Stress Separation by Means of Phase Shifting in Photoelasticity

Abstract

Photoelasticity has served as a valuable experimental method for performing stress analysis for decades. Since its inception, it has been applied in solving a tremendous number of engineering problems. This paper presents an automatic approach for the evaluation of isochromatics and isoclinics in photoelasticity using complimentary phase shifting. The phase map of the isoclinics is obtained from 4 images acquired in the plane polarizer arrangement by rotating the polarizer and analyzer simultaneously, as shown in Fig. l(a). Ambiguity exists due to the isoclinic phase values are wrapped in a range of (0,π/2), which indicate the angle made by either σ₁ or σ₂ with horizontal axis. We present a novel method to extend the range of isoclinic phase value to (- π/2, π/2), which represent the orientation of σ₁ only, as shown in Fig. l(b). In circular polariscope, phase shifting can be applied to isochromatic fringe patterns if the orientation of σ₁ is given analogous to Tardy compensation. Phase maps for the isochromatics are then achieved at 8 specifically selected discrete orientations through sequential analyzer rotations. With the knowledge of σ₁ orientation, a whole-field description of the phase values of the isochromatics is then constructed, as shown in Fig. 2(a). The absolute phase value of isochromatics can be obtained through an unweighted leastsquares phase unwrapping processing, as shown in Fig. 2(b). Sophisticated software has been developed for automatic photoelastic data processing from image acquirement to stress analysis. In an effort to validate the process and illustrate application, an example of the proposed method is presented using a plate loaded in diametrical compression. Stress components at three horizontal sections of the circular plate are calculated with the shear stress differential method (Fig. 3). Results show good agreement with the theoretical solution and the method is easy to conduct and applicable to engineering problems.