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.     

The generic nature of the absolute-retardation method of photoelasticity

The method of absolute-retardation measurements does not depend upon the use of any specific interferometer. Any one of the many extended field interferometers can be employed, including the Series, Michelson, Mach-Zehnder and Fizeau types. Where adequate monochromatic purity of light source is available, reflections from the two surfaces of the model can form the interferogram, thus dispensing with the necessity of any separate optical interferometer. The two-dimensional stress-optical relationships are derived in their most general form. The relationships are identical for all instruments or interference systems—only the calibration constants change with different systems. Interferograms from four distinctly different systems are shown. Interference-fringe sharpening is introduced and demonstrated. A laser-light source was used with two systems to provide high monochromatic purity. The interferometric method of Nisida and Saito is correlated with the absolute-retardation method. The opportunity to obtain information for a complete stress solution from one photograph makes the method attractive for both static and dynamic problems.     

New compensation method in photoelasticity

Proposed compensation method eliminates the necessity to align the principal directions in the model with compensator for determination isoclinic parameter and fringe order. The advantage and limitation of the proposed method are discussed from the point of view of its potential use in the automatic data collection.     

A scattered-light method in photoelasticity

The birefringence and, thereby, the stresses in a photoelastic model are investigated utilizing the light scattered from a beam of light propagating through the model. The retardance from the entry point of the beam into the model to a certain point along the beam is expressed in terms of the intensity of the scattered light. The retardance for a short distance along the light path within the model is determined as a function of the total retardances from the entry point of the model to the two end points of the distance investigated. The effects of retarders and polarizers on the state of polarization of the light beam are treated by Mueller calculus. It is not necessary to make other assumptions than those made in the usual stress-freezing and slicing method.     

The gamma-ray-irradiation method applied to three-dimensional thermal photoelasticity

It has recently been shown that a gamma-ray irradiation fixes the birefringence in photoelastic models of Araldite B. The method has hitherto only been used to fix the birefringence in specimens subjected to constant forces. This work applies the irradiation method to determine the thermal stresses in a thick-walled cylinder with a temperature gradient along the radius. The model behaved in the following way during the experiment. The material relaxed when the temperature gradient was applied, and the model was irradiated when it was stress free. Real stresses, which were equal to the thermal stresses but with opposite sign, appeared when the temperature gradient was removed. As the problem is mathematically two-dimensional, it is possible to determine the birefringence by means of the slicing technique. Good agreement was obtained between the stress determined experimentally and those calculated analytically. The irradiation sensitivity of a number of materials has been determined, and some new materials have been used that are superior in two important ways to that used earlier in that they require a much lower irradiation dose and their mechanical properties are considerably better.     

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.     

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.     

A new method of stress analysis in photoelasticity

A new method of stress analysis in photoelasticity has been developed in this paper. Only the orders of isochromatic fringes and boundary conditions in three sections are adopted to analyse the stress components in these sections. The method requires minimum known data and can quickly analyse stress components. It reduces computational programs.     

Two-wavelength method for full-field automated photoelasticity

A new method for the whole-field determination of the isoclinic angle α and the isochromatic parameter ϕ is presented. The problems appearing during the calculation of these two parameters are solved with the use of two different wavelengths. Indeed, when a monochromatic light is used as an incident light, α is not measurable at the points where ϕ is equal to 2kπ. In this method, each monochromatic light can compensate for the influence of ϕ to obtain the isoclinic angle for the entire model. Also, most of the methods calculate the fractional fringe order that is unwrapped afterward to obtain the isochromatic parameter. This unwrapping process needs an initialization, which cannot be automatic with only one isochromatic fringe pattern. The use of two wavelengths permits a complete automatic unwrapping of the isochromatic parameter, even for the initialization of the process.     

Direct oblique-incidence method for reflection photoelasticity

Experimental Techniques - The method presented in this paper has a good practical application, which may be used in all cases of oblique-incidence measurements in reflection photoelasticity. The...     

An analytic separation method for photoelasticity

A method for separating principal stresses in photoelasticity is presented. This method is based upon the series solution of Laplace's equation and the determination of the unknown coefficients arising in this series by a least-squares numerical technique. By selecting an adequate number of terms in the series, the representation of the boundary values of the first stress invariant can be established as accurately as the initial photoelastic data. This form of representation of the first stress invariant at interior points in the region is moe accurate than the boundary values employed.     

A new method to increase the sensitivity of photoelasticity

A method is proposed to read the isochromatic-fringe order continuously as a function of position. It utilizes the fact that the fringe order is a continuous function of the light intensity, which is converted into the density of a photographic negative and then traced out either by a microdensitometer or isodensitracer. Explicit relationship between the fringe order and the film density is obtained. Hundreds of points can be read between a half and an adjacent integral order. The method is whole field in nature and offers the possiblity of direct computer processing of photoelastic information.     

Separation of the isochromatics-isopachics patterns by use of retarders in holographic photoelasticity

By double passing the object beam in photoelastic-holographic interferometry, separation of the isochromatic-isopachic patterns can be achieved. The object beam must then interact with a suitable polarizing element between the first and second pass. This problem is analyzed using Jones' matrices. This analysis shows that, apart from active and passive rotators, half-wave and quarter-wave retarders can also be used as polarizing elements. Possible experimental arrangements of the method are reviewed and experimental verifications are presented.