The case of weak birefringence in integrated photoelasticity

Abstract

The main difficulties connected with the application of integrated photoelasticity are as follows: (1) in general (when rotation of the principal axes is present) one has to measure three characteristic parameters for each ray (instead of two in two-dimensional photoelasticity and in the frozen stress method); (2) the characteristics parameters are connected with the stress distribution in a very complicated manner: to determine the stress distribution from their basis is difficult. If the birefringence is weak, then measurements can be simplified. In the latter case a usual plane polariscope may be used for measurements, and simple approximate integral relationships between the experimental data and the distribution of birefringence on the ray are valid, if rotation of the principal axes is moderate. The paper attempts to establish the domain where application of these relationships is justified. By the aid of numerical experiments it is shown that simple integral relationships can be applied if optical retardation is less than a quarter of a wavelength and rotation of the principal axes is less than π/6. In the latter case by investigating a three-dimensional model the parameter of isoclinic and the optical phase retardation are measured exactly in the same way as by investigating a two-dimensional model.