Ballistic performance of p -aramid fabrics impregnated with shear thickening fluid;Part II

Abstract

The objective of this research was to characterize the ballistic performance of p-aramid fabrics impregnated with shear thickening fluid (STF) focusing on the fabric count and shot location. Panels made of fabrics with different fabric counts were tested against 9 mm bullets at 436 m/s for body armor application. Panels with higher fabric count dissipated a higher fraction of the given impact energy through tensile dissipation and this led to a lower backface signature. The decrease in backface signature value by the hybridization of neat and STF impregnated fabrics was smaller for panels of densely woven fabric due to the larger difference in the warp and weft crimp ratios. Shot location affected the ballistic limit value (V₅₀), as well as the BFS value of the panels, where both values increased as the shot location approached the edge. The energy transferred to the backing material upon an impact was calculated based on the weight dropping test results, where the dent volume was proportional to the impact velocity.

Keywords

shear thickening fluid fabric count crimp shot location ballistic limit backface signature kinetic dissipation

Introduction

Shear thickening fluid (STF) is a fluid which behaves like a solid when it encounters mechanical stress or shear. Thus, STF behaves like a liquid until an object strikes or agitates it forcefully. Due to its shear thickening characteristic, STF has special industrial uses such as traction control and is also studied for applications as flexiblebody armor. To gain a better understanding of the shear thickening phenomenon, many researchers have conducted studies on the rheological behavior of dilatant fluid,^1–4 mechanisms of shear thickening,^5,6 important parameters related to the phenomenon,^7,8 and methods to show the phase transition.^9,10 Some have attempted to model the shear thickening phenomenon.¹¹

Lee et al.¹² conducted a study to improve the ballistic property of Kevlar woven fabric by applying STF to the fabric. The STF treated Kevlar was expected to remain flexible at normal conditions and instantly harden upon impact. They used a panel size of 5 cm × 5 cm for the ballistic tests and reported that the ballistic performanceof Kevlar woven fabric improved with STF application.

Ballistic performances such as the ballistic limit (V₅₀) or the backface signature (BFS) of a fabric panel greatly depend on the size of the soft body armor panel. We have prepared larger panels that are closer in size to actual body armor, 38 cm × 38 cm, for this study. The objective of our study was to characterize the ballistic performance of p-aramid fabrics impregnated with STF. From a preliminary study, we have found that the V₅₀ value of STF impregnated fabric panels using a 5.56 mm fragment simulating projectile (FSP) slightly decreased with the increase of STF add-on, especially when it came to a practical protection level (>300 m/s). This phenomenon can be attributed to the infrangibility of the FSP and increased stress localization upon impact due to the increased friction by STF impregnation.

Thus, in part I and part II of this study, we characterized the ballistic performance of p-aramid fabrics impregnated with STF against a frangible and more widely used bullet, 9 mm FMJ RN, especially focusing on the laminating sequence in hybrid panel, the effect of fabric count and the evaluation of practical performance at set shot locations.

In part I, we have investigated the effect of STF impregnation and the laminating sequence of STF impregnated fabrics in hybrid panels on the ballistic performance of Kevlar panels. When STF impregnated fabrics were laminated behind neat Kevlar layers (N/S-panel), smaller BFS was observed compared to the all neat panel (N-panel) and the hybrid panel where STF impregnated layers were placed in front of neat Kevlar layers (S/N-panel). STF increased the frictional force acting on each crossover point within the Kevlar fabric, thus, reducing the elongation of the yarns facing the bullet. The superior ballistic performance of the N/S-panel was assumed to be due to the higher synchronization of the elongation of the facing yarns in the frontal layers and those in the rear layers upon impact. The experimental results in part I were analyzed focusing mainly on the tensile dissipation of each panel.

In part II, we investigate the effect of fabric count (i.e. weave density), and crimp ratio on the ballistic performance of N/S-panels. The effect of shot-to-edge distance, (i.e. shot location) on the ballistic limit and BFS of the panels was also investigated. Finally, a method to estimate the kinetic dissipation in a ballistic event is described and the calculation results are presented.

Experiments

Materials

The STF was composed of silica particles and polyethylene glycol medium. The silica sol used in this study was composed of 30 wt% SiO₂ and 70 wt% methanol, and the silica particles had a nominal average diameter of 45 nm. Polyethylene glycol (MW 200) was selected as a dispersant, and methanol was used in the sol as a diluent to facilitate the impregnation of STF into the Kevlar fabrics.

