Showing papers on "Stress field published in 1989"

Altered-Stress Fracturing

Abstract: Altered-stress fracturing is a concept whereby a hydraulic fracture in one well is reoriented by another hydraulic fracture in a nearby location The application is in tight, naturally fractured, anisotropic reservoirs in which conventional hydraulic fractures parallel the highly permeable natural fractures and little production enhancement is achieved by conventional hydraulic fracturing Altered-stress fracturing can modify the stress field so that hydraulic fractures propagate across the permeable natural fractures A field test was conducted in which stress changes of 250 to 300 psi (17 to 21 MPa) were measured in an offset well 120 ft (37 m) away during relatively small minifracs in a production well These results show that stress-altered fracturing is possible at this site and others Analytic and finite element calculations quantify the effects of layers, stresses, and crack size Reservoir calculations show significant enhancement compared to conventional treatments 21 refs, 12 figs, 3 tabs

Dynamic rupture modeling with laboratory‐derived constitutive relations

Abstract: A laboratory-derived state variable friction constitutive relation is used in the numerical simulation of the dynamic growth of an in-plane or mode II shear crack. According to this formulation, originally presented by J. H. Dieterich, frictional resistance varies with the logarithm of the slip rate and with the logarithm of the frictional state variable as identified by A. L. Ruina. Under conditions of steady sliding, the state variable is proportional to (slip rate)−1. Following suddenly introduced increases in slip rate, the rate and state dependencies combine to produce behavior which resembles slip weakening. When rupture nucleation is artificially forced at fixed rupture velocity, rupture models calculated with the state variable friction in a uniformly distributed initial stress field closely resemble earlier rupture models calculated with a slip weakening fault constitutive relation. Additional rupture models are calculated in which rupture nucleation is achieved naturally, with numerical simulations of the quasi-static response of the fault leading to the onset of unstable, dynamic rupture. When rupture nucleation with the state variable friction law takes place naturally, a large fraction of the fault accelerates before accelerating slip is concentrated in what ultimately becomes the rupture nucleation patch. The state evolution accompanying this accelerating slip leads to higher average rupture speeds or a more rapid rupture acceleration to near P wave rupture speeds. Rupture models are also calculated for the seismological asperity problem, that is, the failure of a highly stressed fault patch surrounded by a region of zero stress drop. Dynamic overshoot of slip into the region of zero stress drop roughly agrees with a simple energy balance analysis; the final size of the rupture is proportional to the square of the size of the high stress patch. Earlier frictional stability analyses have led to the definition of a critical fault patch size for rupture nucleation. This critical patch size is generally different from critical crack lengths determined from crack tip energy balance considerations applied to a simpler slip weakening law. In the model calculations, dynamic rupture does not nucleate if the starting patch size is less than the critical patch size. This is consistent with the frictional stability analyses. Thus these model calculations suggest that dynamic rupture following a state variable friction relation is similar to that following a simpler fault slip weakening law. However, when modeling the full cycle of fault motions, rate-dependent frictional responses included in the state variable formulation are important at low slip rates associated with rupture nucleation. The critical rupture nucleation dimension appropriate for a slip weakening fault does not predict the critical nucleation dimension for a state variable fault.

Origin of regional, rooted low-angle normal faults: A mechanical model and its tectonic implications

Abstract: Rooted listric low-angle normal faults (< 20°) of regional extent have been recognized widely in the past few years in the North American Cordillera and elsewhere. The low-angle geometry of these crustal-scale normal faults conflicts with Anderson's [1942] classic theory of faulting. In that theory the orientations of principal stresses are assumed to be vertical and horizontal; the predicted dip angle of normal faults is about 60° rather than 20° or less. Recent geological and geophysical studies in the mid-Tertiary extensional terrane of southeastern California and western Arizona suggest that thick mylonitic gneisses in the lower plates of low-angle detachment faults may represent unidirectionally sheared laminar flow in and below the midcrust. Directed ductile flow, possibly related to the gravitational spreading of thickened lower crust, may induce a shearing traction on the horizontal or subhorizontal base of the brittle upper crust. Thus the orientations of the principal stresses can no longer be vertical and horizontal at this interface. A simple elastic model incorporates the effect of basal shearing due to gravitational spreading on stress distributions in an elastic upper crust. This model shows that parallel belts of compression and extension can be produced if a shearing traction acting on the base of the elastic upper crust is considered. In particular, appropriate stress conditions for the formation of regional low-angle normal faults (< 20°) can be produced by the superposition of two stress fields: a basal shear stress field induced by the basal shear traction and a contractional stress field in which the horizontal deviatoric stress is compressional and the vertical gradient of the horizontal normal stress component is constant. This superposed stress field may represent a tectonic setting where a stress field with compressional deviatoric stress induced by plate subduction or convergence is superposed on a basal shear stress field induced by gravitational spreading of thickened lower crust. These results may explain both puzzling parallel belts of extension and compression and the occurrence of major low-angle normal faults in some orogenic systems.

