Showing papers on "Stress field published in 2002"

The ball on three balls test for strength testing of brittle discs: stress distribution in the disc

Abstract: Biaxial strength testing of brittle materials is claimed to have some benefits compared to uniaxial testing, e.g. the much simpler specimen preparation, the avoiding of tensile loaded edges, the similarity of the stress state to those from typical loading (e.g. during a thermal shock loading) and the fact, that biaxial stress states are more revealing of defects than uniaxial stress states. The experience of the past showed, that biaxial strength testing has its own problems, to avoid these led to the development of several variants. One of these variants, the ball on three balls test, seems to be extremely simple: a disc is supported by three balls and then axially loaded from the opposite side via a fourth ball. In this system small deviations from the requested geometry, especially some out of flatness of the disc, are mentioned to be tolerable, but the threefold bending symmetry makes an exact analytical assessment of the stress state in the loaded disc extremely difficult. A numerical approach has yet not been performed. In this paper a FE analysis of the stress state in a ball on three balls tested disc is performed. The stress field scales with the maximum principle stress, which occurs in the centre of the tensile surface. For this stress an analytical approximation (which has been fitted to the numerical results) is given, which accounts for the influence of all relevant geometrical and material parameters. The investigated range of parameters considers the values typical for testing of brittle materials.

Principles of Fracture Mechanics

Abstract: Most chapters include an Introduction, Summary, References and Exercises. 1. Introduction to Fracture Mechanics. Historical Overview of Brittle Fracture. Elementary Brittle-Fracture Theories. Crack Extension Behavior. 2. Elements of Solid Mechanics. Concepts of Stress and Strain. Equations of Elasticity in Cartesian Coordinates. Equations of Elasticity in Polar Coordinates. Solution of the Biharmonic Equation. The Problem of the Elliptical Hole. 3. Elasticity of Singular Stress Fields. Overview. The Williams Problems. The Generalized Westergaard Approach. The Central Crack Problem. Single-Ended Crack Problems. The Effect of Finite Boundaries. Determining the Geometric Stress Intensity Factor. The Three-Dimensional Crack Problem. 4. Numerical Methods for K Determination. Boundary Collocation. The Finite Element Method. 5. Experimental Methods for K Determination. Overview. Classical Photoelesatic Methods. The Method of Caustics. Strain Gages. Multi-Parameter Full-Field Methods: Local Collocation. Interference Patterns. Moire Patterns. Photoelasticity. 6. A Stress Field Theory of Fracture. The Critical Stress-State Criterion. Crack-Tip Plasticity. The Effect of Variables on Fracture Toughness. R-Curves. 7. The Energy of Fracture. Griffith's Theory of Brittle Fracture. A Unified Theory of Fracture. Compliance. 8. Fracture Toughness Testing. Fracture Toughness Standards. Nonstandard Fracture-Toughness Tests. 9. Fatigue. Stages of Fatigue Crack Growth. Mathematical Analysis of Stage II Crack Growth. The Effects of Residual Stress on Crack Growth Rates. Life Prediction Computer Programs. Measuring Fatigue Properties: ASTM. 10. Designing against Fracture. Fracture Mechanics in Conventional Design. The Role of NDE in Design. U.S. Air Force Damage-tolerant Design Methodology. Designing by Hindsight: Case Studies. 11. Elastoplastic Fracture. Nonlinear Elastic Behavior. Characterizing Elastoplastic Behavior. Comments on the J-Integral in Elastoplastic Fracture Mechanics. Appendix A: Comprehensive Exercises. General Comments. Appendix B: Complex Variable Method in Elasticity. Complex Numbers. Complex Functions. Appendix C: An Abbreviated Compendium of Westergaard Stress Functions. Appendix D: Fracture Properties of Engineering Materials. Appendix E: NASGRO 3.0 Material Constants for Selected Materials. Index.

Stress field in granular systems: loop forces and potential formulation.

