Showing papers on "Stress field published in 1993"

On the numerical integration of interface elements

Abstract: SUMMARY Eigenmode analyses of the element stiffness matrices have been used to assess the impact of the applied integration scheme on the stress predictions of two- and three-dimensional plane interface elements. It is demonstrated that large stress gradients over the element and coupling of the individual node-sets of the interface element may result in an oscillatory type of response. For line elements and linear plane interface elements the performance can be improved by using either a nodal lumping scheme or Newton-Cotes or Lobatto integration schemes instead of the more traditional Gauss scheme. For quadratic interface elements the same holds true except for a nodal lumping scheme. Interface elements are a powerful tool in the modelling of geometrical discontinuities in different kinds of structures. In finite element analysis of civil engineering structures a large variety of applications for interface elements is present. Interface elements can be used to model soil reinforcement interaction,' to model the intermediate layer between rock and concrete, e.g. in arch dam or in the analysis of rock joints.536 Applications in concrete mechanics cover the modelling of discrete cracking,'~~ aggregate interlock9 and bond between concrete and reinforcement."-I4 In rubber parts, interface elements can be of importance when disintegration of rubber and texture is concerned, e.g. in conveyor belts. Furthermore, interface elements are suited to model delamination in layered composite structures' ', or frictional contact in forming processes. Interface elements can bc divided into two elementary classes. The first class contains the continuous interface elements (line, plane and shell interface^),^-^^"-'*, 2"+23 whereas the second class of elements contains the nodal or point interface elernent~,'~'~,~ ~ which, to a certain extent, are identical to spring elements. In this contribution we shall only consider the numerically and lumped integrated continuous interface elements, since nodal interfaces are integrated explicitly. A basic requirement of interface elements is that during the elastic mge of the loading process no significant additional deformations occur due to the presence of these elements in the finite element model. Therefore, a sufficiently high initial dummy stiffness has to be supplied for the interface elemenls. Depending upon the applied numerical integration scheme, this high dummy stiffness may result in undesired spurious oscillations of the stress field. In this paper th'e impact of Gauss, Newton-Cotes, Lobatto and lumped integration schemes on the stress prediction in interfaces is investigated for three-dimensional linear and non-linear analyses. Eigenvalue analyses of the linear elastic and non-linear element stiffness matrices have been carried out to explain the observed oscillatory performance of interface elements. Since we shall focus on 0029-598 1/93/010043+ 24$17.00 0 1993 by John Wiley & Sons, Ltd.

Fault growth and fault scaling laws: Preliminary results

Abstract: We report progress made in the last few years on the general problem of the mechanism of fault growth and the scaling laws that result Results are now conclusive that fault growth is a self-similar process in which fault displacement d scales linearly with fault length L Both this result and the overall nature of along-strike fault displacement profiles are consistent with the Dugdale-Barenblatt elastic-plastic fracture mechanics model In this model there is a region of inelastic deformation near the crack tip in which there is a breakdown from the yield strength of the unfractured rock to the residual frictional strength of the fault over a breakdown length S and displacement d0 Limited data also indicate that S and d0 also scale linearly with L, which implies that fracture energy G increases linearly with L The scaling parameters in these relationships depend on rock properties and are therefore not universal In our prime field locality, the Volcanic Tableland of eastern California, we have collected data over 2 orders of magnitude in scale range that show that faults obey a power law size distribution in which the exponent C in the cumulative distribution is ∼13 If the fault is growing within the brittle field, the zone of inelastic deformation consists of a brittle process zone which leaves a wake of fractured rock adjacent to the fault Preliminary results of modeling the process zone are consistent with observations now in hand both in predicting the preferred orientation of cracks in the process zone wake and the rate of falloff of crack density as a function of distance from the fault The preferred orientation of these cracks may be used to infer the mode and direction of propagation of the fault tip past the point in question According to the model, the width of the process zone wake may be used to infer the length of the fault at the time its tip passed the measurement point, but data have not yet been collected to verify this prediction If the fault displacement has been accumulated by repeated seismic slips, each of these will sweep the fault with a crack tip stress field of a smaller spatial extent than that of the fault tip stress field, producing an inner, more intensely fractured, process zone wake This may be the mechanism that creates the cataclasite zone, rather than simple frictional wear, as has been previously supposed

