High Resolved Shear Stress Research Articles

Deformation microstructure of neutron-irradiated pure polycrystalline vanadium

The deformation microstructure of irradiated pure vanadium has been investigated by transmission electron microscopy. Dislocation pileup on grain boundaries were observed in the deformed specimens irradiated to 0.012 dpa, indicating that the source of channeling could not be grain boundary only. TEM analysis suggested a relationship between tensile direction and channeling-occurred grain: there is a tendency that directions of the applied stress with greater resolved shear stress lie on the trace containing [0 1 1] and [1 1 2] directions. Channel width is wider in case the angle between tensile direction and dislocation slip direction is close to 45°. There is a dose dependence on the correlation between channel width and resolved shear stress, the slope of this correlation decreased with increasing dose. It is suggested that the loss of work hardening capacity in irradiated pure vanadium could be mainly due to dislocation channeling locally formed with high resolved shear stress.

Deformation microstructure of neutron-irradiated pure polycrystalline metals

The effects of neutron-irradiation near 80 °C on the deformation behavior of pure polycrystalline metals vanadium (body centered cubic, BCC), copper (face centered cubic, FCC) and zirconium (hexagonal close packed, HCP) have been investigated. Dislocation channel deformation is observed in all metals, and is coincident with prompt plastic instability at yield. Dislocation pileup was observed at grain boundaries in the deformed vanadium irradiated to 0.012 dpa, indicating that channel formation could lead to dislocation pileup and the resulting stress localization could be a source of grain boundary cracking. TEM analysis suggests that the loss of work hardening capacity in irradiated V, Cu, and Zr at higher doses is mainly due to dislocation channeling in local regions that experience a high resolved shear stress.

The Correlation of Slip between Adjacent Lamellae in TiAl.

ABSTRACTIn lamellar TiAl, concerted deformation occurs in adjacent true-twin related variants (O/OT). When deformation takes place in a given variant, O, by activation of the slip system with highest shear stress, slip proceeds in the companion variant, OT, by operation of a slip system of the same family in mirror orientation, including the slip direction. Depending on load orientation, the latter system may not necessarily exhibit the highest resolved shear stress. The correlation does not depend upon Burgers vector orientation with respect to the interface.This property applies to ordinary dislocations and twinning. The variant that conforms the Schmid law is referred to as the pilot variant, the twin-related variant is dubbed driven.

Dilatancy, brittle strength, and anisotropy of foliated rocks: Experimental deformation and micromechanical modeling

Triaxial compression experiments were performed on the Four‐mile gneiss. The biotite foliation in the Four‐mile gneiss results in dilatancy and strength anisotropies, which become more pronounced with increasing confining pressure. Microstructural observations indicate that when there is high resolved shear stress on the macroscopic foliation, dilatancy arises from extensile microcracks nucleated by frictional slip on biotite grains. Evolution of crack geometry and coalescence are also influenced by the biotite foliation. Motivated by these observations, a damage mechanics model based on sliding wing cracks was adopted to analyze the anisotropic development of dilatancy and brittle fracture. Frictional coefficients for the sliding cracks are inferred to be comparable to those of cleavage surfaces of biotite. The strength anisotropy data of the Four‐mile gneiss can be explained by the variation of the initial damage with the foliation angle. The damage derives from a set of preexisting microcracks with random orientation, and a set of cleavage cracks in mica grains preferentially oriented along the foliation angle. Hence, the initial damage is higher for the intermediate angles, and, consequently, the strength is somewhat lower. The observation that the mechanical strengths of a variety of foliated rocks decrease with increasing mica content can be explained by the same model, with the implication that the initial damage and mica content are linearly related. The mechanical and microstructural data show that dilatancy anisotropy may significantly influence the progressive development of borehole breakout and strain localization.

