Mechanic deformation can lead to the optical property change in an optical media, which is called photo elasticity. Therefore, this principle is commonly adopted to investigate the stress distribution in a material.
testing setup
A setup for stress distribution study by photo elasticity method.
The above is the setup for a stress distribution study.
Theory
Assuming σ3=0 since it 2D model and its thickness is small for a plate; Due to the principle stress σ1 and σ2, the components of light are faster and slower ( v1 and v2) than normal light along these two stressed directions. The optical path difference is
where tb is time for a normal light to pass through and vo is normal light speed in the media. According to Maxwell-Wertheim equations:
After certain math manipulation, it is easy to get:
Therefore, the light path difference, g, is correlated to the stress distribution. As shown in Figure 2, g is related to phase difference, delta, which will result in different interference patterns. Constructive/destructive interference enhances/reduces the transmitted light intensity. In return this interference presents the stress distribution of a media. One good example is as in Figure 3.
More details about the interference calculation can also be obtained in the link.
If white light, the pattern will be colorful, instead of the alternating white/black pattern in the above figure since mono-wavelength is used there.
Reference
- https://en.wikipedia.org/wiki/Photoelasticity
- https://www.uni-saarland.de/fileadmin/user_upload/Professoren/fr84_ProfBoller/FTPuploads/Lehre/SS2019/BF2/HSKL-StrucDur-LabSe4.pdf
- Procedia Engineering 19 (2011) 402 – 406