Numerical investigation on ballistic resistance of aluminium multilayered panels impacted by improvised projectiles
Abstract
This paper presents a numerical study of perforation of the aluminium multilayered targets impacted by steel projectiles in the shape of a ball, nut and nail. For the construction of the protective panels arc, rectangular, V and Ushaped sheets of metal were considered. During the tests the panel thickness was constant at 160 mm. The panels were composed of 1.5mmthick aluminium sheets, and the initial speed of debris was \(500~\mathrm{m{/}s}\). A comprehensive numerical study indicated the shape of the layer that had superior ballistic resistance and the best strengthtoweight ratio. Computational analyses were also used to investigate the influence of thermal softening and strain rate hardening in the Johnson–Cook constitutive model on the ballistic performance of layered targets. The number of layers required to stop the penetrating objects was compared for the rigid and deformable projectiles. Based on the comparative studies, some guidelines for engineering tasks involving exploration of number of possible technical solutions were proposed.
Keywords
Ballistic resistance Multilayered panels Improvised projectiles1 Introduction
The idea of using layered structures in ballistic resistant barriers is not new and has been extensively discussed in the literature. Designing protective panels places great emphasis on ensuring protection against punctures because the injuries from flying debris may carry significant risks for both civilians and military personnel. Previous studies were focused on ballistic resistance of singlelayered targets and on potential improvements from replacing monolithic plates by multilayered structures. However, there are not that many studies of more complex shapes of the component plates and of effectiveness of this solution with respect to ballistic perforation, especially by improvised projectiles.
The behaviour of multilayered panels made of mild steel, stainless steel and aluminium plates under impact was studied in [1]. It was found that layered structures may offer better performance than monolithic plates due to change from plastic energy dissipation to perforation and stretching sheets of metal. Radin and Goldsmith [2] found that the ballistic resistance of a monolithic plate is superior to the structure of the same thickness but made of adjoined layers. It was also found that spaced layers usually displayed lower resistance than plates in contact. Almohandes et al. [3] conducted extensive experimental studies to determine the effects of target configuration on ballistic performance. Through many perforation tests it was established that single steel plates were more effective than multilayered targets, with or without spacing. In the paper by BenDor et al. [4] investigation of ballistic performance of layered targets was performed. They found that the width of the air gap between the layers had no effect on the resistance of target for the conicalnosed impactors. In the corresponding paper [5] it was concluded that the increase in the width of the air gaps and the increase in the number of layers raised the ballistic limit velocity of the target (understood as the velocity required for a projectile to penetrate a particular piece of material). The effect of air gaps upon ballistic properties of the shield was further discussed in [6], where the authors concluded that for the nonconical shape of the projectile changes in the ballistic limit velocity were in the range of several per cent. Woodward and Cimpoeru [7] investigated perforation of laminated and homogeneous plate targets by flatended and conical penetrators. The comparison of calculated and experimental ballistic limit showed that superior resistance occurred for the target system with two plates. In the work of Zukas and Scheffler [8] numerical results of the impact effect in monolithic and layered targets were presented. It was revealed that layering significantly weakened thin and intermediate thickness targets. Liang et al. [9] conducted studies of the resistance performance of multilayered structures based on three conservation laws. They validated their results with the experimental data from Almohandes et al. [3]. Another comparative analysis of computational results and experimental data was presented by Elek et al. [10] where perforation of monolithic and layered targets was considered. They showed that for flatended cylindrical penetrator increasing the number of layers caused degradation of ballistic resistance of the target. Gupta et al. [11] presented experimental and numerical investigation of the ballistic performance of the layered aluminium plates under impact of flat, ogive and hemisphericalnosed projectiles. They showed that residual velocity of the projectile was similar for targets of equivalent thickness with one or two layers. Also, the ogivenosed projectile was found to be the most efficient for multilayered panel. Dey et al. [12] investigated perforation resistance of doublelayered steel plates impacted by blunt and ogival projectiles. They found that double layering of the target increased the ballistic limit velocity for spaced plates by nearly 40% compared to a monolithic target of equal thickness. In contrast, based on numerical investigation of monolithic, double and triplelayered plates FloresJohnson et al. [13] concluded that monolithic plates had a better ballistic performance than a layered target. Multilayered structures in different combinations were also considered in research conducted by Deng et al. [14]. Results of an experimental test of panels with one, two, three or four plates showed that monolithic targets had higher ballistic resistance than layered targets if the total thickness was smaller than the value where petaling or bulging becomes the dominant failure mode. Finally, BenDor et al. [15] presented a comprehensive survey of experimental and numerical investigations of multilayered targets and also delivered a review of analytical methods for optimization of layered panels.
It is crucial to use a material model that can mimic a mechanical response that is in good agreement with the behaviour of a physical target. In this study, the computational model is based on the constitutive model proposed by Johnson and Cook [16, 17]—the one which assures good global damage approximation (cf. [18, 19]), thus appropriate for herein considerations. Since the time it was published, a number of modifications have been proposed but the original formulation is still used for research of perforation [20]. It should be emphasized that the same class of models was developed earlier by Litoński in [21] where the torsion of tubes made of strain ratesensitive plastic material was examined. Li et al. [22] proposed a modified Johnson–Cook model that can provide better coupling for the influence of temperature and strain rate on flow behaviour. The proposed model showed good ability to track the flow behaviour of T24 steel over the entire temperature and strain rate range. A modified version of the Johnson–Cook constitutive relation (the MJC model) was used in research conducted by Børvik et al. [23], where perforation of five different steel plates was investigated. Material constants for the steel plates were based on various material tests, and the data for bullets were mainly taken form the literature. Samantaray