Kink Boundaries Research Articles

Perpendicular Deformation of a Near-Single-Crystal Triblock Copolymer with a Cylindrical Morphology. 2. TEM

A poly(styrene-block-isoprene-block-styrene) (SIS) triblock copolymer with a polystyrene (PS) cylinder morphology was globally oriented via roll-casting. Transmission electron microscopy (TEM) was used to assess the quality of orientation. The roll-casting process produces films with near-single-crystal-like orientation. Large strain deformation was applied perpendicular to the cylinder axis and retained by irradiating the sample with high energy electrons. TEM of sections viewed parallel and perpendicular to the cylinder axis provided real space information on the deformed morphology. For views parallel to the cylinder axis, the initial hexagonal packing of the cylinders distorts into a faulted twinlike texture in which layers of cylinders are oriented at fixed angles with respect to the stretching direction (SD). These fault boundaries are separated by an average distance of about 0.1 μm at 180% deformation. Direct evidence for a chevron texture in which the cylinders kink and turn into the SD was observed at perpendicular incidence. Kink boundaries are separated by an average distance of about 5 μm at a strain of 180%. Optical transforms (OTs) of the TEM images as well as SAXS on deformed irradiated samples are used to directly connect the results to the dynamic SAXS described in a complementary paper. 1 A 3-D model of the deformed morphology summarizes the real space data self-consistently and provides the basis for an interpretation of the dynamic SAXS data.

HREM Observations of Kinking in SiC Induced by Ball Milling

Kinking in SiC during ball milling (BM) at room temperature has been reported in this article. High-resolution electron microscopy (HREM) has been employed to characterize the microstructure at the atomic level. HREM observations show that partial dislocations can be introduced into SiC and glide on the primary (0001) planes under BM at room temperature. When numbers of the gliding partials are piled up along one direction, a kink boundary forms, which will initiate a crack. However, when gliding partials are not piled up, glide of the partials changes the stacking sequence and transformation from 6H-SiC→3C-SiC occurs.

Dislocations, kink bands, and room-temperature plasticity of Ti3SiC2

Transmission electron microscopy (TEM) of aligned, macrograined samples of Ti3SiC2, deformed at room temperature, shows that the deformed microstructure is characterized by a high density of perfect basal-plane dislocations with a Burgers vector of 1/3〈112 0〉. The dislocations are overwhelmingly arranged either in arrays, wherein the dislocations exist on identical slip planes, or in dislocations walls, wherein the same dislocations form a low-angle grain boundary normal to the basal planes. The arrays propagate across entire grains and are responsible for deformation by shear. The walls form as a result of the formation of kink bands. A dislocation-based model, that builds on earlier ideas proposed for kink-band formation in hexagonal metallic single crystals, is presented, which explains most of the microstructural features. The basic elements of the model are shear deformation by dislocation arrays, cavitation, creation of dislocation walls and kink boundaries, buckling, and delamination. The delaminations are not random, but successively bisect the delaminating sections. The delaminations and associated damage are contained by the kink boundaries. This containment of damage is believed to play a major role in endowing Ti3SiC2 and, by extension, related ternary carbides and nitrides with their damage-tolerant properties.

The compressive deformation of cross-linkable PPXTA fibres

A study has been conducted on the compressive deformation behaviour of thermally cross-linkable poly(p-1,2-dihydrocyclobuta phenylene terephthalamide) (PPXTA) fibres. The morphology of the failure zones was examined by scanning electron microscopy and dark-field transmission electron microscopy. On increasing the heat-treatment temperature from 260–400°C, and therefore with increasing cross-link density, fewer kinks per unit length were displayed after compressive deformation. The kink specific energy was estimated to increase by a factor of 30, as determined by quantitative measurements of kink density at a given strain and of the critical strain to kink formation. Thus, the intermolecular cross-links still allowed deformation to proceed by kinking, but significantly raised the energy of kink formation. Finally, rupture zones were predominantly observed in axially compressed PPXTA fibres heat-treated at 440°C. Compressive failure of the fibres changed from kink-dominated failure to brittle rupture with increased heat-treatment temperature, evidently as the result of cross-linking or of chain degradation. A dislocation model of the kink boundary developed by Vladimirov et al. was analysed and critically compared with our data. The analysis of this theory with our experimental results suggested that the dramatic change in compressive behaviour with cross-linking was due to a transition from fine intermolecular shear to blocky interfibrillar shear.

