Showing papers on "Photoelasticity published in 2002"

Principles of Fracture Mechanics

Abstract: Most chapters include an Introduction, Summary, References and Exercises. 1. Introduction to Fracture Mechanics. Historical Overview of Brittle Fracture. Elementary Brittle-Fracture Theories. Crack Extension Behavior. 2. Elements of Solid Mechanics. Concepts of Stress and Strain. Equations of Elasticity in Cartesian Coordinates. Equations of Elasticity in Polar Coordinates. Solution of the Biharmonic Equation. The Problem of the Elliptical Hole. 3. Elasticity of Singular Stress Fields. Overview. The Williams Problems. The Generalized Westergaard Approach. The Central Crack Problem. Single-Ended Crack Problems. The Effect of Finite Boundaries. Determining the Geometric Stress Intensity Factor. The Three-Dimensional Crack Problem. 4. Numerical Methods for K Determination. Boundary Collocation. The Finite Element Method. 5. Experimental Methods for K Determination. Overview. Classical Photoelesatic Methods. The Method of Caustics. Strain Gages. Multi-Parameter Full-Field Methods: Local Collocation. Interference Patterns. Moire Patterns. Photoelasticity. 6. A Stress Field Theory of Fracture. The Critical Stress-State Criterion. Crack-Tip Plasticity. The Effect of Variables on Fracture Toughness. R-Curves. 7. The Energy of Fracture. Griffith's Theory of Brittle Fracture. A Unified Theory of Fracture. Compliance. 8. Fracture Toughness Testing. Fracture Toughness Standards. Nonstandard Fracture-Toughness Tests. 9. Fatigue. Stages of Fatigue Crack Growth. Mathematical Analysis of Stage II Crack Growth. The Effects of Residual Stress on Crack Growth Rates. Life Prediction Computer Programs. Measuring Fatigue Properties: ASTM. 10. Designing against Fracture. Fracture Mechanics in Conventional Design. The Role of NDE in Design. U.S. Air Force Damage-tolerant Design Methodology. Designing by Hindsight: Case Studies. 11. Elastoplastic Fracture. Nonlinear Elastic Behavior. Characterizing Elastoplastic Behavior. Comments on the J-Integral in Elastoplastic Fracture Mechanics. Appendix A: Comprehensive Exercises. General Comments. Appendix B: Complex Variable Method in Elasticity. Complex Numbers. Complex Functions. Appendix C: An Abbreviated Compendium of Westergaard Stress Functions. Appendix D: Fracture Properties of Engineering Materials. Appendix E: NASGRO 3.0 Material Constants for Selected Materials. Index.

Digital photoelasticity: Principles, practice and potential

Abstract: The enormously enhanced power of photoelasticity resulting from adoption of digital technologies is highlighted and discussed. An overview of the principal techniques of digital fringe processing is provided within a single theoretical framework. The practical application of the new technologies using both conventional instruments and novel optical devices is discussed. Experiments involving more I x 10 6 quantitative fringe order measurements are possible and practical on a routine basis using the current technology. Products based on this research are beginning to appear on the market so that many new application areas are opening up for photoelasticity, such as dynamic events, real-time fatigue crack analysis, monitoring polarisation changes at a microscopic level in materials; detailed validation of numerical simulations, particularly of complex geometry and loading; and in-service monitoring using reflection photoelasticity of damage in both homogeneous and heterogeneous materials, such as composites.

Measurements of the corneal birefringence with a liquid-crystal imaging polariscope

Abstract: An imaging polariscope has been used to analyze the spatially resolved polarization properties of living human corneas. The apparatus is a modified double-pass setup, incorporating a liquid-crystal modulator in the analyzer pathway. Keeping the incident polarization state fixed (first passage), we recorded a series of three images of the pupil's plane corresponding to independent polarization states of the analyzer unit. Azimuth and retardation at each point of the cornea were calculated from those images. Results show that the magnitude of retardation increases along the radius toward the periphery of the cornea. Left-right eye symmetry in retardation was also found. Maps of azimuth indicate that the direction of the corneal slow axis is nasally downward.

Computer aided photoelasticity by an optimum phase stepping method

Abstract: In this paper an automated photoelastic method based on the phase stepping technique is described. It provides full-field maps of the isoclinic parameter and the relative retardation. The technique is based on processing six images of a photoelastic specimen acquired using plane and circularly polarized light. The number of acquisitions and the type of polariscope used in this approach have been chosen with the aim at reducing the influence of quarter wave plate errors and obtaining raw photoelastic data in a periodic form suitable for easy applications of automatic unwrapping routines.

