Fotoelasticity

Fotoelasticity, commonly spelled photoelasticity, is an experimental method for visualizing and measuring internal stresses in transparent materials by using stress-induced birefringence. When such a specimen is loaded and viewed between polarizers, distinctive fringe patterns reveal the stress state.

Principle: Under plane stress, the material develops birefringence with a principal index difference Δn proportional to the principal stress difference (σ1 − σ2): Δn = C(σ1 − σ2), where C is the stress-optic coefficient. Light of wavelength λ traversing thickness t acquires retardation Δ = Δn t. A visible fringe order N satisfies Δ = Nλ, giving σ1 − σ2 = (Nλ)/(C t). Isochromatic fringes indicate equal stress difference, and isoclinic fringes show the principal stress directions.

Methods: A plane polariscope (two linear polarizers) yields qualitative fringe patterns; a circular polariscope (polarizer, quarter-wave plate, analyzer) helps separate isochromatic fringes from isoclinics and is more suitable for quantitative work. Digital photoelasticity combines fringe analysis with image processing to compute stress fields.

Applications and limitations: Used in engineering to study stresses in transparent components, plastics, and laminated composites under bending, torsion, and impact. It provides rapid qualitative visualization and, with calibration, quantitative estimates of principal stress differences. Limitations include the need for transparent specimens, predominantly two-dimensional stress fields, thickness uniformity, and careful interpretation of fringe data.

See also: birefringence, stress optics, polariscope, isochromatic and isoclinic fringes.