Showing papers on "Photoelasticity published in 2012"

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.

The influence of inter-particle friction and the intermediate stress ratio on soil response under generalised stress conditions

Abstract: Previous research studies have used either physical experiments or discrete element method (DEM) simulations to explore, independently, the influence of the coefficient of inter-particle friction (μ) and the intermediate stress ratio (b) on the behaviour of granular materials. DEM simulations and experiments using photoelasticity have shown that when an anisotropic stress condition is applied to a granular material, strong force chains or columns of contacting particles transmitting relatively large forces, form parallel to the major principal stress orientation. The combined effects of friction and the intermediate stress ratio upon the resistance of these strong force chains to collapse (buckling failure) are considered here using data from an extensive set of DEM simulations including triaxial and true triaxial compression tests. For all tests both μ and b affected the macro- and micro-scale response, however the mechanisms whereby the force chain stability was improved differ. While friction clearly enhances the inherent stability of the strong force chains, the intermediate stress ratio affects the contact density and distribution of orthogonal contacts that provide lateral support to the force chains.

Optical methods for solid mechanics : a full-field approach

Abstract: 1. Basic Optics 2. Electronic Image Sensing and Processing 3. Phase Decoding and Reconstruction 4. Experimental Stress Analysis: An Overview 5. Digital Image Correlation 6. Rough Surface Interferometry 7. Fringe Projection Profilometry 8. Thermoelastic Stress Analysis 9. Photoelasticity

RGB photoelasticity applied to the analysis of membrane residual stress in glass

Abstract: The measurement of residual stresses is of great relevance in the glass industry. The analysis of residual stress in glass is usually made by photoelastic methods because glass is a photoelastic material. This paper considers the determination of membrane residual stresses in glass plates by automatic digital photoelasticity in white light (RGB photoelasticity). The proposed method is applied to the analysis of membrane residual stresses in some tempered glass. The proposed method can effectively replace manual methods based on the use of white light, which are currently provided by some technical standards.

On the inhomogeneity of residual stresses in tempered glass panels

Abstract: The paper shows that the residual stress at the surface of tempered glass panels may vary both locally (at a distance equal to the distance between the cooling jets) and globally, i.e., stresses near the edges and corners of the panels may be considerably different from the stresses in the middle part of the panels. That should be borne in mind while assessing the degree of temper by non-destructive measuring of the residual surface stress.

Photoelastic Analysis of Edge Residual Stresses in Glass by Automated “Test Fringes” Methods

Abstract: Since the glass is a birefringent material, the analysis of residual stress in glass is usually carried out by means of photoelastic methods. This paper considers the automation of the “test fringes” method which is based on the use of a Babinet compensator or of a beam subjected to bending. In particular, two automated methods are proposed: the first one is based on the use of the centre fringe method in monochromatic light and the second one is based on the use of RGB photoelasticity in white light. The proposed methods have been applied to the analysis of membranal residual stresses in some tempered glasses, showing that they can effectively replace manual methods of photoelastic analysis of residual stresses in glass.

Static photoelasticity of gallium phosphide crystals

Abstract: The piezo-optic effect (POE) in cubic GaP crystals (symmetry class \(\bar 4\)3m) is studied in detail by interferometry. The relations for determining the absolute piezo-optic coefficients (POCs) πim or their combinations on a sample of X/45° cut at all allowable geometries of the experiment are recorded. The determination of a specific coefficient πim at different experimental geometries on samples of right cuts and a X/45° cut made it possible to find the πim values with a high accuracy and reliability.

Determination of Damage in Transparent Optically Active Materials by Using Polarized Light and the Sobel Operator

Abstract: This study deals with determination of the percentage of damage in an optically active, translucent material (polystyrene). We made cracks visible by placing the material into the polariscope (between the polarizer and analyzer), and the numerical value of damage was determined by using Sobel, one of the Matlab’s operators for edge detection.

