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Abstract
The article delves into the use of quasi-static multi-punch shear testing to predict the ballistic performance of transparent armor systems. It examines the correlation between multi-hit ballistic tests and quasi-static punch shear tests, highlighting the importance of understanding energy absorption mechanisms and damage propagation. The study introduces a novel approach using the K-means clustering algorithm to predict the likelihood of a specific transparent armor system passing a multi-hit ballistic test. This method offers a cost-effective and time-efficient alternative to traditional dynamic testing, making it a valuable tool for researchers and engineers in the field of defense and materials science.
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Abstract
Background
Transparent armor systems are traditionally designed following a trial-and-error approach, which involves high development costs associated with ballistic testing. This research article presents a novel methodology, termed quasi-static multi-punch shear testing, within the domain of transparent armor systems.
Objective
The primary aim is to establish a correlation between multi-hit ballistic tests at Level III-A according to the NIJ 0108.01 standard, achieved through an adaptation of the single-shot ballistic limit methodology, and the quasi-static multi-punch shear testing. The objective is to utilize a simple experimental methodology that provides insights into the multi-hit ballistic behavior of transparent armors.
Methods
Parameters such as absorbed energy and observed damage mechanisms were utilized to assess the potential relationship between these tests. Transparent armor samples that underwent testing using the quasi-static multi-punch shear test were subsequently cross-sectioned using a water jet cutting machine to facilitate visualization of material damage. In addition, drawing on insights from quasi-static multi-punch shear testing results, the K-means clustering algorithm was employed to predict the likelihood of a specific transparent armor system passing a multi-hit ballistic test.
Results
Various damage mechanisms were observed as a function of the punch displacement, and correlations were made with the load–displacement curves. Furthermore, the implementation of the K-means clustering algorithm successfully classified transparent armor into two groups: those that passed the ballistic test and those that did not.
Conclusions
This research significantly advances understanding of transparent armor system behavior under multi-hit conditions and offers a promising predictive tool for evaluating their performance through straightforward and cost-effective experimentation.
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Introduction
Transparent armor systems (TAS) are composite structures consisting of stacked layers of glass and plastics, bonded using interlaminate adhesives [1]. Such composite structures are designed to withstand various attacks with as little weight or thickness as possible while keeping their affordability [2]. In order to reduce weight or thickness, ceramics materials have been used in armor applications for the last 70 years due to their exceptional hardness [3]; however, these materials are expensive mainly due to the manufacturing process. Ceramics can be challenging to manufacture into large, transparent pieces with high optical quality. Achieving consistent transparency and controlling defects like bubbles, cracks, or impurities on these materials can be difficult and expensive [4, 5], hence reducing TAS affordability. Therefore, the most widely employed brittle materials in TAS have been soda-lime-silicate and borosilicate glasses, as they are inexpensive, hard, chemically stable, and available in large sizes [6].
It is known that the TAS ballistic capability is highly correlated with the way layers are stacked [7]. This correlation is explained by a variety of parameters associated with the design of TAS, including the number and thickness of layers as well as the mechanical and physical properties of polymers and brittle materials involved. However, there is little information published regarding how the combination of such parameters affects the ballistic performance of TAS; thus, these structures are traditionally designed following an Edisonian approach. This is an unfeasible and time-consuming methodology to understand the role of each variable on the ballistic performance of TAS, as it is a trial-and-error method based on intuition and empirical experimentation. However, with increasing complexity and combinatorial possibilities, this approach becomes impractical [8].
