Photoelasticity of Glass

Glass is the oldest man-made material. Its invention about five thousand years ago should be considered as one of the crucial events in the history of mankind. Glass has given man the possibility to have daylight in his protected living environment and to compensate the defects of his sight. Glass containers and tableware have played and still play an important role in man's everyday life. Glass elements in microscopes and telescopes have given us the possibility to learn the secrets of micro- and macrocosm. Glass participates in the most sophisticated technologies: glass fibers have caused a revolution in telecommunication, glass is used as a material for many modern electronic devices. Although nowadays plastics often make a strong competition to glass, for many applications glass is still the best material due to its specific properties - its hardness, good transparency, resistance to chemicals, the easiness to shape glass articles, feasibility to change the composition of the glass in order to meet new specific demands, etc. Two peculiarities of glass should be pointed out. The first is the fragility of glass - it breaks easily due to tensile stresses. The second is the fact that in every glass item there exist residual stresses due to the complicated technological process during which glass from the state of a viscous liquid at high temperature turns into solid state, while cooled down.

Contenu

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 Sarmont 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- 12.7.4 Tumbler N- 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.