Deformation of upper mantle rocks with contrasting initial fabrics in axial extension
Walid Ben Ismail, Andréa Tommasi, Marco Antonio Lopez Sanchez, Ernest H. Rutter, Fabrice Barou
DDeformation of upper mantle rocks with contrasting initial fabrics in axial extension
Walid Ben Ismail , Andréa Tommasi , Marco Antonio Lopez Sanchez , Ernest H. Rutter , Fabrice Barou Rock Deformation Laboratory, Dept. Earth Sciences, University of Manchester, UK Géosciences Montpellier, CNRS & Université de Montpellier, Montpellier, France submitted to Tectonophysics * Corresponding author: [email protected]
Now at Schlumberger Oilfield Services, The Woodland, Texas, USA bstract (292 words)
To characterize the role of the microstructure (notably grain size) and crystal-preferred orientation (CPO) on the deformation of mantle rocks, we performed axial extension experiments at 1200°C and 300 MPa confining pressure on three natural upper mantle peridotites: a fine-grained mylonitic harzburgite with a weak olivine CPO and two coarse-grained well-equilibrated dunites with olivine CPO of variable intensity. Despite the contrasting initial microstructure and olivine CPO, yield stresses show a limited range of variation (115-165±5 MPa). Fine- and coarse-grained peridotites show, nevertheless, different evolutions of both mechanical behavior and microstructure. In the fine-grained harzburgite, necking produced decrease of the apparent differential stress. Focusing of strain and stress resulted in increase of the olivine CPO intensity and recrystallized fraction and decrease of the recrystallized grain size in the neck. Analysis of the stresses and strains in the neck points to softening in response to the evolution of the microstructure and CPO. In contrast, necking of the coarse-grained dunite samples was not systematically accompanied by a decrease in apparent differential stress. This implies hardening, consistently with the increase in bulk intragranular misorientation with increasing strain in these samples. All coarse-grained dunites displayed a highly heterogeneous deformation. Crystals well oriented to deform by dislocation glide became elongated and developed marked undulose extinction, whereas crystals in hard orientations remained almost undeformed. In the neck, stress and strain concentration (local stresses and extensional strains attained up to 365±15 MPa and 240%) resulted in the formation of kinks in “hard” crystals, dynamic recrystallization in “soft” crystals and, where the axial stress overcame the confining pressure, development of extensional fractures. We interpret the more effective softening of the fine-grained sample as due to easier dynamic recrystallization, probably due to the higher proportion of grain boundaries acting as nucleation sites.
Keywords : olivine, microstructure, grain size, crystal preferred orientations, experimental deformation, anisotropy, dislocation creep, recrystallization, kinks, hardening, softening . Introduction
The deformation processes and, by consequence, the rheology of mantle rocks depend on their microstructure, in particular on the grain size, which controls the relative contribution of grain interiors and boundaries to the deformation (Hirth and Kohlstedt, 2003; Nicolas and Poirier, 1976). They also depend on the olivine crystals’ orientation, since crystal preferred orientation (CPO) may result in significant viscoplastic anisotropy (Hansen et al., 2016, 2012; Mameri et al., 2019; Tommasi et al., 2009; Tommasi and Vauchez, 2001). In nature, both parameters are extremely variable and evolve in response to local deformation and thermal histories. Grain sizes in naturally deformed peridotites are dominantly millimetric, but they may range from a few microns in ultramylonites (e.g., Hidas et al., 2016; Kaczmarek and Tommasi, 2011; Newman et al., 1999) to centimeters in cratonic xenoliths (e.g., Baptiste et al., 2012; Vauchez et al., 2005) and in dunites deformed in presence of melts (e.g., Higgie and Tommasi, 2012; Tommasi et al., 2017). Olivine CPO intensities also vary from very weak (J-indexes ≤
2) to very strong (J-indexes >10) with a peak at moderate strength CPO (J-indexes=4-5; Tommasi and Vauchez, 2015). Most rheological data for olivine-rich rocks have been derived from axial compression experiments (e.g., Chopra and Paterson, 1981; Faul et al., 2011; Karato et al., 1986; Thieme et al., 2018; Zhao et al., 2009). At low strains, these experiments allow a precise determination of stress and strain as a function of time, resulting in reliable flow laws. However, beyond 25% shortening, the central part of the specimen is forced outwards the loading pistons and the deformation becomes inhomogeneous. Thus, most experiments are stopped at 10-15% axial shortening. This prevents the investigation of the effect of an evolving microstructure on the rheological behavior. Moreover, to ensure reproducibility, ost experiments were performed on synthetic olivine polycrystals with random CPO and fine-grain sizes (5-30 µ m). Axial compression experiments up to high strains ( ≤ µ m and moderate olivine CPO) showed, nevertheless, different evolutions of the CPO in samples compressed parallel, normal, or oblique to the preexisting foliation (Boneh and Skemer, 2014). However, a detailed analysis of the evolution of the microstructure and its influence on the mechanical behavior is unavailable. Development of deformation experiments in simple shear (Zhang et al., 2000; Zhang and Karato, 1995) and torsion (Bystricky et al., 2000; Demouchy et al., 2012; Hansen et al., 2014, 2012) allowed deformation of fine-grained synthetic olivine aggregates up to high shear strains (up to 20 in torsion tests). These experiments constrained the evolution of the microstructure and olivine CPO during simple shear and of the effect of this evolution on the mechanical behavior. They showed that dynamic recrystallization first accelerates the rotation of olivine crystals towards easy glide orientations and then stabilizes the CPO (Bystricky et al., 2000; Hansen et al., 2014), an observation that was corroborated by numerical modelling (Signorelli and Tommasi, 2015). Torsion tests also systematically displayed strain softening, probably due to both evolution of the CPO and dynamic recrystallization. However, torsion experiments cannot explore the influence of a large range of initial microstructures, since a high strength of the samples produces decoupling of the sample ends from the rotating piston. Axisymmetric extension experiments also allow attainment of large strains. They are widely used for testing of ductile metals and, although less frequent, have also been successfully applied to rocks (e.g., Brodie and Rutter, 2000; Hart, 1967; Heard, 1963; utter, 1998, 1995). Extension tests on synthetic aggregates of fine-grained iron-rich olivine (Fo50) were reported by Hansen et al. (2016), who used both extension and torsion tests to quantify the viscoplastic anisotropy due to an olivine CPO. In axial extension, the bulk strain may exceed 50%. However, the strain distribution in the sample is often heterogeneous, as geometric instability produces localized necking of the specimen if strain-rate softening due to the non-linearity of the flow law is not counteracted by microstructural hardening ( Hart, 1967; Rutter, 1998). Both stress and strain rate thus vary along the length of a necked sample. For flow at constant volume, the local axial strain is equal to the strain corresponding to the local reduction of area normal to the stretching direction. The stress distribution may also be reconstructed from the variation of the sectional area of the sample (Rutter, 1998). Microstructures and CPO formed at various stresses, strain rates, and finite strains are therefore preserved within a single sample, making extension tests particularly well suited to study the evolution of the microstructure and CPO as a function of strain and stress, in the same way as torsion tests performed on full cylinders. In this article, we examine the mechanical behavior and the evolution of the microstructure and CPO of olivine as a function of the finite strain in a series of extension experiments performed on three natural peridotites with varied initial microstructures and CPO. By comparing their mechanical behavior and microstructural evolution, we analyze the effect of the initial grain size and CPO on the yield strength and active deformation mechanisms and characterize the interplay between deformation and dynamic recrystallization on the evolution of the mechanical behavior. . Methods
