Showing papers on "Stress field published in 2012"

Elastic sheet on a liquid drop reveals wrinkling and crumpling as distinct symmetry-breaking instabilities.

Abstract: Smooth wrinkles and sharply crumpled regions are familiar motifs in biological or synthetic sheets, such as rapidly growing plant leaves and crushed foils. Previous studies have addressed both morphological types, but the generic route whereby a featureless sheet develops a complex shape remains elusive. Here we show that this route proceeds through an unusual sequence of distinct symmetry-breaking instabilities. The object of our study is an ultrathin circular sheet stretched over a liquid drop. As the curvature is gradually increased, the surface tension stretching the sheet over the drop causes compression along circles of latitude. The compression is relieved first by a transition into a wrinkle pattern, and then into a crumpled state via a continuous transition. Our data provide conclusive evidence that wrinkle patterns in highly bendable sheets are not described by classical buckling methods, but rather by a theory which assumes that wrinkles completely relax the compressive stress. With this understanding we recognize the observed sequence of transitions as distinct symmetry breakings of the shape and the stress field. The axial symmetry of the shape is broken upon wrinkling but the underlying stress field preserves this symmetry. Thus, the wrinkle-to-crumple transition marks symmetry-breaking of the stress in highly bendable sheets. By contrast, other instabilities of sheets, such as blistering and cracking, break the homogeneity of shape and stress simultaneously. The onset of crumpling occurs when the wrinkle pattern grows to half the sheet’s radius, suggesting a geometric, material-independent origin for this transition.

