scholarly journals Kinking facilitates grain nucleation and modifies crystallographic preferred orientations during high-stress ice deformation

2021 ◽  
Author(s):  
Sheng Fan ◽  
David Prior ◽  
Travis Hager ◽  
Andrew Cross ◽  
David Goldsby ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Dynamic Recrystallization ◽  
Boundary Migration ◽  
High Stress ◽  
Kink Band ◽  
Coarse Grained ◽  
Compression Axis ◽  
Crystallographic Preferred Orientation ◽  
Kink Bands ◽  
Subgrain Rotation

Kinking can accommodate significant amounts of strain during crystal plastic deformation under relatively large stresses and may influence the mechanical properties of cold planetary cryosphere. To better understand the origins, mechanisms, and microstructural effects of kinking, we present detailed microstructural analyses of coarse-grained ice (~1300 µm) deformed under uniaxial compression at -30°C. Microstructural data are generated using cryogenic electron backscattered diffraction (cryo-EBSD). Deformed samples have bimodal grain size distributions, with thin and elongated (aspect ratio ≥ 4) kink domains that develop within, or at the tips of, remnant original grains (≥ 300 µm, aspect ratio < 4). Small, equiaxed subgrains also develop along margins of remnant grains. Moreover, many remnant grains are surrounded by fine-grained mantles of small, recrystallized grains (< 300 µm, aspect ratio < 4). Together, these observations indicate that grain nucleation is facilitated by both kinking and dynamic recrystallization (via subgrain rotation). Low- (< 10°) and high-angle (mostly > 10°, many > 20°) kink bands within remnant grains have misorientation axes that lie predominantly within the basal plane. Moreover, previous studies suggest the kinematics of kinking and subgrain rotation should be fundamentally the same. Therefore, progressive kinking and subgrain rotation should be crystallographically controlled, with rotation around fixed misorientation axes. Furthermore, the c-axes of most kink domains are oriented sub-perpendicular to the sample compression axis, indicating a tight correlation between kinking and the development of crystallographic preferred orientation. Kink band densities are the highest within remnant grains that have basal planes sub-parallel to the compression axis (i.e., c-axes perpendicular to the compression axis)—these data are inconsistent with models suggesting that, if kinking is the only strain-accommodating process, there should be higher kink band densities within grains that have basal planes oblique to the compression axis (for low kink-host misorientation angles, e.g., ≤ 20°, as in this study). One way to rationalize this inconsistency between kink models and experimental observations is that kinking and dynamic recrystallization are both active during deformation, but their relative activities depend on the crystallographic orientations of grains. For grains with basal planes sub-parallel to the compression axis, strain-induced GBM is inhibited, and large intragranular strain incompatibilities can be relaxed via kinking, when other processes such as subgrain rotation recrystallization are insufficient. For grains with basal planes oblique to the compression axis, strain-induced grain boundary migration (GBM) might be efficient enough to relax the strain incompatibility via selective growth of these grains, and kinking is therefore less important. For grains with basal planes sub-perpendicular to the compression axis, kink bands are seldom observed—for these grains, the minimum shear stress required for kinking exceeds the applied compressive stress, such that kinks cannot nucleate.

scholarly journals Full crystallographic orientation (<i>c</i> and <i>a</i> axes) of warm, coarse-grained ice in a shear-dominated setting: a case study, Storglaciären, Sweden

2021 ◽  
Vol 15 (1) ◽  
pp. 303-324 ◽  
Author(s):  
Morgan E. Monz ◽  
Peter J. Hudleston ◽  
David J. Prior ◽  
Zachary Michels ◽  
Sheng Fan ◽  
...  
Keyword(s):  
Dynamic Recrystallization ◽  
Boundary Migration ◽  
Shear Plane ◽  
Sampling Bias ◽  
Optical Measurements ◽  
Coarse Grained ◽  
Shear Direction ◽  
Preparation Technique ◽  
Thin Sections ◽  
Crystallographic Preferred Orientation

