A neoteric interferometer for use in holographic photoelasticity

A shortcoming of the conventional holographic interferometer used in photoelasticity is that, for the double-exposure cases, the resulting fringe patterns are a complex combination of conventional isochromatic and isopachic fringes. This paper describes a holographic interferometer that may be used to obtain separate but simultaneous isochromatic- and isopachic-fringe patterns for photoelastic models in states of plane stress. The method requires a model with a partially reflecting front surface. Isopachics, which are proportional to the thickness change, are recorded using holographic interferometry from the transmitted light. The isochromatics are obtained from the transmitted light by conventional means. General equations relating the surface displacement of the specimen to the observed fringe patterns are developed, and examples of static and dynamic loadings are shown.     

Advancements in holographic photoelasticity

The success of double-exposure holography as an interferometric technique for experimental stress analysis has lead to several recent publications dealing with the theoretical expression which describes the resulting photoelastic patterns. This paper describes the extension of current theory to include the effect of an intensity difference between the light used during the first exposure and that used during the second exposure. It is shown that as the ratio of these two intensities is changed both the position and the intensity of the photoelastic-fringe pattern is altered. An interpretation of the photoelastic pattern as a simple combination of isochromatic and isopachic-fringe patterns is shown to be possible only under certain conditions. Using a pulsed ruby laser, single- and double-exposure photoelastic holograms of stress waves were obtained, and reconstructions of these holograms are presented. The clarity of the reconstructed images is comparable with photographs taken with a standard polariscope. In addition, the capability of magnifying any particular portion of the image by known holographic reconstruction techniques is illustrated.     

Synchronization problems in dynamic holographic photoelasticity

An analysis of synchronization problems encountered when recording transient-fringe patterns which are dependent on the light source and the method of shock generation is presented. The analysis is specifically designed to be valid on a photoelastic material having either a high or low Young's modulus when the shock generator is an air gun and the light source is a Q-switched ruby laser. Synchronization is performed using integrated circuits in T.T.L. logic which give a triggering order to the ruby laser under the control of the projectile velocity.     

Application of faraday's effect in static and dynamic holographic photoelasticity

The basic principle of applying Faraday's effect to achieve the separation of fringes in static and dynamic holographic photoelasticity, and a study and application of Faraday's light rotator are described in this paper. It is proposed that Faraday's light rotator be used for automating photoelastic instrumentation for measuring isoclinics and the decimal orders of isochromatic fringes.     

Separation of principal stresses in dynamic photoelasticity

A new and effective method used to separate the transient principal stresses for dynamic photoelasticity is proposed. This is a hybrid method combining the optical method of dynamic caustics and the boundary element numerical method. Firstly, a modified Cranz-Schardin spark camera is used to record simultaneously the isochromatic fringe patterns of photoelasticity and the shadow spot patterns in the dynamic process. By means of the isochromatic fringe patterns, the difference between transient principal stresses in the whole domain and the principal stresses along the free boundary can be solved. In addition, the method of caustics is a very powerful technique for measuring the concentrative load. Then, the sum of the principal stresses is calculated by the boundary integral equation obtained from the Laplace integral transform of the wave equation. So, the transient principal stresses can be determined from the experimental and numerical results. As an example, the transient principal stresses in a polycarbonate disk under an impact load are resolved. Concurrently published in the Chinese Edition of Acta Mechanica Sinica, Vol. 26, No. 1, 1994     

The practical use of the hole method in photoelasticity

A small circular hole has already been used in plane elasto-static photoelasticity to determine the stress tensor for any general loading situation. Originally the idea required the determination of the stress at four points at the free boundary of the hole, then it was found that more precision would be obtained if the measurements were taken at points located at a distance from the center of the hole equal to twice its radius. Later it was suggested that probably still better results would be obtained from points located at 1.4 times the radius. This paper has three objectives: (1) to improve the precision of the measurements by taking them at any point in the vicinity of the hole, which requires that the expressions giving the principal stresses be presented in a different form, as a function of the normalized variable distance from the center of the hole; (2) to show the consistent application of the method, using the values of the birefringence at various arbitrary radial locations, to plane elasto-static loading problems; and, (3) to present the application of this approach in a concise form so that its application is practical.     

Separation of isochromatics and isopachics using a Faraday rotator in dynamic-holographic photoelasticity

A method is presented that allows the simultaneous separation of isochromatic- and isopachic-fringe patterns for transient-plane stress problems. Isopachic fringes are obtained by means of holography with a Faraday cell and a pulsed ruby laser flashing dual pulses. As usual isochromatic whole-order fringes are recorded in a circular-light polariscope. The shock generator (air-gun) and its synchronizing system with the ruby laser is described. The procedure is applied to the recording of the isochromatic- and isopachic-fringe patterns in a disk under radial dynamic loads.     