Failure mechanisms of laminated carbon-carbon composites—I. Under uniaxial compression

Failure mechanisms under uniaxial compressive loading are determined for several types of two dimensional (2D)carbon-carbon composites. Compressive strengths ranging from 90 to 180 MPa are observed. As expected, under uniaxial compression, a shear band is formed across the specimen diagonal. Remarkably, no inelastic deformation, either in the form of micro-buckling or microcrack nucleation was observed prior to the terminal shear failure. The crimp angles associated with the weaving pattern are significant not only in pre-setting the angle of the shear band but also in regard to the local kink boundary angle β in the fiber bundles. Hitherto unreported values of β ranging from 50 to 60°, and the kink inclination angle α in the range 35–40°, are observed. A theoretical analysis relating the peak compression load to α and β, with crimp angles as initial imperfections, explains the experimental observations.

Experimental deformation of muscovite

The strength and mechanical anisotropy of muscovite have been investigated by shortening single crystals at 45°, 0° and 90° to the basal plane (001) at temperatures T from 20 to 400°C, confining pressures P c from 10 to 400 MPa, and strain rates ε from 2.5 × 10 −7 to 2.3 × 10 −4 s −1. Samples deformed as 45° to (001) exhibit smooth undulatory extinction in thin section associated with dislocation glide, with few well developed low-angle kink boundaries. Basal shear strengths depend on confining pressure at P c < 50 MPa with a coefficient of internal friction μ of ∼0.4, while shear strengths measured at 100–400 MPa appear to be insensitive to confining pressure. Results for samples shortened at P c ≥ 100 MPa at 45° to (001) and directions [001], [110], [310] and [010] within the basal plane suggest only a weak mechanical anisotropy within (001), corresponding to Burgers vectors 〈100〉, 1/2〈110〉 and 1/2〈110〉. The effects of temperature and strain rate on glide strengths are relatively small. Assuming an exponential relationship between differential stress σ and strain rate ε of the form ε ̇ = A exp (aσ) exp (-Q/ RT) , results from temperature- and strain rate-stepping experiments performed at P c = 200 MPa yield an activation energy Q of 47 ± 19 kJ mol −1 and an exponential constant a of 0.5 ± 0.2 MPa −1. Samples loaded parallel to the basal plane shorten by the development of sharply defined kink bands. Strengths associated with kink band formation are higher than those associated with glide in samples compressed at 45° to (001) and exhibit significant pressure dependence ( μ ≊ 0.8) up to confining pressures of 200 MPa. Kink bands are generated at the ends of samples where contact is made with the pistons. Samples loaded at 90° to (001) are much stronger than samples of all other orientations and deformation is accomplished by fracture. Fracture strengths exhibit a strong dependence on confining pressure ( μ ≊ 0.9), similar in magnitude to other silicates that are brittle at the same conditions. By comparison with biotite, muscovite is weaker in shear on (001) at the experimental conditions tested with an activation energy for glide, Q, that is significantly smaller than that for glide in biotite.

