Earth and Planetary Science Letters xxx (2009) xxx–xxx
EPSL-09676; No of Pages 6
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Large strain shearing of halite: Experimental and theoretical evidence for dynamictexture changes
Hans-Rudolf Wenk a,⁎, Marina Armann b, Luigi Burlini b, Karsten Kunze c, Mauro Bortolotti a
a Department of Earth and Planetary Science, University of California, Berkeley, California 84720, USAb Geological Institute, ETH Zürich, 8092 Zürich, Switzerlandc Electron Microscopy (EMEZ), ETH Zürich, 8093 Zürich, Switzerland
Please cite this article as: Wenk, H.-R., etchanges, Earth Planet. Sci. Lett. (2009), doi
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Article history:
We report results from tors Received 5 December 2008Received in revised form 20 January 2009Accepted 23 January 2009Available online xxxx
Editor: R.D. van der Hilst
Keywords:shear deformationhalitelarge strain
PROion experiments on polycrystalline halite (NaCl) to shear strains γ=8 and observe
a very complex texture evolution. The same behavior was reproduced with polycrystal plasticity simulations,suggesting that we capture the underlying mechanisms. While crystal shapes gradually rotate into the shearplane, crystal orientations change continuously and dynamic texture patterns evolve with increasing shear.This is highly significant for ultra-large deformation, as for example implied from geodynamic modeling forthe deep earth, where seismic anisotropy patterns may develop and locally disappear again as material isdeformed during convection. The study also suggests that caution is required when interpreting deformationmechanisms from simple shear preferred orientation patterns.
Simple shear is important in material science as well as earthsciences. In metallurgy, it is relevant in high-
^speed cutting (Dudzinski
et al., 2002), in geology shear occurs in ductile faults and in geophysicsshear is involved in convection in the deep earth. Many aspects remainenigmatic and a combination of large-
^strain shear experiments
combined with numerical modeling provides new insights.Simple shear deformation is fascinating because, on the crystal
lattice scale, all deformation by dislocation glide occurs in simple shearand an arbitrary deformation of a crystal is accommodated by slip on acombination of different slip systems. On a macroscopic scale,incremental simple shear (Fig. 1b) is related to pure shear (Fig. 1a) bya 45° rotation against the sense of shear. At low strains preferredorientation patterns from coaxial pure shear and non-
^coaxial simple
shear show such a relationship. This has been shown not only for fccmetals (Canova et al., 1984; Bolmaro and Kocks,1992) but also for non-
^cubicminerals such as olivine (Zhang andKarato,1995), calcite (Barberet al., 2007) and quartz (Dell Angelo and Tullis,1989).While the overalldeformation and strain on individual crystalsmay be similar, the strainpath is entirely different, with amonoclinic deformation symmetry forsimple shear versus orthorhombic symmetry for pure shear. Thissymmetry is expressed in the preferred orientation patterns.
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TEThere are two interpretations for textures produced during simpleshear. On one hand polycrystal plasticity theory predicts crystal latticerotations,mainly in the sense of shear, due to activity of slip systems andconfinements by the surrounding grains. These rotations occur atdifferent speed, depending on the activities and orientation of slipsystems. Fig. 2a illustrates lattice rotation increments for a grain of haliteduring shear deformation to γ=
^17.3 in 2% strain steps. Texture maxima
occur where rotations are slowest. There are no stable orientations, incontrast to pure shear or compression (e.g. Wenk et al., 1989a).
On the other hand, an intuitive interpretation suggests that one slipplane aligns with the macroscopic shear plane and a slip direction withthe macroscopic shear direction (Schmid et al., 1981). In halite, at lowtemperature, {110} are the easiest slip planes and b10N the easiest slipdirections. Indeed, if all crystalswere aligned thisway–
^essentiallya single
crystal –^homogeneous deformation could occur without any rotations
and one could use preferred orientations to infer the active slip systems.This “easy slip” interpretation has two main pitfalls: it does not explainhowgrains reach this orientation; and inmost crystalsmore than one slipsystem exist, which constantly change their activity due to rotation.Witha single slip systemone couldnotdeformapolycrystal bydislocationglidewithout having it break apart. In a cubic crystal such as halite, there are sixsymmetrically equivalent {110} planes. Torsion deformation experimentson halite to large strains shed new light onwhether textures continue toevolve during shear or reach a stable position.
