MIT - Massachusetts Institute of Technology



Numerical Simulations of Ballistic Impact of ss109 on Alumina/Steel Armor

Tarin Vanichayangkuranont1, Nuwong Chollacoop2 and Kuntinee Maneeratana1

1 Department of Mechanical Engineering, Chulalongkorn University, Bangkok 10330, Thailand

Tel: 0-2218-6639, Fax: 0-2252-2889, ∗*E-mail: tarinv@ and kuntinee.m@chula.ac.th

2 National Metal and Materials Technology Center (MTEC), Pathumthani 12120, Thailand

Tel: 0-2564-6500 ext 4700, Fax: 0-2564-6403, E-mail: nuwongc@mtec.or.th

Abstract

This article concerns with the ABAQUS simulation of ss109 bullet impacts with initial velocities about 936 m/s on alumina/steel armor plates, which is rated between the level 3A and 4 of the National Institute of Justice (NIJ) standard. The current model setup was extended from the prior investigation [1] of the 9-mm bullet impact with the initial velocity of about 420 m/s (level 3A of NIJ standard), with the implementation of frictional effect between impacting bullet and armor plate. Despite the seemingly simple computational model, the simulation result showed qualitatively agreement with the experimental observations of the armor testing.

Keywords: Ballistic impact, ss109, alumina, steel, ABAQUS

1. Introduction

The National Metal and Materials Technology Center (MTEC) has initiated a project to develop the light weight hard armor, aiming to improve materials, design and produce hard armor prototypes with local materials [2]. As hard armors comprise of layers of alumina, steel and polymer composite plates, the design involves the parameter specification on alumina tile shape/sizes, thicknesses and arrangements of material layers. Thus, the numerical simulation is used to analyze ballistic impacts on the armors in order to obtain rough guidelines, particularly parameter adjustments for the prototype configuration.

The prior studies on various aspects of ABAQUS finite element simulation were the effects of stress wave propagation from dynamic loads, involving elastic and elastic plastic armor plate [3], the impact of elastic bullet on an alumina plate which fails by brittle failure criterion [4], and the preliminary development of the computational model for NIJ level 3A ballistic testing [1].

This study aims to extend the previously developed computational model for the greater damage ballistic testing with the sharper bullet (ss109) and faster speed of 936 m/s. At this high impacting velocity (almost 3x speed of sound in the air), the effect of frictional interaction is significant. Such implementation enables the qualitative prediction of the experimental results.

2. Experimental Observations

The shooting experiments on alumina/steel plates are used for comparison with the simulation [2]. They were conducted at the certification firing range (Fig. 1) in an arsenal on 25-26 August 2005. A single ss109 bullet was fired upon each specimen. The impact was classified between the 3A and 4 threat-level of the NIJ standard [5], which is also adopted into an equivalent code for the Royal Thai Military.

Among many cases, 2 armor specimens, each made up of a layer of alumina on top of a steel back layer, were chosen for numerical study. The alumina layers were constructed from hexagonal ceramic tiles of 8cm2 area, which were bonded together with epoxy and wrapped up by a dynema cloth (shown white in Table 2) before being bonded to the back steel plate with the same epoxy. The thickness of the ceramic tile was 8mm for both samples with the steel plate of 1.5mm thick. The velocity of the bullets V0, measured by the sensors after the bullets left from the barrel (Fig. 1, left), were 924 and 936m/s for sample I and II, respectively. Post firing test revealed that the bullet hit sample I (925m/s) at the edge of the alumina tile while it hit sample II at the center of the alumina tile.

|[pic] |[pic] |

| |[pic] |

Figure 1. Standard firing tests

The images of the plate damages after impact are shown in Table 1. Both specimens showed some localized damages on a single tile while the back steel plates showed full penetration by petal damage in sample I and large bulge on sample II, due to the differences in the locations of the alumina tiles impact. The edges of the alumina tiles were weaker due to the epoxy bond.

Table 1. Plate damages after impacts

|case |ceramic |metal |side |

|I |[pic] |[pic] |front|

| |[pic] |[pic] |back |

|II |[pic] | |front|

| |[pic] |[pic] |back |

3. Numerical Simulations

All finite element simulations in the present study were performed using ABAQUS/Explicit solver [6] due to the high speed, non-linear transient responses in the solutions. An axisymmetric model was chosen for simulations of a spear-shape bullet penetrating layers of alumina and steel plates, as shown in Figure 2.

A real ss109 Full Metal Jacketed (FMJ) bullet is made of an outer copper alloy jacket covering a softer lead core and has the nominal mass of 3.95-5.18 g. In the modeling, the bullet was assumed to be a single piece with a sharp tip and a total length of 18 mm, estimating the commercial bullets in terms of diameter and mass. Meanwhile, the armor plates were assumed to be homogeneous in each layer spanning the total length of 30mm in diameter to minimize the effect from the far field condition. Complication from the finite alumina tiles were not yet taken into account for the present investigation.

