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

TLDR: In this paper, a ramped phase map for the isochromatic parameter is produced in the range -?<??? that can be unwrapped using conventional techniques, and the value of the isoclinic angle is automatically determined in the correct range without unwrapping.

Abstract: 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 .