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Showing papers on "Stress field published in 1987"


Journal ArticleDOI
TL;DR: This study introduces the method of bootstrap resampling to the statistics of this problem and shows that focal mechanisms can be inverted to find the best stress tensor, but the resolution is decreased unless the fault planes can be picked a priori.
Abstract: To allow focal mechanisms to be inverted for the stress field requires a different inversion algorithm than for slickenside data because focal mechanisms do not represent fault slip data unless one can decide which nodal plane is the fault plane. If one can decide which nodal plane is the fault plane, then the focal mechanisms can be inverted with the slickenside inversion algorithm. This decision cannot always be made, so algorithms for inverting focal mechanisms for the stress field are studied. These algorithms either use both of the possible fault planes or attempt to choose the correct fault plane while determining the stress tensor. Simulated focal mechanisms are made from slickenside data and used to provide a control study for the focal mechanism inversion algorithms. The results of this control study show that focal mechanisms can be inverted to find the best stress tensor, but the resolution is decreased unless the fault planes can be picked a priori. The resolution can also be increased by including constraints on the magnitude of the tangential traction on the fault plane. Therefore, using focal mechanisms to study small variations in the stress field requires that other data (e.g., studies of the hypocenters, surface faulting, or structural information concerning the region) be introduced to pick which of the nodal planes is the fault plane. This study also introduces the method of bootstrap resampling to the statistics of this problem. The non-Gaussian nature of the data makes the nonparametric formulation of the bootstrap approach ideal for this problem.

614 citations


Journal ArticleDOI
Mark Kachanov1
TL;DR: In this paper, a simple method of stress analysis in elastic solids with many cracks is proposed, based on the superposition technique and the ideas of self-consistency applied to the average tractions on individual cracks.

472 citations


Journal ArticleDOI
TL;DR: In this paper, the authors obtained an O(e5-approximation for the surface uplift with respect to a point dilatation, which is consistent with the locus of fractures radiating outward from the magma body inferred by seismic methods in Long Valley, California.
Abstract: Approximate solutions are obtained for the stress and displacement fields due to a pressurized spherical cavity in an elastic half-space. The solutions take the form of series expansions in powers of e = a/d, where a is the cavity radius and d is the depth. The leading-order term in the expression for the surface uplift, which arises at O(e3), recovers the well-known result of Mogi for the response to a point dilatation. The first higher-order correction accounts for a cavity of finite size and thus offers the possibility of fitting leveling data for not only the depth but also the radius and pressure increment. However, this correction is of O(e6) and, consequently, is weak. The result provides a formal explanation for the success of the point dilatation model in representing uplift data even when it is known independently that e is not small. The higher-order correction causes the surface uplift to fall off more rapidly in the radial direction, implying that a fit of the point source solution tends to underestimate the depth d. In contrast to the surface displacement, the stress field near the cavity is affected profoundly by the proximity of the free surface. Three higher-order corrections to the stress field are obtained, which result in a uniformly valid approximation to O(e5). The hoop stress at the cavity exhibits a tensile maximum at the circle of tangency with a cone with its apex at the free surface. This result appears to be consistent with the locus of fractures radiating outward from the magma body inferred by seismic methods in Long Valley, California.

429 citations


Journal ArticleDOI
TL;DR: In this article, the results of linear elastic analyses of stress distributions near a wide variety of notches are presented, and it is demonstrated that notch-tip stress fields are similar to each other regardless of the notch geometry and the loading system.

126 citations


Journal ArticleDOI
TL;DR: In this article, a closed-form solution for the stress field induced by gravity in anisotropic rock masses is presented, which is constrained by the thermodynamic requirement that strain energy be positive definite, giving the following important result: inclusion of anisotropy broadens the range of permissible values of gravity induced horizontal stresses.

123 citations


Journal ArticleDOI
TL;DR: In this article, a two-dimensional elastoplastic model of a long cylindrical cavity in an infinite rock mass subject to non-hydrostatic far-field stress loading is presented.