Structural controls on the distribution of gold-bearing quartz veins in the Arltunga gold field, Northern Territory, Australia

The Arltunga gold field in central Australia is a Carboniferous epigenetic vein-type gold deposit which is hosted by quartzite, quartzofeldspathic gneiss, calc-silicate, and mica schist. It is situated within a large ductile shear zone that forms the floor thrust for a series of nappes: the Arltunga Nappe Complex. Gold and other minerals were deposited within quartz veins by fluids that were channeled along the shear zone during the waning stages of greenschist facies metamorphism. A geometric and genetic relationship existed between the evolving structure of the cooling shear zone and progressively emplaced quartz veins with associated gold and sulfide mineralization.Southward thrusting was inhibited late in the history of the shear zone and subsequent strain was partitioned along north-verging kink zones. The kinked anisotropy occurred at high angles to the kink boundary, within the shortening field of the regionally distributed strain pattern. This resulted in the development of simple kink geometries associated with minor buckling, which rotated the laminated rock along the kink zones into the extensional field. The accompanying dilatancy caused the deposition of extensional gold-barren quartz veins along the kink zones that can be divided into two types: en echelon arrays of dilational veins that formed as tension gashes in relatively incompetent mica schists, and tensional veins parallel to the kink zone boundaries. With progressive deformation and waning metamorphic temperatures, strain was further localized within the kink zones as an anastomosing system of narrow, steep south-dipping reverse faults. These faults reflect the transition from ductile to brittle structures and mainly occur in the more competent rock types such as the quartzite, the mica-poor quartzofeldspathic gneiss, and the extensional quartz veins. Where the fracture system transects these lithologies, extensive brecciation caused dilatant zones that host deposits of gold together with quartz, pyrite, chalcopyrite, calcite, and minor silver. Many of the earlier extensional veins that contained vugs filled in with comb quartz became mineralized.The preferred occurrence of gold in the monomineralic quartzites, and the conspicuous lack of wall-rock alteration in all other lithologies, suggests only limited control of the wall rock on gold deposition. General retrograde metamorphic conditions, in particular the fall in ambient temperatures, probably forced the gold out of solution in the same temperature range in which brittle structures were initiated. As a result of the irregular distribution of the anastomosing fault pattern and competent units within the preexisting ductile shear, gold mineralization is highly irregular and discontinuous, making exploration of the Arltunga gold field difficult.

Kinking and Cracking Caused by Slip in Single Crystals of Silicon Carbide

α‐SiC single crystals were compressed parallel to the basal plane, (0001), at temperatures between 900° and 1500°C. Plastic deformation by slip on the basal planes which accompanied kinking occurred above 1000°C. At kink boundaries, two kinds of cracks were observed. One was the cracks elongated parallel to the basal plane. This kind of crack was initiated by the tensile stress produced by piled‐up dislocations on the basal planes against a kink boundary. The other was on a kink boundary, and was induced by the stress of dislocations, heterogeneously distributed on the kink boundary. The initiation of cracks produced by dislocations was considered to be a possible cause of fracture in polycrystalline SiC at high temperatures.

Micromechanisms of kinking in rigid-rod polymer fibres

The tensile strengths of fibres of the rigid-rod polymers poly(paraphenylene benzobisthiazole) (PBZT) and poly(paraphenylene benzobisoxazole) (PBZO) are excellent, and therefore are of particular interest for high-performance structural applications. However, these fibres are a factor of ten weaker in compression, with failure occurring by strain localization in welldefined kink bands. Here, we study the morphology of PBZT and PBZO kink bands in detail, in order to help elucidate the molecular mechanisms involved in this deformation process. We found that the typical dimensions of a kink in the direction of the fibre axis (∼ 30 nm) were smaller than the length of an average PBZT or PBZO molecule (100 nm). Also, the boundary between the kinked and unkinked regions was well-defined. Low-dose, high-resolution electron microscopy (HREM) of the kink interior revealed local, high-angle changes in chain orientation, indicative of covalent bond bending or breaking. The kink boundaries exhibit “sharp” or “smooth” features which seem to be related to the local tensile or compressive nature of the stress field. A model for kink nucleation and propagation in terms of partial dislocations is presented and discussed. A stress analysis using this model has been developed, and comparison with experimental data suggests that kinks tend to propagate towards regions of higher compressive stress. This observation is interpreted in terms of dislocation pinning (in areas of hydrostatic tension) and the nucleation of dislocation pairs (in areas of hydrostatic compression) due to the asymmetric nature of the intermolecular energy potential. Finally, practical methods for improving compressive strength based on these mechanistic insights are proposed.

