Determining isoclinics from fringe patterns

A procedure has been developed which imparts new flexibility and increased usefulness to the bonded-polariscope technique. It also may help to increase the precision of the shear-difference method of principal-stress separation by providing greater precision to the determination of principal-stress directions. The procedure involves bonding a uniaxially stress-frozen plate of model material into a model between Polaroid sheets to function as a bonded polariscope. The fringe data obtained under load provide information for determining the principal-stress directions throughout the model by solution of a simple algebraic relation which lends itself readily to accurate plotting for graphical analysis. The inherent precision should exceed that of isoclinic analysis, particularly in regions where indistinct isoclinics might be expected, since accuracy increases with loading. Accurate fringe-order data also can be obtained by plotting fringe order as a function of position. The basis for the procedure is the modification of the applied-stress field by the presence of the residual (frozen)-stress field. Furthermore, the frozen-fringe order combines with the fringes applied at room temperature as though both stress fields were applied at room temperature. Theory and experimental confirmation are presented, together with a sample principal-stress map which is compared with that obtained from theory, and also from isoclinics. In addition, the chart for rapid graphical solution is included.     

On the fiber-reinforced birefringent composite materials

The isochromatic and isoclinic parameters for fiber-reinforced birefringent materials are examined. Experimental results reveal residual birefringence and an initial isoclinic coincident with the axis of material symmetry. These preliminary data also indicate that the isoclinic angle is neither a measure of the principal strain nor the principal-stress directions within the composite.     

Strain-optic law for a certain class of birefringent composites

A strain-optic law for a certain class of birefringent fiber-reinforced composite materials is developed. The strain-optic law requires both mechanical and optical characterization of the material. Previous investigations have hypothesized the existence of three independent optical properties for the anisotropic birefringent material. The strain-optic relation developed in this study, however, requires only a single strain-optic coefficient, coupled with four independent mechanical material properties, for prediction of the optical response of a birefringent anisotropic material. Experimental results are presented which show good agreement with the developed strain-optic relation. Finally, the isoclinic parameter is investigated and preliminary evidence is presented which indicates a correspondence between principal-strain direction and optical isoclinic angle.     

An experimental investigation on isoclinic parameters in viscoelastoplastic materials under cyclic stresses

Photovisco-elastoplasticity has been developed and applied to various problems in nonlinear stress analysis as an extension of photoelasticity into nonlinear photomechanics. In photoelasticity, because stress is simply related to strain, isochromatics are proportional to either the principal stress difference or the principal strain difference and isoclinics indicate the directions of either principal stresses or principal strains separately. However, in photovisco-elastoplasticity, these optical responses are nonlinearly related to both stress and strain state simultaneously. Thus isochromatics are related nonlinearly with both the principal stress and strain differences. Isoclinics depend on the direction of principal strain as well as that of principal stress. Concerning now isoclinic parameter: according to the results of experiments performed by us for the deformation state where the directions of principal stress and strain do not coincide with one another, it has been found that isoclinic parameter moves gradually from the direction of principal stress to that of principal strain with increasing viscous deformation under constant stress. In the present research, extending our previous investigations, the behavior of isoclinic parameter has been examined experimentally under cyclic stressing, where the direction of principal stress changes alternately. In the course of an experiment, the variation of isoclinic parameter in relation to the number of cycles was measured together with the corresponding strain state on the thin-walled tubular specimen of celluloid softened by heating, subjected to combined loading conditions consisting of constant axial tension and cyclic torsion. The results obtained may be summarized as follows.

1. The cyclic-variation phase of isoclinic parameter lags behind the cyclic-variation phase of the direction of principal stress. The phase difference between these cyclic variations remains constant regardless of the number of cycles.
2. Isoclinic parameter has a value close to the direction of the principal stress within a range of a small number of cycles and decreases with an increase in the number of cycles. However, it does not approach the direction of principal strain but a value between the direction of the principal stress and that of the principal strain, with a certain constant ratio to them.

     

Theoretical analysis and digital photoelastic measurement of circular disks subjected to partially distributed compressions

The disk in diametral compression has been quoted most frequently on developing conventional/digital photoelasticity to illustrate new theories and experimental techniques for several decades. Theoretically, the compression as a concentrated force is more conducive to analysis, but it is impossible to achieve such loading condition experimentally. The distributed compression on a finite area at rim is relatively closer to actual testing and it is complicated to seek an analytical solution. In this paper, we extend the work of Hondros to derive the full-field stress distribution of disk subjected to diametral distributed compression in an explicit functional form. The principal stress difference and principal stress orientation related to isochromatic and isoclinic fringes, respectively, are also expressed in a simple closed form. The maximum shear stress for the whole disk and the validity of using isochromatic fringes to interpret the maximum shear stress are discussed in detail. The isoclinic fringes are compared with theory, and the fringe multiplication isochromatic is compared with simulated image. All of the comparisons are in good agreement with respect to full field.     