State of stress and modern deformation of the Northern Basin and Range Province

Abstract: Constraints on the current stress regime of the actively extending northern Basin and Range province are provided by deformation data (focal mechanisms and fault slip studies), hydraulic fracturing in situ stress measurements, borehole elongation (“breakouts”) analyses, and alignment of young volcanic vents. The integrated data indicate significant variations both in principal stress orientations and magnitudes. An approximately E-W least principal stress direction appears to characterize both the eastern and western margins of the Basin and Range province, whereas in the active interior parts of the province extension occurs in response to a least principal stress oriented NW to N60°W. The contrast in stress orientations between the province boundaries and in the interior suggests that along the margins the least principal stress direction may be locally controlled by the generally northerly trending profound lithospheric discontinuities associated with these margins. Active deformation along the southeastern and western province margins is characterized by a combination of strike-slip and normal faulting. Focal mechanisms along northeastern province margin (Wasatch front) and in central Nevada indicate a combination of normal and oblique-normal faulting. Temporal, regional, and depth-dependent variations in the relative magnitudes of the vertical and maximum horizontal stresses can explain much of the observed variations in deformation styles. However, some depth variation in faulting style inferred from focal mechanisms may be apparent and simply a function of the attitude of fault planes being reactivated. Evidence for significant temporal variation (or multiple cycles of variation) in relative stress magnitude comes from the Sierran front-Basin and Range boundary region where recent earthquakes are predominantly strike slip, whereas the profound relative vertical relief across the Sierra frontal fault zone in the last 9–10 m.y. implies a normal faulting stress regime. Using the best data on stress orientation, relative stress magnitudes are constrained from slip vectors of major earthquakes and young fault displacements. Analysis of well-constrained slip vectors in the Owens Valley, California, area indicate that large temporal variations in the magnitude of the approximately N-S oriented maximum horizontal stress are required to explain dominantly dip-slip and strike-slip offsets on subparallel faults. Similar faulting relations are observed throughout much of the boundary zone between the Basin and Range-Sierra Nevada (including the Walker Lane belt). Along the eastern province margin in the Wasatch front area in Utah, available data suggest that the maximum and minimum horizontal stresses may be approximately equal at depths of <4–5 km. Earthquake focal mechanisms in this area suggest more variability in relative magnitude of the two horizontal stresses with depth. Furthermore, superimposed sets of young fault striae along a segment of the Wasatch fault also indicate temporal variations of relative stress magnitudes. Sources of regional and temporal variations in the stress field may be linked to variable shear tractions applied to the base of the brittle crust related to intrusion, thermally induced flow, and the influence of the San Andreas plate boundary. Although difficult to date accurately, the fault slip data suggest that the temporal variations in relative magnitudes stress may occur on the time scale of both a single major earthquake cycle (1000–5000 years) and multiple earthquake cycles (10,000+ years).

Computation of highly swirling confined flow with a Reynolds stress turbulence model

Abstract: The ability of a turbulence model to capture the interaction between swirl and the turbulent stress field is, therefore, crucial to the predictive performance of the computatinal scheme as a whole. A finite-volume procedure is used here to contrast the performance of the k-epsilon eddy-viscosity model with that of a Reynolds-stress transport closure. It is shown that the former returns a seriously excessive level of turbulent diffusion and misrepresents the experimentally observed flow characteristics. In contrast, the Reynolds-stress model successfully captures the subcritical nature of the flow by returning significantly lower levels of the shear stress components and predicts velocity and turbulence fields that are in good agreement with corresponding measurements. 22 references.