Thirteen axial extension experiments were performed at the Rock Deformation Laboratory, University of Manchester, UK, using a gas-medium, internally-heated triaxial deformation apparatus (Paterson, 1970) modified for extension testing by incorporating a bayonet connector between the bottom loading piston and the top of the internal axial load cell. Cylinders of 10 mm diameter and 21-27 mm long were cored in different orientations relative to the preexisting fabric in the three starting materials (Table 1) to study the effect of the initial fabric on the deformation behavior and the resulting evolution of the microstructure and crystal preferred orientations. After coring, the cylinders were stored in an oven at 80°C until required for use. For the experiments, the samples were enclosed in a double iron jacket, the inner one capped by iron discs, which set the oxygen fugacity at the Fe-FeO buffer. All tests were performed at 1200 °C and 300 MPa confining pressure. Temperature is accurate by ±5°C over a length significantly larger than the sample, avoiding temperature heterogeneity as the sample is stretched. During confined extension tests, as per those presented here, the sample ends do not need to be gripped as the confining pressure pushes the sample against the unloading piston, as long as the axial differential load remains lower than the axial force due to the confining pressure. At the start of a test, the axial load is equal to that due to the confining pressure. During the experiment, withdrawing the piston reduces the axial load. All tests were unloaded at a constant rate of 2.5e-4 mm/s, corresponding to initial strain rates between 9.3e-6 and 1.2e-5 s -1 , depending on the length of the sample (Table 1). During the experiments, strain rate slowly decreases due to rogressive lengthening of the samples (8.6e-6 to 1.1e-5 s -1 at 10% of bulk strain) until necking, which results in a heterogeneous strain distribution and high strain rates in the neck. The strain rate enhancement depends on the length of the most intensely deforming region, but strain rates at the neck are often more than five-fold the bulk ones in highly strained samples. After the experiments, thin sections and polished blocks were cut parallel to the extension direction for optical observation of the microstructure and CPO measurement. Olivine and pyroxene crystallographic orientations were determined by indexation of electron back-scattered diffraction (EBSD) patterns generated on a field-emission scanning electron microscope – the Camscan Crystal Probe X500 FE at Geosciences Montpellier, equipped with the Oxford NordlysNano EBSD detector - and indexed using the AZtecHKL system. EBSD orientation maps of the entire recovered coarse peridotite samples, as well as of the starting material, were obtained with resolutions of 20 to 50 µm. In the highly strained samples, high-resolution (2 µm step) maps of the necking region were also made. For the fine-grained peridotite, two large-area maps were acquired: one in a low strain domain adjacent to the specimen end with a resolution of 2.5 µm and one at the center of the necking zone with a resolution of 1.5 µm. EBSD data analysis, that is, calculation of the orientation distribution functions (ODF) and of the intragranular misorientations, plotting of pole figures, quantification of microstructural parameters (grain sizes, shape, and orientation) and of the geometrically necessary dislocation (GND) densities based on the intragranular misorientations using the Kernel Average Misorientation (KAM) and the Grain Orientation Spread (GOS) proxies, was performed using the MTEX toolbox in Matlab (http://mtex-toolbox.github.io/; achmann et al., 2011, 2010; Hielscher and Schaeben, 2008). ODFs were calculated using a “de la Vallée Poussin” kernel function with a half-width of 10°. Grain boundaries were defined with a misorientation threshold at 15°. Recrystallized grains were segmented based on the grain orientation spread (GOS < 2°). On samples VS14 and VS15, a threshold on the area of the grains was used, in addition to the GOS, to discriminate porphyroclasts and recrystallized grains. Local differential stresses were estimated based on the olivine piezometer of Van der Wal et al. (1993), which was calibrated on experiments using similar starting materials and deformation conditions as those in the present study. We used the GrainSizeTools script v3 (Lopez-Sanchez, 2018) to convert the mean apparent grain sizes expressed as equivalent circular diameters obtained using MTEX to linear intercept values, as in the original piezometer, and a 3D scaling factor of 1.5.
3. Starting material
The starting material consisted of three naturally-deformed peridotites: a harzburgite (sample 90OA87) collected as a loose block derived from a km-scale low-temperature mylonitic zone in the Wuqba massif in the Oman ophiolite and two dunites (samples VS14 and VS15) sampled alongside the eastern boundary of the Balmuccia ultramafic massif in the Alps, at 45°50’15”N, 8°9’40”E. The Oman sample is a spinel-harzburgite (75% olivine Mg µ m in diameter (median at 14 µm), represents ca. 70% volume of the sample; the apparent area-weighted mean grain size is 170 µm. The olivine displays a weak CPO characterized by poor alignment of [100] parallel to the lineation (Fig. 1a). Thermal diffusivity measurements performed on this sample show an almost isotropic behavior, consistent with the weak CPO (Gibert et al., 2003). The composition and microstructure are coherent with its origin in a depleted oceanic lithosphere that has been deformed under low-temperature conditions (<1000°C) in a shear zone normal to the ridge axis (Nicolas and Boudier, 1995). The sample is exceptionally fresh, but minor serpentinization has occurred along some grain boundaries. The two dunites display an annealed microstructure characterized by 1-3 mm wide polygonal grains of iron-rich olivine (Mg ≤
1 mm in size, with no clear internal deformation features. Diopside crystals sometimes display thin amphibole rims and serpentinite films occur locally along grain boundaries. Dehydration of these hydrous phases produced localized partial melting pockets during the experiments (Supplementary Material Fig. S1). Spinel (~1%) occurs as small rounded inclusions within olivine grains or as anhedral, mm-size interstitial grains. The latter display iron-rich rims that continue as films along olivine-olivine grain boundaries. The annealed microstructure nd high iron-content of the dunites suggest significant thermal and chemical re-equilibration with basaltic magmas, consistent with their position as lenses outcropping in contact with metagabbros in the eastern border of the Balmuccia Massif (Boudier et al., 1984). Despite the similar annealed microstructures, dunite VS15 displays a strong orthorhombic olivine CPO, typical of deformation by dislocation creep with dominant activation of the [100](010) slip system, whereas VS14 has an almost isotropic olivine CPO (Fig. 1b,c).
4. Mechanical results
Despite the contrasting initial olivine grain size and CPO of the samples, yield stresses in the 10 experiments that could be brought to completion show a limited range of variation, between 105 MPa and 165 MPa (Fig. 2). The resolution of the internal load cell is 50 N, resulting in an estimated uncertainty of differential stress of ±5 MPa at low strains. The jacketing material contributes about 3% of the local stress value. Differential stresses reported were calculated assuming homogeneous area reduction at constant volume along the length of the sample. Reported strains are bulk strains – overall change in length (after correction for axial apparatus distortion) divided by original sample length. The fine-grained harzburgite 90OA87 displays the highest yield stress and the sample cored parallel to the maximum concentration of [010] axes in coarse-grained dunite VS15 (VS15-b1) exhibited the lowest yield stress. Most coarse-grained samples yielded between 110-150 MPa. However, for many samples, like VS14-4, VS14-7, VS14-9, VS15ab2, and VS15-a1, pinpointing the yield stress is subjective, since they show continuous immediately post-yield hardening up to 10 or even 20% of bulk extension (Fig. 2). he evolution of the mechanical behavior with increasing strain varies from sample to sample, reflecting differences in deformation behavior due to the contrasted initial microstructures and CPO. No attempt was made to correct the evolution of the apparent differential stresses for the effects of heterogenous deformation, because the evolution of the shape of the sample over time cannot be assessed. The distribution of differential stress and strain along the length of the specimen can, nevertheless, be determined at the end of the test (Fig. 3). The apparent strain weakening observed in the mechanical curves of samples 90OA87, VS15a1, VS15ab1, VS15ab1, and VS15b1 (Fig. 2) results therefore, partly or totally, from the cross-sectional area reduction, as typically observed in extensional deformation to high strains (Hansen et al., 2016; Hart, 1967; Rutter, 1998). The continuous apparent weakening, starting at bulk strains as low as 7%, displayed by the fine-grained harzburgite 90OA87 is consistent with a progressive reduction in the cross-sectional area due to strain localization in a wide necking zone. The textured coarse-grained samples VS15 only showed apparent weakening for bulk strains >20%. This apparent weakening probably results mainly from necking, but the growth of fractures at high angle to the extension direction, which are filled by the softer material of the jacket, also contributed to it (Fig. 2). This process led to the ultimate failure of samples VS15-a1 and VS15-b1, which were deformed to >40% bulk strain. In contrast, sample VS14-9 displayed no apparent weakening despite clear necking and the mechanical data for sample VS14-7 recorded solely an abrupt decrease in stress after 40% bulk strain, which is probably associated with the growth of the fracture visible at the center of the cylinder in Figure 2. The absence or limited apparent weakening in the VS14 coarse-grained peridotites points o a hardening process, which counteracts the geometrical weakening due to necking in these experiments. The wide variability of hardening behaviors among the VS14 and VS15 samples in the initial stages of the experiments may be explained by grain sizes being too coarse relative to the sample diameter. Thus, the experimental samples may not be representative volumes of these two rocks and the mechanical behavior observed in each experiment may depend on the orientation of the individual grains comprising the sample. The analysis of the microstructure of the deformed samples corroborates this hypothesis. The variation of axial differential stress, mean stress, and axial strain along the length of the 4 necked samples that did not ultimately fail is presented in Figure 3. The diameter of each sample at 1 mm intervals along its length was measured. Assuming deformation at constant volume, the local axial