Deformation of halite aggregates has been of longstanding interest,in part sparked by projects to use salt rocks as repositories for nuclearwaste (Hwang et al., 1992), CO2 or gas storage due to its limitedpermeability. In addition, salt domes represent cap rocks for oil and
halite: Experimental and theoretical evidence for dynamic texture
Fig. 1. Relationship of pure shear (a) and simple shear (b). The finite strain ellipse ofsimple shear is inclined against the ellipse of pure shear against the sense of shear.
Fig. 2. Viscoplastic simulation of simple shear deformation of halite. (a) Rotationtrajectories of {100} poles for a single grain (initial orientation Bunge Euler anglesϕ1=320°, Φ=75° and ϕ2=24°) to εvm=10 (γ=17.3) in 0.02 increments. Some shearstrain values γ are indicated along the trajectories. Note that the rotations are generallyin the sense of shear. (b) {100} pole figure with 200 orientations after εvm=3 (γ=5.1).Equal area projection, the symbol size is proportional to the grain deformation, the traceof the shear plane is horizontal and shear sense is dextral.
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gas reservoirs (Jackson and Talbot, 1986; Carter et al., 1993). Our maininterest is linked to deep earth rheology since halite has the samestructure and similar slip systems as magnesiowüstite, which is amajor phase in the lower mantle.
2. Experiments
Experiments on halite single crystals established deformationmechanisms (Carter and Heard, 1970) and deformation experimentson polycrystals documented texture development, mainly in com-pression geometry (Kern and Braun, 1973; Franssen, 1994), with a fewexperiments in extension (Skrotzki andWelch, 1983; Lebensohn et al.,2003), pure shear (Skrotzki et al., 1995) and simple shear (Franssenand Spiers, 1990). Interpretation of preferred orientation patterns hasrelied on comparison of measurements on experimentally deformedsamples with polycrystal plasticity simulations. Halite was the firstmineral to which the Taylor theory was applied (Taylor, 1938; Siemes,1974). Application of the viscoplastic self-
^consistent model to halite
deformed in extension revealed differences between the Taylor modelthat relies on strain compatibility and the self-
^consistent approach
that is closer to stress equilibrium (Wenk et al., 1989b). Thesedifferences were further explored by comparison with finite elementsimulations (Lebensohn et al., 2003). All these experiments andsimulations were done to moderate amounts of strain (b100% vonMises equivalent strain εVM, for definition see Hosford, 2005).However, in the torsion experiments presented here much largerstrains were achieved (N600%, i.e. shear γ=√3 εVM
^=^N8).
Fine grained (150–^200 μm) wet (water content ~35 ppm as
measured by FTIR at the University of Utrecht) synthetic haliteaggregates were prepared by cold pressing and annealing of analyticalgrade NaCl powder. Thewater content enhances climb and thus reduceshardening that often leads to early recrystallization (Ter Heege et al.,2005; Pennock et al., 2006). In these experiments we wanted to avoidrecrystallization by nucleation as well as grain boundary migration(Humphreys and Hatherly, 1996), in order to concentrate on deforma-tion by dislocation glide. Torsion experiments were carried out in a highpressure/high temperature Paterson deformation apparatus (Patersonand Olgaard, 2000) to large shear strain at a constant temperature of200 °C, confining pressure of 250 MPa and at two constant twist ratescorresponding to nominal shear strain rates of γ̇=
^3×10−
^3 s−
^1 (sample
P0742) and γ̇=^3×10−
^4 s−
^1 (all others). In torsion every small volume
element of the sample undergoes deformation by simple shear at aconstant strain rate. From the deformed samples polished sectionswereprepared perpendicular to the cylinder radius at the outer samplemargin. Textures were measured by electron backscatter diffraction(EBSD) using an EDAX-
^TSL OIM system with DigiviewFW detector
installed on a SEM CamScan CS44LB.Orientationmaps of selected areas near and parallel to the external
surface of the deformed samples (where shear deformation is amaximum) illustrate a microstructure with increasingly elongatedgrains (Fig. 3) with progressive shear from γ=
^1 to γ=
^8. The foliation
correlates well with the macroscopic deformation illustrated by strainellipses. The grain elongation is inclined towards the shear plane withthe sense of shear, and the angle is reduced with increasing strain.Deformation is fairly homogeneous but some grains deform more
Please cite this article as: Wenk, H.-R., et al., Large strain shearing ofchanges, Earth Planet. Sci. Lett. (2009), doi:10.1016/j.epsl.2009.01.036
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1than others, depending on their orientation. This is most pronounced1at low strain (γ=
^1, Fig. 3a). The sheared elongated grains contain slip
1bands and polygonally shaped subgrains. The misorientations1between subgrains remain minor (b15°) as indicated by the modest1color changes inside the grains in the orientation map (Fig. 3a). With1increasing shear strain (γ=
^3), misorientation between subgrains
1increases with values sometimes exceeding 15°, indicating that1subgrains rotate to form new grains, but most original grains are1still recognizable (Fig. 3b). With further straining, grains becomemore1elongated, consistent with the finite strain ellipse. In the high shear1strain samples (γ=
^5 in Fig. 3c and γ=
^8 in Fig. 3d) subgrain rotation is
1most pronounced, resulting in an apparent grain-^size reduction.
