Showing papers on "Photoelasticity published in 1974"

Acoustical birefringence and the use of ultrasonic waves for experimental stress analysis

Abstract: Stress-induced optical birefringence in transparent materials has long been a common technique of stress analysis. Although stress-induced acoustic birefringence was discovered more than 20 years ago, its development and actual applications are still limited. This paper will look at the similarities and differences between the propagation of light waves in photoelastic materials and the propagation of ultrasonic waves in deformed solids. Critical comparisons of the experimental methods employed in photoelasticity with those available in modern ultrasonic measuring technique show why previous studies on ultrasonic measurement of stresses were not very successful. A new experimental technique is devised for using ultrasonic waves for stress analysis. The technique employs a single rotatable 10-MHz shear transducer as the transmitter and receiver of ultrasonic pulses. The enlarged display of the 10-MHz modulated-pulse pattern of reflected echoes provides a convenient way to determine the directions of principal axis of the stress within ±3 deg. The pulse-echo-overlap method is used to measure the absolute velocities of the two principal shear waves. The difference in principal stresses is then calculated from the velocity measurements. Test results of common structural-aluminum and steel specimens under uniaxial compression show a linear relation between the velocity changes and the applied stress. Ultrasonic measurements of stress distribution in a 6.35-cm diameter, 1.9-cm-thick aluminum disk under diametric compression are also reported.

Differentiation, organogenesis, and the tectonics of cell wall orientation. ii. separation of stresses in a two‐dimensional model

Abstract: This paper describes a polarographic technique for the separation of tension and compression stresses in a two-dimensional plastic model of a sectioned cotton ovule. Compression and tension stress trajectories in the model comprise two families of lines which are mutually perpendicular and which, in the "nucellar" region of the model, coincide with cell wall patterns seen in sectioned ovules. This arrangement of stresses is demonstrated, by direct manipulation of the model, to be dependent on the pressure of the integuments. The integuments insure that compressive stresses generated during the growth of the nucellus do not collapse the embryo sac but pass around it, leaving it as a compression-free space within the growing ovule. THE TECHNIQUE of photoelastic stress analysis makes it possible to obtain relatively accurate information on the direction, magnitude, and sign of the principal stresses in an appropriately loaded plastic model. The technique is founded on the work of Sir David Brewster (1816) and relies on the property of certain otherwise isotropic materials which become birefringent under stress. Since at any point on a stressed two-dimensional model the two axes of maximum birefringence can be determined in polarized light, the direction of the two principal stresses can also be determined. A multiplicity of well-documented and easily applicable visual techniques exists in the literature on experimental stress analysis. Most of these techniques, including the use of birefringent coatings and brittle lacquers as well as the more commonly used three-dimensional techniques, such as frozen stress analysis, have been specificially developed for the evaluation of design prototypes and the localization of stress concentrations in critically loaded structures. Some of these techniques can be enhanced by the application of optical-fringe multiplication, which increases the accuracy of quantitative measurements severalfold. A variety of different materials is available for the construction of photoelastic models, including plastics of several kinds, epoxies, gelatin, and glass. These materials provide the experimenter with a variety of different Young's moduli, Poisson ratios, and stress-optical coefficients to work with, each with its own limitations and ad1 Received for publication 27 October 1972. The author wishes to express his thanks for the critical assistance and equipment provided by Dr. William Godden of the Department of Mechanical Engineering, University of California, Berkeley, and for the graphical assistance and encouragement of Mr. James Crawford. 2 Present address: Department of Biology, Stanford University, Stanford, California 94305. vantages. These techniques are well described and coherently presented with an extensive bibliography in Photoelasticity for Designers by R. B. Heywood (1969). For this investigation two-dimensional techniques were employed, since this provided the most direct analogy with two-dimensional sectioned material. There are several qualifications which should be placed on the mechanical analogy between living thin-walled plant tissue and a nearly perfectly elastic and homogeneous plastic, although in general the stress distribution in a model is unaffected by differences in Young's modulus and Poisson's ratio (Heywood, 1969). One of these qualifications is that the analogy only holds true for small amounts of stress which do not result in structural failure of the living tissue; and secondly, information derived from a two-dimensional sectional model can only be generalized to the three-dimensional case to the extent that the latter can be considered its volume of rotation. Despite these limitations, however, information which clarifies considerably the structure and the development of the cotton ovule and the role of the integuments in this process can be obtained from the two-dimensional model. MATERIALS AND METHODS-The shape of the plastic model was derived from a tracing of an axial section of an immature cotton ovule (Fig. 3) modified by rendering it symmetrical about its axis and eliminating space between the integuments due to specimen shrinkage. It can be considered to represent a generalized crassinucellate ovule. The outline was transferred to a sheet of 1/8 in. clear urethane plastic (Photolastic Inc. Malvern, Pa.). This is a rubbery material which is difficult to cut smoothly; after freezing in liquid

New automatic polariscope system

Abstract: Due to expanded use of experimental stress analysis, the need of automation of the data-collection system increased. The desirability of such a system is greatest in photoelasticity, where the information was collected visually, using time-consuming compensation methods.

