Showing papers on "Photoelasticity published in 2005"

Infrared grey-field polariscope: A tool for rapid stress analysis in microelectronic materials and devices

Abstract: The infrared grey-field polariscope (IR-GFP) has been developed to provide rapid, full-field stress analysis for infrared-transparent materials. Grey-field photoelastic theory is outlined and the advantages of this implementation for microelectronic materials inspection highlighted. The capabilities of this scientific tool are proven using standard sample geometries fabricated from single crystal silicon substrates and the general applicability of the instrument demonstrated on bonded devices and silicon wafer geometries. Stress resolution in silicon wafers is better than 0.1MPa at wafer inspection speeds of 10s for a 100mm wafer. Initial applications of the IR-GFP have shown that the tool provides improvements in defect detection and stress quantification when compared to conventional infrared transmission imaging while also providing several important advantages over other currently utilized inspection technologies.

Photoelastic tomography for residual stress measurement in glass

Abstract: The paper describes an algorithm of photoelastic tomography and its application for residual stress measurement in glass articles of complicated shape. The algorithm is based on a linearized solution of the equations of integrated photoelasticity. The problem of tensor field to- mography is decomposed into several problems of scalar field tomogra- phy for normal stress components of the stress tensor. The method is implemented with an automated polariscope supplied with a rotary stage. Software for the control of tomographic measurements and for the calculation of the stress fields has been elaborated. Several examples illustrate application of the method. © 2005 Society of Photo-Optical Instrumenta-

A new photoelastic model for studying fatigue crack closure

Abstract: The photoelastic analysis of crack tip stress intensity factors has been historically developed for use on sharp notches in brittle materials that idealize the cracked structure. This approach, while useful, is not applicable to cases where residual effects of fatigue crack development (e.g., plasticity, surface roughness) affect the applied stress intensity range. A photoelastic model of these fatigue processes has been developed using polycarbonate, which is sufficiently ductile to allow the growth of a fatigue crack. The resultant stress field has been modeled mathematically using the stress potential function approach of Muskhelishvili to predict the stresses near a loaded but closed crack in an elastic body. The model was fitted to full-field photoelastic data using a combination of a generic algorithm and the downhill simplex method. The technique offers a significant advance in the ability to characterize the behavior of fatigue cracks with plasticity-induced closure, and hence to gain new insights into the associated mechanisms.

Two-dimensional stress separation using phase-stepping interferometric photoelasticity

Abstract: A phase-measuring method is proposed for stress separation in two-dimensional interferometric photoelasticity. A Mach–Zehnder-type interferometer combined with a circular polariscope is used for the observation of isochromatics and isoclinics as well as isopachics. Phase-stepping is performed for the determination of the phase values of isochromatics and isoclinics by rotating both a quarter-wave plate and an analyser. On the other hand, the phase of the isopachics is analysed from images obtained by shifting a mirror in the interferometer. Then, the phases of isochromatics and isoclinics without ambiguity are obtained by introducing a load-stepping technique. The phases obtained by the load-stepping are also used for unwrapping the phases of isochromatics and isopachics. In the present paper, light intensity equations for the proposed optical set-up are derived using Jones calculus. Then, the effectiveness is demonstrated by applying the proposed method to a simple problem.

Evaluation of stress field parameters for an interface crack in a bimaterial by digital photoelasticity

Abstract: Photoelastic evaluation of the stress intensity factor (SIF) for a crack in a bimaterial tangential to the interface is hitherto confined to the use of only a singular stress field equation. In this paper, the multi-parameter stress field equations of Deng are simplified for use by experimentalists to evaluate the stress field parameters by digital photoelasticity using an overdeterministic least-squares technique. A bimaterial Brazillian disc with a central interface crack is selected as the model for study as different mode mixities could be easily simulated by changing the crack orientation angle. The use of SIF evaluation based on a singular stress field equation is found to be inadequate for the problems considered. On the other hand, the use of a multi-parameter stress field equation is quite successful in evaluating the stress field for various mode mixities and for two values of bimaterial constant. It is shown that the new procedure allows data collection from a larger zone, which helps to simpli...