1However, even at γ=^8 some original grains are recognizable with
1distinct color patterns. There is no evidence for nucleation and growth1along grain boundaries and little grain boundary migration.1500
^,000
^single orientation measurements over a maximum area of
17×9mmwere thenused to calculate anorientationdistribution (OD)with15°×5°×5°cells and smoothing with a 7.5° Gauss filter. From the OD, pole1figureswere constructedwhichwe apply to display texture development.1While the evolution of strain is regular, changes in orientation patterns1with shear strain are striking and unexpected (Fig. 4, left side). At low1strains,111 and 110 polefigures have a “hexagonal” appearancewith a 1111maximum normal to the shear plane and a 110 maximum in the shear1direction (γ=
^1). This distribution attenuates and becomes more asym-
1metric, with a strong asymmetric 100 maximum (γ=^2). With increasing
1strain, the 100maximum rotates towards the shear plane normal and the1110maximum in the shear direction increases in strength (γ=
^3 andγ=
^6).
1At thehighest strain (γ=^8), thepreferredorientation canbedescribed as a
1“rotated cube” with a 100 maximum normal to the shear plane and two1{100}maximaat45° to the sheardirection.At all stagesof thedeformation1history, there is awide spread of orientations, as is obvious from the color1differences in the orientationmaps (Fig. 3) aswell as from thepolefigures1with many orientations not associated with the maxima (pole figure1minima are larger than 0.2 multiples of a random distribution or m.r.d.).1Could the systematic texture changes be due to changes in slip1mechanisms? Using the easy slip interpretation we could ascribe the1low strain texture to {111}b ¯̄110N slip and the high strain texture to1{100}b011N slip. Here polycrystal plasticity simulations to large strains1may help us understand.
13. Model
1For polycrystal plasticity we used the viscoplastic self-^consistent
1computer code VPSC (Molinari et al., 1987; Lebensohn and Tomé, 1994)1modified for large strains. The viscoplastic approach assumes that the1strain rate is linked to the stress by a power law. If the stress exponent
halite: Experimental and theoretical evidence for dynamic texture
Fig. 3. Microstructures of halite experimentally deformed in torsion. High resolution orientation imaging maps measured by EBSD using a scanning step size of 0.5 μm. The shearplane is horizontal and shear sense is dextral. Color key is according to inverse pole figures of the shear plane normal. Only a small sector of the measured area is shown. a) Sampledeformed to a shear strain of γ=1, showing a typical deformation microstructure with elongated grains containing polygonal subgrains. b) At a shear strain of γ=3 the apparent grainsize is reduced compared to the low shear strain sample due to subgrain rotation. c) At a shear strain of γ=5 a secondary foliation outlined by original grain boundaries develops. d) Ata shear strain of γ=8 there is pervasive grain size reduction due to subgrain rotation recrystallization, but some old grain boundaries are still visible.
3H.-R. Wenk et al. / Earth and Planetary Science Letters xxx (2009) xxx–xxx
occurs until the critical shear stress (crss) is reached. In minerals smalldeformation occurs below the crss. VPSC can be used for a variety ofconditions rangingbetweenhomogeneous deformation (strain compat-ibility or Taylor model) and stress equilibrium (Sachs model). The self-
^consistent application is intermediate. It considers each grain as aninclusion in an anisotropicmedium,which is the average over all grains.The inclusion deforms viscoplastically, controlled by slip systems andorientation, against the medium. As a grain deforms by slip, latticerotations occur, caused by the slip geometry and the macroscopic grainshape rotation. Fig. 2a illustrates a rotation trajectoryof {100} for a singlegrain to an equivalent strain εVM=
^10 in 0.02 strain increments. Note the
change in rotation rates with strain. Also, differently oriented grainsdeform differently. Fig. 2b displays a set of 200 originally randomorientations after εVM=
^3 deformation with the symbol sizes propor-
tional to the finite grain deformation. Clearly there are systematicdifferences in orientation and grain deformation.