Determination of stress-intensity factors from photoelastic data with applications to surface-flaw problems

Abstract: ATaylor-series correction to the maximum inplane shear stress was studied as a means of extending the data zone in photoelastic determination of stress-intensity factors beyond the singular region of a two-degree-of-freedom analysis. Convergence properties were obtained by comparing with several complete two-dimensional solutions. Experiments were performed on two kinds of three-dimensional problems, plates containing surface flows in both bending and extension. Results were analyzed by both a two-degree-of-freedom and aTaylor-series correction method (TSCM). Results were compared to theories of F. W. Smith and A. S. Kobayashi and R. C. Shah. It was concluded that:

An interferometric method for the direct evaluation of principal stresses in plane-stress fields

Abstract: If a monochromatic and coherent light beam is normally incident on a thin plate under generalized plane-stress conditions, it is analysed into two plane-polarized bundles, whose directions of oscillation coincide with the principal stress directions. The plane-polarized rays are retarded when traversing the plate according to the Neumann-Maxwell law. The absolute variations of the optical paths depend on the thickness and the refractive index variations. Interference of the two primary reflections from the front and rear faces of the plate yields a contour map of the thickness and refractive index in the unloaded state, while the variation of the interference pattern express the variations of these quantities due to loading. If the incident light is successively polarized along either of the principal directions, the interference pattern of the reflected light rays along each direction yields the values of principal stresses. Loading of the specimen creates a displacement of the interference fringes along the field. By counting the number of fringes passing across each point, we can evaluate separately the two principal stresses. This pointwise method is much more sensitive and accurate than classical photoelasticity, since it measures absolute variations of the optical path. The method was applied to a concrete problem of elasticity and compared with other similar methods.

Stress intensity factors for deep cracks emanating from the corner formed by a hole intersecting a plate surface

Abstract: The stress intensity factors (SIFs) at the end points of flaws emanating from the corner formed by the intersection of a plate with a hole were determined using stress freezing photoelasticity and a numerical technique known as the Taylor series correction method to extract the SIF values from the photoelastic data. The geometries studied were crack depth to thickness ratios of about 0.2, 0.5, and 0.75; crack depth to crack length ratios of about 1.0 to 2.0; and crack length to hole radius ratios of about 0.5 to 2.0. The SIFs were determined at the intersection of the flaw border with the plate surface (KS) and with the edge of the hole (KH). It is shown that extension of a crack emanating from a corner of intersection of a hole with a plate under monotonically increasing load is not self-similar and that as the flaw depth increases, KH decreases and KS increases. Existing theories and design criteria significantly overestimate the SIF at both the hole and the surface except for shallow flaws at the hole and deep flaws at the surface.

Distribution of local stresses across the thickness of cracked plates under bending fields

Abstract: A series of three-dimensional photoelastic experiments were conducted on plates containing through cracks which were loaded in bending with sufficient extension to prevent closure on the compressive side of the plate. Cracked plate geometries were selected so as to span the transitional “thin to thick” range. Slices were made parallel to the plate surfaces in the stress frozen material so as to remove the region around the crack tips. These slices were analyzed photoelastically and functions were evaluated experimentally corresponding to stress intensity factor distributions through the plate thickness. Results were compared with the theory of G. C. Sih. Agreement was excellent with theory for “thin” cracked plate geometries. For “thicker” cracked plate geometries results diverged progressively. For all cases studied, the use of a linear distribution of the stress intensity factor function through the plate thickness appeared to be satisfactory.

A scattered-light method in photoelasticity

Abstract: The birefringence and, thereby, the stresses in a photoelastic model are investigated utilizing the light scattered from a beam of light propagating through the model. The retardance from the entry point of the beam into the model to a certain point along the beam is expressed in terms of the intensity of the scattered light. The retardance for a short distance along the light path within the model is determined as a function of the total retardances from the entry point of the model to the two end points of the distance investigated. The effects of retarders and polarizers on the state of polarization of the light beam are treated by Mueller calculus. It is not necessary to make other assumptions than those made in the usual stress-freezing and slicing method.

