Analytical and numerical simulations of ballistic impact on composite lightweight armours

Transcription

1 Projectile Impacts: modelling techniques and target performance assessment 191 Analytical and numerical simulations of ballistic impact on composite lightweight armours V. Sánchez-Gálvez & L. Sanchez Paradela Universidad Politécnica de Madrid, UPM, Spain Abstract This paper summarizes the utilization of analytical and numerical computation as valuable tools for lightweight armour design optimisation. Several analytical models for ballistic impact simulation onto composites and ceramic faced targets have been developed at our department. This paper shows a few examples of the utilization of those models as well as numerical computations using commercial hydrocodes. Keywords: ballistic impact, lightweight armours, analytical simulation, numerical simulation. 1 Introduction The deployment of peacekeeping forces in conflict areas (Afghanistan, Iraq) has dramatically increased the danger of casualties caused by terrorist attacks [1]. The use of Improvised Explosive Devices (IEDs) by insurgents has produced a very high number of injuries among the soldiers in the area. Protection systems of both vehicles and personnel designed to defeat less effective threats such as low calibre ammunition appear often ineffective against the more efficient threats used by terrorists, such as shrapnel or debris produced by heavy weight explosive loads. The utilization of advanced materials such as ceramics or composites appears as a promising solution to improve protection capability of armours keeping their weight under acceptable levels. Advanced ceramics (such as alumina, silicon carbide, silicon nitride) and composites (Aramid, polyethylene fibres) have been used to manufacture lightweight bulletproof vests and helmets since several decades ago. doi: / /019

2 192 Projectile Impacts: modelling techniques and target performance assessment Also, advanced materials begin to be included in the armour structure of lightweight military vehicles, either to retrofit traditional armours or to produce liners aimed to protect occupants. Several Infantry Fighting Vehicles (IFV) are now including advanced ceramics as a mean to improve their protection capability. Although ballistic impact behaviour of ceramics and composites has been widely studied, published information is scarce, probably due to classification reasons. Hence, designing lightweight armours using advanced materials either as a main armour or to improve protection of an existing armour usually requires launching a research programme aiming to find out the behaviour of the optimal combination of materials among a very high number of possible solutions. The exclusive use of experimental procedures (firing tests) to achieve an optimal design of composite armour to defeat a definite threat is expensive, due to the high number of parameters (materials, thicknesses) involved. The utilization of analytical or numerical simulation of penetration phenomena appears advantageous as these valuable tools reduce the experimental effort. The numerical simulation of ballistic impact is carried out using finite element method (FEM) or finite difference method (FDM) codes (hydrocodes) to discretize both target and penetrator and solve the equations governing the penetration process. Several commercial hydrocodes, for instance LS-DYNA and AUTODYN, are available. The numerical simulation of phenomena involving ballistic impact into composite armours provides a great amount of information (such as stress, strain, velocity histories, damage extension, erosion, crater dimensions). However, a numerical simulation is a difficult task especially when advanced materials are involved, due to the lack of reliable models of materials behaviour, particularly in the context of fracture criteria and post-failure behaviour [2]. On the other hand, an analytical simulation is based on the integration of laws of mechanics of continuous media, to which several simplifying hypotheses are introduced leading to equations governing the penetration process. Although analytical models are less accurate in predicting actual ballistic behaviour than numerical simulations, they permit the investigation of a large number of parameters, due to their simplicity, leading to a high reduction of time and cost of armour designing. This paper presents a methodology for lightweight armour design optimisation based on a combination of all three approaches mentioned. 2 Lightweight armour design The methodology proposed for lightweight armour design when advanced materials (ceramics, composites) are used is a combination of the three approaches mentioned, empirical, analytical and numerical and it is sketched in figure 1. After defining the threat (specifying, among others, geometry, material, striking velocity, impact obliquity) and the requirements of the protection (maximum weight, thickness, cost), analytical models may be used for rough

3 Projectile Impacts: modelling techniques and target performance assessment 193 computations to make a clear distinction among the preliminary solutions. Subsequent to that, numerical simulation is a valuable tool to tune the solution and to validate the analytical model. Finally, firing tests are always required to check the performance of the solution. Figure 1: Flow chart of the proposed methodology of armour design. 3 Analytical simulation As previously mentioned, an analytical simulation is based on the development of expressions, derived from the equations of continuum mechanics and able to describe the penetration process and to yield valid data concerning, among others, perforation, crater dimensions, residual velocity and mass of projectile after perforation. Often, equations governing the process are quite involved requiring the use of the computer to solve for the unknowns [3] but computations may be carried out in a few seconds, thus a very high number of parameters can be analysed very rapidly. The degree of accuracy achieved by analytical models depends on the simplifying hypotheses adopted. Ballistic impact is a very complex phenomenon, thus its analytical modelling requires the making of several assumptions, neglecting some effects considered less important as compared to those considered as the controlling ones. In recent years, several analytical models for high-speed impact onto composite targets have been developed at the authors department. In the following, the main features of such models are summarized as well as some relevant results achieved are presented. 3.1 Modelling ballistic impact onto composites Composite materials are currently being used to produce body armours and helmets to provide protection to personnel (soldiers and police officers) against impact from fragments and low calibre ammunition, as well as to produce liners