The geometry and kinematics of a suite of conjugate kink bands, southeastern Australia

A conjugate set of subvertical kink bands is exposed in coastal outcrops of well-foliated Ordovician turbidites near Mystery Bay, Australia. All kink bands with widths exceeding 3 cm have complex internal structures including compound and parasitic kinks, stepped kink boundaries, internal crenulations, variable kink angles and prismatic voids. The kink bands are interpreted to result from rotation of short foliation segments between fixed kink planes with subsequent widening and modification by layer-parallel shear external to the kink band. Layer-parallel shear of both sinistral and dextral sense accompanied kinking and indicates a variable stress system during kink band development. Conjugate kink bands are abundant and are used to estimate bulk strain orientations. In general, the dominant kink set of a conjugate pair is inclined at a lower angle to the external foliation than the weaker set and this angular disparity increases with increasing dominance of one set. These observations are at variance with relationships described from experimental bulk pure shear deformation of anisotropic materials. It is suggested that orthogonal constraints in these experiments restrict layer-parallel shear to within a developing kink band and are, therefore, unlike many natural kink systems. Simple shear experiments can produce structures geometrically similar to natural kink bands.

Temperature and orientation dependence of the deformation and fracture in Ni 75Al 20Ti 5 single crystals

The temperature and orientation dependence of the deformation and fracture behavior of Ni 75Al 20Ti 5 single crystals was investigated by tensile tests at temperatures to 1273 K. The yield stress showed a positive temperature dependence to a peak temperature ( T p) which depended on orientation. At temperatures below T p, where {111} slip operated, fracture occurred on operative {111} planes, cleavage {001} planes and non-crystallographic planes depending on orientation. This tendency was not changed with temperature. In this temperature range, a decrease in elongation with increasing temperature was found for all orientations, which was explained by an increase in the formation and joining of the microcracks caused by the increased stress level with increasing temperature. Above T p, with the operation of both {001} and {111} slips except [001] oriented specimen, a fan-like fracture, {111} cracking and fracture on kink boundary were observed depending on orientation. The occurrence of {111} cracking decreased with increasing temperature. A large elongation was obtained by the insufficient operation and intersection of {111} slip bands. Under steady-state deformation, fracture surface had a jagged, spongy appearance with deep cavities.

Orientation dependence of deformation and fracture behavior in Ni 3(Al, Ti) single crystals at 973 K

Deformation and fracture behavior in Ni 3(Al, Ti) single crystals at 973 K was investigated as a function of orientation. {001} 〈110〉 slip system operates in all the specimens except for [001] orientation, where {111} 〈110〉 slip system operates. Kinking appears in the [1̄15], [1̄14] and [1̄13] specimens, which is explained in terms of bend gliding due to grip constraints under uniaxial tensile deformation. In the [1̄11] specimen inhomogeneous {111} 〈110〉 slip system operates as a secondary one after steady-state deformation of {001} 〈110〉 and leads to rapid work hardening. [001] specimen fractures with the cleavage on (001) and exhibits small elongation. [1̄13] specimen accompanied by kinking fractures along a kink boundary after considerable elongation. [1̄11] specimen in which {111} 〈110〉 slip system operates as a secondary one, fractures partly along {111} planes. Large elongation is obtained in the specimens [1̄12] and [2̄23], which have hard orientation for the observed fracture modes of (001) cleavage, kink boundary fracture and {111} cracking.