Effects of impedance mismatch on the strength of waves in layered solids

Abstract: This research program was conducted to study the effects of acoustic-impedance mismatch between materials in a layered elastic solid on the amplitudes of the head waves generated at the interface as a stress wave develops and propagates in one of the layers. Dynamic photoelasticity methods were employed. The isochromatic-fringe patterns used for analysis were recorded with a Cranz-Schardin multiple-spark camera operating at a framing rate of approximately 188,000 exposures per second. Acoustic-impedance ratios from a low of 1.7∶1 to a high of 17.4∶1 were studied. Small charges of lead azide were used to generate the original dilatational (P 1) wave. Results of the study confirm the existence of all waves predicted by theory except for theP 1 P 1 waves reflected from the free surface and from the interface near the source in the low-impedance layer. In the region near the explosive detonation, the head waves are important since they have significant magnitudes for certain impedance ratios and they appear to attenuate at a rate much lower than the rate associated with the incidentP 1 wave or the reflectedP 1 S 1 waves.

A new method to increase the sensitivity of photoelasticity: A new method using the continuous relationship between fringe order and fringe density as recorded on film is proposed for whole-field interpolation of isochromatic-fringe patterns

Abstract: A method is proposed to read the isochromatic-fringe order continuously as a function of position. It utilizes the fact that the fringe order is a continuous function of the light intensity, which is converted into the density of a photographic negative and then traced out either by a microdensitometer or isodensitracer. Explicit relationship between the fringe order and the film density is obtained. Hundreds of points can be read between a half and an adjacent integral order. The method is whole field in nature and offers the possiblity of direct computer processing of photoelastic information.

Close-field optical analysis of an explosive-loading function - Dynamic photoelasticity methods were used to investigate the formation of a stress wave in a region very close to an explosive detonation in a two-dimensional model. Results provide an accurate description of the loading function for use in future analytical and experimental studies

Abstract: This research program was conducted to study the formation of a stress wave resulting from the detonation of an explosive charge in a circular hole in a large thin plate Dynamic photoelasticity methods were employed The isochromatic-fringe patterns were recorded with a Cranz-Schardin multiple-spark camera operating at a framing rate of 500,000 exposures/second Experimental procedures developed during the course of the investigation eliminated fracturing of the model in the vicinity of the explosive and permitted recording of the dynamic fringe patterns at the boundary of the hole during the entire period of loading

Photoelasticity with additional physical fields and optically active models

Abstract: The aim of the paper is to enlarge the class of three-dimensional stress distributions which can be investigated in a transmission polariscope. The experimental data are shown to contain more information about the stress distribution on the wave normal if the rotation of the principal axes or that of the plane of polarization is induced. This can be obtained by additional physical fields or by using optically active models. Three examples are described. First, an exact theory for investigating bending stresses in plates by the aid of prefrozen models has been developed and applied to evaluate the experimental data. Second, the application of the magnetophotoelastic method to determine stress-concentration factors by cylindrical bending of plates is considered. Third, a nonlinear stress distribution along the wave normal has been determined experimentally in an optically active model.

Instrumentation improvements for scattered-light photoelasticity: Devices and techniques are discussed for controlling the polarization of the incident beam and for studying the scattered-light fringes

Abstract: Devices which simplify the collection and improve the quality of scattered-light photoelastic data are described. These devices include electromechanically controlled optics for varying the polarization of the incident-light beam and a photometric scanner for observing the scattered-light fringes.

Holographic photoelasticity: Influences of inaccuracies of optical retarders on isochromatics and isopachics

Abstract: In this paper the influence of inaccuracies of the optical retarders on the isochromatic and isopachic fringes obtained by holographic photoelasticity is studied.For the single-exposure hologram it is shown that the isochromatic visibility decreases as for light- and dark-field configurations, whereas the isochromatic fringes are distorted only for the dark-field configuration.For the double-exposure hologram it is shown that the isopachic fringes are generally distorted; with the isochromatics there is a decrease of fringe visibility.Experimental results confirming the theory are reported.

Photoelastic Study of Stresses in Fabrics and Fabric-Like Structures:

Abstract: Photoelastic techniques were used to evaluate an assortment of materials to determine stress trajectories in fabrics, embedded fabrics, and embedding media. Photoelastic compounds were evaluated and molds, pressure injector-molding apparatus, a method of measuring stiffness, and a polariscope were developed. Photoelastic color change of monofilament yarns in fabrics, due to stress, was found to be related to fiber thickness and the Michel-Levy scale of birefringence. A method was discovered for evaluating the condition of clamping devices with respect to stress distribution in the specimen tested.