113 citations


Journal ArticleDOI
TL;DR: In this article, a hybrid stress model based on the modified complementary energy principle and taking into account the transverse shear deformation effects is developed for the analysis of laminated composite plates.

112 citations


Journal ArticleDOI
TL;DR: In this article, the force balance method and the principle of minimum complementary energy were used to solve the problem of interlaminar stresses at a straight free edge in a composite laminate.
Abstract: The solution to the problem of interlaminar stresses at a straight free edge in a com posite laminate is obtained in closed form for two special and important cases: angle-ply and cross-ply laminates. These solutions are derived using the Force Balance Method and the principle of minimum complementary energy. The results are favorably compared to the predictions of other analyses found in the literature. The solution procedure is found to be simpler and more efficient than other analytical methods. In addition, for some special cases of cross-ply laminates, the solution is shown to be identical to the predictions of a modified plate theory that includes through-the-thickness stretching.

99 citations


Journal ArticleDOI
TL;DR: In this article, the stress field due to polymer additive is calculated using a new molecular model, based on the physical picture of the polymer molecules unravelling in strong flows and Batchelor's theory for the stress in a suspension of elongated particles.
Abstract: The conical-channel flow of a dilute polymer solution is investigated theoretically. The stress field due to polymer additive is calculated using a new molecular model, based on the physical picture of the polymer molecules unravelling in strong flows and Batchelor's theory for the stress in a suspension of elongated particles. Good agreement is obtained with the experimental results of James & Saringer (1980). The absence of a significant polymer effect in a two-dimensional case (the wedge-channel flow), observed by the same authors (James & Saringer 1982 a ), is also explained. The fundamental differences between the proposed model and the elastic-dumbbell models are discussed.

93 citations


Journal ArticleDOI
TL;DR: In this article, the steady-state, two-dimensional creeping flow of an Upper-Convected Maxwell fluid between two eccentric cylinders, with the inner one rotating, is computed using a spectral/finite-element method (SFEM).
Abstract: The steady-state, two-dimensional creeping flow of an Upper-Convected Maxwell fluid between two eccentric cylinders, with the inner one rotating, is computed using a spectral/finite-element method (SFEM). The SFEM is designed to alleviate the numerical oscillations caused by excessive dispersion error in previous finite-element calculations and to resolve the stress boundary-layers that exist for high elasticity, as measured by the Deborah number De . Calculations for cylinders with low eccentricity (ϵ = 0.1) converged to oscillation-free solutions for De ≈ 90, extending the domain of convergence over traditional finite-element methods by a factor of thirty. The results are confirmed by extensive refinement of the discretization. At high De , steep radial boundary layers form in the stress, which match closely with those predicted by asymptotic analysis. Calculations at higher eccentricity require extreme refinement of the discretization to resolve the variations in the stress field in both the radial and azimuthal directions associated with the existence of the recirculation region. Results for ϵ = 0.4 show that the recirculation region present for the Newtonian fluid ( De = 0) shrinks and then grows with increasing De . Calculations for ϵ = 0.4 are terminated by a limit point near DeL ≈ 7.24 for the finest discretization used. The Fourier series approximations are not convergent for this mesh, so the limit point must be considered to be an artifact of the discretization.

87 citations


Journal ArticleDOI
TL;DR: In this article, a model for coupled heat, moisture and stress field in freezing soil is proposed for solving practical frost heave problems in which the heave is coupled with deviatoric creep, such as under foundations or around chilled buried pipelines.

