Coupled Strain and Fresnel Response of Photoelastic Coatings at Oblique Incidence

Abstract

This paper presents a theoretical model and corresponding experimental results of the oblique-incidence response of a luminescent photoelastic coating (LPC). LPCs use a luminescent dye that both partially preserves the stress-modified polarization state and provides high emission signal strength at oblique surface orientations. These characteristics enable the technique to acquire full-field strain separated measurements and principal strain directions, potentially on complex three-dimensional geometries, without the use of supplemental experimental or analytical techniques. Results of a single-layer LPC on a disk in diametral compression are presented to assess a theoretical model and evaluate the measurement sensitivity.

Appendix

Expressions for the coefficients A and B in equation (8) are

$$ \begin{array}{*{20}c} {\frac{A} {{\phi _{{{\text{qe}}}} \phi _{a} E_{{{\text{ex}}}} }}}{ = {\left( {t_{{IIo}} t_{{IIi}} \cos ^{2} \theta \prime + t_{{IIo}} t_{{IIi}} \sin ^{2} \theta \prime \cos \delta * - \frac{1} {2}t_{{IIo}} t_{{ \bot i}} \sin 2\theta \prime \sin \delta *} \right)}\cos \alpha \prime } \\ {}{ + {\left( {\frac{1} {2}t_{{ \bot o}} t_{{IIi}} \sin 2\theta \prime - \frac{1} {2}t_{{ \bot o}} t_{{IIi}} \sin 2\theta \prime \cos \delta * + t_{{ \bot o}} t_{{ \bot i}} \cos ^{2} \theta \prime \sin \delta *} \right)}\sin \alpha \prime } \\ \end{array} $$

(21)

and

$$ \begin{array}{*{20}c} {\frac{B} {{\phi _{{{\text{qe}}}} \phi _{a} E_{{{\text{ex}}}} }}}{ = {\left( { - \frac{1} {2}t_{{IIo}} t_{{ \bot i}} \sin 2\theta \prime + \frac{1} {2}t_{{IIo}} t_{{ \bot i}} \sin 2\theta \prime \cos \delta * + t_{{IIo}} t_{{IIi}} \sin ^{2} \theta \prime \sin \delta *} \right)}\cos \alpha \prime } \\ {}{ - {\left( {t_{{ \bot o}} t_{{ \bot i}} \sin ^{2} \theta \prime + t_{{ \bot o}} t_{{ \bot i}} \cos ^{2} \theta \prime \cos \delta * + \frac{1} {2}t_{{ \bot o}} t_{{IIi}} \sin 2\theta \prime \sin \delta *} \right)}\sin \alpha \prime } \\ \end{array} . $$

(22)