Abstract. Microstructures provide key insights into understanding the mechanical behavior of ice. Crystallographic preferred orientation (CPO) develops during plastic deformation as ice deforms dominantly by dislocation glide on the basal plane, modified and often intensified by dynamic recrystallization. CPO patterns in fine-grained ice have been relatively well characterized and understood in experiments and nature, whereas CPO patterns in “warm” (T>-10∘C), coarse-grained, natural ice remain enigmatic. Previous microstructural studies of coarse-grained ice have been limited to c-axis orientations using light optical measurements. We present the first study of a axes as well as c axes in such ice by application of cryo-electron backscatter diffraction (EBSD) and do so in a shear-dominated setting. We have done this by developing a new sample preparation technique of constructing composite sections, to allow us to use EBSD to obtain a representative, bulk CPO on coarse-grained ice. We draw attention to the well-known issue of interlocking grains of complex shape and suggest that a grain sampling bias of large, branching crystals that appear multiple times as island grains in thin sections may result in the typical multimaxima CPOs previously identified in warm, coarse-grained ice that has been subjected to prolonged shear. CPOs combined from multiple samples of highly sheared ice from Storglaciären provide a more comprehensive picture of the microstructure and yield a pronounced cluster of c axes sub-normal to the shear plane and elongate or split in a plane normal to the shear direction as well as a concomitant girdle of a axes parallel to the shear plane with a maximum perpendicular to the shear direction. This pattern compares well with patterns produced by subsampling datasets from ice sheared in laboratory experiments at high homologous temperatures up to strains of ∼1.5. Shear strains in the margin of Storglaciären are much higher than those in experimental work. At much lower natural strain rates, dynamic recrystallization, particularly grain boundary migration, may have been more effective so that the CPO represents a small, final fraction of the shear history. A key result of this study is that multimaxima CPOs in coarse-grained ice reported in previous work may be due to limited sample sizes and a sampling bias related to the presence of island grains of a single host that appear several times in a thin section.

High-stress crystal plasticity of amphibole and quartz in pseudotachylyte-bearing gneisses and dislocation creep in concordant quartz-rich layers from the Silvretta basal thrust (Austria)

2021 ◽  
Author(s):  
Lisa Marie Brückner ◽  
Claudia A. Trepmann
Keyword(s):  
Crystal Plasticity ◽  
Rotation Axis ◽  
High Stress ◽  
Polarized Light ◽  
Dislocation Creep ◽  
Crystallographic Preferred Orientation ◽  
Dislocation Glide ◽  
Kink Bands ◽  
Mechanical Twins ◽  
Quartz Grains

&lt;p&gt;Pseudotachylyte-bearing amphibole-rich gneisses with concordant quartz-rich layers from the base of the Silvretta nappe, Austria, are analyzed by polarized light microscopy, scanning electron microscopy and electron back scattered diffraction. Amphibole grains show microfractures, undulatory extinction, deformation lamellae, kink bands, mechanical twins and locally recrystallized grains restricted to sites of high strain, e.g. along microshear zones and twin boundaries. The twins are characterized by a twin plane parallel to (-101), a rotation axis parallel to [101] and a misorientation angle of 178&amp;#176;. The (-101) amphibole twins document the high differential stresses during crystal plasticity coeval with pseudotachylyte formation, given their high critical resolved shear stress of 200 MPa. Directly at the contact to twinned amphibole within the gneisses, quartz grains commonly show subbasal deformation lamellae, short-wavelength undulatory extinction and cleavage cracks mostly parallel to {10-11} rhombohedral planes that are decorated by recrystallized grains with a diameter of &lt; 10 &amp;#181;m. The small recrystallized grains show a crystallographic preferred orientation (CPO) that is controlled by the orientation of the host grains. This quartz microstructure consistently indicates high-stress crystal plasticity of quartz concurrent with high-stress crystal plasticity of amphibole and pseudotachylyte formation.&lt;/p&gt;&lt;p&gt;Quartz-rich layers (&gt;90% quartz) concordant to the foliation of the gneisses commonly show evidence of dynamic recrystallization in the regime of dislocation creep. The recrystallized grain microstructure is mostly homogenous without a gradient towards the lithological contact to the amphibole-rich gneisses. Locally, however, a gradient of decreasing strain towards the contact can be observed as indicated by a decreasing number of recrystallized grains. Close to the contact, quartz grains are coarse with long axes of a few mm. A core-and-mantle structure, where recrystallized grains surround a few hundred &amp;#181;m wide and mm-long porphyroclasts, is occurring in transition towards an almost completely recrystallized microstructure. The recrystallized grains show a CPO indicating rhombohedral &lt;a&gt; dislocation glide. Recrystallized grains are isometric and subgrains in porphyroclasts are of similar shape and size, indicating dynamic subgrain rotation recrystallization. Stresses on the order of hundred MPa are suggested by the diameter of recrystallized grains of in average about 10 &amp;#181;m. Locally, the recrystallized quartz aggregate is affected by subsequent low-temperature plasticity, as indicated by shear fractures offsetting the recrystallized microstructure. The missing or decreasing strain gradients of dislocation creep within the quartz-rich layers towards the amphibole-rich gneisses indicate that dislocation creep in the quartz-rich layers cannot be responsible for transferring high stresses required for high-stress crystal-plasticity of quartz and amphibole as well as pseudotachylyte-formation and suggest that dislocation creep of quartz represents an independent earlier stage of deformation.&lt;/p&gt;

