# Analysis of Optimal Loading Angle in Dynamic Flattened Brazilian Disc Splitting Test for Concrete
## 5 Results and Analysis
### Strain Analysis of Crack Propagation in BD Specim  
To confirm the results obtained by DIC, the location and sequence of crack initiation were also examined from the strains recorded by strain gauges at different locations of the disc specimen under different loading angles, as shown in Figure 15. As can be seen from Figure 15, the maximum principal strain at the monitoring point under impact loading first exhibits a nonlinear variation, indicating an increasing degree of damage at this point. Fracture occurs when the damage at this point reaches its maximum level. The sudden increase in strain at the monitoring point is defined as the failing moment for each strain gauge. Due to the dense data, it is not appropriate to discern from the graph, but the strain value of the mutation point can be accurately identified in the raw data text. Since the sampling frequency of the dynamic acquisition instrument is set to 2 MHz, the strain value corresponding to each time can be seen in the raw data text. By importing the data into origin in the form of a picture that cannot be easily discriminated, the mutation point can be easily identified through the raw data text. Hence, the point where the sudden change in strain occurs in the experiment is taken as the fracture point of the specimen, and the failure strain at this time is reliable from the data of previous studies. It can be seen that the average failure strain is 6.61 \(\times\) 10\({}^{-3}\) at an impact velocity of 9.6 m/s and a loading angle of 20\({}^{\circ}\). Under the action of the average impact speed of 4.9 m/s, when the loading angle is less than 26\({}^{\circ}\), the time of fracture of the 5\(\mu\) strain gauge is earlier than that of the 1\(\mu\) strain gauge, and the response to the force wave action is the first; the overall trend at the moment of fracture of the strain gauge is left high and right low as shown in Figure 16a, indicating that the crack propagation starts from the A\({}_{2}\) end; with the increase in the impact speed,  
Figure 14: Vertical strain field of BD specimen at different loading angles and impact velocities. the moment of fracture of the strain gauge changes, and the overall trend is left low and right high (Figure 16b,c), indicating that the crack propagation starts from the A1 end. The validity and correctness of DIC and numerical simulation are further verified. When the loading angle is greater than 26\({}^{\circ}\), the moment of fracture of the SCC is not affected by the impact speed, and it occurs in the middle of the specimen. It is clear from Figure 16d that as the loading angle increases, the first crack point of the crack moves closer to the middle of the specimen. The time of crack propagation in the BD is directly related to the impact velocity, and the overall performance is that the time for the crack to expand in the BD is shortened with the increase in speed. When the cracking point is amalgamation, the crack propagation time is 53 \(\upmu\)s at a velocity of 4.9 m/s. At a speed of 9.6 m/s, the crack propagation time is 32 \(\upmu\)s, and the time is reduced to 39.6%. When the  
Figure 16: (**a**) Crack extension time sequence at 4.9 m/s; (**b**) Crack extension time sequence at 9.6 m/s; (**c**) Crack extension time sequence at 12.5 m/s; (**d**) Start cracking point sequence. Figure 15: Strain history of the crack opening. crack is cracked in the center, the crack propagation time is relatively shortened, expanding from the center point to both sides, and the expansion time is basically maintained at 20 us. The crack propagation time is about half as short as that of non-intermediate initiation. The test and theoretical analysis get consistent results, corroborate each other's correctness and further reduce the size of the platform loading angle, improve the accuracy of the test, and better serve similar materials such as concrete.