Tricolor photoviscoelastic technique and its application to moving contact

A new technique for simultaneous determination of both fringe order and principal direction of birefringence in practical photoviscoelastic analysis using white incident light with a set of the primary colors, called tricolor photoviscoelasticity, is described. This method can determine both the fringe order and principal direction of birefringence from a single-color photoviscoelastic image under plane polarization. Then, the authors evaluate time dependent stresses and strains around a contact region in a viscoelastic strip plate under nonproportional loading condition. The variations of the principal stresses and strains are easily obtained over a wide time range by use of the optical constitutive equations of photoviscoelasticity and the characteristic material property functions.     

Experimental analysis of rolling contact stresses in a viscoelastic strip

An experimental approach to two-dimensional, viscoelastic, steadily moving rolling contact is described. The photoviscoelastic technique is employed for the analysis of rolling contact stresses between a viscoelastic plate and a rigid rolling cylinder in which the principal axes of stress, strain and birefringence are not coincident with each other. Using an elliptically polarized white light, the distribution of isochromatic fringe order and the principal axes of birefringence at an instant are determined from a single photoviscoelastic image. The time variations of the differences of the principal stresses and strains, as well as their directions, are obtained by use of the optical constitutive equations of photoviscoelasticity. The experimental results involving the time variation of the stresses around the contact surface and their distributions are analyzed.     

Time-dependent optical characterization in the photoviscoelastic study of stress-wave propagation

Dynamic photoviscoelastic analysis requires the time and temperature dependency of the material to be taken into account. Mechanical relaxation processes have generally been incorporated in dynamic analysis, but there has been no widespread application of optical relaxation or creep functions over the complete time spectrum in photomechanics of birefringent polymers. Using material characterizations previously developed, this study compares a theoretical viscoelastic solution and its predicted fringe patterns for stress-wave propagation in a thin rod of polyurethane material (Solithane 113) with the photoviscoelastic data from a similar experimental arrangement. The agreement demonstrates both the validity and general necessity of such an approach for the time-domain characteristic of wave-propagation phenomena in low-modulus polymers.     

A photoviscoelastic analysis of time-dependent stresses in a polyphase system

The method of photoviscoelastic stress analysis is used to predict time-dependent stress redistributions in a polyphase-material system having a viscoelastic binder and subjected to applied exteernal-loading conditions. The polyphase-material model studied is composed of a photoviscoelastic matrix material and contains rigid inclusions and voids, thus simulating a threephase composite system. In order to perform the study, a photoviscoelastic model material is developed. An epoxy-resin system consisting primarily of Shell Epon 828 and Epon 871, optimized to display the properties desirable for such application, is utilized. The time-dependent stess distributions obtained by the photoviscoelastic analysis are compared with results obtained by applying the “correspondence rule” to a finite-element solution for the elastic stress field of a mathematical model of the three-phase material system. The comparison of results indicates that the technique of photoviscoelastic stress analysis is extremely applicable to complex models such as the one studied. The feasibility of this application to more complex polyphase models with varying loading conditions is indicated.     

Photomechanical behavior of cellulose acetate under viscoelastoplastic deformation

To confirm the possibilities of cellulose acetate as a material for a model analysis during viscoelastoplastic deformation, the time-dependent photomechanical properties of the material were examined by means of creep tests under constant stress and recovery tests after removal of stress. Consequently, though the strain and the fringe order of cellulose acetate during creep and recovery are greatly influenced by stress and room temperature, both of them can be described simply by a power function of time, and the coefficient of each of these formulas can be represented by a function of the ratio of active stress to yield stress only. The effect of temperature is included in the formulation of the yield stress. In addition, the strain and the fringe order can be represented by the viscous-viscoelastic model proposed by Findleyet al.,^1,2 in which both of them are divided into four components: elastic, plastic, time-dependent irrecoverable viscous and time-dependent recoverable viscoelastic. The relation between viscoelastic strain and viscoelastic fringe order, and the relation between viscous strain and viscous fringe order were verified to be equivalent to that between plastic strain and plastic fringe order, all of which do not depend on stress, temperature or time. Therefore, the strain distribution of cellulose acetate under viscoelastoplastic deformation can be determined directly from the value of the fringe order measured.     