Characterization and Control of Residual Stress and Curvature in Anodically Bonded Devices and Substrates with Etched Features

Abstract: While anodic bonding is commonly used in a variety of microelectromechanical systems (MEMS) applications, devices and substrates that incorporate this processing technique are often subjected to significant residual stress and curvature that create post-processing and reliability issues. Here, using an anisothermal anodic bonding procedure, residual stresses and the resulting wafer curvature in these structures are controlled by varying the initial bond temperatures of the silicon and Pyrex wafers independently. Residual stresses are quantified by measuring bulk wafer curvature and, locally, stress concentrations are measured using infrared photoelasticity accompanied by 3-D thermomechanical finite element analysis. Based on the good agreement between numerical predictions and experimental results, this process can be used to determine the bulk post-bond wafer curvature and to reduce the likelihood of structural failure at these sites, by changing the residual stresses from tensile in nature, which may drive initiation and growth of cracks, to compressive, which can suppress such failures.

Polariscope stress measurement tool and method of use

Abstract: The present invention provides a tool for and method of using an infrared transmission technique to extract the full stress components of the in-plane residual stresses in thin, multi crystalline silicon wafers including in situ measurement of residual stress for large cast wafers. The shear difference method is used to obtain full stress components by integrating the shear stress map from the boundaries. System ambiguity at the boundaries is resolved completely by introducing a new analytical function. A new anisotropic stress optic law is provided, and stress optic coefficients are calibrated for different crystal grain orientations and stress orientations.

Flexural effects of sandwich beam with a plate insert under in-plane bending

Abstract: The local stress concentrations in sandwich beam with a plate insert under in-plane bending are concerned in the study An improved six-step phase shifting method in digital photoelasticity is employed to calculate the whole-field shear stressThe shear load transfer is realized by shear bands which connect the top and bottom sheet faces through adhesively-bonded interfaces The plate insert plays a role in load transfer in the sandwich structure, and the fact that debonding might occur at more sites of the interfaces may also leads to the failure of the structure The local stress concentrations at the insert end change with the load under three-point bending loads, while they remain as the initial residual shear stress under four-point bending loads The local stress concentration effects generated by the plate insert is essentially caused by the mismatch of elastic properties of the core materials and the irrational geometry of the insert

Linear and Nonlinear Algorithms for Stress Separation in Photoelasticity

Abstract: An experimental-numerical hybrid method for the stress separation in photoelasticity is proposed in this study. In the proposed method, boundary conditions for a local finite element model, that is, tractions along boundaries are inversely determined from photoelastic fringes. Two algorithms are proposed for determining the boundary condition. One is a linear algorithm in which the tractions are obtained by the method of linear least-squares from both principal stress difference and principal direction. Another is the nonlinear algorithm in which the tractions are determined only from the principal stress difference. After determining the boundary conditions for the local finite element model, the stresses can be obtained by finite element direct analysis. The effectiveness is demonstrated by applying the proposed method to a perforated plate under tension and contact problems. Results show that the boundary conditions of the local finite element model can be determined from the photoelastic fringes and then the individual stresses can be obtained by the proposed method. Furthermore, the stresses can be evaluated even if the boundary condition is complicated such as at the contact surface. It is expected that the proposed method can be powerful tool for stress analysis.

Digital laser explosion loading dynamic photoelasticity experimental system

Abstract: The utility model discloses a digital laser explosion loading dynamic photoelasticity experimental system which comprises a laser, a beam expanding lens, a field lens assembly, a left 1/4 wave plate, a right 1/4 wave plate, a polarization analyzer, an explosion loading device, a detonator, a numeral high-speed camera and a computer. The laser persistently emits linear light beam, the linear light beam is converted into circularly polarized light by the beam expanding lens, a field lens and the left 1/4 wave plate, the circularly polarized light irradiates a specimen on the explosion loading device, then the circularly polarized light is converged by the right1/4 wave plate, the polarization analyzer and a field lens and irradiates the lens of the numeral high-speed camera, and finally an explosion loading image is formed by the synchronous detonation of the detonator and starting of the numeral high-speed camera to shot. The system can record and analyze the propagation process of the stress wave in the specimen, the stress spatiotemporal distribution and other information under the explosion load, is simple in light path system, low in experiment environmental requirement and experiment cost, short in period and high in precision, and realizes successive observation of the whole fracture process.

Photoelastic Tomography with Linear and Non-linear Algorithms

Abstract: Tomography is a powerful method for the investigation of the internal structure of 3D objects from human bodies to atomic reactors. Classical tomography has been elaborated for the determination of scalar fields, i.e. fields, each point of which is characterized by a scalar. Due to that, algorithms of classical tomography can not be directly applied by investigating stress fields since stress is a tensor. In this paper it is shown that photoelastic tomography can be based on the equations of integrated photoelasticity. In the linear approximation the problem of stress field tomography is decomposed into a number of problems of scalar field tomography for single components of the stress tensor. In the non-linear case the axisymmetric stress field can be determined using a genetic algorithm. The paper is illustrated by several examples.