Stress intensity factor and crack velocity relationship for polyester/TiO2 nanocomposites

Abstract: The dynamic fracture behavior of polyester/TiO2 nanocomposites has been characterized and compared with that of the matrix material. A relationship between the dynamic stress intensity factor,KI and the crack tip velocity,a, has been established. Dynamic photoelasticity coupled with high-speed photography has been used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the nanocomposites. Single-edge notch tension and modified compact tension specimens were used to obtain a broad range of crack velocities. Fractographic analysis was conducted to understand the fracture process. The results showed that crack arrest toughness in nanocomposites was 60% greater than in the matrix material. Crack propagation velocities prior to branching in nanocomposites were found to be 50% greater than those in polyester.

Reconstruction of spatially inhomogeneous dielectric tensors through optical tomography.

Abstract: A method to reconstruct weakly anisotropic inhomogeneous dielectric tensors inside a transparent medium is proposed. The mathematical theory of integral geometry is cast into a workable framework that allows the full determination of dielectric tensor fields by scalar Radon inversions of the polarization transformation data obtained from six planar tomographic scanning cycles. Furthermore, a careful derivation of the usual equations of integrated photoelasticity in terms of heuristic length scales of the material inhomogeneity and anisotropy is provided, resulting in a self-contained account about the reconstruction of arbitrary three-dimensional, weakly anisotropic dielectric tensor fields.

Measurement of residual stress in multicrystalline silicon ribbons by a self-calibrating infrared photoelastic method

Abstract: This article reports on a method for the measurement of residual stress in multicrystalline silicon ribbons, based on the infrared photoelastic technique. This self-calibrating method allows the in situ determination of the photoelastic coefficients and can thus be used for any crystal orientation. The method was validated by the experimental determination of the photoelastic coefficient of monocrystalline (100) silicon wafers and by comparison with strain measurements using asymmetrical x-ray diffraction. The distribution of residual stress in multicrystalline silicon ribbons was also measured. The results showed strong evidence for tensile stress in the central region and compressive stress near the edges of the ribbons. Both the measured residual stress and the photoelastic coefficient distributions are correlated to grain boundaries.

Three-dimensional investigation of thick single-lap bolted joints

Abstract: Stresses in single-lap bolted joints of thick plates are complex and difficult to analyze. Previous studies involving stresses through the thickness of bolted joints have been limited to finite element method (FEM) simulations and have been implemented only for the joining of relatively thin plates. In this paper we report on several experimental and numerical analyses that were conducted to evaluate the stress distribution inside thick bolted plates along the bearing plane normal to the plate surface. Experimental analysis was conducted via embedded-polariscope photoelasticity and embedded resistance strain gages. The FEM analysis was performed with the ABAQUS commercial code using material properties and other data obtained experimentally as input. Experimental and numerical results agreed reasonably well, and are believed to depict the behavior of the joint under load well enough to assist in development of improved joint design.

Full-Field Determination of Principal-Stress Directions Using Photoelasticity with Plane-Polarized RGB Lights

Abstract: In this paper, we propose a new three-wavelength method for automatic measurement of principal-stress directions over an entire model on the basis of four-step phase shift method. This method uses four fringe patterns captured by a color charge-coupled devices (CCD) camera corresponding to four angular position arrangements of polaroids in a dark-field plane polariscope. The principal-stress directions can be determined by a single calculation. The method is applied to a circular disc under compression. The principal-stress direction distributions obtained from the proposed method are compared with those obtained from a conventional method and theory. It can be obviously seen that the proposed method accurately yields the principal-stress directions compared with the conventional method.

Photoelastic analysis of matrix stresses around a high modulus sapphire fibre by means of phase-stepping automated polariscope

Abstract: The matrix stress field has been quantified and the micromechanics of fragmentation of sapphire fibres in an epoxy matrix have been investigated using phase-stepping photoelasticity and fluorescence spectroscopy. Contour maps of the isochromatic fringe order (related to the difference in principal stresses) have been used to describe in detail the changes in matrix stress field during stress transfer in the presence of a matrix crack and interfacial debonding. The profiles of interfacial shear stress at various levels of applied matrix stress indicate clearly the extent of interfacial debonding. The results show that the matrix crack significantly reduces the efficiency of stress transfer at the interface. The frictional shear stress at the debonded interface has been found experimentally to be 3–10 MPa for a sapphire fibre embedded in the LY5052/HY5052 epoxy system. The relationship between interfacial shear stress and axial fibre stress is discussed. The interfacial shear stress profiles obtained from photoelasticity has been compared to that calculated from the axial fibre stress measured by shifts in fluorescence spectral bands.