On the studies of residual stresses in glass plates

The theoretical foundation of the photoelastic methods being presently used for measuring and analyzing residual stresses in glass is insufficient for studying development of transient viscoelastic stress states in glass plates during tempering process and for an explanation of the actual material behavior. It is shown that the basic knowledge of photoviscoelastic effect in glass over a wide range of electromagnetic radiation and temperature is necessary for such on analysis. Some photoelastic properties of plate glass are presented.     

Fast quantitative processing of particle image velocimetry photographs by a whole-field filtering technique

A fast quantitative processing of particle image velocimetry photographs by a whole-field spatial filtering technique is described. Photographs are observed through a conventional filtering setup. This produces fringe patterned images with each fringe corresponding to a fixed value of one velocity component. These images are acquired with a CCD camera and digitally processed to retrieve the fringe centerline positions. The interpolation of these data provides the velocity value on a grid of regularly spaced points.Photographs taken from a Rayleigh-Bénard convective flow have been processed with this technique and with a previously reported point-by-point technique. Results from both techniques compare well.This work was supported by Diputación General de Aragón under Grant No. PCB6-90     

Image-processing techniques in laser-speckle photography with application to hybrid stress analysis

Six techniques for analyzing speckle halo fringes for fringe spacing and orientation using a digital image analyzer are presented. Each of the techniques were tested for range, accuracy, and computer run-time through analysis of a known case of rigid-body motion. Application of these techniques to two-dimensional hybrid stress analysis is described where speckle-displacement data around the high-stress region of a notched bar in tension is used as input data to a plane-stress finite-element program. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14, 1985.     

Optical and mechanical properties of birefringent polymers

The stress-strain behavior and corresponding birefringence of several polymers have been investigated within a limited range of temperatures (from ?65 to 70°F) and strain rates (from 0.0027 to 0.1613 sec^?1). One of these materials, a polyethylene resin, has been studied in more detail to ascertain the existence of a simple relationship between stress history, temperature, strain rate and birefringence. When the results were compared with the photoviscoelastic relations developed by E. H. Dill for a simple rheological material, it was concluded that the polyethylene tested does not completely satisfy this model. Polyethylene as well as the other materials investigated—nylon, a polyester, cellulose acetate butyrate, cellulose nitrate—exhibits a linear relation between birefringence and strain, independent of rate within the limits of the present experimental range.     

Characterization of photoviscoelastic materials by a nonlinear constitutive equation

On the basis of a phenomenological theory which is guided by the results on the macroscopic material behavior, a nonlinear constitutive equation is derived to characterize the photoviscoelastic behavior of homogeneous, isotropic, and nonaging amorphous plastics, including large deformations. It is shown how to determine four memory functions by running creep tests in pure tension and simple shear. The testing equipment and the methods of test evaluation are explained. Results are reported for some typical materials. They show how to simplify the basic equation for applications in the analysis of plane states of stress in polymeric structures under quasistatic isothermal loading conditions.     

Effects of imperfections on the buckling response of compression-loaded composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The results identify the effects of traditional and non-traditional initial imperfections on the non-linear response and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The non-traditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, non-uniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity non-linear shell analysis procedure that accurately accounts for the effects of these traditional and non-traditional imperfections on the non-linear responses and buckling loads of the shells is described. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable response characteristics.     

Determination of integral fringe order in photoelasticity

The paper describes a method to determine the integral fringe order associated with a fractional fringe value that is measured using Tardy or other similar compensators. The method makes use of two different wavelengths of light to determine the fractional fringe values. Further, it does not assume the independence of the material fringe constant on the wavelength of light used. From these measured fractional fringe values, the associated integral fringe order is determined. A method to construct a ready-reckoner table is also described which helps to identify the integral fringe order from any two measured fractional fringe values.     

