Polarization tomography for residual stress measurements in a hexagonal single crystal

Abstract

The application of tensor field tomography for non-destructive reconstructions of residual stresses in a long hexagonal single crystal is studied. The residual stresses are considered to be of a tempering character. Thus, it is assumed that there exists a temperature field T(x,y,z), the so-called fictitious temperature, which causes a stress field that is equal to the stress pattern. Transformation of the polarization of light is measured in a plane orthogonal to the optical axis of a crystal. Stresses are determined within the framework of the Maxwell piezo-optic law (linear dependence of the permittivity tensor on stresses) and the small rotation of principal stress axis. This paper generalizes a method of integrated photoelasticity for the case of a hexagonal single crystal.

Inverse problem of thermoelasticity of fiber gratings

“…Therefore, the rst and third types of stresses are to be reconstructed. The quasi-plane-stressed state is reconstructed by the local method based on reconstructing the values of the axial stress and two rst derivatives of this stress with respect to the axial direction [14]. The algorithm of the reconstruction of the third type of stress state is based on the decomposition of the axial stresses in a Fourier series over entire length of period of grating.…”

“…This fact gives an opportunity to apply reconstruction method properly. The goal of this article is the detailed investigation of the inverse thermoelastic problem in the case of periodical variation of residual stresses along the ber axis [14].…”