary into grain #2 forming a curved non-basal band with a diffuse end (Figs. 1f, g and 5). A shear band of similar orientation also developed in grain #2 from the left edge of the sample and was linked to the grain boundary by a more diffuse strain localisation band. Strain localisation in the non-basal bands was accompanied by the formation of subgrains, kinks, and, in the curved one, dynamic recrystallization (Fig 1c). In parallel, a ~7 mm wide shear band developed within grain #1 parallel to its basal plane at a high angle (77.5°) to the imposed shortening (Figs. 1f, g and 5). Already at 0.28% of bulk shortening, this shear band crosscut the entire grain and propagated into the neighbouring grains (~1.5-4 mm wide), affecting the entire sample width. The orientation of the shear band parallel to the basal plane of crystal #1 indicates that most deformation was accommodated by basal slip despite the moderate Schmid factor of the grain (~0.2, see Fig. 1d). The shear band is on average thinner in the neighbouring grains where it is not parallel to the basal plane. Transient (at bulk shortenings between 0.28-1%) strain localisation occurred at the intersection between the band and the boundary of grain #1 on the right, which is another site with severe development of dynamic recrystallization (cf. Figs. 1f, g and 5). Strain concentration at this boundary decreased with the propagation of the shear band into the neighbouring grains up to the free surface of the sample (see movie A2 in Supplementary Material). Within grain #1, this shear band produced neither dynamic recrystallization nor significant dislocation substructures, remaining invisible in the optical image and the crystallographic orientation map (cf. Figs. 1cb, c vs. f, g). From ~1.8% bulk shortening onwards, a slightly thinner basal shear band developed in this same grain spaced from the first one by ~1 cm. It did not propagate into neighbouring grains but produced some strain localisation and limited recrystallization at its interception with the boundary of grain #1 on the left (see movie A2 in Supplementary Material).

Strain localisation: Sample B
After the initial transient stage, DIC data show that strain in sample B was mostly accommodated in a network of mm-wide (apparent thicknesses vary between 3 and 7.5 mm) intragranular shear bands oblique (13° to 45°) to the compression (Figs. 2f, g and 6). Macroscopically, the development of this shear band network corresponds to the weakening stage evidenced by the increase in strain rate over time (Fig. 3c). Shear bands formed mainly in coarse grains with high Schmid factors (>0.4) following the orientation of the basal plane, specifically in grains #1, #4 and #6 (Figs. 2a vs f, g). However, a few shear bands do not follow basal planes (Figs. 2c, f, g). Grains #1 and #6 also display conjugate shear bands perpendicular to the basal planes associated with subgrain boundaries (Fig. 2f). Grain #7 displays strong strain localisation linked to a kink band. In grain #6, the non-basal shear band nucleated already in the transient stage from a triple junction (Fig. 4). The non-basal shear bands are thinner (in grain #6) or less marked (in grain #1) than the basal ones.
The DIC sequence shows that strain localisation started at multiple sites and that the shear bands propagated unevenly across the sample. The formation of shear bands started as early as 0.14% of bulk shortening in the lower part of the sample (Fig. 4). The basal shear band affecting grain #6 propagated from the triple junction between grains #6, #4, and a tiny grain with a very low Schmid factor value located between grains #4, #6, and #7 and evolved fast crosscutting the entire grain #6 at a bulk shortening ~0.7% ( Fig. 6 and Movie B2 in the supplementary material). Strain localisation became progressively stronger in grain #6, and at bulk shortening of ~1.4% the basal shear band propagated into grain #4 towards the other shear band system (Fig. 6).
The best-developed shear bands in Sample B propagated with a basal orientation from the top of the sample into grain #1 at a bulk shortening of 0.73% (see Movie B2), continued into grain #2 as a non-basal deformation band with a fuzzy strain distribution, and propagated into grain #4 as a basal shear band at a bulk shortening of ~0.8% (Figs. 2f, g and 6; see also Movie B2). The deformation band stalled at the grain boundary between grains #4 and #5, producing a marked strain concentration along the grain boundary (Figs. 2f, g and 6). Lastly, diffuse build-up of strain in grain #5 and its neighbours, which had undergone extensive recrystallization, connected the shear band system to the right edge of the sample, producing a strain localisation network that crosscut the entire sample. Within grain #2, the shear band propagation was accompanied by the development of a crack normal to the shear direction at a bulk shortening of 1.4% and extensive dynamic recrystallization (Figs. 1f, 5 and Movie B2).