A bonded polariscope for three-dimensional photoviscoelastic studies

A method of incorporating an internally bonded polariscope into a transparent model has been developed for use with viscoelastic materials. The newly developed technique serves to isolate one or more planes in a three-dimensional model so that a threedimensional photoviscoelastic analysis can be performed. The model may be subjected to a variety of loadings at room temperature, and only the photomechanical effects in the isolated plane will be observable. In the experimental program, a viscoelastic cement was developed whose mechanical properties matched those of a chosen model material. The cement was used to bond the polarizing sheet into the model. The restraining effect of the stiff elastic Polaroid sheet was reduced by cutting a gridwork of slits into this material. Tests performed on simple disk models and on star-grain rocket models containing bonded-polariscope elements showed structural continuity through the cemented joint. The fringe pattern observed through the bonded polariscope in star-grain models was the same as that observed using a conventional polariscope. On the basis of the favorable test results, the newly developed technique was judged acceptable.     

The interferometric strain gage

The interferometric strain gage consists of two very shallow grooves ruled on a highly polished surface. The grooves are cut with a diamond and are 4×10^?5 in. deep and 5×10^?3 in. apart. Coherent, monochromatic light from a He?Ne gas laser incident upon these grooves will produce fringe patterns. A fringe pattern with the fringes parallel to the grooves is formed on each side of the impinging beam. The position of these patterns in space is related to the distance between the two grooves. As this distance changes, the fringes shift. Measurement of these fringe shifts enables one to determine the local strain of the specimen. In this paper, the theory of the measurement is developed first. The strain, ∈, is given by ∈=ΔFλ/d _o sin α _o where ΔF is the average fringe shift of the two patterns, λ is the wavelength of light,d _o is the initial distance between grooves, and α _o is the angle between the incident light beam and the fringe patterns. A procedure for making static measurements with the interferometric strain gage is presented. The sensitivity for these measurements is 0.5 percent strain per fringe shift, and the maximum strain is 4 percent. The method is evaluated by comparing its results with other accepted means of measuring large plastic strain. These other techniques are: post-yield foil gages, a 2-in. clip gage, and an Instron testing machine. The average percent difference among these techniques is less than 0.4 percent based on a full-scale measurement of 4-percent strain. The interferometric strain gage has the following features: a gage integral with the specimen surface, a very short gage length, relatively easy application, and the ability to measure large strains.     

Inversion of speckle interferometer fringes for hole-drilling residual stress determinations

Speckle interferometric fringe patterns record stress-relief displacements induced by the drilling of blind-holes into prestressed objects. The quantitative determination of residual stress state from such stress patterns is difficult because of the ambiguity in the order of the observed fringes. The plane stress magnitudes are provided directly from selected fringe positions using a stochastic, iterative least squares minimization approach. The inversion requires prior knowledge of the experimental geometry and an appropriate uniaxial stress-relief displacement basis function derived from three-dimensional finite element calculations. Superpositioning of the rotated and scaled displacement basis functions allows the stress-relief relaxation for any biaxial state of stress to be determined. In this paper, fringe patterns were forward modeled from a large ensemble of calculated biaxial stress-relief displacement fields. Inversion of these noise-free fringe patterns reproduced the biaxial stresses with negligible error. Analysis of more realistic fringe patterns that include speckle noise gave stress magnitude errors that diminished rapidly with the number of selected points to better than 3 percent for 100 points. Sensitivity of the optical method is influenced by a number of factors, but the ensemble of model fringe patterns studied indicates that the stress magnitudes (nomalized with respect to the material's Young's modulus) from 3×10^–4 to 10^–2 can accurately be determined with visible laser radiation. The method is amenable to automation and can easily be extended to study near surface gradients in the residual stresses or applied to other optical recording techniques such as moiré and phase-shifting interferometry.     

Accuracy of heterodyne holographic strain and stress determination

The basic equations for the evaluation of surface displacement, strain and stress from holographic interferograms are derived. The object shape and the geometry of the optical setup are taken in to account. A corresponding computer program is described. Heterodyne holographic interferometry is used for fringe interpolation (better than 1/1000 of a fringe) to get sufficient accuracy and spatial resolution. Errors and accuracy of holographic strain and stress determination are discussed with the aid of the computer program. A cylindrical tube under pressure load is presented as a numerical example.     

