PSI - Issue 35

Deniz ÇelikbaŞ et al. / Procedia Structural Integrity 35 (2022) 269 – 278 D. C¸ elikbas¸ / Structural Integrity Procedia 00 (2021) 000–000

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Fig. 4. a) Surface profiled tiles, b) di ff erent hitting locations.

projectile is modeled with the Simplified Johnson-Cook material model with constant stress solid element formulation. An initial velocity of 878 m / s is assigned to the projectile. AUTOMATIC NODES TO SURFACE contact type is used. The friction value between the bullet and ceramic plate is used as 0.28, Tepeduzu and Karakuzu (2019).

Table 4. Ceramic tile’s geometrical specifications. Sphere Radius, r ( mm )

Plate Thickness, t ( mm )

Mass, m t ( gram )

Mass Di ff erence (%)

0 (flat)

9

222.3 222.9 223.5 217.6 224.9 219.6 224.7 218.1 225.3 221.8 222.4 216.7 219.7

-

1.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

8.5 8.0 7.5 7.5 7.0 7.0 6.5 6.5 6.0 6.0 5.5 5.0

-0.3% -0.5% 2.1% -1.2% 1.2% -1.0% 1.9% -1.3% -0.2% -0.0% -2.5% -1.2%

In this study, only spherical surface profiles are examined. The radius of the spheres is varied to explore its e ff ect on the tile’s ballistic performance. Figure 4.a shows the geometrical properties of the surface profiled tiles. To compare the surface profile e ff ect, the results are compared with those of the flat 9 mm × 80 mm × 80 mm alumina ceramic tile. We aim to keep the weights of the surface profiled tiles to be the same as that of the flat plate. For this purpose, the thicknesses of the surface profiled plates are adjusted. However, the poor resolution of the SPH nodes prevents us from obtaining exactly the same weight values for the surface profiled plates as that of the flat plate. Therefore, we find the thicknesses of the surface profiled plates that yield within ± 3% proximity of that of the flat plate. Table 4 lists these sphere radius values and the corresponding plate thickness values (that provide similar weight values to that of the flat plate). Note that since we use the kinetic energy absorbed by the unit mass (SKEA) as the ballistic performance metric and the weight di ff erences in Table 4 are small, we consider that the e ff ect of these weight di ff erences are acceptable. The absorbed specific energy is calculated from Eq. (11). Figure 4.b shows di ff erent hitting locations of the bullet, and the e ff ect of the hitting location is further discussed in Section 3.

1 2

1 2

KEA m t

2 o −

2 r

; KEA =

m b v

m b v

(11)

S KEA =