Tensile fracture of rock at high confining pressure: implications for dike propagation

Abstract: Field observations indicate that zones of inelastic deformation produced at the tips of propagating dikes can be much larger than those produced at the tips of tensile cracks in laboratory experiments. This is in direct conflict with the concept that fracture toughness and fracture energy are rock properties, independent of crack size and loading configuration. A Barenblatt model that treats fracture resistance as an internal cohesive stress acting at the crack tip is used to investigate the effect of confining pressure on rock tensile failure. When the confining pressure exceeds the cohesive strength of the rock, as it does at depths greater than several hundred meters, Linear Elastic Fracture Mechanics is inapplicable and the near-tip stress field of a propagating crack is determined by the crack size and loading configuration as well as by rock properties. As inelastic deformation depends upon the near-tip stress field, it follows that fracture energy may also depend upon crack size and loading configuration. For a propagating dike, the near-tip stress field is dominated by the large suction acting within a small (∼several meter) cavity at the tip generated by viscous flow of magma within the dike. Perturbations to the ambient stress are on the order of the cavity suction and act over regions on the order of the cavity length. The tip cavity pressure may be maintained by exsolution of magmatic volatiles or by influx of host rock pore fluids; inelastic deformation is enhanced by the latter. For a tip cavity pressure maintained by influx of pore fluids, the pore pressure exceeds the least compressive stress off the dike plane, even while it equals the least compressive stress at the dike tip. This can lead to tensile failure off the dike plane and the formation of observed dike-parallel joints. Shear stresses scale with the cavity suction and may produce shear failure off the dike plane; such deformation is generally enhanced if the dike is intruded perpendicular to the least compressive stress. For sills intruded parallel to bedding, shear failure in the form of bedding plane slip can lead to the observed blunting and fingering of the intrusion front. Because the tip cavity grows with dike size, the energy consumed by rock fracture also increases with dike size and is potentially as significant for large dikes as for small dikes, a view not adopted by existing fluid mechanical models of dike propagation.

Dislocation loops at crack tips: nucleation and growth— an experimental study in silicon

Abstract: The nucleation of dislocation loops at crack tips and the development of the plastic zone were studied in single-crystal silicon samples precracked at room temperature and loaded at T ⩾ 900 K under well-controlled conditions (mode I loading, constant loading rate). Several crystallographic orientations with different cleavage planes and crack front orientations were investigated. In situ observations by synchrotron X-ray topography were supplemented by chemical etching after fracture. Special attention was paid to the early stages of plastic zone formation. Dislocation nucleation appeared to be very heterogeneous along the crack front and may be favoured at free surfaces and cleavage edges. Activated slip systems and dislocation arrangements are discussed. It is shown that considerations based on the crack tip stress field to not suffice to account for the observed slip systems. The ledge crack mechanism of Zhou and Thomson has probably been observed but cannot be proved to be the main emission mechanism.

Magmatic processes under arcs and formation of the volcanic front

Abstract: Temperature structure and stress under arcs are simulated in a two-dimensional cross section taking into account the flow induced by the subducting slab in the mantle wedge. Results of the calculations show three important features with respect to magmatic processes under arcs: (1) Temperature structure in the crust and the mantle wedge under arcs is insensitive to the angle and velocity of slab subduction, the temperature structure of the slab, and that of the back-arc region. This indicates that physical conditions such as temperature and pressure are similar under various arcs. It is thus inferred that primary magmas generated under various arcs should have similar chemical compositions, if chemical composition and the flux rate of fluid from the slab are similar and the chemical compositions of mantle wedge materials are the same. (2) Calculated deviatoric stress magnitude is relatively large (more than a few tens of megapascals) in the partially molten mantle. Cracks may open under high differential stress, and magma can easily segregate and accumulate through interconnected cracks while the buoyancy driven compaction of partially molten mantle proceeds. (3) The deviatoric stress values in the region over the partially molten mantle are relatively large, and the direction of the principal stress changes horizontally; the direction of the maximum compressional stress is nearly vertical under the volcanic zone and is nearly horizontal under the fore-arc region. It is considered that magma segregated in partially molten mantle migrates upward through the brittle mantle and crust by the magma fracturing mechanism. The propagation direction of magma-filled fissures is controlled by the stress field in the crust and mantle and is parallel to the maximum principal stress. The calculated stress is highly compressive horizontally on the trench side, while it becomes tensile on the back-arc side. The location of this stress transition coincides with that of the volcanic front. The location of this transition indicates that the volcanic front marks a change in the ease of upward migration of the magma-filled cracks under relatively high differential stress field.

