The influence of a grain-shape fabric on the mechanical behaviour of rock salt: Results from deformation experiments

Accepted Manuscript The influence of a grain-shape fabric on the mechanical behaviour of rock salt: Results from deformation experiments

Jolien Linckens, Gernold Zulauf, Michael Mertineit PII: DOI: Reference:

S0040-1951(18)30421-9 https://doi.org/10.1016/j.tecto.2018.12.009 TECTO 128000

To appear in:

Tectonophysics

Received date: Revised date: Accepted date:

26 April 2018 20 November 2018 9 December 2018

Please cite this article as: Jolien Linckens, Gernold Zulauf, Michael Mertineit , The influence of a grain-shape fabric on the mechanical behaviour of rock salt: Results from deformation experiments. Tecto (2018), https://doi.org/10.1016/j.tecto.2018.12.009

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ACCEPTED MANUSCRIPT The influence of a grain-shape fabric on the mechanical behaviour of rock salt: Results from deformation experiments

Jolien Linckens*,a, Gernold Zulaufa, Michael Mertineitb Department of Geosciences, Goethe University Frankfurt am Main, Altenhöferallee 1, 60438

Bundesanstalt für Geowissenschaften und Rohstoffen (BGR), Stilleweg 2, 30655 Hannover,

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b

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Frankfurt am Main, Germany. *[email protected]

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a

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Germany

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Abstract

In order to assess the effect of shape preferred orientation (SPO) of halite grains on deformation

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of rock salt, ductile plane strain deformation experiments have been conducted. Natural halite

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cubes with and without an SPO from the Asse mine of northern Germany were deformed at 345°C, atmospheric pressure and a strain rate of ~10-7 s-1. The SPO was oriented at different

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angles (ß = 0°, 45° and 90°) to the main shortening direction, Z. The sample is confined in the Y direction and can freely move to the principal stretching direction, X. Most of the strain was

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accommodated by dislocation creep. The qualitative analysis of the stress-strain data shows the clear influence of the SPO on the mechanical data. At a shortening strain of ca. -10%, the samples with ß = 0° and 45° are weaker than the samples without an SPO. In contrast, the sample with ß = 90° is stronger than the samples without an SPO. A new SPO is formed in all samples with the long axis of the grain shape fabric being subparallel to the principal stretching axis, X. At these larger shortening strains, the samples show similar strength, with an exception of the 90° oriented sample that is still stronger than the samples without an SPO. Even though the experimental set up has to be improved to obtain quantitative results on the influence of 1

ACCEPTED MANUSCRIPT SPO on mechanical strength of rock salt, the results show that the SPO of rock salt likely has to be taken into account when building a repository for nuclear waste and could have an effect on the stability of caverns.

Keywords: rock salt; ductile deformation; shape preferred orientation (SPO); anisotropy;

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subgrains

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1. Introduction

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Rocks often show an anisotropy, which can be intrinsic (e.g. shape-preferred orientation, SPO; crystallographic preferred orientation, CPO) or extrinsic (e.g. layering, cracks). Undeformed

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rock salt, where rock salt consists dominantly of halite, can have a strong SPO (Talbot and Jackson, 1987). In addition, an SPO in rock salt can also develop during deformation (e.g.

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Schléder and Urai, 2007; Zulauf et al., 2009, 2010; Thiemeyer et al., 2016). Results of previous

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deformation experiments suggest that dislocation creep (e.g. Skrotzki et al. (1996); Carter and Hansen (1983); Franssen (1994); Peach et al. (2001)) and pressure-solution creep (e.g. Urai et

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al. (1986); Spiers et al. (1990); Urai and Spiers (2007)) are the dominant deformation mechanisms in rock salt. Pressure solution can occur when a thin fluid film is present on the

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grain boundaries (Spiers et al., 1990). This deformation process is important in rock salt as grain boundaries of halite are often associated with fluid inclusions (e.g. Urai et al. (1986); Küster et al. (2008); Desbois et al. (2012); Kneuker et al. (2014)). The theoretical expression for pressure solution is equivalent to solid state grain boundary diffusion creep accommodated by grain boundary sliding (Spiers et al., 1990). In dry rock salt, and in coarse-grained (cmscale) wet rock salt, dislocation creep is the dominant deformation process in rock salt (e.g. Urai et al., (2008)). During dislocation creep, grain boundary migration (GBM) and subgrain formation take place in naturally and experimentally deformed rock salt (e.g. Franssen, 1994; 2

ACCEPTED MANUSCRIPT ter Heege et al., 2005; Desbois et al., 2010). Experiments show that the subgrain size in rock salt depends on the differential stress (Carter et al., 1993) and that the average subgrain boundary misorientation increases with strain (Pennock et al., 2005). However, up to a natural strain of 50%, the average subgrain boundary misorientations remains <5°, and extensive subgrain rotation (SGR) is not observed (Pennock et al., 2005). When dislocation creep is the

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dominant deformation mechanism in rock salt, an SPO and CPO form, as observed in

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deformation experiments (e.g. Franssen, 1994; Pennock et al., 2005; Trimby et al., 2000; Zulauf

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et al., 2010). However, as far as we know, a CPO in naturally deformed rock salt has not been recorded yet. The absence of a CPO in naturally deformed rock salt is likely due to the activity

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of GBM and/or dominance of deformation by pressure solution (Urai and Spiers, 2007). The importance of grain-boundary orientation with respect to the applied stress during deformation

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by pressure solution and dislocation creep is unclear. If the grain boundaries are aligned at 45° to the maximum principal stress, the shear stress on these grain boundaries will be at a

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maximum (Twiss and Moores, 1992). In this orientation, a larger contribution of grain boundary

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sliding to the deformation might be expected. In addition, the fluids on the grain boundary, as common in rock salt, likely increase the ease of sliding (White and Knipe, 1978). In contrast,

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when the grain boundaries are aligned perpendicular to the applied stress, the shear stresses will be zero (Twiss and Moores, 1992), and sliding along the grain boundaries is unlikely to occur.

