A Non-linear Algorithm of Photoelastic Tomography for the Axisymmetric Problem

Abstract

A non-linear algorithm of photoelastic tomography for the measurement of axisymmetric stress fields has been elaborated. It is free of any assumptions concerning the value of the birefringence or rotation of the principal stress axes along the light rays. The algorithm is based on the measurement of characteristic directions and phase retardation in two parallel sections of the test object. Stress components are presented in the form of power series along the radial coordinate. A differential evolution algorithm has been used for finding the stress field parameters, which fit the measurement data best. Application of the method is illustrated by residual stress measurement in a drinking glass.

Modern Photoelasticity for Residual Stress Measurement in Glass

“…An algorithm of non-linear photoelastic tomography is described in Ref. [20]. Figure 7 shows the geometry of a high-pressure lamp and normal stress distribution in the critical section AB.…”

Annealing of Compression Molded Aspherical Glass Lenses

“…This will allow the axial stress r z and shear stress s rz to be determined directly from isoclinic angle u and retardation D [14][15][16][17]. The relations between u, D, and the components of the stress tensor along a light ray L can be expressed as [14] Dk…”

“…other stress components, radial stress r r , and circumferential stress r h , are determined [16,17]. C 1 is the integration constant determined by the boundary conditions at the surface of the specimen.…”

“…To evaluate the impacts of the annealing experiments, residual stresses and refractive index variation of the molded glass lens of pre-and postannealing were compared. The residual stresses were studied by a circular polariscope based on the property of birefringence of a glass lens [14][15][16][17]. The refractive index variation was measured and reconstructed by an optical setup based on MachZehnder interferometer [7,18].…”

Whole-field measurement of three-dimensional stress by scattered-light photoelasticity with unpolarized light

“…This is mainly caused by the rotation of the principal stress directions along the light path. The optical phenomena occurring in a 3-D photoelastic model have been studied theoretically by many researchers [1][2][3][4], and it is well known that any 3-D photoelastic model can be reduced to an optically equivalent model consisting of a pure rotator and a linear retarder. These two sets of principal axes at the entrance and exit of the equivalent model are termed the primary and secondary characteristic directions, and the retardation is termed the characteristic phase retardation [2].…”