The Mechanics of Dislocations in Strained-Layer Semiconductor Materials

Abstract: Publisher Summary This chapter discusses the mechanics of dislocations in strained-layer semiconductor materials. A principal difficulty with strained-layer structures is that the stress associated with the strain gives rise to a driving force for structural defects in the strained-layer lattice. The means of controlling these defects has become a concern of central importance in the field. The elastic energy stored in a crystal associated with an applied stress field can be reduced by the advance of a dislocation through that crystal, and this effect leads to the concept of an applied force on a dislocation, defined as the reduction of the mechanical energy of the body associated with an advance of the dislocation. On the other hand, the presence of a free surface leads to a counter effect. In this chapter, selected properties of the stress and deformation fields of dislocations in elastic bodies are summarized in Section II. Of particular interest are the fields of a long, straight dislocation in a half-space for the case when the dislocation line is parallel to the free surface. Section III discusses isolated dislocation in a strained layer. Section IV analyzes the driving force in more complex situations.

Mechanism diversity of the loma prieta aftershocks and the mechanics of mainshock-aftershock interaction.

Abstract: The diverse aftershock sequence of the 1989 Loma Prieta earthquake is inconsistent with conventional models of mainshock-aftershock interaction because the aftershocks do not accommodate mainshock-induced stress changes. Instead, the sense of slip of the aftershocks is consistent with failure in response to a nearly uniaxial stress field in which the maximum principal stress acts almost normal to the mainshock fault plane. This orientation implies that (i) stress drop in the mainshock was nearly complete, (ii) mainshock-induced decreases of fault strength helped were important in controlling the occurrence of after-shocks, and (iii) mainshock rupture was limited to those sections of the fault with preexisting shear stress available to drive fault slip.

State of stress, faulting, and eruption characteristics of large volcanoes on Mars

Abstract: The formation of a large volcano loads the underlying lithospheric plate and can lead to lithospheric flexure and faulting. In turn, lithospheric stresses affect the stress field beneath and within the volcanic edifice and can influence magma transport. Modeling the interaction of these processes is crucial to an understanding of the history of eruption characteristics and tectonic deformation of large volcanoes. We develop models of time-dependent stress and deformation of the Tharsis volcanoes on Mars. A finite element code is used that simulates viscoelastic flow in the mantle and elastic plate flexural behavior. We calculate stresses and displacements due to a volcano-shaped load emplaced on an elastic plate. Models variously incorporate growth of the volcanic load with time and a detachment between volcano and lithosphere. The models illustrate the manner in which time-dependent stresses induced by lithospheric plate flexure beneath the volcanic load may affect eruption histories, and the derived stress fields can be related to tectonic features on and surrounding martian volcanoes.

Singular Stress Field Near the Corner of Jointed Dissimilar Materials

Abstract: In this paper, the characteristics of the stress field near a corner of jointed dissimilar materials are studied as a plane problem. It is found that the order of singularity is dependent not only on the elastic constants of materials and the local geometry of corner, but also on the deformation mode. The dependence of the order of singularity was established for the case of mode I and the case of mode II. An explicit closed-form expression is given for the singular stress field at the close vicinity of the corner, in which the stress field is expressed as a sum of the symmetric state with a stress singularity of 1/r 1-λ1 and the skew symmetric state with a stress singularity of 1/r 1-λ2 . When both λ1 and λ2 are real the singular stress field around the point singularity is defined in terms of two constants K 1 , λ1 , K 11 , λ2 , as in the case of crack problems.