scholarly journals The microstructural record of porphyroclasts and matrix of partly serpentinized peridotite mylonites – from brittle and crystal-plastic deformation to dissolution–precipitation creep

Solid Earth ◽  
2013 ◽  
Vol 4 (2) ◽  
pp. 315-330 ◽  
Author(s):  
J. Bial ◽  
C. A. Trepmann
Keyword(s):  
Plastic Deformation ◽  
Upper Mantle ◽  
Boundary Migration ◽  
High Stress ◽  
Preferred Orientation ◽  
Dislocation Creep ◽  
Polarization Microscopy ◽  
Crystallographic Preferred Orientation ◽  
Fine Grained ◽  
Serpentinized Peridotite

Abstract. We present microfabrics in high-pressure, metamorphic, partly serpentinized peridotite mylonites from the Voltri Massif, in which porphyroclasts and matrix record independent deformation events. The microfabrics are analysed using polarization microscopy and electron microscopy (SEM/EBSD, EMP). The mylonites contain diopside and olivine porphyroclasts originating from the mantle protolith embedded in a fine-grained matrix consisting mainly of antigorite and minor olivine and pyroxene. The porphyroclasts record brittle and crystal-plastic deformation of the peridotite at upper-mantle conditions and differential stresses of a few hundred MPa. After the peridotites became serpentinized, deformation occurred mainly by dissolution–precipitation creep resulting in a pronounced foliation of the antigorite matrix, crenulation cleavages and newly precipitated olivine and pyroxene from the pore fluid at sites of dilation, i.e. in strain shadows next to porphyroclasts and folded fine-grained antigorite layers. Antigorite reveals a pronounced associated shape preferred orientation (SPO) and crystallographic preferred orientation (CPO) with the basal (001) cleavage plane oriented in the foliation plane. In monomineralic antigorite aggregates at sites of stress concentration around porphyroclasts, a characteristically reduced grain size and deflecting CPO as well as sutured grain boundaries indicate also some contribution of crystal-plastic deformation and grain-boundary migration of antigorite. In contrast, the absence of any intragranular deformation features in newly precipitated olivine in strain shadows reveals that stresses were not sufficiently high to allow for significant dislocation creep of olivine at conditions at which antigorite is stable. The porphyroclast microstructures are not associated with the microstructures of the mylonitic matrix, but are inherited from an independent earlier deformation. The porphyroclasts record a high-stress deformation of the peridotite with dislocation creep of olivine in the upper mantle probably related to rifting processes, whereas the serpentinite matrix records dominantly dissolution–precipitation creep and low stresses during subduction and exhumation.

scholarly journals Axial-Compressive Behavior, Including Kink-Band Formation and Propagation, of Singlep-Phenylene Terephthalamide (PPTA) Fibers

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
M. Grujicic ◽  
S. Ramaswami ◽  
J. S. Snipes ◽  
R. Yavari ◽  
C.-F. Yen ◽  
...  
Keyword(s):  
Detrimental Effect ◽  
Mechanical Response ◽  
Topological Defects ◽  
Kink Band ◽  
Coarse Grained ◽  
Computational Investigation ◽  
Band Formation ◽  
Longitudinal Tensile Strength ◽  
Kink Bands

