A three-dimensional photoelastic method for analysis of differential-contraction stresses

The property of homogeneous and isotropic contraction accompanying the slow polymerization of a photoelastic epoxy resin is utilized to produce a photoelastic model of the same size and shape, at the elevated cure temperature, as the container in which it was cast. Reducing the temperature of the bonded model-container composite structure through the epoxy material transition-temperature range results in frozen-stress photoelastic patterns which correspond to the forces of mutual elastic restraint of differential thermal contraction. The requirements for model-prototype similarity and the model-calibration method are discussed. Particular experiments with calibration specimens and with more complex structures in two and three dimensions are described. The validity of the technique is further demonstrated by correlation with a three-dimensional numerical solution. The properties of a material that was specially developed for use in this new technique are given.     

A composite three-dimensional photoelastic method

Care must be taken in preparation and testing of three-dimensional composite photoelastic models. Some problems encountered in modeling the prototype and during model testing are: model-material failure, loss of fringe pattern in slicing, inherent shrinkage response in freezing, inadequate bonding between materials, and modular ratio difficulties. The selection of the correct plastic can eliminate the first four problems, but the correct modular ratio between the matrix and the insert has to be obtained. This investigation illustrated the behavior of commercially manufactured plastics as inserts, with a matrix material of Epon 828 epoxy. The effective moduli of elasticity of these plastics are reported for pure tension and for flexure. Since the manufactured plastics produced varying results, the use of Epon 828 epoxy as an insert was investigated. The inserts were cast in tygon tubing and their curing cycle was altered from that used for the matrix material to produce a different effective modulus of elasticity. The Epon 828 inserts gave excellent results in the beams. The use of the same material for matrix and insert eliminates many of the problems associated with composite three-dimensional photoelasticity.     

An approximate method of orthotropic photoelastic analysis

An approximate strain-optic law has been derived for photoelastic analysis of orthotropic model materials. Principal-strain difference and the direction of major principal strain can be obtained from only two photoelastic measurements (isochromatic-fringe order and isoclinic angle) by means of this strain-optic law. Limited experiments on models subjected to uniaxial and biaxial stresses indicate good agreement between the experimental results and predictions of the strain-optic law. A parametric study demonstrates that the direction of major principal strain can be predicted to within a few degrees of the exact value and that the principalstrain difference can be predicted within ±20 percent for most practical values of degree of orthotropy and ratio of principal strains. The error levels are quite acceptable considering the significant ease in analysis provided by the new law and the fact that such error levels are not uncommon in experimental investigations.     

Polarimetry for spatiotemporal photoelastic analysis

This paper describes a new photoelastic technique for the spatiotemporal stress analysis. In a polarimeter developed, an elliptically polarized signal beam of light, modulated in state of polarization by two-dimensional principal-stress distributions interferes with a reference beam of light consisting of orthogonal linearly polarized two components. A time-sequential series of two-dimensional interference patterns are received one after another by a MOS video camera, followed by a computer. Of the elliptically polarized signal beam, the orthogonal field components along the directions of the principal stresses in a two-dimensional photoelastic sample can be computed from a recorded interference pattern, which offer the data needer for mapping the spatiotemporal principal-stress distribution over the sample. Not only each of the two orthogonal principal stresses but also the principal-stress difference are mapped in a time-sequential diagram. No use of any movable polarization element such as a rotating analyzer allows us to follow a rapid change in stress distribution within the maximum frame rate 2066 s⁻¹ of the MOS video camera.     

Optical theory of the multilayer-reflection technique for three-dimensional photoelastic studies

Using the theory of characteristic directions developed previously by the author^{2, 3} optical phenomena by the multilayer-reflection technique¹ in the general case are studied. Recursive formulas which enable successive determination of the parameters of all the photo-elastic layers without any complication of the experimental technique are derived.     