Digital image processing and isoclinics

Isoclinics contain very important information about the direction of principal stresses. Unfortunately, it is frequently found that the isoclinics are vague or vanish altogether in certain regions of a plate. The isoclinic lines representing stress direction and the isochromatic lines representing stress magnitude are superimposed on each other. It is extremely difficult to separate them and to get isoclinics.In 1985, Zhang and Su introduced the TX-1 digital-image-processing system and sought new ideas to track isoclinics. In 1986, Yao developed a new image-division method (IDV) which is easy to apply in the digital image processing techniques to track isoclinics. This paper introduces other new methods: an image-differentiation method (IDF) and an image-division and differentiation method (IDD), and discusses some image-processing techniques. Experiments with a disk in diametral compression and with a slice from a three-dimensional frozen model are used to demonstrate such methods.     

Determination of the stress distribution in assemblies of photoelastic particles

An optical measuring method and a calculation procedure for determining the distribution of the stress tensor in a plane-strained three-dimensional assembly of random-shaped photoelastic particles are described. The stress tensor at an arbitrary point of the model is determined by an integration procedure, based on the equations of equilibrium of stresses. The distribution of the principal-stress direction and the relative principal-stress difference and at least two normal stresses in a plane have to be known to perform the integration. The distribution of the principal-stress directions and their difference are measured optically by scanning the model with an optical filter system with a single rotating polarizer.     

Photoelastic Stress Analysis by Use of Hybrid Technique and Fringe Phase Shifting Method

0Introduction Photoelasticityisanopticalmeasurementmethodforstressanalysis.Itcanperformwhole field measurementduetotwo dimensionalsignalprocessingoflight.Alsoitcanperformnon contact measurementbecauseoftransmissionorreflectionoflightonaspecimen.Photoelast…     

Extension of oblique-incidence method to photo-orthotropic elasticity

With the interpretation of isochromatic and isoclinic fringes in transparent, birefringent, orthotropic composites established, efforts have been in progress to determine the-individual values of the principal stresses or strains. Several methods have recently been proposed. Some of them utilize the photoelastic results only partially and rely on numerical procedures. Others have attempted to obtain the required information based entirely on experimental data. In this paper, the classical oblique-incidence technique is applied to transversely isotropic-birefringent composites. The proposed extension is verified by applying it to the problem of an orthotropic half-plane subjected to an edge-load.     

Rectilinear and circular analysis of a plane slice optically isolated in a three-dimensional photoelastic model

Because of the coherence of scattered light, it is possible to produce a speckle image from a plane beam of light passing through a transparent model. When two plane parallel beams of light are transmitted through the model the slice between the beams is then optically isolated. The two speckle patterns corresponding to the two beams are superposed and provide optical data relative to the slice (principal stress directions, birefrengence), the data being collected on high contrast photographic plates or by optical filtering to obtain the square of the contrast. The isoclinic and isochromatic fringes are shown to exist. The concepts of rectilinear or circular analysis are extended to the observation of a plane slice in a three-dimensional model without freezing or cutting the model.     

Limitation of fourier transform photoelasticity: Influence of isoclinics

The application of the Fourier transform to photoelasticity was used in the evaluation of the retardation using a carrier system of fringes. In photoelasticity, the light intensity from the analyzer in a circular polariscope depends on both the retardation (isochromatics) and the isoclinic parameter. The theoretical analysis shows that the angle between the principal stresses in the model and in the carrier system of fringes influences the evaluation of the retardation (isochromatics), as occurs when misaligned compensators (namely, Babinet) are used. As a consequence, this method may not be applied as a full-field technique, although the error is small if the angle between the principal stresses in the model and in the carrier is less than 25 deg. Numerical simulations and experimental tests were conducted to corroborate this prediction.     

Measurement of mechanical vibration damping in orthotropic,composite and isotropic plates based on a continuous system analysis

The problem of free and forced transverse vibration of an orthotropic, composite, and isotropic thin square plates with uniformly distributed damping and simply supported boundary conditions has been solved, using a modal expansion technique. A load of the type P₀cosΩt applied at the center of plate has been considered and the phase angle between the forcing function and the vibration response at the center, as a function of the forcing frequency and the damping parameter determined. This theoretical relationship together with the experimentally measured phase angle between the applied mechanical forcing and the resulting vibration response at various forcing frequencies was used to determine an equivalent viscous damping parameter. This technique has been found to be particularly useful for the measurement and comparison of the relative damping in composite or orthotropic materials. Also, a theoretical relation for the energy loss due to viscous damping in vibrating plates has been developed and the theoretical energy loss at various frequencies has been compared with the experimentally measured energy loss at the same frequencies. Typical damping results are presented for aluminum, steel and aluminum/graphite-fiber composite materials.     