Magma transport and reservoir formation by a system of propagating cracks

Abstract: A system of propagating cracks may explain magma transport and the evolution of a volcano. This paper considers only a basaltic magma. The system is controlled by two boundary conditions: the stress field, and the production rate of the magma-filled cracks in the mantle. Numerical solutions of crack propagation for various stress conditions, with a constant production rate high enough to coalesce isolated cracks, were performed, and the results applied to different tectonic conditions. For the hydrostatic stress conditions, most magma-filled cracks beneath a polygenetic volcano become trapped either in the lower crust, because there the density difference between magma and the host rocks (Δρ) becomes suddenly small, compared with that in the mantle, or trapped in the upper crust, because there Δρ is near to zero. Magma traps composed of such cracks may grow into magma reservoirs if the production rate of cracks in the mantle is large. If horizontal stress with a vertical gradient is superimposed on the hydrostatic condition in the crust, that is, tensile stress which increases upward or compressional stress which increases downward, magmafilled cracks, even if the density of magma is higher than that of the crust, may ascend directly without trapping. When the crust undergoes relative tension, magma-filled cracks may become trapped. Then, the lower part of the trap may grow into a magma reservoir, while the upper part may become filled with dikes. When the production rate of cracks is small, an initial magma-filled crack can rise directly to the surface only when the stress with a gradient is superimposed as mentioned above, or when the average density in a crack decreases, owing to, for example, vesiculation of volatile components.

On improved hybrid finite elements with rotational degrees of freedom

Abstract: A set of three new hybrid elements with rotational degrees-of-freedom (d.o.f.'s) is introduced. The solid, 8-node, hexahedron element is developed for solving three-dimensional elasticity problems. This element has three translational and three rotational d.o.f.'s at each node and is based on a 42-parameter. three-dimensional stress field in the natural convected co-ordinate system. For two-dimensional, plane elasticity problems, an improved triangular hybrid element and a quadrilateral hybrid element are presented. These elements use two translational and one rotational d.o.f. at each node. Three different sets of five-parameter stress fields defined in a natural convected co-ordinate system for the entire element are used for the mixed triangular element. The mixed quadrilateral element is based on a nine-parameter complete linear stress field in natural space. The midside translational d.o.f.'s are expressed in terms of the corner nodal translations and rotations using appropriate transformations. The stiffness matrix is derived based on the Hellinger–Reissner variational principle. The elements pass the patch test and demonstrate an improved performance over the existing elements for prescribed test examples.

A Model for stress generation and relief in oxide — Metal systems during a temperature change

Abstract: When an oxidized metal is cooled from a high temperature, stresses are produced at the metal-scale interface, owing to the difference in thermal expansion rates of the oxide and metal. Such stresses become time- and temperature-dependent if the scale or underlying metal creeps as cooling occurs. A model is presented which describes thermally induced stresses in the scale and accounts for partial stress relaxation by creep of the metal substrate and/ or the scale. The expected stresses are a function of the material parameters: thermal expansion coefficients, elastic modulii, and creep rates of both metal and scale. To illustrate a range of behaviors, we have presented example calculations for three Cr2O3 forming metals, Ni-30Cr, pure Cr, and MA-754. The effect of stress relaxation during thermal cycling was also examined briefly. In these examples, creep of the Cr2O3 scale was not expected to be important.

Micromechanics of Fracture in Structural Adhesive Bonds

Abstract: The high mode-I fracture surface energies, GIC , of structural adhesives can be attributed to their ability to form large crack-tip deformation zones prior to failure. It has been suggested that this feature also controls the dependence of the adhesive bond GIC on bond thickness. The proposed explanation asserted that the physical constraint of the adherents and the nature of the crack-tip stress field in an adhesive joint alter the size and shape of the deformation zone, and this in turn changes the fracture behaviour. To examine this hypothesis, motion pictures were taken of fracture specimens during loading, and the stress whitening that occurred at the crack tip was used to judge the relative dimensions of the deformation zone. The results generally support the hypothesis. Moreover, the pictures furnish a clear image of the deformation zone's growth patterns during loading, and this provides a critical test for future modelling efforts.