Journal ArticleDOI
TL;DR: In this paper, the stress field due to olivine-spinel phase transition in and around a descending plate is studied based on the calculations for an equilibrium phase transition with a constant Clapeyron's slope and for a nonequilibrium transition taking a kinetic effect into consideration.
Abstract: The stress field due to olivine-spinel phase transition in and around a descending plate is studied based on the calculations for an equilibrium phase transition with a constant Clapeyron's slope and for a nonequilibrium transition taking a kinetic effect into consideration. The material concerned is assumed to be a viscoelastic body whose physical coefficients are functions of temperature and pressures. The calculated stress distribution for the equilibrium transition is characterized by a compressional stress near the upper and/or lower surfaces of the plate and by a tensional stress at the central part in the depth range from 200 to 550 km, the magnitude of principal stress being greater than 0.5 GPa. However, for the nonequilibrium transition a tensional stress predominates near the upper and lower surfaces, and the central part is compressional in the depth range from 300 to 600 km, unlike the case of equilibrium transition. The maximum principal stress in the latter case is greater than 2 GPa, which is much more than that for the equilibrium transition. The principal axes in the high stressed region are oriented almost parallel to the descending direction in both cases. Comparison of the calculated results to the actually observed seismicity-depth relation and to focal mechanisms of deep focus earthquakes in descending plates beneath island arcs shows that the nonequilibrium phase transition agrees better with the observations.

Journal ArticleDOI
TL;DR: In this paper, a theoretical model is presented to predict the Burgers vector and the glide plane of dislocations generated at thin-film edges on silicon substrates, based on a theoretical analysis of the stress field at the film edge.
Abstract: A theoretical model is presented to predict the Burgers vector and the glide plane of the dislocations generated at thin‐film edges on silicon substrates. The model is based on a theoretical analysis of the stress field at the film edge. It is shown that the external force acting upon a dislocation with a known Burgers vector is a linear combination of the stress‐field components. In equilibrium the total external glide force is balanced by the counteracting line tension force and the critical glide force, both only depending on the length of the Burgers vector and not on its orientation. The (a/2)〈110〉‐type dislocation on which the largest external climb and glide force is exerted will nucleate first and subsequently grow by gliding to its equilibrium shape and position.

Journal ArticleDOI
TL;DR: In this paper, the authors examined the effects of changes in crack density and changes in aspect ratio on the propagation path of split shear-wave VSPs and found that the polarization alignments were not significantly altered between 1979 and 1984, implying that the direction of the regional stress field has not changed significantly.
Abstract: Summary. Almost all shear-waves from local earthquakes recorded on closely-spaced three-component seismometer networks deployed near the North Anatolian Fault, Turkey, in two experiments in 1979 and 1980, display shear-wave splitting. The observations are consistent with the presence of EDA (extensive-dilatancy anisotropy), distributions of fluid-filled cracks and microcracks aligned by the regional stress field. Temporal changes in the stress-field, which may occur before an earthquake, may modify the geometry and possibly the orientation of the EDA-microcracks, and lead to corresponding changes in the behaviour of the split shear-waves. A third experiment was undertaken in 1984 to investigate EDA further and to search for possible temporal variations of the polarization of the leading split shear-wave and the time delay between split shear-waves. Observations indicate that the polarization alignments, which are parallel to the strike of the parallel vertical EDA-cracks, are unaltered between 1979 and 1984, implying that the direction of the regional stress field has not changed significantly. Temporal changes in the stress field are more likely to cause changes in the crack density and/or aspect ratio, which would result in a corresponding change in time delay between the split shear-waves. We examine observations of time delay in relation to their propagation path with respect to the crack geometry since it is then possible to separate the effects of changes in crack density and changes in aspect ratio. With this procedure, a small temporal variation of time delays is found between 1979 and 1984, consistent with a decrease in crack density, and consequently a relaxation of stress, in this time period. No evidence was found for any observable variation of time delay over a six month observation span in 1984. We suggest that analysis of repeated shear-wave VSPs offers a technique for monitoring stress changes before earthquakes.