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These theoretical studies indicate that an SPO of rock salt could have a large influence on the deformation behaviour and corresponding mechanical strength of rock salt. This in turn is important when building a repository for nuclear waste and for the stability of mines and caverns in salt rocks. Although many deformation experiments have been conducted on rock salt, the influence of an SPO of halite grains on the deformation behaviour and mechanical strength has not been studied in detail. Previous experiments on the influence of structural anisotropy on rock salt viscosity have mainly focused on bedding planes (rock salt interbedded with impurities like anhydrite, 3

ACCEPTED MANUSCRIPT clay, etc.) and deformation in the brittle (dilatation) field (Hatzor and Heyman, 1997; Dubey and Gairola, 2000, 2008; Dubey, 2018). We performed experimental ductile deformation experiments on coarse-grained (cm sized) natural rock salt with an SPO of halite grains at different orientations to the main shortening direction. The deformation experiments have been carried out at T = 345°C and atmospheric

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pressure. At these deformation conditions, it is expected that the dominant deformation

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mechanism in these coarse-grained samples will be dislocation creep (based on the flow laws

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by Carter et al., 1993; Spiers et al., 1990). As observed in deformation experiments done at similar conditions (Fransen, 1994), GBM will likely not play a large role. The small amount of

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GBM will make sure that the SPO will not be erased quickly during the experiments, so that the influence of SPO and the change in SPO during deformation can be observed. The aim of

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this research is to determine the effect of halite grain SPO on the mechanical behaviour, and

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related changes in the microstructural evolution of rock salt.

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2. Methods

2.1 Deformation experiments

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In order to quantify the effect of SPO on the viscosity of rock salt, we carried out plane strain deformation experiments on natural rock salt cuboids (6.0 x 6.0 x 3.5 cm) with and without an

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SPO at atmospheric pressure, temperature of 345°C, strain rate of ~10-7 s-1 to different finite strains. The planar fabric, which is based on the long axes of the elongated halite grains, was orientated in different orientations to the main shortening direction, Z (Fig. 1). The angle between the SPO and the main shortening direction, ß, was chosen as 0°, 45° and 90°. For comparison, we additionally performed experiments on rock salt without SPO (Fig. 1). Cuboids (6.0 x 6.0 x3.5 cm) with an SPO (Fig. 3A) were dry cut from samples (6.0 x 7.0 x 4.5 cm or 6.0 x 6.0 x 4.5 cm) collected from the z2HS unit (Hauptsalz of the second Zechstein cycle) at a depth of between 540-700 m of the Asse mine, Germany. Impurities consist of minor amounts 4

ACCEPTED MANUSCRIPT (≤ 1 wt.-%) of anhydrite and polyhalite, and the main constituent is halite. Cuboids (6.0 x6.0 x 3.5 cm) without an SPO were prepared from samples (6.0 x 6.0 x 6.0 cm), which also derived from the z2HS unit from the Asse mine. Photos were made of the cuboids before deformation. A thick section of the YZ plane was prepared for microstructural analysis of the starting material.

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For the deformation experiments we used a specially designed coaxial deformation apparatus,

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described in detail in Zulauf et al. (2009) (Fig. 2). In this deformation machine, large (up to 18

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cm) cubic samples can be deformed under constrictional, plane or flattening conditions (Fig. 2). After the sample is loaded into the machine, the four plates are heated up slowly (12°C/h)

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until the target temperature of 345°C is reached. The temperature in each plate is measured by seven thermocouples, and the uncertainty is less than ±0.1 °C. Some space is left between the

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plates and the sample to account for the thermal expansion of the sample during heating. After the target temperature is attained, the plates are slowly moved into contact with the sample.

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Then the sample is left overnight to make sure the entire sample reached the target temperature.

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Initial experiments have shown that the sample reaches the same temperature of the plates after three hours (Zulauf et al., 2009).

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During plane strain, two sides of the cuboid sample (6.0 cm) are bounded by the plates (Y direction); the short axes of the sample (3.5 cm) can extent in the front and back (X) direction

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(Fig. 2). During the deformation experiment, the bottom plate moves towards the top plate at a speed of 1mm/day during the experiment (vertical, Z direction in Fig. 2). In the Y (horizontal) direction the plates do not converge, however the left bounding plate is moved up (passively) by the movement of the bottom plate (Fig. 2). We use the longitudinal strain, e, during our experiments (change in length divided by initial length), therefore, as the starting length is 60 mm, a shortening strain of -10% (6 mm) in the Z direction is achieved after 6 days. The sample elongates in the X direction (starting length is 35 mm). During the experiment, the stress is measured in the Z and Y direction by point load cells (yellow dots in Figs. 1 and 2). The nominal 5

ACCEPTED MANUSCRIPT load bearing capacity of both load cells is 72 kg and therefore the maximum applied stress in both directions is set to 4.6 MPa. Due to this load limit and to represent stress experienced by rock salt in nature, we perform the experiments at elevated temperature. Temperatures that rock salt experience in nature, and temperatures that are relevant for engineering, are in the range of 20-200°C (Urai et al., 2008).

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After the target strain is reached, the plate movement is stopped, and the heating is turned off.

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Twelve hours after shutting down the heating, the plates are at ~65°C. After the plates are

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cooled down to room temperature, the plates are carefully moved apart and the sample is taken out. A thick section is made parallel to the XZ plane, at least 1 cm away from the edge of the

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sample to avoid boundary effects.

