Showing papers on "Photoelasticity published in 1987"

Experimental investigation of wave velocity and dynamic contact stresses in an assembly of disks

Abstract: Dynamic photoelasticity and strain-gage techniques are employed to study wave propagation and dynamic load transfer in granular media. The granular medium is modeled as one- and two-dimensional deterministic and random arrays of circular disks of polyester material Homalite 100. The dynamic loading is achieved by explosive excitation. The experimental data are analyzed to determine the wave velocities, to identify the characteristic load transfer paths, and to quantitatively obtain the dynamic contact forces in the granular assembly. It is observed that the wave-propagation and dynamic-load-transfer phenomenon depends on the disk diameter and the obliqueness and flexibility of the load-transfer paths. The wave speed drops significantly in the first few granules after which the decay is more gradual. The load transter is characterized by the contact length and the friction between the contacting granules. The peak loads drop as the distance of the contact points from the point of explosive loading increases. For two-dimensional wave propagation, the load-transfer paths and the magnitude of contacting forces depend on the angles made by the normals of the contacting disks at the contact point.

Basic theory and experimental techniques of the strain-gradient method

Abstract: The theories of presently used experimental methods of stress and deformation analysis which employ radiant energy as a detector are based on the assumption that light propagates rectilinearly within both undeformed and deformed bodies which are initially homogeneous and isotropic when diffraction phenomena are negligible. This assumption is not correct: light propagation within deformed bodies is nonrectilinear in a general case. Although this has already been observed and applied practically by some researchers in photoelasticity, it has not so far been generally acknowledged and accepted in experimental mechanics. On the basis of empirical data produced by the authors in the period 1948–1983, we present theories and foundations of the techniques of a new experimental method which is based on the relations between stress/strain gradients and curvatures of light beams. This method is called the strain-gradient method or, less rigorously, gradient photoelasticity.

Residual stress effects on refractive indices in undoped silica‐core single‐mode fibers

Abstract: It is reported for the first time that refractive indices are reduced remarkably by residual stress in undoped silica‐core/fluorine‐doped silica‐clad single‐mode fibers. The very high residual stress concentrated at the small diameter core is induced by drawing tension because of the difference in viscosity between the core and cladding. The decrease in refractive indices results from photoelastic effects due to residual stress in the core.

Use of photoelasticity to determine orthotropicK I stress-intensity factor

Abstract: A new experimental method of obtaining orthotropic stress-intensity factor,K I , is presented. The orthotropic photoelasticity and orthotropic linear-elastic fracture-mechanics laws are combined. The combined set of equations is used along with half-fringe photoelasticity to determineK I in a compact-tension specimen made of a transparent unidirectional fiberglass-epoxy material. The results are compared with finite-element-method solutions.

On The Use Of Photoelasticity And Some Numerical Methods

Abstract: Photoelasticity has been used recently by the authors to conduct many tests related to the determination of stresses in the field of tall beams, and to the optimization of those beams. Numerical methods (in particular finite-elements, and solutions of Laplace's equations) have also been used to supplement or to verify the results obtained photoelastically. The opportunity seems appropriate to weigh some of the advantages and limitations of the methods used. Photoelasticity gives readily the field solution of Tmax. An approximate method can be used to obtain normal stresses using equilibrium conditions and photoelastic data. The photoelastic test can also be used to determine the boundary conditions, or part of them when they are not known, as in the case of many hyperstatic structures. The complete and precise knowledge of the boundary conditions is not always necessary. Numerical solution of Laplace's equation which corresponds to the sum of the principal stresses can be obtained easily for the whole field with the computer. Knowledge of boundary condition is necessary. Complete solution in terms of individual principal stresses can be obtained using finite-elements. Knowledge of boundary conditions is necessary. When gradients are high, the size of the elements must be small which may require longer time in the computer. The decision on what method to use depends to a large extent on 1) The availability of a photoelastic laboratory; 2) The availability of a computer and the program; 3) The availability of personnel with the necessary experience; 4) The knowledge, or lack of knowledge of all the boundary conditions.

