PSI - Issue 13

Israr ul Haq et al. / Procedia Structural Integrity 13 (2018) 1955–1960 Author name / Structural Integrity Procedia 00 (2018) 000–000

1957

3

Fig. 1 shows finite element model for ballistic impact analysis. Fine mesh is generated in the impact zone and are selected (kept aspect ratio 1) after performing mesh independence study. Reduced integration and stiffness based hourglass control is selected for the elements. General contact method is considered between projectile and target. Target is clamped at the edges whereas projectile striking velocity is defined at projectile reference point (located at its center) in coarse mesh is generated in the surrounding. C3D8R 8-node linear brick with an edge length of

the negative -direction. 2.1. Constitutive Model

Definition of inappropriate constitutive material model for a numerical simulation can lead to unacceptable numerical results. Johnson and Cook proposed the first model to predict plastic flow stress of material in 1983 (Johnson, 1983) and also extensively used in ballistic impact simulations. It can predict material flow stress at various strain rates and temperatures. In (Sjöberg, Sundin, & Oldenburg, 2013), Johnson-Cook model followed high strain rate experiment results for Inconel-718. Therefore, Johnson-Cook model is considered to be used for current work. Johnson-Cook plasticity model relates von-Mises stress to equivalent plastic strain as follows,

(1)

(2)

Equation (1) considers the effect of strain hardening, strain rate hardening and thermal softening of the material. Equation (2) represents relations for * for various temperature ranges. Johnson-Cook plasticity parameters for Inconel-718 presented by (Ren et al., 2014) are given in Table 1. Johnson-Cook also proposed a model (Johnson & Cook, 1985) to represent failure of materials which includes effects stress triaxiality, strain rate & temperature on material strain until fracture and is represented by equation (3), (3) and are material dependent parameters, * is the ratio of average normal stress to von-Mises equivalent stress. Equation (3) considers stress triaxiality on fracture, strain rate and temperature at fracture strain. Johnson-Cook failure parameters published in (Erice, Pérez-Martín, & Gálvez, 2014) are presented in Table 1. where , , ,

Table 1 Johnson-Cook Plasticity Parameters for Inconel-718

Johnson-Cook Plasticity Parameters

Source

A (MPa)

B (MPa)

N

C

m

(Ren et al., 2014)

860

1100

0.5

0.0082

1.05

Johnson-Cook Failure Parameters

Source

D 1

D 2

D 3

D 4

D 5

0.04

0.75

-1.45

0.04

0.89

(Erice et al., 2014)

2.2. Analysis of Spherical Projectile Model is simulated for striking velocity of

at fixed time increment of seconds. Fig. 2 shows comparison of experimental and simulation results for deformed Inconel-718 target. Fig. 2 (a) & (e) shows experimental result of front and back side of the target plate respectively. Fig. 2 (c) & (g) shows plug ejected during experiment. Fig. 2 (b), (d), (f) & (h) shows corresponding numerical results. It can be seen that target is deformed with the formation of petals and ejection of plug. Petalling is formed with 5 primary petals numbered 1-5 with 2 secondary petals 4a and 4b shown in Fig. 2 (e). Numerical results at same striking velocity successfully predicted deformation behaviour of the target as shown in experimental results. Mass and average diameter of plug for experimental results are and respectively. Whereas mass and average diameter of plug from numerical predictions are 0.52g and respectively. It can be seen that numerical results also well predicted the size and shape of plug formed during the experiment.