## 3 Numerical Simulation
### Numerical Simulation Analysis  
To investigate crack propagation velocity, a group of gauge points is sown on the simulation specimen. Each has the same location, in line with the fine wire of the CPGs. The time when the running crack tip arrives at the gauge point can be obtained automatically. Then, the crack propagation velocity of simulation can be calculated by the velocity formula, where average velocity between two gauge points is equal to distance divided by time, as the distance between two gauge points is constant and equal to 2.25 mm. Figure 9 shows the crack propagation velocity curves obtained by numerical simulation under three loading rates' impact. It is seen that the crack propagation speed in both simulation and experiment has a highly consistent change trend. After initiation, the speed of the running crack increases with time inconstantly, while the propagating speed decelerates sharply when the running crack approaches the two hole zone. It is observed that the average speed of the main crack in the simulation has a relationship with the loading rate. With a higher loading rate, the average propagating speed of the HT-3 specimen, 443.07 m/s, is faster than the HT-1 specimen, with velocity 394.97 m/s. Comparing with Figure 9a,c, the fluctuation of propagating crack velocity under a high loading rate is more drastic than in the one with a low loading rate. Meanwhile, under a high loading rate, the  
Figure 8: Simulation results of crack propagation paths calculated by AUTODYN. (**a**) Comparison of specimen HT-1 between numerical simulation and experiment. (**b**) Comparison of specimen HT-2 between numerical simulation and experiment. (**c**) Comparison of specimen HT-3 between numerical simulation and experiment. deceleration of the propagating velocity is more sensitive. In other words, the two hole zone has a more dominant influence on running crack under a higher loading rate. Figure 9: Contrast diagram of crack propagation velocity under different loading rates (**a**) The crack propagating velocity curves of HT-1 specimen under loading rate 1000 GPa s\({}^{-1}\). (**b**) The crack propagating velocity curves of HT-2 specimen under loading rate 1500 GPa-s\({}^{-1}\). (**c**) The crack propagating velocity curves of HT-3 specimen under loading rate 2000 GPa-s\({}^{-1}\). Therefore, the influence of the two hole zone should respond to dynamic crack propagation behaviour. For this purpose, a narrow study, focused on the two hole zone, is conducted to reveal the effect of the two empty holes on the crack propagation behaviour. Figure 10 shows three significant moments of the process, where main cracks cross the two hole zone, with their particle velocity vector contour plotted. When t = 294.2 \(\upmu\)s, the main crack tip arrives in front of the two hole zone with a very high speed, and then velocity declines immediately, according to previous analysis. From Figure 10a, it is evident that the surface of the two empty holes has a distinct deformation, transforming the circle to an ellipse, as shown in Figure 10d. This is because, when the incident stress wave arrives in the two hole area, the stress wave reflects on the front surfaces of the holes' shaping reflected tensile wave, and the compressive wave reflected from the bottom of the specimen works on the back surfaces of the holes. These contribute to the deformation of the two holes. It is the deformation of the two empty holes that prompts the particles between two holes to move toward the symmetric axle of the specimen and shapes a compressive stress field between them. This compressive stress field plays a crucial role in reducing the velocity of the running crack.