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Different researchers have been trying to predict the composite’s ballistic performance using the quasi-static shear punch test (QS-PST) [9‐11]. The QS-PST is a low strain-rate rate test, generally performed using a universal testing machine (UTM), in which a specimen is indented utilizing a hardened steel punch assembled to the upper grip of the UTM. Although such low strain-rate tests do not account for dynamic phenomena, some damage mechanisms presented at high (dynamic) and low strain rates have similar characteristics [9]. Owing to this similarity, it has been possible to develop penetration models using the information obtained from the QS-PST to predict the dynamic penetration mechanisms and the ballistic performance [10]. For instance, Potti and Sun [10] have built a methodology to predict the residual velocities and ballistic limits of different composite configurations through the QS-PST. Moreover, Jenq and Jing [12] have found an agreement between the predicted ballistic limit and the results obtained from the analysis of the load vs displacement curves, which are typically acquired during the QS-PST run. In addition, Gama et al. [13] have investigated the punch shear energy absorption behavior of thick-section hybrid composites considering the material’s penetration resistance under QS-PST. With this information, they were able to compare the penetration resistance of composite laminates with different fiber through the thickness that were made from fiber S-2 glass/SC15 [13]. Furthermore, in subsequent years, Gama et al. [14] employed the QS-PST test with different support conditions, specifically varying the Span to Punch Ratio (SPR), to mimic the deformation cone’s evolution observed in impacts on S-2 glass/SC15 laminated composites. As a result, they devised a predictive model for the ballistic limit, which depended on the energy obtained from an envelope curve constructed using the maximum force–displacement points from the assessed SPRs. Using this model, they were able to estimate an energy value of 81% in relation to the energy generated by a high-velocity impact. Years later, in the study conducted by Husain Abbas et al. [15], the QS-PST perforation energy and a dynamic increase factor were utilized to estimate the ballistic limit of concrete slabs enhanced with textile-reinforced mortar and externally bonded carbon fiber-reinforced polymer (CFRP) sheets. Although the perforation energy during projectile impact was higher than that of quasi-static penetration, the effective prediction of the ballistic limit highlights a strong correlation between dynamic and quasi-static perforation energies.
Regarding the failure mechanisms, investigations conducted by [16] revealed a significant relationship between QS-PST and ballistic tests performed in accordance with the NIJ 0101.03 standard, level II-A, using 9 mm FMJ ammunition. This relationship was associated with the observed damage mechanisms in FRP composites, including fiber and matrix failure, matrix cracking, and delamination noted in both testing contexts. Additionally, Muniraj Dhanarasu and Sreehari VM conducted QS-PST and high-speed impact tests on sandwich structures featuring CFRP face sheets. Their findings indicated that peak load values were related to deflection in both the quasi-static and dynamic tests [17].
Regarding the behavior of brittle materials such as glass, when these materials are loaded with a relatively blunt object, they will deform elastically until reaching their ultimate strength, which depends on the indenter’s position and radius [18, 19]. After the elastic deformation capacity of a glass is reached, some cracks appear at a critical load, which may show considerable scatter, following the “Auerbach’s law” which states that the critical load required for a hard, spherical indenter to produce a cone crack in a flat, brittle specimen is proportional to the radius of the indenter [18‐20]. Such cracks produce a cone-shaped fracture developed in the contact region between the glass and the indenting object. This phenomenon called The Hertzian fracture was first investigated by Hertz in the 1880s by using hard spheres [21, 22]. This Hertzian fracture begins as a surface ring crack outside the elastic contact and when a critical load is reached, those initial cracks propagate downward and expand outward within a tensile field into a stable, truncated cone configuration [21, 23]. In fact, common glasses (e.g., most silicate glasses) under indentation experiments, feature radial-medium cracking and apparent pile-up which results from plastic flow [24]. In addition, densification is another important mechanism in brittle materials to dissipate the mechanical energy under sharp contact and it has been shown that the addition of atoms with high self-adaptivity (such as Boron) in the glass structure, has increased the crack resistance of oxide glass [24].
This article develops the technique of quasi-static multi-punch shear testing in transparent armor. The primary objective is to propose a straightforward experimental approach aimed at establishing a correlation between multi-hit ballistic tests and QS-PST. This correlation is assessed through parameters such as absorbed energy and observed damage mechanisms. However, the objective of this article is not centered on evaluating the ballistic performance differentials of the TAS. It’s crucial to emphasize that QS-PST does not aim to replicate the dynamic conditions of ballistic tests. This is because strain rates can differ significantly between the two tests, by up to 6 orders of magnitude. Consequently, materials behave differently due to their sensitivity to strain rates. Nevertheless, QS-PST serves to explore potential similarities between the test conditions, particularly in multi-hit scenarios. This is especially relevant when dealing with brittle materials, where each impact may compromise the structural integrity and energy absorption capability of the transparent armor system (TAS). Finally, leveraging the insights gained from QS-PST results, an alternative approach utilizing the K-means clustering algorithm is proposed to predict the likelihood of a specific TAS passing a multi-hit ballistic test.
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Experimental
In this section, we provide details about the materials utilized in manufacturing transparent armor specimens. Although some specific information is confidential, equivalent values are provided for all TAS that are representative and sufficient to explain the results obtained in the research. Additionally, experimental setups and equations relevant to ballistic testing and the QS-PST are presented.