The mechanical response ofp-phenylene terephthalamide (PPTA) single fibers when subjected to uniaxial compression is investigated computationally using coarse-grained molecular statics/dynamics methods. In order to construct the coarse-grained PPTA model (specifically, in order to define the nature of the coarse-grained particles/beads and to parameterize various components of the bead/bead force-field functions), the results of an all-atom molecular-level computational investigation are used. In addition, the microstructure/topology of the fiber core, consisting of a number of coaxial crystalline fibrils, is taken into account. Also, following our prior work, various PPTA crystallographic/topological defects are introduced into the model (at concentrations consistent with the prototypical PPTA synthesis/processing conditions). The analysis carried out clearly revealed (a) formation of the kink bands during axial compression; (b) the role of defects in promoting the formation of kink bands; (c) the stimulating effects of some defects on the fiber-fibrillation process; and (d) the detrimental effect of the prior compression, associated with fiber fibrillation, on the residual longitudinal-tensile strength of the PPTA fibers.

scholarly journals Dynamic Recrystallization in a Naturally Deformed Albite

1983 ◽  
Vol 5 (4) ◽  
pp. 219-237 ◽  
Author(s):  
J. D. Fitz Gerald ◽  
M. A. Etheridge ◽  
R. H. Vernon
Keyword(s):  
Dynamic Recrystallization ◽  
Grain Boundaries ◽  
Boundary Migration ◽  
Experimental Studies ◽  
Shear Zones ◽  
Optical Microscope ◽  
Coarse Grained ◽  
Transmission Electron ◽  
Subgrain Growth ◽  
Diffraction Patterns

Coarse-grained, deformed albite occurs in veins within a blueschist from the Cazadero region, California. In some grains, deformation and recrystallization are concentrated in narrow shear zones less than 50 μm wide. We have examined the substructural progression across these zones by transmission electron microscopy (TEM), in an attempt to determine the details of the dynamic recrystallization mechanism. The misorientation across subgrain and recrystallized grain boundaries has been determined by analysis of electron diffraction patterns.Dynamic recrystallization apparently proceeded by the following stages: 1) the formation of a well-ordered substructure from a more tangled, cell-like array, 2) increasing misorientation between subgrains, 3) rapid growth of subgrains at a misorientation between 3° and 5° to produce new “grains” with straighter grain boundaries and lower internal dislocation densities and 4) continued deformation and rotation of the recrystallized grains with local grain-boundary migration to maintain relatively equiaxed shapes. The ultimate recrystallized structure in the narrow deformation zones consists of grains misoriented by between 5° and at least 30°, most of them containing a well-developed substructure.The combination of subgrain growth and rotation explains a number of features common to dynamically recrystallized minerals. The smaller subgrains present prior to growth and also within recrystallized grains form a population distinct from the larger subgrains and recrystallized grains of approximately equal size, which are those observed in an optical microscope. The smaller subgrains are visible only in TEM. Individual recrystallized grains may remain through substantial straining, rotating in response to dislocation and sub-boundary motion within them, thus preserving and even enhancing the crystallographic fabric (texture). The retention of an initial recrystallized grain population throughout significant continuing deformation may explain the absence of strain softening in some recent experimental studies.

Dynamic Recrystallization of Dense Polycrystalline NaCl: Dependence of Grain Size Distribution on Stress and Temperature

2004 ◽  
Vol 467-470 ◽  
pp. 1187-1192 ◽  
Author(s):  
J.H. ter Heege ◽  
J.H.P. de Bresser ◽  
C.J. Spiers
Keyword(s):  
Grain Size ◽  
Dynamic Recrystallization ◽  
Boundary Migration ◽  
Elevated Pressure ◽  
Dislocation Creep ◽  
Grain Boundary Migration ◽  
Subgrain Rotation ◽  
Recrystallized Grain Size ◽  
Flow Laws ◽  
Size Data

Only few models explain the development of a steady state grain size during dynamic recrystallization, and their microphysical basis is poorly understood. In this study, we investigate mechanical and microstructural data on dry and wet NaCl, deformed at a range of stresses and temperatures at elevated pressure, with the aim to evaluate the different models. The results show that dry NaCl continuously work hardens and shows evidence for recrystallization dominated by progressive subgrain rotation, while the wet material shows, at similar conditions, oscillating stressstrain behaviour and recrystallization dominated by grain boundary migration. Taking into account the distribution of grain size, deformation of wet NaCl is best described by flow laws based on composite grain size sensitive (GSS) solution-precipitation creep and grain size insensitive (GSI) dislocation creep. The recrystallized grain size data in wet NaCl can be modeled with the hypothesis that recrystallized grain size organises itself in the boundary between the GSS and GSS creep domains.