Apparatus for measuring photoelasticity

Abstract: An apparatus for measuring photoelasticity permitting to control mechanical stress applied to an elastic body, by visualizing phase differences of polarized light transmitted by the elastic body is disclosed. In such a prior art apparatus a quarter wavelength plate was used in order to obtain circularly polarized light. However, the precision of the circularly polarized light is worsened, when it works in a wide wavelength region. To the contrary, in an apparatus according to this invention, circularly polarized light is obtained by means of Fresnel's rhombic body. As the result good circularly polarized light can be obtained for a wide wavelength region from the visible region to the near infrared region and control of products including thin films and semiconductor substrates can be effected by visualizing mechanical stress therein.

Transmission photoelasticity of centrally loaded generally and specially orthotropic beams

Abstract: Transmission photoelastic patterns for generally and specially orthotropic beams and an isotropic beam are presented. Theoretical isochromatic and isoclinic results for these beams, calculated from classical elasticity stress equations and stress-optic laws, are also presented and compared with experiment. The agreement between the theory and experiment is excellent. For the orthotropic beams, a stressoptic law which accounts for the effects of residual birefringence was used. The residual birefringence observed for the composite used in this study is greater than one fringe order and results from a matrix residual tension which is about one fourth of the resin's ultimate tensile strength. Finally, the influence of such a large residual birefringence on beam and calibration photoelastic data is discussed in detail.

New Computer Automated Holo-Photoelastic Method For Measuring Planar Principal Stress Magnitudes And Orientation

Abstract: A complete experimental determination of the stress and strain fields in an arbitrary deformed structure is generally unavailable. However, for two dimensional elasticity problems, such determinations are possible since in those cases one needs only to solve for three stresses (two normal and one shear). In fact, such determinations have been conducted quite often. By using isochromatic and isoclinic photoelastic data, the shear difference and numerical iteration techniques (1) and the least squares techniques (2) have been successfully used for complete stress field determinations of two dimensional elasticity problems. Though the shear difference technique can be particularly sensitive to cumulative errors resulting from numerical integration, the least squares technique is not affected by this and appears to yield better accuracy. The methods just cited use both experimental data and one or more mechanics conditions(e.g., the equations of equilibrium) to determine the stress field. However, the stress field can also be obtained from experimental data alone for planar elasticity problems, if there is enough of it to solve for the three stresses. For example, the Moire* technique or the combination of isochromatic, isoclinic, and isopachic data (for transparent models) can be used for such determinations. Further, with the marriage of advanced image processing equipment to computers, such analyses using this type of data can be conveniently conducted. It is even possible that such analyses could be more accurate than those using the combined experimental/numerical techniques cited above. The purposes of this report are two fold: i) to describe a single apparatus for obtaining isochromatic, isopachic, and isoclinic results for complete stress field determinations of two dimensional transparent models, and ii) to compare experimental and theoretical stress field values for an antisymmetrically loaded beam obtained using that apparatus.© (1987) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Dynamic Photoelasticity and Its Application to Stress Wave Propagation, Fracture Mechanics and Fracture Control

Abstract: Since research in the field of dynamic photoelasticity was initiated by Tuzi(1) in 1928, there has been a continuous development of new and improved high-speed photographic systems. With the development of new higher speed films, more intense light sources, ingenious camera designs, and reliable electronic circuitry, continuous improvement has been made in the quality of the photographs of dynamic events with objects or images propagating at high velocity. Three different photographic systems have been specially adapted for application involving dynamic photomechanics which provide whole field representation of the data. All three of these systems may be considered adequate for photographing high-density fringe patterns propagating at velocities as high as 100,000 in/sec (2540 m/sec), but each system exhibits advantages and disadvantages.

The Image Photo-Carrier Theory And Its Application To The Determination Of Principal Stress Direction

Abstract: The image photo-carrier theory as a new technique in photomechanics is described in this paper. The idea of high frequence photo-carrier which can transform the photoelasticity fringe into moire fringe and the single phase carrier method are presented by the author. According to the idea as mentioned above the physics and mathematics relation between the principal stress direction and moire fringe obtained from photo-carrier is established. The photo-carrier possesses some special functions which make it possible to determine automatically the fringe order and the fractional fringe value by the image processing system, in consequence of which provides an effective technique for collection and processing automatization in photomechanics.