Time dependent variation of the deformation of a strip with circular hole under constant compressive load

Abstract: In the present paper, the deformation and stress state and their time dependent variation of a strip with circular hole of an elastic-viscoplastic material are investigated experimentally by using the photorheological method in the period from the instant of application of a constant compressive load to the static equilibrium state under the same load. As the result, it is made clear that the effect of viscosity of the material in the transient period is remarkable, and thus the deformation and stress state in the equilibrium state are quite different from those at the instant of loading. Deformation of the hole is measured in relation to time, which shows that the deformation during the transient period is far larger than that at the instant of loading. Moreover, the stress distribution in the minimum cross section of the strip and its time dependent variation are discussed in detail comparing with the existing data obtained by elastic theory or photoelasticity.

A Phenomenological Study of the Coincidence of Stress, Strain, and Birefringence Tensors in Rheologically Simple Materials

Abstract: The time‐dependent transient values of the stress, strain, and dielectric susceptibility tensors were measured in a circular disk made of a rheologically simple material and subjected to two equal pairs of diametric loads oriented at right angles. The instantaneous application or release of each pair of loads was programmed at different time intervals so that the loading configuration was suddenly transferred from a four‐load rheologic equilibrium situation to a transition state with only one pair of diametric loads. In this way the isotropic point (stress, strain, or birefringent) existing at the center of the disk for the four‐equal‐load configuration split into a pair of isotropic points moving along the diameter of the disk towards its circular boundary as the recovery process in the viscoelastic material developed. The velocities of movement of this pair of isotropic points along the diameter of the disk in the recovery process allowed the study of the phase lag between the stress, strain, and optical principal axes. The material chosen for the experiments was a strongly plasticized epoxy polymer, designated as C‐100‐60‐8, which presented a strong viscoelastic behavior at room temperature. However, the study extended along the whole viscoelastic spectrum of the material from its glassy to its rubbery state, by applying the principle of reduced variables. Important results were revealed for the mechanical and optical viscoelastic behavior of rheologically simple materials extensively used in photoelasticity.

Application of Holography to Photoelasticity

Abstract: The holographic image of a birefringent object is not transparent. The reconstructed image scene includes a three-dimensional distribution of visible interference effects, in addition to, and superposed upon the replicated array of illuminated object elements. This circumstance contains two reciprocally related implications which provide the theme of this discussion: (1) when the pattern of birefringence in the object space can be inferred from a knowledge of the interference display in the image space, a possible engineering application of holography is indicated. (2) on the other hand, when qualitative and/or quantitative features of the interference pattern can be inferred, given a known distribution of birefringence, then the operational rules which govern the apparatus, as an interferometer, are exhibited.

Use of the optical polarization method to model the states of stress of linings of underground structures in creeping rock

Abstract: In this article we propose a method of modeling the stresses under these conditions by means of optical polarization measurements We give the results of an investigation of circular linings in a two-layer medium with various viscoelastic properties Application of the optical polarization method to this problem must answer the following principal questions: a) How to choose or synthesize materials for the model with viscoelastic properties similar to those of the rocks, b) How to find the relation between the optical path difference and the stresses in the model c) How to establish similarity criteria and to find formulas for converting the stresses (deformations) of the model to those in the prototype Materials for the Models Since we were interested in the stresses in elastic linings due to creep deformation of the rocks, the model linings were made of the usual optically sensitive material ~D5-MTFA, used in the photoelasticity method Viscoelastic materials to simulate the properties of various rocks in conformity with the similarity conditions were synthesized on the basis of ~D-5 epoxy resin with low-viscosity Thiokol Materials based on the epoxy-thiokol compounds possess marked creep and stability and their properties can be varied over a wide range In the elastic linings of the models the difference between the principal stresses was found from the wellknown Wertheim equation,

Depolarization of Light Reflected from CdS and ZnO in the Exciton Region

Abstract: The method of photoelasticity is extended to the case of reflection in the region of optical resonances. Random strain fields in the crystals give rise to a large amount of depolarization of the reflected light near the resonances. Information about the crystal perfection is thus obtained, and magnitudes of the internal strains are derived.

The use of polymers for model investigations based on dynamic photoelasticity

Abstract: The possibility of taking the inelastic characteristics of polymeric and nonpolymeric materials into account in the photoelastic modeling of dynamical problems has been investigated. The proposed method is an approximate one based on the use of the Kelvin-Voigt model for both types of materials. The results of comparative experimental investigations of certain plane dynamical problems are presented and the experimental and theoretical data are compared.

Theory of Photoelasticity of Semiconducting Crystals

Abstract: A simplified extension of the empirical pseudopotential method is developed for calculation of the electronic contribution to the photoelasticity of semiconductors. Lattice contributions are calculated from the theory of Humphreys and Maradudin, by employing experimental phonon pressure dependence data to determine the microscopic interatomic potential and dipole moment of the crystal.