Photoelasticity - Principles

Principles

The method is based on the property of birefringence exhibited by certain transparent materials. Birefringence is a property where a ray of light passing through a birefringent material experiences two refractive indices. The property of birefringence (or double refraction) is exhibited by many optical crystals. But photoelastic materials exhibit the property of birefringence only on the application of stress, and the magnitude of the refractive indices at each point in the material is directly related to the state of stress at that point. Thus, the first task is to develop a model made of such materials. The model has a similar geometry to that of the structure on which stress analysis is to be performed, ensuring that the stress in the model is similar to the stress in the structure.

When a ray of plane polarised light is passed through a photoelastic material, it gets resolved along the two principal stress directions and each of these components experiences different refractive indices. The difference in the refractive indices leads to a relative phase retardation between the two component waves. The magnitude of the relative retardation is given by the stress optic law:

where R is the induced retardation, C is the stress optic coefficient, t is the specimen thickness, σ₁₁ is the first principal stress, and σ₂₂ is the second principal stress.

The two waves are then brought together in a polariscope. The phenomena of optical interference takes place, and a fringe pattern is revealed, which depends on relative retardation. By studying the fringe pattern one can determine the state of stress at various points in the material.