Showing papers on "Stress field published in 1992"

First‐ and second‐order patterns of stress in the lithosphere: The World Stress Map Project

Abstract: To date, more than 7300 in situ stress orientations have been compiled as part of the World Stress Map project. Of these, over 4400 are considered reliable tectonic stress indicators, recording horizontal stress orientations to within <±25°. Remarkably good correlation is observed between stress orientations deduced from in situ stress measurements and geologic observations made in the upper 1–2 km, well bore breakouts extending to 4–5 km depth and earthquake focal mechanisms to depths of ∼20 km. Regionally uniform stress orientations and relative magnitudes permit definition of broad-scale regional stress patterns often extending 20–200 times the approximately 20–25 km thickness of the upper brittle lithosphere. The “first-order” midplate stress fields are believed to be largely the result of compressional forces applied at plate boundaries, primarily ridge push and continental collision. The orientation of the intraplate stress field is thus largely controlled by the geometry of the plate boundaries. There is no evidence of large lateral stress gradients (as evidenced by lateral variations in stress regime) which would be expected across large plates if simple resistive or driving basal drag tractions (parallel or antiparallel to absolute motion) controlled the intraplate stress field. Intraplate areas of active extension are generally associated with regions of high topography: western U.S. Cordillera, high Andes, Tibetan plateau, western Indian Ocean plateau. Buoyancy stresses related to crustal thickening and/or lithospheric thinning in these regions dominate the intraplate compressional stress field due to plate-driving forces. These buoyancy forces are just one of several categories of “second-order” stresses, or local perturbations, that can be identified once the first-order stress patterns are recognized. These second-order stress fields can often be associated with specific geologic or tectonic features, for example, lithospheric flexure, lateral strength contrasts, as well as the lateral density contrasts which give rise to buoyancy forces. These second-order stress patterns typically have wavelengths ranging from 5 to 10+ times the thickness of the brittle upper lithosphere. A two-dimensional analysis of the amount of rotation of regional horizontal stress orientations due to a superimposed local stress constrains the ratio of the magnitude of the horizontal regional stress differences to the local uniaxial stress. For a detectable rotation of 15°, the local horizontal uniaxial stress must be at least twice the magnitude of the regional horizontal stress differences. Examples of local rotations of SHmax orientations include a 75°–85° rotation on the northeastern Canadian continental shelf possibly related to margin-normal extension derived from sediment-loading flexural stresses, a 50°–60° rotation within the East African rift relative to western Africa due to extensional buoyancy forces caused by lithospheric thinning, and an approximately 90° rotation along the northern margin of the Paleozoic Amazonas rift in central Brazil. In this final example, this rotation is hypothesized as being due to deviatoric compression oriented normal to the rift axis resulting from local lithospheric support of a dense mass in the lower crust beneath the rift (“rift pillow”). Estimates of the magnitudes of first-order (plate boundary force-derived) regional stress differences computed from modeling the source of observed local stress rotations magnitudes can be compared with regional stress differences based on the frictional strength of the crust (i.e., “Byerlee's law”) assuming hydrostatic pore pressure. The examples given here are too few to provide a definitive evaluation of the direct applicability of Byerlee's law to the upper brittle part of the lithosphere, particularly in view of uncertainties such as pore pressure and relative magnitude of the intermediate principal stresses. Nonetheless, the observed rotations all indicate that the magnitude of the local horizontal uniaxial stresses must be 1–2.5+ times the magnitude of the regional first-order horizontal stress differences and suggest that careful evaluation of such local rotations may be a powerful technique for constraining the in situ magnitude stress differences in the upper, brittle part of the lithosphere.

Linear electro-elastic fracture mechanics of piezoelectric materials

Abstract: The concepts of linear elastic fracture mechanics, generalized to treat piezoelectric effects, are employed to study the influence of the electrical fields on the fracture behavior of piezoelectric materials The method of distributed dislocations and electric dipoles, already existing in the literature, is used to calculate the electro-elastic fields and the energy-release rate for a finite crack embedded in an infinite piezoelectric medium which is subjected to both mechanical and electric loads The energy-release rate expressions show that the electric fields generally tend to slow the crack growth It is shown that the stress intensity factor criterion and the energy-release rate criterion differ when the energetics of the electric field is taken into account The study of crack tip singular stress field yields a possible explanation for experimentally observed crack skewing in the presence of a strong electric field

