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.

Automated summary

Photoelasticity as a technique can be used for internal stress detection and quality control in crystals. However, to fully exploit its potentials, a suitable theoretical analysis is required for different crystallographic structures and observation planes. For cubic crystal specimens with non-coherent geometry with crystallographic directions, a set of equations can be derived to estimate the refractive indices based on residual stress. An explicit estimate of the residual stress intensity can be obtained for cubic crystals if the piezo-optic tensor component, orientation of two non-parallel specimen faces with respect to crystallographic axes, and principal directions of refractive indices on the observation face are known.