Superposed structures in the Mona Complex at Rhoscolyi Ynys Gybi, North Wales

1992 ◽  
Vol 129 (4) ◽  
pp. 475-490 ◽  
Author(s):  
H. Roper
Keyword(s):  
Simple Shear ◽  
Large Scale ◽  
Axial Direction ◽  
Kink Band ◽  
Alternative Interpretation ◽  
First Episode ◽  
Band Model ◽  
Kink Bands ◽  
The North ◽  
Island Group

AbstractThe Bedded Series of the Mona Complex at Rhoscolyn comprises two groups of clastic metasediments: the Holy Island Group, consistingof quartzites, impure psammites and pelites, with well-preserved bedding, is overlain conformably by the New Harbour Group, which is for the most parthomogeneously semi-pelitic without surviving bedding. Both groups have undergone the same two major tectono-metamorphic episodes, but with differing response. In the Holy Island Group the first episode (Dx) produced nearly upright and upward-facing folds (Fx) with an axial planar foliation (Sx), which varies from an anastomosing or rough-spaced cleavage in quartzites to a penetrative phyllitic schistosity in pelites. In the New Harbour Group Dx has generally obliterated original bedding surfaces, replacing them with a composite foliation (Sx) of fine compositional banding and a penetrative schistosity, together with a stretching lineation (Lx), the latter being at a high angle to the Fx axial direction. The Dx structures are attributed to a major episode of compressional tectonics.The structures attributed to the second deformation (Dy) includestrata-bound sets of quartz-filled tension fractures (attributed by most previous authors to an earlier episode), abundant NNW-verging asymmetric folds (Fy) of Sx, and a sporadically developed set of shear fractures which constitute a crenulation cleavage (Sy) axial planar to the folds. It is suggested that all these structures were produced by a single agency. One interpretation is that the observed shear fractures and folded tension fractures correspond fairly closely to and provide a natural analogy of those obtained in the classical simple shear experimentsof Riedel. In this case all the Dy structures can be accounted for by the action of a large-scale simple shear couple (Cy), whose vergence and shallow dip were both towards the NNW. Such a mechanism may imply a gravity-dominated regime of net horizontal extension in a NNW-SSE direction, with extension being less constrained to the north than to the south. J. W. Cosgrove has suggested an alternative interpretation, that all the Dy structures can be explained as reverse kink bands; the simple shear interpretation is here preferred because the angle between Sy and the estimated direction of Pmax during Dy was < 45°; the kink band model would require an angle > 45°.The fact that cleavage vergence boundaries for both Sx and Sy occur close to the hinge zone of the Rhoscolyn Antiform is consistent with either Dx or Dy age for the initiation of this fold. However, when fold limb length (or limb rotation) vergence is considered, the presence of an Fx0 vergence boundary but absence of an Fxy vergence boundary (and by implication of an Fy0 boundary) is consistent with a Dx age but difficult to reconcile with a Dy age.

Residual Stress Measurement around the Interface of Copper Bicrystal Deformed by Uniaxial Extension

2010 ◽  
Vol 64 ◽  
pp. 125-134
Author(s):  
Hanabusa Takao ◽  
Ayumi Shiro ◽  
Tatsuya Okada
Keyword(s):  
Residual Stress ◽  
Synchrotron Radiation ◽  
Grain Boundary ◽  
Residual Stresses ◽  
Uniaxial Extension ◽  
Kink Band ◽  
X Rays ◽  
X Ray ◽  
Kink Bands ◽  
Crystal Orientations

Residual stresses of a copper bicrystal were measured by X-ray diffraction and synchrotron radiation. A copper bicrystal specimen with a 90-degree tilt boundary was fabricated by the Brigdman technique. After the plastic extension of 30%, kink bands developed in a deformed matrix along the grain boundary. In this study, we focused on the residual stress distribution along the transverse direction of the specimen surface and the residual stresses in deformed matrix and kink band near the grain boundary. Residual stresses were evaluated by the X-ray single crystal measurement method. Stereographic projections were used to determine crystal orientations of deformed regions. It was found that crystal orientations were different between the deformed matrix and the kink band. Residual stresses in the direction along the grain boundary were compressive in the vicinity of the boundary and tensile in the region apart from the boundary. Residual stresses in the kink band were large in compression in compared with those in the deformation matrix. The difference in the results between X-rays and synchrotron radiation suggests that there is a depth variation in the deformation and therefore the residual stress development.