Study of Stresses in Thin Silicon Wafers with Near-infraredphase Stepping Photoelasticity

Abstract: This paper reports on a study of stress in thin silicon plates sectioned from wafers by a near-infrared transmission technique. Phase stepping was incorporated to determine the magnitude and orientation of stress from fractional birefringence fringe images. The anisotropic relative optic-stress coefficient of (100) silicon was determined and the limitation of the stress orientation measurement is discussed.

Complete determination of the stress tensor of a polarization-maintaining fiber by photoelastic tomography.

Abstract: The use of photoelastic tomography to obtain the two-dimensional axial stress profile of a polarization-maintaining (PM) fiber with high resolution and accuracy is described. We illustrate, for what is believed to be the first time, the two-dimensional distribution of the local principal axes of the fiber's cross section, which is directly related to the fiber's PM ability. We demonstrate that the stress-induced anisotropy as well as all the stress tensor components of the fiber can be fully determined.

Photoelastic and acousto-optical properties of Cs2HgCl4 crystals.

Abstract: We use a Mach–Zehdner interferometric technique to study the piezo-optical properties of Cs2HgCl4 crystals at room temperature. All piezo-optical (πmn) and photoelastic (pin) tensor constants are obtained. A substantial photoelastic effect and low ultrasonic velocities in these crystals determine a relatively high figure of merit M2 for isotropic diffraction (for a certain geometry of acousto-optical interactions, M2 ∼ 110 × 10-15 s3/kg). The new material may be considered, therefore, a candidate for applications in acousto-optical devices. The dependence of the acoustic walk-off angle on the direction of sound propagation is calculated for the principal crystallographic planes.

Dynamic stress chain formation in a two-dimensional particle bed

Abstract: Cure cast plastic bonded explosives (PBXs) consist of relatively hard particles in a soft binder. Under compressive loading, the explosive cyrstals come into contact that causes high stress concentrations. The lines along which the crystals are loaded are called stress chains. Damage done to these particle beds during compressive loading can lead to reaction. The photoelastic effect of PMMA is exploited to examine the stress state within a two-dimensional particle bed. Stress chain development within the bed is recorded and is shown to increase the stress state within some particles while leaving others unloaded. These concentrations form early in the loading process, leading to fracture along the stress bridges and generating likely reaction initiation sites. Through material point method simulations, contact friction is shown to have a large effect on the stress distribution within the particle bed.

The use of phase-stepping for the measurement of characteristic parameters in integrated photoelasticity

Abstract: A three-dimensional photoelastic body can be represented by an optically equivalent model, which consists of a linear retarder, δ, at a certain angle, θ, and a pure rotator, χ. These have been described as the characteristic retardation, δ, and the primary and secondary characteristic directions, θ and θ+χ. Until now these characteristic parameters have only been determined using manual, point-by-point collection methods which are involved and time consuming. Therefore an automated phase-stepping method has been developed to enable the determination of the three characteristic parameters for three-dimensional or integrated photoelasticity. Expressions have been derived to obtain δ, θ and θ+χ from six phase-stepped images. These images are collected using a CCD camera and the full-field data is processed using a standard personal computer. This novel method allows accurate, full-field maps of all three characteristic parameters to be obtained in a relatively short time, which makes full-field tomographic reconstruction of photoelastic data a real possibility.

Simulation of injection-compression molding process, Part 3: Effect of process conditions on part birefringence

Abstract: Simulations of the injection-compression molding (ICM) process based on a Leonov viscoelastic fluid model has been employed to study the effects of processing conditions on the birefringence development and distribution in injection-compression molded parts. A numerical algorithm combined with a modified control-volume/finite-element method is developed to predict the melt front advancement and the distributions of pressure, temperature, and flow velocity dynamically during the injection melt-filling, compression melt-filling, and postfilling stages of the entire process. Part birefringence was then calculated from residual stresses following the thermal-mechanical history of the entire molding process. Simulations of a disk part under different process conditions including compression speed, switch time from injection to compression, compression stroke, packing pressure, and postfilling time were performed to understand their effects on birefringence variation. The simulated results were also compared with those required by conventional injection molding (CIM). It has been found that an ICM part shows a significant reduction of part birefringence near the gate area as compared with CIM parts. However, ICM parts exhibit higher birefringence values near the rim of the disk. The minimum birefringence occurs around the location where injection is switched over to compression. Although longer postfilling time and higher packing pressure result in higher birefringence values, their effects are not very significant. On the other hand, higher compression speed, larger compression stroke, and shorter switch time exhibit greater effects on the increase of part birefringence. Flow-induced residual stress is the major origin of birefringence formation in the present case. The simulated birefringence for both ICM and CIM parts show good coincidence with those obtained from measurements by using a digital photoelasticity technique. © 2002 Wiley Periodicals, Inc. Adv Polym Techn 21: 177–187, 2002; Published online in Wiley Interscience (www.interscience.wiley.com). DOI 10.1002/adv.10024

