PSI - Issue 72

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

439

̅ = ( + ( ̅ ) )[1 + ( ̅̇ ̅̇

0 )](1− ∗ )

(8) where A is the yield stress, B and are strain hardening constants, n is the strain hardening exponent, ̅̇ ̅̇ 0 ⁄ is the normalized plastic strain rate equivalent (usually normalized to 1.0 s -1 ), and ∗ is the homologous temperature defined as presented in Eq. 9. ∗ = ( − 0 )/( − 0 ) 0 < < (9) Thus, the equation to define the modified strain rate factor is based on Eq. 8, which is an application of the fracture model as presented in Eq. 10. ̅ ( ̅ , ̇̅ , ∗ )=[ 1 + 2 ( 3 ̅ )][1+ 4 ̅̇ ̅̇ 0 ][1+ 5 ∗ ] (10) Parameters 1 to 5 are material parameters obtained from various types of mechanical testing. 1 , 2 , and 3 relate to stress triaxiality while 4 is a damage parameter influenced by strain rate. 5 relates to strain affected by temperature. In addition, the stress-triaxiality ratio is expressed as σ m ⁄σ̅ , where denotes the average stress. 3. Finite Element Setup This paper aims to conduct a numerical analysis of the perforation of plate structures on the side hull of a ship based on experiments conducted in previous studies. In this study, finite element method (FEM) analysis (Prabowo et al., 2016a,b; Aranđelović et al., 2021; Radojković et al., 2021; Amara et al., 2022; Carvalho et al., 2023; Ridwan et al., 2023; Wiranto et al., 2024) was performed using ABAQUS software to replicate the experiments conducted by Piekutowski et al. (1996). The projectile and target plate geometry matched the geometry used in the Piekutowski et al. (1996) experiment, as shown in Fig. 1.

a)

b)

Fig. 1. Geometrical model for finite element analysis: (a) Geometry of 3.0 circle-radius-head projectile; and (b) Geometry of the target plate based on information in reference (Piekutowski et al., 1996).

The material used for the target plate in this study is Aluminum 6061-T651, which has potential applications in the military field due to its strength, low cost, and high impact resistance (Yunfei et al., 2020). In general, the response of materials to high-speed impacts involves consideration of the effects of strain, strain rate, and temperature (Wang and Shi, 2013). This study modeled the target plate using the Johnson-Cook (JC) model, with the constants shown in Table 1. The JC model (Schulze and Zanger, 2011; Mirza et al., 2013; Buzyurkin et al., 2015; Valoppi et al, 2017; Ansori et al., 2022; Pratama et al., 2023) describes the stress behavior of the target plate material. Meanwhile, the deformation of the projectile is ignored and considered a rigid body.