The fabrics used were plain woven Kevlar KM-2 600 denier 1027 style and 1025 style (Barrday Inc.). The specifications of the Kevlar KM-2 600 denier yarn and the two types of fabrics are given in Table 1. Using a CO₂ laser cutter, the fabrics were cut into 38 cm × 38 cm square specimens.

Table 1.

The nominal specifications of KM-2 Kevlar yarn and the fabrics used

Yarn	Tenacity (N/tex)	2.47
	Breaking strength (N)	165
	Elongation at break (%)	3.8
	Modulus (N/tex)	55.6
	Moisture regain (%)	7.0
Fabric	Yarn count (tex)	66.7
	Fabric count (yarns/cm, warp × weft)	11.0 × 11.0 (1027 style); 13.4 × 13.4 (1025 style)
	Areal density (g/m²), dry	149 (1027 style); 181 (1025 style)
	Thickness (mm)	0.20 (1027 style); 0.25 (1025 style)
	Fabric system	plain weave

STF preparation and impregnation

STF with 68 wt% silica was prepared. Neat Kevlar fabrics were immersed into a diluted STF dispersion (silica:PEG:methanol, 30:14.118:70 wt:wt:wt), squeezed with a pressure of 10 kg/cm² for 10 seconds and dried at 65°C. The STF add-on was controlled to 20% owf.

Single yarn tensile test

The tensile behavior of a single yarn in each fabric was investigated using Instron 5543. The neat Kevlar fabrics and the STF impregnated Kevlar fabrics (68 wt% silica content, 20% owf) of 1027 style and 1025 style were cut into 50 mm × 220 mm-sized samples. A single warp or weft yarn with a gauge length of 100 mm was elongated at the rate of 1000 mm/min, with a primary load of 0.5% (0.75 N/yarn) of its tenacity (refer to part I).

Ballistic impact test

Each target panel (38 cm × 38 cm) was mounted on a backing material fixture that was filled with conditioned oil-based clay of 13 cm thickness and backed with removable plywood. To validate the BFS test result, both pre- and post-drop tests were conducted on the conditioned clay with a 1.043 kg steel sphere at the height of 2 m (NIJ Standard-0101.04). Just after the drop test, each target panel was held in contact with the backing material and secured to the backing material fixture using mounting straps. The impactor was a 9 mm bullet (FMJ RN, 8.0 g) described in NIJ Standard-0101.04, and the target measured velocity for BFS measurement was around 436 m/s (threat level III-A).

To investigate the effect of fabric count on V₅₀, target panels of 24 and 26 plies of 1025 style neat fabric (areal density of 4.37 and 4.71 kg/m², respectively) were tested and the results were compared to those of target panels of 27 and 30 plies of 1027 style neat fabric (4.02 and 4.47 kg/m², respectively). In the case of the 26 ply-1025 style fabric panels, two sets of panels were prepared, where one was cross-diagonally stitched through all layers at a 7.62 cm (3 inch) interval using a high tenacity nylon/cotton spun blend yarn, and the other was not. The measurement of V₅₀ was conducted as described in NIJ Standard-0101.06. To investigate the effect of fabric count on BFS value, target panels of 26 ply N- and 24 ply N/S(12 ply/12 ply)-1025 style fabric (4.71 and 4.78 kg/m², respectively) were compared to those of 32 ply N- and 29 ply N/S(14 ply/15 ply)-1027 style fabric (both 4.78 kg/m²). The shot location for these tests was at least 8 cm apart from the edges as shown in Figure 1 (left).

Figure 1.

Shot locations in the ballistic tests to investigate the effects of fabric count (left) and shot-to-edge distance (right) on V₅₀ and BFS.

To study the effect of shot location on BFS and V₅₀, the shot location for BFS measurement was between 51 and 70 cm from the edge of the panel and that for V₅₀ measurement was the center of the panel or 11 cm from the edge as shown in Figure 1 (right). For this test, two sets of each type of panel were prepared with 1025 style fabric, one stitched and the other unstitched. The 26 ply N-panel (4.71 kg/m²) was cross-diagonally stitched at a7.62 cm interval through all layers, while only the neat Kevlar layers were stitched likewise for the 24 ply N/S(14 ply/10 ply)-panel (4.77 kg/m²). The multilayers of the panels were interconnected at the four corners for the ballistic impact test.