Polariscope and microlithography projection system provided with the same

Abstract: PROBLEM TO BE SOLVED: To attain a low manufacturing cost and high transmittance with a simple design. SOLUTION: A polariscope which is suited for converting linearly or circularly polarized incident light to emitted light polarized in a radial or tangential direction essentially with no transmission loss, in one of the embodiment, a plate made of a birefringent material which has small zones (11, 12) provided with deflection structures (8, 9) with a shape of a diffraction grating or a Fresnel surface formed on an entrance surface and on an outgoing surface thereof. A crystallographic axis (5) of the birefringent material is aligned parallel to the incident luminous flux. The deflection structures deflect light propagating along a transmission direction (13) inclined on the crystallographic axis (5) and cause phase transition of transmitted light among field constituent elements. COPYRIGHT: (C)2003,JPO

Photoelastic Evaluation of Stress Fields and Fracture During Dynamic Splitting Experiments

Abstract: Dynamic tensile-splitting experiments were conducted on brittle polyester disks, manufactured from Homalite ®-100, to photoelastically visualize stress field development in the specimens and, ultimately, specimen fracture A Split Hopkinson Pressure Bar (SHPB) was used to load the specimen dynamically and record load data as a function of time Images of the stress field were captured with high-speed photography and interpreted using photoelastic analysis The experiments determined that the specimens reached an equilibrium state relatively quickly, and remained in equilibrium until fracture Fracture began with in-plane cracks forming on either side of the specimen Transverse cracks emanated from the in-plane cracks, then propagated across the specimen mid-plane at velocities up to 60% of the shear wave velocity in the material Contact loads calculated from photoelasticity agreed favorably with SHPB results These experiments also allowed for the determination of the dynamic splitting strength of the Homalite ®-100 as a function of strain rate The dynamic splitting strength of the material increased with the increasing strain rate, reaching a maximum value of about twice the static splitting strength

Applications of modern automated photoelasticity to industrial problems

Abstract: The very latest advances in modern photoelastic analysis techniques now offer the opportunity to carry out real-time stress monitoring of components or structures. No more time-consuming complex coating applications, no more time consuming manual reading of fringes- a simply applied, quick cure coating and a fully automated polariscope system linked to a high speed CCD camera can monitor changing stress patterns as they happen. The old, time-consuming, high skill requirement, photoelastic technique is finally bought up to date and offers a unique efficient full-field dynamic stress analysis method. This paper highlights the advantages of automated photoelastic stress analysis with examples of its use and introduces a new dynamic photoelastic system and the wide potential for its further use.

