## 2 Materials and Method  
### Theoretical Background  
Photoelasticity describes the changes in the optical properties of a material under mechanical deformation, and this experimental method can be used to analyze the stress and strain field. A photoelastic material has isotropic properties in normal conditions but exhibits anisotropy when an external force is applied. Birefringence can be observed when light is transmitted after applying an external force to the photoelastic material. Birefringence is a phenomenon in which a single light wave with the same wavelength is split into two light waves and refracted when incident on an optically anisotropic material. At this time, if the travel speeds of the two refracted light waves are \(v_{1}\) and \(v_{2}\), respectively, and the thickness of the photoelastic material is \(h\), the time difference between the two refracted light waves is called relative retardation, \(\delta\), which can be expressed as follows [21]:  
\[\delta=2\pi f\bigg{(}\frac{h}{v_{1}}-\frac{h}{v_{2}}\bigg{)}=2\pi h\frac{c}{ \lambda}\bigg{(}\frac{1}{v_{1}}-\frac{1}{v_{2}}\bigg{)}=\frac{2\pi h}{\lambda} (n_{1}-n_{2}) \tag{1}\]  
where \(f=\) the frequency of the incident light; \(h=\) the thickness of the photoelastic material; \(c=\) the velocity of the light; \(\lambda=\) the wavelength of the incident light; and \(n_{1}\) and \(n_{2}=\) the refractive indices of two light waves. [PERSON] [31] defined the relationship between refractive index and stress as follows:  
\[(n_{1}-n_{2})=C(\sigma_{1}-\sigma_{2}) \tag{2}\]  
where \(\sigma_{1}\) is the maximum principal stress; \(\sigma_{2}\) is the minimum principal stress; and \(C\) is the relative stress-optic coefficient. Substituting Equation (2) into Equation (1), Equation (3) can be obtained as follows:  
\[\delta=\frac{2\pi h}{\lambda}C(\sigma_{1}-\sigma_{2}) \tag{3}\]  
There are two main types of photoelastic techniques: transparent and reflective. For both methods, light from the light source passes through a plane polarizer, a quarter wave plate, and a photoelastic material. Here, the planar polarizer is composed of a polarizer that linearly polarizes the incident light and an analyzer that is used to observe the light passing through the photoelastic material. The quarter wave plate causes circular polarization by giving a phase difference of \(\lambda/4\) with respect to the linearly polarized light passing through the planar polarizing plate. To observe the birefringence phenomenon, the optimal method is to use circularly polarized light in which the azimuth is symmetrical. Figure 1 shows the difference between the transparent and reflective techniques. In the transparent technique shown in Figure 1a, the light of the light source passes through the polarizer-1/4 wave plate-photoelastic material-1/4 wave plate-analyzer in the order that it is observed. However, in the reflective technique shown in Figure 1b, the light of the light source observes the light passing through the polarizer-1/4 wave plate-photoelastic material-reflector-photoelastic material-1/4 wave plate-analyzer in the order of the photoelastic material and is passed through twice. For this reason, the relative delay in the reflective technique is calculated by setting \(h\) to \(2h\) in Equation (3) above. In the reflective method, because the light source and the observer are located in the same direction facing the specimen, structure analysis can be performed more easily compared to the transparent method. In this study, a sheet with a reflective coating on the back of a transparent photoelastic material was used to utilize the reflective technique. The light intensity of the light passing through the polarizer, a quarter wave plate, and the analyzer was calculated by Equation (4) shown below [21]:  
\[I=I_{a}sin^{2}\frac{\delta}{2} \tag{4}\]  
where \(I_{a}\) is the brightness of the incident light.