Seven types of subgrain boundaries in octachloropropane

Subgrain boundaries in thin sheets of octachloropropane deformed at 0.7–0.8 T M on the stage of a microscope are seen to appear in the material in seven different ways. Type I boundaries show the classical evolution by polygonization of bent crystals. Type II are essentially kink boundaries, which migrate sideways during deformation to reach their present positions in the crystals. Type III develop at the sites of former grain boundaries, by reduction of misorientation of adjacent grains. Type IV and V originate by impingement of migrating grain boundaries or subgrain boundaries, respectively. Type VI propagate in their own planes behind migrating grain boundaries to which they are attached. Type VII develop statically from optically strain-free grains by a process probably otherwise similar to the Type I process. Two thirds of the boundaries are Types I or II. In view of the variety of subgrain boundary histories in OCP, interpretation of similar features in minerals ought to be undertaken cautiously. Criteria are needed for telling the different types of subgrain boundaries apart in situations where only a final view of the structure is available, as in optical and electron micrographs of rocks.

Jumps in deformation gradients and particle velocities across propagating coherent boundaries

Grain boundaries and axial surfaces of folds are geological examples of thin transition zones, which can be modelled mathematically as surfaces of discontinuity. Here we consider coherent boundaries, across which no material lines are ever discontinuous, but deformation gradients and particle velocities can be so. A discontinuity in particle velocity requires that a coherent boundary propagate (migrate) through the material. The geometry and kinematics of coherent boundaries were studied by Hadamard (1903) and reviewed by Truesdell and Toupin (1960). Here, we rederive their results in a geological context, using modern notation and simple coordinates. We conclude that velocity gradient, stretching and spin can all be discontinuous. Applied to ideal kink bands in non-dilatant foliated materials, the theory predicts that kink boundaries rotate through the material at exactly the rate needed to maintain fold symmetry. In a polycrystalline aggregate, easily migrating coherent grain boundaries are mechanically analogous to slippery incoherent boundaries: both kinds support little shear stress.

The geometry of micas around kink band boundaries I. A crystallographic model

An improved crystallographic model is proposed to account for the angular characteristics of kink boundaries in one-layer biotite and two-layer muscovite. The model involves the near-coincidence between the lattices of the two (assumed) low index planes which limit each limb of a kink, within the kink boundary. The cases of [010] and 〈310〉 kink axes are examined. Expectable solutions are screened through a minimization of the misfit. External rotation and asymmetry angles so derived are found in reasonable agreement with published measurements made with the optical microscope on tectonically and experimentally deformed micas. Our preliminary TEM measurements are also included in the comparison. Complex directions of kink axes are most probably the dominant cause of departure from predicted angles, especially for dynamically deformed biotites. The earlier model by Starkey is reexamined, and we conclude on a likely important role of the crystallographic control on the stabilization of the kink-boundary geometry.

Vein arrays as kinematic indicators in kinked anisotropic materials

Vein arrays associated with natural kink bands have been, even recently, used by some workers as kinematic markers to distinguish between the migration and the rotation models of kink band mechanics. In an outcrop of schistose meta-agglomerate, conjugate kinks and synthetic sinistral shears are associated with a component of sinistral slip along the foliation. Discordant scalariform vein arrays form in association with the shears, but not the kinks. Tension gash elements of the arrays form by combined layer-parallel slip and layer-parallel extension along the rotated schistosity. They are only kinematically significant at the scale of the length of the rotated segment anisotropy. Applying this analysis to kink bands elsewhere, it is concluded that discordant vein arrays are not diagnostic of the rotational kink band model, or of high resolved shear stress on kink boundaries.