Experimental study of the load distribution in bearings by the method of caustics and the photoelasticity method

Abstract: In this paper the theoretical consideration of the caustics and the photoelasticity due to a concentrated load applied at a point of the straight boundary of the semi-infinite plate was studied. Then, the load distribution in a roller bearing was experimentally determined in terms of caustics and photoelasticity.

Principal formulas of integrated photoelasticity in terms of characteristic parameters

Abstract: Recent advances in integrated photoelasticity have opened the possibility of determining tomographically arbitrary three-dimensional stress fields. Since photoelastic tomography is based on experimental measurement of the characteristic parameters, the dependence of these parameters on the stress distribution on a light ray is considered in detail. The possibility of determining certain integrals of the stress components is analyzed, and the linear approximation of integrated photoelasticity has been rigorously treated.

Phase-stepping photoelasticity for quantifying the interfacial response in fibre composites at fibre-breaks

Abstract: A phase-stepping photoelastic technique has been used to study the fragmentation of E-glass fibre and evaluate quantitatively the effect of an interphase region on interfacial shear strength at a fibre-break and hence the efficiency of the interfacial bond. To investigate the interfacial response of an E-glass fibre in the presence of a soft interphase, it was coated with an epoxy resin of lower Young's modulus and yield strength than that of the matrix resin. This enables the effect of a sizing or modified matrix region to be quantified. The micro-mechanical response in the matrix at the interface/interphase has been described in detail using contour maps of fringe order. From these, the profile of the interfacial shear stress at fibre-breaks has been calculated, which demonstrated that in this cold-cured epoxy resin a good interface formed with uncoupled and unsized E-glass. In the presence of a modified matrix or interphase region the stress transfer process was modified and the stress concentration associated with a transverse crack reduced.

Digital shifting photoelasticity with optical enlarged unwrapping technology for local stress measurement

Abstract: In this paper, photoelasticity combined with phase shifting technology is used to obtain stress distribution within the stress concentration zone. Both the optical enlarged unwrapping technology and the combined path shear difference technology are provided for evaluating the local stress information. By means of a phase shifting photoelastic experiment of a diametric-compressed disc, the stress components surrounding the local loading zone are determined. The results show not only a good improvement compared with conventional photoelastic analysis but also a good agreement with theoretical data.

Dynamic photoelastic study of wave fields in elastic plates with stress concentrators

Abstract: The method of dynamic photoelasticity is used to study the dynamic failure of structural members in the form of plates with a curvilinear (circular or elliptic) hole and an isolated crack under impulsive loading. The time-dependences of the stress intensity factors and the crack tip velocity are investigated for two types of models

Measurement of Stokes Parameters by Quarter-Wave Plate and Polarizer

Abstract: Formulations of the theory of automated photoelasticity are expressed simply by use of the Stokes parameters. In the automated photoelasticity, the measurement of the total relative phase retardation must often be performed over a wide wavelength range. The Stokes parameters (S0, S1, S2 and S3) need to be measured over a wide wavelength range. The Stokes parameters of monochromatic light can be measured by the adjustable azimuth settings of a retarder and analyzer (ARA) method. When undertaking the measurement of the Stokes parameters of light of an arbitrary wavelength over a wide wavelength range, the measurement of S3 by the conventional ARA method is dependent on the phase difference error
ρ i of a quarter-wave plate mismatch as well as Stokes parameter S2. The measurement of S3 by a judicious choice of azimuth settings of a quarter-wave plate and a polarizer (JCAQP) as in the method proposed can be obtained by considering
ρ I . The JCAQP method is clarified by employing the Poincare sphere. It is shown that application of the JCAQP method yields the principal axis and the relative phase retardation of the birefringent plate free from the
ρ i of the quarter-wave plate for incident elliptically polarized light of an arbitrary wavelength.

Developments in RGB Photoelasticity

Abstract: In this paper the combined use of both RGB and phase stepping photoelasticity is proposed. The method is characterised by the following features: maximum measurable order greater than that of the RGB method, ability to determine the total fringe order without necessity of unwrapping.