Experimental Examination of the Arching Mechanism on the Micro Level

Abstract: The arching phenomenon is manifested through the reduction of stresses experienced by underground structures. Arching plays an important role in geotechnical engineering construction such as; excavations, retaining structures, pile groups, tunnel boring machines, culverts and underground facilities. The arching mechanism is intrinsic to granular material/rock mass independent of scale effect. Its fundamental mechanism relates to the ability of discrete units to transfer loads through interaction in a preferable geometry and, thus, to bridge between the zone (or point) of load application to the zone (or points) of reaction. The testing results of an advanced experimental technique is presented and analyzed. A model of granular material made of photoelastic particles is utilized. The model and the sophisticated image and global data acquisition system allow to track the development of the arching within ideal granular material during a trap door experiment by following the motion of each particle and the contact forces between the particles. Visual and quantitative analyses are presented demonstrating the relationship between the global arching phenomenon and the particle interaction on the micro-level. The obtained information allows one to observe the changes associated with the arching mechanism and the stress variation resulting from it. The arching mechanism is observed in details that previously could not have been achieved. Photoelastic Discrete Simulation (PDS) De Josselin de Jong and Verruijt (1969) suggested that the interparticle contact force magnitude could be determined as a function of the relative size of the isochromatic fringes at the contact, and the corresponding contact force direction followed a line connecting the center of gravity of isochromatic fringe near the contact. The isochromatic fringes can be observed through a circular polariscope, which consist of quarter -wave plates and polarizers. Further development and testing of the above method has been presented by Paikowsky et. al. (1993). A calibration process establishing the relationship between the photoelastic isochromatic fringes and the contact force magnitude and direction were developed, allowing to accurately monitor the interparticle contact forces. Independent digital images acquired in parallel, enable to follow markings on the particles. These images allow to monitor the motion of each particle (translation and rotation) as presented by Paikowsky and Xi (2000). The two techniques were combined into an experimental system that enable s the investigation of both, kinematic behavior and interparticle contact force variation of photoelastic particles. This experimental system was termed Photoelastic Discrete Simulation (PDS). Experimental Setup The PDS was used to construct a granular mass made of photoelastic particles, and conduct trap door experiments. A trap door testing system has been developed to study the

Polarimetry in the human eye using an imaging linear polariscope

Abstract: We have studied the polarizatio np arameters of the human eye associated with ocular birefringence from double-pass retinal images by using an imaging linear polariscope. A series of nine images corresponding to combinations of linear independent polarization states in both generator and analyser units was recorded. Retardation and azimuthal angle obtained when considering the human eye as a linear retarder have been compared to those calculated with a Mueller matrix polarimeter. Results in young eyes show only small differences, of about 2 ◦ for azimuth and 6 ◦ for retardation, between these methods. Moreover, changes in the polarization state of the central part of double-pass images are very different from those corresponding to the tails. Although the simpler linear polariscope is mainly designed for studies in physiological optics and clinical diagnosis, it can also be used for the analysis of in vitro biological samples and crystals.

Determination of stresses around beads in stressed epoxy resin by photoelasticity

Abstract: Microphotoelasticity gives the possibility of determining stresses in systems with small inclusions. We studied four systems with the same matrix (epoxy resin) and different inclusions of spherical shapes. The distributions of stresses and pressure, after the application of external tensile forces, were determined. In a matrix with a hard inclusion, tensile stresses concentrated at the pole. For a soft inclusion, that is, a poly(vinyl acetate) bead or an air bubble, the tensile stresses concentrated at the equator with some compression at the pole. The soft inclusion promoted the stress relaxation by the change in its shape. In the matrix with a stiff inclusion, such as a steel or glass bead, debonding was observed at the interface near the pole area. In such a case, the stress concentration region moved toward the tip of the debonding. For a hard inclusion, the pressure at all points of the interface was negative, and the maximum was found at the pole near the inclusion surface from −6 to −10 MPa. This region was sensitive to the initiation of destruction processes such as cavitation and debonding. For a soft inclusion, the pressures at the pole and equator were comparable, but the signs were opposite, being positive at the pole (compression) and negative at the equator (expansion). © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 1436–1444, 2002

MATLAB® for Photomechanics- A Primer

Abstract: Selected papers: Introduction Principles of optical methods Photomechanics Introduction to MATLAB MATLAB for image processing. MATLAB for Photomechanics (PMTOOLBOX): Introduction Image processing in photomechanics MATLAB demonstration Conclusion. Digital Photoelasticity: Digital polariscope Phase-shifting method with a normal circular polariscope Dynamic phase shift photoelasticity MATLAB demonstration. Moire Methods: Digital moire Moire of Moire Gabor strain segmentation Differentiation of low density fringe patterns. Digital Holography: Digital holography Digital holographic interferometry MATLAB demonstration Conclusion. Speckle Methods: Laser and white light speckles Sampled speckles MATLAB demonstration Curvature contouring

Two-dimensional optical measurement techniques based on optical birefringence effects

Abstract: Some dielectric materials become birefringent when subjected to an external force, such as an electric field or a mechanical force. For more than a decade, our research group has been engaged in developing two-dimensionaloptical measurement techniques for the dynamic measurement of charge distributions on a dielectric surface using the electro-optic Pockels effect, the dynamic measurement of electrical field distributions in a liquid using the electro-optic Kerr effect, and the measurement of birefringence vector distributions in plastic plates using the photoelastic effect. The system nonuniformity and the system reliability are the inevitable problems in two-dimensional measurement systems, and make two-dimensional measurements quite different from point measurements. The common image-processing techniques that have been specially developed to overcome these problems are analyzed and summarized; detailed mathematical analysis is avoided.

