Reverse ballistics penetration of Kevlar® fabric with different indenters at different loading rates

Abstract

In this study, the mechanical load on a bullet-shaped indenter when impacted by a single-ply Kevlar fabric was experimentally investigated using a reverse ballistics method at both quasi-static and dynamic rates. Different indenter geometries, namely the 9-mm Luger, .223 Remington, and .308 Winchester bullet geometries, were used. The penetration load of the stationary indenter was measured using a force transducer located behind the indenter, and the penetration load was then plotted against the impact velocity of the fabric sample. Different mechanisms of penetration were observed at different impact velocities. Penetration mechanisms were also found to be highly dependent on projectile nose geometry. A modified method to obtain an approximate ballistic limit based on the impact loads was used to compare the efficacy of different geometry types.

Keywords

reverse ballistics quasi-static dynamic single-ply geometry indenter

The capability of a bullet-resistant ballistic fabric in stopping a projectile (typically measured using the V50 ballistic limit) during impact is dependent on several mechanisms, such as fiber and fabric mechanical properties (e.g. density and tensile modulus), fabric weave structure, far-field boundary conditions, and projectile geometry. The energy-absorption mechanism of the fabric is dependent on the projectile striking velocity. Below the ballistic limit, there is limited to no penetration, implying that the striking velocities below that limit have zero residual velocity. Past the ballistic limit, the residual velocity is typically observed to increase rapidly for a small range of velocities before increasing relatively linearly with respect to the striking velocity at high velocities.¹ The change in residual velocity behavior across the whole range of velocities indicates a possible change in failure modes and energy-absorption mechanisms. In particular, previous studies have shown that at high velocities, the only dominant energy-dissipation mechanism is via tensile loading of the yarn.^2,3 Previous studies by Cunniff^3,4 and Hudspeth et al.⁵ have shown that the effect of aperture size is negligible above the V50 limit, indicating that the damage done at high-impact velocities tends to be localized. On the other hand, at velocities below the V50 limit, mechanisms such as inter-yarn friction, yarn–projectile friction, etc., tend to play a part in dissipating energy as well, and these mechanisms involve a much larger zone of impact. The projectile geometry, in any case, accounts for differences in fabric ballistic performance,⁵ which is the reason destructive testing of bullet-resistant vests is dependent on bullet type and threat level.

The typical energy-absorption curve is characteristically µ-shaped, that is, the energy-absorption increases with striking velocity up to the V50 limit before decreasing for a range of velocities. Past the V50, the kinetic energy absorbed by the fabric system is calculated by subtracting the residual kinetic energy from the striking kinetic energy; thus, the energy absorption is dependent on the square of the striking velocity. A previous study by Cunniff³ indicated a possible increase in energy absorption again at extremely high striking velocities. Of interest in this study is the regime where the energy absorption decreases (when the striking velocity exceeds the V50) due to a change in absorption mechanism, and this regime is not well-studied. Insight into this regime would allow for more accurate modeling in future studies.

While normal ballistics allows us to measure the ballistic capabilities of the target fabric, the mechanics of the penetration process cannot be accurately examined. Reverse ballistics (in which the typical target is launched at the projectile) provides us with more insight into the effects of the stopping power of the single-ply fabric on the projectile. Reverse ballistics experiments also have the advantage of removing the effects of inertia, which are inherent in normal ballistics experiments when measuring the load on the projectile.

The aim of this study is to examine the resistive load on a projectile when penetrating a single layer of high-performance fabric, as well as investigating the effects of projectile nose geometry pertaining to the V50 ballistic limit by measuring the resistive load acting on the different geometries. Hockauf et al.⁶ used a novel reverse Hopkinson bar to measure and characterize the loading profile on different indenter geometries when impacted by multiple layers of fabric. However, such a method may not be practical or feasible for a single layer of fabric, or for a wide range of velocities. Previous studies by Montgomery et al.⁷ and Lim et al.⁸ have also examined the effects of perforating a single-ply fabric using different projectile geometries, but the analyses were still largely fabric system-oriented rather than projectile-oriented.