strain is equal to the ratio of the locally reduced area of the specimen normal to the extension direction to the area calculated assuming homogeneous deformation to the final bulk strain of the sample. As the axial force is equal at every point along the sample, the final axial force divided by the local area gives the local differential stress at the end of the test (Fig. 3). The accuracy of differential stress measured in low strain domains is expected to be ±5 MPa, but it is degraded to ca . ±15 MPa towards and in the neck. Necking resulted in a ca. three-fold enhancement of the differential stress compared to the specimen ends in all samples, except for VS15-ab1 that was deformed to a lower finite strain (Fig. 3). Maximum strains in the neck are more than five-fold the bulk strain. Focusing of strain in the neck implies a corresponding increase of strain rate. If one considers that at the end of the experiment, strain is concentrated over <5 mm of the length f the sample, strain rates in the neck are >5e-4 s -1 , that is, at least 5 times the initial ones. This combination of high strain rate, strain, and stress at the end of the test will be reflected in the microstructure of the neck region in the recovered samples. Note that due to the non-linearity of the dislocation creep behavior, which in olivine is characterized by a stress exponent ~3 (cf. review in Hirth and Kohlsted 2003), a five-fold strain rate enhancement will result in an increase of the flow stress by a factor 1.7. Thus, the enhancement of the final stresses in the neck relative to the initial flow stresses by a factor 1.75 displayed by sample VS15-ab2, suggests that throughout the large strains this sample displays in fact nearly steady-state flow. The higher stress enhancement (factor ~3) determined for the other coarse-grained samples implies they are still mildly hardening. In contrast, for the fine-grained harzburgite, the final stresses in the neck are similar to the yield stress (~165 MPa) despite the increase in strain rate. This implies that the fine-grained harzburgite displayed significant strain-softening. The peak values of axial differential stress in two coarse-grained samples exceed 300 MPa (the confining pressure) by up to 50 MPa of real tensile stress (Fig. 3). These tensile stresses are limited to the neck. High values of compressive load are maintained at the ends of the sample, preventing the separation of the sample ends from the loading pistons. These observations indicate that olivine-rich rocks deforming by viscoplastic processes at 1200°C can support large true tensile stresses without cavitation or fracture. However, fractures started to develop in all necked coarse-grained samples and samples VS15-a1 and VS15-b1 ultimately failed at similar or even lower apparent differential stresses as that of sample VS14-9, suggesting that the conditions at the neck were close to the tensile limit. . Microstructure evolution In the coarse-grained dunites, olivine accommodates most of the deformation. It displays extensive evidence for deformation by dislocation creep, such as: elongation parallel to the stretching axis and strong undulose extinction, which evolves with increasing strain to closely-spaced planar subgrain boundaries, then to a network of irregularly-shaped to polygonal subgrains, and finally into recrystallized domains (Fig. 4). The importance ofdislocation creep in olivine is corroborated by the analysis of the intracrystalline misorientation, which documents a steady increase in the geometrically-necessary dislocation (GND) density in olivine with increasing strain (Fig. 5). Enstatite and spinel often preserve their original shapes, but may also be locally elongated parallel to the stretching direction, but less so than olivine. The strain distribution is highly heterogeneous. Within a sample, the intensity of deformation of olivine depends on the location (whether in the neck or outside, Fig. 4) and the orientation of the crystal relative to the imposed extension. The first-order control on the strain and stress distribution by the necking process is recorded by the spatial variation in the GND density in olivine (Figs. 6 and 7). Recrystallization restricted to the neck region also documents focusing of strain and stress. However, even coarse-grained samples deformed to <20%, which did not neck, display a heterogeneous deformation at the grain scale, recorded by the spatial variation of the GND density revealed by the KAM proxy in olivine (Figs. 5 and 6). Crystals initially well oriented for glide of dislocations of the [100](010) and [100](001) systems (bluish to purple grains in Figs. 7 and 8) are elongated and have a high density of subgrains, the boundaries of which are delineated by high KAM values (Figs. 5 and 6). In contrast, initially poorly-oriented crystals (greenish grains in Figs. and 8) have more equant shapes and lower densities of GND, recorded by lower KAM values (Figs. 5 and 6). Recrystallization occurs preferentially within grains well-oriented to deform by dislocation glide, often starting at the contacts with less well-oriented olivine crystals or with pyroxenes and extending towards the interior of the grain (Fig. 4d). Recrystallized grains have polygonal shapes and average sizes ranging from 11 to 13 µm (Table 2). The detailed study of the recrystallization microstructures and the analysis of the effect of recrystallization on the CPO evolution, based on high-resolution maps of selected zones from the neck region of all samples deformed to > 20%, is presented in a companion article (Lopez-Sanchez et al., 2021). Another characteristic microstructure of the coarse-grained peridotites is the development of heterogeneous deformation at the grain scale in grains poorly oriented for dislocation glide in the form of kink bands (Figs. 8, 9, 10). The kink bands have lens- or flame-like shapes and accommodate variable misorientations (from a few degrees to up to 85°) predominantly around the [001] axis (Fig. 10 and supplementary material Fig. S2), though rotations around <104>, <014>, <114>, <214>, and <142> were also documented (Supplementary material Fig. S2). In highly deformed domains, close to the neck, recrystallization develops along kink boundaries (Fig. 11). Although only a single test was performed on the fine-grained harzburgite 90OA87, the evolution of the microstructure with increasing strain can be characterized by the comparison of EBSD maps from the necking region, where the sample was submitted to high stresses and strain rates, accumulating high finite strains, with those from the low strain zone close to the pistons, where the initial microstructure was largely preserved (Fig. 2). Since the starting material had already a partially recrystallized initial microstructure, the changes are less marked. The imposed extensional strain increases the elongation of the olivine porphyroclasts (which may attain aspect ratios as high as 10:1), creating a strong stretching lineation. In both low strain and high strain (neck) zones, the olivine porphyroclasts display a high density of subgrain boundaries and sinuous grain boundaries, but subgrain shapes change and the sizes of subgrains and the length scale of the sinuosity of the grain boundaries are smaller in the neck. In the low strain zone, straight subgrain boundaries normal to the grain elongation predominate with a second family normal to it, whereas olivine porphyroclasts in the neck have subgrain boundaries with more irregular shapes and variable orientations, which often form closed loops. Increasing extensional strain also produces a marked increase in the recrystallized fraction, which varies from ~20% in the low strain zone to 34% in the neck (Fig. 12). Dynamic recrystallization occurred mainly along grain boundaries by subgrain rotation and minor grain boundary bulging. It led to significant grain size reduction; average recrystallized grain sizes vary from 16 µm in the low strain zone, where they were probably inherited from the natural deformation forming the initial mylonitic microstructure, to 9 µm in the neck (Table 2). Effective dynamic recrystallization probably accounts for the maintenance of low mean intragranular misorientations in olivine even in the neck zone (Fig. 5). As in the coarse-grained peridotites, the deformation is essentially accommodated by olivine. Coarse pyroxene and spinel grains remain largely undeformed (cf. coarse pyroxene in the neck region in the photomicrograph in Fig. 2), but may be locally stretched and fractured at high angle to the imposed extension (Fig. 12d,e). . Olivine Crystal Preferred Orientations
Olivine in the starting material for the fine-grained peridotite 90OA87 sample had already a CPO, characterized by a poor alignment of [100] at low angle to the preexisting stretching lineation (Fig. 1a). The extension was applied roughly parallel to this direction. Comparison of this initial olivine CPO to that in the low strain domain close to the piston and to that in the necking region (Fig. 12c,f) highlights: (i) a marked enhancement in the strength of the CPO and (ii) reorientation of the olivine crystals with development of a strong maximum of the <101> axes parallel to the stretching direction. The coarse grain size in the other samples hinders the evaluation of the CPO evolution with increasing strain, as either finite strains were low (bulk strains <20°) or they were heterogeneous along the sample and representative volumes for each strain intensity could not be analyzed. However, the increase in the area filled by blueish to purplish grains, which have their [100] to <101> axes aligned with the imposed extension with increasing strain of the sample and within the neck zone in the necked samples, suggests a similar tendency in the CPO evolution (Figs. 8, 9).