Partial hybrid stress element for the analysis of thick laminated composite plates

Abstract: The variational principle of this element can be derived from the Hellinger-Reissner principle through dividing six stress components into a flexural part (σ x , σ y , τ xy , σ z ) and a transverse shear part (τ xy , τ yz ). The element stiffness matrix can be formulated by assuming a stress field only for transverse shear stresses, while all the others are obtained from an assumed displacement field. A twenty-node hexahedron element is employed in each layer for the displacement field. The equilibrium equation is enforced by the variational principle

Acceleration instability in elastic‐plastic solids. I. Numerical simulations of plate acceleration

Abstract: Acceleration instability occurs when a body is accelerated by surface tractions. This situation resembles classic Rayleigh–Taylor instability, but differs due to the temporal and spatial variation of the stress field in the accelerated body caused by wave propagation and the time dependence of the accelerating forces. These factors produce phenomena in acceleration instability which are without precedent in classical Rayleigh–Taylor analyses. An extensive numerical study of acceleration instability using a Lagrangian finite‐difference wavecode has determined the influence of various parameters including amplitude and wavelength of initial surface perturbations, material yield strength, and time dependence of the driving force. The nature of the criteria determining stability or instability is established, and the fundamental physical quantity controlling perturbation growth at an interface is shown to be the local stress gradient.

Multilayer theory for delamination analysis of a composite curved bar subjected to end forces and end moments

Abstract: A composite test specimen in the shape of a semicircular curved bar subjected to bending offers an excellent stress field for studying the open-mode delamination behavior of laminated composite materials. This is because the open-mode delamination nucleates at the midspan of the curved bar. The classical anisotropic elasticity theory was used to construct a ‘multilayer’ theory for the calculations of the stress and deformation fields induced in the multilayered composite semicircular curved bar subjected to end forces and end moments. The radial location and intensity of the open-mode delamination stress were calculated and were compared with the results obtained from the anisotropic continuum theory and from the finite element method. The multilayer theory gave more accurate predictions of the location and the intensity of the open-mode delamination stress than those calculated from the anisotropic continuum theory.

Application of 3-D weight functions. II: The stress field and energy of a shear dislocation loop at a crack tip

Abstract: T he General weight function expressions given in G ao (J. Mech. Phys. Solids37, 133, 1989), referred to here as part I, for combined-mode crack-dislocation interaction problems in the three-dimensional regime are applied to solve for the stress field and energy of a shear dislocation loop emerging from the tip of a half-plane crack. The results are compared to the previously proposed approximate estimates for shear loops by A nderson and R ice (J. Mech. Phys. Solids35, 743, 1987), who solved exactly for prismatic opening dislocation loops that are co-planar with the crack and also for the analogous 2-D cases of general crack tip-parallel line dislocations. The energy results are presented in terms of a correction factor m, following Anderson and Rice, to the usual estimate of energy for an emergent crack tip loop as half the energy of a full loop (identified as the emergent loop and its image relative to the crack front) in an uncracked solid. For a full circular shear loop the energy is U = [(2 − ν)μb2r/4(1-ν)] In (8r/e2r0), where r0 denotes the core cut-off parameter and μ, ν are the shear modulus and Poisson ratio. Thus for a semicircular loop emerging from the crack tip, the energy is expressed as U = [(2 − ν)μb2r/8(1-ν] In (8mr/e2r0), where the constant m depends on the orientation angle Ψ of the Burgers vector relative to a line normal to the crack tip and the inclination angle φ of the dislocated plane relative to the crack plane. The m factors are calculated at selected angles φ for rectangular and semicircular loops. This involves multiple numerical integrations based on the weight functions of part I, first to obtain the stress field and then to integrate it over the dislocated area to get the energy, and requires a large amount of computing CPU time. An approximate formula for m is proposed for general inclined dislocation loops, based on known 2-D results for m factors for arbitrary angles φ calculated by A nderson and R ice (1987) and the 3-D m(φ = 0) results given here for shear dislocation loops in the crack plane. It compares well to the exact results.

