photoelasticity

Photoelasticity is a non-destructive optical technique for visualizing and measuring internal stresses in transparent materials by exploiting stress-induced birefringence. When a transparent specimen is loaded and viewed through a polariscope, its isotropic refractive indices split along orthogonal principal stress directions, creating birefringence that induces a phase retardation between the orthogonally polarized light components. This retardation leads to fringe patterns in which each isochromatic fringe corresponds to a constant difference between the principal stresses.

In linear photoelasticity, the relationship between stresses and fringes is σ1 − σ2 = N λ /(C t), where N is the fringe order, λ the illumination wavelength, t the specimen thickness, and C the material's stress-optic coefficient (the fringe value). Equivalently, optical retardation δ = (2π/λ) t C (σ1 − σ2). The technique thus maps the difference between principal stresses to observable fringe patterns.

A common arrangement is the plane polariscope, which uses crossed polarizers to reveal isochromatic fringes. Under white light, fringes appear in color and provide qualitative stress information; with monochromatic light, the fringe order is more easily counted for quantitative analysis. Modern practice often employs digital photoelasticity, combining image capture with calibration and analysis to obtain quantitative full-field stress distributions, frequently in conjunction with finite element results.

Applications include structural analysis of beams, plates, and joints, education and demonstrations, and verification of analytical or numerical models. Limitations include the requirement for transparent, elastic materials, the need for proper calibration, and the fact that measurements are most straightforward in plane stress and near the surface.