Materials
Transparent armor specimens were fabricated by employing two of the most commonly used brittle materials in the production of such products. These brittle materials were intricately bonded using various transparent adhesives, each characterized by distinct Young’s Modulus values and thicknesses. To mitigate the potential ejection of glass fragments following a ballistic impact, polycarbonate was strategically incorporated as a spall shield material in the backing section of the TAS. The combination of these materials resulted in eight diverse TAS compositions (F1 – F8), as detailed in Table 1. In the table, the symbol (*) denotes a brittle material layer, while (**) signifies the presence of a polycarbonate layer. Additionally, each composition’s Equivalent Elastic Modulus (\({E}_{equiv}\)) provided, calculated in accordance with Eq. 1.
where \({v}_{i}\) is the volume fraction of the layer i, \({E}_{i}\) is the Elastic Modulus of the layer i, and n is the total number of layers of the TAS. The modulus of elasticity of the brittle layers was acquired from the glass supplier, with values of 64 GPa for borosilicate glass and 70 GPa for sodalime glass. The modulus of elasticity for each polymer layer was determined according to the ASTM D638-14 Standard [25].
In addition, the Equivalent Elastic Interlayer Strength (\(\sigma_{equiv}\))values for each composition are also shown in Table 1. This strength is obtained according to Eq. 2 as follows.
where \({v}_{j}\) is the volume fraction of the interlayer j, \({\upsigma }_{j}\) is the Elastic Interlayer Strength of the interlayer j, and m is the total number of interlayers of the TAS. This Elastic Interlayer Strength was measured from stress–strain curves of uni-axial tensile tests as shown in Fig. 1. A cross-head rate of 500 mm/min was utilized, with five specimens per polymer being tested, all of which were conditioned for 24 h at 22 °C. The explicit presentation of stress–strain curves for polymers is omitted in this document owing to its confidential nature. Nevertheless, the Equivalent Elastic Interlayer Strength offers a representative value indicative of the elastic limit pertaining to the combination of interlayers constituting each composition.
Fig. 1
Schematic representation of the Polymer Elastic Strength measurement from the stress–strain curves
Out of the 8 compositions evaluated, F1 was an optimized TAS in terms of its areal density, and it was the only composition that included borosilicate glass, while the others were made using soda-lime glass. In addition, F3, F4, F5, F6, and F7 compositions were designed with a lower thickness than F1 (18.77 mm), while F2 and F8 had the greatest overall thickness. F3, F4, F5, and F7 compositions had the same arrangement of brittle materials (BM). Although all compositions included polycarbonate as a spall shield material, F1 and F6 used two layers of this material while the others incorporated just one layer that was 3 mm thick, excluding the F5 composition, which had a 4.5 mm thick polycarbonate on its backing section. Finally, F3 and F7 compositions have the same arrangement of materials, differing from each other in the polycarbonate, being composition F7 the one which includes a treated polycarbonate.
V50 Multi-hit
In recent times, most ballistic tests have primarily focused on evaluating the performance of armor against single hits. Consequently, the V50 Multi-hit test method was proposed to address the lack of ballistic procedures capable of accurately assessing the multi-hit strength capability of TAS [26]. Existing standards such as NIJ 0108.01, VPAM, EN 1063, and STANAG 4569 typically rely on qualitative outcomes, determining success based solely on whether penetration occurred or not. As a result, tests conducted according to these standards are often classified as either "failure" or "approved." To address this limitation, efforts are being made to quantify the proximity of a TAS to passing a multi-hit test by computing the kinetic energy of multiple impacting bullets [27]. Achieving this goal necessitates the use of high-speed cameras to track the velocity of bullets after perforation through the target.
The ballistic set-up for the present method is shown in Fig. 2. The barrel gun was positioned at a distance of 5 m from the target, following the ballistic standard NIJ-IIIA. To measure the bullet velocity in case of a perforation of the target, a phantom VEO 1310 high-speed camera was used. This velocity is known as the residual velocity. The videos were recorded with 40,000 FPS and with an image resolution of 640 × 480 pixels. In addition, a LED lighting system was used to properly visualize the recordings. In order to measure the bullet strike velocity, a 57 photoelectric screen Oehler was located between the target and the gun barrel.