Effects of Nb and Al on the microstructures and mechanical properties of high Nb containing TiAl base alloys

The influence of Nb and Al contents on the microstructure and yield strength of high Nb containing TiAl base alloys was investigated. The experimental results show that the yield strength at 900 °C of the alloys with the same type of microstructure, such as fully lamellar (FL), nearly lamellar (NL) and degraded fully lamellar (DFL), increases with increasing Nb content and decreasing Al content in the composition range of 0–10 at.% Nb and 44–49 at.% Al. DFL is the degraded form of FL microstructure after exposure at 1050 °C for 30 h. It is shown that the Nb addition in the alloys increases the value of the σ 0 term in the Hall–Petch relation of yield stress vs. lamellar spacing. This result has been related to TEM observations of dislocation structure in deformed specimens. The observations indicated that high level of Nb solute in the γ-TiAl matrix leads to a high critical resolved shear stress (CRSS) of dislocation loops. High Nb addition also reduces the degradation rate of FL microstructure after exposure at 1050 °C for 30 h. Both effects of high Nb addition are related to the change of the directionality of Ti–Ti (Nb) and Nb–Al bonds in the lattice. The decrease in Al content results in an increase in the volume fraction of α 2 phase, which leads to a decrease in the lamellar spacing of the lamellar structure. The high temperature strength of the alloys is determined by the lamellar spacing λ through the Hall–Petch equation k λ λ −1/2.

Deformation of NiTiCu shape memory single crystals in compression

Single-crystal orientations of NiTi10Cu alloys were studied under incremental, cyclic compression conditions to establish the pseudoelastic and shape memory response of this class of alloys. This material exhibits a two-step transformation involving cubic to orthorhombic martensite (B2 → B19) followed by orthorhombic to monoclinic martensite (B19 → B19′). The transformation parameters (shear magnitudes and directions for habit and twin planes) were determined associated with the B2 → B19 transformation. The growth of monoclinic martensite correspondent variant pairs (CVPs) emanating from the orthorhombic structure was also analyzed. The transformation strain for the B2 → B19 case was orientation dependent and lower than the B19 → B19′ transformation in compression for all orientations except those near the [001] pole. The experimental results show that the critical transformation stress is orientation dependent and is in the range 30 to 58 MPa. Orientations that exhibit lower transformation stress (or high resolved shear stress factors, [100] and [012]) produce higher recoverable strains (as high as 4 pct), while other orientations ([011], [111], and [123]) with lower resolved shear stress factors result in recoverable strains less than 3 pct. At higher strains, inelastic deformation develops, limiting recoverability. The recoverable strains are lower than the theoretical values for two main reasons: the transformation is curtailed first by austenite slip and subsequently by martensite slip, and the orthorhombic structure does not fully transform to the monoclinic martensite.

Shock-induced deformation twinning and omega transformation in tantalum and tantalum–tungsten alloys

Effects of high strain-rate and high plastic-strain deformation on the development of deformation substructures in tantalum and tantalum–tungsten alloys (Ta–2.5 wt.% W and Ta–10 wt.% W) shocked at 15 and 45 GPa have been investigated. In addition to dislocation cells/walls, and {112}<111>-type deformation twinning, a shock-induced omega phase (hexagonal) is also found within polycrystalline tantalum shocked at 45 GPa. The orientation relationships between the omega phase and parent (bcc) matrix are {10 1 ̄ 0} h ‖{211} b ,[0001] h ‖<111> b and <1 2 ̄ 10> h ‖<0 1 ̄ 1> b . The lattice parameters of omega phase are a h ≈ 2 a b =0.468 nm and c h ≈( 3 /2)a b =0.286 nm (c h /a h =0.611). Since both deformation twinning and omega transformation occur preferably in the {211} b planes with high resolved shear stresses, it is suggested that both can be considered as alternative paths for shear transformations in shock-deformed tantalum. A greater volume fraction of twin and omega phase formed in Ta–W than in pure Ta reveals that shock-induced shear transformations can be promoted by solid solution alloying. While deformation twinning is resulted from 1/6<1 1 ̄ 1 ̄ > homogeneous shear in consecutive {211} planes, omega transformation can be attributed to the 1/12<1 1 ̄ 1 ̄ >, 1/3<1 1 ̄ 1 ̄ > and 1/12<1 1 ̄ 1 ̄ > inhomogeneous shear in consecutive {211} planes. Dislocation mechanisms for shock-induced twinning and omega transformation are proposed and critically discussed.