Kinetics of Indentation Cracking in Glass

Abstract: The propagation of indentation radial cracks in soda—lime silicate glass is measured as a function of time after indentation. Rapid lift-off of the indenter from the specimen surface causes a step-function perturbation in the radial crack mechanical energy release rate, thus providing access to a large range of observable crack velocities in the indentation stress field. Analysis of the data shows distinct threshold, reaction-limited, and transport-limited behavior in the crack velocity responses, in agreement with measurements made using macroscopic crack geometries. Atomistic models of fracture kinetics in reactive environments are fit to the data and are deconvoluted to yield the underlying atomic-scale, bond-rupture parameters. These latter are used to calculate potential functions for activated fracture and predict crack velocity responses as a function of temperature and pressure.

The nature of the landers-mojave earthquake line.

Abstract: The Landers, California, earthquake of 28 June 1992 (magnitude = 7.3) is the latest of six significant earthquakes in the past 60 years whose epicenters and slip directions define a 100-kilometer alignment running approximately N15 degrees W across the central Mojave region. This pattern may indicate a geologically young throughgoing fault that replaces numerous older strike-slip faults by obliquely cutting across them. These older faults, and perhaps also the bend in the San Andreas fault, may be losing their ability to accommodate upper crustal deformation because they have become unfavorably oriented with respect to the regional stress field.

A three‐dimensional multilayer composite finite element for stress analysis of composite laminates

Abstract: A three-dimensional multilayer composite finite element method has been developed based on a composite variational functional which takes three in-plane strains ex, ex, exy and three transverse stresses σz, σyz, σxz as the basic variables. The continuity of the transverse stresses σz, σyz, σxz across the laminate thickness is assured a priori by introducing a partial stress field parameter α which is associated with the lower and upper surfaces of a lamina in a laminate. A method has been developed to form the partial stress field based on the assumed displacement field. With this method, a three dimensional (3-D) multilayer composite finite element is formulated for stress analysis of composite laminates. A numerical example is given, which shows some advantages of this composite element.

Three‐dimensional singularities of elastic fields near vertices

Abstract: For the computation of the singular behavior of an elastic field near a three-dimensional vertex subject to displacement boundary conditions we use a boundary integral equation of the first kind whose unknown is the boundary stress. Localization at the vertex and Mellin transformation yield a one-dimensional integral equation on a piecewise circular curve γ in IR3 depending holomorphically on the complex Mellin parameter. The corresponding spectral points and packets of generalized eigenvectors characterize the desired stress field and are computed by a spline-Galerkin method with graded meshes at the corner points of the curve γ. © 1993 John Wiley & Sons, Inc.

Rocky Mountain foreland uplifts: Products of a rotating stress field or strain partitioning?

Abstract: Stress-tensor analysis of minor faults near the structural range fronts of diversely oriented Laramide foreland uplifts in the central Rocky Mountains, Wyoming, indicates that paleo-σ 1 was horizontal and oriented nearly perpendicular to uplift trends. Trend directions for σ 1 vary from east-northeast in the north-trending Laramie Range, to northeast in the northwest-trending Bighorn Mountains, to north at east-trending Casper Mountain and in the east-trending central Owl Creek Mountains. Although these compression directions are compatible with models invoking temporally changing stress directions during the Laramide orogeny, the apparent similarity in timing of uplift in these ranges suggests that the computed stress tensors may not reflect regional stress conditions. Recent stress determinations in transpressional regimes suggest that strain partitioning may be an important factor in considering local stress patterns in the vicinity of mountain belt structures oblique to regional trends. In light of these studies, caution should be used in interpreting regional paleostress from structures measured close to the tectonic fronts of Laramide uplifts.

