PSI - Issue 72

Toeri Fathuddin Yusuf et al. / Procedia Structural Integrity 72 (2025) 436–444

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shear resistance. In a study conducted by Børvik et al. (2009), using Eq. 1, a lower value was obtained compared to the measurement results, with a difference of 4%. Therefore, it can be concluded that the results agree with the experiments conducted. 2.2. The effect of lamination For a laminated target with a wide air gap between the plates, the decrease in value can be calculated. Two plates with thickness are placed far enough apart that the nose of the projectile can pass through the first plate before hitting the second plate. Based on Eq. 1, the ballistic limit velocity for this target with two plates is as Eq. 3. 2 ( × 2) = 2 ∙ 2 ( ) (3) Then, for N separate target plates as follows 2 ( × ) = ∙ 2 ( ) (4) Based on Eq. 4, the formulation for a target plate consisting of N separate plates of different thicknesses ( ) and strengths ( ) can be obtained, which is expressed in the following equations.       2 2 2 2 1 2 2 bl bl bl bl N rt i p ff V V H V H V H H L                   (5) With as the effective resisting stress at the i-th plate, Eq. 5 shows that the value of is not affected by the plate order. Based on the simple analysis performed, the values of and are very close to the experimental results, so they can be used to predict these values for the laminated target plates. 2.3. The transition from the dishing to the ductile hole enlargement mechanism The calculation of the work required to open a hole of diameter ( D ) in a ductile plate of the same thickness is based on the stress in the target plate (Woodward, 1978). Based on this calculation, the effective radial stress acting on the hole wall is twice that of the material flow stress of the target plate. To determine the amount of work, the radius of the hole in the plate ( r ) the thickness of the target plate ( ), and the flow stress ( ) are required (see Eq. 6). = 2 ∙ ∙ 2 (6) The analysis of perforation in fragile target plates is carried out through a dishing mechanism, where the material around the hole is pushed toward the projectile trajectory (Thomson, 1955; Bresson et al., 2012; Cech et al., 2014; Sun et al., 2016; Kurzawa et al., 2018). The value of effort required under these conditions can be calculated as presented in Eq. 7. = 2 ∙ ∙ 2 (7) With Y t ⁄2 as the effective holding stress controlling the release on the thin plate. 2.4. Johnson-Cook model In this study, the target plate is modeled using Johnson-Cook (JC) to describe the materials' stress behavior. JC describes the von Mises stress ( ̅ ) as a function of the equivalent plastic strain ( ̅ ), equivalent plastic strain rate ( ̅̇ ), and temperature ( ) as presented in Eq. 8 (Wang and Shi, 2013).