Experimental procedure

The Kevlar® fabric samples were prepared from a Point Blank Pathfinder Special bulletproof vest manufactured in 2008 by Point Blank Body Armor. The fabric within the vest layers were 600 d Kevlar® (the specific fiber type was not provided by the manufacturer), with an areal density of 175 g/m², weave density of 12.00 × 13.50 ends/picks per cm, and a fiber failure strain of 4.42 ± 0.26%.

In order to launch the fabric sample, the fabric was fixed on a polyurethane foam sabot using a 1/8″ (3.2 mm) polyvinyl chloride (PVC) foam fixture ring, using epoxy to attach the fabric to the sabot at eight points around the circumference of the recess. Care was taken to ensure that the principal yarns themselves were not attached to the foam; only the corners located 45° from the principal directions were attached. The fabric sample and sabot are shown in Figure 1.

Figure 1.

Kevlar® fabric fixed on polyurethane foam sabot using a polyvinyl chloride foam ring (a) and a 1.25-inch (32 mm) deep recess in the sabot (b).

The fabric window measures 1.6 × 1.6 square inches (41 × 41 mm²), with a slight chamfer on the corners where the fabric is secured to the PVC ring and sabot. These dimensions were chosen to ensure maximum exposure area of the fabric within the gas gun bore without compromising the secure attachment of the ring–sabot interface with the fabric or the radial strength of the sabot. A larger window size is also desired to minimize the effects of the boundary on the load signal, especially at low striking velocities.

The indenters used in this experiment were 9-mm Luger, .223 Remington, and .308 Winchester snap caps manufactured by A-Zoom. These geometries were chosen because they represent a variety of shape profiles and presented areas, and are typically used in calibration and certification of bullet-resistant vests. These snap caps are made of hard anodized aluminum. The resultant impact force was recorded by a Kistler 5000 lb-f (22,246 N) force transducer located behind the indenter. Table 1 gives the dimensions of the bullet-shaped indenters.

Table 1.

Bullet geometries used in the experiment

	9-mm Luger	.223 Remington	.308 Winchester
Profile	Elliptical	Ogival	Ogival
Diameter (mm)	9.01	5.70	7.85
Length (mm)	10.54	12.70	19.94

The quasi-static experiments were performed using an MTS 810 servo-hydraulic system, as shown in Figure 2, with the crosshead speed varied between 1, 10, and 100 mm/s for one full loading–unloading cycle. An Interface 200 lb-f (890 N) force transducer located behind the indenter was used to measure the indentation load.

Figure 2.

Quasi-static setup of the reverse ballistics indentation experiment.

The dynamic experiments were performed using a high-pressure smooth-bore gas gun, with an inner bore of 2.5 inches (63.5 mm). A recess within the sabot was molded to ensure that the indenter only penetrates the fabric, which was not backed up by the polyurethane foam. A 2-inch (51-mm) thick ballistic shield was placed in front of the indenter, with the indenter tip protruding from a ¾″ through-hole, as in Figure 3. This ballistic shield serves as a barrier to protect the force transducer from impact damage, as well as ensure that any damage to the fabric only comes from the snap cap bullet tip and not the entire round. The corresponding striking velocities were measured using two pairs of laser diodes and sensors.

Figure 3.

Ballistic shield with indenter protruding from the through-hole.

In order to reduce the effects of the fabric sample’s kinetic energy due to different masses in the dynamic experiment, the projectiles were molded and machined to have an average mass of 87.7 ± 3.6 g. These were fired at velocities ranging from 29.5 to 245 m/s. A total of 45 samples were tested in the quasi-static experiments, with five samples tested per loading rate per indenter. A total of 36 samples were tested in the dynamic experiments.

Results and discussion

Quasi-static experiments

At low velocities below the ballistic limit, the projectile does not penetrate the single-ply Kevlar® fabric. This implies that the main mechanism dissipating the kinetic energy, apart from yarn strain, is the pulling out of the principal yarns when impacted by the indenter. This yarn pull-out mechanism during quasi-static penetration of the indenter can be observed in Figure 4. Each curve represents the combined average load–displacement curve for five samples.