Influence of the fiber length on the stress transfer from glass and carbon fibers into a thermoplastic matrix in the pull-out test

Abstract: The stress field arising in the single fiber pull-out test is analysed within the framework of the linear theory of elasticity by means of the finite element method, utilizing an idealized model. The finite element analysis is compared with the frequently employed shear lag theory. It is shown that the stress distribution in the vicinity of the fiber is extremely inhomogeneous with strong concentrations in the boundary layer, at the matrix surface as well as at the fiber end, which are not predicted by the shear lag theory. The influence of the fiber length to diameter ratio on the stress field in the fiber and in the interface is analysed for an E-glass fiber and a high-modulus carbon fiber embedded in a polycarbonate matrix by varying the length to diameter ratios between 2.5 and 15.

Refined shear deformation theory of laminated shells

Abstract: This paper analyzes the effect of shear deformation in thick laminated anisotropic shells using a mixed formulation based on the functional proposed by Jing and Liao. The displacement field uses a zigzag function in addition to the Reissner-Mindlin type in-plane displacements and a constant transverse deflection. The effect of transverse shear deformation is included through an independently assumed transverse shear stress field. The initial curvature effect is included in the strain-displacement relations, stress resultants, and the assumed shear stress field

Curving cross joints and the lithospheric stress field in eastern North America

Abstract: Cross joints are late-formed nonsystematic fractures that extend across intervals between systematic joints. Traces of such cross joints are seen on bedding-plane surfaces of Devonian Catskill clastic sedimentary rocks of the Appalachian Plateau of western New York State, where the maximum horizontal principal stress (S H ) is oriented ∼N65°E, as indicated by in situ stress measurements. Between pairs of closely spaced systematic joints, traces of cross joints are commonly planar and orthogonal to the preexisting joints. However, in the mid-region between some widely spaced systematic joints in western New York, cross joints strike parallel to the S H of the present lithospheric stress field, but then curve to abut the preexisting joints at right angles. A curving trace reflects a local perturbation of the regional stress field in the vicinity of preexisting joints, and the perpendicular termination indicates that the preexisting joints were open. Depending on their age, the strike of the mid-region of curving cross joints denotes the orientation of either the neotectonic stress field or its Tertiary predecessor in the North American lithosphere.

The stress field of the north west shelf and wellbore stability

Abstract: Boreholes drilled in the search for hydrocarbons in the Barrow-Dampier Sub-Basin (North West Shelf, Australia) commonly exhibit an elliptical cross-section believed to be due to stress-induced wellbore failure known as borehole breakout. The azimuths of the long axes of 138 discrete breakouts identified in nine different wells in the Barrow-Dampier show a consistent 010°−030°N trend implying that maximum horizontal compressive stress is oriented 100°−12G°N. The orientation of horizontal stress determined in this study (and that from the Timor Sea area which is rotated some 50°−60° with respect to the Barrow-Dampier) is consistent with that derived from theoretical modelling of the stress within the Indo-Australian plate based on the plate tectonic forces acting on its boundaries. The rotation of the horizontal stress orientations along the North West Shelf, between the Barrow-Dampier and the Timor Sea, is a reflection of the present-day complex plate convergence system at the north-eastern boundary of the Indo-Australian Plate. Vertical stress magnitudes, Sv, in the Barrow-Dampier were determined from density and sonic log data. Minimum and maximum horizontal stress magnitudes, Shmin and Shmax, were determined from mini-hydraulic fracture (or modified leak-off) test results. These data suggest that the fault condition of the Wanaea/Cossack area is on the boundary between normal faulting (extension) and strike-slip, i.e. Sv ≈ Shmax > Shmin. However, in other parts of the Barrow-Dampier the evidence suggests a strike-slip fault condition, i.e. Shmax > Sv > Shmin. Given the orientation of the stress field and the fault condition, inferences can be drawn regarding the stability of horizontal wells. Furthermore, experience from vertical wells can be utilized to determine the upper and lower bounds to the mud-weight envelope as functions of deviation and wellbore orientation. Since a horizontal well will see Sv and a horizontal stress, stress anisotropy around a wellbore in the Wanaea/Cossack area (and hence wellbore instability) will be minimized by drilling in the Shmin direction i.e. 010°–030°N.