Accuracy of compensation methods in photoelastic fringe-order measurements

A complete photoelastic stress analysis depends, in the majority of cases, on the accuracy of the fractional-fringe-order measurements. The error involved due to an error in the measurement of the isoclinic angle has been studied. It was found that the Tardy method was more accurate than the Sénarmont method, assuming negligible errors in the optical elements.     

A new application of differential interferometry for stress analysis

In the past, differential interferometry has found interesting applications in gas dynamics. The gradients of density could be measured in gas flows. Now, a first trial is made to extend this method to the experimental treatment of stress problems. A Wollaston prism with polarizing elements is used in the optical arrangement. This prism combines two beams of light which have penetrated the model at locally separated points. A field of interference fringes can be produced behind the Wollaston prism. The deflections of the different conjugated light beams, which are caused by the deformed elements of the model, lead to a shifting of the interference fringes. A Stress Differential-interferometer Law is derived theoretically in order to interpret the optical data According to this theory, the optical effect caused by the deflection in this arrangement is proportional to the gradient of the sum of principal stresses. A calibration test is performed by using a circular disk, this method is applied to a circular ring for measuring the stress gradients. Under special conditions, interference fringes could be produced which represent the loci of equal stress gradient. Plexiglas plane models are loaded diametrically by single loads. The experimental results verify the statements of the developed theory.     

Full-field isopachic generation in photoelastic coatings

A method has been developed for the generation of isopachic fringes in photoelastic coatings. This method requires that the front (outer) surface of the coating be deposited with a thin metallic film to increase the front-surface reflellctivity. The light which penetrotes the photoelastic coating reflects from the rear surface, emerges from the front surface and then combines with the frontsurface reflection to yield a system of “carrier” fringes. When the model is loaded, the carrier-fringer system is modulated by the principal-strain sums and the principalstrain differences. Superposition of the modulate carrierfringer system with the original one (by double exposure or by superposition) yields isopachic and isochromatic fringes. The isochromatics can be suppressed by proper selection of the photoelastic material to yield only isopachics for the unambiguous determination of principal-strain sums over the full field.     

Photoviscoelastic stress analysis of a plate with a central hole

An epoxy resin containing excessive plasticizer was developed and characterized. The material, which deforms viscously at room temperature, has optical properties that depend on stress and strain. A tensile specimen was prepared from the epoxy resin so that the mechanical and optical properties of the epoxy resin could be characterized. The elastic and plastic behavior was determined at 37°C using tensile stresses between 4 and 26 MPa. The birefringence was also recorded as a function of time and stress. From these results, a photoviscoelastic constitutive equation was constructed to describe the dependence of the birefringence on stress and strain. The constitutive equation was then applied to study the deformation of a tensile specimen containing a central circular hole. By using the isochromatic fringes in combination with the isoclinic, the time-dependent variation of the stress field in the specimen was solved.     

Full-field automatic evaluation of an isoclinic parameter in white light

In this paper, a technique for full-field evaluation of the isoclinic parameter is presented. It combines the phase-shifting method with true color imaging technology to minimize the interaction between isoclinic and isochromatic fringes. The paper also shows how the proposed technique can be suitably integrated with known methods for evaluating the retardations. Furthermore, a digital algorithm for filtering wrapped phase data obtained by general phase-shifting techniques is presented.     

Transmission photoelasticity of centrally loaded generally and specially orthotropic beams

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. Paper was presented at the 1986 SEM Spring Conference on Experimental Mechanics, held in New Orleans, LA on June 8–13.     

The double-light-beam method in three-dimensional scattered-light photoelasticity

This paper presents a new scattered-light photoelasticity technique which may be called the double-light-beam measurement method. Principal-stress directions and relative retardations related to the principal-stress differences can be measured at any point within an ordinary three-dimensional photoelastic model by this method. This method does not need double loading and the quantities to be measured depend only on the relative light intensity. Moreover, the output signals alternate, providing improved accuracy and stability. If supported by an appropriate program-control and digital processing system, the double-light-beam method can be used to quickly determine the internal stress distribution in ordinary three-dimensional photoelastic models.