Figure 4.

Averaged load signal for all indenters at 1 mm/s indentation rate.

The 9-mm indenter is observed to have the highest resistive load from the fabric during penetration, followed by the .308 and .223 indenters. For all three indenters, there is a slight oscillatory phenomenon occurring throughout the indentation process due to stick-slip when the yarns are uncrimping and translating. This phenomenon is reflected in Figure 5, which shows distinct yarn pull-out and uncrimping features along both the perpendicular warp and weft directions of the impact site.

Figure 5.

Yarn pull-out effects along both warp and weft (principal) directions in fabric impacted by the .223 Remington indenter at 1 mm/s.

As the indenter begins to push on the fabric during the indentation process, the initial portion is dominated by the uncrimping of the principal yarn. As the indenter moves further in, more yarns in the principal directions of the impact site begin to uncrimp. The number of yarns uncrimping and the rate at which they uncrimp are dependent on the geometry of the indenter. Figure 6 illustrates how these geometrical differences result in their unique load histories, and a brief explanation of this mechanism is proposed. In the case of the 9-mm indenter, it has a larger radius of curvature at the nose-tip, which implies that the yarns are uncrimping and translating at a similar rate relative to each other. This results in a large peak near the end of the indentation loading cycle as all the yarns begin to translate at approximately the same time after being fully uncrimped, and this drop in yarn pull-out load signifies the start of the yarn-translating stage.⁹ On the other hand, the sharper ogival indenters, while experiencing the same mechanism of yarn uncrimping/translating, cause the yarns nearer to the tip of the indenter to start translating, while the remaining yarns in the impact zone are still being uncrimped with more of a “puncturing” type of movement. Instead of having the yarns uncrimp and translate at relatively the same time, the yarns take turns uncrimping (during which the pull-out load increases) and translating (during which the pull-out load decreases). A more drastic comparison would be between a flat-nosed projectile (infinite radius of curvature) compared to an extremely sharp cone (extremely small radius of curvature) and the projectile geometry effects are immediately seen.

Figure 6.

Yarn pull-out mechanism for a 9-mm Luger indenter with a larger radius of curvature (a) compared to a sharper .223 Remington indenter (b).

Due to the different calibers and sharpnesses of the indenters, we propose to normalize the load signals by their respective presented areas A_p and normalized radii of curvature ρ_N, with some reference to Montgomery et al.’s⁷ previous work investigating the effect of nose geometry. The normalized radius of curvature of the indenters is defined by

ρ_{N} = \frac{R^{2} / R^{2} L L}{2 R} = \frac{R}{2 L}

(1)

where R is the indenter bullet radius and L is the bullet length of the indenter. These calculated values are given in Table 2. By scaling and normalizing these geometries with respect to A_p and ρ_N, the indenter profiles are mathematically manipulated into one general shape (Figure 7). These two parameters are especially effective, since the indenter geometries can be accurately approximated with an elliptical curve. The post-normalization quasi-static indentation load for the data in Figure 4 is then reduced to that in Figure 8.

Figure 7.

Diagram of original indenter geometries (a), geometries after scaling with respect to radius (b), and after normalizing with respect to A_p and ρ_N (c).

Figure 8.

Post-normalization averaged load signal for all indenters at 1 mm/s.

Table 2.

Calculated geometric parameters

	9-mm Luger	.223 Remington	.308 Winchester
A_p (mm²)	63.8	25.5	48.4
Radius of curvature (mm)	1.93	0.640	0.772
ρ_N	0.214	0.112	0.098

The quasi-static load histories at higher indentation velocities (10 and 100 mm/s) were observed to display similar trends (Figure 9), with the 9-mm indenter having the highest peak pre-normalization loads and the .223 having the lowest. These peak load values were then plotted against the loading rate as a comparison of the rate effects, demonstrating the efficacy of normalizing the load signal with respect to A_p and ρ_N.