Dislocation - Grain Boundary Interaction in Nickel Bicrystals Evolution of the Resulting Defects under Thermal Treatment

ABSTRACTThe interactions between lattice dislocations and grain boundaries were studied in nickel bicrystals. Three types of grain boundaries, according to their energy, were investigated : singular σ3 {111}, vicinal near σ11 {311} and general near σ11 {332} grain boundaries. The experiments were performed by transmission electron microscopy using a set of techniques : conventional, weak beam, in situ and high resolution transmission electron microscopy. Dislocation transmission from one crystal to the other was only observed for σ3 {111} GB. It consists in a decomposition within the grain boundary of the trapped lattice dislocation followed by the emission of one partial in the neighbouring crystal. A high resolved shear stress is required to promote the emission process. Most often, the absorbed lattice dislocations or extrinsic grain boundary dislocations react with the intrinsic dislocation network giving rise to complex configurations. The evolutions with time and upon thermal treatment of these configurations were followed by in situ transmission electron microscopy. The evolution processes, which differ with the type of grain boundaries, were analyzed by comparison with the existing models for extrinsic grain boundary dislocation accommodation. They were tentatively interpretated on the basis of the grain boundary atomic structures and defects obtained by high resolution transmission electron microscopy studies.

Deformation characteristics of polysynthetically twinned (PST) crystals during creep at 1150 K

The creep deformation characteristics of a lamellar polysynthetically twinned (PST) crystal of the composition Ti–48 mol% Al was investigated as a function of the lamellar orientation with respect to the compression axis and the applied stress. The creep resistance of hard PST orientation with the lamellar plates parallel or perpendicular to the compression axis was substantially higher than that of soft orientations with their lamellar plates oriented at intermediate angles to the compression axis. This fact could be associated with the predominant deformation of the hard orientations by deformation modes with the slip plane inclined to the lamellar interfaces in contrast to the predominant deformation of the soft orientations by deformation modes with the slip plane parallel to the lamellar plates. In the soft orientations, mainly straight ordinary dislocations with the Burgers vector b=1/2[1-10] aligned parallel to the lamellar interfaces were encountered in domains with a high resolved shear stress as well as in domains with no resolved shear stress. In the hard orientations, ordinary dislocations b=1/2[110] and superdislocations with a Burgers vector of the type b=1/2〈112] were observed. Despite a high resolved shear stress in certain oriented domains, superdislocations of the type b=〈101] were not found to play a considerable role during creep deformation under the investigated conditions. Cross twinning contributed to the deformation in favourably oriented variants, but twinning parallel to the lamellar interfaces was much more pronounced in the soft orientations leading to a substantial lamellar refinement. This microstructural hardening during creep results in the observed stress exponents of the soft orientations near unity at high stresses. A change in stress exponent from near unity at high stresses to about 9 at low stresses occurs at about 200 MPa. A critical stress of about 200 MPa for parallel twinning is proposed as a reason for the change in stress exponent.

Shock-Induced Omega Phase in Tantalum

The deformation substructure developed within polycrystalline tantalum under a high shock pressure (45 GPa) with a 1.8 {micro}s duration has been examined using transmission electron microscopy. A shock-induced {beta} (bcc) {yields} {omega} (hexagonal) displacive transformation is observed for the first time within tantalum. Needle- or plate-like {omega} phase is found to form accompanied with the {l_brace}112{r_brace} type deformation twins within shock-recovered tantalum. The orientation relationships between the shock-induced {omega} and parent {beta} phases are determined to be {l_brace}10{bar 1}0{r_brace}{sub {omega}} {parallel} {l_brace}211{r_brace}{sub {beta}}, [0001]{sub {omega}} {parallel} {sub {beta}} and {sub {omega}} {parallel} [0{bar 1}1]{sub {beta}}. The lattice parameters of {omega} phase are a{sub {omega}} = ({radical}2a{sub {beta}}) = 0.468 nm and c{sub {omega}} = ({radical}3/2) a{sub {beta}} = 0.286 nm (c/a = 0.611). Both deformation twins and shock-induced {omega} phase are primarily formed along the {l_brace}211{r_brace}{sub {beta}} slip planes with high resolved shear stresses, and have a common habit plane [i.e. the {l_brace}211{r_brace} plane] with the parent {beta} matrix. It is suggested that shear deformation on the {l_brace}211{r_brace} planes is the major cause for the formation of shock-induced {omega} phase within tantalum.

Strength Evaluation Technique for Dislocation Generation in Si Substrate using Ball Indenter.