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2.2 Microstructural analysis

In order to visualize the subgrain and grain boundaries, the thick sections are etched for 10-20

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s with a NaCl unsaturated solution (~5.5 molar) and quickly cleaned with n-hexane spray (Urai

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et al., 1987). The thick sections of the samples before and after deformation were analysed with transmitted and reflected optical light microscopy. Photos with a small magnification were

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taken from the whole thick sections in order to determine the grain size. These photos were stitched together with Image Composite Editor (ICE, http://research.microsoft.com/en-

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us/um/redmond/projects/ice/). Tracing of the grain boundaries was done on these stitched photos in Adobe Photoshop, and the grain areas were calculated with ImageJ (https://imagej.nih.gov/ij/). The aspect ratio was calculated by dividing the long and short axes of the fitted ellipse. Photos of selected grains were taken with a higher magnification. These photos were used to trace subgrain boundaries in Adobe Photoshop and subgrain area calculations of these traced boundaries with ImageJ. The areas of the (sub)grains were used to calculate the equivalent circular diameters (ECD). At least two grains of each thick section were used to calculate the subgrain size. 6

ACCEPTED MANUSCRIPT Interesting areas that were away from the edges of the sample (in order to exclude boundary effects), were chosen for electron backscatter diffraction (EBSD) analyses. The analyses were performed on a JEOL JSM-6490 Scanning Electron Microscope (SEM) with an acceleration voltage of 15 kV and a beam current of ~8 nA. The step size was chosen between 2 and 12 µm, depending on the magnification. For the data acquisition, the program Flamenco (Oxford

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Channel 5) in combination with a Nordlys camera (Oxford Instruments) was used. The data

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was processed with Oxford Channel 5 software. Isolated points that were misindexed were

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removed (wild spikes), followed by a removal of some zero solutions using a minimum of six indexed neighbours. This last procedure replaces the non-indexed point by the most common

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orientation of six neighbours. An orientation averaging filter (Kuwahara filter, size 3x3 pixel) was applied to improve the orientation accuracy, at the expense of the spatial resolution

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(Humphreys et al., 2001). Orientation maps and equal area, lower hemisphere pole figures and/or inverse pole figures (IPF) were generated using the Channel 5 software Tango and

3. Results

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3.1 Starting material

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Mambo.

The average halite grain size in the starting material is 2.0-2.8 mm (Fig. 3A, Table 1) with a

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large variation between minimum and maximum grain sizes (88 µm and 9.8mm, respectively, see standard deviation in Table 1). Some grains contain subgrains, which have an average size of around 200 µm (Table 1) with a large variation (standard deviation up to 196 µm, Table 1). The size of the subgrains is related to the differential stress by the equation (Carter et al., 1993; Schléder and Urai, 2005): D = 215 -1.15

(1)

Where D is the subgrain size (µm) and  is the differential stress (MPa).

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ACCEPTED MANUSCRIPT The calculated stresses range from 0.9 – 1.4 MPa for the starting material using the average subgrain size. One of the samples without an SPO contains a grain with relatively small subgrains around 75 µm, corresponding to a much higher calculated stress of 3.3 MPa. The subgrain boundaries have a relatively small misorientation (mainly 1-5°, Fig. 3C). Some anhydrite is present in all the samples (Fig. 3B). Fluid inclusions are often found at the

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halite grain boundaries but also within grains. Some samples show bands of fluid inclusions

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that extend along the thin section. The average aspect ratio of the starting material does not vary

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between the samples with and without SPO and ranges between 2.0 and 2.5. The rose diagram shows that, as this is a natural sample, there is some variation in the long axis orientation of

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halite grains. The starting materials with an SPO do not have a CPO (Fig. 3D).

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3.2 Mechanical data

The measured shortening stress vs. shortening strain (vertical, Z direction) graph shows the

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similarity in mechanical response between the different experiments after a strain (ez) of ca. -

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10% (Fig. 4A). The two experiments on samples without an SPO show some variation in measured stress after these strains (blue lines in Fig. 4A). The measured stress in the

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experiments, where the SPO is oriented at 45° and 0° to the applied stress, is lower than the measured stress in the experiments without an SPO (Fig. 4A). In the experiment where the SPO

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is oriented at 90° to the applied stress, the measured shortening stress is higher than the measured shortening stress for the experiments without an SPO (Fig. 4A). All the experiments show strain hardening, and a real steady state is not attained in any of the experiments (Fig. 4A). Therefore, the measured stress is largest (0.92 MPa) in the experiment that continued to the largest strain (eZ = -36%). A striking difference between the individual experiments is obvious at a strain < -10%. The experiments with no SPO and ß=90° have a yield point that lies at smaller strain (~ -1.2% and -1.6%) than the experiments ß= 0° and 45° (around -3%). The yield point for the sample with 8

ACCEPTED MANUSCRIPT an SPO at 90° to the main shortening direction lies at the highest measured stress (0.45 MPa) of all experiments (Fig. 4A). The yield stress for the experiments ß= 0° and 45° is similar (0.3 MPa), and the rest of the stress-strain curve for these two samples is also similar. The yield point of these two samples is less distinct, and the stress-strain curve at low strain (<-5%) shows a gradual increase in measured stress (Fig. 4A).

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During the experiment, the stress in the Y direction is also measured (Fig. 4B). No extension or

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shortening takes place in this direction. The stress-strain curves in the Y direction show no clear

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yield point and two different strain hardening stages. The strain hardening is larger than in the Z direction. With an exception of the experiment with the SPO orientated at 45° to the

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shortening direction, the curves become similar at ez ~ -10% (Fig. 4B). The experiment with the SPO orientated at 45° progresses towards the other curves at ez ~-20%. This sample (ß =

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45°) shows the lowest measured stress in the Y direction.

