PSI - Issue 51

R. Andreotti et al. / Procedia Structural Integrity 51 (2023) 37–43 R. Andreotti et al. / Structural Integrity Procedia 00 (2023) 000–000

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according to Boyce et al. (2007) with Cowper-Symonds parameters C=396500 and p= 3.0745 according to LSTC (2015).

Fig. 3. Section of the bullet with dimensional reference.

3. Load history estimation The load history F(t) is calculated according to the single-material version of the formula introduced by Andreotti et al. (2022): F�t��� � ����� (1) where v= 735 m/s is the impact velocity measured from the camera captures, � � �������� � is the density of the bullet’s material, and ���� is the area of the bullet’s section ideally intersecting the surface of the target at time t , experimentally measured by mapping the section of the bullet all along its axis (Fig. 3). The approach has led to the calculation of the load curve in Fig. 4.

Load History F(t) [N]

0E+00 5E+04 1E+05 2E+05 2E+05 3E+05

Force [N]

0E+00

1E‐05

2E‐05

3E‐05

4E‐05

5E‐05

Time [s]

Fig. 4. Load History [N] estimated from the geometry of bullet's section and the experimentally measured impact velocity. Interaction time [s] in abscissa. 4. Results and discussion The analysis of the captured frames shows a complete fragmentation of the bullet with hundreds of fragments being deflected by the target’s surface in the radial direction around the epicenter of the impact; traces of the fragments being deflected are evident on the impact surface (Fig. 5). The observed phenomenon is therefore compatible with bullet-splash hypotheses by Andreotti et al. (2021, 2022). The residual back-plate deformation was measured and mapped as a function of the distance from the apex (Fig. 7) with a maximum around 8 mm. The results of simulation A (Fig. 6) confirm with very good adhesion the field of back-plate residual displacements with a maximum around 8 mm (red line on Fig. 7). Simulation B (green line on Fig. 7) slightly overestimates the residual displacements within 10 mm from the apex, its prediction is elsewhere accurate, within the experimental range. Simulation C (blue line on Fig. 7) correctly predicts the entire field of residual displacements. It is important to notice that the three simulations have totally different pressure distributions: simulation A applies a pressure field calculated as a result of the FSI algorithm based on ALE; simulations B and C, instead, apply the same