Due to the anticipated severe deformation at contact, a finer mesh was used at the region directly beneath the bullet tip for both alumina and steel layers while a coarser mesh was used in the region further away to reduce computational expense, as shown in Fig. 2. All regions were modeled with axisymmetric 4-node elements with enhanced hour-glass control. There were 95, 9,00 and 1,800 elements for the bullet, alumina and steel sections, respectively.

[pic]

Figure 2. Mesh design for the bullet and central layers of alumina and steel (red).

The fully restrained boundary condition was applied to the outer edge (right side) of the armor plates while the center (left side) of the plate assumed axisymmetric boundary condition. In addition, the interaction between the bullet and alumina layer were governed by the surface-to-surface contact model with friction coefficient of 0.3. Using the kinematic contact method, the bullet nose was assigned to be the master surface while the armor plate was the slave node region. The impact was simulated by assigning the initial downward velocity to the bullet. To ensure numerical accuracy and stable computation, the time step size δt = 3.2 ns.

The elastic bullet was modeled after the gliding copper [7] with the Young’s modulus E of 115 GPa and the Poisson’s ratio ν of 0.307. However, the density ρ was modified to approximate the commercial ss109 bullet mass. The alumina layer was modeled with elastic-perfectly plastic constitutive relation having ρ = 3,900 kg/m3, E = 350 GPa, ν = 0.22, the compressive yield stress σyc = 2400 MPa [8] and the tensile strength σts = 600 MPa [1]. During the impact, the elements were removed when any component of the stress exceeded 600 MPa in tension.

The Johnson-Cook model was used for the steel plate as it has been well suited to model metals that are subjected to high strain rate loadings [9]. The yield stress at non zero strain rate [pic] depends on the strain hardening, strain rate hardening and temperature softening such that

|[pic], |(1) |

where [pic]is the equivalent plastic strain, [pic] is the reference strain rate. The parameters A, B, C, n and m are material parameters measured at or below the transition temperature [pic]. The [pic] is the nondimensional temperature which is equal to 1 when the current temperature [pic] is greater than the melting temperature [pic], 0 when [pic], and linearly proportional in-between. The Johnson-Cook shear failure is based on the damage parameter [pic]

|[pic], |(2) |

where [pic] is an increment of the equivalent plastic strain and [pic] is the strain at failure.

|[pic], |(3) |

where p is the pressure or mean stress, q is the Mises stress, d1 – d5 are failure parameters. Failure occurs when the value of [pic] exceeds a unity.

The parameters values of the steel were adjusted from [9] and [10] such that ρ = 7,870 kg/m3, E = 200 GPa and ν = 0.33. The yield stress and strain hardening parameters were A = 532 MPa, B = 229 MPa and n = 0.3024. It is noted that the values of A and B were reduced from [9] as the normal graded steels, with weaker properties, were used in the experiments. The strain rate hardening constants were C = 0.0114 and [pic]. The temperature softening parameters were specific heat capacity Cp = 452 J/kgK, inelastic heat fraction α = 0.9, coefficient of thermal expansion [pic], m = 1, [pic]= 283 K and [pic]= 1793 K. The fracture strain constants d1 = 0.0705, d2 = 1.732, d3 = −0.54, d4 = −0.015 and d5 = 0.

4. Results and Discussions

The contour plots of von Mises stress on the deformed mesh at various times after initial impact are shown in Fig. 3. Failed elements predicted from the constitutive relations of each layers were deleted from the simulation results for visualization purpose. They exhibits high stresses during the first period after the initial impact at the center of the ceramic plates. The stress values decrease afterwards as elements in the high stress regions fail and are deleted from the grids. Damages at the back sides of the alumina layer, producing many broken pieces, are more extensive than the front sides that receive the direct impact. These damages clearly affect the metal plates in the next layer, causing large deformations in the form of bulging and subsequent the petal damage characteristics. Both damage characteristics of steel plates concur with the photos from experiments in Table 1.

The velocity (V2) and depth (U2) of the bullet tip are also shown in Fig. 4. Note that the negative value of U2 implies the bullet penetrating into the armor layers. The velocity V2 of the bullet is reduced from the initial value of 936 m/s to almost zero at t = 0.2 ms, implying that the bullet has come to a complete stop. Further confirmation on the bullet arresting event is shown by the upcoming energy plots.

The 180( sweep of the axisymmetric deformed plot at t = 0.2 ms with the steel plate profile at various time are shown in Fig. 5 for comparison with the experimental observation in Table 1. The bulge area with diameter of 50 mm predicted by the simulation in Fig. 5 is in a good agreement with the value of 50-55 mm observed in the post-firing samples in Table 1.