Abstract: The transmission of stress through a marginally stable granular pile in two dimensions is exactly formulated in terms of a vector field of loop forces, and thence in terms of a single scalar potential. This leads to a local constitutive equation coupling the stress tensor to fluctuations in the local geometry. For a disordered pile of rough grains this means the stress tensor components are coupled in a frustrated manner. In piles of rough grains with long range staggered order, frustration is avoided and a simple linear theory follows. We show that piles of smooth grains can be mapped onto a pile of unfrustrated rough grains, indicating that the problems of rough and smooth grains may be fundamentally distinct.

Tectonic forces controlling the regional intraplate stress field in continental Australia: Results from new finite element modeling

Abstract: [1] The tectonic forces controlling the present-day regional intraplate stress field in continental Australia have been evaluated through a finite element analysis of the intraplate stresses in the Indo-Australian plate (IAP). Constraint for the modeling is provided by an observed regional stress field based on observations in 12 stress provinces. A weighted “basis set” method has been employed to provide an efficient means to evaluate a very large number of tectonic force combinations and to make a quantitative assessment of the fit between the observed and predicted stress fields. Our modeling results indicate that the major features of the regional stress field in continental Australia can be explained in terms of a geologically plausible array of tectonic forces. While the results continue to substantiate that modeling of the Australian intraplate stress field is inherently nonunique, we are nevertheless able to draw a number of fundamental conclusions about the tectonic settings along the principal plate boundary segments including the following: (1) The Himalayan and New Guinea boundaries exert a compressional force on the IAP. (2) Fitting the stress field in the Bowen Basin requires compressional boundary forces along the Solomon and New Hebrides subduction zones directed toward the interior of the IAP. (3) East-west compression in eastern Australia requires a small compressional force along the Tonga-Kermadec subduction zone. (4) Fitting the stress field in southeastern Australia requires compressional forces along the New Zealand, Puysegur Trench, and Macquarie Ridge boundary segments. (5) Significant tensional slab-pull forces exist only along the Java subduction zone.

Analog experiments on magma-filled cracks: Competition between external stresses and internal pressure

Abstract: We have performed two series of analog experiments using gelatin to study the propagation of liquid-filled cracks in stressed medium. The first series was designed to study the competition between the external stress and the liquid excess pressure in controlling the propagation direction. We systematically controlled the external stress and the liquid excess pressure by changing the surface load and the liquid volume. An ascending crack progressively deflected to be perpendicular to the maximum tensile direction of the external stress. The degree of deflection depends on the ratio of the shear stress on a crack plane to the average liquid excess pressure. More deflection was observed for a crack with a larger ratio. No significant deflection was observed for the ratio less than 0.2. The volcanic activity in a compressional stress field might be understood in the context of this competition. The first series also demonstrated the importance of the gradient of the crack normal stress as a driving force for propagation. The vertical gradient of the gravitational stress generated by a mountain load can control the emplacement depth of magmas, and it might lead to the evolution of eruption style during the lifetime of a volcano. The second series was designed to study the three-dimensional interaction of two parallel buoyancy-driven cracks. The deflection of the second crack takes place, when the ratio of the shear stress generated by the first one to the average excess pressure of the second crack is larger than 0.2. If the second crack reaches the first one, the interaction can lead to the coalescence of two cracks. It has directivity: the region of coalescence extends more in the direction perpendicular to the first crack than in the direction parallel to it. It reflects the stress field around the first crack. This directivity might cause a characteristic spatial variation of magma chemistry through magma mixing.

Geometric formulation of quantum stress fields

Abstract: We present a derivation of the stress field for an interacting quantum system within the framework of local-density-functional theory. The formulation is geometric in nature, and exploits the relationship between the strain tensor field and Riemannian metric tensor field. Within this formulation, we demonstrate that the stress field is unique up to a single ambiguous parameter. The ambiguity is due to the nonunique dependence of the kinetic energy on the metric tensor. To illustrate this formalism, we compute the pressure field for two phases of solid molecular hydrogen. Furthermore, we demonstrate that qualitative results obtained by interpreting the hydrogen pressure field are not influenced by the presence of the kinetic ambiguity.

