Suitability of the photoelastic implementation of polymers with material birefringence

Scattered photoelastic techniques would gain considerable momentum through better understanding of the nature and response of the available photoelastic materials. The influence of the prevailing birefringent effect in the state of load-free polymers on the radiated scattered light energy is investigated. Six different photoelastic materials are considered. The impact of material birefringences on the quality of reading the fringe orders of the scattered radiation in a stressed photoelastic medium is explored. Spectral dependence of the modulation of light vectors in acrylic materials (Plexiglas) is illustrated. The advantage of this characteristic as a convenient means of compensation in scattered photoelasticity is pointed out. Acrylic sheets, a relatively cheap transparent polymer, seem to be suitable for scattered photoelastic analysis. The moiré technique might find application in determining fringe orders in a material such as Homalite-100. Replacing the primary beam by a primary sheet saves the cost and effort consumed in the scanning process. Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

A photoelastic determination of mixed-mode stress-intensity factors

A new evaluation method of the isochromatic-fringe pattern for the determination of mixed-mode stress-intensity factors (SIF) was developed. The method bypasses the error-prone measurements on the isochromatic patterns near to the crack tip and uses data from the far region. Suitable extrapolation laws were given for transferring the far-from-the-crack-tip data to the near region. Then, the well-known Irwin's formulas can be used for the determination of mixed-mode SIFs. Convenient formulas facilitating the calculation of SIFs were established. Experimental evidence corroborated the results obtained by the new method.     

Optimizing thread-root contours using photoelastic methods

The research work described in this paper was part of a program which was conducted to determine stress distributions in a complex multicomponent pressure vessel and in several redesigned versions of the same vessel. Three-dimensional photoelasticity methods were selected for the analyses when it was determined that a number of highly stressed internal areas were inaccessible for evaluation of stresses by electrical-resistance strain gages and uncertainties regarding load transfer between mating components made an analytical determination impractical. The results of the stress determinations in the original vessel indicated that the highest stresses were located in the small fillets at the roots of the sectored threads which were used to permit quick and convenient assembly of the parts. Results of a prototype fatigue study verified the importance of these stresses when it was determined that fracture initiated in this high-stress area. Because of design specifications and the nature of conditions under which the vessel operates, stress reductions had to be accomplished using thread form or rootcontour changes. Since three-dimensional studies are time consuming and expensive, two-dimensional methods were selected to evaluate a number of changes before final evaluation was made in a three-dimensional model. Comparisons between results from the two- and three-dimensional studies indicated that the percent improvements indicated in the two-dimensional studies were roughly obtained in the three-dimensional vessels.     

Overdetermined photoelastic solutions using least squares

The least-squares method is presented for obtaining an overdetermined solution from the various relationships available in photoelastic stress analysis. Equations are presented for incorporating the various relations into a weighted least-squares solution and advantages of this method are illustrated in two example problems. In addition to the greater accuracy possible in the overdetermined solution, the method permits weighting of the varied information and eliminates the need to separately determine the stress-optical constant. Variations of the method are discussed.     

A hybrid technique for improvedK determination from photoelastic data

A hybrid technique for determination of stressintensity factors from static-and dynamic-photoelastic-fringe data is proposed which combines both the generalized Westergaard stress function approach and a boundary collocation method. The new technique is especially useful for problems where a short crack initiates from a shallow notch or a crack approaches a free boundary. Modifications toward a mixed dynamic-near-field static-far-field solution procedure are discussed.     

Studies of contact problems using photoelastic isodynes

Experimental determination of contact stresses is difficult and not often satisfactorily accurate, especially when shear stresses exist in contact areas. Several examples presented in the paper show that, by using isodyne techniques, it is relatively easy and inexpensive to determine not only all stress components in contact regions but also the boundaries of contact areas as well.     

The photoelastic determination of the stresses in vibrating cantilevered beams

A method of determining the dynamic stresses in vibrating cantilevered beams using photoelasticity is presented. The method uses the basic principles of photomechanics and the optic-stress laws. A high-intensity strobe light is timed with the frequency of vibration so that the beam image appears to be stationary. Data are recorded with a camera and analyzed to provide an experimental solution. The theoretical solution is derived from the Bernoulli-Euler equation of motion. Two basic types of beams were investigated, an aluminum beam coated with a birefringent material to simulate an actual structural member and a birefringent model that was dynamically similar to the aluminum beam. The feasibility of extending the technique to more complicated shapes is suggested by this investigation. The experimental results and feasibility of the concept are verified by close correlation with the analytical solution.     

Effects of artificial cracks and poisson's ratio upon photoelastic stress-intensity determination

A series of stress-freezing photoelastic experiments were performed with multiple replications upon edge-cracked strips for three types of “cracks” in current use:

1. Rectangular slots 0.152 mm wide,
2. 1.59-mm-wide slots terminating in a 30-deg vee notch of approximately 0.025-mm root radius, and
3. Natural cracks (approximately 0.0025-mm root radius).

Stress-intensity results were compared with the Gross-Srawley analysis; in addition (1) was compared with Savin's solution. It was concluded that (2) and (3) yield the same results but (1) was slightly higher. Both (2) and (3) were about 12 percent higher than the Gross-Srawley results. This is shown to be related to a Poisson's ratio effect.     

