## 4 Simulation Results and Discussion
### Eight Millimetre and Ten Millimetre Diameter Ball Bearings  
As might be expected, the heavier ball bearings required larger charge masses to accelerate them to similar peak velocities, as shown in Figure 9. The phases of flight were similar to those observed in simulations of other ball bearing sizes and in the 5 mm diameter ball bearing experiments reported in [17]. Peak velocity increased with an increasing charge mass for a given charge diameter but was less sensitive to charge mass when the charge diameter was increased to 30 mm. The drop in velocity due to interaction with the reflected blast waves from the witness plates increased with increasing charge mass.  
The simulated hydrostatic pressure histories for 8 mm ball bearings from two different explosive charge detonations are shown in Figure 10. The shapes of the two sets of  
Figure 9: Simulated ball bearing velocity–time histories for 8 mm and 10 mm diameter ball bearings at different charge masses.  
pressure progressions are similar. A high pressure (slightly over 30 GPa) compressive stress propagated through the bearing and then reflected back as a tensile wave from the free surface of Face A. Similar hydrostatic pressure histories were obtained for the 10 mm diameter ball bearings (not shown).  
The arrival time for the hydrostatic compressive stress in Face B (the embedded side) was earlier in the higher charge mass simulation, as shown in Figure 10. This was due  
Figure 10: Simulated hydrostatic pressure development in an 8 mm ball bearing subjected to (**a**) 11 g charge, 18 mm diameter, (**b**) 20.37 g charge, 30 mm diameter.  
to the higher charge diameter and hence the shorter charge length of the 20.37 g charge, meaning that the detonation wave travelled further to reach the bearing in the 11 g charge. Interestingly, the 11 g charge detonation resulted in higher compressive and tensile peak stresses within the bearing, despite a lower predicted peak velocity (Figure 9).  
The tensile stresses observed near the free surface of Face A appeared \"noisy\" (after 3-4 us in Figure 10a, 4-5 us in Figure 10b). The discontinuities are attributed to extensive cracking in the bearing. There was a second tensile peak in Face B approximately 6 us after detonation in Figure 10a, with a magnitude of approximately 20 GPa. With a similar but lower magnitude (approximately 16 GPa), a secondary tensile peak in Face B was observed in the 20.37 g detonation simulation (Figure 10b) after approximately 5 us. This may indicate that the tensile failure in both halves of the ball bearing would occur in the 11 g detonation but not in the 20.37 g case. This suggests that the aspect ratio of the charge significantly influences both the bearing flight characteristics and the damage predicted within the ball bearing, with higher aspect ratio charges inflicting greater damage than lower aspect ratio ones.  
One of the limitations of the current modelling is the lack of a fracture and fragmentation model for the ball bearing, limited by the available computational approaches to this highly complex and non-linear problem and the lack of well-defined parameters for the bearing materials itself. Nonetheless, the current simulations show that it is certainly possible at higher charge masses (and appropriate aspect ratios) for detonations to generate internal hydrostatic stresses within the ball bearing that are capable of breaking the bearing into multiple fragments within the first few microseconds of the load applications. The short time to fracture will influence the flight characteristics of the subsequent fragments both in terms of trajectory and velocity magnitude. This has implications for IED research, where embedded solid objects within the charge contribute to many IED-related injuries and deaths.