Spatial heterogeneity of tectonic stress and friction in the crust

Abstract: The complex geometry of faults, seismicity, and diversity of earthquake mechanisms suggest that the stress and strength in Earth's crust are spatially heterogeneous. We investigated the degree of heterogeneity using the following two end-member models. In one end-member model, we assumed that the orientation of stress is uniform in the crust as is assumed in many stress inversion studies. In this model, the variability of earthquake mechanisms means that friction during faulting must vary for each event. We computed friction μ from the ratio of the resolved shear stress to the effective normal stress on the fault plane with the assumption of hydrostatic pore pressure. The values of μ vary over a large range from 0 to 1.5. In the other extreme model we assumed optimally oriented slip and a constant μ = 0.6, as is suggested by Byerlee's law, for all the earthquakes, and determined the local stress orientation for each earthquake. The orientation of the stress changes drastically from one earthquake to another, and the assumption of uniform stress field commonly used in stress inversion is not warranted. An important conclusion is that a regionally uniform stress field and constant friction on optimally oriented faults are mutually exclusive. The actual situation in the crust is most likely to be intermediate between these two end-member models. From the existing data alone, we cannot determine the degree of heterogeneity uniquely, but both μ and the local stress field near earthquake faults are likely to vary substantially, and studies on earthquake rupture dynamics must take these heterogeneities into consideration.

An elastoplastic theory of dislocations as a physical field theory with torsion

Abstract: We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastic material as a T(3) gauge theory. We obtain Yang-Mills-type field equations which express the force and the moment equilibrium. Additionally, we discuss several constitutive laws between the dislocation density and the moment stress. For a straight screw dislocation, we find the stress field which is modified near the dislocation core due to the appearance of moment stress. For the first time, we calculate the localized moment stress, the Nye tensor, the elastoplastic energy and the modified Peach-Koehler force of a screw dislocation in this framework. Moreover, we discuss the straightforward analogy between a screw dislocation and a magnetic vortex. The dislocation theory in solids is also considered as a three-dimensional effective theory of gravity.

Fault reactivation, leakage potential, and hydrocarbon column heights in the northern north sea

Abstract: To investigate the question of how faults affect the migration of fluids in petroleum reservoirs, we evaluated the state of stress and pore pressure acting on the major faults in four oil and gas fields in the northern North Sea. Many of the faults bound hydrocarbon reservoirs. Our goal was to test the hypothesis that faults that are being reactivated in the current stress field are permeable and thus tend to leak, whereas those that are not (i.e. faults that are inactive in the current stress field) are likely to seal. To address this question, we utilize a detailed analysis of the magnitude and orientation of all three principal stresses in a number of wells in each field. These data, along with information on pore pressure, allowed us to resolve the shear and effective normal stress acting on distinct 100 m × 100 m elements of individual fault planes. By comparing the stress state resolved on each fault element to expected stress at failure (using a Coulomb failure criterion) we created color-shaded maps showing the proximity to fault slip (and hence leakage) along each fault. Fault reactivation and hydrocarbon leakage in this area appears to be caused by three factors: (1) locally elevated pore pressure due to buoyant hydrocarbons in reservoirs abutting the faults, (2) fault orientations that are nearly optimally oriented for frictional slip in the present-day stress field, and (3) a relatively recent perturbation of the compressional stress caused by postglacial rebound. We demonstrate that the combination of these three factors may have recently induced fault slippage and gas leakage along sections of previously sealing reservoir-bounding faults in some fields, whereas in others, the stress and pore pressure are not sufficient to cause fault reactivation. We show that only in cases where reservoir-bounding faults are not potentially active, the pore-pressure difference across faults can become quite high. Hence, the leakage potential of reservoir-bounding faults appears to exert an important influence on potential hydrocarbon column heights.