Photoelasticity of Glass

Abstract: One The Basics of Photoelasticity and Glass.- 1 Basic Elasticity.- 1.1 Elasticity.- 1.2 Force and Stress.- 1.3 Plane Stress.- 1.4 Equations of Equilibrium.- 1.5 Boundary Conditions.- 1.6 Strain.- 1.7 Relations Between Stresses and Strains.- 1.8 Plane Strain.- 1.9 Equations of Compatibility.- 1.10 Stress Function.- 2 Residual Stresses in Glass.- 2.1 Introduction.- 2.2 Dependence of the Mechanical Strength on Residual Stresses.- 2.3 Stresses Due to Indentations.- 2.4 Residual Stresses Due to Thermal Annealing or Tempering.- 2.4.1 The First Approaches.- 2.4.2 The Viscoelastic Theory.- 2.4.3 The Structural Theory.- 2.4.4 Membrane Stresses and Form Stresses.- 2.4.5 Stress Redistribution by Cutting.- 2.5 Stresses Due to Chemical Tempering.- 2.5.1 Stress Buildup.- 2.5.2 Strengthening of Glass.- 2.6 Stresses Created in Glass by Radiations.- 2.6.1 Corpuscular Radiation.- 2.6.2 Electromagnetic Radiation.- Thermal Effects.- Color Centers.- 2.7 Stresses Due to Heterogeneities.- 2.8 Stresses in Composite Glass Articles.- 2.8.1 Stresses in Glazes and Enamels.- 2.8.2 Stresses in Optical Fibers.- 2.8.3 Stresses in Glass-Metal and Glass-Ceramic Seals.- 2.8.4 Stresses Due to Inclusions.- 3 Basic Photoelasticity.- 3.1 Polarized Light.- 3.1.1 Nature of Light.- 3.1.2 Natural and Polarized Light.- 3.1.3 Different Descriptions of Polarized Light.- 3.2 Artificial Double Refraction.- 3.3 Stress-Optic Law.- 3.4 The Plane Polariscope.- 3.5 The Circular Polariscope.- 3.6 Use of Double-Exposure Photography for the Elimination of the Isoclinics.- 3.7 Construction of Polariscopes.- 3.8 Measurement of Optical Retardation.- 3.8.1 Color Matching.- 3.8.2 Polariscope with a Tint Plate.- 3.8.3 The Babinet and Babinet-Soleil Compensators.- 3.8.4 Senarmont Method.- 3.8.5 The Azimuth Method.- 4 Two-Dimensional Photoelasticity.- 4.1 General.- 4.2 Stress Trajectories.- 4.3 Separation of Principal Stresses.- 4.3.1 Oblique Incidence Method.- 4.3.2 Shear Difference Method.- 4.3.3 Numerical Solution of the Compatibility Equation.- 4.3.4 Methods Based on Hooke's Law.- 4.4 Superposition of States of Stress.- 4.5 Determination of the Photoelastic Constant.- 5 The Scattered Light Method.- 5.1 Introduction.- 5.2 Scattering of Light.- 5.3 The Scattered Light Method with Polarized Incident Light.- 5.4 The Scattered Light Method with Unpolarized Incident Light.- 5.5 Using Interference of Coherent Scattered Light Beams.- 6 Integrated Photoelasticity.- 6.1 Introduction.- 6.2 Principle of Integrated Photoelasticity.- 6.3 Basic Equations.- 6.4 Theory of Characteristic Directions.- 6.5 Symmetric Photoelastic Media.- 6.6 The Case of Constant Principal Stress Axes.- 6.7 The Case of Weak Birefringence.- 6.8 Integrated Photoelasticity as Optical Tomography of the Stress Field.- 6.9 Investigation of the General Three-Dimensional State of Stress.- 6.10 Axisymmetric State of Stress Due to External Loads.- 7 Photoelastic Properties of Glass.- 7.1 Introduction.- 7.2 Discovery of the Photoelastic Effect in Glass.- 7.3 Influence of the Glass Composition.- 7.4 Theories of the Photoelastic Effect.- 7.5 Influence of the Temperature and of the Thermal History.- 7.6 Dependence of the Photoelastic Constant on Wavelength.- 7.7 Anomalous Birefringence.- Two Stress Analysis in Flat Glass.- 8 Thickness Stresses.- 8.1 Different Kinds of Thickness Stresses.- 8.2 Measurement of Thickness Stresses.- 8.2.1 Using the Bending of the Light Rays.- 8.2.2 Conventional Photoelasticity.- 9 Membrane Stresses.- 9.1 Introduction.- 9.2 Uniaxial Membrane Stresses.- 9.2.1 Edge Stresses.- 9.2.2 Stresses Across a Ribbon.- 9.3 Bidimensional Membrane Stresses.- 10 Determination of the Total Stresses.- 10.1 Introduction.- 10.2 The Measurement of Surface Stresses.- 10.2.1 Differential Refractometry.- 10.2.2 The "Mirage" Methods.- Observation of the Guided Waves Close to the Surface.- The Case of Flat Samples.- The Case of Curved Samples.- The Case of Stress Gradient Near the Surface.- Observation of the Guided Waves at Infinity.- Theory of the Differential Refractometry with Guided Waves.- Linear Index Profile.- Determination of Stresses.- An Example.- Alternative Numerical Methods.- Curved Surface.- Thermally Tempered Glass.- 10.3 Measurement of Total Residual Stresses.- 10.3.1 The Scattered Light Method.- Spatial Modulation Method.- Phase Modulation Method.- 10.3.2 Magnetophotoelasticity.- Three Stresses in Glass Articles of Complicated Shape.- 11 Axisymmetric Glass Articles.- 11.1 General Case of Axisymmetric Residual Stress Distribution.- 11.1.1 Peculiarities of the Determination of the Residual Stress.- 11.1.2 Determination of the Axial and Shear Stress Distributions.- 11.1.3 Additional Tomographic Measurements.- 11.2 Application of the Equilibrium and Boundary Conditions.- 11.3 Stresses on the External Surface.- 11.4 Average Value of the Circumferential Stress.- 11.5 Stresses in Long Cylinders.- 11.6 Spherical Symmetry.- 11.6.1 Stress Distribution in Spheres.- 11.6.2 Quenching Stresses Around a Spherical Inclusion.- 11.7 Bending of Light Rays.- 11.8 Determination of the Components of the Dielectric Tensor.- 11.9 Optimization of the Number of Terms in Stress Polynomials.- 11.10 Experimental Technique.- 11.10.1 Polariscopes.- 11.10.2 Immersion Technique.- 11.10.3 The Case of Mismatching Immersion.- 11.11 Examples.- 11.11.1 Quenched Long Cylinder.- 11.11.2 An Article of Optical Glass.- 11.11.3 High Voltage Insulator.- 11.11.4 Closed Tube.- 11.11.5 Two Bonded Tubes.- 12 Containers and Other Thin-Walled Glassware.- 12.1 Introduction.- 12.2 Traditional Methods.- 12.3 Determination of Stress in Cylindrical Part of the Container.- 12.4 Axial Stress in an Arbitrary Section.- 12.5 Determination of the Stresses Due to the Internal Pressure.- 12.6 Sandwich Glassware.- 12.7 Examples.- 12.7.1 A Champagne Bottle.- 12.7.2 A Beer Bottle.- 12.7.3 Tumbler N 1.- 12.7.4 Tumbler N 2.- 12.7.5 Salad Bowl.- 12.7.6 Electric Lamp.- 12.7.7 Ampule of a Fire Extinguisher System.- 13 Optical Fibers and Fiber Preforms.- 13.1 Introduction.- 13.2 Axisymmetric Fibers and Fiber Preforms.- 13.2.1 Refractive Index Profiles.- 13.2.2 Determination of the Stress Distribution.- 13.2.3 Application of the Method of Oblique Incidence.- 13.2.4 Examples.- 13.3 Fiber Preforms of Arbitrary Cross Section.- 13.3.1 Determination of the Axial Stress Distribution.- 13.3.2 Determination of Other Stress Components.- 13.3.3 Internal Rotation of the Birefringence Axes in Polarization-Holding Fibers.- 13.3.4 Examples.- Author Index.