Digital Phase-Shifting Photoelasticity

Abstract: Digital phase-shifting photoelasticity 1)2) can be regarded as an extension of recently introduced computer-aided phase-shifting methods, the objective of which is the detection of one phase (e.g. 3)4)), to a two-phase problem. The two phases governing, in a general case, intensity distributions of photo-elastic patterns of planely stressed bodies are: relative retardation S(xl,x2), which is related to the difference of local principal stresses, and isoclinic parameter a(x1,x2), which describes the angular position of local principal axes belonging to principal stresses ai ?ooli. It is known from photoelastic point methods (compensation and ac-phase measurement techniques5)) that phase-shifting of photoelastic patterns is achieved by independent rotation of two polarizing components of a polariscope.

Measuring anisotropy in rocks using laser‐generated ultrasound

Abstract: Summary. Measurements using standard contacting piezoelectric transducers and non-contacting laser sources and detectors, have been investigated for the study of ultrasonic anisotropy in rocks. An ultrasonic polariscope has been constructed in order to obtain reproducible travel-time and amplitude nieasurements. Three case studies are described to demonstrate the apparatus. namely isotropic halite, anisotropic calcite and transversely anisotropic mudstune. A novel technique has been developed in order to construct pseudo-particle motion diagrams. to highlight shear-wave birefringence in rock samples using 2.25 MHz transducers. A pulsed laser has been used to generate compressional and shear waves for comparison with piezoelectric transducer results. The pulses generated by laser irradiation have many advantages for the study of velocity and attenuation anisotropy because of their known characteristics. broad bandwidth and high level of reproducibility. The use of a non-contacting laser source and detector eliminates the need for elaborate coupling agents. stress bonding or immersion techniques. Point-source and line-focusing of the laser beam provides ail indirect method of studying shear-wave polarization phenomena. Results from rotation of the line-focused laser beam and rotation of piezoelectric shear-wave transducers with respect to anisotropy, are compared for both velocity and amplitude phenomena in an anisotropic rock sample.

A new integrated photoelasticity method for axisymmetric stress distribution

Abstract: The general axisymmetric problem involves three photoelastic unknowns. Experiment yields two of these factors: the characteristic retardation and the characteristic direction. A third independent condition is thus required for the solution. Two cases for which this information can be easily obtained are considered here. They are the stress-frozen cases, i.e., μ=0.5, and some restricted cases of thermal stresses which obey the sum rule, i.e.,\(\sigma _r + \sigma _\theta = \sigma _z \). A new approach to the solution which involves expressing the radial displacement (the key factor in such analyses) and the shear stress as separate polynomials is presented. The results are compared with earlier solutions.

Static and dynamic photoelasticity and caustics, recent developments

Abstract: Contents: H. Aben: Integrated photoelasticity and its applications.- A. Lagarde: Modern nondestructive methods of coherent light photoelasticity with applications in two- and three-dimensional problems in statics, contact stresses, fracture mechanics and dynamic impulse.- J.W. Dally: Dynamic photoelasticity and its application to stress wave propagation, fracture mechanics and fracture control.- J.F. Kalthoff: The shadow optical method of caustics.

Dynamic Contact of Solids — A Dynamic Photoelastic Investigation

Abstract: Dynamic photoelasticity and the method of caustics (or shadow-patterns) in conjunction with high-speed photography are utilized to study the dynamic contact of elastic bodies and surface wave propagation during impact. Sequences of experimentally recorded isochromatic fringe patterns and caustic shadow patteras allow for the determination of contact size, contact force as well as momentum and energy transfer across contacts.

Light intensity in 3-D photoelastic analysis

Abstract: Normalized minimum light intensity of a three-dimensional photoelastic medium, measured in a direct illumination polariscope by crossed arrangement of filters, is explored as a reliable characteristic quantity. The variation of the light intensity, for a given wavelength, resulting from superimposing non-coinciding co-planar bending and membrane stresses is studied as a function of their ratio. The graphical representation of this relation yields interesting novel information. This relation has been formulated in a mathematical model that might be used to determine the ratio for measured values of the light intensity. An additional independent experimental set of data can be obtained by carying the wavelength of the light source. It is shown that the quality and interpretation of the data so obtained is affected significantly by the selected wavelength. Furthermore, it appears that the discrete representation of photoelastic medium as a pile of birefringent plates is applicable only for low values of the stress ratio.

