## 2 Superimposed Static and Dynamic Loading Experiments
### DIC Technique  
It is necessary to spray speckles on the specimen surface for the full-field strain measurement by the DIC technique. Some specimens with speckle are shown in Figure 3. These speckles are used to calculate the field of displacement and can be treated as the signatures on the surface of a specimen [49]. The displacement field and strain field of the specimen surface are obtained by the image matching techniques and registration algorithms. Figure 4 shows the basic principles of the DIC technique.  
The digital speckle image before deformation is taken as the reference image, and the square area with \(f_{1}(x,y)\) as the center is used as the reference subarea. Assuming that the gray level of the sub-region remains unchanged or changes linearly after the deformation, the target subarea with \(f_{2}(x,y)\) as the center and with the largest correlation coefficient to the reference subarea can be found in the deformed image by searching point by point. The horizontal and vertical displacement components \(u(x,y)\) and \(v(x,y)\) of the calculated point are then obtained. The coordinate of any measuring point on the digital speckle image before and after deformation meets the following relationship:  
\[\left.\begin{array}{l}f_{2}(x)=f_{1}(x)+u(x,y)\\ f_{2}(y)=f_{1}(y)+v(x,y)\end{array}\right\} \tag{1}\]  
The principle of 3D-DIC is to set up two high-speed cameras or high-resolution CCD industrial cameras, which form a certain angle with each other, calibrate the dual camera system with checkerboard target or dot mark plate, then record the same scene in space synchronously by using these two cameras, and then obtain the target subarea for two images of the specimen surface by matching algorithm at the same time. Finally, according to the camera's internal and external parameters, the spatial coordinates of the surface points are calculated. As shown in the image of Figure 5, it is possible to recover the three-dimensional position of the true object points by recording simultaneous image points using two cameras (C and C'). The 3D points Q and R are two points on the same projection ray (C, P), which proves that there are infinite 3D points corresponding to the image point P. For example, when two image points are (p, q'), the unique 3D point is Q. If the corresponding image points are (p, r'), the unique 3D point is R.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test Case** & \begin{tabular}{c} **Ratio of Static** \\ **Pre-Stress to UCS** \\ \end{tabular} & \begin{tabular}{c} **Static** \\ **Pre-Stress/MPa** \\ \end{tabular} & \
\begin{tabular}{c} **Dynamic Strain** \\ **Rate/s\({}^{-1}\)** \\ \end{tabular} \\ \hline D1 & 40\% & 30.84 & \\ D2 & 50\% & 38.55 & \\ D3 & 60\% & 46.26 & \\ D4 & 70\% & 53.97 & \\ \hline D5 & 40\% & 30.84 & \\ D6 & 50\% & 38.55 & \\ D7 & 60\% & 46.26 & \\ D8 & 70\% & 53.97 & \\ \hline D9 & 40\% & 30.84 & \\ D10 & 50\% & 38.55 & \\ D11 & 60\% & 46.26 & \\ D12 & 70\% & 53.97 & \\ \hline \hline \end{tabular}
\begin{tabular}{c} D13 \\ D14 \\ D15 \\ \end{tabular} & 40\% & 30.84 & \\ D10 & 60\% & 38.55 & \\ D11 & 60\% & 46.26 & \\ D12 & 70\% & 53.97 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Loading schemes.