PSI - Issue 68

Hande Vural et al. / Procedia Structural Integrity 68 (2025) 573–580

576

4

Vural et al. / Procedia Structural Integrity 00 (2024) 000–000 Table 2: Plasticity and damage parameters of Armox 500T [Go¨c¸men et al. (2023)].

σ 0 [MPa]

q 1 [MPa]

b 1

q 2 [MPa]

b 2

1250

470

109.1

488.6

1.903

C

˙ ε 0 (1 / s)

D 1

D 2

D 3

0.0617

1

0.09

4.406

2.993

Each single parameter damage model is calibrated with a smooth round bar specimen, which is also used for modeling plasticity, to predict the onset of damage. Since there is only one damage parameter, a single test is su ffi cient for calibration. Implicit FE analyses are performed for each model and the damage accumulation rules shown in Table 1 are applied through a user-defined subroutine (USDFLD). The critical value is determined from the FE result at the experimentally observed fracture point. The failure point for all models is selected at the same location. As illustrated in Figure 1b, the FE results are plotted up to the fracture initiation point. The critical damage parameter values ( C i ) are presented in Table 3.

50.0

20

40.0

30.0

R15

F [kN]

20.0

22

10.0

Exp. (Poplawski et al. (2020)) FE

3

14.3

0.0

0

0.5

1

1.5

2

2.5

3

3

U [mm]

(a)

(b)

Fig. 1: a) FE model and geometry of smooth round bar. Dimensions are given in mm. b)Force-displacement curve of smooth round bar.

Table 3: Damage parameters of criteria for Armox 500T.

Ayada-m( C 1 )

Brozzo ( C 2 )

LR ( C 3 ) 1027.831

MC ( C 4 )

OH( C 5 )

0.731

0.976

2.617

0.976

RT ( C 6 )

CL ( C 7 ) 1918.703

Freudenthal ( C 8 )

Ayada ( C 9 )

KH( C 10 )

1.890

1541.747

0.450

2.684

3. Ballistic Impact Simulations

In this study, the ballistic performances of various damage models are analyzed with a user-defined field subroutine (VUSDFLD) in Abaqus / Explicit. The three-dimensional finite element model consists of a deformable target and a rigid projectile. A hemispherical projectile and a 7.62 API projectile, the dimensions of which are shown in Figure 2, are used, and the weight of these projectiles is 5.5 grams. Target plates are arranged in di ff erent configurations. An 8 mm monolithic target is employed to examine the ability of the damage criteria to predict residual velocity, while 2 mm thick targets are used for multilayer studies. The six di ff erent target configurations shown in Figure 2 are as follows: T4 is a 2 mm single-layer target; T2-2 is a 1 mm double-layer target; T2(6)2 is a 1 mm two-layer target with a 6 mm air gap; T1-3 and T3-1 are targets with one 0.5 mm and one 1.5 mm layer; T1111 is a four-layer target with 0.5 mm thick layers. The 200 mm square target is modeled as a quarter to reduce computational time. The outer edges of the target are fully constrained, and the displacement is restricted only in the direction perpendicular to the plane on the symmetry planes.