Multiplicative phase-shifting interferometry using optical flow

Abstract: Fringe patterns with a multiplicative phase shift among them appear in experimental techniques as photoelasticity and RGB shadow moire, among others. These patterns cannot be processed using standard phase-shifting demodulation techniques. In this work, we propose to use a multiframe regularized optical flow algorithm to obtain the interesting modulating phase. The proposed technique has been applied to simulated and experimental interferograms obtaining satisfactory results.

Noise-Free Determination of Isochromatic Parameter of Stereolithography-Built Models

Abstract: Recently, stereolithography, one of the rapid prototyping (RP) techniques, has simplified the process of making three-dimensional (3-D) photoelastic models. One of the issues in stereolithography-made models is the noise due to porosity of the model. This is undesirable for data handling in digital photoelasticity. A preliminary study showed that the thickness of the slice has an influence on the appearance on the noise. In this paper, use of 10-step phase-shifting technique (PST) and refined three-fringe photoelasticity (RTFP) is explored to determine the isochromatic data as accurately as possible. A slice cut from a 3-D model of a spline shaft made of stereolithographic material is used for isochromatic determination. It is found that with suitable postprocessing, the quantitative results obtained from 10-step PST and RTFP are comparable. The relative merits of these two techniques for analysing stereolithographic models are brought out.

Evaluation of stress intensity factor of multiple inclined cracks under biaxial loading

Abstract: A finite rectangular plate of unit thickness with two inclined cracks (parallel and non parallel) under biaxial mixed mode condition are modelled using finite element method. The finite element method is used for determination of stress intensity factors by ANYSIS software. Effects of crack inclination angle on stress intensity factors for two parallel and non parallel cracks are investigated. The significant effects of different crack inclination parameters on stress intensity factors are seen for lower and upper crack in two inclined crack. The present method is validated by comparing the results from available experimental data obtained by photo elastic method in same condition.

New numerical methods for the photoelastic technique with high accuracy

Abstract: The objective of this research is to find new equations for a novel phase-shifting method in digital photoelasticity. Some innovations are proposed. In terms of phase-shifting, only the analyzer is rotated, and the other equations are deduced by applying a new numerical technique instead of the usual algebraic techniques. This approach can be used to calculate equation of phase with a larger sequence of images. Each image represents a pattern and a measurement of the stresses present in the object. A reduction in the difference between the theoretical and experimental values of stresses was obtained by increasing the number of images in the equations for calculating phase. Every photographic image has errors and random noise, but the uncertainties due to these effects can be reduced with a larger number of observations.

Contactless Torque Sensor Development

Abstract: This paper presents the development of a contactless torque sensor, which operates on a new principle. The used method is based on the birefringence effect of optically anisotropic materials. Experiments made are similar to the reflective photoelasticity. Instead of conventional photoelastic coating a Perspex tube of thin wall thickness was used. When torque was applied, stress had arisen in the tube, which could be measured optically. The main goal of this study was to create a torque sensor, which could be used in industry too. The paper deals with the theoretical basics, it gives an overview of the development up to now, presents measurement results, shows possible practical realizations for small and large torques, and also proposes possibilities for further developments.

Evaluation of drying stresses in coatings using an optical method

Abstract: In this paper, it is shown how an optical birefringence technique can be used to determine drying stresses in alumina films. The specimen geometry consists of a transparent plate as a substrate material that is coated on both sides with colloid dispersions. The homogeneous compressive stress in the substrate is determined from the optical retardation of a laser beam. The tensile stress in the coating can be easily calculated from the force balance, without any assumptions for its mechanical properties. The stress measurement principle based on photoelasticity, calibration of the experimental setup and initial results on drying stress evolution in alumina films are presented.