Numerical Simulation of 3D Hydraulic Fracturing Based on an Improved Flow-Stress-Damage Model and a Parallel FEM Technique

Abstract: The failure mechanism of hydraulic fractures in heterogeneous geological materials is an important topic in mining and petroleum engineering. A three-dimensional (3D) finite element model that considers the coupled effects of seepage, damage, and the stress field is introduced. This model is based on a previously developed two-dimensional (2D) version of the model (RFPA2D-Rock Failure Process Analysis). The RFPA3D-Parallel model is developed using a parallel finite element method with a message-passing interface library. The constitutive law of this model considers strength and stiffness degradation, stress-dependent permeability for the pre-peak stage, and deformation-dependent permeability for the post-peak stage. Using this model, 3D modelling of progressive failure and associated fluid flow in rock are conducted and used to investigate the hydro-mechanical response of rock samples at laboratory scale. The responses investigated are the axial stress–axial strain together with permeability evolution and fracture patterns at various stages of loading. Then, the hydraulic fracturing process inside a rock specimen is numerically simulated. Three coupled processes are considered: (1) mechanical deformation of the solid medium induced by the fluid pressure acting on the fracture surfaces and the rock skeleton, (2) fluid flow within the fracture, and (3) propagation of the fracture. The numerically simulated results show that the fractures from a vertical wellbore propagate in the maximum principal stress direction without branching, turning, and twisting in the case of a large difference in the magnitude of the far-field stresses. Otherwise, the fracture initiates in a non-preferred direction and plane then turns and twists during propagation to become aligned with the preferred direction and plane. This pattern of fracturing is common when the rock formation contains multiple layers with different material properties. In addition, local heterogeneity of the rock matrix and macro-scale stress fluctuations due to the variability of material properties can cause the branching, turning, and twisting of fractures.

Stress before and after the 2011 great Tohoku‐oki earthquake and induced earthquakes in inland areas of eastern Japan

Abstract: [1] Stress fields in inland areas of eastern Japan before and after the Tohoku-oki earthquake were estimated by inverting focal mechanism data. Before the earthquake, s1 axis was oriented EW in Tohoku but NW-SE in Kanto-Chubu. The stress fields changed after the earthquake in northern Tohoku and in southeastern Tohoku near Iwaki city, where the orientations of the principal stresses became approximately the same as the orientations of the static stress change associated with the earthquake. This indicates that differential stress magnitudes in these areas before the earthquake were smaller than 1 MPa. The stress field did not change in central Tohoku, even though the stresses loaded after the earthquake had nearly reversed orientations, which indicates that the differential stress magnitudes there were significantly larger than 1 MPa. In Kanto-Chubu, stresses having nearly the same orientations as the background stresses were loaded after the earthquake, and the stress fields did not change as expected. This may have caused very high induced seismicities in Kanto-Chubu. Citation: Yoshida, K., A. Hasegawa, T. Okada, T. Iinuma, Y. Ito, and Y. Asano (2012), Stress before and after the 2011 great Tohoku-oki earthquake and induced earthquakes in inland areas of eastern Japan, Geophys. Res. Lett., 39, L03302,