Use of J-integral as fracture parameter in simplified analysis of bonded joints

Abstract: The simplified analytical approaches based on beam or plates theories are commonly used to solve the stress field in bonded laminates. However, to be correctly applied, these methods require an appropriate fracture criterion. In this paper, the use of J-integral as a fracture parameter in these simplified analytical approaches is discussed. After examining its path independence, the J-integral is calculated along two particular paths showing first that this integral is equal to the product of the strain energy at the end of the joint (i.e. at the debond tip) by its thickness. This relationship reveals the partitioning of the opening mode I and the shearing mode II. Secondly, the general expression of J as a function of the loading conditions is derived. It is shown that this parameter can be related to the strain energy release rate in the cases of small scale yielding conditions and for usual fracture mechanics specimens.

State of stress in the Long Valley caldera, California

Abstract: Earthquake focal-plane mechanisms and well-bore breakouts in the Long Valley caldera, California, indicate that the resurgent dome and caldera south moat are characterized by a northeast extensional stress field, consistent with geodetically determined extensional strain within the caldera. Similar data from the western caldera indicate that it is characterized by a markedly different, northwest-trending, extensional stress field. We hypothesize that this localized rotation of the stress field is possible because of near-lithostatic pore pressure at depth. Because an east-west extensional stress field appears to have existed in the western caldera at the time of emplacement of the Inyo volcanic deposits (500-1000 yr ago), the state of stress in the Long Valley caldera appears to be both spatially and temporally heterogeneous, most likely as a consequence of intracaldera processes related to magmatic resurgence.

Lithospheric stresses associated with nontransform offsets of the Mid-Atlantic Ridge: Implications from a finite element analysis

Abstract: Nontransform offsets are a fundamental aspect of the offset geometry exhibited along the mid-oceanic ridge system, independent of spreading rate. Along the slow/intermediate opening (<40 mm/y full rate) Mid-Atlantic Ridge these offsets of the ridge axis range in length from less than 10 km to approximately 30 km and vary in age offset from 0.5 to 2.0 m.y. The variable morphotectonic geometries associated with these discontinuities indicate that horizontal shear strains are accommodated by both extensional and strike-slip tectonism and that the geometries are unstable in time. In many cases, there appears to be an evolutionary relationship between transform fault boundaries and nontransform offsets as the result of prolonged differential asymmetric spreading between adjoining ridge segments. The finite element method is used to study the complex stress field associated with these small-offset discontinuities of ridges with slow (30 mm/y) and fast (100 mm/y) total opening rates. A plane stress plate model examines the variation in the horizontal tectonic stress field produced by offsets with different lengths and changes in the ratio of a ridge-normal tensile stress resisting plate separation to a shear stress resisting relative plate motion along the discontinuity. The predicted fault patterns based on the calculated stress field are compared with seafloor observations in terms of the morphotectonic patterns and evolution of nontransform offsets. For a slow spreading rate, the analysis shows that all structural geometries observed can be modeled by a range of offset lengths (5, 10, 20, 30, and 40 km) and by a ridge-normal stress 3 to 5 times greater than the discontinuity shear stress. These findings suggest that nontransform offsets are zones of mechanical weakness relative to the surrounding lithosphere. An offset length between 10 and 20 km is predicted to be the threshold length for maintaining a transform fault geometry. As inferred from ridge axis morphology, there seems to be a strong link between the magnitude of the stress ratio and the time varying magmatic activity along and between ridge segments. While our models are consistent with a weak discontinuity shear stress relative to the ridge-normal stress to explain the geometries of nontransform offsets of slow-spreading centers, a weaker ridge-normal stress to discontinuity shear stress most closely models the development of an overlapping spreading center geometry, the distinctive geometry of nontransform offsets of spreading centers opening at fast rates. This difference is attributed to magma supply along-axis, relatively continuous for fast-spreading centers and intermittent for slow-spreading centers, and a preexisting zone of mechanical weakness linked to the evolution of nontransform offsets from transform faults on slow-spreading centers.