Laser-induced stress changes in optical fibers

Abstract: The precise determination of residual stress profiles in optical fibers allows drawing conclusions about radiation-induced density-changes of the fibers doped core glass. The corresponding index changes partially contribute to the phenomenon of photosensitivity, i.e. the modification of the refractive index of a glass through the irradiation with an appropriate laser source. Photosensitivity is widely exploited for the fabrication of fiber Bragg gratings which are in-fiber filter devices whose spectral response can be designed with great versatility. Fiber Bragg gratings find broad application nowadays in the field of telecommunication as well as in sensing applications. The polarimetric assessment of the integrated transverse fiber birefringence serves as a means to gather information about both stress and strain profiles of the fiber. Birefringence is introduced in the optical fiber due to the photo-elastic effect. In this work, a highly sensitive polariscope with sub-micron resolution has been developed. The captured birefringence data has been interpreted to be basically strain and not stress-induced, which allowed the proper discrimination between an inelastic, stress-free strain contribution and a strain part essentially accompanied by elastic stress. In earlier interpretations of the polarimetric data, all birefringence had been attributed to be purely stress-induced, which excluded the existence of inelastic strain and even led to contradictory results in some cases. The reinterpretation in terms of strain, however, results in a consistent picture of both stress and strain-induced birefringence. The polariscope has been used in the following to determine radiation-induced stress changes for different optical fibers and irradiation sources. Femtosecond-laser induced core stress changes in SMF-28® standard telecommunication fibers have been measured tomographically and correlated with corresponding index changes. Furthermore, stress has been correlated to the refractive index change in highly germanium-doped fibers irradiated with cw-irradiation at 244 nm. The annealing behavior of stress, strain and index in this fiber has been studied. Approximately the same linear correlation between stress and index change was found for all germanium-doped fibers under investigation. In addition, stress changes were measured for phosphorus- and nitrogen-doped fibers drawn at different tensions before and after irradiation with an ArF excimer-laser. The impact of the drawing force on fiber stress and inelastic strain anisotropy has been determined as well as radiation-induced stress modifications. The observed stress increase has been compared to those obtained for germanium-doped fibers. Atomic Force Microscopy of cleaved and subsequently etched fiber end-faces is a powerful means to gather topographic information on a nanometer scale due to differential etching of the doped core and the undoped silica cladding. Within this work, the technique has been used to acquire information about etch rate changes in fibers drawn from the same nitrogen-doped preform with different drawing conditions. Furthermore, the impact of UV-irradiation on the etch rate has been determined for phosphorus- as well as nitrogen-doped fibers. Comparison of the results, with stress measurements allowed the attribution of the etch rate changes to a modification of the color center population.

Investigation of the stress field of a near-surface circular hole

Abstract: By observing experimentally obtained photoelastic fringe patterns and applying classical solutions for an infinite plate containing a circular hole under remote tension and the modified Hertz contact theory, a replaced superposition method is proposed. In this paper we use this method to investigate the state of stress around a near-surface circular hole in a semi-infinite plate under a concentrated load. The well-matched conditions between the reconstructed and experimental photoelastic fringe patterns indicate the applicability of the proposed method.

Use of automated photoelasticity to determine stress intensity factors of bimaterial joints

Abstract: A new systematic experimental procedure has been developed to obtain the stress intensity factors governing the singular stress field that occurs near the intersection between the interface and free edges of bimaterial joints. A preliminary theoretical study of the singular stress field is carried out by the well-known Airy stress function method. The obtained stress laws are properly combined with the basic law of photoelasticity in order to define a procedure that permits the zone dominated by the singularity to be located and the stress intensity factors (SIFs) to be computed on the basis of full field data provided from automated photoelasticity. In particular, a systematic error analysis is used to determine the model zone where the experimental data have to be collected in order to obtain accurate SIF evaluation. As an example, the proposed method is applied to determine the SIFs of various aluminium/ PSM-1 specimens under different external loading conditions using Fourier transform photoelasticity...

