Stress field

About: Stress field is a research topic. Over the lifetime, 11926 publications have been published within this topic receiving 226417 citations.

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.

Widespread extension in the core of the western Alps revealed by earthquake analysis

Abstract: The western Alps are an active collision belt whose current stress field is inhomogeneous [Muller et al., 1992]. We report new seismological data which significantly improve our knowledge of this stress field. About 1600 earthquakes which occurred in the western Alps during the last 10 years were precisely located, and 79 new focal solutions were computed. The analysis of this database shows that widespread extension affects all the internal zones of the belt. To better constrain the associated stress regime, six stress tensors were computed using the Gephart and Forsyth [1984] method. They show that the current tectonics of the western Alps are contrasted with close variation in the stress regime (transpression to the front of the belt contrasting with extension in the core of the belt). The extensional direction is radial to the arcuate geometry of the belt and bounded outboard by the former thrust of the internal zones onto the external zone, suggesting extensional reactivation of this inherited crustal discontinuity. Such widespread extension within the inner part of an actually ongoing collision belt cannot be explained by simple collision-related tectonics. We propose that intrabelt buoyancy forces, such as those produced by a slab retreat or slab break-off, interfere with the boundary forces driven by the ongoing Europe-Africa convergence.

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.

Plastic instabilities: Implications for the origin of intermediate and deep focus earthquakes

Abstract: Adiabatic or catastrophic plastic shear has been reported in metals, polymers, and metallic glasses. The phenomenon is associated with rapid stress drops and audible pings or clicks as the material deforms in a plastic manner. The driving force for the plastic instability is the stored elastic strain energy of the loading system, and in many respects the behavior is reminiscent of the shear stress response arising from stick slip events during unstable frictional sliding, although the precise mechanism is different. It is shown here that adiabatic plastic shear is capable of explaining the detailed distribution of intermediate and deep focus earthquakes within subduction zones, the earthquake events being the result of instabilities in material undergoing plastic flow. It is argued that for a particular strain rate there exists a critical temperature, TC, which is depth dependent; for temperatures below TC the material is strain rate softening and, for a soft enough loading system, may undergo catastrophic plastic shear. For temperatures above TC the material is strain rate hardening and is always stable during plastic shear. The cutoff depth for deep focus earthquakes then corresponds to the transition from strain rate softening to strain rate hardening material, and for commonly accepted geothermal gradients within the slab corresponds to approximately 800 km. The precise distribution of earthquakes within the slab is a function of the subtle interplay between the geothermal gradient and the TC gradient. In particular, a decrease in seismic activity is to be expected below about 300 km in the slab with total stress drops decreasing from a maximum of 700 MPa above 300 km to a maximum of ≈ 50 MPa below 300 km. The differences in foci distribution between subduction zones such as Tonga, New Hebrides, and Peru result from minor differences in the geothermal gradients within the slabs. The model predicts the development of triple seismic zones high in the slab, double seismic zones down to approximately 300 km, and single seismic zones down to ≈ 800 km. Such a distribution is to be expected of relatively young, cool slabs; as the slab heats up, the seismic activity retreats up the slab. The paper only proposes a deformation mechanism for earthquake generation, it does not address the stress field within the slab but only the distribution of strength. Thus the distribution of focal plane mechanisms is not considered, only the locations where earthquakes due to plastic instabilities are possible. The absence of earthquakes does not necessarily mean that the slab does not exist, it only means that the slab is too hot to undergo plastic instability. This means that aseismic subduction is a distinct possibility in many regions of high geothermal gradient within the slab (i.e. > circa 3°C km−1).