Results and discussion

Effect of fabric count on the tensile behavior of a single yarn in Kevlar fabrics

Figure 2 shows the single yarn tensile test results of 1025, 1027 style neat fabrics and STF impregnated fabrics in the warp and the weft directions. As indicated by the wider plateau at the early stage of elongation, the warps had a higher crimp ratio than the wefts in all fabrics, and the difference in crimp ratios of warp and weft was much larger for 1025 style fabrics. Generally, the crimp ratio of warp increases with the increase of weave density, while that of weft is less affected. The difference in the warp and the weft crimp ratios of as received 1027 and 1025 style fabrics was 0.3% and 2.5–3.0%, respectively. The most notable phenomenon shown in the figure was the suppression of the crimp effect by STF (i.e. less retardation of the increase in load with elongation by STF treatment), especially in the warp of 1025 style fabric. This is due to the increased frictional force due to the increased number of crossovers and undulation of yarns with higher crimp ratio. Although the decrease in the difference between warp and weft crimp ratios due to STF treatment was higher for 1025 style fabric, the absolute value of difference between warp and weft crimp ratios was still higher for 1025 style fabric. Thus the elongation and tension of facing warp and weft yarns in a single layer of 1025 style fabric will be less synchronized when a projectile hits the layer compared to 1027 style fabric.

Figure 2.

Load-elongation curves of single warp and weft yarns in neat and STF impregnated fabrics of 1027 style (a) and 1025 style (b).

Effect of fabric count on ballistic properties

Ballistic limit (V₅₀)

Table 2 shows the V₅₀ values of neat (N) Kevlar panels with different fabric counts. From these values and the areal density of each panel, the specific energy absorption of each panel was calculated. The specific energy absorption values of N-panels of 1027 and 1025 style fabrics were estimated to be 195–200 J and 174–180 J/(kg/m²), respectively. The specific energy absorption value of the target panels made of the more densely woven fabric, 1025 style, was about 12% lower than those made of 1027 style. From the specific energy absorption values, the energy absorption value ( $\frac{1}{2} {mV}_{50}^{2}$ ) of each N-panel having the same areal density of 4.77 kg/m² was calculated. The result was 835 J for the N-1025 panel and 935 J for the N-1027 panel, respectively. The maximum possible kinetic dissipation of an N-panel (32 ply, 1027 style) was estimated to be around 100 J in part I, thus, that of a N-panel of higher density fabric (26 ply, 1025 style), which showed a smaller BFS (see next section), will definitely be smaller than 100 J. Assuming that the maximum possible kineticdissipation of the N-1025 panel is around 80 J, then the tensile dissipation of the panel should be 755 J (∵ 835 (max. energy absorption) – 80 (max. kinetic dissipation) = 755 (max. tensile dissipation)), which is 80 J less than that of the N-1027 panel. This means that either the number of facing yarns in a panel of a denser weave should be less than that in a panel of a coarser weave, or if the number of facing yarns is the same in both panels, then the gauge length of the tensile event should be shorter for an N-panel of denser weave. The first presumption is related to bullet expansion, and the second is related to the speed of sound in the yarn within the fabric and the contact time with the bullet (∵ l = c · Δt). As will be shown in the next section, the bullet expansions of N-1025 and N-1027 panels were almost identical, so the first presumption that the number of facing yarns in a panel of a denser weave should be less than that in a panel of a coarser weave is not appropriate. Meanwhile, the speed of sound in the yarn is influenced by the crimp ratio.^13,14 As shown in Figure 3, the pullout of warp yarns in several frontal layers of the N-1025 panel was restrained compared to that of the N-1027 panel. Also, from the same figure, we can see that the longitudinal wave front of weft yarns has reached the edge of the panel, while that of warp yarns in the N-1025 panel has not. Only after the 6th or 7th layer of the panel, wrinkles could be clearly observed in the warp direction. Along with the crimp ratio, which is related to the longitudinal wave speed, the stiffness of the panel also affects their ballistic behavior. Stiffer materials have a shorter contact time with a bullet.

Figure 3.

Photographs of strained yarns in ballistic panels of 1027 and 1025 style fabrics. (The longitudinal wave front of the warp yarn in 1025 style fabric panel does not reach the edge of the panel in the 3rd layer, but wrinkles in the warp direction are clearly observed from the 7th layer of the panel).

Table 2.