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|Figure 3. The deformation and von Mises stress at time instant t = 5, |

|10, 15, 35, 95 and 200 (s after the impact. |

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|Figure 4. The velocity and depth of bullet penetrating into the armor |

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|Figure 5. The deformed plot at t = 0.2 ms for bulge area measurement |

|(top) with the steel layer profile at various time (bottom) |

In the explicit runs, the amount of artificial strain energy, AE, which are generated by the programs in order to prevent unduly high deformation and distortion of elements, has to be considered. This artificial energy should be low compared to the total internal energy, IE, of the system for reliable results [6]. Figure 6 shows that the ratio of artificial energy over internal energy (AE/IE) for the present simulation never exceeds of 5%, the recommended value from ABAQUS [6]

The energy of the systems, namely the internal strain energy (IE), the kinetic energy (KE) and total energy (TE), during impacts are plotted in Fig. 7, along with the frictional work from the interaction between penetrating bullet and armor plate.

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|Figure 6. The ratio of the artificial strain energy to the internal |

|energy (AE/IE) during the simulation run. |

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|Figure 7. The energy distribution plots for all parts (top: IE = |

|Internal Strain Energy, middle: KE = Kinetic Energy, and bottom: TE = |

|Total Energy, Fric = Frictional work) |

From the kinetic energy graphs in Fig. 7, the KE of bullet decreases rapidly for the first 0.015 ms, which corresponds to the duration where the bullet is being stopped in the alumina layer, as shown in Fig. 3. This is consistent with the much larger energy absorption in the alumina layer, as shown by the IE plot. Between t = 0.015-0.05 ms, the KE decreases further but with a slower rate till it almost vanishes about 0.075 ms, corresponding to when the bullet is completely stopped by the steel layer shown in Fig. 3. Note that the shape of the bullet KE plot is consistent with the bullet velocity in Fig. 4.

From strain and total energy plots, it can be seen that the armor plate can effectively dissipate the impact energy of the bullet into the internal strain energy in each layer and the frictional work due to the contacting interactions. Note that the friction during the bullet impact is significant, which is about half the internal strain energy absorbed in the participating armor layers.

5. Conclusions

The computational model from the previous studies [1, 3-4] was extended and modified to simulate the ballistic impact of ss109 bullet traveling with the speed of over 900 m/s upon the armor plate, consisting of alumina and steel layers. The results show that alumina layer absorbs about two-thirds of the impact energy from the bullets with the remaining one-thirds dissipating into frictional work from the contacting interaction. The most severe damages to the armor occur at the back side of the alumina layer due to the superposition of reflecting stress waves [1]. The Johnson-Cook material model can effectively simulates the damages characteristics of the steel layer, with the bulge area qualitatively consistent with the experimental observation.

Acknowledgments

This research is supported by the National Metal and Materials Technology Center (MTEC), contract no. MT-B-48-CER-07-188-I. Special thanks are due to Dr. K. Sujirote, Dr. D. Atong, Dr. K. Prapakorn, Dr. A. Manonukul, Assc. Prof. Dr. T. Amornsakchai, Asst. Prof. Dr. S. Rimdusit and Maj. Gen. Dr. W. Phlawadana.

References

[1] Vanichayangkuranont, T., Maneeratana, K., and Chollacoop, N., 2006. Numerical Simulations of Level 3A Ballistic Impact on Ceramic/Steel Armor, Proceedings of the 20th Conference of Mechanical Engineering Network of Thailand (ME-NETT20), Nakhon Ratchasima, Thailand, October 18-20, 2006.

[2] MTEC, 2005. MT-B-48-CER-07-188-I Report, 1-year progress report, National Metal and Materials Technology Center, Thailand.

[3] Vanichayangkuranont, T., Maneeratana, K., and Chollacoop, N., 2005. Simulations of stress wave propagation from dynamic loads, Proceedings of the 19th Conference of Mechanical Engineering Network of Thailand (ME-NETT19), Phuket, Thailand, October 19-21, 2005.

[4] Vanichayangkuranont, T., Chollacoop, N., and Maneeratana, K., 2006. Numerical simulation of ballistic impact on ceramic armor, Proceedings of the 4th Thailand Materials Science and Technology Conference (MSAT IV), Pathumthani, Thailand, March 30 - April 1, A02.

[5] NIJ, 2001. NIJ Standard–0101.04, Revision A: Ballistic Resistance of Personal Body Armor, National Institute of Justice, U.S. Department of Justice.

[6] Habbitt, Karlsson and Sorensen Inc., 2003. ABAQUS version 6.3 Theory Manual, Pawtucket.

[7] Automation Creations, Inc., 1996-2006. MatWeb: Material Property Data. (accessed on may 2005).

[8] Roeder, B. A., and Sun, C. T., 2001. Dynamic penetration of alumina/aluminum laminates: Experiments and modeling. International Journal of Impact Engineering, Vol. 25, No. 2, pp. 169-185.

[9] Borvik, T., Hopperstad, O. S., Berstad, T., and Langseth, M., 2001. Numerical simulation of plugging failure in ballistic penetration. International Journal of Solids and Structures, Vol. 38, pp. 6241-6264.

[10] Park, M., Yoo, J., Teak Chung, D., An optimization of a multi-layered plate under ballistic impact. International Journal of Solids and Structures 42 (2005), pp. 123-137.

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