Figure 9.

Peak indentation load versus loading rate pre-normalization (a) and post-normalization (b) with respect to the presented area and normalized radius of curvature.

Within the range of quasi-static velocities tested, no significant rate effects were found, a trend reflected by a single out-of-plane yarn pull-out from the same fabric.^9,10 Normalized peak load data is shown to have a significant reduction in scatter compared to pre-normalization of the data, as shown in Figure 9.

Dynamic experiments

Post-mortem qualitative analysis of the impacted fabric samples shows four main regimes of deformation mechanisms as follows.

No penetration. At low velocities, samples only show slight dents and transverse deformation without penetration.

Yarn pull-out. Samples showing yarn pull-out effects demonstrate further transverse deformation, yarn uncrimping, and yarn translation, but without complete indenter penetration. The uncrimping and translation are visible along the principal yarn directions.

Nose-through. The fabric samples were shown to have been penetrated completely by the indenter tip; however, the yarns appear to have just moved aside by the projectile “nosing through” the fabric without fracture.

Yarn rupture. At high velocities, the yarns rupture at the impact site, and this is accompanied by nosing-through of the indenter (within the velocities tested) without significant yarn pull-out.

These four regimes are shown in Figures 10 –12. Note that these regimes are just a spectrum for qualitative analysis and there are overlaps in the mechanism. In particular, any nosing through of the projectile through the fabric is typically accompanied with a certain degree of yarn pull-out, since the yarns have to be translated slightly from their original position. A typical dynamic experiment impact load signal obtained from these experiments is shown in Figure 13.

Figure 10.

Four different regimes of impact for the 9-mm Luger indenter: (a) no penetration; (b) yarn pull-out; (c) projectile nose-through; (d) yarn rupture.

Figure 11.

Four different regimes of impact for the .223 Remington indenter: (a) no penetration; (b) yarn pull-out; (c) projectile nose-through; (d) yarn rupture.

Figure 12.

Three different regimes of impact for the .308 Winchester indenter: (a) no penetration; (b) yarn pull-out; (c) projectile nose-through. Yarn rupture was not observed within the samples obtained.

Figure 13.

Impact load signal of dynamic reverse ballistics test with respect to time.

The dynamic load signal is typically within the order of 1 ms (providing ample time for numerous longitudinal wave reverberations), thus negating the need for longitudinal wave analysis. With the calculated striking velocity and the known distance between the laser diode and the indenter tip, the impact load can be verified as the first signal peak by calculating the time delay between the velocity trigger and the load signal data. Subsequent peaks are due to further crushing of the sabot and failure of the epoxy, as well as any residual air pressure behind the projectile. Further discussion of impact loads is assumed to be about this initial peak, unless stated otherwise. The impact loads were then plotted against the striking velocity for each indenter geometry, differentiating between the deformation mechanism regimes. These plots are shown in Figures 14(a)–(c).

Figure 14.

(a) Plot of impact load versus striking velocity categorized by the deformation mechanism regime for the 9-mm Luger indenter. (b) Plot of impact load versus striking velocity categorized by deformation mechanism regime for the .223 Remington indenter. (c) Plot of impact load versus striking velocity categorized by deformation mechanism regime for the .308 Winchester indenter.

Post-shot analysis of the indenter tips showed no visible deformation; thus, the energy absorbed during impact due to tip deformation can be neglected. It can be observed from the impact load versus striking velocity plots that at lower velocities, the main mechanism resisting bullet penetration is the pulling out of yarns in the principal directions. In this low-velocity regime, the impact load increases due to yarn uncrimping and pull-out, and increases with striking velocity. As the striking velocity increases further, the deformation mechanism begins to shift towards the projectile nosing through the fabric or even yarn rupture. At these velocities, there appears to be minimal yarn pull-out and the resistive impact load is observed to begin leveling out or even decreasing with respect to striking velocity. Due to its rounded geometry, the resistive load for the 9-mm indenter appears more scattered near the critical velocity, where any nosing-through of the projectile is also accompanied with more yarn pull-out compared to the ogive geometries of the .223 and .308 indenters.