Regional patterns of tectonic stress in Europe

Abstract: Nearly 1500 stress orientation determinations are now available for Europe. The data come from earthquake focal mechanisms, overcoring measurements, well bore breakouts, hydraulic fracturing measurements, and young fault slip studies and sample the stress field from the surface to seismogenic depths. Three distinct regional patterns of maximum compressive horizontal stress (SHmax) orientation can be defined from these data: a consistent NW to NNW SHmax stress orientation in western Europe; a WNW-ESE SHmax orientation in Scandinavia, similar to western Europe but with a larger variability of SHmax orientations; and a consistent E-W SHmax orientation and N-S extension in the Aegean Sea and western Anatolia. The different stress fields can be attributed to plate-driving forces acting on the boundaries of the Eurasian plate, locally modified by lithospheric properties in different regions. On average, the orientation of maximum stress in western Europe is subparallel to the direction of relative plate motion between Africa and Europe and is rotated 17° clockwise from the direction of absolute plate motion. The uniformly oriented stress field in western Europe coincides with thin to medium lithospheric thickness (approximately 50–90 km) and high heat flow values (>80 m W/m2). In western Europe a predominance of strike-slip focal mechanisms implies that the intermediate principal stress is vertical. The more irregular horizontal stress orientations in Scandinavia coincide with thick continental lithosphere (110–170 km) and low heat flow (<50 m W/m2). The cold thick lithosphere in this region may result in lower mean stresses associated with far-field tectonic forces and allow the stress field to be more easily perturbed by local effects such as deglaciation flexure and topography. The stress field of the Aegean Sea and western Anatolia is consistent with N-S extension in a back arc setting behind the Hellenic trench subduction zone. The stress field is influenced in places by regional geologic structures, e.g., in the Western Alps, where SHmax directions show a slight tendency toward a radial stress pattern. Not all major geologic structures, however, appear to affect the SHmax orientation, e.g., in the vicinity of the Rhine rift system horizontal stress orientations are continuous.

Stress field constraints on intraplate seismicity in eastern North America

Abstract: Focal mechanisms of 32 North American midplate earthquakes (mo = 3.8-6.5) were evaluated to determine if slip is compatible with a broad-scale regional stress field derived from plate-driving forces and, if so, under what conditions (stress regime, pore pressure, and frictional coefficient). Using independent information on in situ stress orientations from well bore breakout and hydraulic fracturing data and assuming that the regional principal stresses are in approximately horizontal and vertical planes (_ 10o), the constraint that the slip vector represents the direction of maximum resolved shear stress on the fault plane was used to calculate relative stress magnitudes defined by the parameterb = (S2 - S3)/(S - S3) from the fault/stress geometry. As long as the focal mechanism has a component of oblique slip (i.e., the B axis does not coincide with the intermediate principal stress direction), this calculation identifies which of the two nodal planes is a geometrically possible slip plane (Gephart, 1985). Slip in a majority of the earthquakes (25 of 32) was found to be geometrically compatible with reactivation of favorably oriented preexisting fault planes in response to the broad-scale uniform regional stress field. Slip in five events was clearly inconsistent with the regional stress field and appears to require a localized stress anomaly to explain the seismicity. Significantly, all five of these events occurred prior to 1970 (when many regional networks were installed), and their focal mechanisms are inconsistent with more recent solutions of nearby smaller events. The frictional likelihood of the geometrically possible slip on the selected fault planes was evaluated in the context of conventional frictional faulting theory. The ratio of shear to normal stress on the fault planes at hypocentral depth was calculated relative to an assumed regional stress field. Regional stress magnitudes were determined from (1) S/S3 ratios based on the frictional strength of optimally oriented faults (the basis for the linear brittle portion of lithospheric strength profiles), (2) the computed relative stress magnitude (b) values, and (3) a vertical principal stress assumed equal to the lithostat. Two end-member possibilities were examined to explain the observed slip in these less than optimally oriented fault planes. First, the frictional coefficient was held constant on all faults, hydrostatic pore pressure was assumed regionally, and the fault zone pore pressure was determined. Since pore pressure is a measurable quantity with real limits in the crust (P0 < S3), this end-member case was used to determine which of the geometrically possible slip planes were frictionally likely slip planes. Alternately, pore pressure was fixed at hydrostatic everywhere, and the required relative lowered frictional coefficient of the fault zone was computed. Slip in 23 of the 25 geometrically compatible earthquakes was determined to also be frictionally likely in response to an approximately horizontal and vertical regional stress field derived from plate-driving forces whose magnitudes are constrained by the frictional strength of optimally oriented faults (assuming hydrostatic pore pressure regionally). The conditions for slip on these 23 relatively "well-oriented" earthquake faults were determined relative to this regional crustal strength model and require only moderate increases in pore pressure (between about 0.4-0.8 of lithostatic, hydrostatic is about 0.37 of lithostatic) or, alternately, moderate lowering (<50%) of the frictional coefficient on the faults which slipped. Superlithostatic pore pressures are not required. Focal mechanisms for the two other earthquakes with slip vectors geometrically consistent with the regional stress field, however, did require pore pressures far exceeding the least principal stress (or extremely low coefficients of friction). These events may reflect either local stress rotations undetected with current sampling or poorly constrained focal mechanisms. The analysis also confirmed a roughly north to south contrast in stress regime between the central eastern United States and southeastern Canada previously inferred from a contrast in focal mecha- nisms between the two areas: most central eastern United States earthquakes occur in response to a strike-slip stress regime, whereas the southeastern Canadian events require a thrust faulting stress regime. This contrast in stress regime, with a constant maximum horizontal stress orientation determined by far-field plate-driving forces, requires a systematic lateral variation in relative stress magnitudes. Superposition of stresses due to simple flexural models of glacial rebound stresses are of the correct sense to explain the observed lateral variation, but maximum computed rebound-related stress magnitude changes are quite small (about 10 MPa) and do not appear large enough to account for the stress regime change if commonly assumed stress magnitudes determined from frictional strength apply to the crust at seismogenic depths.