The relationship between foliation and strain: an experimental investigation

A multilayered salt/mica specimen with embedded strain markers was shortened to produce a fold and the distribution of strain was subsequently mapped out over the profile plane. On a fine scale the initial foliation, which is parallel to the undeformed layers, is folded by tight kinks to produce two new foliations; one is defined by the preferred orientation of kink boundaries and the other by the preferred orientation of (001) of mica. In the hinge region of the fold the first of these new foliations is parallel to the local λ 1 λ 2-principal plane of strain whereas the preferred orientation of mica is bimodal and is symmetrical about the λ 1 λ 2-plane. Elsewhere the two new foliations are not parallel to the principal plane of strain and angular divergencies of up to 30–35° are measured. If a March model with initial random mica orientation is assumed for the development of mica preferred orientation then the correct value of strain is predicted but the orientation of the principal plane of strain can be grossly in error. A theoretical analysis of the angular relationships to be expected between kink boundaries and the λ 1 λ 2-plane of strain confirms that for the type of geometries experimentally developed, large divergences of up to 35° should be common. In rocks where the foliation has developed by processes similar to those recorded here, large angular divergencies between the foliation and the λ 1 λ 2-principal plane of strain should be expected as the rule.

The development of folds in bedded chert and related rocks in the Malaguide Complex, southern Spain

Abstract Folds and folding mechanism in a chert sequence and related rocks of the Malaguide Complex (the uppermost tectonic unit of the Betic Zone) have been investigated. The geometric study shows that folds that developed in the chert sequence are usually angular in shape and asymmetric. Chevron and conjugate folds are common. Folding in bedded chert is explained in terms of a suggested model: 1. (1) Development of folds by kink and conjugate kinking. 2. (2) As the shortening increases, the interlimb angles decrease; in the kink folds this is caused by a reduction of the angle between the layers within the kink and the kink boundaries. There seems to be a relationship between this angle and the asymmetrical thinning-out in the limbs of many folds: the smaller is the angle between the kink boundary and the layers within the kink band, the larger is the reduction of the thickness in these layers. Single limestone layers embedded in slate deform very probably by a buckling mechanism, implying tangential longitudinal strain and an additional flattening.

Deformation structures in solid‐state extruded polyethylene

AbstractDeformation structures resembling kink bands have previously been reported in a number of oriented semicrystalline polymers which have undergone various modes of deformation. In the present work, such structures have been observed and studied in solid‐state extruded polyethylene which has been processed to give a biaxial, “single crystal” texture. Deformation of this material by bending followed by unbending has been observed to lead to shear during the bending stage and to void formation during the unbending stage. The kink bands which form during this treatment exhibit a single morphology regardless of the axis of bending so long as the direction of compression during bending is parallel to the original extrusion direction. Besides intracrystalline slip, which is known to contribute at least in part to the process of kink band formation, mechanisms involving interlamellar slip and interfibrillar slip are also considered. These mechanisms are considered in terms of three distinct experimental observations: the relationship between the kink boundary and the x‐ray long period, the process of void formation during unbending, and the single characteristic morphology of the kink bands.

Several types of natural deformation in olivine, an electron microscope study

Olivines from several lherzolites and peridotites that were deformed in varying geological environments were investigated by high-voltage (1 MeV) electron microscopy. Undeformed to weakly deformed Iherzolite nodules from lavas (Dreiser Weiher, W. Germany; Auvergne, France) can be distinguished from orogenic, weakly to highly deformed peridotites (Finero, Switzerland; Alpe Arami, Switzerland; Kittelfjäll, Sweden) by dislocation substructures. Progressive deformation, known from geological descriptions of these rocks, is represented by sequences of different dislocation substructures. Criteria for progressive deformation and recovery appear to be: (1) increasing individual dislocation density; (2) general configuration of the (100) arrays, especially a decrease in spacings between the arrays and between the dislocations in the arrays is of major importance; (3) increase in elongate cell structure parallel to [010]; (4) increase in the number of cross arrays. Most of the dislocations, b = [100], are arranged in arrays parallel to (100), forming low-angle tilt boundaries which have been identified as kink boundaries using the optical microscope. Polyphase deformation is suggested to be the cause for strong deviations as dense bands of b = [001] dislocations, in the overall dislocation substructure.