scholarly journals Mechanical Properties and Deformation Mechanisms of Graphene Foams with Bi-Modal Sheet Thickness by Coarse-Grained Molecular Dynamics Simulations

Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5622
Author(s):  
Shenggui Liu ◽  
Mindong Lyu ◽  
Chao Wang
Keyword(s):  
Mechanical Properties ◽  
Elastic Recovery ◽  
Structural Connectivity ◽  
High Stress ◽  
Sheet Thickness ◽  
Functional Materials ◽  
Deformation Mechanisms ◽  
Coarse Grained ◽  
Graphene Sheets ◽  
Graphene Foams

Graphene foams (GrFs) have been widely used as structural and/or functional materials in many practical applications. They are always assembled by thin and thick graphene sheets with multiple thicknesses; however, the effect of this basic structural feature has been poorly understood by existing theoretical models. Here, we propose a coarse-grained bi-modal GrF model composed of a mixture of 1-layer flexible and 8-layer stiff sheets to study the mechanical properties and deformation mechanisms based on the mesoscopic model of graphene sheets (Model. Simul. Mater. Sci. Eng. 2011, 19, 54003). It is found that the modulus increases almost linearly with an increased proportion of 8-layer sheets, which is well explained by the mixture rule; the strength decreases first and reaches the minimum value at a critical proportion of stiff sheets ~30%, which is well explained by the analysis of structural connectivity and deformation energy of bi-modal GrFs. Furthermore, high-stress regions are mainly dispersed in thick sheets, while large-strain areas mainly locate in thin ones. Both of them have a highly uneven distribution in GrFs due to the intrinsic heterogeneity in both structures and the mechanical properties of sheets. Moreover, the elastic recovery ability of GrFs can be enhanced by adding more thick sheets. These results should be helpful for us to understand and further guide the design of advanced GrF-based materials.

Synthesis and elastic and mechanical properties of Cr2GeC

2008 ◽  
Vol 23 (8) ◽  
pp. 2157-2165 ◽  
Author(s):  
Shahram Amini ◽  
Aiguo Zhou ◽  
Surojit Gupta ◽  
Andrew DeVillier ◽  
Peter Finkel ◽  
...  
Keyword(s):  
Mechanical Energy ◽  
Kink Band ◽  
Max Phase ◽  
Elastic Solids ◽  
Max Phases ◽  
Kink Bands ◽  
Young’S Moduli ◽  
Microscale Model ◽  
Energy Dissipated ◽  
Nonlinear Elastic

Herein we report on the synthesis and characterization of Cr2GeC, a member of the so-called Mn+1AXn (MAX) phase family of layered machinable carbides and nitrides. Polycrystalline samples were synthesized by hot pressing pure Cr, Ge, and C powders at 1350 °C at ∼45 MPa for 6 h. No peaks other than those associated with Cr2GeC and Cr2O3, in the form of eskolaite, were observed in the x-ray diffraction spectra. The samples were readily machinable and fully dense. The steady-state Vickers hardness was 2.5 ± 0.1 GPa. The Young’s moduli measured in compression and by ultrasound were 200 ± 10 and 245 ± 3 GPa, respectively; the shear modulus and Poisson’s ratio deduced from the ultrasound results were 80 GPa and 0.29, respectively. The ultimate compressive strength for a ∼20 μm grain size sample was 770 ± 30 MPa. Samples compressively loaded from 300 to ∼570 MPa exhibited nonlinear, fully reversible, reproducible, closed hysteretic loops that dissipated ∼20% of the mechanical energy, a characteristic of the MAX phases, in particular, and kinking nonlinear elastic solids, in general. The energy dissipated is presumably due to the formation and annihilation of incipient kink bands. The critical resolved shear stress of the basal plane dislocations—estimated from our microscale model—is ∼22 MPa. The incipient kink band and reversible dislocation densities, at the maximum stress of 568 MPa, are estimated to be 1.2 × 10−2 μm−3 and 1.0 × 1010 cm−2, respectively.

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