Photoelasticity of Glass

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 Sénarmont 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.