et al. [24] performed a comparative study of Johnson–Cook, modified Zerilli–Armstrong and Arrheniustype constitutive models. The experimental data from compressive tests were used to establish material constants for each of those formulations. In contrast to the previous works it was found that the Johnson–Cook model was incapable of providing a good description of flow behaviour of 9Cr–1Mo steel over the entire range of strain rates, temperatures and strains. The significance of the use of strain rate and temperature parameters in the model was confirmed in the work presented by Børvik et al. [25]. The fully coupled model where thermal and strain rate effects were included showed best agreement between experimental and numerical results. A comprehensive study of the extruded aluminium panels was presented by Børvik et al. [26]. The experimental results were used to calibrate a modified version of the Johnson–Cook constitutive relation and failure mode. This computational effort delivered a very good agreement between numerical and experimental data since the mechanical behaviour of the target was captured. In the corresponding study by Holmen et al. [27] perforation of empty and sandfilled aluminium panels was investigated. It was shown that though the combination of the finite element analysis (Johnson–Cook plasticity and failure models) and the discrete particle method can be used to describe interaction between solid and granular media, still some challenges remain.
In the work done by Corran et al. [1] it was shown that the nose shape, in particular the nose radius, was extremely important in regard to likelihood of the target penetration. Wingrove [28] found that flatended projectiles penetrate the target with less resistance than spherical and ogiveshaped impactors. This phenomenon was attributed to the change in failure mode from adiabatic shear zones for the blunt projectiles, to the plastic tearing for the spherical and ogiveshaped objects. Wilkins [29] showed that the minimum ballistic velocity was lower for a sharp projectile perforating thick targets than for a blunt projectile. In case of thin targets, an opposite dependence was found. In papers [30] and [31] perforation of steel plates by three different projectiles was examined. Both experimental and computational experiments showed that hemispherical and conical shaped impactors gave ballistic limit velocity close to \(300~\mathrm{m{/}s}\), while for the blunt projectile this parameter was about \(185~\mathrm{m{/}s}\). Furthermore, it was stated that at the highest impact velocities, deformation of the projectile might become a significant factor and might influence the overall resistance of the panel. Gupta et al. [32] presented experimental and numerical investigations of perforation of thin aluminium plates by blunt and hemisphericalnosed projectiles. The results obtained in that study were similar to those previously discussed; namely higher ballistic limit was found for the hemispherical projectile. In the investigation by Arias et al. [33] good agreement between experimental and numerical results was obtained for the cylindrical, conical and hemispherical projectiles. It was shown that residual velocity after perforation was similar for a conical and a hemisphericalshaped object, while the lowest value was found for a cylindrical projectile. Visible correlation between the projectile shape and the energy absorption capacity of a target was presented in the paper by Kpenyigba et al. [34]. It was found that the hemisphericalnosed impactor was the least efficient, followed by conical and two double nosed. In the work by Rusinek et al. [35] primary focus was on studying the conical projectile diameter in relation to its perforation performance. Numerical and experimental analysis revealed that a linear relation existed between ballistic limit velocity and projectile diameter. In the paper by Iqbal et al. [36] the influence of the targettoprojectile diameter ratio D/d on the ballistic resistance and failure mechanism was investigated. For the bluntnosed projectile the increase in the ballistic limit velocity was observed up to the point where D/d was equal to 10; after that the change in the value of ballistic limit velocity was negligible. For the ogivenosed projectile the value of limit velocity was increasing up to the point where D/d was 25; after that, the relation between ballistic limit velocity and the targettoprojectile ratio was not observed.
The influence of strain rate and temperature on material parameters was investigated by Klepaczko [37] and formulated into a power law constitutive relation. In [38] four constitutive models for metals were researched in terms of the work hardening limitations. It was concluded that the original form of Johnson–Cook model may be inadequate for describing the behaviour of metals that exhibit inversely proportional relation between work hardening and strain rate. In the work by Rusinek et al. [39] energy absorption properties of a target under various strain rates were examined. It was observed that the work hardening of the analysed material (AISI 304 steel) was independent of plastic strain. Pothnis et al. [40] found that for both aluminium alloy 7075 T651 and IS 2062 mild steel tensile yield strength was enhanced when different strain rates were applied, if compared to quasistatic loading. Hor et al. [41] conducted a number of compression and shear tests involving a wide range of temperatures (20–\(1000^{\circ }C\)) and strain rates (\(10^{2}\)–\(10^{5}\,\,1/\hbox {s}\)). They found strong coupling of three main phenomena: effect of the temperature, effect of the strain rate and the strain hardening–softening. Thus, the material model that includes those effects was required in case of dynamic loading. In [42] the dynamic mechanical response of Febased hightemperature alloy over a wide range of strain rates and temperatures was investigated. The effects of strain rate hardening and thermal softening were visible in the presented data and were the base for the formulation of power law constitutive model.
One of the goal of this study is to provide a set of guidelines for those who are interested in the properties of computational models of spaced multilayered targets (composed of thin metallic sheets) perforated by the improvised impactors. We have examined the behaviour of layered structures including or excluding thermal and strain rate effects in various configurations. Rigid and deformable projectiles were also used to establish how these constraints translated to the ballistic resistance of the panel. The ballistic performance of numerical models of nail, nut and ballshaped impactors in different orientations was examined. Furthermore, ballistic performance of four different shapes of the component layers was tested against projectiles in three different points of impact.
This paper extends previous research of the authors regarding perforation of multilayered panels by rigid projectiles [43]. Here, the results include the study of the impact of deformable projectiles, and new shapes of panel layers are considered as well. Moreover, different combinations of the work hardening and thermal softening effects in the computational model and their impact on mechanical response of the layered panel are examined.
2 Mathematical modelling
2.1 Fundamental concepts
2.2 Evolution function for yield stress
Parameters  Material  

