 Photoelastic fringe value

The photoelastic fringe value $f_{\sigma }$ is the material-and-wavelength scale connecting photoelastic fringe order to principal-stress difference times specimen thickness in the linear stress-optic law. With vacuum wavelength $\lambda$ and stress-optic coefficient $C$, use the magnitude conventionHere $N=|\delta |/(2\pi )$ counts full relative-phase cycles and $t$ is specimen thickness. Since $C$ has units $\mathrm{P}{\mathrm{a}}^{-1}$, $f_{\sigma }$ has units $\mathrm{Pa}\mathrm{m}=N/m$. A value expressed in $\mathrm{MPa}\mathrm{mm}$ equals the same numerical value in $kN/m$. The wavelength dependence of $C$ must be retained.^[ref]

For an original example, take $\lambda =600\mathrm{nm}$ and $|C|=50\times 10^{-12}\mathrm{P}{\mathrm{a}}^{-1}$. Then $f_{\sigma }=12000N/m$. A3mm specimen at fringe order2.5 has stress-difference magnitude $2.5(12000)/0.003=10\mathrm{MPa}$. One additional complete phase cycle changes the inferred magnitude by4MPa for that thickness.

A uniaxial calibration supplies a known stress difference away from grips and other stress concentrations. For a rectangular strip of width10mm and thickness3mm, load300N gives stress10MPa. If the corresponding referenced fringe order is2.5, the measured fringe value is $10(3)/2.5=12\mathrm{MPa}\mathrm{mm}$. Repeating at several loads tests the assumed linear regime; counting from a referenced unloaded state helps separate the applied-load change from pre-existing retardation.

A primary instructional apparatus uses a manual leadscrew, load-cell readout, monochromatic illumination, polarizing elements and a camera. Those components connect a known mechanical load to the observed optical pattern.^[ref] A single intensity value does not uniquely identify an absolute phase cycle, so fringe order requires continuity, reference information or another phase-resolving method.

The magnitude convention loses the sign of $C$ and does not separately determine the two principal stresses. It also assumes the stated through-thickness optical/stress model. A varying stress field along the light path requires the appropriate retardation model rather than inserting one arbitrary local stress into the uniform-specimen formula.