Effect of fabric count on ballistic limit (V₅₀) and specific energy absorption

Fabric style	Number of laminated plies	Areal density (kg/m²)	Stitching interval	V₅₀ (m/s)	Specific energy absorption* (J/(kg/m²))
1027	27	4.02	×	445.0	197.04
	30	4.47	×	468.8	196.67
			7.62 cm	473.7	200.80
1025	24	4.34	×	437.0	176.01
	26	4.71	×	453.0	174.28
			7.62 cm	461.6	180.96

$specific energy {absorption}^{*} = \frac{\frac{1}{2} {mV}_{50}^{2}}{areal density}$

Though not dealt with in this paper, our previous study showed that the energy absorption capability of the N-1027 panel (areal density <3.5 kg/m²) against an infrangible and very light bullet, a 5.56 mm FSP, was slightly higher than that of the N-1025 panel having the same areal density at velocities below 450 m/s. Since the FSP is infrangible, the total number of facing yarns throughout all the layers in both panels will be the same, and both panels will favor tensile dissipation over kinetic dissipation because the mass of the FSP is quite small (1.1 g) compared to that of a 9 mm bullet (8.0 g) used in this study. So the probable explanation for the given result was that the less dense and thus more flexible N-1027 panel had a somewhat longer contact time with the bullet, causing the stress wave to travel farther in the facing yarns of a few frontal layers, and at the same time, the kinetic dissipation increased. But at a higher FSP impact velocity (>550 m/s), both N-1025 and N-1027 panels (areal density >5.0 kg/m²) exhibited nearly identical energy absorption capabilities. The increased impact velocity and higher bending stiffness due to the increased areal density must have decreased the contact time of the facing yarns with the bullet in both panels. As a result, the facing yarns could fail before the longitudinal wave front travels far enough to reach the edge of the panels (‘stress localization’ or ‘shearing’). Thus, the benefit attributable to the flexibility of the coarser weave observed at lower impact velocities was not effective at high impact velocities.

The mass of a bullet or the relative mass of an impactor to a target is also thought to be correlated with the contact time. So the velocity range where coarsely woven fabrics have an advantage over densely woven fabrics, as mentioned above with an FSP, can be varied if a 9 mm bullet is the impactor. Therefore, it is thought that not only the retardation of the longitudinal wave due to its high crimp ratio but also the shorter contact time due to its higher bending stiffness must have contributed in lowering the ballistic limit of the N-1025 panel.

Backface signature (BFS), perforation ratio and bullet expansion

In this section, the panels were prepared to have areal densities above 4.5 kg/m². Table 3 shows the ballistic test results of four different panels having areal densities in the range of 4.71–4.78 kg/m². As shown in Figure 4, the panels of more densely woven 1025 style fabric gave lower BFS values for both N- and N/S- panels. The lower BFS values are presumed to be due to the higher bending stiffness of the denser fabric. The reduction in BFS through the hybridization with STF impregnated fabrics was larger for 1027 style fabric panels compared to 1025 style fabric panels, where the decrease in BFS value of N/S-panels compared to the N-panels of 1027 and 1025 style fabric was 23.5 and 12.7%, respectively.

Figure 4.

Effect of fabric count on back face deformation.

Table 3.

Effect of fabric count on BFS value of N- and N/S-hybrid panels

Fabric style	Panel (ply)	velocity (m/s)	BFS (mm)	Perforation ratio^a (%)	Bullet expansion^b (mm)
1027	N- (32)	442.08	39.5	28.1	16.5
		443.64	44.5	34.4	16.0
		444.13	43.5	31.3	15.5
		445.16	42.5	18.8	16.0
	(avg.)	(443.75)	(42.5)	(28.2)	(16.0)
	N/S- (14/15)	443.10	33.0	24.1	20.0
		450.37	34.0	27.6	19.0
		439.49	30.0	20.7	18.0
		444.01	33.5	24.1	16.0
	(avg.)	(444.24)	(32.6)	(24.1)	(18.3)
1025	N- (26)	443.03	36.0	38.5	15.5
		441.35	36.0	30.8	15.5
		435.74	35.0	30.8	16.5
		440.83	35.5	34.6	16.0
	(avg.)	(440.24)	(35.6)	(33.7)	(15.9)
	N/S- (12/12)	440.43	29.0	37.5	16.0
		440.47	30.5	33.3	16.0
		442.11	30.0	25.0	16.5
		438.76	34.0	41.7	15.5
	(avg.)	(440.44)	(30.9)	(34.4)	(16.0)

Perforation ratio = (Number of perforated plies ÷ Number of laminated plies) × 100 (%); ^bBullet expansion, forward diameter of expanded (mushroomed) bullet after the impact.

Figure 5 shows the effect of fabric count on perforation ratio. As can be deduced from the higher BFS value, the more flexible 1027 style fabric panels dissipated a higher fraction of the given impact energy through kinetic dissipation. On the other hand, the stiffer 1025 style fabric panels showed lower kinetic dissipation and higher perforation ratio. Although the perforation ratios of N-1025 and N/S-1025 (12/12) panels were similar, when normalized by the number of layers, those normalized by areal density were slightly lower for theN/S-1025 (12/12) panel since the surviving layers contained STF. When compared with the N-panel, the larger mass of the surviving layers in the N/S-panel ispresumed to have done its part in lowering the BFSvalue.