Aluminium  Steel  
A (MPa)  324  640 
B (MPa)  113  113 
n (−)  0.42  0.42 
m (−)  1.34  1.34 
\(\vartheta _{\mathrm{melt}}\) (\(^{\circ }\)C)  925  1200 
\(\vartheta _{\mathrm{transition}}\) (\(^{\circ }\)C)  293.2  293.2 
\(\bar{\rho }\) (kg/m\(^3\))  2703  7850 
Young’s modulus (GPa)  69  209 
Poisson’s ratio (−)  0.3  0.3 
C (−)  0.002  0.002 
\(\dot{\varepsilon _{0}}\) (1/s\(^{1}\))  1  1 
\(c_p\) (J/kg \(\cdot \) K)  910  460 
\(\chi \) (−)  0.9  0.9 
2.3 Damage initiation and fracture conditions
Input parameters for the Johnson–Cook dynamic failure model [44]
Parameters  Material  

Aluminium  Steel  
\(d_1\) (−)  \(\)0.77  3 
\(d_2\) (−)  1.45  0 
\(d_3\) (−)  0.47  0 
\(d_4\) (−)  0.00314  0 
\(d_5\) (−)  1.6  0 
In the present study, when the failure initiation criterion was met, the stress components were set to zero (in each Gauss point), which is equivalent to removing an element from the mesh. This behaviour was imposed by setting the fracture energy parameter to zero.
The projectile was additionally modelled as a rigid body for the purpose of certain analyses as mentioned. In those cases steel density was the only property required by the FE solver to calculate the projectile behaviour. Hard contact formulation was used to define the pressure–clearance relationship.
3 Description of the numerical experiments
The main tool used in our research is the numerical model of the multilayered panel and the projectile which was subjected to many perforation tests. An example of a perforation test is presented in Fig. 1. The speed of the projectile and its current position relative to the initial position were recorded throughout the simulation. The objects were modelled in the threedimensional space; hence, these parameters were tracked for three axes. The analysis was iterative, which means that the simulation started with an initial number of layers in the panel and if the object was not stopped by the panel (i.e., at the end of the analysis it had a nonzero speed), the number of layers was increased and the analysis repeated. The basic analysis time was set at \(9.6 \times 10^{4}\) s and was modified if necessary.
In our research we examined properties of barriers built with plane sheets of metal and also more complicated shapes, as shown in Fig. 4b. Therefore, for some panels more than one initial position of the projectile had to be included in the simulations. For every nonflat plate three different places of impact were identified: concave, convex and intermediate between these two—see Fig. 4a. Every panel used in the simulations was rectangular cuboid with a square base that was \(0{.}25~\times ~ 0{.}25~\mathrm{m}{^2}\) in size and had a casing made of two additional flat plates placed at the front and back of the multilayered structure. The thickness of the panel was 0.16 m and was constant, while the thickness of a single layer was variable and changed with the number of layers. The thickness of aluminium plates used in this study was 1.5 mm. The basic dimensions were chosen to ensure an adequate distance from the place of impact to the edges of barriers; thus, boundary effects were eliminated.
Aluminium layers were modelled with S4R (shell, 4node, reduced integration) elements, whereas C3D8R (continuum, 3D, 8node, reduced integration) elements were used for modelling the projectile. The maximum number of elements in the FE mesh was \({\sim }1{.}3\times 10^6\).
4 Results
In the numerical analysis the material model is a key element that significantly influences the outcome. In general, the more accurate the model, the closer to the behaviour of the real object is the behaviour of the tested structure. Introducing thermal and rate effects to the basic Johnson–Cook formula increased the complexity and the number of model parameters but did not yield better results in terms of engineering significance.
In the first part of the study we examined the relation between thermal and strain rate effects and the behaviour of the panel made of metal plates. Plane sheets were chosen since any profile could compromise the results by changing the trajectory of the projectile. The different perforating objects (ball, nut and nail) and different impact orientations assured that our research was independent of the shape of the projectile. At this stage the impactors were modelled as rigid bodies. The impact of the previously mentioned phenomena was assessed by recording the number of layers required to stop the impactor.
Comparison of different shapes revealed that only the nail is worth investigating further (Fig. 5). Moreover, the mechanical model of the projectile does not introduce any noticeable change (Fig. 6). In other words, a rigid impactor is stopped by the panel of the same design, which is sufficient to stop the deformable object. This last conclusion was unexpected regarding our previous experience; so it was be developed in the following (second) part.
We notice that eight layers were required when the projectile punctured the concave part of the arcshaped panel (cf. Fig. 7a). In this layer arrangement the same number of layers is effective only for the case of convex position. The intermediate point was recognized as a spot where the difference in projectile behaviour was the greatest. The rectangular shape (Fig. 7b) was a much more stable solution as an equal number of layers for the rigid and deformable objects was sufficient to prevent perforation. Again, the biggest difference in the behaviour of different models of projectiles can be observed in the intermediate point. For both of these cases the difference exists because in the intermediate position the impactor had to perforate additional material, which caused significant deformation of the projectile, resulting in considerable loss of its velocity. The same phenomena occurred in the convex point of the Vshaped panel but with less intensity, as there is only twolayer gap—see Fig. 7d. In other cases the perforation by the rigid or deformable objects had the same intensity in a specific position. The barrier with the Ushaped layers required seven layers to stop the projectile if it hits the concave part. Moreover, it was the only case where there was a difference between the results for the rigid and deformable objects.
Simulation time depending on the shape of the aluminium plates
Shape of the sheet  Rigid body  Deformable 