7. Discussion
Owing to the coarse initial grain size of the VS14 and VS15 dunites (Fig. 1), the experimental samples of these rocks are not representative volumes. The experimental cylinders have on average 2 to 5 grains across the initial diameter (Figs. 8, 9). By consequence, the mechanical behavior of these samples is strongly dependent on the behavior of individual grains in any transect and cannot be described by homogenization chemes. Thus, strain localization is not only controlled by the non-linearity of the stress-strain relationship (Hart, 1967; Rutter, 1998), but principally by the location of grains in easy glide orientations. This explains the high variability of mechanical behavior among the coarse-grained samples (Fig. 2). This effect is enhanced by the presence of an initial CPO, as in VS15 (compare Figs. 8 and 9). However, the exceptionally coarse initial grain size of olivine in these samples (>1 mm), compared to the dominantly <50 µm grain sizes used in deformation experiments on synthetic olivine polycrystals (e.g., Bystricky et al., 2000; Faul et al., 2011; Hansen et al., 2016, 2014, 2012; Karato et al., 1986; Zhao et al., 2009), allows investigation of processes that are usually not observed in experiments but may occur in nature, where millimetric size olivine dominates, such as the role of the strong viscoplastic anisotropy of olivine crystals and interactions between crystals with different orientations on dynamic recrystallization and the development of kinks (Figs. 4, 10, 11). Moreover, the comparison between the mechanical and microstructural data of the two coarse-grained samples to that of the fine-grained one permits investigation of the links between mechanical response and microstructure evolution over a range of grain sizes akin to those observed in nature.
Analysis of the mechanical data shows that the fine-grained harzburgite displays the highest yield stress – 165±5 MPa (Fig. 2). These stresses are lower than that predicted for the present deformation conditions based on experimental data from dry synthetic aggregates of San Carlos olivine (Fo90) deformed by dislocation creep in axial compression ( ≥
300 MPa, Hirth and Kohlstedt, 2003; Thieme et al., 2018). They are, owever, within the range of those measured for natural dunites without pre-deformation thermal treatment at similar temperatures and strain rates - 90 and 175 MPa for samples with mean initial grain sizes of 100 and 900 µm, respectively (Chopra and Paterson, 1981), which as the present samples deformed in presence of minor melt fractions due to breakdown of hydrous phases along grain boundaries in the starting material (Supplementary Material Fig. S1). The dunites yielded at even lower differential stresses, between 115 and 150 MPa. The higher iron contents of olivine (Fo82-83, compared to Fo90 in the harzburgite) may explain the lower initial strength of the dunites. Based on the flow law by Zhao et al. (2009) and considering solely the influence of the variation in iron content of olivines, the dunites should support stresses on the order of 0.74 times that of the harzburgite, that is ~122 MPa, which is in the lower range of the observed values. However, given the large difference in initial average grain sizes, one could expect a higher contribution of diffusional or grain boundary processes to deformation in the fine-grained harzburgite (area-weighted mean grain size of 170 µm), which should reduce its strength relative to that of the coarse-grained dunites. Considering a grain size exponent of -2 and a stress exponent of 3 (Hirth and Kohlstedt, 2003), a variation in average grain size from 170 µm to 1 mm should result in an increase in strength by a factor 12. If one considers that samples with average grain sizes ≥
250 µm deform in a grain-size independent regime the difference reduces to a factor 1.3. Combining the effects of composition and grain size variations, the coarse-grained dunite samples are expected to display yield stresses similar or higher than the fine-grained harzbugite sample. However, all dunites yielded at lower differential stresses than the harzburgite. This implies that either grain size-related weakening played a minor role in he present experiments or that another processes further weakened the dunite samples. The present data also contrast with previous results on “wet” natural dunites, which showed lower strengths for the finer-grained samples (Chopra and Paterson, 1981). A possible explanation could be the presence of higher melt fractions in the dunite samples. Partial melt pockets were indeed most easily documented in the coarse-grained samples (Supplementary Material Fig. S1). However, all initial materials had minor contents of hydrous phases locally along grain boundaries, which dehydrated during the experiments producing localized melt pockets. As discussed in the previous section the extreme variability in mechanical behavior among the dunites stems from the combined effect of very coarse grain sizes relative to the sample diameter and of the high viscoplastic anisotropy of olivine crystals. Indeed the strength of an olivine crystal perfectly oriented to deform by dislocation glide on the easy [100](010) system is at least three times higher than that of a crystal perfectly oriented to deform by dislocation glide on the hard [001](010) system (Bai et al., 1991) and a crystal oriented with its [100] or [010] axes parallel to the imposed extension theoretically cannot deform by dislocation glide, since resolved shear stresses on all possible slip systems are zero. The observed initial strengths of the VS15 samples subjected to axial extension in different directions relative to the olivine CPO (Fig. 2) are consistent with the relative strengths predicted by viscoplastic self-consistent simulations using the same CPO and boundary conditions. The exception is sample VS15-b1, which should have presented a higher yield strength, similar to that of samples VS15-a1 and VS15-ab1 (cf. Supplementary Material). A nalysis of the olivine orientation map for VS15-b1 (Fig. 9) shows, nevertheless, that deformation in this sample was concentrated in a zone where most rystals had their [100] at low angle to the imposed extension and hence a lower strength, further corroborating the major effect of viscoplastic anisotropy on the mechanical behavior of these samples.
