Numerical simulation of ceramic composite armor subjected to ballistic impact

Abstract

Armor systems made of ceramic and composite materials are widely used in ballistic applications to defeat armor piercing (AP) projectiles. Both the designers and users of body armor face interesting choices – how best to balance the competing requirements posed by weight, thickness and cost of the armor package for a particular threat level. A finite element model with a well developed material model is indispensible in understanding the various nuances of projectile–armor interaction and finding effective ways of developing lightweight solutions. In this research we use the explicit finite element analysis and explain how the models are built and the results verified. The Johnson–Holmquist material model in LS-DYNA is used to model the impact phenomenon in ceramic material. A user defined material model is developed to characterize the ductile backing made of ultra high molecular weight polyethylene (UHMWPE) material. An ad hoc design optimization is carried out to design a thin, light and cost-effective armor package. Laboratory testing of the prototype package shows that the finite element predictions of damage are excellent though the back face deformations are under predicted.

Introduction

Both the designers and users of body armor face interesting choices – how best to balance the competing requirements posed by weight, thickness and cost of the armor package for a particular threat level. An armor system made of a single material may be good enough to resist the impact of small caliber ammunition. However a multi-component armor system such as a hard faced ceramic armor with composite backing is necessary and is widely used to defeat armor piercing (AP) projectiles. These projectiles have a hard core material such as hardened steel or tungsten carbide and the ceramic face helps blunt and erode the projectile tip during impact. The composite backing absorbs the kinetic energy of the decelerated projectile and also catches the ceramic and projectile fragments preventing them from doing further harm.

Alumina (Al₂O₃), Boron Carbide (B₄C), Boron Silicon Carbide (BSC) and Silicon Carbide (SiC) are some of the ceramics that are commonly used. The range of composite materials used as backing and spall minimizing material include UHMWPE materials, aramid woven fabrics such as Kevlar and Twaron, fiber glass materials such as S2-glass and E-glass and so on.

A number of different analytical models have been developed to model ceramic and ceramic composite armors. Anderson and Walker [1] develop an analytical model that describes the dwell or interface defeat of the projectile during its impact against a ceramic. Dwell or interface defeat is where the projectile erodes with no penetration. This erosion is due to the pressure at the interface between the ceramic and the projectile exceeding the erosion strength of the projectile [9]. There is an inverse relationship between hardness and fracture toughness of the armor ceramics [18]. Hardness of the ceramic blunts the tip of the AP projectile whereas high fracture toughness provides multi-hit capability to the armor. Generally B₄C ceramics have high hardness and low fracture toughness whereas SiC ceramics have low hardness and high fracture toughness compared to B₄C. Boron Silicon Carbide (BSC) a B₄C–SiC blend ceramic has light weight, high strength and high fracture toughness which provide ballistic resistance against armor piercing threats. It combines the high hardness of Boron Carbide and high fracture toughness of Silicon Carbide.

Benloulo and Sanchez-Galvez [3] develop a simple one dimensional analytical model to simulate the ballistic impact of ceramic composite armor. The penetration process is divided into three phases. In the first phase the ceramic is intact, and the velocity and mass erosion of the impacting projectile are described by Tate’s equation. The fracture of ceramic and the damage to the composite occurs in the second phase. In the last phase, failure of the composite takes place.

Lee and Yoo [21] discuss the numerical modeling and experimental study of ceramic metal armor systems with a metal backing. Using smoothed particle hydrodynamics (SPH), the ceramic (Alumina) is modeled using Mohr–Coulomb strength model and linear equation of state (EOS) in AUTODYN. Lundberg [26] uses Johnson–Holmquist (JH1 model for SiC and JH2 model for Alumina and Boron Carbide) model in AUTODYN. The determination of transition velocity (transition from interface defeat to penetration) for various combinations of projectile, target material and target configuration is studied. Simha et al. [31] develop and use a constitutive model for ceramic (Alumina) and implement into EPIC Lagrangian finite element code. The model consists of strength model based on Hugoniot elastic limit for compression, viscoelastic flow rule, damage model for compression and tension and Mie-Gruneisen EOS.

Nemat-Nasser et al. [29] discuss experimental techniques used to study the performance of Alumina armor tiles wrapped with thin layers of several different materials such as carbon–fiber/epoxy, E-glass-/epoxy, etc. Details and results from a two-dimensional finite element model using DYNA2D are presented. They show that release waves emanating from the projectile edges reduce the pressure and increase the shear stress at a distance equal to the projectile diameter, ahead of the projectile. Grujicic et al. [11] analyze the performance of ceramic/composite armor subjected to AP projectile impact. They model the Alumina ceramic in AUTODYN using a polynomial equation of state, Johnson–Holmquist 2 (JH-2) strength model [16] and JH-2 failure model along with an erosion model. The composite material, S2-glass, is modeled using an orthotropic material model [6].

UHMWPE materials are widely used in ballistic applications because of their low weight, high tenacity and high specific modulus. These materials have a unidirectional construction in which the fibers lie parallel to each unlike fabrics that are woven. A thermoplastic resin is used as the binding agent. Typically, the material used for armor applications is made up of several 0–90° layers (or plies). The two most popular examples of UHMWPE material are Spectra® manufactured by Honeywell [4] and Dyneema® manufactured by DSM (DSM [8]). The UHMWPE fibers have a modulus in the range of 90–140 GPa and a failure strain of 2.9–3.8% [14]. These fibers have a very high energy absorption capability and high sonic velocity compared to aramid, S2-glass, polyamide and similar materials.

As stated earlier, some armor packages include ceramics and a backing material. There are different ways of bonding the two materials including use of spray on adhesive, adhesive tape, autoclaving/vacuum bagging, etc. Zaera et al. [34] study the effect of the adhesive layer thickness on the performance of the ceramic/metal armor. They show that the adhesives – a soft adhesive (polyurethane) and a hard adhesive (rubber–modified epoxy) show strain rate dependent behavior. In the follow up publication [23], the adhesive is modeled in AUTODYN using Steinberg–Guinan model and the Mie-Gruneisen EOS. By analyzing the depth of penetration and the projectile residual velocity, the authors conclude that the thickness of the epoxy resin adhesive significantly affects the performance of the system.

A finite element model with a well developed material model is indispensible in understanding the various nuances of projectile–armor interaction and finding effective ways of developing lightweight solutions. In this research we use the Lagrangian solver and explain how the models are built and the results verified using LS-DYNA [24]. The Johnson–Holmquist material model [7] in LS-DYNA is used to model the impact phenomenon in ceramic material. A user defined material model is developed to characterize the ductile backing (UHMWPE) material. The modeling and calibration of the ceramic material model are presented in Section 2. In Section 3 we review the development of constitutive model for the UHMWPE composite. In Section 4 we present the ballistic simulation of ceramic composite armor and compare the simulation results with tested samples. Finally, we present some thoughts on the current work and potential for future improvements.