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.     

Simulation of errors in automated photoelasticity

In automated photoelasticity, there are some advantages in using white light; however, the theory underlying many such systems, namely phase stepping, is based on monochromatic light. The effect of using white light has been investigated both by experiment and by a simulation of a polariscope. The simulation has been validated and used to explore the use of bandwidth filters to control the errors caused by using white light. These errors were found to be dependent on the form of the spectrum of the light and to be large for high fringe orders.     

Full-field separation of principal stresses by combined thermo- and photoelasticity

The combined use of thermoelastic stress analysis and full-field reflection photoelasticity based on the phase-stepping technique has been developed for twodimensional problems. The first method determines the sum of the principal stresses, the latter evaluates the difference of the principal stresses. Thus the principal stresses were separated at each point in the field of view without reference to neighboring points. An evaluation of this approach has been performed using a tensile plate with a central circular hole. The results show that the analysis carried out combining thermo- and photoelasticity incurred errors no larger than those of each system working independently.     

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.     

A measurement method of scattered light photoelasticity using unpolarized light

This paper describes an automatic measurement method for the stress analysis of a three-dirnensional photoelastic model having the rotation of the principal stress by scattered-light photoelasticity using unpolarized light. The relative phase retardation and the principal stress directions of a linear retarder for a distance in the solid model are expressed in terms of measurable Stokes parameters. The method was used for measurements on a frozen stress sphere under diametral compression.     

Towards Criteria Characterizing the Metrological Performance of Full-field Measurement Techniques

Users of full-field measurement methods like Digital Image Correlation (DIC) often aim to perform measurements with the best trade-off between spatial resolution, bias and measurement resolution. Whenever two full-field methods are compared, it is essential that these criteria are taken into consideration. Recently a metrological efficiency indicator for full-field measurements has been proposed and discussed. This indicator combines measurement resolution and spatial resolution. It has been shown to be invariant to the subset size in the case of Local DIC. The goal of this article is to discuss a method, which determines both the spatial and the measurement resolutions for a given bias for two different DIC methods, in order to obtain the metrological efficiency indicator for each of these methods. The benefit of this indicator is that it does not depend on setting parameters such as the subset size, which are chosen by the user. As such, it can be considered as intrinsic to each technique, thus enabling fair comparison. Local DIC and triangular finite element based Global DIC will be the subject of this investigation. With this setting, their respective subset and triangular element sizes will be related to the spatial resolution of both methods for a given acceptable bias. By using the metrological efficiency indicator, the performance of the two methods will be compared and discussed to a new level of detail. Generally speaking, the indicator shows that the metrological performance of both methods is similar, confirming their popularity. However, it will be shown that, depending on the choice of what an acceptable bias is, one of the method may be preferred to another. The results show that for the specific DIC versions used in the study, for cases for which a significant bias is acceptable, Local DIC outperforms Global DIC, while the opposite is true in the case for which the bias requirements are more stringent. Finally, the quadratic versions of both DIC versions are shown to significantly outperform their respective linear versions.

     

2D and 3D separation of stresses using automated photoelasticity

A procedure for the separation of full-field photoelastic images for use with an automated polariscope is described. Regions of background in the image are identified thus producing the boundary of the model. The shear difference method is used to calculate the components of stress along all raster lines in the image using photoelastic parameters at the boundary points to calculate the initial values of stress. Algorithms were also used to evaluate the stress components along raster lines which did not contain boundary points. A plastic template was used to evaluate the efficiency of the boundary routine. It was found that it was able to identify edges to within approximately one pixel on screen. The complete procedure for stress separation was evaluated using a stress frozen disc in compression and a turbine slot. The values of stress found using the automated polariscope with the stress-separation procedure were found to agree well with theory and with results determined using the method of Tardy compensation and manual analysis. The automated polariscope was also used to analyze three-dimensional stress components along arbitrary lines of a 3D model. A two-model slicing regime was used to analyze a strut subjected to a vertical load. This work was compared to results obtained by Frocht and Guernsey on an identical model machined from Fosterite and subjected to a higher load. Good agreement was found between the results for points away from the region of loading. Significant differences were found near to the load point, however. A finite element analysis of the same problem suggested that this was due to the effects of plasticity.     

Dynamic-stress concentration using photoelasticity and a laser light source

Since experimental techniques using dynamic photoelasticity are, in general, limited by suitably intense monochromatic light sources, it was of primary importance to describe a ruby-laser system which would completely remove this particular aspect of the problem. Modulation of the system, in this case by a Kerr cell, provides the necessary control of the light output such that a complete series of results can be obtained by putting together the results of many individual tests recorded on a conventional still camera. In this case, the dynamic-stress-concentration factor in a strut with a symmetrically located circular discontinuity was determined to establish definitely the potential of the system.     

Role of light ellipse in photoelasticity and new methods for isoclinic-parameter determination

In dealing with various types of polariscopes the transformations that the light ellipse undergoes as it traverses through several optical elements give a better physical insight than the conventional trigonometrical transformations that are generally applied to the light vectors. Further, an understanding of the transformations of the light ellipse suggests several interesting methods for the determination of the isoclinic parameter.     

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.     

New methods in photoelasticity

The principle of polarization of scattered light is applied to determine the principal stresses in the interior of a model. On the basis of the theorem which states that “a series of birefringents is equivalent to a unique birefringent, followed by a medium endowed with rotational power,” it can be assumed that, if the characteristics of a series of birefringents are known, it is possible to find the characteristics of an interior section. The measurement of the characteristics of a birefringent (eventually following a medium endowed with rotational power) can be accomplished by means of the new methods, making use of a photomultiplier, a constant-speed rotating analyzer and a servomechanism These new methods of measurement are applicable to two-dimensional photoelasticity.     

Some techniques for employing a continuous-wave gas laser as a light source in scattered-light static photoelasticity

Experimental Mechanics -     

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.     

High-precision stress determination in photoelasticity

Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics. The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization. To improve the accuracy of stress calculation,a novel meshless barycentric rational interpolation collocation method(BRICM) is proposed. The derivatives of the shear stress on the calculation path are determine...     

Data analysis in dynamic photoelasticity

A method to separate the principal stresses and to obtain displacements from dynamic photoelastic fringe patterns is presented. The method utilizes geometric characteristics of either the model or the stress wave to provide the additional equation necessary for separation. The method is illustrated in ten specific cases.     

Holography and interferometry in photoelasticity

A physical explanation of photoelastic interferometry and holography is presented. Reasons for special properties and specific restrictions are argued in relation to this physical picture. The controlling intensity relationships for interferometry and holography are derived by simple physical analysis. The relationship between absolute retardation, isochromatic- and isopachic-fringe systems is clarified. Model material requirements for photoelastic interferometry and holography are shown to be identical.1971 William M. Murray Lecture was presented at 1971 SESA Fall Meeting held in Milwaukee, Wisc., On October 19–22.     

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.     

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.     

Analysis of scattered-light methods in photoelasticity

The use of scattered light for nondestructive analysis of general photoelastic models is becoming quite common and, during the last few years, several methods have appeared in the literature to determine the directions of the secondary principal stresses and their differences at any general point. Among the methods suggested, some are mentioned as “exact” and some “approximate”. Even the exact methods have limitations in their applicability for a generally stressed model. The present discussion attempts to bring out the inaccuracies involved in the various exact methods. Also, a few modifications to improve the accuracy and a new method called the Mini-max method are proposed. References 1, 2 and 3 give the general methods and the derivations of equations used in the present analysis.