Models for Studying Free-edge Effects

Abstract: A historical/technical review is given, depicting the development of analytical models of the free-edge delamination phenomenon. Emphasis is placed on the role and importance of the free-edge problem in laminate elasticity in fostering an understanding of interlaminar stresses and their influence on composite response. From the early modeling work of Hayashi in 1967, and the definitive experiments of Foye and Baker in 1970, we trace analytical developments over the past two decades. The concept of ply elasticity or effective-modulus representation is discussed, as well as its consequences in laminate modeling. The first elasticity solution of the free-edge problem by Pipes and Pagano using finite differences is then described. This solution has been very instrumental in defining the general character of the interlaminar stress field in the neighborhood of a free edge. We then provide results for the elementary modeling of the effect of stacking sequence on laminate response and derivation of simplified equations to either optimize or minimize this effect in test specimens. Thence, a description of a model based upon the concept of a plate on a smooth foundation is given to capture the essence of the distribution of interlaminar normal stress, its boundary layer zone, and its implication on initiation of delamination. This model leads naturally to the formulation of a variational theorem for laminates that provides an accurate way to compute composite stresses. The chapter culminates with a derivation of the global-local model, which provides a practical way to describe the stress field in a multi-layered composite laminate, and a review of some recent modeling activities that have their basis in the concepts given earlier here. Numerous results are shown for stress fields within laminates which have both practical and theoretical importance.

Crustal Stresses in Eastern Canada

Abstract: Canada east of the Cordillera is being compressed along the northeast-southwest azimuth, and represents an extensive and relatively uniform stress province (which also includes the eastern and midcontinental United States), likely dominated by the forces driving the tectonic plates. Deglaciation severely stressed the North American plate about 10,000 years ago. Postglacial near-surface stresses were dominated by the radial flexural stresses induced near the ice margin; these were often orthogonal to the contemporary regional stresses which replaced them as the transient postglacial stresses waned. That the paleostresses no longer dominate the direction of the stress field in the southeast suggests that residual, glaciation-induced stresses make only a small contribution to the contemporary stress field.

Microscopic imaging of residual stress using a scanning phase-measuring acoustic microscope

Abstract: A high‐resolution scanning phase‐measuring acoustic microscope (SPAM) has been developed and used to image the near‐surface residual stress field around features etched in sputtered alumina via the acoustoelastic effect. This microscope operates at 670 MHz and has a resolution of 5–10 μm, depending upon the amount of defocus. Relative velocity changes of sample surface waves as small as 50 ppm are resolved. Images of the stress field at the tip of a 400‐μm‐wide slot etched in alumina are presented and compared with a finite element simulation. The SPAM uses an unconventional acoustic lens with an anisotropic illumination pattern which can measure anisotropic effects and map residual stress fields with several μm resolution and a stress sensitivity of 1/3 MPa in an alumina film.

Focal Mechanisms and Crustal Stresses in the Baltic Shield

Abstract: The results from regional seismic networks in the Baltic shield area are presented. About 200 earthquakes in the size ML=0.1–4.9 have been located and analysed. The fault plane solutions have been used for estimating the orientation of the regional deviatoric stress. The principal horizontal compression is oriented N60W. Strike-slip faulting on subvertical faults is the dominating mechanism. The existing fracture systems determine together with the regional stress field the type of faulting. The focal depths of the events indicate at least two different seismogenic layers: the upper crust down to 13–17km depth, and the middle crust 18–35km depth. At the depth range 18–28km the median size of the events is 0.7 magnitude units larger than at shallower or deeper depths. The Baltic shield earthquakes seem to be due to asperities in quietly sliding faults. The size of the slip may then be the most informative dynamic source parameter.

Banding and stability in plastic materials

Abstract: In this paper we have examined the question ofmaterial stability. More specifically, we have probed the conditions under which materials become “unstable” in the sense that given a homogeneous stress field in a materials domain, their constitutive equation allows the onset of a discontinuous, yet compatible, strain field in a finite subdomain (a “stress band”)while the state of stress in the entire domain remains unchanged. The central conclusion is that plastic materials are unstable in all inelastic stress states.

Characteristic Features of Intraplate Earthquakes and the Models Proposed to Explain Them

Abstract: An evaluation of various aspects of intraplate earthquakes (IPE) suggests that they occur by reactivation of a variety of pre-existing features in response to the current stress field. In this review, I first list the various methods of identifying these features, and then describe the characteristic elements of IPE. Reactivation occurs by one or more of three ways. These include a localized build-up of stress on the potentially seismogenic feature due to the ambient stress field, the superposition of a triggering stress and the reduction of strength of the feature(s) by mechanical and/or chemical means. The various models that have been suggested to explain IPE contain one or more of these elements.