The fine-grained harzburgite and the coarse-grained dunites display markedly different strength evolutions (Fig. 2), which are related to different strain distributions at the macroscopic scale, illustrated by the analysis of the final shapes of the samples (Fig. 2 and 3), and different microstructures (Figs. 4 to 12). The fine-grained harzburgite shows a well-defined yield point at ~2% strain, consistent with a sharp transition from elastic to viscoplastic deformation, and a short steady-state followed, from 7% of bulk strain onwards, by a steady decrease in apparent strength. This decrease in apparent strength may be largely explained by the necking of the sample, with the deformation progressively focused in smaller and smaller volumes; the progression of necking leading to continuous decrease of the cross-section of the actively deforming region (Figs. 2 and 3). Analysis of the local differential stresses and finite strain attained at the end of the test shows that the maximum stresses at the neck (169±15 MPa) are similar to the yield stress of this sample (167±5MPa) despite local strain rates at least 5 times higher (finite strains in the neck are up to five times the bulk strain at the end of the experiment). If this sample deformed dominantly by dislocation creep, with a stress-dependence to a power of 3, an enhancement in strain rate by a factor 5 should result in a stress enhancement by a factor 1.7. The present data imply that the microstructural evolution in this sample, in particular the effective dynamic recrystallization, counteracts his strain-rate hardening. This inference is corroborated by the low area-weighted mean GOS of olivine in the neck zone (Fig. 5b). Effective grain size reduction by dynamic recrystallization – the recrystallized volume increases from ~20% to 34% and the average recrystallized grain size decreases from 16 µm to 9 µm from the low strain zone to the neck (Fig. 12) – may also increase the contribution of diffusional processes to deformation in the neck. Yet, in itself, this marked reduction in grain size indicates that dislocation creep played a major role during most of the deformation of the sample. Another possible source of strain weakening during deformation by dislocation creep is the evolution of the CPO. To isolate this effect, we ran viscoplastic self-consistent simulations (VPSC) where we compare the strength of aggregates having the olivine CPO measured in the low strain zone and in the neck region (Fig. 12) when submitted to boundary conditions reproducing those of the experiments, using a similar approach as in Mameri et al. (2019). Input parameters and full results of the VPSC simulations are presented in the Supplementary Material. These simulations predict that the moderate change in the CPO between the low strain and the neck region would result in moderate hardening, by a factor 1.1, if the sample was deformed solely by dislocation creep. This hardening stems from to the progressive rotation of the olivine [100] axes towards the extension direction, which results in a progressive decrease of the resolved shear stresses on the easy [100]{0kl} systems. However, the VPSC simulations also predict that in absence of dynamic recrystallization the CPO evolution would have been faster and the associated hardening at >100% of finite strain that has been attained in the neck, stronger. In conclusion, dynamic recrystallization weakened this sample via two processes. It kept intragranular dislocation densities low (Fig. 5) and changed the CPO evolution, reducing he hardening due to the CPO evolution associated with deformation in axial extension by dislocation glide (cf. Supplementary Material Fig. S3). Surprisingly, the differential stress predicted based on the average recrystallized grain size in the neck using the paleopiezometric relation of Van der Wal et al. (1993) – 219 MPa (Table 2) – is significantly higher than that estimated from the macroscopic data - 165±15 MPa. We do not have a simple explanation for this discrepancy, as this piezometer has been established based on experiences on similar starting materials and deformation conditions. However, Van der Wal et al. (1993) already observed that, at the same stress level, recrystallized grain sizes in samples of the initially fine-grained Anita Bay dunite (100 µm) were systematically smaller than those of the initially coarse-grained Aheim dunite samples (900 µm). The piezometer fit, which is based on the entire dataset, overestimates therefore the stresses for the Anita Bay samples (cf. Fig. 2 of Van der Wal et al., 1993). In contrast, the coarse-grained dunites show an extended hardening behavior up to 10-20% bulk strain and either a weak apparent softening or an apparent steady-state behavior despite necking at >20% bulk strain (Fig. 2). This behavior implies continuous hardening of the samples, though the apparent softening observed for the necked VS15 samples suggest a decreasing rate of hardening at high strains. The observed mechanical behavior is consistent with the measured steady increase in the mean GOS with increasing strain (Fig. 5), that records a steady increase in the dislocation density. As previously discussed, the differences in the mechanical behavior between the coarse-grained samples result from differences in the orientation of the olivine crystals that compose each sample, with clear concentration of strain in those crystals in easy glide (soft) orientations. In all amples, necking occurred in domains with a high concentration of such crystals (purple crystals in Figs. 8 and 9). Concentration of the deformation in domains with a higher volume of olivine grains in soft orientations probably resulted in macroscopic softening of the sample, but the latter was counteracted by the local increase in strain rate (to compensate for deformation accommodated in a smaller volume) and by the increase in the intragranular dislocation density, which is markedly higher in the neck zones (Figs. 6 and 7). Flow stresses at the neck of the coarse-grained samples estimated based on the minimum final diameter (ignoring the fractures) range between 325 and 470 MPa (Fig. 3). The lowest enhancement of the final stresses in the neck relative to the initial flow stresses (by a factor 1.75) is displayed by sample VS15-ab2. This value is equivalent to the increase in stress associated with the increase in strain rate in the neck estimated from the finite strain distribution, suggesting that this sample attained nearly steady-state flow. In all the remaining coarse-grained samples, the final stress in the neck was higher by a factor three than the initial flow stress, corroborating continued microstructural hardening in addition to the increase in stress associated with the increase in strain rate. This is despite the onset of dynamic recrystallization in all necked samples. Recrystallized volumes remained nevertheless small and much of the strain was still accommodated by dislocation glide and kinking in the coarse olivine grains (Fig. 4). As a consequence of this hardening, the peak values of axial differential stress in the neck of the coarse-grained samples VS14-9 and VS15-ab1 exceeded the confining pressure, leading to up to 50 MPa of real tensile stress accommodated by ductile flow (Fig. 3). Ductile metals and ceramics can support large true tensile stresses without cavitation or racture, as solid-state diffusion may suppress the growth of crack-like openings along grain boundaries. Olivine aggregates can do the same at high temperature, although separation and ultimate failure are expected ultimately to supervene. Up to five-fold elongation was obtained in initially extremely fine-grained (< 500nm) aggregates of forsterite + minor diopside or periclase in tensile tests at 1450°C and ambient pressure, before failure at stresses of ~30 MPa (Hiraga et al., 2010). In the present experiments, the development of a grain shape fabric probably also delayed fracturing as it reduced the area of grain boundaries subjected to interface-normal extension (Fig. 4a). However, fractures eventually started to develop in all necked samples and samples VS15-a1 and VS15-b1 ultimately failed at similar or even lower apparent differential stresses as that of sample VS14-9. This suggests that 50 MPa is close to the tensile limit for olivine rich-rocks at the tested grain sizes and temperature and pressure conditions. The peak values of axial differential stress in the neck of the coarse-grained samples estimated from the macroscopic data (250 to 365±15 MPa) are significantly higher than those estimated based on the recrystallized grain sizes (159 to 182±5 MPa). This suggests a delay in the reequilibration of the microstructure, with the recrystallized grain sizes recording the lower differential stresses that preceded the final stress at which the test was terminated. Recrystallized grain sizes in the coarse-grained dunites are larger than those determined for the fine-grained harzburgite (Table 2), despite the much lower maximum stress at the neck attained in the fine-grained harzburgite (Fig. 3). This apparently contradictory observation might be explained by a more progressive evolution and more homogeneous strain and stress conditions in the fine-grained sample, allowing for a more effective re-equilibration of the microstructure. omparison of the microstructures of the highly strained coarse-grained dunites and the fine-grained harzburgite reflects the higher volume fraction of newly recrystallized grains in the latter. The mechanical data point to effective strain softening in the fine-grained harzburgite, which manifests itself as necking almost immediately after yielding, whereas the coarse-grained samples harden or at best attain steady-state flow conditions. Altogether, these observations are consistent with the major role of dynamic recovery and dynamic recrystallization in counteracting microstructural hardening (Nicolas and Poirier, 1976; Rollett et al., 2004). However, we may ask why dynamic recrystallization should be more effective in the fine-grained harzburgite? The present data hints at a major role of the higher initial density of grain boundaries, which acted as preferential nucleation sites in the fine-grained harzburgite. In the coarse-grained dunites, a large part of the recrystallization process is intragranular, requiring significant densities of dislocations of at least three independent slip systems to create closed subgrains that may evolve into new recrystallized grains. By consequence, dynamic recrystallization was only effective in the neck zone and occurred preferentially in soft grains close to the contact with hard ones, implying that it required both high strain and high stresses, which are only achieved locally, due to intergranular interactions. We discuss this point in a companion article (Lopez-Sanchez et al, submitted), which is based on the analysis of high-resolution EBSD maps of the recrystallized domains.
In both the coarse- and fine-grained samples, the microstructures and CPO evolution point to deformation mainly accommodated by dislocation creep of olivine, with activation of ultiple slip systems, but predominance of [100] glide (Figs. 4, 8, 9, 12), accompanied by dynamic recrystallization in highly strained zones (Figs. 4, 11, 12). However, the coarse-grained dunites also show microstructures that are rarely observed in olivine: kink bands (Fig. 10, 11, and Supplementary Material Fig. S2). Kink bands are planar deformation features characteristic of highly anisotropic materials, which possess insufficient slip systems to satisfy the Taylor/Von Mises criterion for homogeneous plastic flow (Barsoum et al., 1999; Burnley et al., 2013; Nicolas and Poirier, 1976; Raleigh, 1968). They provide an additional degree of freedom for deformation by producing sharp reorientation of volumes of crystals that are poorly oriented to deform by dislocation glide on the existing systems. This is consistent with observation of kink bands essentially in olivine crystals with the [010] axis subparallel to the imposed extension (Figs. 8, 9, 10 and Supplementary Material Fig. S2). In the present experiments, misorientations across kink bands are essentially accommodated by rotations around [001], suggesting that dislocations of the dominant [100](010) slip system played an important role in their formation. The onset of recrystallization along kink boundaries (Fig. 11) is consistent with local stress concentration and high dislocation densities. However, misorientation angles across kink boundaries are too high to be explained solely by the accumulation of dislocations, suggesting that microfracturing may also play a role. Cracks assisting strain accommodation in kink bands were indeed observed by TEM in highly anisotropic ceramics, in particular for high misorientations (Barsoum et al., 1999). Kink bands in olivine are extremely rare in naturally deformed peridotites, but have been documented in meter to centimeter-scale shear zones in the Finero massif in the Alps (Matysiak and Trepmann, 2015) and in the ductile root of detachment faults in the South est Indian Ridge (Bickert et al., 2021). In both cases, initial olivine grain sizes were multimillimetric to centimetric and the development of kinks is followed by dynamic recrystallization leading to extreme grain size reduction. Kinks were also observed in Mg GeO olivine deformed experimentally under high-pressure (0.6-1.3 GPa) and high-stress conditions (1.3-2.5 GPa; Burnley et al., 2013). The present observations and these three examples share many characteristics: (1) kinks limited to crystals in hard orientations, (2) highly variable misorientations along the kink boundary, which may attain 90°, (3) consistent crystallographically-controlled rotation axis across the kink bands, which point to a contribution of dislocations of the dominant slip system, (4) high differential stresses, >100 MPa for olivine, and (5) coarse grain sizes (relative to the sample dimensions in the experiments), leading to dominant intragranular deformation by dislocation glide.