The second stage of strain hardening occurs at eZ > ca. -25%. The stress-strain curves in this

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second stage are steeper than during the first strain hardening stage. The measured stresses in

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the Y direction are larger than the measured stress in the Z direction for all experiments.

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3.3 Macro- and microfabrics of experimentally deformed samples The optical appearance of the grains changes significantly during experimental deformation;

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from relatively clear to white-grey (milky) crystals (compare Fig. 3A with Fig.5). The shape of the deformed samples clearly reflects inhomogeneous deformation (Fig. 5). Two diagonal X axes remain undeformed, whereas the two other diagonal X axes experienced the maximum deformation (Fig. 5). The inhomogeneous deformation at the borders is due to the shear forces at the sides of the machine. These are caused by the difference in movement between the passive upward movement of the left plate (by the bottom plate), and stationary right plate (Fig. 2). Due to the inhomogeneous deformation, the thick sections of the deformed samples contain a strain gradient. All of the EBSD and (sub)grain analyses were done on the half of the thick section 9

ACCEPTED MANUSCRIPT that underwent the maximum amount of experimental deformation and away from the boundaries. As in the starting material, fluid inclusions are located at some of the grain boundaries and also within grains (Fig. 6A). The bands of fluid inclusions that extend throughout the thin section remain after deformation. The average grain size after deformation remains the same (1.7 - 2.5

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mm, with a large standard deviation of around 1.6 to 1.9 mm, Table 1). Some grain boundaries

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are bulging (Fig. 6A), indicative of grain boundary migration. The experiments without SPO

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develop an SPO during deformation, where the long axes of the grains are roughly parallel to the elongation axis (Fig. 7A). The pole figures indicate that, although an SPO develops during

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deformation, a CPO is not discernable from the data (Fig. 7B).

Even though the cooling down of the experiment to ~30 °C takes around 24 hours,

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microstructures are preserved. The subgrain size decreased substantially during experimental deformation and ranges from 34-55 µm (Table 1, Figs. 8A and 9A) corresponding to calculated

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stresses of 3.4-5.0 MPa. No correlation between strain and subgrain size is evident from the

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data. If we take into account the large standard deviation in the subgrain size (up to 51 µm), the range in calculated stresses is also large (around 2-22 MPa, with unrealistic values up to 1735

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MPa for one of the samples without SPO, see Table 1). Taking into account the large standard deviation, the stresses calculated from the subgrains are still higher than the maximum stresses

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measured by the point load cells in the vertical (0.92 MPa) and horizontal direction (2.5 MPa) except for the sample “No SPO 1” (Fig. 4). In addition to the decrease in subgrain size, a larger volume fraction of grains contain subgrains after experimental deformation (Figs. 8A and 9A). Some grains without subgrains occur in every deformed sample (Fig. 6B) indicating grain boundary migration recrystallization. The subgrains are mainly equiaxed (Fig. 8A). Subgrains in some grains display boundaries, which are aligned throughout the grain. These subgrain boundaries are always at an angle to the X direction (Figs. 8A and 9A), but the angle changes from grain to grain. One grain of the 10

ACCEPTED MANUSCRIPT experiment ß = 45° and -20% strain shows the alignment of boundaries in two directions (area C in Fig. 9A). Some grains of this experiment contain alternating bands with small and large subgrains (Fig. 9B). These alternating bands have also been observed in the experiment with ß = 90°. The small subgrains (red coloured bands in Fig. 9B) have, on average, boundaries with a larger misorientation than the large subgrains (mainly 1-5°, blue bands in Fig. 9B). The

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orientation data of two grains that contain the alternating bands show the development of

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extended high-angle boundaries (Figs. 9B and C). The misorientation profile shows that the

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boundary of the subgrain bands can have large misorientations (i.e. up to 40°, see misorientation profiles in Fig 9). In addition, some new subgrain-sized grains are formed in the bands (see

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arrows in Fig. 9B and C).

Representative EBSD maps of equiaxed subgrains (Figs. 8B and C) show the small

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misorientation of the equiaxed subgrain boundaries (mainly 1-5°). Some stretches of subgrain boundaries have larger misorientations of 5-10° and >10° (Figs. 8B and C). None of the newly

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developed grain boundaries (i.e. boundaries with a misorientation >10°) encircle a single

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subgrain and no new subgrain-sized grains are formed.

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4. Discussion

4.1 Mechanical data and the effect of SPO

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As the experimental strain is not homogenously distributed in the deformed samples (Fig. 5), the mechanical data cannot be used quantitatively, but only as a comparison between the different experiments. The inhomogeneous deformation is assumed to be related to friction between the sample and the walls of the machine. As not the complete sample is deformed, the calculation of the shortening strain, eZ, is not correct. The initial length of the sample that is actually experimentally deformed is shorter than the total initial length of the sample (i.e. 6 cm). The shortening strain, eZ, in the experimentally deformed domain is therefore larger, and the strain rate, ėZ, is faster than assumed. The friction in the machine might have contributed to the 11

ACCEPTED MANUSCRIPT fact that the experiments did not attain a steady state deformation, but instead show strain hardening (Fig. 4). The friction in the machine can also account for the high stresses measured in the Y direction. In cases of pure shear, the stresses measured in the Y direction should be half the stresses measured in the Z direction and show a similar stress-strain curve. The high stresses in the Y

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direction combined with the shape of the deformed samples indicate that in addition to the plane

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strain deformation, some shear stresses acted on the sample. With increasing strain, an

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increasing large component of shear stresses will have acted on the samples. The orientation of these shear stresses with respect to the SPO is not straightforward, and therefore the

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interpretation of SPO vs. Z is also not straightforward. The larger average stresses (3.4-5.0 MPa, see Table 1) calculated from the average subgrain sizes indicate that the stresses measured with

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the load cell in the Y and Z direction are not representative for the stresses experienced by the samples, which could also be explained by the inhomogeneous deformation.