Links between the strain field and microstructures
In both samples, basal-slip shear bands produced undetectable microstructural changes in polarised optical images or crystallographic orientation maps, whereas non-basal shear bands left a clear signature in the microstructure in the form of strong orientation gradients, kink bands, or dynamic recrystallization (Figs. 1 and 2 and movies A2 and B2 in Supplementary material). In sample B, grains #1, #4 and #6, deformed mainly through basal-slip shear bands, underwent a notable change in shape during deformation consistent with the high strain they accumulated. However, this change in shape can only be assessed because the initial stage is known. In contrast, although many non-basal strain localisation bands are linked with kink bands or closely spaced subgrain walls, these microstructures are not systematically linked with significant long-lasting strain localisation (cf. kink bands in grain #4 of sample B, Fig. 2).
There is a correlation between the sites where the shear band propagation stalled and the generation of severe dynamic recrystallization. Three sites in sample B display severe recrystallization (Fig. 2b, c vs g). One is the boundary between grains #4 and #5, where the basal shear band in grain #4 stalled due to the strong misorientation between the two grains. The other corresponds to grain #2, a grain with an exceptionally low Schmid factor which acts as a strain transfer zone between the basal shear bands in grains #1 and #4. The development of a small crack in grain #2 at ~1.4% bulk shortening indicates that it supported high local stresses even as the bulk sample was weakened, as indicated by the increase in bulk strain rate (Fig. 3c). The last severe recrystallization site in Sample B links the lower left termination of the shear band, characterised by diffuse deformation in grain #5, to the edge of the sample.
Comparison of the initial Schmid factor for basal slip and the average finite strain from DIC for a few coarse grains from both samples shows that the two parameters are uncorrelated (Fig. 7). This explicitly indicates that the local stress field strongly deviates from the macroscopic one due to interactions between neighbouring grains. Colour maps indicate cumulative equivalent strain at 2% bulk shortening.

Comparison between experimental observations and simulations
Comparison of the simulated and experimental strain fields (Fig. 8) reveals a satisfactory prediction for sample A, where the simulation correctly forecast the intragranular basal shear band that crosses grain #1 and accommodates most of the strain in the sample. For sample B, although the general strain distribution at the sample scale is correctly forecasted, the shear bands are not. For both samples, the comparison between observations and simulations suggests that dynamic recrystallization developed preferentially in sites where the work was high, suggesting a link between the two. This is clear for grain 2 in sample B, which shows strong recrystallization and high work in the simulations (cf. Figs. 2 and 8). However, some sites with higher-than-average work did not correlate with severe recrystallization sites in the experiments but with kinks or subgrains. Similarly, the strong recrystallization around grain #5 in sample B does not correspond to high work sites in the simulation.

Experimental data
The most striking observation when comparing the evolution of the strain field and that of the microstructure in both samples is the decoupling between finite strain and the development of microstructures linked to the accumulation of geometrically necessary dislocations, such as crystal lattice distortion, recrystallization, or the development of kink bands. The most effective strain localisation, well recorded by DIC, occurred through intracrystalline shear bands parallel to the basal planes of the crystals and this deformation produced little lattice distortion (intragranular misorientation) or dynamic recrystallization within the grains, but a marked change in shape. This strain at grain scale can only be quantified by in situ observational techniques such as DIC or if the initial state is known, which is rarely the case in nature. Our results agree with the large body of evidence that creep deformation in single-grain and polycrystalline ice proceeds mainly by dislocation slip on basal planes (Duval et al., 1983;Weertman, 1983). However, most of the deformation accommodated by basal slip remains undetectable to observations based on intracrystalline misorientation (e.g. AITA, EBSD) resulting from the accumulation of geometrically necessary dislocations (GNDs). We therefore explain why, even when deformation is largely accommodated by basal slip, non-basal dislocations contribute up to 35-40% of the total intracrystalline misorientation in Ice Ih polycrystals analysed post-mortem (Chauve et al. 2017;Weikusat et al. 2017). Therefore, estimating the (geometrically necessary) dislocation density of a crystal based on misorientation proxies -such as the grain orientation spread (GOS), the kernel average misorientation (KAM), or the average misorientation between subgrains-does not gauge the total viscoplastic strain of the grain. Therefore, caution should be applied when using such proxies to estimate the strain intensity at local scales.
Dynamic recrystallization occurred mainly near grain boundaries and triple junctions, as in previous studies (Chauve et al., 2015;Piazolo et al., 2015), but it developed best along grain boundaries with misorientations that hindered the transfer of dislocation motion associated with basal slip between grains (e.g., at the interface between grains #4 and #5 in Fig. 2). Accordingly, the intensity of recrystallization is related to the deformation incompatibility between neighbouring grains caused by a local concentration of stress and strain. This means that, under the experimental conditions tested, dynamic recrystallization is a consequence rather than a driver of strain localisation, insofar as it relaxes the deformation incompatibility between neighbouring grains. In other words, dynamic recrystallization is not the seed of strain localisation in the early stages of ice deformation.
The limited number of grains in the samples studied limits the analysis of their bulk mechanical response, as the samples do not constitute a representative volume element. Still, some qualitative conclusions can be drawn from the evolution of the strain field documented by DIC. Sample A developed a strain localisation network crossing the entire sample already at 0.45% bulk shortening (Fig. 6) and shows a simple mechanical evolution, where primary creep (hardening) is followed by steady-state deformation (Fig. 5). In sample B, the development of a strain localisation network crossing the entire sample is slower and completed at ~1% bulk shortening (Fig. 7). The development of the strain localisation network can be related to the marked weakening following the end of the primary creep (Fig. 5). The hardening stage characterizing sample B from 2.9 up to 9.5% bulk shortening (Fig. 3) may be linked to the observed decrease in strain localisation in the shear band network (see full DIC sequence for ROI of Sample B in the supplementary material). However, the small area over which it was possible to map the strain field at large bulk strains due to the speckle deterioration makes it difficult to analyse the causes of this change in behaviour.