Modern tectonic stress field in the Mediterranean region: evidence for variation in stress directions at different scales

Abstract: SUMMARY A compilation of more than one thousand stress indicators (which include in situ stress measurements, focal mechanisms, microtectonic and other geological data) allowed us to reconstruct the modern stress field in the Mediterranean region and the surrounding area. Average stress directions at different scales have been reconstructed by means of a linear interpolation method. This method takes into account the distribution, scale and quality of stress data. The results of the interpolation at plate scale, allow us to recognize slightly deformed regions such as the northwestern European platform, where average maximum horizontal stress direction is oriented roughly NNW-SSE, subparallel to absolute and relative plate velocity directions. Other regions such as the Caucasus, Alps and Pyrenees, where recent tectonic deformation and seismicity are present, display important variations of stress directions. The reconstruction of the average stress directions at different scales within the French Alps pointed out that the average stress field pattern may vary from one scale to another. Nevertheless, variations of stress directions at a given scale are consistent with the kinematics of faults of the same scale.

Chapter 2 Fabrics of Experimental Fault Zones: Their Development and Relationship to Mechanical Behavior

Abstract: The fracture array of simulated fault zones is shown to evolve in a predictable and reproducible manner, from a stepwise fashion to a steady-state condition. At low confining pressures and increasing shear strain the sequence is: (1) Homogeneous shearing by grain-to-grain movements. (2) R 2 - and R 1 -fractures initiate at about the same time but propagate only a few grain diameters. They are at relatively high angles to the gouge-forcing block interface and widely spaced. These first two stages are one primarily of gouge compaction characterized by strain hardening. (3) Extension of R 1 S and coincident reorientation to lower angles closely paralleling the interface with the forcing blocks. P-fractures initiate. These occur from the ultimate strength through a strain softening stage. (4) Y-fractures form along which most of the displacement is accommodated, with the fracture array now close to steady state. Y's initially are close to one or both interfaces with the forcing blocks, but with increasing shear strain shift to the interior of the gouge. At this stage, sliding may change from stable slip to periodic oscillations, characteristic of stick-slip sliding. The development of the fracture array is interpreted to be the result of a reorientation of the stress field across and within the gouge zone. Riedel shears form in response to Coulomb failure, but Y-fractures appear as a result of the kinematic constraint produced by the more rigid bounding blocks. Modeling of the weak gouge zone within a stronger medium shows that the stress field may rotate to higher angles at the gouge boundaries. This is consistent with recent field observations. A significant implication is that without this recognition, laboratory values of frictional coefficients may be overestimated.

The regional intraplate stress field in South America

Abstract: A compilation of lithospheric stress directions for continental South America and the inferred major patterns of the regional intraplate stress field are presented. Stress orientations are based primarily on earthquake focal mechanisms and Quaternary fault slip inversion published in the literature. Four new focal mechanisms based on short-period P wave modeling, and selected centroid-moment-tensor solutions (published by U.S. Geological Survey) consistent with P wave first motions at South American and other World-Wide Standard Seismograph Network stations are also included in the data base. The observed patterns of intraplate stresses may be useful in constraining numerical models of the plate driving forces in the South American plate. In the Andean plateau (altitudes greater than 3000 m), N-S extensional stresses predominate. E-W compressional stresses are observed in the sub-Andean and platform regions extending up to about 1000 km east of the Andes. The maximum horizontal stress (SHmax) is uniformly oriented in the E-W direction throughout western South America. Averages of the SHmax direction at grid points spaced 2.5° were taken as representing the “regional” field. The E-W direction of this regional field is not affected by the change of strike of the Andean chain nor by the contact of a flat subducted slab underneath. The regional SHmax direction is oriented 15° more clockwise than the direction of the Nazca plate convergence. The difference between the regional SHmax orientations and the absolute plate motion may be only about 6°. This may indicate that contact forces with the Nazca plate may not be the only major contributor to the intraplate stresses in western South America. The eastern limit of this Andean stress province seems to coincide with aseismic regions in the Upper Amazon basin and in the Parana basin. In the central Amazonian region, seismicity and stress data suggest a seismic province with N-S compressional stresses. The origin of these stresses is not yet clearly understood but could possibly be related to lower crustal loading along the middle Amazon basin. In northeastern Brazil, seismicity is characterized by upper crustal strike-slip earthquakes bordering the Potiguar marginal basin. A model is proposed for this region in which the stress field is the result of a superposition of regional E-W compressional stresses and local extensional stresses (oriented perpendicular to the continental margin) possibly related to density contrasts and sediment loading in the continental shelf.