The use of precision castings in the three-dimensional photoelastic analysis of threaded tubular connections

A new, room-temperature formulated, epoxy-resin system with superior stress-freezing photoelastic properties is presented. The ease of producing relatively large, high-quality, precision castings is discussed. Stress-optical, rheological, and mechanical properties are given. Cylindrical tubes joined by integrally cast Stub Acme and American Standard rolled thread profiles with typical geometric parameters are loaded in tension and analyzed using the stressfreezing method. Results are presented for surface axial stress distributions for the wall surfaces opposite the threaded profiles. Additionally, the fillet stress distribution for the first engaged thread as a function of the distance along the thread helix from the location of initial contact is presented. Comparison with a finite-element analysis is given. Paper was presented at the 1983 SEM Spring Conference on Experimental Mechanics held in Cleveland, OH on May 15–19.     

A multilayer-reflection technique for three-dimensional photoelastic studies of perforated plates in bending

A photoelastic investigation was conducted to determine the stress-concentration factors around a large, symmetrically reinforced central hole in a square plate under 1∶1 and 2∶1 biaxial bending. Tapered-edge rings served as the reinforcement, and a major objective was to determine the ring proportions such that the maximum stress at the hole would be equal to the value which would be present in an unperforated plate under the same nominal stress. Because the stress distribution at the periphery of a hole in such a plate structure varies in the radial, tangential and thickness direction, it was necessary to employ a three-dimensional photoelastic technique. There were a number of serious disadvantages in the use of any of the standard procedures and a new three-dimensional technique for room-temperature use was developed which is particularly suitable for the determination of boundary stresses around holes in bending experiments. With the technique in its present state of development, the three-dimensional isochromatic distribution in the plate can be determined from a single model and, from this, the boundary value of stress. The new technique utilized a laminated-plate model. Selective aluminizing of the laminations allowed for the determination of fringe-order distributions in the thickness direction as well as in the radial and circumferential directions at the boundary of the hole in flat models. Uniaxial maximum fringe orders were determined and, from these, the biaxial values were obtained by superposition.     

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.     

An application of holography to complete stress analysis of photoelastic models

A new procedure is proposed by which holographic principles may be extended to include stress analysis of three-dimensional photoelastic models. A sixth independent equation can be obtained to permit a complete stress solution by using the double-exposure hologram technique in conjunction with an immersion tank. The salient feature of the method is that no stress relieving is necessary between exposures of the hologram. Two experiments were performed to compare the stress-relieving method to the immersion method. In both experiments, a two-dimensional model was used to simplify the demonstration of the general techniques, which are also applicable to slices from frozen-stress models.     

Algorithms for fully automated three-dimensional particle tracking velocimetry

A three-dimensional Particle Tracking Velocimetry (3-D PTV) technique has been developed to provide time-resolved, three-dimensional velocity field measurements throughout a finite volume. This technique offers many advantages for fundamental research in turbulence and applied research in areas such as mixing and combustion. The data acquired in 3-D PTV is a time sequence of stereo images of flow tracer particles suspended in the fluid. In this paper, the implementation of the technique is discussed in detail, as well as the results of an extensive statistical investigation of the performance of the algorithms. The technique has been optimized to allow fully automatic processing of long sequences of image pairs in a computationally efficient manner, hereby providing a viable, practical tool for the study of complex flows.List of symbols x, y, z Particle position - u, v, w Particle velocity This work was supported by a grant from Ford Motor Company, Powertrain Research Department. Their support is gratefully acknowledged.     

Gelatin models for photoelastic analysis of gravity structures

The potential of gelatin as a highly sensitive photoelastic material has long been known but seldom utilized. This paper describes a series of tests to show that body-force stress distributions can be conveniently found with gelatin models. Problems arising from the extreme variability of gelatin, including edge dehydration and bacterial attack which have plagued investigators in the past, may be overcome or even turned to advantage by careful control of the mixture and simultaneous calibration. Previous work with gelatin in this country and abroad has been reviewed in order to indicate the available information on the instantaneous physical and optical properties. Data from the calibration test performed at Princeton were used to obtain both the instantaneous and the linearly viscoelastic creep behavior of the gelatin mixture chosen in terms of constant moduli which can be compared with other time-dependent, prototype materials. Apparatus and procedure for both calibration and model tests are outlined, and test results for one of the wedge-shaped gravity structures investigated are compared with analytic predictions.     