A finite element study of the stress and strain fields of InAs quantum dots embedded in GaAs

Abstract: We report on a stress and strain analysis, using the finite element method, of the heterosystem of InAs quantum dots embedded in GaAs. The methodology of using the finite element method to simulate the lattice mismatch is discussed and a three-dimensional (3D) model of the heterostructure shows the 3D stress distribution in the InAs islands embedded in a matrix of GaAs substrate and cap layer. The initial shape of the InAs islands is pyramidal. The stress and strain distribution calculated corresponds well with the strain induced by the lattice mismatch. Factors such as the height of the spacer layer and the height of the island are found to play an important role in the stress and strain distribution. With the island having the shape of a truncated pyramid, the stress and strain distribution deviates from that of a full pyramidal island showing the effects that a change of shape in the islands has on the stress field. The stress distribution contributes to the driving force for the mechanism of surface diffusion in molecular beam epitaxy. The effects of anisotropy on the strain distribution are also studied.

Asymptotic Stress Fields for Stationary Cracks Along the Gradient in Functionally Graded Materials

Abstract: Stress field for stationary cracks, aligned along the gradient, in functionally graded materials is obtained through an asymptotic analysis coupled with Westergaard's stress function approach. The first six terms of the stress field are obtained for both opening mode and shear mode loading. It is observed that the structure of the terms other than r?1/2 and r0 are influenced by the nonhomogeneity. Using this stress field, contours of constant maximum shear stress are generated and the effect of nonhomogeneity on these contours is discussed. ©2002 ASME

A study of viscoelastic free surface flows by the finite element method: Hele–Shaw and slot coating flows

Abstract: A pseudo-solid domain mapping technique coupled with the DEVSS finite element formulation is applied to study the effects of viscoelasticity on free surface flows Two distinct flow types are analyzed: the flow induced by a long air bubble steadily displacing a polymeric liquid confined by two parallel plates, ie Hele–Shaw flow, and the slot coating of viscoelastic fluids in the low metering rate limit The Oldroyd-B, FENE-CR, and FENE-P constitutive equations are used to model the viscoelastic fluid Our study reveals the formation of an elastic boundary layer in the capillary-transition region near the bubble front at moderate Weissenberg numbers while the stress field in the parallel flow region remains largely unaffected by the dynamics of the free surface Our calculations show that the increase in the hydrodynamic coating thickness due to viscoelasticity often reported in planar injection experiments [Physica A 220 (1995) 60; J Non-Newtonian Fluid Mech 71 (1997) 73] is associated with the onset of these elastic boundary layers and is strongly dependent on the physical properties of the coating fluid

New Constraints on Tectonics of Interior Alaska: Earthquake Locations, Source Mechanisms, and Stress Regime

Abstract: We used the joint hypocenter determination (JHD) method to relocate 3611 crustal earthquakes that occurred from 1988 to 1999 in central Alaska. The new earthquake locations provide more details on the structure of the Kantishna cluster and better locations for the aftershock sequence of the 29 November 2000 M L 5.6 earthquake in the Minto Flats seismic zone. The JHD locations for the aftershocks of the 1995 M W 6.0 Minto Flats earthquake and 22 October 1996 M W 5.8 earthquake near the Denali fault are also available. A catalog of 196 fault-plane solutions consisting of the moment tensor solutions for the earthquakes with magnitude 4.0 or above and P -wave first-motion solutions for the earthquakes with magnitude 3.4 and above that occurred from 1988 to 2000 was composed. Moment tensor solutions were calculated using regional broadband data. This catalog was used to calculate principal stress orientations in the crust. The stress orientations change across central Alaska. In particular, the maximum principal stress orientation rotates clockwise from SE-NW to SSW-NNE direction as one moves from west to east. These stress orientations are consistent with the stress field transferred from the plate convergence in southern Alaska. In addition, we tested different velocity structures in the moment tensor inversion procedure to identify velocity models for calculating the Green's functions. The moment tensor inversion study shows that it is possible to obtain a reliable moment tensor solution for moderate-sized earthquakes ( M L ≥ 4) using three-component records from a single broadband station when the epicentral distances are between 50 and 300 km. Manuscript received 8 June 2001.