Present-day stress orientations adjacent to active strike-slip faults: California and Sumatra

Abstract: Present-day stress directions interpreted from well bore breakouts adjacent to two crastal-scale, active, strike-slip faults (the San Andreas fault in California and the Great Sumatran fault in Sumatra) indicate that the maximum horizontal stress direction (SH) is oriented at a high angle (70°–90°) to both faults. The regionally defined stress fields spanning these faults show that adjacent young or actively growing folds have formed orthogonal to SH and are therefore in the thrust-fault orientation. These observations indicate a decoupling of the strike-slip and compressional components of the deformation within these broadly transpressive zones. Borehole breakouts in 118 wells in western California indicate a regionally consistent stress pattern with SH generally oriented NE-SW, nearly perpendicular (80°–90°) to the strike of the San Andreas fault. The orientation of SH nearly perpendicular to the San Andreas fault implies low shear stress on the fault and is consistent with geological interpretations of the Coast and Transverse Ranges indicating active compressional deformation, fault plane solutions for recent dip-slip-style earthquakes, principal stress directions determined from inversion of earthquake focal mechanisms, and induced hydraulic fracture orientations. A stress trajectory map for western California is computed using an iterative statistical algorithm in which observed directional data, such as breakout directions, are used to obtain a model regional stress field. Analysis of well bore breakouts in 25 wells within the central and southern oil districts of Sumatra indicates that the regionally defined SH adjacent to the active Great Sumatran strike-slip fault is oriented at a high angle (70°–80°) to the fault This orientation of SH is consistent regionally with geologic stress indicators and focal mechanisms of dip-slip earthquakes. Preliminary analysis of the stress field in the vicinity of the Philippine and Alpine faults suggests SH is also oriented at a high angle to these active strike-slip faults. Similarly, the minimum horizontal stress Sh is oriented at a high angle to the the Kane and Dead Sea transforms. The observation of SH and Sh in the vicinity of active strike-slip faults being oriented nearly perpendicular and parallel to the faults suggests that large, crustal-scale strike-slip faults may, in general, be inherently weak surfaces.

Tectonic stress field in the Indian subcontinent

Abstract: A map of maximum horizontal compressive stress orientation in the Indian subcontinent has been prepared using orientations derived from three different stress indicators: borehole elongation breakouts, in situ hydraulic fracturing measurements, and earthquake focal mechanisms Most part of the subcontinent appears to be characterized by a compressional stress regime (thrust and strikeslip faulting) imposed by plate boundary forces although SHmax orientations do not, in general, show clear correlation with the direction of motion of the Indian plate Four provinces are recognized on the basis of regionally consistent orientations These are the midcontinent stress province, the southern shield, the Bengal basin, and the Assam wedge Their boundaries have been determined taking into consideration regional tectonics and seismicity Central and northern India, including the Shillong Plateau stretching up to the great Himalaya, Pakistan, and Nepal are included in a broad “midcontinent” stress province characterized by NNE-ENE oriented SHmax The mean orientation of SHmax in this province is N23°E, subparallel to the direction of compression expected to arise from the net resistive forces at the Himalayan collision zone, suggesting that it is largely determined by the tectonic collision processes Much of southern India (Mysore plateau and the high-grade metamorphic terrain south of the plateau) appears to be part of a second stress province characterized by NW oriented SHmax These appear close to those of the intraplate stress field prevailing in the central Indian Ocean A third stress province was recognized in the Bengal basin including parts of West Bengal, Tripura, Manipur, and Mizoram in northeastern India and most of Bangladesh This province extends eastward from the marginal fault in the western margin of the Bengal basin to the Indo-Burma subduction zone and is bounded on the north by the E-W striking Dauki fault SHmax within the sedimentary pile of the Bengal basin is oriented in E-W direction, while P axes of earthquakes within the basement and the crust beneath the basin and within the subducted slab of the Indian plate beneath the Indo-Burman ranges generally trend north - N30°E SHmax orientations within the sedimentary pile of the basin are parallel to the local (approximately E-W) direction of the convergence of Indian and Burmese plates, suggesting a casual relation to the resistive forces at the subduction zone in the Indo-Burma region Interestingly, the stress field in the basement and the crust beneath the Bengal basin and in the subducted slab is similar to the one prevailing in the midcontinent stress province Assam wedge stress region occupies the northeastern corner of the Indian plate, including Upper Assam, Arunachal Pradesh, and much of Nagaland This region subducts beneath a sharply bent continental collision boundary consisting of the northeastern limb of the Himalayan and northern limb of the Indo-Burman fold belts As a result, the stress field in this province is depth-differentiated and most likely responsible for the absence of consistent SHmax directions

Stress orientation profile to 3.5 km depth near the San Andreas Fault at Cajon Pass, California

