Experimental Assessment and Implementation of Photoelastic Tomography

3-D photoelasticity is a destructive and time-consuming experimental stress analysis technique
that assesses internal stress by the construction of a stress frozen polymeric prototype
that is sliced and analysed section by section by 2-D photoelasticity. Non-destructive 3-D
internal stress reconstruction, such as Photoelastic Tomography has been the main subject
of this research. Photoelastic Tomography can be taken as an optical tomography. However, it is not possible to apply directly the equations used in conventional tomography since
the mathematical approach of the Radon equation is just for scalar fields but Photoelastic
Tomography intends to obtain a tensor stress field. The directions and values of the principal
stresses vary through the thickness of the material which makes it difficult to process and
to relate the measured data with the non-linear stress distribution. Szotten, in his thesis ``Limited data problems in X-Ray and polarised light tomography'', proposes a mathematical
method for the solution of the stress tensor using Photoelastic Tomography. Numerical results
presented in his thesis showed evidence that this mathematical approach could be used to reconstruct the internal stress. This research aims to experimentally assess the
mathematics and the tensor stress reconstruction algorithms developed by Szotten to
obtain quantitative measurements of the 3-D internal stress in birefringent materials. The
research began with a critical audit of an existing rig used in previous preliminary research
of Szotten’s method. As a result of this audit, essential and considerable improvements were made to the
photoelastic tomography apparatus, methodology and software. The assumptions of the
mathematical approach require no refraction of the light passing through the specimen, so
key developments were made in the refractive index matching procedure within a tolerance of
0.001-2. Szotten’s method also requires rotations of the specimen about three different axes. In previous work, this repositioning of the sample was initially carried out manually. In this work, an automated
repositioning system and associated control programs were designed, manufactured and
commissioned, avoiding contamination of the matching fluid which may introduce noise
into the results. The introduction of a new camera to improve the signal to noise ratio
in the characteristic parameters was validated by a comparison between Fourier Polarimetry
and phase stepping methods.
Furthermore, the post-processing of the acquired images was
also improved by the development of algorithms that automatically detects the edges of the
specimen to cut the unnecessary background information not related to the sample to
save computational time. Experimental results in this research showed noise, patterns that did not follow a trend associated with the internal stress and no evidence of the relationship between the signal to noise ratio and the experimental variables tested. The conclusion drawn from this is that Szotten’s mathematical model does not agree with experimentation, and the reconstruction algorithms of the Photoelastic Tomography method need further theoretical developments before they can be used in practice.