Construction of complex photoelastic models using thin molded-epoxy sheets

The construction and analysis of complex thin-shell photoelastic models are discussed. Examples of both two- and three-dimensional applications are presented. The first example concerns an investigation of the structural supports of a new and unique blastfurnace design. The second example is directly related to the design and analysis of complex thin-shell pressure vessels and manifolds. Existing laboratory techniques were used successfully to construct the photoelastic models. The construction method is basically an extension of the techniques previously associated with the contour-sheet method of preparing photoelastic coatings. As such, it does not involve new or untried concepts, but rather it extends the existing in-house capabilities of many laboratories.     

A simple method for the digital determination of the photoelastic fringe order

A new and simple approach to the digital determination of a photoelastic fringe order using two different loads is proposed. The relationships between the intensity values of light and the isochromatic fringe orders generated from two different loads are derived. The scheme used for the automated determination of the total fringe orders of a full-field photoelastic fringe pattern is described. The usefulness of this method is demonstrated using two isochromatic fringe patterns under two different loads. Extra filters are not needed in the proposed method as in the case of the two-wavelength method.     

Integrated-plane photoelastic method—Application of photoelastic isodynes

It has been shown by Pindera and Mazurkiewicz that a new type of scattered-light modulation in the plane of a two-dimensional photoelastic object can be obtained when the stationary integrated photoelastic method developed by Pindera and Straka is applied in a scanning mode and when the transfer function of the photoelastic system satisfies certain conditions. The new type of light modulation, called field of isodynes by the authors, carries information on stress components normal to the direction of propagation of primary beam, and on corresponding total-force component. The points where this stress component is equal to zero can be easily determined. The classical scattered-light modulation along a chosen line represents a cross section of a corresponding isodynes field. It is shown that these features of the method of isodynes make it possible to easily determine the distribution and values of normal stress components at any arbitrary rectilinear cross section, and to check immediately the accuracy of measurements. The experimental determination of contact stresses and contact regions using the method of isodynes is especially simple and elegant.     

The determination of the refractive index of a photoelastic specimen by immersion technique

Conventional methods for determining the refractive index demand specimens of optical quality, the preparation of which is often very difficult. An indirect determination by matching the refractive indices of specimen and immersion liquid is a practical alternative for photoelastic specimen of nonoptical quality. An experimental arrangement used for this technique and observations made while matching the refractive indices of three different specimens are presented.     

Analysis of cylindrical shells of nonuniform thickness using two-dimensional photoelastic models

An experimental method is described whereby symmetrically loaded cylinders of nonuniform thickness are analyzed using two-dimensional photoelastic models mounted on elastic foundations. The technique is most conveniently applied to ring-stiffened or notched cylinders. The particular model studied simulated a notched cylindrical pressure vessel which had been previously studied with three-dimensional photoelasticity. The stress-concentration factors at the base of the notch, found using both methods, showed excellent agreement. An analysis was also performed which allows estimation of the error involved when a beam-on-elastic-foundation model does not rigorously simulate a cylinder.     

Stress tensor measurement using birefringence in oblique transmission

A method for measuring the stress tensor of liquids obeying the stress-optical rule is presented. In particular, the procedure makes it possible to determine the shear stress, and the first and second normal stress differences for rheometric flows. This technique is an extension of the procedure recently described by Burghardt and coworkers (Brown et al., 1995) wherein light is sent obliquely through a sample sheared between transparent plates. However, in the present development, the light is transmitted in the plane containing the velocity gradient and neutral directions, thereby reducing the necessary optical measurements by one. A polystyrene-tricresyl phosphate (TCP) solution is used as the test sample. The first and second normal stress differences in steady shear flow measured by this method show good agreement with the mechanical results measured by Madga et al. (1993) using a modified cone and plate rheometer. The transient behavior of the first and second normal stress differences following the start-up of shear flow is also presented.     

Obtaining stress maps from photoelastic data using a digital computer

A general procedure for the analysis of photoelastic isochromatic and isoclinic photographs by digital computer to produce plots of coordinate normal and shear stresses is presented. The solution for normal stresses, involving a finite-difference iterative harmonization of the Laplace equation, is discussed, including treatment of the boundaries and selection of an appropriate network grid. The results of a classical problem, solved by this technique, are included.     

Trapped particle detection in bonded semiconductors using gray-field photoelastic imaging

In this paper we present inspection results from several bonded wafer systems using a newly developed infrared gray-field polariscope (IR-GFP). This device measures the residual stress-fields associated with defects trapped at the bonded interface to enable the detection of subwavelength defects. Results from IR-GFP imaging are contrasted with conventional infrared transmission (IRT) imaging of the same samples, showing marked improvements in defect detection as well as the ability to quantify the residual stress fields. This inspection method reveals that interfaces deemed defect-free using IRT imaging may be, in fact, teeming with defects.     

两种多天线GNSS定姿方法的精度分析

基于高精度多天线GNSS基线分量及精度估计结果,实现了两种常用的多天线定姿方法:直接姿态法和最小二乘姿态法。利用一套车载三天线GNSS实测数据和高精度惯性导航系统(陀螺漂移0.005(°)/h,加速度计零偏优于10~(-3)g)输出的姿态结果,深入分析了两种定姿方法的内、外符合精度。实验结果表明:两种定姿所解算的航向角、俯仰角和横滚角的精度分别为:直接法的内符合精度约为0.3°~0.5°、0.3°~1.0°、0.5°~1.0°,最小二乘法约为0.1°、0.2°~0.5°、0.5°~2.0°,即最小二乘法对航向角估计有明显改善,对俯仰角和横滚角改善不明显;两种方法的姿态外符合精度(消除航向系统偏差)基本一致,约为0.08°、0.15°、0.42°,但是最小二乘法得到的航向角系统偏差更小。