Stress waves in pyramids by photoelasticity

The propagation of stress waves in pyramids was studied photoelastically with the application of a laser-photomultiplier tube system and an internal polariscope for recording moving fringes. Dispersion and attenuation of stress waves were considered in a straight bar, a 5-deg pyramid, and a 20-deg pyramid made of Hysol 4290 epoxy plastic. In the straight bar and 5-deg pyramid, longitudinal waves propagate without any dispersion even though the waves attenuate as they progress down the models; in the 20-deg pyramid, however, the dispersion of the stress waves is quite significant. The distributions of the axial and radial stresses and the photoelastic fringe patterns obtained on the 20-deg pyramid show that the stress wave front is spherical with the maximum stress along the central axis of the pyramid. A one-dimensional theory of wave propagation without correction factors in a small-angle infinite cone compares well with the experimental results.     

The use of phase-stepping for the measurement of characteristic parameters in integrated photoelasticity

A three-dimensional photoelastic body can be represented by an optically equivalent model, which consists of a linear retarder, δ, at a certain angle, θ, and a pure rotator, χ. These have been described as the characteristic retardation, δ, and the primary and secondary characteristic directions, θ and θ+χ. Until now these characteristic parameters have only been determined using manual, point-by-point collection methods which are involved and time consuming. Therefore an automated phase-stepping method has been developed to enable the determination of the three characteristic parameters for three-dimensional or integrated photoelasticity. Expressions have been derived to obtain δ, θ and θ+χ from six phase-stepped images. These images are collected using a CCD camera and the full-field data is processed using a standard personal computer. This novel method allows accurate, full-field maps of all three characteristic parameters to be obtained in a relatively short time, which makes full-field tomographic reconstruction of photoelastic data a real possibility. Both are SEM Members.     

Absolute determination of the isochromatic parameter by load-stepping photoelasticity

A new approach to full-field automated photoelasticity is presented in which a circular polariscope is used to enable the isochromatic phase value () to be determined unambiguously and without input of a known isochromatic value obtained using an auxiliary technique. Values of cos are obtained from light-field and dark-field images for three loads of small incremental steps. Using a relatively straight-forward procedure, ramped phase maps for are produced which can be unwrapped using conventional techniques. The resulting distribution of is then found absolutely using information provided by which is the incremental change in the isochromatic phase value between the load steps. The results obtained for disk-in-compression tests presented here in comparison with theoretical solutions demonstrate that the technique is both simple to use and very accurate. A similar approach may be adopted using three wavelengths instead of three load steps.     

An investigation of propagating cracks by dynamic photoelasticity

A 16-spark gap, modified schardin-type camera was constructed for use in dynamic photoelastic analysis of fracturing plastic plates. Using this camera system, dynamic photoelastic patterns in fracturing Homalite-100 plates, 3/8 in. × 10 in. × 15 in. with an effective test area of 10 in. × 10 in., loaded under fixed grip condition were recorded. The loading conditions were adjusted such that crack acceleration, branching, constant velocity, deceleration and arrest were achieved. The Homalite-100 material was calibrated for static and dynamic properties of modulus of elasticity, Poisson's ratio, and stress-optical coefficient. For dynamic calibration, a Hopkinson bar setup was used to record the material response under constant-strain-rate loading conditions. The precise location of the dynamic isochromatic patterns in relation to the crack tip was determined by a scanning microdensitometer. This information was then used to determine dynamic stress-intensity factors which were compared with corresponding static stress-intensity factors determined by the numerical method of direct stiffness. Although the response of the dynamic stress-intensity factor to increasing crack length was similar to the static stress-intensity-factor response, the dynamic values were approximately 40 percent higher than the static values for constant-velocity cracks. for decelerating cracks, the peak values of dynamic stress-intensity factors were 40 percent higher than the corresponding static values.     

Evaluation of three-dimensional stresses in shrink-fit problems by scattered-light photoelasticity

Stresses caused by shrink fits are commonly evaluated by using Lame's solution or by other analytical methods in which it is assumed that the radial stresses on the surface of contact are distributed uniformly, or in some stepwise manner, and that friction forces between the bodies are zero. These assumptions were not necessary in the experimental problem solved. Heretofore, no experimental techniques have been available to check the existing theories on a three-dimensional basis. The stresses which result when a short, hollow, thick-walled cylinder is shrunk over a shaft which is a solid shaft or a thick-walled, hollow shaft were determined. Equipment and techniques using scattered-light three-dimensional photoelasticity with a laser light source were developed and applied.     

Three-dimensional photoelasticity of the rotating body

Report covers the stress distribution of a hydraulically loaded pump impeller obtained with the aid of the stress-freezing method. The similarity of stress distribution of an actual metallic impeller and the photoelastic model is discussed dynamically and hydrodynamically. From the experiments by freezing stresses under centrifugal force and hydraulic forces, the stress distribution of the actual metallic impeller has been estimated on the basis of similarity.     

Contribution to the analysis of errors in photoelasticity

Photoelasticity data are expressed in terms of the direction and the differences of the principal stresses. To determine the principal stresses, separation is necessary. The author deals with some of the numerical methods of separating principal stresses, permitting evaluation of the stresses along straight sections. In the first part of this paper the author presents methods of separation and in the second part the errors involved.