For input of the plasticity model we need to know slip systems, theirrelative crss and their strain rate sensitivity. Deformation experimentson halite single crystals have established that at 200 °C {110}b ¯̄110N is theeasiest system (crss=
^1), followed by {111}b ¯̄110N (crss=
^2) and {100}b
011N (crss=^3)^(Carter and Heard, 1970). For stress exponent n we use 8
(strain rate sensitivity 1/8=^0.125). In the model presented here we
assume that no work hardening occurs and that grain shapes are onlyupdated until they reach an aspect ratio (long to short axis) of 4. Thismimicks subgrain formation with increasing misorientations. 2000random orientations were simulated to deform in 1000 steps with a
Please cite this article as: Wenk, H.-R., et al., Large strain shearing ofchanges, Earth Planet. Sci. Lett. (2009), doi:10.1016/j.epsl.2009.01.036
strain increment of 0.02, resulting in a final von Mises equivalent strainof εVM=
^20 (in plane strain), corresponding to a shear γ=
^√3 εVM=
^28. To
our knowledge these are some of the largest strain texture simulationsthat have beenperformed. The results are fairly robust tominor changesin the assumed parameters and here we are interested in the overallpattern. For the same conditions, we performed both self-
^consistent
simulations and Taylor simulations and results are similar. It appears,based on details of the texture patterns, that initially the self-
^consistent
deformation ismore applicable, i.e. grainsdeformdifferently, dependingonorientation, tomaintain stress equilibrium.With increasing strain theTaylor model describes details better and homogeneous deformation isapproached, with all grains of similar shape.
The individual orientations at various strain steps were transformedinto an OD and from this, pole figures were calculated, similar to theprocedurewithEBSDmeasurements. Thesepolefigureson the right sideof Fig. 4 illustrate simulated texture changes with increasing strain. Thesimulated pole figures show a similar transition from a texture with 111normal to the shear plane and 110 in the sheardirection to a texturewith100 normal to the shear plane and 110 in the shear direction, just as inthe experiments. In addition to texture patterns, the simulations alsoprovide information about mechanisms and they can be extended tomuch larger strains than attained in the experiments.
4. Discussion
A detailed analysis reveals that during the whole strain history, anaverage of 4–
^6 individual slip systems are active in each grain (with an
halite: Experimental and theoretical evidence for dynamic texture
Fig. 5. Viscoplastic polycrystal plasticity simulation of large strain simple shear deformation of halite to γ=35. Bottom shows activity of slip systems (in %), and above some {100} polefigures and plots of main grain elongation axes. The trace of the shear plane is horizontal and shear sense is dextral.
Fig. 4. Pole figures of halite deformed in simple shear. (left) EBSD measurements on samples from torsion experiments at 200 °C. (right) Polycrystal plasticity simulations, startingwith self-consistent assumption (50% and 100%) and continuing with homogeneous strain at higher deformation. Equal area projection, linear contour intervals. The trace of the shearplane is horizontal and shear sense is dextral.
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activity of N5%), two ormore of which contributemore than 20% to thestrain in most grains. Initially (in the random aggregate) 54% of thestrain is accommodated by the easiest {110} systems, 36% by {111}-
^slip
and 10% by the hardest {100} systems (Fig. 5). From the texture pattern(Fig. 4, γ=
^0.9) we could have guessed that {111}b ¯̄110N slip is mainly
active because {111} planes are preferentially oriented in the shearplane, which is clearly not the case. As texture evolves {110} slipbecomes less favored and already at γ=
^3.5 activity drops below 20%,
while activity on the harder {111} and {100} systems steadily increases(to N50% for {111} and 35% for {100}). At γ=
^5, the “rotated cube
texture”, the dominant slip system (N50%) is {111}b ¯̄110N and thus therotated cube texture is not due to prevailing {100}b011N slip as onemay have intuitively suspected. A surprising conclusion is that largestrain simple shear experiments can be misleading when it comes tothe interpretation of slip systems from texture patterns. If the goal ofan experiment is to infer slip systems from preferred orientation, lowstrain compression experiments are more relevant than high straintorsion experiments.
