PSI - Issue 35

Deniz ÇelikbaŞ et al. / Procedia Structural Integrity 35 (2022) 269 – 278 D. C¸ elikbas¸ / Structural Integrity Procedia 00 (2021) 000–000 5 where A , B , C , and n are material constants, ¯ ε p is the e ff ective plastic strain, and ˙ ε ∗ is the normalized e ff ective strain rate. The mechanical properties of the Johnson-Cook material model are given in Table 2. 273

Table 2. Mechanical parameters for steel projectile (MAT 98 – Simplified Johnson Cook) Toussaint and Polysois (2019). Parameter Symbol Value

Unit

kg / m 3

Density

7800

ρ

Elastic Modulus Poisson’s ratio

E

210

GPa

0 . 3

−

υ

Quasi-static tensile yield Hardening coe ffi cient

A B m

2 . 4824 1 . 4985

GPa GPa

Hardening exponent

0 . 19

− −

Strain rate sensitivity coe ffi cient

C

0 . 027

2.4. Validation of Alumina Tile

The numerical ceramic tile model was validated by the experimental results presented in the literature Toussaint and Polysois (2019). In their experiments, Toussaint et al. used a steel spherical projectile to impact alumina ceramic tile with varying velocities. They experimented on two di ff erent thicknesses of the tile, 9 mm or 13 mm . The dimensions of the tile were 101.6 mm × 101.6 mm . To compare their experimental results and their numerical model, they used radial and conical cracking parameters. An example of experimental result is shown in Figure 2.a. The conical parameters, α , β , and b , are shown in 2.b. At the impact zone cracking starts with the mirror fractures then the crack changes its direction and mist fractures were formed. In Figure 2.b, blue line represent mirror fractures, which has a smooth characteristics, green line represents mist fractures, which has rougher characteristics.

Fig. 2. a) Cone, b) cone parameters, c) cone formation in simulations Toussaint and Polysois (2019).

They examined three di ff erent material models to find the best match with their experimental results. They obtained the closest numerical results to the experiments when the SPH element formulation with the JH2 material model was used together. In that model, both projectile and plate are modeled using SPH elements. The particle spacing between the particles was 0.5 mm . The simulations run up to 25 µ s until the radial and conical cracks were formed. In Figure 2.c, the cone formation on numerical simulations is shown. To decrease the computational time quarter model was used. The comparison of their experimental and numerical models are shown in Figure 3 and listed in Table 3. To validate our ceramic tile model, we use the experimental results of Toussaint and Polysois (2019). Ceramic tile is modeled with JH2 material model with SPH element formulations. After the model determines the failed SPH nodes, they are transferred to MATLAB, and then the core dimensions are measured by using boundary functions. The comparison of the results can be seen in Table 3. The results indicates that our numerical model achieves closer results to Toussaint’s et. al. experimental results. In the subsequent studies, this validated ceramic tile model is used.