The Italian present-day stress map

Abstract: SUMMARY In this paper, we present a significant update of the Italian present-day stress data compilation not only to improve the knowledge on the tectonic setting of the region or to constrain future geodynamic models, but also to understand the mechanics of processes linked to faulting and earthquakes. In this paper, we have analysed, revised and collected new contemporary stress data from borehole breakouts and we have assembled earthquake and fault data. In total, 206 new quality-ranked entries complete the definition of the horizontal stress orientation and tectonic regime in some areas, and bring new information mainly in Sicily and along the Apenninic belt. Now the global Italian data set consists of 715 data points, including 499 of A–Cquality,representinganincreaseof37percentcomparedtothepreviouscompilation.The alignment of horizontal stresses measured in some regions, closely matches the ∼N–S firstorder stress field orientation of ongoing relative crustal motions between Eurasia and Africa plates. The Apenninic belt shows a diffuse extensional stress regime indicating a ∼NE–SW direction of extension, that we interpret as related to a second-order stress field. The horizontal stress rotations observed in peculiar areas reflect a complex interaction between first-order stress field and local effects revealing the importance of the tectonic structure orientations. In particular, in Sicily the new data delineate a more complete tectonic picture evidencing adjacent areas characterized by distinct stress regime: northern offshore of Sicily and in the Hyblean plateau the alignment of horizontal stresses is consistent with the crustal motions, whereas different directions have been observed along the belt and foredeep.

Acoustoelastic Lamb wave propagation in biaxially stressed plates

Abstract: Acoustoelasticity, or the change in elastic wave speeds with stress, is a well-studied phenomenon for bulk waves. The effect of stress on Lamb waves is not as well understood, although it is clear that anisotropic stresses will produce anisotropy in the Lamb wave dispersion curves. Here the theory of acoustoelastic Lamb wave propagation is developed for isotropic media subjected to a biaxial, homogeneous stress field. It is shown that, as expected, dispersion curves change anisotropically for most stresses, modes, and frequencies. Interestingly, for some mode-frequency combinations, changes in phase velocity are isotropic even for a biaxial stress field. Theoretical predictions are compared to experimental results for several Lamb wave modes and frequencies for uniaxial loads applied to an aluminum plate, and the agreement is reasonably good.

Coseismic and postseismic stress rotations due to great subduction zone earthquakes

Abstract: [1] The three largest recent great subduction zone earthquakes (2011 M9.0 Tohoku, Japan; 2010 M8.8 Maule, Chile; and 2004 M9.2 Sumatra-Andaman) exhibit similar coseismic rotations of the principal stress axes. Prior to each mainshock, the maximum compressive stress axis was shallowly plunging, while immediately after the mainshock, both the maximum and minimum compressive stress axes plunge at ∼45°. Dipping faults can be oriented for either reverse or normal faulting in this post-mainshock stress field, depending on their dip, explaining the observed normal-faulting aftershocks without requiring a complete reversal of the stress field. The significant stress rotations imply near-complete stress drop in the mainshocks, with >80% of the pre-mainshock stress relieved in the Tohoku and Maule earthquakes and in the northern part of the Sumatra-Andaman rupture. The southern part of the Sumatra-Andaman rupture relieved ∼60% of the pre-mainshock stress. The stress axes rotated back rapidly in the months following the Tohoku and Maule mainshocks, and similarly in the southern part of the Sumatra-Andaman rupture. A rapid postseismic rotation is possible because the near-complete stress drop leaves very little “background” stress at the beginning of the postseismic reloading. In contrast, there has been little or no postseismic rotation in the northern part of the Sumatra-Andaman rupture over the 7 years since the mainshock. All M ≥8.0 subduction earthquakes since 1990 with an adequate number of pre- and post-mainshock events were evaluated, and not all show similar coseismic stress rotations. Deeper earthquakes exhibit smaller coseismic stress rotations, likely due to increasing deviatoric stress with depth.

Fault geometry, rupture dynamics and ground motion from potential earthquakes on the North Anatolian Fault under the Sea of Marmara