4 194 Projectile Impacts: modelling techniques and target performance assessment that improve protection to occupants of military vehicles when subjected to blast or projectile impact [4]. Body armours and liners are soft materials in the form of cross-stitched multilayer fabrics; helmets are produced by pressed lamination multilayer fabrics into a polymeric matrix to achieve a rigid composite material that reduces trauma to the head. Analytical modelling of high-speed impact onto composites is a very difficult task. The target is inhomogeneous and anisotropic and usually manufactured by lamination of several layers. Hence, the mechanical behaviour of the laminate is not easily derived from data obtained by testing fibres or even fabrics. Hence, a set of hypotheses should be adopted to make the analysis of the phenomenon tractable. Based on the ideas firstly introduced by Roylance [5] and Smith, [6] several analytical models aiming to simulate high-speed penetration into composite targets have been developed at the authors department. The basic hypotheses are the following (see fig. 2). Figure 2: Sketch of yarns impacted transversely. When the target is impacted, an elastic longitudinal wave propagates along the yarns, spreading the impacted surface. The matrix is immediately fractured, and thus it is assumed that only the fibres are responsible for decelerating the penetrator. Nevertheless, the matrix mass is taken into account in computing the reduction of linear momentum of the penetrator as well as in calculating the stress wave speed. The process continues until either the projectile comes to rest or fibre breakage (full perforation of the target) occurs. The differences among those models are found in the additional hypotheses adopted. Parga s model [7] assumes that friction between yarns at cross-overs is the parameter controlling the stress decay along the yarns. It is able to predict the ballistic limit V 50 (striking velocity for 50% probability of full perforation) but it requires adjusting arbitrarily the friction coefficient to match experimental data. Chocron s model [8] uses an energy balance equation to to derive an expression for the residual velocity of the projectile after perforation. Fig. 3 shows a good agreement between analytical results and experimental data obtained by Cunniff [9] firing FSP (fragment simulating projectiles) onto Kevlar 29 fabric. However, Chocron s model assumes that fibre failure takes place when a parameter R reaches a critical value that is also chosen to match experimental data. Finally, the newest Sanchez Paradela s model [10] does not require utilisation of any parametric quantity to derive equations that predict residual velocity, ballistic limit as well as target shape and energy absorption and, at the same time, is in

5 Projectile Impacts: modelling techniques and target performance assessment 195 good agreement with experimental results. See for instance fig. 4 that illustrates ballistic limit V 50 vs. areal density for the impact of a 16 grain (1.1 g) FSP onto UD 66 Dyneema target (High performance polyethylene fibre). Dots are experimental results obtained by van Gorp [11] and the solid line is the analytical model prediction. Figure 3: Experimental [9] and analytical results [8] for FSP impact onto Kevlar 29 fabric. Figure 4: Experimental results [11] and analytical predictions [10]. Ballistic limit against areal density for 1.1 g FSP impact onto UD 66 Dyneema fabric.

6 196 Projectile Impacts: modelling techniques and target performance assessment 3.2 Modelling ballistic impact onto ceramic faced targets Advanced ceramics (such as alumina, silicon carbide, silicon nitride, boron carbide, titanium diboride) are being increasingly used to achieve more efficient armours against kinetic energy projectiles, shape charges, explosive forming projectiles (EFP) while keeping armour weight under acceptable levels. Advanced ceramics have been proven to exhibit a much higher ballistic efficiency compared to that of traditional materials (steel, aluminium). Ceramics however are quite brittle, being fractured a few microseconds after high-speed impact. The utilisation of ceramics for armour production requires therefore the inclusion of a ductile backing plate, either a metallic alloy or a composite to withstand the effects of the fractured ceramic. Such structures are known as composite armours, which can be employed as the main armour (for instance, rigid body vests, helicopter seats) or attached to the main armour of the vehicle (add-on armour). The penetration process into ceramic faced composite armours is sketched in fig. 5. A few microseconds after the initial contact, a cone of comminuted ceramic is produced, distributing the pressure on the ductile backing plate. The penetrator is decelerated and eroded while penetrating the ceramic and the backing plate is bulged. The process ends either by projectile arrest or by backing plate fracture in tension along a spread surface. Figure 5: Sketch of ceramic faced armour impacted by high-speed penetrator.

