Determination of All Stress Components of Axisymmetric Stress State in Photoelastic Tomography

In this paper we describe the application of photoelastic tomography for determining stresses in glass. The basic equations of linear approximation in photoelastic tomography are presented. Since these equations permit direct determination only of the axial and shear stress, a method for calculating the other stress components is described. In the case of the residual stresses, it uses the equilibrium equation and the generalized sum rule. In the case of stresses due to external loads, it uses the equilibrium and compatibility equations. It is shown, both graphically and analytically, that integration of these equations must start at the axis and proceed along the positive direction of the radial axis. As an example, residual stresses in the stem of a wine glass are determined. Results are verified by comparing the birefringence, calculated from the determined stress state, with measured birefringence. The numerical algorithm for the case of stresses due to external loads is verified by using the theoretical solution for a Hertzian contact stress problem.