Abstract: A detailed profile of the orientation of the apparent maximum horizontal compressive stress was constructed over the depth interval 1.75–3.46 km in the Cajon Pass drill hole, located 4.2 km from the San Andreas fault in southern California. The profile is based on the analysis of stress-induced well bore breakouts and consists of 32,616 orientation determinations at a basic sampling interval of ∼4 cm. The azimuth of the apparent maximum horizontal compressive stress around the borehole is 057° (s.d. = 19°). Depth-dependent variations in breakout azimuths, from a few degrees to as much as 100°, occur over depth intervals of several centimeters to hundreds of meters in the borehole, with wavelengths showing a self-similar distribution over a range of depth intervals. The variations in breakout orientation at depth seem to reflect stress fluctuations associated with active faults penetrated by the drill hole. Assuming linear elastic behavior, perturbations in stress magnitude and orientation were computed for predrilling slip on these faults. Fault stress drops limited to the ambient shear stress (i.e., up to total stress drop), along with occasional, local extreme stress drops and geometrical complications, can explain the variations in breakout orientations in the drill hole. The penetrative stress inhomogeneity may suggest that the average orientation of borehole breakouts in Cajon Pass, which indicates left-lateral shear on planes parallel to the San Andreas fault, may not be representative of the state of stress near the fault at depth in this region. Rather, the stress orientation profile indicates the superposition of numerous local stress perturbations on an average stress field which is characterized by an absence of appreciable right-lateral shear on planes parallel to the San Andreas. Combining these observations with the highly variable stress state in shallow boreholes in the western Mojave Desert, it is suggested that the heterogeneous stress field in this region, representing a spectrum of seismic events, may extend over substantial distances across and along the San Andreas fault zone. If the average measured breakout orientation in Cajon Pass is representative of the state of stress near the San Andreas in this region, then substantial left-lateral shear stress is resolved on planes parallel to the fault, in contradiction to the sense of its long-term motion. We use an elastic dislocation model to compute the net stress change near the Cajon Pass drill site since just prior to the large 1812 earthquake, taking into account coseismic slip in major earthquakes and aseismic accumulation of slip on the San Andreas and San Jacinto faults. The model suggests that the net change in fault-parallel shear stress during the current earthquake cycle in the Cajon Pass area is nearly negligible. The difference between the measured and computed results requires that additional left-lateral shear stress be superimposed on a generally fault-normal maximum horizontal compressive stress. The results suggest that during the great Fort Tejon earthquake of 1857, left-lateral shear stress parallel to the San Andreas fault in the region of Cajon Pass may have played a role in terminating the southeastward extent of the rupture propagation.

The recent crustal stress field in central Europe: Trajectories and finite element modeling

Abstract: The recent crustal stress field of Central Europe and especially of the adjoining areas to the east is presented in terms of the directions of maximum horizontal stress (SHmax). The analysis is based on fault plane solutions, in situ stress measurements, geologic fault slip determinations, and repeated precise geodetic triangulations. A bending of the direction of SHmax from the well-known NW-SE direction in the western part of the study area to directions of NE-SW to E-W in the eastern part is shown. First results on the recent crustal stress field of the study area were presented by Grunthal and Stromeyer (1986), who substantiated this tendency of bending in the central and eastern parts of the study area by few observations only. Therefore one aim of this paper was to compile observations on the areas with few data points. Generally, these additional data confirm the previously established pattern; in some areas, especially in the Pannonian basin, the stress features became more complicated compared with those solely based on a few data points. The second part of the paper presents steady state elastic finite element model calculations to provide some possible explanations of the observed stress orientations as a result of plate driving forces. Simulation of the North Atlantic seafloor spreading and the northward directed motion of the African plate by appropriate boundary loads produces a pattern of SHmax directions for the western part of the Eurasian plate which is compatible with the broad-scale observed stress directions. Subregional anomalies such as the fanlike stress pattern perpendicular to the arc of the Western Alps or the radial directions around the Pannonian basin can be explained only when additional stress producing features are introduced overmodulating the regional field. Rigorous introduction of physically constrained model parameters for all these features was not feasible to date. Therefore the preliminary empirical model calculations presented in this paper are attempts to discuss which features have the most influence on the stress field. They are, in a regional scale, the North Atlantic seafloor spreading, the northward motion of the African and the Arabian plate, and obviously, subregionally, increased stiffness of the Apulian promontary as well as of the Bohemian massif.

Model validation of a 3d simulation of dislocation dynamics: discretization and line tension effects

Abstract: Some fundamental aspects of 3D computer modelling of plastic flow are presented together with the results of a detailed study of related approximations, such as the discretization of space and of dislocation line curvature. More specifically, the stress field generated by different discretizations of dislocation loops and the critical stress for dislocation multiplication through the Frank-Read mechanism, are compared to the predictions of the elastic theory of dislocations in the isotropic approximation. Although crude in appearance, the approximation adopted in these simulations to describe the curvature does not drastically affect the behaviour. Moreover, it leads to critical stress values for a pinned dislocation segment in excellent agreement with previous computations.