8. Conclusion
Natural upper mantle peridotites with contrasting initial microstructures and variable CPO subjected to axial extension at 1200°C and 300 MPa confining pressure showed similar initial strengths, ranging between 115±5 and 165±5 MPa, with the finer-grained sample displaying the highest yield stress. The lower initial strength of the coarse-grained samples may be partially explained by the higher iron content of olivine. However, the difference in composition did not suffice to counteract the expected contrast in strength due to the difference in initial grain size. Thus, either the fine-grained sample had lower contents of minor hydrous phases along grain boundaries, leading to lower melt fractions during the experiments, or grain-size sensitive processes did not significantly affect the yield strength of this sample. ll samples deformed to > 20% bulk strain became necked. However, fine- and coarse-grained peridotites showed markedly different evolutions of both mechanical behavior and microstructure. The fine-grained harzburgite displayed, after yielding, a progressive decrease in the apparent differential stress consistent with the observed necking. It showed an increase in the olivine CPO intensity and recrystallized fraction and a decrease in the recrystallized grain size. These features recorded strain, strain rate, and stress focusing in the neck. The marked decrease in recrystallized grain size points to a major contribution of dislocation creep despite the fine initial grain sizes. Stresses in the neck at the end of the experiment were similar to the initial yield stress despite significant strain localization, which implied strain rates in the neck up to five times higher than the initial ones. This indicates that this sample was subjected to significant strain softening. We infer that this softening is due to continued dynamic recrystallization, which kept dislocation densities low, favored the development of favorable crystal orientations for dislocation glide and, probably, enhanced the contribution of grain-size dependent creep processes. In contrast, most coarse-grained samples showed hardening in the initial stages of deformation and no or little decrease of the apparent differential stress after necking. This is consistent with the increase in the bulk intragranular misorientation with increasing strain in these samples, absence of evidence for dynamic recrystallization in the non-necked samples, and limited recrystallized volumes in the necked ones. The coarse-grained samples systematically displayed a highly heterogeneous deformation. Crystals well oriented to deform by dislocation glide became elongated with strong undulose extinction, whereas those in hard orientations remained weakly deformed. The initiation of the neck as controlled by local concentrations of crystals in soft orientations. In the neck, stress concentrations resulted in formation of kinks in crystals in “hard” orientations for dislocation glide and dynamic recrystallization in crystals in “soft” orientations and, at bulk strains >40%, development of extensional fractures that produced a rapid drop in the apparent differential stress. Differential stresses in the neck estimated based on recrystallized grain sizes were significantly lower than those estimated using the neck minimum diameter, suggesting that the recrystallized grain sizes were established at the lower differential stress that preceded the final stress peak. Differential stresses greater than the confining pressure, implying development of local true tensile stresses of ca. -50 MPa, were recorded in the neck regions of the coarse-grained dunite samples. This indicates that, at high temperature, olivine-rich rocks can sustain substantial tensile stresses before cavitation or fracturing. The highest recorded stress values are probably close to the ductile tensile limit of these samples under the present experimental conditions, as indicated by the eventual onset of fracturing and ultimate failure of some samples. Comparison of the mechanical and microstructural observations on the coarse and fine-grained samples suggests that the inhibition of dynamic recrystallization, probably due to the lower density of grain boundaries acting as nucleation sites, resulted in significant hardening and activation of high-stress deformation processes, such as kinking and fracturing, in the coarse-grained peridotites. This effect is particularly marked in the present experiments where dynamic recrystallization is dominated by nucleation, since the fast strain rates largely overwhelm grain boundary migration rates. In nature, at much slower train rates, the importance of nucleation in controlling the effectiveness of dynamic recrystallization to produce strain softening might be lower.
9. Acknowledgments
We dedicate this article to A. Nicolas, an exceptional researcher who set the basis of the petrophysical analysis of mantle deformation. The experiments were carried out with support from an EU-Marie Slodowska-Curie postdoctoral fellowship to WBI. The data analysis was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 882450 – ERC RhEoVOLUTION) and by a postdoctoral fellowship co-funded by the European Union and the Government of the Principality of Asturias (Spain) [grant number ACA17-32] within the Marie Sk ł odowska-Curie COFUND Actions FP7 to MALS. Senior experimental officer Robert Holloway (Rock Deformation Laboratory) provided invaluable training and maintained the equipment. Françoise Boudier and Adolphe Nicolas are thanked for the providing the Oman sample and David Mainprice for helpful discussions.
10. References °C. Phys. Earth Planet. Inter. 278, 34–46. https://doi.org/10.1016/j.pepi.2018.03.002 Tommasi, A., Knoll, M., Vauchez, A., Signorelli, J., Thoraval, C., Logé, R., 2009. Structural reactivation in plate tectonics controlled by olivine crystal anisotropy. Nat. Geosci. 2, 423–427, doi: 10.1038/NGEO528. https://doi.org/10.1038/NGEO528 Tommasi, A., Langone, A., Padrón-Navarta, J.A., Zanetti, A., Vauchez, A., 2017. Hydrous melts weaken the mantle, crystallization of pargasite and phlogopite does not: Insights from a petrostructural study of the Finero peridotites, southern Alps. Earth Planet. Sci. Lett. 477, 59–72. Tommasi, A., Vauchez, A., 2015. Heterogeneity and anisotropy in the lithospheric mantle. Tectonophysics 661, 11–37. Tommasi, A., Vauchez, A., 2001. Continental rifting parallel to ancient collisional belts: An effect of the mechanical anisotropy of the lithospheric mantle. Earth Planet. Sci. Lett. 185, 199–210. Van der Wal, D., Chopra, P., Drury, M.R., FistGerald, J., 1993. Relationships between dynamically recrystallized grain size and deformation conditions in experimentally deformed olivine rocks. Geophys. Res. Lett. 20, 1479–1482. Vauchez, A., Dineur, F., Rudnick, R., 2005. Microstructure, texture and seismic anisotropy of the lithospheric mantle above a mantle plume: Insights from the Labait volcano xenoliths (Tanzania). Earth Planet. Sci. Lett. 232, 295–314. Zhang, S., Karato, S., 1995. Lattice preferred orientation of olivine aggregates in simple shear. Nature 375, 774–777. Zhang, S., Karato, S., Fitzgerald, J.D., Faul, U.H., Zhou, Y., 2000. Simple shear deformation of olivine aggregates. Tectonophysics 316, 133–152. Zhao, Y.H., Zimmerman, M.E., Kohlstedt, D.L., 2009. Effect of iron content on the creep behavior of olivine: 1. Anhydrous conditions. Earth Planet. Sci. Lett. 287, 229–240. https://doi.org/10.1016/j.epsl.2009.08.006
Figures and Tables
Fig. 1.
Microstructure and olivine crystal preferred orientation (CPO) of the three starting materials: plane-polarized photomicrographs and inverse pole figures of the orientation of the long axis of the photo in the crystal reference frame. In (a) this orientation is at ~20° of the preexisting stretching lineation of the sample. Same colorscale for all IPFs.
