Editing Photoelasticity (section)

==Experimental principles==
[[File:Plastic Protractor Polarized 05375.jpg|thumb|Tension lines in a plastic protractor seen under cross-polarized light]]

The experimental procedure relies on the property of [[birefringence]], as exhibited by certain transparent materials. Birefringence is a phenomenon in which a ray of light passing through a given material experiences two [[refractive index|refractive indices]]. The property of birefringence (or double refraction) is observed in many optical [[crystal]]s. Upon the application of stresses, photoelastic materials exhibit the property of birefringence, and the magnitude of the refractive indices at each point in the material is directly related to the state of stresses at that point. Information such as maximum [[shear stress]] and its orientation are available by analyzing the birefringence with an instrument called a [[polariscope]].

When a ray of [[Electromagnetic radiation|light]] passes through a photoelastic material, its electromagnetic wave components are resolved along the two [[Stress (mechanics)|principal stress directions]] and each component experiences a different refractive index due to the birefringence. The difference in the refractive indices leads to a relative [[Phase (waves)|phase]] retardation between the two components. Assuming a thin specimen made of [[Hooke's law|isotropic]] materials, where two-dimensional photoelasticity is applicable, the magnitude of the relative retardation is given by the ''stress-optic law'':<ref>Dally, J.W. and Riley, W.F., ''Experimental Stress Analysis,'' 3rd ed., McGraw-Hill Inc., 1991 {{ISBN?}} {{page?|date=September 2024}}</ref>

: <math> \Delta = \frac{2\pi t} \lambda C ( \sigma_1 - \sigma_2) </math>

where &Delta; is the induced retardation, ''C'' is the '''{{vanchor|stress-optic coefficient}}''', ''t'' is the specimen thickness, ''λ'' is the vacuum wavelength, and ''σ''<sub>1</sub> and ''σ''<sub>2</sub> are the first and second principal stresses, respectively. The retardation changes the polarization of transmitted light. The polariscope combines the different polarization states of light waves before and after passing the specimen. Due to optical [[Interference (wave propagation)|interference]] of the two waves, a fringe pattern is revealed. The number of fringe order ''N'' is denoted as

: <math> N = \frac \Delta {2\pi}</math>

which depends on relative retardation. By studying the fringe pattern one can determine the state of stress at various points in the material.

For materials that do not show photoelastic behavior, it is still possible to study the stress distribution. The first step is to build a model, using photoelastic materials, which has geometry similar to the real structure under investigation. The loading is then applied in the same way to ensure that the stress distribution in the model is similar to the stress in the real structure.