## 4 Simulation Results and Discussion
### Three Millimetre and Five Millimetre Diameter Ball Bearings  
Figure 6 shows the simulated velocity histories for 3 mm and 5 mm diameter bearings subjected to different charge mass detonations. The phases of flight are similar to those in [17]. There was a rapid rise in velocity followed by a constant peak velocity once the blast momentum was transferred to the bearing. As expected, the peak velocity increased with an increasing charge mass and was greater for the lighter 3 mm diameter ball bearing. A slight drop in velocity is predicted when the blast wave reflection from the witness plate opposes the bearing motion. The percentage velocity drop ranged from approximately 4% to 20%, with larger percentage decreases observed for higher charge masses and charge diameters (as the reflected shock pressure will be greater). A plateau phase ensued prior to impact with the witness plate; the impact caused a rapid linear deceleration of the bearing until it stopped. The results from a 5.13 g detonation (18 mm diameter charge) are shown in Figures 7 and 8 as this was one of the few experiments in which the ball bearing was recovered and identified. Face B was the side of the bearing embedded in the explosive charge. The hydrostatic pressure history for gauges in hemispheres A and B are shown in Figure 7a. In general, gauges 4 and 10 (Face B) had similar pressure histories but different arrival times, as expected. The initial compressive stress wave propagated from gauges 4 and 10 with similar magnitude (approximately 32 GPa) and, in Figure 7c, the shape of the compressive stress front is curved as it passes gauge 10 (after 1.4 us). Figure 6: Simulated velocity–time histories for 3 mm and 5 mm diameter ball bearings at different charge masses, from detonation to impact point. The peak pressure increased to approximately 36 GPa on Face A at gauge 25 (after approximately 1.7 \(\upmu\)s, Figure 7) as there was a focusing effect due to the curvature. This strengthened compressive wave was reflected as a tensile wave (indicated by the negative pressure). The pressure increased to approximately 36 GPa on Face A at gauge 25 (after approximately 1.7 \(\upmu\)s, Figure 7) as there was a focusing effect due to the curvature. This strengthened compressive wave was reflected as a tensile wave (indicated by the negative pressure  
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hydrostatic pressure in Figure 8 at 2.2 \(\upmu\)s) and reached a maximum at 2.3 \(\upmu\)s, which caused internal cracking as the tensile stress exceeded the maximum tensile failure stress of 21 GPa. At 2.3 \(\upmu\)s, the material at gauge 35 had failed, indicated by the negative pressure spike and its sudden relaxation to near-zero pressure. It is worth noting that the ball bearing had not yet reached its peak velocity by this point (Figure 5a). Figure 8 shows an image of the simulated equivalent plastic strain distribution in the ball bearing and a photograph of the cross-section of the blasted bearing. Internal cracking was observed in the cross-section of the bearing in the same location as the simulated internal cracks. Lastly, while the model did not indicate fragmentation around the equator, the maximum effective plastic strain was shown to be in a similar region as the actual fragmented location. The hydrostatic pressure history also showed a peak in the tensile stress at gauge 10 (Face B) after 3.2 \(\upmu\)s, but the magnitude was slightly less than the tensile failure stress, hence there was no cracking in that region of the previously embedded hemisphere. The lack of fragmentation in the model could be due to the limited capability of the failure model used in the simulation. The simulations showed that internal cracks (Figures 7 and 8) formed due to tensile spalling. The location of the cracking was a result of the geometry of the ball bearing as the hydrostatic pressure waves reflected from the curved free surface of Face A and caused an internal hydrostatic tensile pressure state that coincided at the crack location.