An Approximate Analysis of Axisymmetric Stress Field by Using Transmission Light Flow Birefringence Technique

A method was devised for analyzing an approximately axisymmetric stress field. It was assumed in the method that the extinction angle obtained from the isoclinic pattern is almost equal to the inclination of the principal axis of a refractive index ellipsoid and that the phase difference is dependent only on the local values of the double refractive index. An approximate equation was employed to analyze the local values of the primary double refractive index. This method was applied to analysis of stress for the flow around a sphere as an example of an axisymmetric flow field. According to the results of numerical calculation of the extinction angle and the optical equation, it was found that the above assumptions were reasonable. Values of the primary refractive index obtained by using the equation were somewhat lower than the actual value. It may be concluded that the method is effective for approximate stress analysis of axisymmetric flow fields with double refractive indices rising to the axis, if suitable correction for double refractive indices is made.