Fig. 2
a Ballistic set-up used to carry out V50 multi-hit test. b Ballistic configuration and devices used for the test
At least five samples of 500 mm × 500 mm size per configuration were required in this test. In the first sample, all the shots were fired near the maximum velocity defined in the NIJ 0108.01, level IIIA ballistic standard. In order to get approval, this standard states that the armor should withstand five shots at 426 ± 15 m/s without complete penetration following the impact pattern shown in Fig. 3. The ballistic testing procedure employed the up-and-down method [28] for the final impact, aiming to maintain a consistent impact velocity range across the preceding 4 impacts. Given the intention to fire at or near the upper limit of the velocity stated by the standard, intending to make the test more rigorous, the first specimen in this study was impacted with five shots at around 441 m/s ± 5 m/s. If a complete penetration occurred in any of these shots, then the residual velocity needed to be measured by using the high-speed camera. In the case of a penetration occurrence in the last shot, the first four shots of the following sample should be fired again at around 441 m/s, and the last shot should be fired 30 m/s below this velocity, corresponding to a velocity of around 411 m/s. Conversely, if no penetration occurs in the last shot of the first specimen, the initial four shots of the following target will keep their velocity (441 m/s) and the last shot should be fired at 30 m/s above the this velocity, at around 471 m/s. This procedure should continue until getting at least two penetrations and two no penetrations. The 30 m/s step velocity was selected in alignment with the velocity tolerance specifications outlined in the NIJ 0108.01 Level IIIA ballistic standard. While opting for a lower step velocity enhances the precision of the ballistic limit assessment, it also necessitates firing numerous samples of a single composition to gather the requisite penetration and non-penetration data for computing the ballistic limit.
Fig. 3
Schematic representation of the NIJ 0108.01 multi-hit shooting pattern
where \({E}_{k}\) is the kinetic energy of the bullet, \({m}_{p}\) is the projectile mass, \({V}_{S}\) is the strike velocity, and \({V}_{R}\) is the residual velocity.The ballistic energy absorbed by the target is then the sum of these individual kinetic energies, which is computed by using Eq. 4:
Equation 4. Withstand energy by a transparent armor
where \({E}_{ballistic}\) is the total absorbed energy by the TAS, \(i\) is the number of the impact and \({E}_{{k}_{i}}\) is the kinetic energy absorbed by each shot.
Quasi-Static Punching Test
This study’s main aim is to measure each composition’s multi-punch capability and correlate it with the corresponding ballistic performance. For this purpose, QS-PST was performed using a fixture designed for the development of this research. The central components of the QS-PST fixture are shown in Fig. 4. An Universal Testing Machine, Instron 5586, with a load cell capacity from 100 N up to 250 kN, was configured to maintain a cross-head rate of 10 mm/min. A hardened steel cylindrical flat-tip punch was used with a diameter (\({D}_{p}\)) of 10.9 mm. This dimension was selected in accordance with the diameter of the 0.44 MAG SWC ammunition. A square specimen of 200 mm × 200 mm of each composition was mounted over a 12.7 mm thick bottom plate with five holes distributed in the same shooting pattern as the standard NIJ-IIIA. The distance between each hole (L) as well as the spans to punch ratio (\(SPR={D}_{p}/{D}_{s}\)), which is the ratio between the punch diameter and the hole diameter (\({D}_{s}\)), were variated as follows (Fig. 4).
The absorbed energy by the different damage mechanisms during the execution of QS-PST can be calculated using Eq. 5. This calculation was performed employing the Riemann Sums, owing to the difficulties to find a proper function of the load vs displacement curves. Thus, the area under these curves was obtained as the definite integral by using the trapezoid rule over the data recorded during the QS-PST.
Equation 5. Absorbed energy by different mechanisms during QS-PST
where \({E}_{p}\) is the absorbed energy per each punch, \(x\) is the punch displacement, and \(t\) is the specimen thickness. \({PC}_{s}\) is the critical polycarbonate strain, thus the absorbed energy is computed until the polycarbonate exhibits failure. For clarity, the point \(t+{PC}_{s}\) becomes apparent when the last polycarbonate layer is completely penetrated by the punch. This occurrence (\(t+{PC}_{s}\)) is reflected in the force versus displacement curve by a sudden final drop in load, as illustrated schematically in Fig. 5. The total absorbed energy under the QS-PST by each configuration is then computed using Eq. 6.
Fig. 5
Schematic representation of the last polycarbonate failure point
Equation 6. Total punch energy absorbed by a transparent armor.
Where \({E}_{punch}\) is the total absorbed energy under QS-PST and \(i\) is the number each punch.