Journal ArticleDOI
TL;DR: In this paper, the authors prove the existence of a displacement field and a stress field that satisfy the dynamical equation for continuous media and the Prandtl-Reuss constitutive law of elasto-perfect plasticity.
Abstract: We prove the existence of a displacement field and of a stress field that satisfy the dynamical equation for continuous media and the Prandtl-Reuss constitutive law of elasto-perfect plasticity. First we obtain the existence of a displacement rate in a space of functions of bounded deformation, where the constitutive law is satisfied in an integral form, then we show that one can choose a good representative for the stress in such a way that the Prandtl-Reuss law is satisfied almost everywhere with respect to the deformation measure.

Journal ArticleDOI
TL;DR: In this paper, the standard boundary element method is modified to take explicit account of the singularity in the stresses at a crack-tip, and the known expansion terms of the crack tip displacement and stress fields are subtracted to remove the numerical difficulties associated with the representation of a singular stress field at the cracktip.
Abstract: In order to compute stress intensity factors accurately, the standard boundary element method is modified to take explicit account of the singularity in the stresses at a crack-tip. The known expansion terms of the crack tip displacement and stress fields are subtracted to remove the numerical difficulties associated with the representation of a singular stress field at the crack-tip. Hence the accuracy of calculation is much improved, without appreciably increasing the amount of computation involved. Furthermore, the stress intensity factor is directly obtained as a part of a solution and no extrapolations are required. The improved formulation is applied to a configuration, which is representative of a part of the wing in a civil transport aeroplane. This configuration consists of a pair of circular cut-outs (supply ports) near to which smaller holes exist; these small holes are particularly susceptible to cracking.

Journal ArticleDOI
TL;DR: In this paper, the influence of an external stress field on the growth and morphological evolution of a coherent precipitate is examined within the context of the thermodynamics of crystalline solids and interfaces.
Abstract: The influence of an external stress field on the growth and morphological evolution of a coherent precipitate is examined within the context of the thermodynamics of crystalline solids and interfaces. Equilibrium interfacial concentrations are obtained that are shown to be strong functions of position along the precipitate-matrix interface. These variations in concentration may be larger than the usual capillarity term and are a result of elastic considerations and not a result of changes in the local interfacial curvature. The interfacial concentrations directly influence the precipitate growth rate and result in changes in the precipitate morphology. Depending upon the signs and magnitudes of the coherency strains, the applied stress field and the elastic inhomogeneity of the system, the shape evolution may be approximated by ellipsoids of revolution.

Journal ArticleDOI
TL;DR: In this article, the influence of polydispersity on small deformations and the coupled effects of viscous and interfacial forces present in the foam films on both small and large deformations were investigated.
Abstract: A constitutive model for foams developed previously is extended here to study the influence of polydispersity on small deformations and the coupled effects of viscous and interfacial forces present in the foam films on both small and large deformations. A formalism for describing cell motion at large strains is also presented. To investigate the effects of polydispersity, the cell deformation and stress—strain behavior for a foam with a bimodal cell size distribution are calculated. The yield stress, critical (yield) strain and the stress—strain relation are found to be independent of the size distribution about a constant mean cell size and are coincident with that of foam consisting of monodisperse, regular hexagonal cells. The introduction of liquid viscosity into the model produces strong deviations from previous results in both the stress field and in the cell deformation for modified capillary numbers larger than 0.01. Further, these viscous effects are dependent on initial cell orientation. Although the magnitude of the viscous stress is not large, it affects the total stress by changing the cell structure. For smaller Ca′, however, viscosity has a minimal effect on the foam rheology. For large deformations, initial cell orientation and viscosity strongly affect the time periodicity of the system. For certain orientations, the cell structure and stresses showed aperiodic behavior regardless of the magnitude of the ratio of the viscous to the interfacial forces (Ca′), whereas for other initial orientations they were periodic. For large Ca′ the cells become highly elongated indicating the possibility of cell rupture.

Journal ArticleDOI
TL;DR: Oriented granite cores from the Illinois borehole UPH-3 contain planes of secondary fluid inclusions, which represent healed microcracks They record the orientation of a paleostress field with the maximum stress in the horizontal plane oriented to the NNW about 90° from the present stress field orientation as discussed by the authors.