Characterization of interfacial failure using a reflected light technique

Abstract: A simple optical method of observing and tracking interface failure in transparent matrix composites is developed to extend the range of material systems that can be tested with the cruciform test for measuring the normal strength of a bi-material interface. This technique of detecting debonds using reflected light is demonstrated on two model material systems with fibers 140 and 15 μm in diameter. The reflected light technique is more reliable and provides information about the interface that cannot be obtained with previous methods of debond detection, such as photoelasticity, surface strain gages, and acoustic emission. Using this technique, debond initiation, location, length, and shape are measured as a function of applied load; thus, all the required parameters for calculating the normal strength of the interface, as well as the interfacial energy release rate are acquired.

Optical anisotropy and strain-induced birefringence in dislocation-free silicon single crystals

Abstract: Birefringence measurements, using a scanning infrared polariscope (SIRP) with high sensitivity, have been carried out in as-grown dislocation-free silicon single crystal ingots. A small amount of birefringence due to 〈110〉 optical anisotropy, which is predicted not by the classical optics theory but by the Lorentz's spatial dispersion theory, is observed in the θ – Z optical configuration, for which a probing polarized light is introduced from the as-grown cylindrical ingot surface and then the polarization of the light transmitted through the opposite surface is analyzed. On the other hand, in the R – θ optical configuration, for which the probing polarized light is introduced along the 〈001〉 crystal growth direction from the (001) sliced and polished surface and then the polarization of the light transmitted through the opposite (001) surface is analyzed, the birefringence is still observed although it is extremely small. It is found that this 〈001〉 optical anisotropy is not constant over the (001) cross-section of the ingot but consists of two different components, i.e. a symmetric component distributed over the whole sample, probably caused by point defects, and an asymmetric component distributed randomly near the peripheral region, related to dents and chips on the as-grown cylindrical surface.

Application of Photoelasticity for analysis of residual stresses in CDs

Abstract: Residual stresses appeared with time due to the imperfection of the material production process. Sometimes the redistribution of residual stresses is the reason of cracks initiation in the tested object on one of the manufacturing stages or this redistribution increases them up to the critical value, when a small external load results in breakage ofthis object. Relaxation is the main reason of redistribution of residual stresses and it can occur without extemal influence or ifthere is heating, static and cyclic loads. Relaxation results in change of the sizes and shapes of the tested object. The dimensional stability is especially important in modern high technologies, in particular in the use of compact discs for the storage of information. Modem CDs are produced from polycarbonate, possessing an effect of birefringence. It allows to make an estimation of stresses at CDs by the method of photoelasticity. A metallized coating put on one of a CD surfaces provides ideal conditions for registration of interference picture observed in the reflected light. When investigating the stresses in CDs with the use of reflective V-type plane polariscope the solving equations become similar to those used in a photoelastic coating method. The present work discusses the results of the research of the residual stresses in CDs with various operation time produced by various firms and by different technologies (punching, laser recording). A simple optical method ofthe NDT ofCDs at various stages oftheir manufacturing is offered.

Method and apparatus for enhancing visualization of mechanical stress

Abstract: Photoelastic elements are formed deliberately with stress concentrations so that, when evaluated with a polariscope, more pronounced isochromatic bands or fringes result when loads are applied to these elements or to assemblies of these elements. A kit of photoelastic elements, at least some of which have stress concentrations formed therein, is also disclosed. In addition, a toy for producing color patterns is disclosed.

Alternative equations of magnetophotoelasticity and approximate solution of the inverse problem.

Abstract: In magnetophotoelasticity, photoelastic models are investigated in a magnetic field in order to initiate rotation of the plane of polarization that is due to the Faraday effect. The method has been used for the measurement of stress distributions that are in equilibrium on the wave normal and therefore cannot be measured with the traditional photoelastic technique. In this category belong bending stresses in plates and shells and residual stresses in glass plates. Two new systems of equations of magnetophotoelasticity are derived. One of them describes evolution of the polarization of light in a magnetophotoelastic medium in terms of eigenvectors, the other in terms of distinctive parameters. For the latter system, an approximate closed-form solution has been found. The integral Wertheim law has been generalized for the case of stress states in equilibrium when rotation of the plane of polarization is present.