Results and Discussion
V50 Multi-hit
The total energy absorbed by each of the eight configurations during the ballistics tests is shown in Fig. 6. The error was defined as the median deviation estimated in the energy calculation of the five specimens tested per configuration. F4 was the armor that absorbed the lowest amount of energy with a mean of 6325 Joules, while F2 was the composition that absorbed the highest amount of energy followed by F1 and F8 composition. These latter compositions did not fail the test under the velocities of the standard the NIJ 0108.01, level IIIA, while compositions F3, F4, F5, F6, and F7 presented at least one failure.
Fig. 6
Total energy absorbed by each configuration in the ballistic test
As previously mentioned, the velocities in the standard NIJ-IIIA should be between 411 m/s and 441 m/s, and the mass of the Magnum 44 projectile is around 15.5 g. Thus, the equivalent kinetic energy that a composition must withstand to pass the test for the five impacts variates from 6545 Joules up to 7536 Joules. However, it is important to notice that it is very unlikely and risky to test a composition at the lower velocity of the standard (411 m/s or 6545 Joules). In consequence, a configuration that withstands five shoots at least at the nominal velocity of 426 m/s (7032 Joules) will have a higher chance to pass the test than a composition absorbing lower values of energy. Based on this, configurations F1, F2, and F8 are the ones that might approve the NIJ 0108.01, level IIIA test as was confirmed in this research.
Span to Punch Ratio SPR and Punching Distance L Effect on the Energy Absorption
In order to define the most suitable plate that allows a good agreement with the ballistic energy behavior, the effect of variating the SPR and the distance L (see Fig. 4) was analyzed in F3 and F4 configurations. As can be seen in Fig. 7, the energy absorption distribution per punching varies according to the SPR and the punching distance (L). As this distance increases, the energy absorption of the composition tends to rise. On the other hand, as the SPR increases the energy absorption decreases. Both results could be a consequence of the effect of the damage propagation. When the L distance is quite long, the crack propagation caused by the first punching is not able to affect the region of the following punches. For this reason, in the SPR = 4 and the L = 100 mm data, four of the five perforations showed the lowest energy absorption. On the other hand, when the SPR is wide enough, the laminate composite is able to bend freely. Therefore, as the SPR decreases, the laminate’s resistance increases owing to the plate under the laminate giving support to the specimen. Hence, the laminates absorb less energy when the test is performed using the SPR = 4 than the plate with SPR = 2. In consequence, the plate with SPR = 2 and L = 100 mm obtained the greatest energy absorption during the five perforations.
Fig. 7
Energy absorbed per punching in the composition F3, using a SPR = 2 and L = 60 mm., SPR = 2 and L = 80 mm SPR = 2 and L = 100 mm. SPR = 4 and L = 100 mm
It is important to notice that independently of the L distance and SPR, the first punch energy absorption is higher than the last one (fifth punch). This might be explained by the damage propagation on the surface of each layer of the composite laminate. As seen in Fig. 8(A), the laminate remains intact at the beginning of the test. Then, in the first punch, the specimen is completely penetrated as shown in Fig. 8(B). Some radial cracks propagate around the second, third, and fourth punching areas and some circumferential cracks achieve the center of the sample (fifth punching area). Then, in the second punching (Fig. 8(C)), the fracture zone considerably affects the center zone of the specimen, and an array of radiating cracks reaches a small area around the third punching. The same effect can be observed in the third and fourth punches, in Fig. 8(D) and (E), respectively. After the fourth punch (Fig. 7(F)), the material damage is spread throughout the entire the strike-face surface and high crack bifurcation reaches the center of the sample. This high concentration of cracks undoubtedly diminishes the capability to absorb energy of the armor in the last punch.
Fig. 8
Damage propagation in the transparent armor in QS multi-punching test using SPR = 2 and L = 100 mm. A Moments before first punch B First punch damage C Second punch D Third punch E Fourth punch F Fifth punch
After this analysis, the SPR = 2 and L = 60 mm plate was chosen to carry out the rest of the QS-PST in all eight samples, considering the correlation found between the damage pattern and the ballistic fracture behavior. In addition, the energy absorption capacity loss after each punch that was observed with this plate configuration accounts for the damage evolution of the sample.