Abstract: SUMMARY Using the 3-D finite-element method, we develop dynamic spontaneous rupture models of earthquakes on the North Anatolian Fault system in the Sea of Marmara, Turkey, considering the geometrical complexity of the fault system in this region. We find that the earthquake size, rupture propagation pattern and ground motion all strongly depend on the interplay between the initial (static) regional pre-stress field and the dynamic stress field radiated by the propagating rupture. By testing several nucleation locations, we observe that those far from an oblique normal fault stepover segment (near Istanbul) lead to large through-going rupture on the entire fault system, whereas nucleation locations closer to the stepover segment tend to produce ruptures that die out in the stepover. However, this pattern can change drastically with only a 10° rotation of the regional stress field. Our simulations also reveal that while dynamic unclamping near fault bends can produce a new mode of supershear rupture propagation, this unclamping has a much smaller effect on the speed of the peak in slip velocity along the fault. Finally, we find that the complex fault geometry leads to a very complex and asymmetric pattern of near-fault ground motion, including greatly amplified ground motion on the insides of fault bends. The ground-motion pattern can change significantly with different hypocentres, even beyond the typical effects of directivity. The results of this study may have implications for seismic hazard in this region, for the dynamics and ground motion of geometrically complex faults, and for the interpretation of kinematic inverse rupture models.

High fluid pressure and triggered earthquakes in the enhanced geothermal system in Basel, Switzerland

Abstract: [1] We analyzed 118 well-constrained focal mechanisms to estimate the pore fluid pressure field of the stimulated region during the fluid injection experiment in Basel, Switzerland. This technique, termed focal mechanism tomography (FMT), uses the orientations of slip planes within the prevailing regional stress field as an indicator of the fluid pressure along the plane at the time of slip. The maximum value and temporal change of excess pore fluid pressures are consistent with the known history of the wellhead pressure applied at the borehole. Elevated pore fluid pressures were concentrated within 500 m of the open hole section, which are consistent with the spatiotemporal evolution of the induced microseismicity. Our results demonstrate that FMT is a robust approach, being validated at the meso-scale of the Basel stimulation experiment. We found average earthquake triggering excess pore fluid pressures of about 10 MPa above hydrostatic. Overpressured fluids induced many small events (M < 3) along faults unfavorably oriented relative to the tectonic stress pattern, while the larger events tended to occur along optimally oriented faults. This suggests that small-scale hydraulic networks, developed from the high pressure stimulation, interact to load (hydraulically isolated) high strength bridges that produce the larger events. The triggering pore fluid pressures are substantially higher than that predicted from a linear pressure diffusion process from the source boundary, and shows that the system is highly permeable along flow paths that allow fast pressure diffusion to the boundaries of the stimulated region.

Unusual shallow normal‐faulting earthquake sequence in compressional northeast Japan activated after the 2011 off the Pacific coast of Tohoku earthquake

Abstract: [1] After the occurrence of the 2011 Mw9.0 off the Pacific coast of Tohoku earthquake, an unusual shallow normal-faulting earthquake sequence occurred near the Pacific coast at the Ibaraki-Fukushima prefectural border. We have investigated why normal-faulting earthquakes were activated in northeast (NE) Japan, which is otherwise characterized by E–W compression. We computed the stress changes associated with the mainshock on the basis of a finite fault slip model, which showed that the amount of additional E–W tensional stresses in the study area was up to 1 MPa, which might be too small to generate normal-faulting earthquakes in the pre-shock compressional stress regime. We thus determined focal mechanisms of microearthquakes that occurred in the area before the mainshock, which indicated that the pre-shock stress field in the area showed a normal-faulting stress regime in contrast to the overall reverse-faulting regime in NE Japan. We concluded that the 2011 Tohoku earthquake triggered the normal-faulting earthquake sequence in a limited area in combination with a locally formed pre-shock normal-faulting stress regime. We also explored possible mechanisms for localization of a normal-faulting stress field at the Ibaraki-Fukushima prefectural border.

Acoustoelastic Lamb Wave Propagation in Biaxially Stressed Plates (Preprint)

Abstract: : Acoustoelasticity, or the change in elastic wave speeds with stress, is a well-studied phenomenon for bulk waves The effect of stress on Lamb waves is not as well understood, although it is clear that anisotropic stresses will produce anisotropy in the Lamb wave dispersion curves Here the theory of acoustoelastic Lamb wave propagation is developed for isotropic media subjected to a biaxial, homogeneous stress field It is shown that, as expected, dispersion curves change anisotropically for most stresses, modes and frequencies Interestingly, for some mode-frequency combinations, changes in phase velocity dispersion curves are isotropic even for a biaxial stress field Theoretical predictions are compared to experimental results for several Lamb wave modes and frequencies for uniaxial loads applied to an aluminum plate, and the agreement is reasonably good

Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks

Abstract: A 2-D numerical model for brittle creep and stress relaxation is proposed for the time-dependent brittle deformation of heterogeneous brittle rock under uniaxial loading conditions. The model accounts for material heterogeneity through a stochastic local failure stress field, and local material degradation using an exponential material softening law. Importantly, the model introduces the concept of a mesoscopic renormalization to capture the co-operative interaction between microcracks in the transition from distributed to localized damage. The model also describes the temporal and spatial evolution of acoustic emissions, including their size (energy released), in the medium during the progressive damage process. The model is first validated using previously published experimental data and is then used to simulate brittle creep and stress relaxation experiments. The model accurately reproduces the classic trimodal behaviour (primary, secondary and tertiary creep) seen in laboratory brittle creep (constant stress) experiments and the decelerating stress during laboratory stress relaxation (constant strain) experiments. Brittle creep simulations also show evidence of a critical level of damage before the onset of tertiary creep and the initial stages of localization can be seen as early as the start of the secondary creep phase, both of which have been previously observed in experiments. Stress relaxation simulations demonstrate that the total amount of stress relaxation increases when the level of constant axial strain increases, also corroborating with previously published experimental data. Our approach differs from previously adopted macroscopic approaches, based on constitutive laws, and microscopic approaches that focus on fracture propagation. The model shows that complex macroscopic time-dependent behaviour can be explained by the small-scale interaction of elements and material degradation. The fact that the simulations are able to capture a similar time-dependent response of heterogeneous brittle rocks to that seen in the laboratory implies that the model is appropriate to investigate the non-linear complicated time-dependent behaviour of heterogeneous brittle rocks.

The Stress Field in a Standardized Brazilian Disc: The Influence of the Loading Type Acting on the Actual Contact Length

Abstract: The aim of the present study was to determine the stress field developed in a Brazilian disc under conditions closely approaching those of the actual test executed according to the standardized procedure suggested by the International Society for Rock Mechanics. Advantage is taken of a recently introduced analytic solution for a mixed fundamental contact problem where the disc and the jaw are considered as a system of two interacting elastic bodies. Using the outcomes of that study, the complex potentials method is employed here for the solution of a first fundamental problem for a Brazilian disc under a parabolic load distribution. Analytic full-field formulae for the components of the stress field developed in the disc are given. The solution is then applied for the case of a disc made from Dionysos marble. The results are compared to existing ones obtained from solutions adopting statically equivalent loads either in the form of distributed (uniform or sinusoidally) radial pressure acting along the actual contact rim or in the form of diametrically acting point (line) loads. While the stress field in the major part of the disc seems to be rather insensitive to the exact load application mode, critical differences are detected in the vicinity of the loaded arc of the disc. The solution is assessed according to the results of a short series of Brazilian disc tests with PMMA specimens. The agreement between theoretical predictions and experimental data is satisfactory. Finally, it is indicated that, as opposed to previous solutions, the stress field (even at the disc’s center) is a non-linear function of the externally applied load depending, among others, indirectly on the properties of the disc’s and jaw’s materials, the combination of which dictates the extent of the contact angle.

Effects of Pore Position in Depth on Stress/Strain Concentration and Fatigue Crack Initiation

Abstract: The stress field around a pore was analyzed as a function of the pore position in depth in the surface of a linear elastic solid using finite element modeling It was found that the pore depth dominated the stress field around the pore on the surface and that the maximum stress was increased sharply when the pore intercepted with the surface at its top Given the applied nominal stress, the magnitude of the maximum main stress only depended on the relative depth of the pore, while the pore size affected the stress distribution in the surface An elastic-plastic model was also used to account for the yielding effect in the region where stress was over the yield strength The results still indicated a significant maximum stress concentration when the pore was just buried underneath the surface, but with a lowered value than that of the linear elastic model These results were consistent with the experimental observations that fatigue cracks were preferably initiated from pores and particles, which were just intercepted at their top with the sample surface or just buried beneath the surface

A three-dimensional stress field solution for pointed and sharply radiused V-notches in plates of finite thickness

Abstract: By making use of the generalized plane strain hypothesis, an approximate stress field theory has been developed according to which the three-dimensional governing equations lead to a system where a bi-harmonic equation and a harmonic equation should be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, and the latter provides the solution of the corresponding out-of-plane shear notch problem. The system can be applied not only to pointed three-dimensional V-notches but also to sharply radiused V-notches characterized by a notch tip radius small enough. Limits and degree of accuracy of the analytical frame are discussed comparing theoretical results and numerical data from FE models.