Figure 5.

Effect of fabric count on perforation ratio. Perforation ratio = (Number of perforated plies ÷ Number of laminated plies) × 100 (%).

Figures 6–8 show the effect of fabric count on bullet expansion, the relationship between the perforation ratio and bullet expansion, and that between the perforation ratio and the BFS value, respectively. The bullet expansion values of the tested panels were similar except for the N/S-panel of 1027 style fabric. This is presumed to be due to the better synchronization of elongation of warp and weft in a single layer of 1027 style fabric, and at the same time enhanced coupling of elongations of facing yarns in frontal and rear layers of N/S-panel of 1027 style fabric. The panels of denser fabric showed lower BFS values with less bullet expansions, which resulted in increased perforation ratio. So a higher fraction of the impact energy was presumed to be dissipated mainly through tensile dissipation early on in the event of impact for denser fabrics. Photographs of the expanded bullets from the test are shown in Figure 9.

Figure 6.

Effect of fabric count on bullet expansion.

Figure 7.

The relationship between perforation ratio and bullet expansion.

Figure 8.

The relationship between perforation ratio and BFS.

Figure 9.

Photographs of expanded bullets from each panel.

Effect of shot location

The shot-to-edge distance is related to the actual effective covering area of soft body armor, and the edge limit described in NIJ Standard-0101.06 was considered in this test. Table 4 shows the BFS value of the panels when the shot location was 51–70 mm from the panel edge. Panels made of 1025 style fabric were used in this experiment since their blunt trauma performance was superior to those made of 1027 style fabric. The BFS value of the unstitched N-1025 panel (26 ply) increased from 35.6 mm (in Table 3) to 41.5 mm when the shot location was close to the edge of the panel, and both the perforation ratio and bullet expansion decreased slightly. The N/S-panels with slightly different hybridization ratios, 12/12 vs. 14/10, also showed a similar amount of increase (30.9 mm → 36.9 mm) in BFS value as the shot location was shifted outwards.

Table 4.

Ballistic test results of 1025 style fabric panels with shot-to-edge distance of 51–70 mm

Panel (ply)	Stitching interval	velocity (m/s)	BFS (mm)	Perforation ratio (%)	Bullet expansion^a (mm)
N- (26)	×	445.30	36.0	34.6	15.5
		449.85	44.0	30.8	15.0
		443.68	43.0	26.9	15.5
		445.72	44.5	32.5	15.0
	(avg_.)	(446.14)	(41.5)	(31.6)	(15.3)
	7.62 cm	444.34	38.5	34.6	15.3
		450.09	34.5	30.8	15.2
		442.69	37.0	26.9	15.0
		443.80	35.0	38.5	14.8
	(avg_.)	(445.23)	(36.3)	(32.7)	(15.1)
N- (24)	×	449.10	38.5	45.8	15.0
		435.93	40.0	33.3	14.5
		443.97	52.0	54.2	15.5
		445.47	39.0	41.7	15.0
	(avg_.)	(443.62)	(42.4)	(43.8)	(15.0)
N/S- (14/10)	×	442.90	37.0	41.7	15.5
		436.73	34.5	41.7	16.0
		447.22	36.0	41.7	15.5
		441.31	40.0	50.0	16.0
	(avg_.)	(442.04)	(36.9)	(43.8)	(15.8)
	7.62 cm	444.73	36.0	50.0	16.0
		448.85	34.5	37.5	16.0
		443.31	37.0	29.2	16.0
		446.50	35.0	50.0	15.5
	(avg_.)	(445.85)	(35.6)	(41.7)	(15.9)

Bullet expansion, forward diameter of expanded (mushroomed) bullet after the impact (= average of major axis and minor axis when elliptically expanded).

This is because a higher fraction of the given impact energy tends to dissipate through kinetic dissipation when the effective mass of the target decreases. Here, the effective mass is presumed to be related to the contact time of the bullet (i.e. bulged part) with a single layer andthe number of survived layers at a certain point of time. If we assume that a bullet of mass m₁ at a velocity v₁ hits a stationary target of mass m₂, and both the bullet and the target move together at a velocity v₂ just after thecollision (i.e. perfect inelastic collision), then the conservation of momentum and the difference of the kinetic energy (ΔE) before and after the collision should be as follows.