Load carrying capacity of systems within a global safety perspective. Part I. Robustness of stable equilibria under imperfections

The problem of the practical stability of structures is addressed in a modern way by considering the effects of both static and dynamic perturbations. The major historical contributions, due to Euler, Koiter and Thompson, are reviewed and illustrated by an archetypal model permitting to highlight the main mechanical and dynamical points. It is found that a global approach is necessary for a reliable safety estimation, especially in the neighborhood of (static) critical loads. Considering that the admissible load threshold has to account for robustness to finite perturbations, the Koiter critical load must be lowered, obtaining the so called Thompson critical load. It is shown how these two thresholds share some properties (e.g., both depend in a sensitive way on imperfections, which must be known for practical calculations), while having a deep different meaning: the former is related to static imperfections, and requires only a local analysis, while the latter is related to dynamical imperfections, and requires a global analysis. It is shown that P^crit_Euler≥P^crit_Koiter≥P^crit_Thompson, i.e., that the advancement of knowledge leads to a lower estimation of the actual critical load.     

Photoviscoelastic analysis of thermal stress in a quenched epoxy beam

This paper reports on a procedure for photoviscoelastic analysis where the axes of principal stress, principal strain and polarization of light coincide in the presence of a large temperature change. More specially, the transient-thermal stress and strain due to stress in an epoxy beam subjected to quenching from both the upper and lower surfaces, are determined using the time-temperature-equivalent law for stress, strain and birefringence. The transient-thermal stress and strain in the beam were determined experimentally using hereditary integrations from the measurement of the transient temperature and birefringence due to the quenching of the beam. The transient thermal stress and strain were also calculated theoretically using the linear-viscoelastic theory. The experimentally determined thermal stress agrees closely with the theoretical results. The experimentally determined strain agrees qualitatively with the theoretical values. Thus, it is concluded that the photoviscoelastic technique is useful in analyzing the proposed problem.Paper was presented at 1982 SESA/JSME Spring Meeting held in Maui and Oahu, HI on May 23–28, 1982.     

Ein nichtlineares Stoffgesetz für die ebene photoviskoelastische Spannungsanalyse

On the basis of a phenomenological theory of photoviscoelasticity which is guided by the results on the macroscopic behaviour of materials, nonlinear constitutive equations in the form of a single-integral representation are derived, being valid for homogeneous, isotropic, and non-aging, amorphous plastics, including large deformations. They yield the basic equations of two-dimensional nonlinear photoviscoelasticity which are used for the experimental analysis of plane states of stresses in polymeric structures under static or quasistatic isothermal loading. The example of an unsaturated polyester material labeled Leguval E 81 shows how to determine the material functions in the constitutive equations. The results allow us to make some simplifications which reduce the amount of numerical calculations when applying the proposed non-linear photoviscoelastic method.     

A fringe-compensation technique for stress analysis by reflection holographic interferometry

The use of holographic interferometry for stress analysis of nontransparent objects is limited by rigid-body displacements of the object. These displacements can alter the fringe patterns and often cause the fringes to disappear completely. A technique of compensation for this deterioration of the fringe pattern forreal-time holographic interferometry is described in this paper. It is especially designed to permit the accurate measurement of the out-of-plane component of strain near regions of stress concentration in plates that are subjected to in-plane loading. It is first shown that the fringes caused by a pure rigid-body displacement can be eliminated almost completely by translations of the hologram and rotation of the illumination wave. This procedure is first described when the displacement is known; then when it is unknown. A method to estimate the error made in the correction is presented. In actual stress-analysis problems, the object is both rigidly displaced and strained. Assuming the rigid displacement is known and corrected as previously, the analysis is developed to relate the fringe pattern to the strain-related displacement. This analysis takes into account the optical modifications of the system that are necessary to achieve the rigid-body-displacement correction. When the rigid-body displacement is unknown, the method is shown still to be workable through the use of various symmetries and boundary conditions. Two sample interferograms are presented as illustrations. Quantitative treatment of data from one of these are presented in a companion paper.