Stress near geometrically complex strike-slip faults: Application to the San Andreas Fault at Cajon Pass, southern California

Abstract: A model is presented to rationalize the state of stress near a geometrically complex major strike-slip fault. Slip on such a fault creates residual stresses that, with the occurrence of several slip events, can dominate the stress field near the fault. The model is applied to the San Andreas fault near Cajon Pass. The results are consistent with the geological features, seismicity, the existence of left-lateral stress on the Cleghorn fault, and the in situ stress orientation in the scientific well, found to be sinistral when resolved on a plane parallel to the San Andreas fault. It is suggested that the creation of residual stresses caused by slip on a wiggle San Andreas fault is the dominating process there.

Nucleation and Self-Accommodation of the R-Phase in Ti–Ni Alloys

Abstract: Transformation and self-accommodation mechanisms of the R-phase in Ti-Ni-Fe and Ti-Ni-Al shape memory alloys were studied by means of optical and electron microscope observations Sequences of transformation events were recorded successfully with video tapes using a TV camera Through the observation we found the following The R-phase transformation takes place by nucleation and growth in a heterogeneous manner Nucleations take place at stress concentrated places, eg, matrix-inclusion interfaces and dislocation The R-phase can nucleate from the stress field of a single dislocation

Calculation of steady-state viscoelastic flow through axisymmetric contractions with the EEME formulation

Abstract: The EEME/finite-element method is used to compute steady flows of fluids with constitutive behavior described by the Modified Upper Convected Maxwell Model of Apelian and a modified form of the dumbbell model of Chilcott and Rallison through abrupt, axisymmetric contractions. Both constitutive models predict constant viscosity and shear thinning first normal stress coefficient, but differ qualitatively in the behavior of the elongational viscosity. Asymptotic analysis for both models predicts that the solution has Newtonian-like spatial structure near the reentrant corner and integrable stresses and velocity gradients there. With the Newtonian-like asymptotics, the stress field can be approximated by conventional Lagrangian finite elements and computed by the streamline upwind Petrov Galerkin (SUPG) method. The finite element calculations are stable and convergent: higher values of Deborah number are reached with increasing mesh refinement. Moreover, the predicted asymptotic structure of the stress and velocity fields is recovered near the corner in the calculations. Calculations with both constitutive equations show the stretching of the Newtonian corner vortex toward the reentrant corner and its growth upstream with increasing Deborah number for 4:1 and 8:1 contraction ratios. The characteristics of the computed vortex are in semi-quantitative agreement with experiments for Boger fluids for which the flow is axisymmetric and steady.

Stress field determinations in France by hydraulic tests in boreholes

Abstract: The stress field has been determined at eight different sites in France (four in crystalline or metamorphic rocks, four in sedimentary formations) by hydraulic tests in boreholes. For seven of these sites the complete stress field has been determined using the hydraulic tests on pre-existing fractures (HTPF) inversion method. Validity of the results is demonstrated by the good fit between a priori and a posteriori values for the data and by the low values of the a posteriori standard deviation on the unknowns. For four sites, results have been compared with those derived according to the hydraulic fracturing theory. The two methods yield comparable results for the orientation of the maximum horizontal principal stress σH, a generally satisfactory fit for the magnitude of the minimum horizontal principal stress σh, but a very poor agreement for the magnitude of σH. This latter misfit has been attributed to the effect of fluid percolation prior to the actual opening of the fractures. Below a depth of 500 m, a homogeneous σH direction (N150°E) has been determined at the crystalline sites (Auriat, Echassieres, Le Mayet de Montagne, Chassoles), all located in the northern Massif Central. For three of these sites the vertical stress is significantly lower than the weight of overburden as computed from the rock density and the depth of the corresponding measurement. At Auriat and Echassieres the stress field is consistent with a mostly strike-slip faulting regime. At Le Mayet de Montagne and Chassoles the maximum stress is vertical but nearly equal to σH. The stress field has been found to be much more heterogeneous at two of the four sites in sedimentary rocks because of the large variability in mechanical rock properties. In such heterogeneous formations, inversion with the HTPF method must be limited to those data which pertain to the same rock horizon. However, because of its structure this heterogeneity does not restrict the possibility of defining large-scale uniform principal stress directions. All the results are consistent with the local seismotectonics.