Since Si substrates do not contain any dislocations, it is important to estimate not only the critical stress of dislocation movement, but also the critical stress of dislocation generation, taking into account the fabrication process of semiconductor devices. Therefore, we propose a method for evaluating the critical strength for dislocation generation near the surface of Si substrate using a ball press test. An electromagnetic actuator was used to press a sapphire ball against a {100} oriented Si substrate at high temperature under vacuum. Several press tests were performed using a variety of load conditions. After each press test, the Si substrate was dipped into an etching solution containing fluoric acid, which allowed all dislocations to be observed. The stress conditions under the ball were estimated, thereby revealing the relationship between the stress and dislocation generation. Dislocations are located on the {111} planes in the directions, and are generated around the center of the ball indenter, where the highest resolved shear stress is on the Si surface. The method appears to be useful not only for measuring the critical strength of dislocation generation, but also for observing the influence of surface treatment on the Si substrate.

The effects of localized deformation on melting processes in ice

Polycrystalline ice deformed in pure shear and in plane strain at approximately −1°C exhibited plastic flow, accommodated by intracrystalline slip and grain boundary migration. A film record of the plastic flow shows that deformation becomes localized along slip-lines that correspond to zones of high resolved shear stress. During this deformation melting occurs. While a simple calculation shows that more melt is present that can be explained by the mechanical energy input, the localization of this melting is closely related to the deformation. For example, melting is initiated along zones of high shear strain. We evaluate the possible reasons for the localization of this melting phenomenon in the ice by comparing microstructural observations on the distribution of melt in space and time with the distribution of shear strain in space and time in a numerical analogue to the experiment. The localized incompatibility of strain across grain boundaries, particularly at triple point junctions, is bound to create significant stresses in the vicinity of these boundaries and this leads to heating. From this we infer the likelihood of higher spot temperatures being realized at grain boundaries and in the zones of high shear strain. The energy concentration at these spots may help to overcome the energy barrier needed to initiate melting in the sample.

Deformation and metamorphism of massive sulphides at Sulitjelma, Norway

AbstractThe copper-bearing stratabound pyritic massive sulphide bodies contained in metamorphosed basic eruptives of Ordovician age at Sulitjelma in Nordland County, Norway, form one of the important fields of sulphide mineralisation within the Köli Nappe Complex. The sulphide bodies and their enclosing rocks were subject to successive stages of penetrative deformation and recrystallisation during the cycle of metamorphism and tectonic transport caused by the Scandian Orogeny. Textures within the ores and the immediate envelope of schists show that strain was focused along the mineralised horizons. The marked contrast in competence between the massive pyritic sulphides and their envelopes of alteration composed dominantly of phyllosilicates, and the metasediments of the overlying Furulund Group, led to the formation of macroscale fold and shear structures. On the mesoto microscale, a variety of textures have been formed within the pyrite-pyrrhotite-chalcopyrite-sphalerite sulphide rocks as a result of strain and recrystallisation. Variations in pyrite:pyrrhotite ratios and in the texture and proportions of associated gangue minerals evidently governed the strength and ductility of the sulphide rocks so that the same sulphide mineral can behave differently, displaying different textures in different matrices. In massive pyritic samples there is evidence of evolution towards textural equilibrium by recrystallisation, grain growth and annealment during the prograde part of the metamorphic cycle. Later, brittle deformation was superimposed on these early fabrics and the textural evidence is clearly preserved. By comparing published data on the brittle-ductile transformation boundaries of sulphide minerals with the conditions governing metamorphism at Sulitjelma, it is concluded that most of the brittle deformation in the sulphides took place during or after D3 under retrograde greenschist conditions. Grain growth of pyrite in matrices of more ductile sulphides during the prograde and early retrograde stages of metamorphism produced the coarse metablastic textures for which Sulitjelma is well-known. In some zones of high resolved shear stress, pyrite shows ductile behaviour which could be explained by a dislocation flow mechanism operating at conditions close to the metamorphic peak. In those horizons in which pyrrhotite is the dominant iron sulphide, the contrast in ductility between silicates, pyrite and pyrrhotite has led to the development of spectacular tectonoclastic textures in which fragments of wall rock have been broken, deformed, rolled and rotated within the ductile pyrrhotite matrix.