From previous extensive studies by Cunniff,^1,2,4 the ballistic limit is largely dependent on the areal density ratio of the armor system to the projectile in a forward ballistics setting. However, in a reverse ballistics frame of reference, the “projectile” is the indenter, and since the indenter is stationary in this study, the indenter mass in this case does not serve any practical meaning. Moreover, the residual velocity of the indenter or the fabric cannot be obtained practically in order to determine the fabric ballistic limit value. A modified method to quantitatively estimate the efficacy of the indenter geometry in penetrating the fabric system is therefore proposed.

In a typical normal ballistics experiment, the residual velocity is observed to increase sharply at the ballistic limit, indicating a sudden drop in resistive load acting on the projectile by the fabric. Similarly, from the impact load versus striking velocity curves, the load decreases sharply. However, there is no certain way of knowing where exactly the load would decrease. Compare Figure 14(b), where the load decrement is observed after the peak yarn pull-out load, to Figure 14(c), where the decrement is observed before the peak pull-out load. This suggests that there is a crossover zone in which either mechanism could be in place. Near this zone of uncertainty, the projectile is either held back by the yarns pulling out, or it manages to nose through the fabric. There is a large peak load value due to the yarn pull-out mechanism (without full indenter penetration), as well as a local impact load minimum due to the indenter nosing through the fabric. This may explain the fact that in a normal forward ballistics test, the V50 is the point where, statistically, the projectile has a 50% chance of penetration.

Two linear fits were therefore performed on both the non-penetration (No penetration and Yarn pull-out) and the penetration regimes (Nose-through and Yarn rupture) to obtain an estimate of the ballistic limit. From here on, this estimated ballistic limit lower-bound value will be termed the rV_crit so as not to confuse the term with the proper technical definition. Due to the crossover zone near the ballistic limit, when the projectile only has a finite probability of penetrating the fabric, penetration from the projectile nosing through causes the local load minimum, and therefore these significantly outlying points were excluded in order to obtain a proper R² value for the linear fits. The rV_crit values for the 9-mm Luger, .223 Remington, and .308 Winchester are 118.3, 86.8, and 105.8 m/s, respectively.

Comparison between different mechanisms

The load histories during the impact process were examined. The impact time was determined as in Figure 13, while the time of complete penetration is estimated using the indenter nose length and the measured velocity. As the load histories for different indenters at different mechanisms look relatively similar, only the 9-mm Luger load histories are presented here for brevity. These plots are given in Figure 15 and are time-adjusted. The No penetration phase is essentially just the yarn pull-out mechanism at low velocities and therefore is not included.

Figure 15.

Load histories for the 9-mm Luger indenter arranged by increasing velocity for different mechanisms: (a) and (b) yarn pull-out; (c) and (d) nose-through; (e) and (f) yarn rupture.

For the yarn pull-out mechanism, the load histories display two distinct peaks, similar to the quasi-static load histories in Figures 4 and 8. The first peak value appears to increase with an increase in striking velocity. As the velocity increases further past the rV_crit, the projectile begins to nose through the fabric, at which point the load history appears to smooth out over the impact duration. Increasing striking velocity results in a distinct single peak when the yarns rupture at the impact site. Similar to the reverse ballistics study by Hockauf et al.,⁶ an analysis of the impact energy was subsequently performed by integrating the area under the load–displacement curve, with the indenter displacement approximated using the striking velocity and the impact time. Figure 16 shows the integrated load–displacement energy curves.

Figure 16.

Energy versus striking velocity for all indenter geometries.

Figure 17.

Plot of rV_crit against A_pρ_N.

The general trend of the impact energy appears to increase with striking velocity up to the rV_crit, after which the integrated load–displacement energy decreases as the striking velocity increases further. This curve is similar to the energy-absorption curve obtained from the residual velocities,³ as well as in comparison with the calculated missile kinetic energy loss versus striking velocity as explicitly investigated by Wilde¹¹ and Termonia.¹² The energies for the 9-mm Luger appear to be more scattered near the rV_crit because of the larger projectile presented area and radius of curvature resulting in a larger range of velocities where both yarn pull-out and nosing-through might occur. The ogival indenter energies are considerably much sharper at the peak near the rV_crit.