InP acoustic cavity phonon spectra probed by Raman scattering

Abstract: We present a Raman scattering study of the phonon spectra of an InP acoustic phonon cavity. ${\mathrm{Ga}}_{0.47}{\mathrm{In}}_{0.53}\mathrm{As}∕{\mathrm{Al}}_{0.48}{\mathrm{In}}_{0.52}\mathrm{As}$ phonon mirrors, lattice matched with InP, are used for the acoustic phonon confinement. High-resolution backscattering Raman measurements evidence a doubling of the folded acoustic phonon spectra. Photoelastic model calculations, with a continuum model for the acoustic vibrations that include the appropriate boundary conditions at the structure-air interface, are presented to interpret the data. The Raman spectra are shown to be highly sensitive to the details of the structure, thus allowing a proper characterization of the device. We found that the InP cavity longitudinal optical phonon linewidth is increased by residual strain and disorder, but that the anharmonic contribution is substantial at room temperature. This implies that acoustic cavities could be used for optical phonon decay time engineering in InP optoelectronic devices.

Optimization of Defense Hole System for Biaxial Loaded Plate with Three Coaxial Holes

Abstract: Optimum design of elliptical Defense Hole System (DHS) under biaxial loading in a finite plate with a row of circular holes is presented. Maximum stress reduction is made possible by introducing elliptical auxiliary holes close to the mainmain holes in the areas of low stresses along the principal stress direction. A systematic study is undertaken by using the finite element analysis (FEA) to determine the optimum shape, location and size of the auxiliary defense hole system. These parameters are examined in relation to plate dimensions for a number of plates with different mainmain-hole-diameter to plate-width ratios and different pitch to main-hole-diameter ratios. Maximum stress reductions from 6–18% were achieved. With such reduction in the maximum stress level the improvement in fatigue life of a structural part can be very significant. The FEA results are validated experimentally by applying an enhanced RGB- photoelasticity technique. The photoelasticity experimental results and the FEA results show...

On interpretation of fringe patterns produced by time average photoelasticity

Abstract: Photoelasticity 1,2 is a classical optical technique for static stress analysis. Time average photoelasticity would be of interest in some application areas. The subject of the current analysis is not dynamic photoelasticity3 where a set of slides is photographed during the dynamic process. It is time average photoelasticity where one picture is formed averaging over the whole dynamic process. An example of potential application could be in ultrasonic motors4 where the interaction between elastic vibrating elements plays a key role in the dynamic behavior of the system. Stroboscopic illumination1 can be used for photoelastic analysis of vibrating components. An alternative technique to stroboscopic illumination is the time averaging procedure which could be used for direct interpretation of time averaged patterns of photoelastic fringes. As viscoelastic material behavior can take place at higher frequencies of oscillation, such effects need to be evaluated.

An overdetermined phase-stepping strategy for the capture of high-quality photoelastic data

Abstract: An overdetermined extension to the phase-stepping approach to digital photoelasticity is described in order to obtain high-quality photoelastic data for use in the examination of contact problems. ...

A photoelastic clinical study of the static load distribution at the stump/socket interface of PTB sockets.

Abstract: It is recognized that the assessment of prosthetic socket fit is based largely on the subjective clinical judgement of the prosthetist. This study assesses a novel technique, photoelasticity, for use as a tool for the qualitative and quantitative assessment of socket fit. Photoelasticity is a visual technique that produces contours of principal stress or strain differences. The colour and/or distance between the contours can be qualitatively or quantitatively assessed, using a polariscope, to give a full-field analysis of the stresses on the sockets's surface. This paper presents qualitative photoelastic socket surface contour data gathered during several prosthesis fitting sessions for two male trans-tibial amputees. Results are compared with the actual known contact regions at the stump/socket interface to determine if a relationship exists. This comparison of results has then been used to conclude the suitability of photoelasticity as a tool for the assessment of socket fit and recommendations are made as to the future developments of the technique. A direct relationship between the stump/socket contact regions and the qualitative photoelastic contours was demonstrated. Given further development this photoelastic technique may therefore be suitable for qualitative analysis of the interactions between the stump and prosthetic socket.

Complete Isochromatic Fringe-order Analysis in Digital Photoelasticity by Fourier Transform and Load Stepping

Abstract: In this paper, a new fully automated photoelastic technique based on both the Fourier transform and the envelope of the fringe centres, is presented. Using two images of the isochromatics acquired with different loads and a simple calculation routine, the method allows the user the complete determination of the isochromatic fringe retardation on any arbitrary line chosen over the model domain, without the need for supplementary external information or calibration. Various experiments have corroborated the accuracy of the method, estimated theoretically to about 0.07 fringe orders. As a result of its simplicity and sufficient accuracy, the method can be used in the industrial field also by a non-expert user.