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Even though there are some major issues with the experimental set up, we can still compare the

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experiments, as sample size and deformation conditions were the same in each experiment. The mechanical data obtained along Z, indicate that if eZ > -10%, the SPO does not have a significant

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influence on the mechanical behaviour of the investigated samples of rock salt. The difference in measured stress between the two samples without an SPO indicates the variation expected

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due to the natural variation of samples. After -10% strain, the variation between these samples is equal to the variation between the experiments with an SPO and without an SPO. Nevertheless, it is interesting to note that the sample with an SPO oriented at 90° to the Z direction is the strongest, and the ones with an SPO oriented at 45° and 0° to the Z direction are the weakest. In contrast to the similar mechanical response after eZ = -10%, the difference in mechanical response at the beginning of the experiment is significant. This could be related to both the presence and evolution of the SPO during deformation. The experiments without an initial SPO 12

ACCEPTED MANUSCRIPT develop an SPO with the grains elongated in the X direction after eZ = -20% (Fig. 7A). However, no experiment without SPO was carried out at smaller shortening strains, and the development of this SPO could take place at smaller strains. Looking at the similarity between the experiments after eZ = -10%, it is likely that this SPO is produced after eZ = -10% . This would imply that under the deformation conditions used in the present study, an SPO in rock

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salt is mechanically only important at small shortening strains, due to a fast grain boundary

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alignment during deformation. However, a variation in measured stress between the

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experiments persists at the larger strains (Fig 4A).

The similar curves in the Y direction for all samples, except the 45° sample, indicate that the

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high measured stresses in the Y direction are not related to the starting SPO in the samples. Although friction, and the corresponding shear stresses, could explain the higher stresses

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measured in the Y direction, this does not explain the different stages of strain hardening. As the curves in the Y direction are similar in all the experiments, we speculate that this strain

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hardening and strain hardening stages are related to the development of SPO during the

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deformation (Fig. 7A). This could lead to inhomogeneous deformation due to anisotropy and larger measured stresses in the Y direction. However, this difference between the measured

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stresses in the Z and Y directions is then unrelated to the initial SPO. Similar stages in strain hardening have been observed in previous experiments carried out under bulk pure constriction

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on unfoliated rock salt (Zulauf et al., 2009; Linckens et al., 2016).

4.2 Deformation mechanisms and influence of SPO The ubiquitous occurrence of subgrains, and the flattened grains in the deformed samples (Figs. 6A, B, 7A) indicate that, as expected, dislocation creep was active during experimental deformation. The large grain size in the starting material (average of ~2.0-2.8 mm, Table 1) favours the activation of dislocation creep, but is hardly compatible with pressure solution, which is sensitive to the grain size. In addition, it is possible that diffusion and therefore 13

ACCEPTED MANUSCRIPT pressure solution is less effective in the samples with an SPO due to the elongated grains (Raj and Ashby, 1971). However, although many grains have a high aspect ratio, the average aspect ratio in the initial samples is relatively small (2.0-2.5, Table 1). The smaller grains often have smaller aspect ratios (Fig. 3B) and it is these smaller grains that are more likely to deform by pressure solution creep, based on the deformation mechanism equations.

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When we use the flow law of dislocation creep for low stresses and slow strain rates (Carter et

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al., 1993), a deformation at T = 345°C and ėZ = 4 x 10-7 s-1 (we assume that only half of the

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sample is actually experimentally deformed) will result in a differential stress of 4.0 MPa, which fits well with the observed subgrain size. When combing this flow law for dislocation creep

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with the pressure solution flow law for rock salt from Spiers and Carter (1998), the grain size at which pressure solution would be faster than dislocation creep can be put at around 420 µm.

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It is therefore possible that the smaller grains in the sample deformed by pressure solution. However, this is difficult to assess just by the microstructures of the etched thick sections. The

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relatively small grains (i.e. <500 µm) show a subgrain structure, which indicates the activity of

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dislocation creep in these smaller grains.

Grain boundary orientation during dislocation creep could be important if the deformation is

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accommodated by grain boundary sliding (GBS). GBS might be easier when the grain boundaries are aligned at 45° to the applied stress. The mechanical data show some variation

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in strength, with 0° and 45° being the weakest and 90° being the strongest orientation. Previous brittle deformation experiments on foliated rocks (e.g. slate, Donath (1961); phyllite, Ramamurthy et al. (1993); bedded rock salt, Dubey and Gairola (2008)) found a U-shaped ß vs. strength curve, where 0° and 90° have a similar high strength and are the strongest, and the 3040° orientation are the weakest. At the 30-40° the shear fractures that form during the experimental deformation follow the pre-existing foliation, explaining the low strength of these orientations. Analogue models of shear fractures in anisotropic material show that models with ß= 90° show a stress peak 1.4 to 2.6 times higher than the models with ß=60° (Gomez-Rivas 14

ACCEPTED MANUSCRIPT and Griera, 2012). With ongoing deformation the stress-strain curves converge in these analogue models. Previous ductile deformation experiments on foliated rocks (mylonitic gneiss) (Liu et al., 2016) perpendicular (ß=90°) and parallel (ß=0°) to the foliation show that the strength of samples shortened perpendicular to the foliation is larger. In the experiments on the mylonitic gneiss,

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the difference in strength is explained by the formation of a new foliation in the samples

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deformed perpendicular to the foliation. The original foliation is destroyed in these samples, in

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contrast to the samples deformed parallel to the foliation that are deformed along their original foliation. However, ductile deformation of similar samples (mylonitic gneiss) with their

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foliation at 30°, 45°, and 60° to the main shortening direction were weaker than both the 0° and 90° orientations, with 45° the weakest orientation (Liu et al., 2017). This is not what we observe