The effects of lithospheric thickness and density structure on Earth′s stress field

Abstract: SUMMARY Lithospheric density and thickness variations are important contributors to the state of stress of the plates. The relationship between the lithosphere's isostatic state, subcrustal structure and stress field, however, remains unresolved due to the uncertainties on its thickness, composition and rheology. To study the influence of lithospheric structure on intraplate stresses, we use a new model of global lithospheric structure (TDL) that accounts for the presence of depleted mantle to explore the effects of isostatic compensation, mantle density structure, lithospheric thickness (base depth) and mechanical coupling within the lithosphere on wavelengths >200 km. We compute the mean lithostatic stress (Ω) of 2°× 2° lithospheric columns and then solve for the resulting global ‘tectonic’ stress field for a homogeneous elastic lithosphere with the finite element package ABAQUS. For a 100 km base depth, a historically common value for lithospheric thickness, tectonic stress patterns are largely insensitive to mantle density structure and match patterns in the world stress map, for both isostatically compensanted and non-compensated lithospheric structure. Increasing the base depth up to 250 km to account for thick continental roots, however, leads to sharp variations in the stress field between isostatic lithospheric structure models and TDL as the mantle portion of the lithosphere dominates Ω. Decreasing the model base depths up to 25 km as a proxy for vertical strength variations due to low viscosity channels within the crust or lithosphere as a whole, strongly alters stresses in magnitude, azimuth and regime, as the influence of topography and shallow crustal structure increases. We find that restricting spatial changes in Ω to a specified region to mimic lateral variations in strength also has a large effect on the resulting stresses, which leads us to conclude that regional models may not always be adequate for modelling the stress field. Strong deviations from long-wavelength patterns on the world stress map in models with a shallow ( >150 km) uncompensated model base depth likely reflect that the globally averaged lithospheric thickness is close to 100 km and large deviations from this depth generate unrealistic stress patterns related to uncompensated buoyancy forces. Because the stresses are so sensitive to base depth, we conclude that using Ω to represent spatial and vertical variations in lithospheric structure is not an adequate approximation. Our results suggest that future studies must incorporate the full 3-D variations in density and rheology of the lithosphere to elucidate the source and nature of the lithospheric stress field. These studies have become possible with the advent of modern computational tools and advances in our knowledge of lithospheric structure and rheology.

Fatigue & Fracture of Engineering Materials and StructuresNew experimental set-up to approach pipeline fracture behaviour by three-point bending specimens

Abstract: A new experimental set-up for Drop Weight Tear Tests (DWTT) is proposed. Its principal characteristic is the adoption of inclined supports driving the hinges connected to the specimen. This choice accomplishes the need that the specimen was subjected to a persistent stress field in the ligament, thus approaching the stress field experienced by a crack propagating in a pipeline. This set-up requires a proper processing of the data that is accurately explained in the paper. The tests are conducted under a quasi-static loading but the method has been designed to apply in dynamic tests.

Thermo-Elastic Analysis of a Cracked Half-Plane Under a Thermal Shock Impact Using the Hyperbolic Heat Conduction Theory

Abstract: The transient thermal stresses around a crack in a thermo-elastic half-plane are obtained under a thermal shock using the hyperbolic heat conduction theory. Fourier, Laplace transforms and singular integral equations are applied to solve the temperature and thermal stress fields consecutively. The integral equations are solved numerically and the asymptotic fields around the crack tip are obtained. Numerical results show that the hyperbolic heat conduction have significant influence on the dynamic temperature and stress field. It is suggested that to design materials and structures against fracture under thermal loading, the hyperbolic model is more appropriate than the Fourier heat conduction model.

A numerical assessment on two-dimensional failure criteria for composite layered structures

Abstract: This paper is devoted to the most popular failure criteria which are employed in the design and analysis of anisotropic materials/layered plates. In-plane stress (or strain) states are considered and both classical and advanced criteria are illustrated and compared. The advantages and disadvantages of different approaches are discussed through FEM numerical results, by referring to composite material data currently employed. Layer-wise plate models are adopted to provide quasi three-dimensional stress field and to limit the error of modeling. Failure envelopes emphasizing the in-plane shear influence in the case of biaxial traction/compression are proposed. The maximum strain, maximum stress, Tsai–Wu, Tsai–Hill, Hashin and LaRC03 failure criteria are described and compared for various benchmark problems.