(1)

(2)

The difference of the kinetic energy (ΔE) may act as a driving force for destructing the target (i.e. tensile dissipation in case of a fabric panel), and this value increases with the increase of the ratio of m₂ to m₁. So a target of smaller mass can store a higher portion of the impact energy in kinetic form (E₂), which will result in a larger BFS and a higher V₅₀ compared to a target of higher mass. This agrees well with the phenomenon that although the areal density is the same, small sized body armors tend to have larger BFS, and larger sized body armors tend to be more easily perforated. Although an actual ballistic event may not be a perfectinelastic collision, the probable reason for this phenomenon could be easily explained with equations 1–2.

Stitching decreased the BFS value of the N-1025 panel (26 ply), but it did not affect the N/S-1025 panel. A similar result was shown in part I, where the stitching of N/S-panel did not decrease its BFS value. When the shot location was closer to the panel edge, the expanded shape of the bullet became non-circular. So the bullet expansion value was redefined as the average of the major axis and the minor axis when the bullet was elliptically expanded.

Figure 10 shows the ballistic limit value (V₅₀) of the same panels given in Table 4, but with the shot location differed, being shot 11 cm apart from the panel edges. The V₅₀ value of the unstitched N/S-panel (26 ply) was highest among all the panels. The V₅₀ value of the N-panel (24 ply) increased when it was stitched, while that of the stitched N/S-panel decreased. The most noticeable V₅₀ value was that of the unstitched N-panel (24 ply), which was 436.8 m/s, meaning that there is a 50% probability that every single layer in the panel will be perforated at the impact velocity of 436.8 m/s. The perforation ratio of this panel with shot-to-edge distance of 51–70 mm was 43.8% on an average at the velocity of 436.7–447.2 m/s. This also confirms that the shot location not only affects BFS, but also V₅₀.

Figure 10.

Ballistic limit test results of 1025 style fabric panels (shot-to-edge distance of 110 mm). CP, complete perforation; PP, partial penetration; 3 inch stitch, cross-diagonally stitched with 7.62 cm intervals.

Table 5 shows the specific energy absorption values of panels of 1025 style fabric and the energy absorption per layer of each panel, where the latter can be an important criterion in concealable soft body armor. As shown in Tables 4–5 and Figure 10, by backing STF impregnated Kevlar to unstitched neat Kevlar, the penetration resistance increased as well as the blunt trauma resistance in terms of areal density and thickness.

Table 5.

Energy absorption capability of ballistic panels made of 1025 style fabric (9 mm FMJ RN, 8.0g) at their ballistic limits

Panel (ply)	Stitching interval	Specific energy absorption (J/(kg/m²))	Energy absorption per layer (J/layer)
N- (26)	×	174.42	31.57
	7.62 cm	181.11	32.78
N- (24)	×	175.69	31.80
N/S- (14/10)	×	184.10	36.10
	7.62 cm	173.27	33.98

Meanwhile, the reduced shot-to-edge distance (or reduced panel size) may slightly decrease the total tensile work of the panel due to the unsymmetrical elongationofthe facing yarns as shown in equations 3–6 and Figure 11.

(3)

(4)

(5)

(6)

where E_T is the tensile dissipation of a single yarn; F_i is the force in the ith interval from the shot location (refer to part I); Δl_i is the displacement of the ith interval, which is proportional to F_i; k is a proportional constant;c is the number of crossovers in a single facing yarn from the center to the edge; a is the number of crossovers in a single facing yarn from the center to the shot location; E_T_,_center is the tensile dissipation of a single facing yarn involved in a center shot; E_T_,_edge is the tensile dissipation of a single facing yarn involved in a near-edge shot.

Figure 11.

A schematic diagram of stress distribution along the yarn direction (a) and the difference in tensile dissipation with varied shot location (b).

Thus, as shown in equations 7–9, the increase in kinetic dissipation (ΔE_K) should be larger than the decrease in tensile dissipation (ΔE_T) when a panel is shot closer to the edge of the panel because of the increased V₅₀.

(7)

(8)

(9)

Calculation of the kinetic dissipation

The kinetic dissipation was experimentally measured using the weight dropping method, which was similar to that used in Karahan's study.¹⁵

First, the relationship between impact energy and dent volume was investigated. Then the kinetic dissipation was calculated based on this relationship and the measured trauma volume from the ballistic test. A steel ball of 1.043 kg with a diameter of 63.5 mm (NIJ ballistic test standards) was used in the drop test. The steel ball was dropped freely on the conditioned oil-based clay, which was used in the ballistic test, from the heights of 0.5, 1.0, 1.5 and 2 m. The average penetration depth was measured and the dent volume was calculated from equation 10.