Dynamic Shear Stress Evaluation on Micro-Turning Tool Using Photoelasticity

Abstract: The paper presents an experimental methodology for evaluation of shear stress induced on a micro-turning tool during micro-turning operation A micro-turning tool manufactured by Sandvik Coromant was used for micro- turning of a brass spindle The front face of the tool was cleaned, polished and coated with a thin layer of Ethylene-Vinyl Acetate (EVA), a birefringent material Subsequently, reflection photoelastic experiments were conducted to find the shear stresses induced on the micro-tool A custom designed grey field poledioscope was used for this purpose which was pre-calibrated and verified using disk under compression test The tool was subjected to turning operation and dynamic images of the tool were captured using Casio ELIXIM ZR-200 camera in high speed movie mode at 1000 fps (frames per second) for four different orientations of the analyzer simultaneously These images were processed using a code developed in MATLAB software to generate a shear stress map of the tool dynamically at different time instants of the machining process

Cosserat gyro-birefringence. An introduction to nonsymmetrical photoelasticity

Abstract: Mechanical couple stresses modify at a microscopic level optical properties of some materials so they can display gyro-birefringence phenomena. The Optical Cosserat medium is defined and optical rotation tensor relative to couple stress is introduced. The generalized tensor of the dielectric permittivity is written for the Cosserat medium. Split of the plane-polarized light wave on passing through the Cosserat medium is shown and rotation of the azimuth of polarization is expressed by components of the couple stress tensor.

RGB profiles in digital image analysis for the description of interference colors produced on photoelasticity studies of the plastic film deformation

Abstract: Over the last years image analysis has taken great positioning in the automation of industrial processes, digital photoelasticity employs techniques supported in the digital image analysis applied to studies based on measuring of the intensity of light and the reconstruction of the phase maps generated in the transmission of light through the studied material. This paper proposes the implementation of profiles RGB image analysis to describe the behavior of the interference colors produced in photoelasticity studies during deformation of plastic films, these techniques aim to study the photoelastic characteristics of plastic films starting from the analysis of the content of an image generated through a pattern of polarization. Plastic films samples are subjected to tensile mechanical, optical polarization assemblies are used for observing the phenomenon of photoelasticity, a digital camera is used to capture changes in interference colors, and RGB profiles are used for image analysis. The use of the implemented technique allows to identify the transition points for the change of order in the colors of interference, and to describe the behavior of the color stripes in the same order.

Full-field stress analysis by holographic phase-stepping implementation of the photoelastic-coating method

Abstract: In this paper, we describe a system for polariscopic and holographic phase-shifting implementation of the photoelastic-coating method for a full-field stress analysis. The easiest way to build the combined system is to employ a laser light source. However, coherent illumination introduces a signal-dependent speckle noise which worsens the accurate phase estimation and unwrapping. To answer the question of how it affects the phase retrieval of isochromatics, isoclinics and isopachics, we modeled in the present paper the phase-shifting photoelastic measurement in the presence of speckle noise through the calculation of the complex amplitudes in a Mach–Zender interferometer combined with a circular polariscope and made denoising of simulated and experimental fringe patterns. The latter were recorded at pure tensile load for PhotoStress®-coated samples with a mechanical stress concentrator.

New numerical method for the photoelastic technique

Abstract: The objective of this research is to find new equations for a novel phase-shifting method in digital photoelasticity. Some innovations are proposed. In terms of phase-shifting, only the analyzer is rotated, and the other equations are deduced by applying a new numerical technique instead of the usual algebraic techniques. This approach can be used to calculate a larger sequence of images. Each image represents a measurement of the stresses present in the object. Every photographic image has errors and random noise, but the uncertainties due to these effects can be reduced with a larger number of observations.

Laser frequency modulator

Abstract: The utility model provides a laser frequency modulator, which comprises a machine frame and a detection assembly arranged on the machine frame, wherein a workpiece fixing assembly is arranged on the machine frame; more than two quartz crystal oscillators are arranged on the workpiece fixing assembly, and a laser emitter is arranged above the workpiece fixing assembly; the detection assembly is provided with a detection head for detecting resonance signals of the quartz crystal oscillators, and transmits the detected signals to a controller; a polariscope system is arranged in the laser emitter and is provided with a polariscope lens and a polariscope controller for controlling the polariscope lens to do motion continuously; and the polariscope controller receives the signals transmitted by the controller. By the laser frequency modulator, a plurality of quartz crystal oscillators can be positioned and cut simultaneously, so the laser frequency modulator is high in work efficiency and low in production cost.