Quasi-Static Punch Energy
To evaluate the accumulated energy absorption capacity of each configuration shown in Table 1 under the QS-PST, the support plate of SPR = 2 and L = 60 mm was used. These results are shown in Fig. 9. Most of the configurations withstand about a tenth of the energy absorbed in the ballistic test. F1 was the composition that obtained the highest capacity to absorb energy with 875 J followed by F2 with 633 J. On the other hand, F4 exhibited the least energy absorption capacity, with just 475 J. High energy absorbing capability of composition F1 is attributed to its interlayer strength, the overall thickness, and the mechanical response of the borosilicate glass. In general, compositions including low-strength interlayer polymers exhibit a low energy absorbing capacity during penetration, which is observed in the F4 composition. Even though F2 composition has a low Equivalent Elastic Interlayer Strength value, its energy-absorbing capacity is attributed to the total glass thickness, which is the highest. In addition, polycarbonate plays an important role in the energy-absorbing capacity of the armor, which is demonstrated by comparing F3 and F5 compositions. An increase of 1.5 mm in the polycarbonate thickness in F5 composition results in an increase of 117 J during the five punches, which represents an increase of 23% in the energy absorbing capability under quasi-static conditions. Finally, there is not a significant difference between the means of F7 and F3 composition, which means treated polycarbonate does not affect the energy-absorbing capacity behavior of the structure under a quasi-static regime.
Fig. 9
Total energy absorbed by each composition in the quasi-static punching test
Figure 10 shows the energy absorbing capacity of the eight compositions per each punch. It was expected that during the first punch the compositions exhibit the larger capability to absorb energy because the structures have not accumulated damage. On the other hand, in most compositions, during the fifth punch, the energy absorption capacity of the composition decreases, due to radial and circumferential cracks propagating from former punches and lumping together in the fifth punch zone, giving a high-density crack area. Thus, variations in the energy-absorbing capacity per punch are highly dependent on the crack density of the penetration zone. The inclusion of high-strength interlayers promotes the reduction of crack-spreading areas in brittle materials. This is supported by the fact that the compositions that incorporate at least one high-stiffness polymer interlayer show an increase of the energy absorption capacity in the third punch to the energy obtained during the second punch. Aversely, compositions F2 and F4, which include low strength polymer interlayers, present a major crack density area during first and second punch affecting the performance of the third, fourth and fifth punch.
Fig. 10
Energy absorbed per punch by each composition in the quasi-static punching test
Punch-Load Versus Displacement Curve and Damage Evolution
Figure 11 shows a typical load vs displacement curve obtained during the QS-PST. For most of the configurations, six important peaks appeared at different punch displacements, labeled in Fig. 11 as A, B, C, D and E.
Fig. 11
Load vs displacement curve of F2 composition under quasi-static punch shear
During the initial stages of interaction between the punch and the strike face of the laminated glass (Fig. 12(A)), no visible damage is observed. As the load gradually increases, following a linear trend, it reaches a local maximum at peak A, indicating an elastic behavior region. The Peak A is accompanied by the formation of the first bundled radial cracks near the punching zone, followed by the propagation of coarse radial cracks. This occurs at approximately 1 mm of punch displacement, where a slight drop in load is registered, as illustrated in Fig. 12(B). Subsequently, the load continues to rise until it reaches a global maximum at peak B (Fig. 12(C)), where secondary bundled ring cracks form in proximity to the punching area. Beyond this point, a sharp decline in load occurs due to the fracture of all glass layers. As the punch further penetrates the specimen, fan cracks—radially fractured segments—develop, facilitating the propagation of circumferential secondary cracks originating from the punch zone. These cracks then branch outwards repeatedly, as depicted in Fig. 12(D) and Fig. 12(E) (corresponding to the peaks C to D). Ultimately, the punch exerts strain on the spall shield material until failure at peak E, marked by a sudden drop in load. Following this, the punch fully penetrates the specimen, and a plateau behavior ensues due to frictional sliding. Numerous radial cracks form at this stage, with some branches generating a cone-shaped crack zone characterized by higher bifurcations.
