13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- The computational model was setup as shown in Fig. 2. A panel of dimension 100 × 100 mm2 was rigidly fixed at its edges and is impacted by a projectile at its centre. The projectile/bullet shape was simplified as a cylinder, 9 mm in diameter and 9.5 mm long with a semi-hemisphere of radius 4.5 mm at the end. The initial velocity of the bullet was set to 310 m/s. The computational model was simulated for 6 ms after the bullet impact. Both the panel and projectile were discretised with a particle spacing of 1 mm. A particle convergence (equivalent to mesh convergence in FEA) analysis using the von Mises stress showed that the stress varied by less than 2% with a change in model resolution from 1.25 to 1 mm particle spacing, establishing the resolution of 1 mm was sufficiently accurate. Depending on the thickness, the SPH panel was made up of between 61,206 - 71,407 particles and the projectile contained 1,246 particles. The projectile was modelled as solid copper with a Johnson Cook plasticity model [33]. MDF and polycarbonate were modelled using the material properties in Table 1. The model was solved using the LS-DYNA SPH solver. 4. Results 4.1 High speed impact tests High speed photographs of a representative example of MDF and PC tested are given in the following section. The behaviour of the simulant materials and the associated advantages and disadvantages in relation to simulating backspatter are summarised in Table 2. For each material, two samples were tested, denoted by MDF1 and MDF2 for the Medium density fiberboard samples, and PC1 and PC2 for the Polycarbonate samples. Fig. 3 shows the fracture pattern for MDF panels. Small particles (1-2 mm in size) were observed to travel in the direction opposite to the line of fire for both tests. Particles emerged in a radial cone shape with most debris travelling in the upwards direction (Fig. 3c-d). Smaller particles travelled away from the model, whilst larger particles and fragments remained in the region of impact (Fig. 3c). The time for the initial splashing backspatter to occur after bullet impact was 0.28 ms. The backspatter continued to expel from the hole for 6.35 ms. The size of the entrance hole was 9.0 mm with no evidence of radial cracking from the impact site. Large fragments of MDF fractured off leaving damage areas of around 15 mm in diameter at the exit site. Observation of the blotch paper revealed a majority of spattered material was located between 0.5 - 1 m from the model setup. Two plain 4.5 mm polycarbonate panels as the skull simulant were also tested with PC1 highlighted in Fig. 4. The projectile induced a concave bend in the entire panel. A local radial wave travelled outwards to the edges of the panel 0.19 ms after impact in both cases. Following this the entire panel vibrated sending ripples through the panel. No backspatter was observed for PC panels. The entrance hole was much larger for polycarbonate compared to that observed for MDF. (a) 0 ms (b) 0.25 ms (c) 1 ms (d) 4 ms Figure 3. Fracture pattern and backspatter due to projectile impact on MDF (MDF1)
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