(10)

where R is the radius of the steel ball (mm); p is the penetration depth (mm).

The test results are listed in Table 6, and Figure 12 shows the linearly regressed relationship between the dent volume and the impact velocity which was calculated from equation 11.

(11)

where v is the impact velocity (m/s); g is gravitational acceleration (i.e. 9.80665 m/s²); H is drop height (m).

Figure 12.

Impact velocity vs. dent volume of a 1.043 kg steel ball.

Table 6.

Result of drop weight test

Drop height (m)	0.5	1.0	1.5	2.0
Avg. penetration depth (mm)	10.0	15.0	18.0	20.0
Calculated dent volume (mm³)	8927.4	18908.5	26210.3	31520.6

The linear relationship between the impact velocity and the dent volume was also derived from equations 12–16, and the experimental results reflected this relationship well.

(12)

(13)

(14)

(15)

(16)

where E_K is the kinetic energy of the impactor; m is the mass of the impactor; v is the impact velocity; E_Potential_,_clay is the energy absorbed by the oil-based clay; k is the spring constant of the oil-based clay; x is the displacement at a certain point, where the sum of all equals the dent volume; s is the contact surface of a sphere with the oil-based clay; C₁, C₂ are the proportional constant and constant of integration, respectively.

Since it is clear that the dent volume of oil-based clay has a linear relationship to the impact velocity, it is possible to make an estimation of the amount of kinetic dissipation in a ballistic event if the dent volume is measured. The dent profile was measured at an interval of 5 mm from the center to both ends of the circle on a reference plane, and quadratic regression was used to interpolate the values between the measured values (Figure 13). Finally the dent volume was calculated using mensuration by parts, with the trauma diameter fixed to 66.7 mm.

Figure 13.

An example profile and dimension of a trauma.

The most difficult problem in calculating the kinetic dissipation is determining the mass of the impactor. The impactor in this case is not the bullet itself, but the bulged part of the ballistic panel upon impact. Though not described in detail here, C₁ and C₂ in equation 16 vary with the mass and aspect ratio of an impactor, where the mass is related to the mass density and diameter (or volume) of a sphere. Since the resisting force of the oil-based clay, such as drag force, against backface bulging of a panel is proportional to the cross-sectional area of the penetrating object, it is plausible to use the relationship between the dent volume and kinetic dissipation of an impactor having the dimension similar to the trauma diameter. The trauma diameter of the ballistic test was mostly around 65 mm, thus the regressed relationship from the steel ball having 63.5 mm diameter (1.043 kg) was directly used to calculate the kinetic dissipation.

Firstly, the impact velocity of the steel ball of 1.043 kg was calculated from the dent volume using the regression equation 17 in Figure 12, and then the kinetic energy of the steel ball which is equal to the kinetic dissipation (E_K) of the ballistic panel, was calculated using equation 18.

(17)

(18)

where, v is the velocity of a steel ball of 63.5 mm diameter; m is the mass of a steel ball of 63.5 mm diameter (1.043 kg).

Figure 14 shows the presumed relationship between trauma depth (or dent volume) and kinetic dissipation in the ballistic test of panels against 9 mm bullets. The measured dent volume data in the relationship includes only concentric ogival profiles which were mostly the case with near-center shots. In the case of near-edge shots, most profiles became eccentric. In this case, trauma depth in the figure was directly used to estimate the kinetic dissipation.

Figure 14.

Presumed relationship between trauma depth (or dent volume) and kinetic dissipation in the ballistic test of panels against 9 mm bullets.

The calculated result of the amount of kinetic dissipation of each panel is given in Table 7. When shot near the center of the panel, hybridization (i.e. backing of STF impregnated fabrics to neat fabrics in 1027 and 1025 style panels) decreased the kinetic dissipation by 29.6 J and 12.7 J (25.6 and 20.9% decreases), respectively. When shot closer to the edge of the panel, hybridization of the 1025 style panel decreased the kinetic dissipation by 14.7 J (18.6% decrease). With the shotlocation shifted outwards, the kinetic dissipation of N-1025 and N/S-1025 panels increased by 18.3 and 16.3 J (30.1 and 34.0% increases), respectively.

Table 7.