Fig. 2.
Mechanical data for all successful experiments (Table 1). Apparent differential stresses (corrected for the strength of the iron jacket) are calculated assuming homogeneous reduction of specimen cross sectional area at constant volume along the length of the sample. They represent the actual differential stresses for samples that did not neck. In the samples subjected to necking, stresses vary strongly along the sample length (Fig. 3). Strains are bulk strains, that is, overall change in length (after correction for axial apparatus distortion) divided by the original sample length. Final sample shapes are illustrated by scans of the recovered samples cut parallel to the extension axis as close to the cylinder center as possible. For the fine-grained harzburgite 90OA87, a crossed-polars micrograph of the most deformed domain is also displayed; note the strong inclusion behavior of the coarse orthopyroxene crystal (dark rounded grain) close to the neck region.
Fig. 3.
Axial differential stress, mean stress, and extensional strain distributions along the sample length for the four necked samples that did not break. All three starting materials are represented. Apparent axial differential stress and bulk strain are indicated for comparison. The neck region, outlined in gray, is subjected to significantly higher stresses and strains; its width varies strongly from sample to sample. Sample VS15-ab2 shows abrupt variations in strain and stress, suggesting development of a new instability within the initial neck zone.
Fig. 4.
Representative olivine deformation microstructures (coarse-grained dunite VS14-9). (a) Low enhancement cross-polars photomicrograph highlighting the contrast in microstructure due to strain concentration in the neck. (b) Detail of (a) illustrating an extremely elongated (aspect ratio ~ 20:1) olivine crystal (ol) with strong undulose extinction, a complex subgrain pattern and recrystallization seams in the neighboring olivine crystals, and coexistence between spinels (sp) undeformed and stretched by fracturing. (c) Detail of the neck region showing highly deformed olivine crystals crosscut by fine-grained recrystallization seams, displayed in detail in (d). The extension direction is parallel to the long side of the image in (a,c,d) and at ~10° to it in (b).
Fig. 5.
Bulk (sample scale) intracrystalline misorientation in olivine represented as the grain orientation spread (GOS) as a function of the final bulk axial strain. (a) Arithmetic mean GOS excluding the recrystallized grains from the calculation; error bars indicate the standard error at 95% of confidence. RX means recrystallized grains. (b) Area-weighted mean GOS including all grains, which should be indicative of the contribution of the intragranular dislocation density to the sample strength. The lower area-weighted GOS relative to the arithmetic mean GOS in the neck region of sample 90OA87 (star symbols) reflects the contribution of dynamic recrystallization towards decreasing the intragranular dislocation density. The coarse-grained samples have similar or higher area-weighted GOS relative to the arithmetic mean GOS, consistent with their low recrystallized volumes. The higher area-weighted GOS values result from the presence in the mapped area of coarse grains with high intragranular misorientations. Data are presented in Supplementary Material Table S1.
Fig. 6.
Evolution of the geometrically-necessary dislocation (GND) density of olivine with increasing strain illustrated by KAM maps for VS14 dunites deformed to different bulk finite strains (numbers below sample name). High KAM values (hotter colors) delineate the subgrain structure. Grain boundaries are displayed in black. Pyroxenes, spinels, dynamically recrystallized olivine grains, and missing material (lost during preparation of the sections for EBSD analyses) are displayed in white. Scale is the same for all deformed sample maps. Note: (1) the on-average higher GND densities denoting stress and strain concentration in the neck domains of samples stretched by >20% bulk strain and (2) the heterogeneity in the GND spatial distribution in all samples denoting stress and strain heterogeneity at the grain scale.
Fig. 7.
Evolution of the geometrically-necessary dislocation (GND) density of olivine with increasing strain illustrated by KAM maps for VS15 dunites deformed to different bulk finite strains (numbers below sample name). High KAM values delineate the subgrain structure. Grain boundaries are displayed in black. Pyroxenes, spinels, dynamically recrystallized olivine grains, and missing material (lost during preparation of the sections for EBSD analyses) are displayed in white. As in Fig. 6, the heterogeneity in the GND spatial distribution in all samples reflects stress and strain heterogeneity at the grain scale and the on-average higher GND densities denote stress and strain concentration in the neck domains of samples stretched by >20% bulk strain.
Fig. 8.
Evolution of the microstructure and of the CPO of olivine with increasing strain illustrated by crystal orientation maps and inverse pole figures (IPF) that indicate the orientation of the bulk extension direction relative to the crystal reference frame for all VS14 samples. Maps are colored as a function of the orientation of the bulk extension direction relative to the crystal reference frame (IPF legend in the insert on the top map). Grain boundaries are displayed in black. Pyroxenes, spinels, dynamically recrystallized olivine grains, and missing material (lost during preparation of the sections for EBSD analyses) are displayed in white. Contours of IPF plots are at 0.5 multiples of a uniform distribution. The blotchiness of the IPFs results from sampling a too small number of grains even when analyzing the full specimen cross-section; the maxima mark the orientations of the coarser crystals.
Fig. 9.
Evolution of the microstructure and of the CPO of olivine with increasing strain illustrated by crystal orientation maps and inverse pole figures (IPF) indicating the orientation of the bulk extension direction relative to the crystal reference frame for VS15 dunites. Maps are colored as a function of the orientation of the bulk extension direction relative to the crystal reference frame (IPF legend in the insert on the top map). Grain boundaries are displayed in black. Pyroxenes, spinels, dynamically recrystallized olivine grains, and missing material (lost during preparation of the sections for EBSD analyses) are displayed in white. Small cylinders show the orientation of the initial fabric relative to the imposed extension in the different experiments.
Fig. 10.
Kinked olivine crystal in coarse-grained dunite VS15-a1 (location indicated in Fig. 8). (a) Orientation map in which kink boundaries with variable misorientation angle are highlighted. (b) Misorientation angle and axes distributions across the kink boundaries highlighted in (a).
Fig. 11.
Photomicrographs of a kinked and partially recrystallized olivine crystal in the neck region of coarse-grained dunite VS15-ab2 (location indicated in Fig. 8). Bulk extension direction is parallel to the long side of (a).
Fig. 12.