Fig. 12
Damage propagation in a multi-punching test with SPR = 2 and L = 100 mm A First contact between the punching and the strike face B First radial and coarse cracks appears at 2 mm of the punching displacement C Cone cracks start to propagate at other layers. D The number of radial crack increase and the zone of bifurcation increase as well. E The punching had perforated the total thickness of the sample. F Slide frictional zone and identified damage patterns after complete perforation
The internal damage of the samples was assessed in configurations F2 and F3, as depicted in Fig. 13. In peak A, initial cracks manifest, forming a cone-shaped crack zone within the first glass layer, with average angles of 36.1° and 19.5° in compositions F2 and F3, respectively. Subsequently, the cone-shaped crack zone propagates to subsequent layers (peak B). In the case of F2, it extends to the third glass layer with an average angle of 40.3°, while in F3, the angle averages 20.4°. At peak C, the cracks in the cone zone become coarser, with angles increasing to 54.7° and 39.9° in configurations F2 and F3, respectively. Near point D, the polycarbonate begins to bend in configuration F2, while in F3, it exhibits minimal deformation. However, there is not a significant increase in the angles at point D, likely due to the extensive damage caused to the structure by the punch at this location. The punch continues through the laminate with a constant load until reaching point E, where the polycarbonate breaks in F2, whereas in F3, it undergoes plastic deformation before breaking. In the frictional zone, the polycarbonate experiences further deformation, resulting in a widened hole. Furthermore, upon examining the cross-sectional profiles of compositions F2 and F3 in Fig. 13, it becomes evident that the fracture cone angles measured for composition F3, in comparison to those of composition F2, are generally smaller. This difference can be attributed to the reduced extent of damage evolution within the inner layers of the specimen, despite being at the same stage of the force–displacement curve. This phenomenon is likely due to the incorporation of a stiffer interlayer in composition F3. This interlayer enhances the equivalent elastic strength of the composition, resulting in a more localized distribution of shear stresses generated during the QS-PST as the punch gradually penetrates the multilayered structure.
Fig. 13
Comparison of Quasi-static punching test damage modes in the configuration F2 and F3
An attempt to predict the ballistic behavior of the compositions tested without performing dynamic testing becomes relevant because quasi-static tests are less expensive than ballistic or dynamic ones. This allows making a pre-selection of potential formulas, which probably meet the requirements of NIJ 0108.01, level IIIA standard before performing ballistic validation. As stated in section A, compositions F1, F2 and F8 showed the best ballistic energy absorption capacity and passed the ballistics tests under NIJ 0108.01, level IIIA standard, which means, the projectile did not perforate the compositions in none of the five impacts under a velocity range between 411 m/s and 441 m/s.
Even though F1 and F2 were the compositions that absorbed the most energy under QS-PST, which agree with ballistic results, the hypothesis that the energy absorbing capacity under a quasi-static regime can be totally correlated with the energy absorbed during ballistics tests is not completely true. This is because F8 composition absorbed less energy under QS-PST than F6 and F5 compositions. In addition, the total energy absorption capacity of F2 is close to F5 composition and less than F1, which does not correlate well with the absorbed energy during the ballistic test by those structures. This can be explained since the QS-PST does not account for dynamic effects. Although the damage mechanisms observed in both QS-PST and ballistics tests were similar—such as bundled and coarse radial cracks, circumferential glass cracking, fan cracks, radial expansion due to penetration, and polycarbonate bulging—distinct differences emerged during impact tests. Notably, impact tests revealed extremely fine-scale crack branching, along with a heightened extent and severity of damage. Additionally, while QS-PST can induce bending proportionally to the value of the SPR, which primarily triggers the fracture of internal layers within transparent armor [29], its quasi-static nature does not lead to the occurrence of super stress conditions or spalling. High-velocity impacts entail a significant transfer of kinetic energy from the projectile to the target material within a short duration. This rapid energy transfer induces dynamic loading conditions, resulting in elevated stress levels and more extensive material deformation compared to the gradual loading of quasi-static tests. Furthermore, the dynamic loading involved in high-velocity impacts introduces additional effects such as stress waves, shock waves, and inertia forces, which contribute to the primary damage [30]. These dynamic effects exacerbate damage severity by fostering localized stress concentrations, propagating cracks, and inducing fragmentation or spalling within the material. The strain rate sensitivity of materials can also lead to increased brittleness or reduced ductility under high-velocity impact conditions, accelerating crack propagation and potentially resulting in catastrophic failure.
Given the aforementioned considerations, it’s crucial to emphasize that the purpose of conducting QS-PST is not to replicate the phenomena associated with a ballistic event. Rather, its value lies in providing a simplified approach to comprehend certain energy absorption mechanisms during penetration. Through this understanding, it becomes possible to glean insights into the potential ballistic performance of a target. Therefore, it is essential to approach QS-PST as a tool for gaining valuable insights rather than as a direct replication of ballistic scenarios. Hence, relying solely on the total absorbed energy parameter proves inadequate for establishing a meaningful correlation between QS-PST and ballistic behaviors. Nonetheless, an alternative methodology can be devised to discern ballistic performance from the results of QS-PST conducted on transparent armor. In this instance, the implementation of a classification model, specifically the k-means algorithm, proved beneficial.
