---
title: "Photoelastic Stress Viewer Interactive Lab | Sandbox Physics"
description: "How do colorful polarization fringes map the principal-stress difference inside a loaded object?"
canonical_url: "https://sandboxphysics.com/labs/photoelastic-stress-viewer/"
language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/photoelastic-stress-viewer/"
last_modified: "2026-10-29"
---

Optics 078 · Polarization, anisotropy, and modulation

# Photoelastic Stress Viewer

**How do colorful polarization fringes map the principal-stress difference inside a loaded object?** Under load, a transparent material turns birefringent in proportion to the difference of its principal stresses. Between polarizers that delay appears as colored fringes, each a line of equal stress difference. A circular polariscope removes the dark bands tied to stress direction. Fringe orders still have to be counted, and equal principal stresses, such as uniform pressure, give no fringes.

Load three specimens with analytic stress solutions in a 3D polariscope. Compare fringes in plane and circular polarization, probe the stress tensor at any point and record exposures under LED light.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

The stress fields come from linear elasticity for reference geometries, with an assumed constant stress-optic coefficient. The plate is a crop of an infinite plate, and the regions at the disk's point contacts are excluded. The LED channels are ideal. White-light color rendering and recovering stress from the fringes are not included.

Physics tutorial

## Audit the physics of Photoelastic Stress Viewer

**Background** Under load, a transparent polymer acts as a retarder that varies from point to point. Its optical axes line up with the two principal stress directions. The stress-optic law is $\delta=\frac{2\pi C t}{\lambda}\Delta\sigma$. The thickness is the actual path of light through the specimen at normal incidence, and stresses are in megapascals. The material coefficient is an assumed constant, not fitted to a real sample. Every specimen is drawn in its undeformed reference shape.

**Why it matters** How do colorful polarization fringes map the principal-stress difference inside a loaded object?

Start with the essentials

- **Focus question**: How do colorful polarization fringes map the principal-stress difference inside a loaded object?
- **One-sentence intuition**: A circular dark-field stack removes the extinction that depends on orientation, leaving $I_{\rm circ}/I_0=\sin^2(\delta/2)$. A plane crossed pair adds a factor that depends on orientation. Rotating that pair moves the dark isoclinics, while the stress field stays the same. Neither image gives the hydrostatic stress or a unique fringe order directly.

### Core mathematical model

#### Principal stresses and optical phase

$$
\begin{aligned}\Delta\sigma&=\sqrt{(\sigma_{uu}-\sigma_{vv})^2+4\sigma_{uv}^2}\\N_\lambda&=\frac{Ct\Delta\sigma}{\lambda}\\C&=60\times10^{-12}\,\mathrm{m^2/N}\end{aligned}
$$

The coefficient is a stated teaching assumption. When the two principal stresses are equal, the principal direction is undefined, and no false horizontal axis is drawn there. Stress and thickness are converted to pascals and metres exactly once.

#### Plane versus circular dark field

$$
\begin{aligned}I_{\rm plane}/I_0&=\sin^2[2(\phi-\theta_P)]\sin^2(\pi N_\lambda)\\I_{\rm circ}/I_0&=\sin^2(\pi N_\lambda)\end{aligned}
$$

Intensity is normalized to the light leaving the preparation polarizer. In circular mode, two ideal quarter-wave plates sit on either side of the sample, with opposite axes relative to the crossed pair. The screen receives the normal rays one to one, as in geometrical optics, and diffraction is neglected.

#### Three different boundary loads

$$
\begin{aligned}\text{beam:}\quad q&=\frac{6M}{th^2},\quad\sigma_{uu}=-\frac{2qv}{h}\\\text{hole:}\quad q&=\sigma_\infty,\quad\sigma_{\theta\theta}(a,\pi/2)=3q\\\text{disk:}\quad q&=\frac{F}{Dt},\quad\Delta\sigma(0)=\frac{8q}{\pi}\end{aligned}
$$

The beam is loaded by opposing couples at its ends. The hole uses the Kirsch field for an infinite plate. The disk uses equal and opposite point loads plus a uniform correction that keeps its rim free. The regions within two millimetres of the singular contact points lie outside the model. There is no finite-element solver, deformation, failure prediction or stress inversion.

### Common difficulties

#### Brighter means more stress?

**Typical misconception** A bright pixel uniquely determines both principal stresses.

**Better mental model** Intensity repeats as the principal-stress difference grows, so each whole fringe order is dark again. In plane optics, a point also goes dark when its optical axis lines up with the polarizer. Adding the same hydrostatic stress to both principal stresses changes neither image. The reference stress tensor here comes from analytic mechanics, not from a photograph.

### Run the experiment

1. 01

   #### Scene 1: Pure bending beam

   In pure bending, raise the stress scale and probe above and below the neutral axis. The stress changes sign across the axis, but the stress difference and the circular intensity are symmetric.

   **What to observe:** Light travels along positive X. Looking downstream from in front of the screen, right is positive Z and up is positive Y. The specimen coordinates follow these directions, and positive angles turn from right toward up.

2. 02

   #### Scene 2: Infinite plate around a hole

   Choose the hole window and drag the probe to the top of the hole. There the tangential stress is three times the remote tension. The edges of the rectangular window are a crop, not free edges of the plate.

   **What to observe:** The intensity image appears only on the physical receiving screen; no copy floats in space. The specimen thickness really changes, but no mechanical deflection is shown.

3. 03

   #### Scene 3: Diametric disk compression

   Choose diametric compression and compare the center with the two excluded contact patches. The solution uses opposed point forces; it is not a Hertz contact calculation.

   **What to observe:** Three independent narrow-band LEDs feed ideal red, green and blue channels. This is not a white-light spectrum, calibrated camera color or a real achromatic waveplate design.

Physical conclusion

A polariscope shows how birefringence varies across the specimen; it is not an unambiguous photograph of stress. Keep the mechanics, the polarizer geometry and the recorded intensities separate when you compare them.

## Related experiments and articles

Fracture mechanics · Reading path

### Fracture mechanics from Griffith’s energy balance to branching cracks

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why a crack needs energy to grow**](https://sandboxphysics.com/stories/fracture-mechanics/why-cracks-need-energy/)
2. [Lab **Griffith Criterion for Crack Growth** Grow a crack and track where the work goes](https://sandboxphysics.com/labs/griffith-crack-growth/)
3. [Lab **Stress–Strain Material Tester** Measure modulus and yield stress](https://sandboxphysics.com/labs/stress-strain-tester/)
4. [Article **Stress near a crack tip and the stress intensity factor**](https://sandboxphysics.com/stories/fracture-mechanics/stress-near-the-crack-tip/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)