Calculated kinetic dissipation of panels having the same areal density

Panel (ply)	Shot location	BFS (mm)	Kinetic dissipation (J)
N-1027 (32)	Near-center	42.5	81.5
N-1025 (26)	Near-center	35.6	60.7
	Near-edge	41.5	79.0
N/S-1027 (14/15)	Near-center	32.6	51.9
N/S-1025 (12/12)	Near-center	30.9	48.0
N/S-1025 (14/10)	Near-edge	36.9	64.3

Conclusions

Both the ballistic limit (V₅₀) and BFS value were lower for panels made of fabrics with higher fabric count (1025 style) because they favor tensile dissipation over kinetic dissipation when impacted at high velocity. By backing STF impregnated fabrics to neat fabrics, both the penetration resistance and trauma resistance increased in terms of areal density as well as thickness. The extent of decrease in BFS by hybridization was smaller for 1025 style fabric panels but the absolute BFS value of the hybridized 1025 style fabric was smaller than the hybridized 1027 style fabric panel. This is presumed to be due to the larger difference in crimp ratio between the warp and weft directions in the more densely woven fabric, 1025 style. The shot-to-edge distance not only affected the ballistic limit of the panel but also the BFS value. Shots located closer to the edge of the panel resulted in larger BFS values, and shots located closer to the center resulted in higher perforation ratio. The kinetic dissipation in ballistic tests with 9 mm bullets was calculated from the linear relationship between the dent volume ofoil-based clay and the impact velocity of a 1.043 kg steel ball.

Footnotes

Funding

This study was supported by the Agency for Defense Development (ADD) through the Dual Use Technology Center (DUTC) project (07-DU-MP-02) funded by the Ministry of Knowledge Economy (MKE) and Defense Acquisition Program Administration (DAPA), Republic of Korea.

References

Hoffman

. Discontinuous and dilatant viscosity behavior in concentrated suspensions. I. Observation of a flow instability. J Rheology 1972; 16(1): 155–173.

Barnes

. Shear thickening (dilatancy) in suspensions of non-aggregating solid particles dispersed in Newtonian liquids. J Rheology 1989; 33: 329–366.

Bossis

Brady

. The rheology of Brownian suspensions. J Chem Phys 1989; 91(3): 1866–1874.

Boersma

Laven

Stein

. Viscoelastic properties of concentrated shear thickening dispersions. J Colloid Interface Sci 1992; 149(1): 10–22.

Hoffman

. Explanations for the cause of shear thickening in concentrated colloidal suspensions. J Rheology 1998; 42: 111–123.

Chadwick

Goodwin

Vincent

Lawson

Mills

PDA

. Rheological behaviour of titanium dioxide (uncoated anatase) in ethylene glycol. J Colloid Interface Sci 2002; 196: 234–245.

Bender

Wagner

. Reversible shear thickening in monodisperse and bidisperse colloidal dispersions. J Rheology 1996; 40(5): 899–916.

Maranzano

Norman

. The effects of interparticle interactions and particle size on reversible shear thickening: Hard-sphere colloidal dispersions. J Rheology 2001; 45(5): 1205–1222.

Bender

Wagner

. Optical measurement of the contributions of colloidal forces to the rheology of concentrated suspensions. J Colloid Interface Sci 1995; 172(1): 171–184.

10.

Maranzano

Norman

. Flow-small angle neutron scattering measurements of colloidal dispersion microstructure evolution through the shear thickening transition. J Rheology 2002; 49(3): 719–746.

11.

Phung

Brady

Bossis

. Stokesian dynamics simulation of Brownian suspensions. J Fluid Mechanics 1996; 313: 181–207.

12.

Lee

Wetzel

Wagner

. The ballistic impact characteristics of Kevlar woven fabric impregnated with a colloidal shear thickening fluid. J Materials Sci 2003; 38: 2825–2833.

13.

Roylance

Wilde

Tocci

. Ballistic impact of textile structures. Textile Res J 1973; 43(1): 34–41.

14.

Roylance

. Stress wave-propagation in fibers-effects of crossovers. Fiber Sci Technol 1980; 13(5): 385–395.

15.

Karahan

. Comparison of ballistic performance and energy absorption capabilities. Textile Res J 2008; 78(1): 718–730.

Ballistic performance of p -aramid fabrics impregnated with shear thickening fluid;Part II – Effect of fabric count and shot location

Abstract

Keywords

Introduction

Experiments

Materials

STF preparation and impregnation

Single yarn tensile test

Ballistic impact test

Results and discussion

Effect of fabric count on the tensile behavior of a single yarn in Kevlar fabrics

Effect of fabric count on ballistic properties

Ballistic limit (V50)

Backface signature (BFS), perforation ratio and bullet expansion

Effect of shot location

Calculation of the kinetic dissipation

Conclusions

Footnotes

Funding

References

Ballistic limit (V₅₀)