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in our experiments, where the strength of the 45° samples is similar to the 0° samples. However, as stated before, it is likely that, in addition to the shortening stress, shear stresses acted on the

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sample. The angle of the SPO to the shear stresses will be different to the angle between SPO

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and shortening stress. Therefore, a comparison between our experiments and these previous experiments done on mylonites is not straightforward. We do observe, similar as in the

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mylonites, a development of a new foliation (SPO) with deformation, which is parallel to the elongation direction X (Fig. 7A) and the short axis parallel to Z. Looking at the sketches of the

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experiments (Fig. 1), the ß=90° and ß=45° experiments should already have this SPO at the beginning of the experiment and thus might be expected to deform easier. On the other hand, we used natural samples and selected our initial samples based on the SPO in the YZ plane (i.e. front side of the cubes in the sketch). In an ideal case, the SPO would be similar as depicted in the sketches, however the grains often do not show as clear of a SPO in the other directions. The strength differences derived from the experiments do suggest that more stress is needed to evolve the SPO for the 90° samples into the SPO formed during the deformation. 4.3 Microstructures 15

ACCEPTED MANUSCRIPT The experimentally derived microstructures are similar in each of the experiments and independent of the SPO. No CPO is visible from the orientation measurements (Fig. 7B), however, due to the coarse grain size, only around 100 grains were measured. More grains have to be measured in order to say something conclusive about CPO development in the deformed samples. A lack of CPO is in contrast to results on previous deformation experiment done on

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rock salt in the dislocation creep field (e.g. Franssen, 1994; Pennock et al., 2005; Armann,

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2008).

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Subgrains have similar sizes, shapes and misorientation angle (mainly 1-5°) in all experiments (Figs. 8 and 9). Apart from one exception (Fig. 9B), there is no evidence for subgrain rotation

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recrystallization in the experiments. The same small misorientation angles were also observed in constriction experiments done at similar deformation conditions (Linckens et al., 2016).

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Pennock et al. (2005) also found that the majority of the equiaxed subgrain boundaries have misorientations less than 5° after a natural strain of 50%. Their experiments were done on fine-

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grained (120-400µm), dry rock salt at 165°C. They also observed a small dependence of

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average subgrain boundary misorientation on initial grain size, with smaller average subgrain boundary misorientations for larger initial grain sizes. The grain size in our experiments were

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almost a factor ten larger, which could therefore lead to smaller average subgrain boundary misorientations. In addition, Armann (2008) also observed in their torsion experiments on fine

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grained (150-300 µm) synthetic rock salt, that SGR was dominant only after a shear strain of 600% (at 100°C). The lack of SGR in our samples it therefore likely related to the relatively small strains and larger grain sizes. Grain boundary migration occurs in the samples (Fig. 6) but is not dominant, and the subgrainrich microstructure is preserved in most grains. This microstructure is similar to the microstructures observed in deformation experiments done by Franssen (1994) under the same deformation conditions.

16

ACCEPTED MANUSCRIPT Alternating bands with large and small subgrains were also previously observed in constriction experiments at similar deformation conditions (Linckens et al., 2016). The difference with these previously observed bands is that the long boundaries that border the bands in these experiments have a large misorientation (i.e. >10°). These newly developed high angle boundaries bordering the bands, might not be simple “subgrain boundaries” but orientation splitting boundaries as

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observed by Pennock et al. (2004) and described by Drury and Pennock (2007). Drury and

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Pennock (2007) state that these boundaries develop only in grains with an unstable initial

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orientation, and the grain is split into the different orientations to activate different slip systems. An unstable initial orientation is an orientation that is not favourable for slip on the easy slip

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system of halite, i.e. {110}<110>. However, at the high temperatures in our experiments the critical resolved shear stress (CRSS) becomes similar for the three different slip systems in

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halite, {110}<110>, {100}<110> and {111}<110> (Carter and Heard, 1970; Skrotzki and Haasen, 1981) and they are all easy to activate. Armann (2004) only observed the orientation

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splitting boundaries at relatively low temperatures (i.e. 100°C) in halite torsion experiments,

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and not at higher temperature (200°C and 300°C). They explained this observation by the similar low CRSS of the different slip systems at the higher temperatures, which makes it

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unnecessary for the grains to split up in bands. Subgrain bands with alternating orientations were also observed during modelling of subgrain rotation recrystallization, during shearing of

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halite polycrystals (Gomez-Rivas et al., 2017). They also show that all three different slip systems accommodate the strain during the shearing of halite. Similar domains with high-angle boundaries have been observed during deformation experiments on a high purity, single phase, Al-0.13% Mg Alloy (Apps et al., 2003) and during deformation of homogeneous b.c.c and f.c.c. metals (Kuhlmann-Wilsdorf, 1999). Apps et al. (2003) define these domains as granular scale primary deformation bands and KuhlmannWilsdorf (1999) as regular deformation bands. They also state that these bands form because it is energetically easier for a constrained grain to deform by splitting into bands, operating on 17

ACCEPTED MANUSCRIPT fewer than the five independent slip systems required for homogeneous deformation, with strain distributed over the different bands so as to collectively maintain compatibility with its neighbours (Kuhlmann-Wilsdorf, 1999; Apps et al., 2003). They also observe that the primary deformation bands contain secondary deformation bands, or cell block structures, which are also visible in our optical light microscope image (Fig. 9A, they are less clear in the EBSD

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maps). The misorientations evolve at a lower rate in these secondary deformation bands than in

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the primary deformation bands (Apps et al. (2003) and references therein). This is also observed

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in our experiments; the EBSD maps (Figs. 8C and D) show that the misorientation angle of the subgrains within the bands is much smaller than the misorientation angle of the boundaries at

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the border of the bands. The formation of these deformation bands is typical in the first stage of grain subdivision in a coarse grained single-phase alloy (Apps et al., 2003) and results in the

primary deformation band boundaries.

