Theoretical Basis for the Photoelastic Residual Stress Evaluation in Misaligned Cubic Crystals

Photoelasticity is a fast and powerful technique for internal stress detection and quality control in crystals; to fully exploit its possibilities, an appropriate theoretical analysis must be developed for different crystallographic structure and observation planes. For a cubic crystal specimen whose geometry is non-coherent with its crystallographic directions (i.e., observation planes and crystallographic directions are not parallel), we write a set of equations that allow an estimate of the refraction indices as a function of the residual stress. This is obtained upon the assumption that the residual stress may be represented by a plane stress parallel to the observation face. For cubic crystals, we obtain an explicit estimate of the residual stress intensity; this can be achieved provided we know the piezo-optic tensor component, the orientation of two non-parallel specimen faces with respect to the crystallographic axes, and that we can measure the principal directions of the refractive indices on the observation face.