Application of bimaterial interface corner failure mechanics to silicon/glass anodic bonds

Abstract: Motivated by the existence of a universal singular stress field at bimaterial interface corners, a fair amount of work has been performed to support the use of the corresponding critical stress intensities to correlate fracture initiation. The approach is in the spirit of interface fracture mechanics but applicable to a different class of problems, specifically, when a crack does not previously exist (or cannot be detected, at least economically), and when subsequent crack propagation does not necessarily occur along the interface. Here we further progress toward the development, understanding, and application of the approach, both experimentally and theoretically, for a series of silicon/glass anodically bonded structures. To this end we designed and fabricated two series of silicon/glass anodically bonded bimaterial specimens with different interface corner geometries that commonly arise from different silicon etching technologies. Offset three-point flexure tests were performed that resulted in brittle fracture that initiated at the interface corner. From a rigorous stress analysis at the interface corner, we determined the order of the stress singularities and the angular variation of the stress fields. We computed the corresponding stress intensities via full-field finite element analyses of the silicon/glass specimens loaded in offset three-point flexure. Measured fracture data show that although the failure stress varies significantly with bond size, the corresponding critical stress intensity of the dominant mode is constant, thus providing support for its use as a fracture initiation criterion. In the light of both the stress analysis and the measured fracture data, we discuss the effect of mode mixity (loosely shearing versus opening) and show that it has little influence on the results for the specimens and loading considered in this study. Via an idealized model of a small crack, either interfacial or extending into one of the adherends, we study the effects of geometrical perturbations at the interface corner on the stress state, and discuss implications for fracture analysis and interpretation of fracture data. We also explore the prediction of the crack initiation angle and achieve reasonable success with a simple criterion based on the maximum circumferential stress near the uncracked interface corner.

Stress direction history of the western United States and Mexico since 85 Ma

Abstract: [1] A data set of 369 paleostress direction indicators (sets of dikes, veins, or fault slip vectors) is collected from previous compilations and the geologic literature. Like contemporary data, these stress directions show great variability, even over short distances. Therefore statistical methods are helpful in deciding which apparent variations in space or in time are significant. First, the interpolation technique of Bird and Li [1996] is used to interpolate stress directions to a grid of evenly spaced points in each of seventeen 5-m.y. time steps since 85 Ma. Then, a t test is used to search for stress direction changes between pairs of time windows whose sense can be determined with some minimum confidence. Available data cannot resolve local stress provinces, and only the broadest changes affecting country-sized regions are reasonably certain. During 85–50 Ma, the most compressive horizontal stress azimuth 1H was fairly constant at ∼68° (United States) to 75° (Mexico). During 50–35 Ma, both counterclockwise stress changes (in the Pacific Northwest) and clockwise stress changes (from Nevada to New Mexico) are seen, but only locally and with about 50% confidence. A major stress azimuth change by ∼90° occurred at 33 ± 2 Ma in Mexico and at 30 ± 2 Ma in the western United States. This was probably an interchange between 1 and 3 caused by a decrease in horizontal compression and/or an increase in vertical compression. The most likely cause was the rollback of horizontally subducting Farallon slab from under the southwestern United States and northwest Mexico, which was rapid during 35–25 Ma. After this transition, a clockwise rotation of principal stress axes by 36°–48° occurred more gradually since 22 Ma, affecting the region between latitudes 28°N and 41°N. This occurred as the lengthening Pacific/North America transform boundary gradually added dextral shear on northwest striking planes to the previous stress field of SW-NE extension.