Arc shape  00:52:00  18:59:00 
U shape  01:29:00  18:16:00 
V shape  01:00:00  25:51:00 
Rectangular shape  01:01:00  20:04:00 
(hh:mm:ss)  (hh:mm:ss) 
The simulations were carried out on the Intel 64bit PC (CPU 8x2.33 GHz Inter(R) Xeon(R), 16 GB RAM, OS GNU Linux). As it was mentioned earlier, the simulation time can increase significantly for deformable projectiles, as shown in Table 3. This is due to the increase in computational complexity resulting from the deformation of the projectile and creation of a new contact surface due to erosion, two factors which were not present in analysis of a rigid body behaviour. In some cases it can take 25 times longer to finish calculations for the same setup with a different model of impactor.
It is worth noting that erosion of deformable objects requires defining the interior surface, which is not yet supported in the Abaqus/CAE. Therefore, first a model with the exterior surface has to be created and then changes have to be introduced in the resulting input file using the keyword INTERIOR.
5 Conclusion

among various shapes of the component layers tested the Vshaped fulfilment of the panel was found to have the best strengthtoweight ratio,

the impact position of the projectile was significant for the ballistic resistance of the target,

the shape of the projectile had a strong impact on the number of layers required to stop the perforation,

among different combinations of the strain rate hardening and the thermal softening effects applied in the constitutive model, the most noteworthy change in the performance of the target was observed when both were included in the calculations,

for the flat component layers there was no striking difference in the number of layers required to stop the perforation in the case of rigid and deformable projectiles,

the ballistic resistance of targets made of various shapes of the component layers was greater for the deformable impactor, and

the structured component layers are much more efficient than the flat one keeping the overall structure lightweight.
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