Determination Of Characteristic Parameters In Three Dimensional Photoelasticity

Abstract: In the process of determining the complete state of stress at a general point in a three dimensional photoelastic model (in a non-destructive or a semi-destructive manner), the concept of optically equivalent model plays a very important role. There are three parameters that define an optically equivalent model and these are termed as characteristic parameters. In this paper, first a survey is given of the direct and indirect methods used to determine the three characteristic parameters and then a new indirect method to deter-mine these parameters is presented. An algorithm has also been developed to determine the characteristic parameters unambiguously by the new method. The new method is verified experimentally and compared with theoretically determined characteristic parameters using Jones calculus.

Optical fiber measuring instrument

Abstract: PURPOSE:To prevent polarized wave fluctuation by an acoustooptical polariscope, from appearing as an uneven display on a display, by allowing a return light to go into the acoustooptic polariscope after passing through a magneto- optical element, and applying an alternating field to the magneto-optical element. CONSTITUTION:A magnetooptic element 13 is placed in a position where return light goes into an acoustooptic deflector 4 after passing through the magneto- optical element 13. When an alternating field of a prescribed frequency is applied to the magnetooptic element 13 by a driving circuit 14, a plane of polarization of the return light passing through the magneto-optical element 13 rotates in accordance with a period of the alternating field. A period of an optical pulse and a period of the alternating field are not synchronized, therefore, whenever the optical pulse is sent to an optical fiber 8, the plane of polarization of the return light rotates at random. In such a way, strength and weakness of a detecting signal of a photodiode 9 by a periodical rotation of the plane of polarization, based on the characteristic of the optical fiber 8 are not saved after an averaging addition processing, and accordingly, unevenness does not appear on a display 12.

Photoelastic modulator for the infrared.

Abstract: Polarization modulation has been widely used for about twenty years for the measurements of circular or linear dichroism, birefringence, rotatory power, and more recently for ellipsometric studies, e.g., in electrochemistry or for monitoring thin-film growth. This technique is also used now for high frequency (50 kHz) light chopping, which may be of interest for large diameter and large aperture beams as well as for laser beams. This modulation technique makes it necessary to use a birefringent modulator. Among such modulators, the Pockels cell which requires small aperture beams is no longer frequently used. By contrast, photoelas­ tic devices are now very popular since they accommodate large aperture beams, require only low voltages, and suffer optical misalignments. We describe here the extension of our previously developed design' for its use in the infrared region. By comparison with similar existing modulators, the setting up that we propose here is very easy to build and highly reliable, it exhibits no sizable parasitic birefringence and allows infrared light modulation to larger wavelengths. A photoelastic piece (P) of polycrystalhne ZnSe is mechan­ ically excited by two piezoelectric transducers (PZT) glued to P at the centers of two opposite faces [Fig. 1(a)]. The transducers, driven by an electric field applied alongy, oscil­ late along z and produce shear stresses which induce longitu­ dinal standing vibrations in P, at a mechanical eigenfrequency ƒ. Here P resonates in the fundamental Λ/2 longitudinal bulk mode; the dynamic stress and strain are shown in Fig. 1(a). In the same figure we show another design which enables the obtention of a higher stress, hence a modulation to higher wavelengths. This is realized by coupling the above piece with two identical silica blocks (b) by means of a soft adhe­ sive compound. Each silica block is itself excited by two piezoelectric ceramic transducers. All six transducers are then fed with such a frequency that the whole system oscil-

Method for measuring photoelasticity constant

Abstract: PURPOSE:To measure the photoelasticity constant of a matter to be measured with high accuracy, by irradiating the matter to be measured with two light waves crossing to each other at a right angle and having different frequencies and detecting the change in the beat signals of two light waves during the transmission through said matter. CONSTITUTION:Two light waves being linearily polarized lights crossing to each other at a right angle and having different frequencies are generated from a light source 1 and light pervious matte 2 as a test piece is irradiated with two light waves. Two light waves passing through the light pervious matter 2 are inputted to a phase shift detection circuit 5 through a polarizer 3 and a light detector 4. The phase shift detection circuit 5 measures the photoelasticity constant of the light pervious matter from the phase difference between the optical heat signals of two light waves during transmission and the optical heat signal of two light waves before transmission. By this method, the photoelasticity constant of the light pervious matter 2 can be measured with high accuracy without receiving the effect of external disturbance.