An Evaluation of the Iosipescu Specimen for Composite Materials Shear Property Measurement

Abstract: A detailed evaluation of the suitability of the Iosipescu specimen tested in the modified Wyoming fixture is presented. An experimental investigation using conventional strain gage instrumentation and moire interferometry is performed. A finite element analysis of the Iosipescu shear test for unidirectional and cross-ply composites is used to assess the uniformity of the shear stress field in the vicinity of the notch, and demonstrate the effect of the nonuniform stress field upon the strain gage measurements used for the determination of composite shear moduli. From the test results for graphite-epoxy laminates, it is shown that the proximity of the load introduction point to the test section greatly influences the individual gage readings for certain fiber orientations but the effect upon shear modulus measurement is relatively unimportant. A numerical study of the load contact effect shows the sensitivity of some fiber configurations to the specimen/fixture contact mechanism and may account for the variations in the measured shear moduli. A comparison of the strain gage readings from one surface of a specimen with corresponding data from moire interferometry on the opposite face documented an extreme sensitivity of some fiber orientations to eccentric loading which induced twisting and yielded spurious shear stress-strain curves. In the numerical analysis, it is shown that the Iosipescu specimens for different fiber orientations have to be modeled differently in order to closely approximate the true loading conditions. Correction factors are needed to allow for the nonuniformity of the strain field and the use of the average shear stress in the shear modulus evaluation. The correction factors, which are determined for the region occupied by the strain gage rosette, are found to be dependent upon the material orthotropic ratio and the finite element models. Based upon the experimental and numerical results, recommendations for improving the reliability and accuracy of the shear modulus values are made, and the implications for shear strength measurement discussed. Further application of the Iosipescu shear test to woven fabric composites is presented. The limitations of the traditional strain gage instrumentation on the satin weave and high tow plain weave fabrics is discussed. Test results of a epoxy based aluminum particulate composite is also presented. A modification of the Iosipescu specimen is proposed and investigated experimentally and numerically. It is shown that the proposed new specimen design provides a more uniform shear stress field in the test section and greatly reduces the normal and shear stress concentrations in the vicinity of the notches. While the fabrication and the material cost of the proposed specimen is tremendously reduced, it is shown the accuracy of the shear modulus measurement is not sacrificed.

The structure of the near-tip field during transient elastodynamic crack growth

Abstract: T he process of dynamic crack growth in a nominally elastic malerial under conditions of plane strain or plane stress is considered. Of particular concern is the influence of the transient nature of the process on the stress field in the immediate vicinity of the crack tip during nonsteady growth. Asymptotically, the crack tip stress field is square root singular at the crack tip, with the angular variation of the singular field depending weakly on the instantaneous crack tip speed and with the instantaneous stress intensity factor being a scalar multiplier of the singular field. However, for a material particle at a small distance from the moving crack, the local stress field depends not only on instantaneous values of crack speed and stress intensity factor, but also on the past history of these lime-dependent quantities. A representation of the crack tip field is obtained in the form of an expansion about the crack up in powers of radial coordinate, with the coefficients depending on the time rates of change of crack tip speed and stress intensity factor. This representation is used to interpret some experimental observations, with the conclusion that the higher-order expansion provides an accurate description of crack tip fields under fairly severe transient conditions. In addition, some estimates are made of the practical limits of using a stress intensity factor field alone to characterize the local fields.

On tidal triggering of earthquakes at Campi Flegrei, Italy

Abstract: SUMMARY The caldera at Campi Flegrei underwent an inflationary episode during 1982–84 that produced a maximum uplift of 1.6 m at Pozzuoli, Italy. The seismicity at Pozzuoli increased enormously during the time of the uplift, but was delayed by several months. Ground deformation during inflation has been previously well modelled with a finite element model of a pressurized magma chamber in an elastic medium that takes into account the effects of increasing pressure and temperature with depth on elasticity. We used the output from this model to estimate the temporal change in the stress field that presumably controls the seismicity during inflation. The result is that the solid-earth tidal stress should modulate heavily the seismogenic inflationary stress, which in turn should result in some tidally triggered earthquakes. This expectation is based on the assumptions that: (a) the inflationary model is valid; (b) tidal and inflationary stresses can be superimposed; (c) the inflation is smooth on the time-scale of periodic tidal stress variations; and, most importantly (d) earthquakes occur when a critical level of stress has been reached. We checked the Pozzuoli catalogue for evidence of tidal triggering with the Schuster test and found none. The Schuster test is sensitive enough to easily detect a diurnal variation of reported seismicity caused by day-to-night changes in noise levels. The lack of tidal triggering suggests that one (or more) of the above assumptions is wrong. After evaluating each assumption, we conclude that the most likely explanation is that the failure threshold for seismicity is time dependent at Pozzuoli. In other words, earthquakes do not necessarily occur when the stress exceeds the yield strength of a fault for a short time only.

Crustal stress regime in Fennoscandia from focal mechanisms

Abstract: An extensive data set of earthquake focal mechanisms is now available for all of northern Europe and especially for Fennoscandia. These mechanisms are considered to provide representative coverage of the stress field. The maximum horizontal compressional stress orientations are internally very consistent over the area of northern Europe. The dominating NW-SE compressional stresses appear tied to relative plate motion, with Mid-Atlantic Ridge spreading and European-African collision in southern Europe. For Fennoscandia some exceptions to the regional stress pattern exist. The causes of these local anomalies have been investigated. No correlations with geological provinces or province boundaries were found. In addition, there does not appear to be any clear correlation between anomalous stress directions and postglacial uplift in the present earthquake activity. This lack of correlation is in sharp contrast to geological evidence in the form of large faults indicative of large postglacial earthquakes occurring right after the end of the latest ice age, 9000 years ago. Taken together, this evidence suggests a tremendous change of stress field in Holocene time, from one dominated by the postglacial unloading right after the ice age to one dominated by the present plate motion today.