集合組織制御したチタン板の変形挙動に及ぼす酸素の影響

Mechanical properties of α Ti are strongly influenced by texture and oxygen content. The effect of texture and oxygen content on the deformation behavior was investigated using three kinds of textured Ti sheets containing 0.05, 0.1, 0.2 and 0.4 mass%O. Especially, we paid attention to deformation twinning and 〈c+a〉 slip. Consequently, it was found that occurrence of deformation twinning is suppressed and 〈c+a〉 dislocations become operative as the oxygen content increases. Therefore, anisotropy in mechanical properties due to the deformation twinning disappears as the oxygen content increases. However, the operation of 〈c+a〉 slip having high critical resolved shear stress leads to easy cleavage fracture and reduced elongation.

A comparison of reducing the dislocation densities in GaAs grown by the vertical gradient freeze and liquid-encapsulated Czochralski techniques

We have recently applied the quasi-steady state heat transfer/thermal stress model for dislocation generation to the vertical gradient freeze (VGF) process for GaAs, permitting a direct comparison with the original treatment of liquid-encapsulated Czochralski (LEC) growth. Very recent high temperature critical resolved shear stress (CRSS) data on undoped VGF and In-doped LEC specimens were used. We show that the ∼threefold increase in CRSS with In is sufficient to inhibit defect formation in the central ∼75% of 3 in. diameter LEC wafers grown in a high ambient temperature gradient, duplicating the etch-pit density (EPD) data. Undoped VGF wafers are predicted to be nearly dislocation-free. The theoretical results on 3 in. material track the low EPD counts in both the 〈100〉 and 〈110〉 directions in a 5 K/cm gradient imposed on the crystals’ surface. We also discuss the origin of dislocations in regions free of thermal stresses and propose their suppression by the addition of a small amount of In in VGF experiments.

Deformation of single‐crystal clinopyroxenes: 1. Mechanical twinning in diopside and hedenbergite

Laboratory deformation experiments were carried out on two single‐crystal clinopyroxenes: chrome diopside and hedenbergite. Tests were made in a Griggs solid medium, triaxial, hot creep tester. A confining pressure of 1000 MPa was applied in all experiments. Crystals were deformed at strain rates from 10−4 to 10−8 s−1 and at temperatures from 400°C to 1200°C. Two orientations of the crystals with respect to the maximum principal compressive stress were tested. The first orientation subjects the (100), [001] and (001), [100] mechanical twinning systems in clinopyroxene to a high resolved shear stress in the sense appropriate for mechanical twinning to occur. The second orientation subjects these systems to an equal resolved shear stress but in the opposite sense so that mechanical twinning is not possible. Effects of temperature and strain rate on the flow stress are observed for the two clinopyroxene compositions. Mechanical twinning on the system (100), [001] is observed to be the primary deformation mechanism in crystals oriented favorably for twinning. The resolved shear stress required for mechanical twinning on this system is 140 MPa for hedenbergite and 100 MPa for chrome diopside. The smaller twinning stresses for diopside are considered to be due to abundant inclusions in the crystals. The mechanical twinning stress is nearly independent of temperature from 400°C to 850°C and strain rate from 10−4 to 10−8 s−1. Above 850°–1000°C for diopside and 1000°C for hedenbergite, deformation occurs by dislocation glide and is strongly temperature and strain rate dependent. Crystals tested in the orientation for which mechanical twinning is not possible deform by two different dislocation glide mechanisms depending on temperature. Details of these experiments are reported in part 2. Results for mechanical twinning predict that this is not an important deformation mechanism in the earth unless resolved shear stress on the twinning system exceeds 140 MPa. Lack of dependence of twinning stress on strain rate implies that large, rapid strains will occur in this mineral if the twinning stress is reached. Independence of twinning stress in clinopyroxenes from temperature, strain rate, or composition allows use of this mineral as a geopiezometer. At plate margins where stresses are high, presence of mechanically twinned clinopyroxene grains allows determination of the orientation and magnitude of stresses responsible for the deformation.

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.