Half-Fringe Photoelastic Analysis Of Rectangular Plates Subjected To Transverse Loading

Abstract: The technique of half-fringe photoelasticity (HFP) was used to study the applicability of the thin plate theory for cantilever rectangular plates subjected to transverse loading. Results are presented and discussed with those obtained from the finite element method (FEM) for three cases including plates with and without discontinuities.

High-Sensitivity Photoelastic Pressure Sensor

Abstract: By selecting the proper geometry for the reactive element of a photoelastic sensor a considerable improvement in sensitivity over conventional intensity-modulated sensors can be achieved. Other recent photoelastic sensors have consisted of an essentially rectangular prismatic bar of transpqrnt material which is stressed uniformly by a strut connected to a force-summing diaphragml,L. Our alternative is to fabricate the diaphragm itself of a transparent material and use it for both the reactive and force-summing functions. In the basic form reported here the diaphragm consists of a thin glass plate mounted and sealed with zero residual stress on a circular support and subjected to varying differential pressure. Polarized light is directed into one edge of the plate along a diameter and received through an analyzer at the opposite edge. Analysis of the,resulting modulation in received optical power with crossed polarizers shows it to be a sin 4 function of applied differential pressure. The photoelastic phase delay is a linear function of pressure and parameters related to the geometry and material of the plate. For thin plates with maximum sen-sitivity the phase delay is proportional to the cube of the support radius and inversely proportional to the square of the plate thickness. An essentially linear response at zero pressure can be achieved with a quarter wave plate (thick sensor plates) or prestressing (thin sensor plates). Tests on experimental models have shown performance consistent with theory, with a response of 3.68 x 10-4 rad/pbar obtained with a 0.023 cm thick glass plate sealed on a 2.32 cm radius support. Extensive theoretical formulae and experimental data are presented.

A basic study of the plastic strain freezing by photoplastic experiment.

Abstract: It is difficult to solve the problem of stress-strain distribution in plastic regions in comparison with elastic bodies. Thus, an attempt to expand and apply stress- strain analysis by photoelasticity, with regard to polycarbonate resin in plastic photoelasticity, has been promoted so far and many significant achievements have resulted therefrom. This study is an examination of the possibilities of the plastic strain freezing method in comparison with the elastic stress freezing method. First, we attempted to determine the best temperature for plastic strain freezing. Further, it became apparent from systematic experimental results that it is 'strain' and not 'strain' which is frozen in plastic regions. In other words, it was made clear that the Birefringence N in strain freezing was proportional to difference in the principal strains (e1-e2).

Integrated Photoelasticity and Its Applications

Abstract: Main advantage of photoelasticity lies in the possibility to determine stresses also at internal points of a three-dimensional body. However, classical methods used for this purpose (the frozen stress and scattered light methods) are either labour-consuming or need complicated apparatus.

The Effect of Cracks on the Structural Strength of Beams and Portal Frames under Impact

Abstract: As a first stage into the study of the effect of cracks on the dynamic response of beams and portal frames, an elastic analysis is presented. The method combines dynamic photoelasticity with a computer program based on the finite difference formulation of the equations of elasticity. The method is compared to an analytical approach using the Timoshenko beam theory. It is concluded that a hybrid experimental/mathematical model is the most appropriate for practical purposes.

Applications Of Photoelasticity To Elasto-Dynamics

Abstract: The use of methods of experimental mechanics to study physical behavior in elasto-dynamic problems requires high speed photographic recording systems capable of storing images of optical fringe patterns where features often propagate at or above the dilatational wave velocity. This paper discusses the requirements of a very high speed recording system for the dynamic photomechanics class of experiments. The requirements include: exposure time, framing rate, field size, image size and light intensity. The design of a new Cranz-Schardin photographic recording system which has recently been completed at the University of Maryland is described in some detail. The camera system incorporates a novel spark gap design with a reflecting and focusing mirror and a fiber optic output. The fiber-optic bundle adds considerable flexibility in adapting the optical system to a large number of different experiments. The optical system has been designed for operation in both the transmission and reflection modes. In the transmission mode the system records conventional photoelastic fringe patterns, moire and caustic images of transparent media. In reflected light the specimen is mirrored and the system records fringe patterns from birefringent coatings, moire and caustic images from opaque materials.