Photoelasticity is an experimental technique used to measure stress and strain in materials by utilizing the optical properties of transparent materials under mechanical stress. When a transparent material is subjected to stress, it exhibits birefringence, which means that it refracts light differently depending on the direction of the applied stress. This phenomenon is due to the change in the material's refractive index caused by the internal stress.
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Photoelasticity is the dependence of a material’s optical response on stress, used to reveal otherwise invisible mechanical patterns. A transparent material that is optically isotropic before loading can become birefringent under load: orthogonal polarizations acquire different refractive indices and therefore a relative phase retardation.[ref]
For a thin, initially isotropic specimen in a suitable linear regime, the stress-optic law relates induced birefringence to the difference of in-plane principal stresses:Here is a material coefficient with units , is the optical thickness, the vacuum wavelength and the phase delay. This simple form assumes the relevant stress directions and difference do not change along the light path. A general three-dimensional specimen needs a more careful optical and mechanical model.
With ideal crossed polarizers, intensity normalized to the light after the first polarizer iswhere is the angle between the first polarization direction and a principal optical axis. A dark region can therefore arise from axis alignment or from an integer multiple of retardation. Darkness alone does not prove that stress is zero.
For illustrative , and , one full phase cycle corresponds toThese chosen values illustrate conversion from optical delay to a stress difference, not a calibration for every plastic. The method does not directly recover a hydrostatic stress shared equally by the two in-plane directions.
A polariscope makes the measurement visible. The Illinois teaching apparatus places a specimen between a polarizer and analyzer, applies load with a manual leadscrew, measures it with a load cell and records the pattern with a camera. Monochromatic illumination and adjustable polarization optics separate information about stress directions and differences.[ref]
Polariscope and Photoelasticity by the University of Illinois Mechanical Testing Instructional Laboratory. Apparatus description and direction/magnitude settings
Comparing patterns as load changes is a motivating experiment in connecting an optical observable to a mechanical model.