7 Projectile Impacts: modelling techniques and target performance assessment 197 In recent years, several analytical models have been developed at the authors department able to simulate ballistic impact on ceramic/metal [12] as well as on ceramic/composite [13] targets. As pointed out already, analytical models validated by experiments may be very useful tools as a first step towards armour designing. For instance, figs 6 and 7 illustrate some results obtained with the SCARE analytical programme, developed to simulate ballistic impact onto ceramic/metal targets [12]. Fig. 6 depicts optimum results of areal density vs. ceramic thickness/metal thickness ratio for impact of 25 APDS (armour piercing discarding sabot) projectiles onto alumina/aluminium alloy at different obliquities while fig. 7 shows the residual velocity after perforation against ceramic thickness for the same projectile and target materials. Similarly, figs 8 and 9 illustrate analytical results obtained with the model developed to simulate penetration into ceramic/composite targets [13]. Fig. 8 summarizes the analytical predictions of residual velocity vs. striking velocity for alumina/kevlar 29 targets of different areal densities and three different armour piercing (AP) projectiles: 7.62 AP, AP and 14.5 AP. From fig. 8 it is easy to derive the results shown in fig. 9, which depicts the ballistic limit vs. areal density for the three mentioned projectiles. This figure includes also numerical results as will be described in the next section and experimental data, showing a good agreement between the results obtained by the three approaches used. Figure 6: Analytical predictions [12] of optimal design of alumina/aluminium armour to defeat 25 APDS projectiles.

8 198 Projectile Impacts: modelling techniques and target performance assessment Figure 7: Residual velocity vs. ceramic thickness for alumina/aluminium armour perforated by 25 APDS projectiles. 4 Numerical simulation As already pointed out, numerical simulations are carried out by discretizing projectile and target and using either the finite element method or the finite difference method and computing the penetration process step by step with the use of a numerical computation code. The whole process may last from a few minutes up to several hours. The main difficulty in numerical simulations of high-speed impact onto composite targets arises from dearth of material behaviour data. Although the dynamic behaviour of metal alloys is usually well known, the necessary data for advanced ceramics and composites are much scarcer, probably due to classification reasons. Especially, the data needed to feed the failure criterion and the mechanical behaviour of damaged materials are not easily available. Hence, the predictive capability of numerical simulations is limited and often parametric data must be used to match experimental results. On the other hand, numerical simulation, after validation by comparison with experimental results, provides a great amount of information, such as stress and strain distributions, damage extension, penetrator mass and velocity. For instance, fig. 10 shows the perforation of a 20 mm AD 95 alumina + 10 mm 5083 aluminium alloy add-on armour by a 20 mm APDS projectile and 30 obliquity. The figure shows both the numerical simulation with AUTODYN 2D hydrocode as well as experimental results with X-ray shadowgraph for the same time. The comparison between experimental observations and numerical simulation proves that this approach provides reliable results with much less expensive effort. The figure gives also very interesting results; both methods show a high erosion of the projectile, which is destabilized after perforation, being unable to perforate the main armour. Another example of numerical simulation is shown in fig. 11. It illustrates the penetration process into an add-on armour alumina/aluminium by a tungsten APFSDS (armour piercing fin stabilized discarded sabot) projectile. The figure shows the phenomenon several times. The projectile perforates the add-on armour, but suffers a severe deformation and erosion being unable to perforate the steel main armour.

9 Projectile Impacts: modelling techniques and target performance assessment 199 Figure 8: Analytical predictions [13] of residual velocity vs. striking velocity for three armour piercing (AP) projectiles after perforation of alumina/kevlar 29 armours.

10 200 Projectile Impacts: modelling techniques and target performance assessment Figure 9: Analytical, numerical and experimental results of ballistic limit against areal density for optimal design of alumina/kevlar 29 armour to defeat three AP projectiles. Figure 10: Numerical simulation with AUTODYN 2D and shadowgraph of perforation of alumina/aluminium add-on armour by 20 APDS projectile.

11 Projectile Impacts: modelling techniques and target performance assessment 201 Figure 11: Numerical simulation with AUTODYN 3D of perforation of alumina (aluminium add-on armour by a kinetic energy projectile. 5 Conclusions Analytical and numerical simulations are valuable tools for lightweight armour design optimisation with advanced materials. Although firing tests are always required for validation of the solution, the number of shots can be dramatically reduced by previous screening with numerical simulation. This paper shows some examples of utilisation of analytical models and numerical simulation for lightweight armour design.

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