The k-means clustering algorithm is an iterative method used to partition data into k clusters by considering their distances to the centroids. This algorithm assigns each of the n observations to the nearest centroid, effectively grouping them into k clusters. It is worth noting that the value of k is predetermined before the algorithm begins. In this specific scenario, it is advantageous to predefine two clusters (k = 2): one representing the compositions that may pass the ballistic test, and the other representing compositions that fail the test. The algorithm proceeds as follows:
1.
Determine the number of clusters (k).
2.
Initialization method (K-means + +): One observation is uniformly and randomly selected from the dataset, X. This chosen observation becomes the first centroid (c1). Then, the distances from all observations to c1 are determined by using the Manhattan distance method (Eq. 8). Subsequently, the second centroid (c2) is randomly selected from X, with its selection probability (Eq. 7) being proportional to the distance from itself to the nearest centroid, thus the observation having a maximum distance from the nearest centroid is most likely to be selected next as a centroid (c2) [31].
Equation 7. Selection probability for the second centroid.
The distance between the centroid (cj) and the m observation is denoted as \(d\left({x}_{m},{c}_{j}\right)\). This distance is calculated by using the Sum of absolute differences; thus, each centroid is the component-wise median of the points in that cluster.
Compute the distances from each observation to every centroid and assign each observation to its nearest centroid.
4.
Determine the mean of the observations within each cluster to acquire k new centroid positions.
5.
Iterate steps 3 and 4 until there are no further changes in cluster assignments, or until the maximum number of iterations is reached.
To establish the parameters resulting from the QS-PST that will serve as inputs to the k-means algorithm, it was assumed that the energy absorbed by the compositions during the 5 punches (\({E}_{punch}\)) could be an indicator of the accumulated structural degradation behavior of the transparent armor due to multiple perforations, as a result of severe crack propagation in brittle materials. This could potentially serve as a crucial guide of the multi-hit behavior of these transparent armors, thus it was selected as one of the parameters for the k-means algorithm. Additionally, as shown in Fig. 14, compositions F1, F2, and F8 exhibited a higher maximum load required to generate perforation during the first punch. This may be attributed to their ability to erode the lead projectile, specifically the Magnum 0.44 SWC, which loses its penetration power when highly deformed. As a result, the maximum load during the initial punch, where the transparent armor has not yet accumulated damage from previous perforations, was chosen as the second parameter for implementing the classification model.
As can be observed in Fig. 14, all compositions that fail the ballistic test are grouped in cluster 2, while F2, F8 and F1 which pass the ballistic test are grouped in cluster 1. Thus, combining both parameters and using the k-means hard clustering algorithm could be a functional technique to predict if a certain composition could pass a ballistic test under NIJ 0108.01, level IIIA standard without performing dynamic testing.
Conclusion
The predictive capabilities of transparent armor systems’ ballistic performance were explored through quasi-static multi punch shear testing. Eight different configurations were designed to comprehensively evaluate their behaviour across both tests. Implementation of a V50 multi-hit test provided crucial insights into the ballistic performance of the compositions. Meanwhile, the QS-PST, facilitated by a custom-made fixture, enabled thorough analysis of progressive damage modes. The results from the V50 multi-hit test underscored the method’s efficacy in accurately measuring absorbed energy during multi-hit scenarios, offering valuable insights particularly in contexts where trial-and-error methods prove time and cost-intensive. Furthermore, although QS-PST evidently does not replicate the phenomena associated with a ballistic event, its value lies in providing a simplified approach to comprehend certain energy absorption mechanisms during penetration. Hence, the QS-PST emerges as a viable option for conducting preliminary evaluations of TAS capabilities, offering nuanced insights into some of the progressive damage mechanisms inherent in the penetration process of transparent armor. This knowledge can inform targeted modifications or enhancements to specific sections of armor design. Notably, the test results highlight the pivotal roles of polycarbonate and polymer interlayer strength in the armor’s energy-absorbing capacity. Leveraging the k-means hard clustering algorithm, incorporating data such as the first punch peak load and total absorbed energy, presents a practical technique for predicting the likelihood of a given composition passing a ballistic test under the NIJ 0108.01 Level IIIA standard, obviating the need for dynamic testing.
Declarations
Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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