Evolution of the microstructure and the CPO of olivine with increasing strain illustrated by (a and d) crystal orientation, (b and e) ln(KAM) maps and (c and f) inverse pole figures (IPF) indicating the orientation of the bulk extension direction relative to the crystal reference frame and KAM maps for (a-c) low strain (close to the piston) and (d-f) high strain (neck) zones of fine-grained harzburgite 90OA87. Orientation maps are colored as a function of the orientation of the bulk extension direction relative to the crystal reference frame (IPF legend in the insert). High KAM values (hotter colors, note the logarithmic scale) delineate the subgrain structure. Grain boundaries are displayed in black. Pyroxenes and spinels are displayed in white. The small cylinder shows the orientation of the initial fabric relative to the imposed extension. In (a and d) the imposed extension is parallel to the long side of the maps. able 1. Experimental data
Sample Orientation of the cylinder Initial length (mm) Bulk strain (%) Yield / Peak / Final stress (MPa, ±5MPa) Comments VS14-3 In the starting material thin section plane 21.00 9.1 123 / 159 / 159 Force gauge failure VS14-4 Random 26.12 4.7 114 / 114 / 114 Jacket failure VS14-5 Random 23.10 14.9 123 / 147 / 147 Furnace failure VS14-6 Random 22.18 15.4 122 / 144 / 144 Furnace failure VS14-7 Random 26.42 44.7 108 / 156 / 71 Test successfully completed VS14-8 In the starting material thin section plane 25.46 39.4 - Computer crash VS14-9 In the starting material thin section plane 25.05 41.4 120 / 151 / 151 Test successfully completed VS15a-1 // to [100]max 25.92 47.6 131 / 183 / 92 Sample failure VS15b-1 // to [010]max 21.65 48.1 108 / 115 / 20 Sample failure VS15b-3 // to [010]max 22.26 4.1 - Furnace failure VS15ab-1 45° to [100]max and 90° to [010]max 24.01 28.6 143 / 156 / 121 Test successfully completed VS15ab-2 45° to [100]max and 45° to [010]max 24.63 33. 118 / 170 / 150 Test successfully completed 90OA87 At low angle to the preexisting lineation 24.75 49.7 165 / 165 / 73 Test successfully completed able 2. Dynamically recrystallized grain size of olivine and differential stresses estimated using the Van der Wal et al. (1993) piezometer
Sample n arith. mean Conf. Interval at 95% a Stress (MPa) Conf. Interval at 95% lower upper abs err (±) c.v. (± %) b lower upper lower (%) upper (%) vs14-7la 615 12.2 11.7 12.8 0.5 4.3 167.4 162.2 173.1 3.1 3.4 vs14-7rb 1753 12.8 12.5 13.1 0.3 2.3 162.2 159.5 165.0 1.7 1.7 vs14-9 1153 11.7 11.4 12.0 0.3 2.6 172.7 169.4 176.2 1.9 2.0 vs15ab1 1625 12.7 12.4 13.0 0.3 2.3 162.8 160.2 165.7 1.6 1.8 vs15ab2 1259 10.7 10.4 10.9 0.3 2.6 185.5 182.0 189.2 1.9 2.0 vs15ab2-bis 2217 11.6 11.4 11.9 0.2 2.1 174.0 171.2 176.7 1.6 1.6 vs15ab2-ter 330 11.4 10.8 12.0 0.6 5.1 176.5 170.0 183.5 3.7 4.0 vs15b1 849 12.7 12.2 13.1 0.5 3.5 163.2 159.0 167.7 2.6 2.8 90OA87-neck 24711 8.6 8.5 8.6 0.1 0.7 219.0 217.6 220.1 0.6 0.5 90OA87-low strain 12742 15.9 15.7 16.1 0.2 1.2 137.8 136.5 138.9 0.9 0.9 a Confidence intervals for the mean at 95% of certainty using the standard error formula with the t-score (ASTM International, 2013; Lopez-Sanchez, 2020) b Coefficient of variation: Error relative to the arithmetic mean in percentage (100 x abs err / mean) upplementary Material to Deformation of upper mantle rocks with contrasting initial fabrics in axial extension
Walid Ben Ismail , Andréa Tommasi , Marco Antonio Lopez , Fabrice Barou , Ernest H. Rutter Rock Deformation Laboratory, Dept. Earth Sciences, University of Manchester, UK Géosciences Montpellier, CNRS & Université de Montpellier, Montpellier, France
This supplementary material is composed of: • Fig. S1 illustrating isolated partial melting pockets due to the local presence of hydrous phases along grain boundaries in sample VS14-7. • Fig. S2 showing details of the kink bands. • Table S1 presenting the intragranular misorientation data extracted from the EBSD maps and presented in Fig. 5 of the main text. • The presentation of the viscoplastic self-consistent simulations performed to isolate the effect of the olivine CPO on the mechanical behavior of the samples, which includes Table S2 and Figure S3.
Supplementary Material Fig. S1 : Isolated partial melting pockets due to the local presence of hydrous phases along grain boundaries in sample VS14-7. ffect of the olivine CPO on the mechanical behavior of the samples assessed by viscoplastic self-consistent simulations
We compare the instantaneous mechanical response of olivine polycrystals with the olivine CPO measured in the low strain and shadow zone subjected to axial extension in the same orientation as in the experiments to the strength predicted for an olivine polycrystal with an initially isotropic CPO subjected to up to 100% axial extension. We also compare the instantaneous mechanical response of olivine polycrystals with the olivine CPO measured in samples VS15a1, VS15b1, VS15ab1, VS15ab2 to check if the observed differences in initial strength may be explained by the mechanical anisotropy due to the orientation of the olivine CPO of each sample relative to the imposed extension. The mechanical response of the olivine polycrystals was modeled using the second-order formulation of the VPSC model. This approach considers heterogeneous stress and strain rate within the grains and accounts for intragranular strain rate fluctuations to predict the effective polycrystal behavior (Ponte-Castañeda et al., 2002; Lebensohn et al., 2011). Individual crystals deform by dislocation glide on a finite number of slip systems, which are a function of the crystal structure. The relative strength of these slip systems, that is, the critical resolved shear stress (CRSS) needed to activate dislocation glide on each system, depends on the temperature, pressure, and stress. In the present study, we used CRSSs (Table S3) derived from deformation of natural olivine single crystals (Fo ) at high temperatures and low pressure ( Bai et al., 1991) . As the aim of the present simulations is solely to evaluate the effect of the CPO on the mechanical behavior, hardening due to microstructural evolution (dislocation entanglements) is not considered in the simulations.
Table S2:
Slip systems data used in the VPSC simulations
Slip Systems Critical Resolved Shear Stress (010)[100] 1 3 (001)[100] 1.5 3 (010)[001] 2 3 (100)[001] 3 3 (011)[100] 4 3 (110)[001] 6 3 {111}<110> a 𝛽 a 𝛽 a 𝛽 * Lower bound simulations only consider the first four slip systems a dummy slip systems, which represent additional strain accommodation processes and do not contribute to plastic spin Mixed boundary conditions were enforced because they better mimic the actual conditions in the laboratory experiments: imposed axial extension along and homogeneous stress in the plane normal to the piston axis.
𝐿 = $∗ 0 00 ∗ 00 0 1( ; 𝜎 = $−1 ∗ ∗0 −1 ∗∗ ∗ ∗( * = not imposed he relative strength of the VS15 samples subjected to axial extension in different directions relative to the olivine CPO (Table S3) is consistent with the measured strengths, except for sample VS15-b1, which should have presented a higher yield strength, on the same order than samples VS15-a1 and VS15-ab1. Indeed, analysis of the olivine orientation maps for VS15-b1 (Fig. 9 in the main text) shows that deformation in this sample was concentrated in a zone with an anomalous orientation, where most crystals had their [100] at low angle to the imposed extension. The olivine CPO in the neck zone of sample 90OA87, where local strains of up to 100% were estimated (Fig. 3 in the main text), differs significantly to that predicted for an olivine polycrystal with an initially random CPO accommodating up to 100% axial extension by dislocation glide: it is less concentrated and the maximum concentration of [100] is at 16° to the extension direction (Fig. S3). This implies that the CPO evolution in the experiments is significantly modified by dynamic recrystallization. This change in the CPO evolution avoids the hardening that should occur due to the progressive rotation of the [100] towards the extension direction, as the neck region remains weaker than an isotropic aggregate, instead of 1.5 times harder (Fig. S3).
Figure S3.
Evolution of the sample strength (top) and olivine CPO (bottom) as a function of the extensional strain predicted by the VPSC approach for an aggregate with an initially isotropic CPO subjected to axial extension (full lines) and measured in a low strain and the neck regions of the sample 90OA87 (full symbols). The olivine CPO evolution is characterized by the change in CPO strength (quantified by the J-index, which is the integral of the squared orientation distribution function, in black) and by the angle between the [100] maximum and the extension direction (in gray). The inserts show pole figures of the CPO (extension direction is E-W) in a low strain and the neck regions of the sample 90OA87 and at the end of the simulation. able S3 : Summary of the results of all VPSC simulations
Initial olivine CPO Strain (%) Stress* J-index Angle** Strength contrast 90OA87_neck 100 1.62E+01 2.5156 15.9481 9.62E-01 90OA87_shadow 7 1.57E+01 1.3153 16.2901 9.35E-01 VS15a1 0 1.92E+01 3.1901 14.0875 1.14E+00 VS15ab1 (45a/90b) 0 1.95E+01 5.1896 8.0316 1.16E+00 VS15ab2 (45a/45b) 0 1.58E+01 1.3719 29.7466 9.36E-01 VS15b1 0 1.87E+01 4.1774 57.664 1.11E+00 random 0 1.68E+01 1 n/d 1.00E+00 random 20 1.73E+01 1.3132 0.8478 1.03E+00 random 40 1.90E+01 1.8421 0.9364 1.13E+00 random 60 2.15E+01 2.7522 0.9661 1.28E+00 random 80 2.41E+01 3.9754 0.9776 1.43E+00 random 100 2.60E+01 5.3078 0.982 1.55E+00 * Normalized to the CRSS of the [100](010) slip system ** Angle between the [100]max and the extension direction *** Relative to the isotropic behavior
Supplementary Material References