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generation of new widely spaced deformation-induced high angle grain boundaries at the

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The deformation bands in our deformed samples likely form in those grains, where the

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surrounding grains make it easier for the constrained grain to split into bands and to deform on fewer slip systems as suggested by Apps et al. (2003) and Drury and Pennock (2007). We

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postulate that with ongoing deformation, the grains that contain these deformation bands can quickly form new grains and recrystallize much faster than grains that do not form these

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deformation bands.

5. Conclusions and outlook The microfabrics of the experimentally deformed samples of rock salt suggest that most of the strain was accommodated by dislocation creep, however the samples do not show a clear CPO before and after the experiments. Equiaxed subgrains with relatively small misorientation angles (mainly 1-5°) develop in all deformed samples (Fig. 10). Some grains have no subgrains, and together with irregular and bulging grain boundaries are indications that grain boundary 18

ACCEPTED MANUSCRIPT migration occurred. In some of the experiments alternating bands with small and bigger subgrains occur within grains (Fig. 10). The boundaries of the bands are (sub)grain boundaries that are aligned throughout the grain. These band boundaries can have high misorientation angles, up to 40°, and are therefore newly formed grain boundaries. In some of these deformation bands, subgrain sized new grains (i.e. misorientation >10°) develop, which

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indicates that within these bands, subgrain rotation recrystallization is much faster than within

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grains that do not develop these deformation bands.

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Due to friction between the sample interfaces and bounding plates, the samples are inhomogeneously deformed. It is likely that in addition to the shortening stress, some shear

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stresses acted on the samples. In addition, friction might have contributed to the fact that the experiments did not achieve steady state deformation. Therefore, the mechanical data can only

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be used as a relative measure of the effect of SPO on deformation behaviour. Under the experimental conditions used in the present studies, an SPO of halite has an effect on the

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deformation of rock salt up to a shortening strain (eZ) of ca. -10% (Fig. 10). The samples with

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the long axis of the grain shape fabric (SPO) orientated at 0° and 45° to Z are weaker than the samples without an SPO. In contrast, the samples that have the long axis of the SPO oriented

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at 90° to Z are stronger than the samples without an SPO (Fig. 10). At larger strains (i.e. eZ > 10%), the influence of an initial SPO on the strength decreases (grey area in Fig. 10). The

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variation in measured stress between two samples with no SPO is similar to the variation in measured stress between these samples and samples with an SPO. An exception is the 90° oriented sample that is still stronger than the samples without an SPO. A new SPO is formed in all samples with the long axis of the grain shape fabric being subparallel to the principal stretching axis, X (Fig. 10). Even though the experimental set up is not ideal, the experiments show that an SPO of halite has an effect on the mechanical behaviour of rock salt. Therefore, the initial SPO of rock salt

19

ACCEPTED MANUSCRIPT has to be taken into account when building a repository for nuclear waste and could have an effect on the stability of caverns. In further experiments, the friction will be decreased in order to achieve homogeneous deformation of the samples. In addition, experiments on finer grained samples with an SPO would be of interest. These experiments can determine the effect of an SPO on the viscosity of

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rock salt, when pressure solution and grain boundary sliding are the dominant deformation

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processes.

Acknowledgements

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This research was funded by a grant of the Deutsche Forschunsgemeinschaft (DFG, grant Zu73/28-1). We would like to acknowledge the help of Maria Bladt and Nils Prawitz (Goethe

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University, Frankfurt) in preparing the thin sections, and Maik Gern, Ralf Götze and Tobias Faust (BGR) for the help with the sample preparation. All data used in this study are available

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on request from the corresponding author. We thank Colin Peach and an anonymous reviewer

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for constructive comments on a previous version of the manuscript and Enrique Gomez-Rivas,

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R.K. Dubey and the editor Philippe Agard for their constructive comments.

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ACCEPTED MANUSCRIPT Figure captions Fig. 1. Sketch of experiments with the different orientations of the long axis of the grain-shape fabric with respect to the main shortening direction. ß is the angle between the main shortening direction and the orientation of the long axis of halite grains. Vertical is the shortening axis, Z, horizontal is the axis of no change, Y, and the axis coming out of the plane is the elongation

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axis, X. Also sketched is a sample without SPO. The yellow circles are the locations of the load

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cells where the stress is measured during the experiments.

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Fig. 2. Photo of the coaxial deformation apparatus. Indicated with black arrows is the movement direction of the plates during plane strain deformation. The lower plate moves upwards with

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1mm/day. The left plate moves passively with the lower plate. The other two plates remain stationary. The yellow ellipses show the location of the two load cells in horizontal and vertical

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direction. The shortening axis Z, stationary axis Y and elongation axis X are also indicated. The sample can freely extend in the X direction. To hold the temperature constant during the

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experiment, isolating plates in the front and back are mounted on the machine. Fig. 3. Starting material. A. The cuboid (6.0 x 6.0 x 3.5 cm) before deformation with an SPO and ß = 0°. The SPO is vertical and the sample is shortened parallel to this SPO. B. Optical

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reflected light microscope image of a thick section of an initial sample. Traced in red are the

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grain boundaries. Large grains have a high aspect ratio, whereas smaller grains often have a smaller aspect ratio. Some anhydrite inclusions are visible (arrows). C. EBSD orientation map with inverse pole figure colours (IPF) in the X direction. The colours indicate which of the crystallographic axes of halite lies in the X direction (where X is horizontal). The white lines show a misorientation between measured points of 1-5°, the black lines of 5-10°. D. Rose diagram of the halite long axes orientations. E. IPF of 125 manually measured halite grain orientations, indicating no CPO.