Geometry and Mechanical Relationship of Folds to Thrust Fault Propagation Using a Minor Thrust in the Front Ranges of the Canadian Rocky Mountains

ABSTRACT A west-dipping minor thrust fault and an associated NW-plunging anticline-syncline pair found in the hanging wall of the Lac des Arcs Thrust fault were mapped for the purpose of analyzing the structure's geometry and deformation mechanisms. The surface trace of the thrust intersects the Lac des Arcs Thrust to the southeast, and is rooted in the core of an anticline 5 km to the northwest. A syncline to the northeast parallels the anticline for 2.5 km to the northwest, where the surface traces of the axial surfaces intersect. Major deformational mechanisms include thrusting, folding, and bedding-plane slip (implied by style of folding and by the magnitude of the intragranular strains). Minor deformation mechanisms include carbonate twinning and fracturing involving no offset. The minor thrust is concave upward and joins the Lac des Arcs Thrust at depth along a line of intersection apparently plunging gently to the northwest. An orthogonal fracture system exists with a definite relationship to the macroscopic structural geometry. One set intersects bedding yielding a lineation approximating the structural trend and plunge of the area. The poles to the second set represent a similar lineation. Three structural levels have been defined in the structure, all three sloping gently to the northwest. The lower level consists of thrusting and associated drag folding, the upper predominantly of buckle folding. The middle level is a transitional zone between the upper and the lower, having characteristics of both. Three mechanical relationships between thrusting and folding were recognized in the hanging wall of the thrust. The first relationship is that in which the fault acts as a decollement surface. Above the fault a fold pair has developed, thereby resulting in shortening of the hanging wall. The second relationship involves the propagation of the thrust at its leading edge. Shortening of the hanging wall is accomplished as the hanging wall is crumpled toward the leading edge. The third relationship appears to involve propagation of the thrust fracture along the axial surface of an anticline. The leading edge of the thrust fault is mapped in the proximity of a mesoscopic kink-band (or chevron) fold core. The fold's axial surface is in an orientation of high resolved shear stress with respect to the regional stress field. The location of the leading edge close to the axial surface, and the orientation of the axial surface, suggest that propagation of the thrust fracture could be along this surface.

Dynamic interpretation of deformation twins in haematite

Abstract Turner's (1953) technique of the “dynamic interpretation of deformation twins” has been tested in the case of twin gliding on r={10Ī1} in haematite, using an experimentally deformed, haematite ore from Malmberget. Microscopic-structure studies show that r-twin gliding preferably occurs in haematite grains suitably oriented in relation to the applied stress, i.e. in grains which have high resolved shear stresses in the observed glide systems. The distribution of the “derived principal-stress axes” in heavily twinned grains agrees with the axially symmetric stress orientation during the deformation. In a naturally deformed haematite ore from S tripa, analysis of the preferred orientation of [0001] of haematites with various internal structures reveals that the weak [0001] -maximum perpendicular to s in the ore has been generated by postcrystalline r-twinning. The derived principal-stress axes in the most strongly twinned grains indicate a stress field which, during the formation of the r-twins, had the maximum compressive stress subparallel to the fabric axis a and the least principal stress subparallel to the fabric axis c.

Numerical Dynamic Analysis of Quartz Deformation Lamellae and Calcite and Dolomite Twin Lamellae

The method of numerical dynamic analysis has been applied successfully to samples of naturally deformed carbonate-cemented sandstone in which the quartz grains exhibit deformation lamellae and both calcite and dolomite grains exhibit twin lamellae. The naturally deformed samples are from the Foothills and Front Range subprovinces of the Canadian Rocky Mountains. The analysis of the quartz deformation lamellae assumes that the plane of the lamellae is a plane of high resolved shear stress, the sense of shear is negative, and the gliding direction is determined from the c axis and the pole to the lamellae. Using these assumptions, the existing methods of numerical dynamic analysis and the standard (graphic) dynamic analysis have been applied. Existing graphic techniques for the analysis of deformation lamellae yield essentially the same results as does the technique of numerical dynamic analysis. In this study, the correlation of the principal axes derived from numerical analysis of the quartz, calcite, and dolomite is both internally consistent and consistent with the geologic framework from which the samples were collected. It reflects the statistical homogeneity of the stress orientations during the deformation of these rocks. The samples all show a nearly layer-parallel compression of the layer with a range of orientations for the maximum principal stress that agrees well with maximum principal stress orientations calculated from analysis of macroscopic and megascopic structures related to the same thrust.