The s‐version of the finite element method for multilayer laminates

Abstract: SUMMARY A methodology has been developed to accurately resolve the stress field in the vicinity of free edges as well as the overall response of laminated plates without significantly affecting the computational cost. This is accomplished by enriching a set of classical smooth interpolants throughout the thickness direction with Co continuous displacement interpolants (piecewise continuous strain field) in the regions where the most critical behaviour is anticipated. Co continuity of the displacement field is maintained by imposing homogeneous boundary conditions on the superimposed field in the portion of the boundary which is not contained within the boundary of the problem. Numerical experiments for both cylindrical bending and uniform extension of cross-ply laminates are presented to validate the present formulation.

The Hertzian stress field and formation of cone cracks—I. Theoretical approach

Abstract: A complete three-dimensional solution has been derived for the Hertzian stress field. The solution was used to define an expression for the largest tensile stress under a spherical indenter. A numerical method was developed to solve the fracture mechanics equation related to cone crack formation, leading to a simple expression for fracture toughness. Examination of the relation between load, cone crack size and stress intensity showed that the critical stress intensity factor is independent of load and crack size. This suggests a new method to determine fracture toughness of brittle materials using Hertzian indentation.

Lithospheric necking and regional isostasy at extensional basins 2. Stress‐induced vertical motions and relative sea level changes

Abstract: We investigate long-wavelength differential vertical motions at extensional basins which are the result of temporal changes in the intraplate stress field in the lithosphere. These stress-induced vertical motions are intimately coupled to the state of flexure (flexural curvature) of the lithosphere. We compare a previous model of flexure under the sediment load only (FSL model) and a recent more consistent model, which incorporates regional compensation of other vertical loads induced by lithospheric extension as well. These additional loads are controlled by the depth at which the necking of the lithosphere occurs (DON model). Tlie FSL model and models assuming a shallow level of necking (≤15 km) are very similar, they predict tilting of the basin with the hinge point landward of the shelf edge. Compression results in uplift of the landward pan of the basin, which generally corresponds to the coastal plain or inner to middle shelf, and downwarping of the outer shelf and slope. The differential vertical motions correspond to relative sea level cycles which are out of phase in different parts of the basin. Internal architecture of systems tracts can be different from predictions by eustasy. By contrast, deeper levels of necking (>20 km) predict a uniform sense of motion landward of the shelf edge. Type I sequence boundaries can be very easily induced for these conditions, and sequence stratigraphie features are probably hard to distinguish from predictions by eustasy. These results are for a pure elastic plate rheology. Stress-induced vertical motions for a more realistic depth-dependent rheology are more complicated because of the additional effect of stress-induced reduction of flexural rigidity. For these conditions, gradual buildup of tension causes a complete relative sea level cycle. For high tensional stress levels, total vertical motions become rather similar to vertical motions for compression. This may be of importance for the issue of global synchroneity of relative sea level changes.

The dynamics of motion of the South American plate

Abstract: Observations of the intraplate stress field, as compiled and evaluated in the context of the World Stress Map Project, can be compared with stress modelling results to increase our understanding of the dynamics of motion of the lithospheric plates. In this paper we investigate the driving and resistive plate tectonic forces acting on the South American plate in order to establish a detailed basis for future stress modelling. Our basic assumption is that the plate is in mechanical equilibrium; that is, the net torque of the forces acting on the plate vanishes. The complexity of the forces exerted along the margins of the South American plate requires the dynamical analysis to be performed step-wise. Incorporating the forces which are expected to be of major importance, a first-order model is defined. The effect of additional plate boundary forces is subsequently examined in terms of superpositions onto the first-order model. With the first-order model the relation between three resistive forces and shear stress on the base of the lithosphere is derived. The ridge push force, driving the motion of the South American plate, can be quantified independently and is included in the calculations as a known quantity. Solutions are obtained using four different determinations of the Euler vector of absolute motion of the South American plate, which is taken to define the orientation of the basal shear stress. The results demonstrate that the concept of a basal shear stress actively driving plate motion cannot be discarded on the basis of a dynamical analysis. Further, with the assumption that basal drag is entirely concentrated below the continental pan of the lithosphere, estimates of the maximum amount of continental basal shear resistance are derived. Evaluation of an alternative model for the South American plate, excluding the northernmost pan of the Andes, demonstrates the significance of the resistive force exerted on the South American plate due to convergence with the Caribbean plate. It is to be expected that comparison of theoretical distributions of intraplate stress, computed on the basis of the present dynamical analysis, with observations of the actual state of stress will further constrain the range of feasible force models.