Coincidences and mismatches between experimental observations and simulations
As expected, the comparison between the full-field simulations and the experimental observations revealed a general but not one-to-one agreement (Fig. 8). In sample A the shear bands were correctly predicted and there is a general, though not perfect, correlation between severe recrystallised zones and high work. The discrepancy between simulations and observations is particularly noticeable in sample B because processes that change the microstructure, such as kinks or recrystallization, cannot be reproduced in the simulations. We stopped the simulations at 0.5% bulk strain to alleviate this limitation. Yet, DIC data show evidence of the formation of some kink or tilt bands at low strains (Figs. 5 and 6). Since any microstructural change occurring during deformation affects the forecasted evolution of the strain field, this explains the greater discrepancy between observations and simulations for sample B, which was subjected to larger strain and thus to stronger microstructural changes. For example, analysis of the evolution of the strain field with time for sample B (Fig. 6) shows that the shear band in grain #4 developed after the strain concentration associated with recrystallization in grain #2. Thus, despite the lack of oneto-one agreement, the comparison with the simulation suggests that a higher-than-average local work rate is needed to induce severe microstructural changes such as dynamic recrystallization or kinking.

Extrapolation to rocks (and metals) deforming by dislocation creep
Simply put, the present study provides evidence for a decoupling between finite strain and microstructural imprint (as evidenced by misorientation gradients and recrystallization) at the sample and grain scales. Recent experiments using high-resolution (nm-scale) DIC and EBSD crystal orientation mapping in metallic alloys have also found a decoupling between strain intensity and the development of intragranular misorientations during dislocation creep. This phenomenon has been observed in magnesium (Orozco-Caballero et al. 2017), which deforms mainly by basal slip and twinning due to its hexagonal structure, and face-centred cubic nickel alloys (Harte et al. 2020), which activate multiple slip systems. The latter indicates that this decoupling is not restricted to materials with a strong viscoplastic anisotropy that tends to deform by single slip.
The need to deform rock samples at high temperatures and under high confining pressures to avoid fracturing (except for rock salt, but halite is a cubic material more akin to metals than silicate minerals), makes in situ DIC experiments in common rocks unfeasible. Despite this experimental limitation, several lines of evidence indicate that this decoupling phenomenon is extensible to common rocks that deform predominantly by dislocation creep. The evidence is stronger for mantle rocks, which are essentially composed of olivine (>60%), a highly anisotropic orthorhombic mineral with only three independent slip systems of contrasting strengths (Tommasi et al. 2000). Experiments on olivine crystals oriented to activate only the [100](010) slip system, which has the lowest critical resolved shear stress under most natural and experimental deformation conditions, recorded very low misorientation gradients despite substantial shear (Tielke et al., 2019). Further evidence that large strains are decoupled from strong intragranular disorientations at the grain scale is the predominance of strongly elongated olivine porphyroclasts perfectly oriented for single-slip deformation on the easy [100](010) system in olivine polycrystals deformed in torsion (Bystricky et al . 2000) and natural peridotites deformed under various conditions (Falus et al., 2011). Extreme elongation (aspect ratios up to 20:1) without the development of strong intracrystalline misorientations or recrystallization has also been documented for orthopyroxenes in peridotite mylonites (Frets et al., 2014). Another indirect evidence of this decoupling phenomenon in natural and experimentally deformed peridotites is the discrepancy between the relative activity of the slip systems in olivine inferred from the study of the bulk CPO and the intragranular rotation axes. These consistently shows a dominant activation of the [100](010) slip system from the CPO analysis and dominant activity of [100](001) and [001](100) from the rotation axis (Bystricky et al . 2000;Falus et al., 2011;Lopez-Sanchez et al. 2021;Soustelle et al., 2010). In crustal rocks, the evidence is less clear due to their typical polymineralic nature, which leads to further grain scale stress heterogeneity and multiple deformation mechanisms acting in parallel, and because deformation is often accompanied by chemical reactions. However, quartz mylonites formed under low greenschist facies often display monocrystalline quartz ribbons composed of crystals well oriented to deform by dislocation slip on the basal plane (the dominant slip system in quartz at low temperature) with rather low intracrystalline misorientations (e.g., Tommasi et al. 1994;Pauli et al., 1996).
In summary, we propose that the decoupling between strain intensity and the evolution of intragranular misorientations is generalisable to all rocks deforming by dislocation creep. It also means that caution should be applied when using misorientation-based proxies to estimate the strain intensity at local scales. Even if a relationship exists between the bulk strain and the average misorientation over representative elementary volumes (e.g., Hughes et al., 1998;Pennock and Drury, 2003), microstructural parameters (e.g., grain size, CPO) and intensive variables such as temperature will likely affect this relationship, preventing the establishment of a reliable universal approximation.
A second implication of this study is that in the early stages of deformation, dynamic recrystallization may help to localise or delocalise strain at the grain scale but is not a primary controlling factor of strain localisation. Instead, dynamic recrystallization is essentially a process that accommodates local strain incompatibility. A similar relationship between recrystallisation and local strain incompatibility has been documented in experimentally and naturally deformed coarse-grained peridotites with incipient dynamic recrystallization. In these rocks, recrystallisation developed preferentially in olivine grains that are welloriented to deform by dislocation slip in low-strength slip systems in contact with olivine grains in "hard" orientations that remain almost undeformed, or pyroxenes that are stiffer than olivine (Bickert et al., 2021;Lopez-Sanchez et al., 2021). A similar phenomenon was also documented in polymineralic rocks with higher strength contrasts such as granites (e.g., Holyoke and Tullis, 2006). The fact that dynamic recrystallisation is induced by strain incompatibility and linked with local stress concentrations in the early stages of deformation also has implications for paleopiezo(watt)metric relationships based on recrystallised grain size. These relationships should be used with caution when recrystallised volumes are small, as they may proxy local stress or work rates and greatly overestimate the bulk values.