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ACCEPTED MANUSCRIPT Fig. 4. Mechanical data of the experiments showing the measured stress (MPa) vs. shortening strain (%). A. Measured stress in the vertical, shortening direction, Z vs. shortening strain and B. Measured stress in the horizontal, Y direction vs. shortening strain. Fig. 5. Cube of experiment “no SPO 2” after deformation (ez = -36%, ex = 62%) with the X, Y and Z axis and ZX, YZ and YX planes. The horizontal load cell imprint is visible on the wall

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parallel to the XZ principal plane. Clear from this photo is the inhomogeneous deformation.

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Due to friction, there is almost no elongation along the X axis at the right bottom and left top of

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the sample. In contrast, along the X axes at the right top and the left bottom, the sample is elongated.

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Fig. 6. Optical light images of microstructures after deformation (X horizontal, Z vertical). A. Reflected light image of the ß=45° experiment showing a bulging grain boundary (stippled

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line). All grains contain subgrain boundaries (thinner lines). The vertical stripes (also visible in the image in B) are due to polishing and etching of the thick section. B. Reflected light image

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of the experiment “no SPO 1” after deformation, showing two grains, one without subgrains

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(indicated as A) and one with subgrains (indicated as B). C. Transmitted light image of the experiment “no SPO 1” after deformation showing fluids on a bulging grain boundary. The

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fluids continue at depth along the grain boundary. Fig. 7. Orientation data. A. Rose diagram showing the orientation of the long axis of halite

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grains after deformation of experiment “no SPO 1”. The long axes are oriented roughly parallel to X and a SPO develops after deformation. B. Corresponding CPO of the sample. A CPO is not discernable from the data. Fig. 8. Microfabrics of deformed samples (X horizontal, Z vertical). A. Reflected light microscope image of sample ß = 0° after deformation. Horizontal stripes are due to polishing and etching. The thicker lines are grain boundaries, the thinner lines subgrain boundaries. The subgrains are mainly equigranular, in the middle of the image, including were box C is, the 28

ACCEPTED MANUSCRIPT subgrain boundaries show an alignment at around 45° to the X axis. In this region bands with larger subgrains alternate with bands with much smaller subgrains. B. EBSD orientation map with IPF colouring, showing which of the halite axis lies parallel to the horizontal direction. Also plotted are three subgrain boundary types with different misorientation angles. C. EBSD orientation map with IPF colouring of the banded area.

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Fig. 9. Microfabrics of deformed samples (X horizontal, Z vertical). A. Reflected light

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microscope image of sample ß=45°, showing multiple grains with subgrains. Some grains have

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alternating bands of small and larger subgrains (see arrows). Other grains show equiaxed subgrains throughout and no alternating bands of small and large subgrains (see ellipse in the

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middle of the image). Indicated are the locations of the EBSD mappings. B. Detailed EBSD map of the subgrain bands with misorientation boundaries and the location of the misorientation

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profile. White arrows indicate newly developed subgrain sized grains. The colours indicate which of the halite axis is parallel to the X axis (horizontal). The pole figures below the EBSD

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map show the rotation within the grains. The misorientation profile shows the large

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misorientation at the boundary of the bands with small subgrains (up to 40°). C. EBSD map of subgrain bands. Black arrows show subgrains that are almost completely surrounded by a high

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angle grain boundary (i.e. >10°). Indicated is the location of the misorientation profile. Below the EBSD mapping are the pole figures of halite axis, showing the rotation within the grains.

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The misorientation profile shows the misorientation angle deviation from the starting point, which is not larger than 20°. Fig. 10. Overview of the results with the stress-strain curves of the different experiments and sketches of the starting and final microstructures. The grey area indicates the shortening strains at which the different experiments do not show a significant difference in the vertical stress.

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ACCEPTED MANUSCRIPT Table 1 Experimental data of the initial (i) and deformed samples (def); ß is the angle between the main shortening direction and the long axis of the grain shape fabric. eZ is strain in the shortening direction. D is the grain size, D st. dev. is the standard deviation (1σ) of the grain size, A.R. is the aspect

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ratio, d is the subgrain size, d st. dev. is the standard deviation of the subgrain size (1σ) and σ is the stress calculated from the subgrain size using the

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subgrain size and the equation from [Carter et al., 1993; Schléder and Urai, 2005] and σdef range the range in stress during deformation from the

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subgrain size and standard deviation.

ß

0° 45° 90° No SPO 1 No SPO 2

eZ (%)

-30 -20 -20 -20 -36

Di (mm)

2.4 2.8 2.3 2.0 2.2

Di A.R. st.dev. undef (mm)

2.1 1.8 2.0 1.7 2.2

2.5 2 2.2 2.2 2.0

di (µm)

di st. dev. (µm)

D E

C C

T P E 230 214 202 150 217

σi (MPa)

140 196 149 112 134

M

N A

0.9 1.0 1.1 1.4 1.0

A

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Ddef (mm)

Ddef st. dev. (mm)

A.R. def

ddef (µm)

ddef st.dev. (µm)

σdef (MPa)

σdef range (MPa)

2.1 2.5 2.5 1.9 1.7

1.8 1.9 1.7 1.6 1.7

2.3 2.3 3.3 3.2 2.4

34 47 53 51 44

26 32 34 51 34

5.0 3.8 3.4 3.5 3.9

2.9-21.5 2.4-10.1 2.0-13.0 1.9-1735 2.4-14.4

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Highlights Coarse-grained rock salt samples with and without SPO were experimentally deformed

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Until z of -10%, samples with ß = 0° and 45° are weaker than samples without SPO

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Until z of -10%, sample with ß = 90° is stronger than the samples without an SPO

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At z >-10% strengths are similar, new SPO forms with long grain axis parallel to X

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RI

PT



31

Figure 1

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Figure 3

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Figure 9