Comparison between different indenter geometries

In a forward ballistics scenario, the V50 limit is dependent on the areal density ratio of the fabric to the projectile, given by Cunniff³ as A_dA_p/m_p, where A_d is the areal density of the armor system, A_p is the projectile presented area, and m_p is the projectile mass. In general, it appears that the change in V50 is relatively linear within a small areal density ratio range. However, there is a need to modify the equations with certain assumptions based on the differences in reverse ballistics experiments.

It can be assumed that within a small areal density range, the V50 varies linearly as a function of the areal density of the projectile.¹ The areal density of the fabric system is not necessary in this study, as the same fabric is being used and therefore reduces to a constant. Furthermore, in order to compare the effects of indenter geometry and not the striking kinetic energy, we require the mass to be the same in all cases; therefore, the rV_crit is proportional to the presented area (in this reverse ballistics case, of the indenter).

With a blunter nose profile, the radius of curvature is larger and the rV_crit is expected to be higher, implying that the rV_crit is somewhat proportional to ρ_N. Since the rV_crit is proportional to both A_p and ρ_N, the rV_crit value is plotted against the parameter A_pρ_N as in Figure 17. This parameter is also used in normalizing the quasi-static peak load values.

While the data appears to vary relatively linearly with respect to A_pρ_N, there are still insufficient data points for a conclusive fit. Further studies would provide further insight into the effects of the parameter A_pρ_N on the predicted rV_crit values.

Conclusions

A reverse ballistics method of investigating the effects of geometry on the penetration of a single-ply bullet-resistant fabric was developed, with the bullet as the indenter and the fabric as the projectile. At quasi-static loading rates of 1, 10, and 100 mm/s, yarn pull-out was the dominant mechanism in resisting the indenter. Load histories exhibit characteristics of yarn pull-out behavior that appear to be geometry-dependent. Normalization of the peak indentation loads with respect to the parameter A_pρ_N as in Figure 17 showed significant reduction in scatter across indenter geometries and all loading rates.

Dynamic impact experiments of the indenters were performed with a smooth bore gas gun. Over the whole range of striking velocities, different mechanisms of indentation and penetration were experienced by the fabric, as evidenced by post-mortem analysis of the impacted fabric samples. At low velocities, yarn pull-out was the dominant mechanism in the resultant resistive force acting against the indenter; at high velocities, projectiles either nosed through the fabric or the yarns were ruptured.

Impact loads were shown to level off or decrease past a certain critical velocity, which coincides with the change in mechanism of penetration from yarn pull-out and no penetration to the projectile nosing through. The restrictions of the reverse ballistics method necessitated a modification to the usual method of determining the V50 ballistic limit of a system by taking advantage of the distinct drop in energy absorbed by the fabric over the range of striking velocities to assume a change in gradient of the impact load versus striking velocity plot. Linear regressions for both regimes were performed to estimate a lower-bound of the V50, named in this study as the rV_crit. Near this value, either the yarn pull-out mechanism dominates in preventing the indenter from penetrating, or the indenter manages to nose through the fabric, resulting in a drop in impact load. In a forward ballistics sense, this explains the statistical significance of the V50, where 50% of projectiles fired would penetrate the system.

Normalization of the rV_crit with respect to the parameter A_pρ_N again showed a good linear fit, suggesting one possible quantitative factor in determining the rV_crit (and, indirectly, the ballistic limit for normal ballistics) is the sharpness. Further studies are recommended to investigate this phenomenon more deeply.

Footnotes

Acknowledgements

The authors would like to thank the U.S. Army, P.M. Soldier Protection and Individual Equipment, Technical Management Directorate for their support . The authors would also like to thank Niranjan Parab and Stephenie Martinez of Purdue University for their help and contribution with the equipment and sample preparation.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

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