Design and fabrication of a twyman-green interferometer for photoelastic stress analysis

Abstract

Interferometric methods of analysing photoelastic specimens are powerful techniques in stress analysis. Unlike the conventional photoelastic stress patterns, the patterns obtained from interferometers contain information regarding the sum and the difference of principal stresses. In the case of two-dimensional models, interferometry gives information about the changes in refractive indices and also the changes in the thickness (which is proportional to the sum of the principal stresses). In the case of three-dimensional models, it gives information about the sum and difference of refractive indices. Nisida and Saito have demonstrated these facts by mathematical models and by conducting experiments using Mach–Zehnder interferometer on two-dimensional photoelastic specimens. However, to evaluate stresses in three-dimensional models, Nisida, Saito and Sawa have used two interferometric stress patterns obtained before and after annealing the slice. The technique of annealing the slice while kept immersed in a matching liquid is a difficult and cumbersome process. Srinath and Mehrotra have described a method of using only one interferometric stress pattern in addition to photoelastic patterns for the complete three-dimensional analysis and thus avoiding the use of the annealing technique. The main objective of this thesis is to design and construct a Twyman–Green interferometer suited for stress analysis and to investigate stress distributions in two and three-dimensional photoelastic specimens. A 100 mm aperture Twyman–Green interferometer was designed and fabricated for this purpose. The design aspects of optical and mechanical components used in this interferometer are presented. In addition, the adjustments of the interferometer and the techniques used to isolate the interferometer from vibrations are given. (a) Plane Stress Case The equation for the intensity of light passing through a two-dimensional model kept in one arm of the interferometer has been derived. The equation shows that it is a product of isopachic and isochromatic functions. Experiments were conducted on a circular disc under diametral compression and on a simply supported beam with a central concentrated load. The method used to determine the stress optic coefficients of the model material is given. Based on Sanford and Durelli's discussions, the fringe orders were determined along the lines of interest. Stress distributions along the lines of interest on these models were determined and found to have good agreement with theoretical values. (b) Three-dimensional Stress Case The general equation of the light passing through a three-dimensional model has been derived and its application to an axisymmetric body is discussed. A diametral slice cut from a stress-frozen cylinder under a central load was used for the experiment. Since the slice was not of an optical quality, it was not suitable for interferometry. It had to be immersed in a liquid of the same refractive index as that of the model material. The refractive index of the material of the slice was determined by dark-ground observation. Distributions of principal stresses along the axis of symmetry were investigated and the results were compared with the theoretical analysis and the results obtained using Mach–Zehnder interferometer and photoelastic techniques. In order to analyse the stresses along a line 30° to the axis of symmetry, the use of conventional transmitted light polariscope in addition to the interferometer was adopted. The isoclinic and isochromatic parameters obtained along the line of interest by viewing the slice under one normal incidence and one oblique incidence were coupled with the interferometric data for the analysis. The results obtained are presented. To check these results, the conventional shear-difference method is suggested. As suggested by Drucker, three isochromatics photographs taken under one normal incidence and two oblique incidences will give sufficient information for the shear-difference method. The equations required for this method have been derived and the detailed procedures to calculate the distribution of principal stresses are also given.