Whole field evaluation of stress components in digital photoelasticity—Issues, implementation and application

Digital photoelasticity has rapidly progressed in the last few years and has matured into an industry-friendly technique. This review thematically classifies all the developments in digital photoelasticity and highlights the relative merits and drawbacks of the various techniques. The overall objective is to provide enough information and guidance to allow an end-user to make an informed choice on the type of technique to be used in a particular situation.

Digital photoelasticity – A comprehensive review

With advancements in digital image processing and data acquisition, a separate branch of photoelasticity namely digital photoelasticity came into existence. Here, intensity information of the acquired image is used for the evaluation of whole-field photoelastic parameters. Digital photoelasticity provides only wrapped phasemaps of isoclinics and isochromatics and they have to be unwrapped in different ways for getting the continuous-phase values. In the case of the isochromatic phasemap, ambiguity removal prior to unwrapping is essential. In this paper, a 10-step phase-shifting methodology is proposed and a new strategy for obtaining the isochromatic phasemap free of ambiguity is demonstrated. Isoclinic unwrapping is performed by a new adaptive quality guided algorithm. Adaptive in the sense that isoclinic phase unwrapping is done autonomously even in the presence of isotropic points/π jumps occurring in the isoclinic phasemap. The isochromatic phasemap is also unwrapped using the quality guided path follower. The methodology is validated for the problem of a ring under diametral compression and later shown for three other models which have complex stress fields. Wherever possible, the parameters obtained by the new methodology are compared with analytical or numerical methods and the comparison is quite good.

Adaptive Quality Guided Phase Unwrapping Algorithm for Whole-Field Digital Photoelastic Parameter Estimation of Complex Models

The red-blue-green (RGB) calibration technique consists in constructing an a priori calibration table of the isochromatic retardation versus the triplet of RGB values obtained with a RGB CCD camera. In this way a lookup table (LUT) is built in which the entry is the corresponding RGB triplet and the output is the given retardation. This calibration (a radiometric quantity) depends on the geometric and chromatic parameters of the setup. Once the calibration is performed, the isochromatic retardation at a given point of the sample is computed as the one that minimizes the Euclidean distance between the measured RGB triplet and the triplets stored in the LUT. We present an enhanced RGB calibration algorithm for isochromatic fringe pattern demodulation. We have improved the standard demodulation algorithm used in RGB calibration by changing the Euclidean cost function to a regularized one in which the fidelity term corresponds to the Euclidean distance between RGB triplets; the regularizing term forces piecewise continuity for the isochromatic retardation. Additionally we have implemented a selective search in the RGB calibration LUT. We have tested the algorithm with simulated as well as real photoelastic data with good results.

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Improved method for isochromatic demodulation by RGB calibration.

The application of phase-shifting photoelasticity to a real-time dynamic event involves simultaneous recording of the four phase-shifted images. Here an instrument, believed to be novel, is developed and described for this purpose. Use of a Multispec Imager is introduced into digital photoelasticity for the first time to our knowledge. This device enables splitting the optical energy of an object into four identical paths, thus permitting recording of the required four phase-shifted images. Experimental demonstration is provided for validation.

Dynamic phase-shifting photoelasticity.

The new approach to phase-stepping photoelasticity known as ‘‘load stepping’’ is used to determine automatically the isochromatic parameter a and the isoclinic angle ?. There is no need for the user to calibrate the results other than to convert the isochromatic parameter into a principal stress difference using the material fringe constant. Four phase-stepped images are collected using a circular polariscope for each of three load steps, which differ by small equal increments. A ramped phase map for the isochromatic parameter is produced in the range -?<??? that can be unwrapped using conventional techniques. Calibrated values of a can then be calculated using the phase map of ??, which is the incremental change in the isochromatic value between the different steps. The value of the isoclinic angle is automatically determined in the correct range -?/2<?????/2 without unwrapping. The results obtained from experimental testing of a disk-in-compression specimen using transmission photoelasticity presented in comparison with theoretical solutions demonstrate the accuracy of the new approach. In another test performed on a bar in torsion using reflection photoelasticity we demonstrate how determination of the isoclinic angle in the range -?/2<???/2 gives results superior to those obtained if the isoclinic angle is determined in the wrapped range -?/4<???/4 .

Matthew J. Ekman

Papers

Completely automated determination of two-dimensional photoelastic parameters using load stepping