Journal ArticleDOI
TL;DR: In this article, the authors deduced the stress field induced by mutual compression of two spheres having dissimilar elastic constants, and found that significant modifications to the Hertzian stress field occur at the surface, and these decay rapidly with depth.
Abstract: The stress field induced by the mutual compression of two spheres having dissimilar elastic constants is deduced. Solutions are found assuming full slip, full stick, and partial slip at the interface, but coupling between the shear traction and vertical displacement of the surfaces is neglected. It is shown that significant modifications to the Hertzian stress field occur at the surface, and that these decay rapidly with depth.

Journal ArticleDOI
TL;DR: In this article, a nonlocal approach for simulating the response near soil-concrete interfaces is proposed, where the stress field is a function of both strain and strain gradients, and no slip occurs at the contact surface between soil and concrete.
Abstract: This investigation explores a method for predicting deformation in the vicinity of interfaces of dissimilar materials. Instead of using a slide‐line algorithm or interface elements, a new nonlocal approach for simulating the response near soil‐concrete interfaces is proposed. It is assumed that the stress field is a function of both strain and strain gradients, and that no slip occurs at the contact surface between soil and concrete. Different response features for the region of localized shear strain adjacent to the interface can be obtained by adjusting material parameters. Numerical results for static and dynamic cases show that softening and localization are handled in a stable manner independent of mesh size.

Book ChapterDOI
01 Jan 1987
TL;DR: In this paper, the authors give thermodynamic sanction to Lindgren's hypothesis that metasomatic processes tend to take place at constant volume and show that the assumption that pressure remains constant and uniform during irreversible diffusion metasomatism is generally not tenable.
Abstract: “Induced stress” and “secondary mass transfer” give thermodynamic sanction to Lindgren’s hypothesis that metasomatic processes tend to take place at constant volume. Owing to the finite strength of minerals and rocks, the assumption that pressure remains constant and uniform during irreversible diffusion metasomatism is generally not tenable. The migration of a nonplanar diffusion-metasomatic zone boundary induces a field of nonhydrostatic stress, except in the special case where the metasomatic reaction at the zone boundary has a zero volume-change. The stress field is created at the expense of the “primary” chemical-potential gradients caused by overstepping of whatever net reaction may be taking place in the whole system, and it is so oriented as to tend to inhibit the displacement and distortional strain that must accompany the migration of the zone boundary. “Secondary” chemical-potential gradients are induced by the stress field. To the extent that “secondary” mass transfer is driven by such gradients, the induced stress-field tends to relax towards constant and uniform pressure. If the secondary mass transfer is so efficient that the induced stress never rises to the threshold value necessary to cause irreversible distortional strain in one or the other zone, the reaction at the migrating zone boundary will be constrained to take place at virtually constant volume.

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed fluid-driven cracks of various geometries and found examples of both stable and catastrophic propagation, and showed that for an isolated crack in a homogeneous medium with remotely applied compressive stresses the stress intensity decreases as the crack tip extends beyond the driving fluid, so that crack propagation is stable and limited by the rate of fluid flow.
Abstract: The recent suggestion that earthquakes at Long Valley caldera, California, are caused by rapid tensile failure under high fluid pressure contradicts the assumption that the speed of propagation of a fluid-driven tensile crack is limited by the speed of motion of the fluid within the crack, so that such cracks cannot radiate seismic waves. In this paper we analyze fluid-driven cracks of various geometries and find examples of both stable and catastrophic propagation. For an isolated crack in a homogeneous medium with remotely applied compressive stresses the stress intensity decreases as the crack tip extends beyond the driving fluid (assumed stationary), so that crack propagation is stable and limited by the rate of fluid flow. On the other hand, for two cracks approaching each other, initially stable behavior gives way to unstable propagation, and the cracks join catastrophically even if the fluid is stationary. A crack approaching a free surface also exhibits a transition from stable to unstable propagation, with the final episode occurring catastrophically. A crack emanating from a pressurized reservoir of cylindrical or spherical shape can also undergo an episode of catastrophic propagation. Propagation begins when the reservoir pressure rises to a critical value, which depends on the regional stress field, the fracture toughness of the rock, and the size of the largest flaw at the surface of the reservoir. This flaw propagates catastrophically until it reaches a certain size and thereafter propagates stably. Microearthquakes caused by hydraulic fracturing have dimensions of at most a few tens of borehole radii and therefore probably are difficult to detect. Volcanic earthquakes can have source dimensions comparable to the radius of the associated magma chamber, so earthquakes as large as those at Long Valley caldera (source dimensions ≅ 10 km) could be caused by tensile failure.