Conclusion
Under the experimental conditions tested, the combination of DIC and crystal orientation mapping reveals that deformation in Ice Ih tends to localise in intracrystalline shear bands dominated by basal slip, which eventually spread across multiple grains by direct transmission or, in neighbouring grains poorly oriented for basal slip, by recrystallisation, kinking or formation of non-basal slip shear bands. The combination of DIC and microstructural data provides clear evidence that unimpeded basal slip can accommodate large strains at the grain scale without leaving any imprint on the final microstructure (orientation gradients, subgrains, or kinks). In contrast, when deformation cannot be accommodated by basal slip, it leaves a measurable imprint on optical images and orientation maps in the form of subgrains (delimited by basal and non-basal dislocations, e.g., Chauve et al. 2017a), kink bands, or dynamic recrystallization. This decoupling between strain intensity and the development of dislocation substructures in ice Ih implies that misorientation-based proxies are unreliable gauges of both the viscoplastic strain intensity at the grain scale and the relative contribution of different slip systems to the bulk deformation. The present results also highlight the role of local strain incompatibility (associated with a local stress increase) in triggering dynamic recrystallization. Under the experimental conditions tested (coarse grains, high temperature, moderate stress, limited finite strain), our data show that grain size reduction by dynamic recrystallization is a consequence rather than a driver of strain localisation.
Experiments on metallic alloys and microstructural data from rocks suggest that decoupling between strain intensity and intragranular microstructure development is a common feature of dislocation creep deformation in crystalline materials. This calls for a general warning on the limits of misorientation-based proxies to gauge the cumulative plastic deformation at the grain scale or smaller or the relative contributions of the different slip systems to the bulk strain. This also calls for further testing of the common assumption of a simple relationship between average intragranular misorientation and finite strain at the polycrystal and larger scales. The heterogeneity in the strain and stress fields documented here results from the viscoplastic anisotropy of ice Ih. Thus, any rock composed of highly anisotropic minerals, such as olivine, quartz at low temperature, or micas will exhibit a similar or greater degree of heterogeneity in stress and strain, with dynamic recrystallization preferentially triggered at high work rate sites. Accordingly, paleopiezo(watt)metry relationships should be used with caution.
The grounds for extending the conclusion that grain size reduction by dynamic recrystallization is a consequence rather than a driver of strain localisation are less robust. Yet, given the similarity of deformation processes in ice Ih and other rock-forming minerals, it is expected that similar cause-andeffect relationship applies to rocks when deformation occurs under low stresses and high homologous temperatures allowing an equilibrium between growth and nucleation kinetics. Under such conditions, dynamic recrystallisation would be unable to produce a reduction in grain size necessary for a transition to grain size-sensitive dominant creep (e.g., Braun et al., 1999).