Optical analysis of photoelastic polariscopes

A full-field interpretation of the photoelastic effect is advanced, supplementing the common pointwise explanation. This “warped-wavefront” viewpoint provides a key for the analysis of resolution, contrast and location of object plane in diffused-light and lens-type polariscopes. The analysis yields quantitative assessment of performance. Two wavefronts with wave normals separated by angle α emerge from the model wherever a gradient of fringe order exists in the interference pattern. It is this angular separation that limits resolution, contrast and object-plane location. Results indicate potentially very high resolution for both types of polariscope, with theoretical resolution being independent of focal length and speed (f-number) of the camera lens. With diffused-light polariscopes, contrast diminishes as fringe gradient increases, but high contrast remains available for common situations. Position and shape of fringes in the isochromatic pattern is affected by location of the plane of focus, which should therefore be fixed in the model. The analysis reveals special considerations applicable to special circumstances, including very high fringe gradients, point-light sources (lasers) and distant model location.     

Complete automatic analysis of photoelastic fringes

TV technology combined with a modern video-frame store is used to store the complete fringe pattern in digitized form in real time. A minicomputer connected to the store has direct access to any picture point in the store. In this manner, it is possible to evaluate the photoelastic-fringe pattern in the computer by special developed software.     

A stress-optic law for photoelastic analysis of orthotropic composites

The feasibility for utilizing transparent filament-resin composites for photoelastic stress analysis was investigated. Satisfactory photoelastic stress patterns were demonstrated in simple models with undirectional and bidirectional fiber orientations. A stress-optic law was formulated, based on the concept that the birefringence components contributed by each component of plane stress are combined according to a Mohr circle of birefringence. Applying this concept, the difference of the physical and optical principal directions was accounted for, and a general method of photoelastic solution for the plane-stress problem in orthotropic sheets was developed. The method of analysis is little more complex than the well-known procedures for isotropic materials, but at least three experimental measurements are required to characterize the optical response of the material to plane stress. Partial confirmation of the proposed stress-optic law was obtained by comparison of the theory to limited experimental data obtained in uniaxial-stress samples. It remains to establish a more positive verification by experiments in a variety of biaxial-stress conditions.     

Experimental techniques employed for photoelastic analysis of cellular shells

The search for a shell construction superior to the usual ring-stiffened shells in strength and stability under external pressure with minimum weight has led to consideration of several other shell wall constructions.¹ The cellular-shell structure is one of the most promising designs of shells because of its ability to withstand high-pressure loading while maintaining a high degree of material efficiency. The analytical treatment of cellular shells has been undertaken only recently² and limited experimental study of these shells has been conducted. Thus, for obtaining reliable design formulas for the cellular-shell construction, these studies were undertaken. The cellular-shell construction may be visualized as two concentric thin cylinders spaced radially by a series of thin rings along their common longitudinal axis. The optimum wall thickness, rib thickness and rib spacing for a cellular shell of a given diameter and material which will result in the most efficient utilization of the material when the shell is placed under external pressure is the information required for shell design. The experimental techniques described in this paper have been employed to assist in the determination of the necessary design parameters.     

An improved oblique-incidence technique for principal-strain separation in photoelastic coatings

This paper presents a generalized theory for oblique-incidence measurement of relative retardation in photoelastic coatings. Using this theory, measurements can be performed from a fixed observation point and do not require rotating the test object. Thus, this technique greatly reduces the time and labor involved in oblique-incidence measurements. Furthermore, the technique is potentially applicable to the separation of dynamic principal strains.     

An upper-bound analysis for frictionless TCAP process

Tubular channel angular pressing (TCAP) process was proposed recently as a novel severe plastic deformation technique for producing ultrafine grain and nanostructured tubular components. In this paper, an upper-bound approach was used to analyze the TCAP process. Deformation of the material during TCAP process is analyzed using upper-bound analysis to determine maximum required load. The effects of TCAP parameters such as channel and curvature angles, deformation ratio (R ₁/R ₂) and tube material on the process pressure were investigated. The results showed that an increase in the second channel angle and decrease in the ratio R ₁/R ₂ lead to lower process loads. In the first and third curvature angles ranging from 25 to 65°, the required load remains almost constant. The apparent punch load decrease when hardening exponent n is increased. To verify the theoretical results, the finite element (FE) modeling was employed. Good agreement was observed between the predicted pressure from upper-bound analysis and FE results.