Journal ArticleDOI
TL;DR: In this paper, the regional stress field and its local variation were determined for the northern part of central Switzerland (Fig. 1) by using overcoring techniques (doorstopper, triaxial strain cell) and observations of breakouts in deep boreholes.

Journal ArticleDOI
TL;DR: In this paper, the deformation of undoped indium phosphide is controlled by the motion of screw dislocations in the stress field of the lattice according to a thermally activated Peierls mechanism.

Journal ArticleDOI
TL;DR: A d.c. potential drop technique has been used successfully to monitor high temperature crack growth in either vacuum or air for commercial purity and phosphorus-doped versions of 2 1 4 Cr -1 Mo steel as mentioned in this paper.


Journal ArticleDOI
TL;DR: In this article, the stress field for the three-dimensional plasticity fracture problem is formulated by reducing the formulation to a system of singular integral equations, referred to as the Singular Integral Operators Method (SIOM).

Journal ArticleDOI
TL;DR: In this article, the self stress field and self energy for a planar 3D dislocation loop emanating from a half-plane crack tip were derived for the 2D case of a line dislocation lying parallel to the crack for arbitrary Burgers vector type and general orientation of the dislocated plane relative to a crack.
Abstract: The self stress field and self energy are estimated for a planar 3D dislocation loop emanating from a half-plane crack tip. While the problem is of greatest interest for analysis of shear loops nucleating from the crack tip in the concentrated stress field there due to applied loadings, it is addressed here in the interest of tractability for 3D prismatic loops lying in the same plane as the crack. Exact elastic calculations for that case are based on recent developments of 3D crack weight function theory and specific results are given for induced stress fields, intensity factors and energy of semicircular and rectangular prismatic dislocation loops. Also, self stresses and energy expressions are derived for the 2D case of a line dislocation lying parallel to the crack for arbitrary Burgers vector type and general orientation of the dislocated plane relative to the crack plane, and those results are used together with the 3D prismatic loop results to estimate approximately the self energy for 3D shear dislocation loops emanating from the tip on planes inclined to the crack plane. Energy results are given in terms of a correction factor m 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 tip) in an uncracked solid. That is, if the energy of a full circular loop of radius r in an uncracked solid is 2πrA0 1n (8re2r0), with r0 = core cut-off and A0 = energy factor, then the energy of a semicircular loop of radius r emerging from the crack tip is shown to take the form πrA0 In (8mre2r0) and the constant m is calculated here as 2.2 for a prismatic loop ahead of a crack and estimated approximately to range from about 1.2 to 1.9 for representative shear loops inclined to the crack plane. The self energy exceeds the half-full-loop value, corresponding to m = 1, and it is observed that this effect increases by √m the predicted loads to nucleate a dislocation loop of the assumed shape from a crack tip.

Journal ArticleDOI
TL;DR: In this article, a Lagrangian formulation is introduced which, for the case of simple shear produces monotonically increasing stress-strain relationships, and the associated flow rule used here preserves the normality rule in the second Piola-Kirchhoff stress space and is equivalent to that of the Cauchy stress space.