The study also highlights differences between shape changes andorientation changes during simple shear deformation. As deformationproceeds, grains become increasingly stretched and the long axes rotatetowards the sheardirection, bothobserved in experiments (Fig. 3) and insimulations (grain major axis “pole figures” are illustrated in Fig. 5,bottom). With increasing deformation, grain shape axes cease rotating,while crystallographic orientations continue to change. From γ=
^0 to
γ=^5 the lattice of most grains rotates by over 90° (Fig. 2a), and this
spinning continues with increasing strain. Slip planes do not rotate intothe shear plane and stay there, yet their rotation rates decelerate. This ismost striking when viewed in a movie of texture evolution displayingthe continuous rotations and changes in patterns during deformation toa shear γ=
^35 (supplementary material). Some snapshots of the movie
are shown in Fig. 5 (top), illustrating that texture strength increases andthen attenuates in repeating cycles. Because of the lattice rotations,simple shear textures never become exceedingly strong. The “tumbling”of orientations is more rapid for higher strain rate sensitivity (lowerstress exponent)
^(Toth et al., 1988). It is also more pronounced if many
slip systems are available, as in cubic crystals but applies to all materialsthat deform by dislocation glide, including quartz (Wenk et al., 1989a).
High shear/high temperature deformation experiments on peri-clase (MgO), which is isostructural with halite and has similar slipsystems, produced similar textures to those for halite, though in somecases the material recrystallized (Yamazaki and Karato, 2002;Heidelbach et al., 2003). Magnesiowüstite (Mg,Fe)O, one of the
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Fig. 6. P-wave velocity surfaces for MgO assuming texture patterns shown in the pole figuresprojection. The trace of the shear plane horizontal. Velocity contours in 10 km/s.
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important minerals of the lower mantle, is much weaker than theprimary lower mantle minerals perovskite and postperovskite (Longet al., 2006) and may control the rheology in the deep Earth.Geodynamic convection simulations suggest that during slab subduc-tion into the lower mantle, very large strains accrue and much of it insimple shear (McNamara et al., 2002;Wenk et al., 2006). Furthermore,at deep earth conditions, materials are highly rate sensitive and thusorientation patterns may continuously evolve, without reaching asteady state or producing strong texture patterns. We have calculatedMgO P-
^wave velocity surfaces corresponding to the simple shear
textures in Fig. 5, by averaging single crystal elastic properties of MgOat lower mantle conditions over the OD, and this illustrates cycles ofanisotropy development followed by attenuation (Fig. 6). This may bea reason for the overall weak seismic anisotropy in the lower mantle(Garnero et al., 2004) and for local heterogeneity (e.g. in the D” zone(Lay et al., 1998; Panning and Romanowicz, 2004; Sidorin et al., 1999)).
5. Conclusions
Fabric development in simple shear is not monotonic and thuscannot be extrapolated. Simple shear deformation experiments onhalite to large strains and polycrystal plasticity modeling illustratethat emerging orientation distributions are complex, with dynamicchanges as deformation proceeds and no convergence into strongtexture patterns. Individual grains do not rotate into “easy slip”orientations and thus shear experiments are inadequate to infer slipsystems. The results illustrated for halite are directly applicable tocubic metals as well as the lower mantle mineral magnesiowüstite. Inthe deep earth, simple shear deformation, compounded by recrys-tallization (Wenk et al., 1997), may produce heterogeneous and notvery strong texture patterns and thus only local and weak anisotropy.
Acknowledgements
We are appreciative to C. Tomé for discussions and help and to tworeviewers for most valuable comments. Research was supported byNSF (EAR-
^0836402) and CDAC. The torsion experiments, including
texturemeasurements, were part ofM. Armann's PhD thesis (Diss. ETHNo. 17633, ETH 0-
^20038-
^02). Laboratory equipment and analyses
were supported by SNF (01066/41-^2704.5) and ETH (02150/41-
^2704.5). R. Hofmann is thanked for the technical support in thelaboratory. We are appreciative to the University of Utrecht for FTIRmeasurements.
of Fig. 5 (top). Note the cyclical development and attenuation of anisotropy. Equal area
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