Rui-guo Han , Yong-jie Qu , Wen-min Yan , Bin Qin , Shu Wang ,Jian-zhong Wang

a State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing,100081, PR China

b Science and Technology on Transient Impact Laboratory, Beijing,102202, PR China

Keywords:Behind armor blunt trauma Ballistic gelatin Pressure wave Body armor

ABSTRACT Pressure wave plays an important role in the occurrence of behind armor blunt trauma (BABT), and ballistic gelatin is widely used as a surrogate of biological tissue in the research of BABT. Comparison of pressure wave in the gelatin behind armor for different rifle bullets is lacking.The aim of this study was to observe dynamic changes in pressure wave induced by ballistic blunt impact on the armored gelatin block and to compare the effects of bullet type on the parameters of the transient pressure wave. The gelatin blocks protected with National Institute of Justice (NIJ) class III bulletproof armor were shot by three types of rifle bullet with the same level of impact energy. The transient pressure signals at five locations were recorded with pressure sensors and three parameters (maximum pressure, maximum pressure impulse, and the duration of the first positive phase) were determined and discussed. The results indicated that the waveform and the twin peak of transient pressure wave were not related to the bullet type.However,the values of pressure wave’s parameters were significantly affected by bullet type.Additionally,the attenuation of pressure amplitude followed the similar law for the three ammunitions.These findings may be helpful to get some insight in the BABT and improve the structure design of bullet.

1. Introduction

Body armor is an important individual protection equipment which is designed to protect the wearers against small-caliber ammunitions by impeding projectile penetration into the human body and diffusing the impact energy of bullet[1].However,even if penetrating injury may be prevented, potential blunt injuries due to defeated bullet are caused by excessive deformation or energy transmission into the body during ballistic impacts; serious and even lethal injuries can be caused by the armor-released energy transferred to the body. This type of injury, caused without penetration, is called behind armor blunt trauma (BABT) [2,3]. Death with very high energy impacts may occur when the stress induced by the pressure wave exceeds the tissue strength (e.g. lung, liver,heart).

Since Shepard et al.[4]reported the existence of BABT,BABT was extensively investigated in the field of wound ballistics and biomechanics via experiments and numerical simulations [5-18].Transient pressure wave in BABT is believed to be one of the most important factors which would result in injuries to organs due to the strong stress wave or high energy transmission [2,9and16]. In the early experimental research, the main targets were living anesthetized animals(e.g.pig,dog,and sheep).However,in recent years,human tissue simulants(e.g.ballistic gelatin,soap,clay)were introduced into the experiments and numerical simulations due to the ethical limitations and legal prohibition in most countries.Ballistic gelatin is widely used in the research of wound ballistics because its mechanical properties are believed to be close to those of human tissue [19-22]. For both hard armor and soft armor, the transient pressure wave formed in the target behind armor have been investigated by experiments and simulations, and the mechanisms for‘twin peaks’in BABT have been explained(van Bree et al.[6-8]; Cronin et al. [10]; Wen et al. [17]; Luo et al.[18]).Prat et al.[14] demonstrated that the maximum pressure impulse was best correlated with the relative pulmonary contusion volume. Wang et al. [15] investigated the effect of different rifle bullets on the characteristics of BABT and the biomechanical response of the organs in landraces. Grimal et al. [23] built a simplified three layers structure (muscle-bone-lung) analytical model without detailed geometry to investigate the pressure impulse on the lung. These studies quantified the maximum pressure or pressure impulse in the targets after ballistic blunt impacts. However, the previous studies mostly measured transient pressure wave basically at one location, and the armor, body simulant and ammunition used in these studies were different, thus the results were difficult to be compared with each other.In addition,it has not been reported that the influences of different rifle bullets with the similar impact kinetic energy on the pressure wave propagation in the gelatin block behind armor in the open literatures.

This paper experimentally studied the transient pressure in gelatin block behind hard/soft composite body armor when subjected to impacting by different rifle bullets.In the experiment,the ballistic gelatin block was protected with National Institute of Justice (NIJ) class III bulletproof armor and shot by three ammunitions (3 shots for each ammunition). The impact kinetic energy was adjusted to the same level by changing the amount of the propellant for three ammunitions. The transient pressure wave signals were recorded with five pressure sensors located at different locations in the gelatin block and three parameters of the transient pressure wave for all shots were determined and analyzed.The aim of this study was to observe dynamic changes in pressure wave propagation in the armored gelatin for different ammunitions and compare the effects of bullet type on the parameters of the transient pressure wave. These findings may be helpful to further understand the BABT and promote the structure design of rifle bullet to increase the wounding effects.

Fig.1. Body armor and ballistic gelatin block embedded with pressure sensors.

2. Materials and methods

2.1. Materials

2.1.1. Simulated target

The simulated target was composed of the National Institute of Justice(NIJ)class III bulletproof armor and ballistic gelatin block,as shown in Fig. 1. The gelatin block in this work followed Fackler model(4°C/10 wt%).Ballistic gelatin with a Bloom strength of 250 was used to manufacture the gelatin block, and its preparation is detailed in Ref. [24]. The gelatin block dimensions of 300 mm×300 mm×300 mm is chosen according to Refs.[17,18].Liquid gelatin at 60°C was put into a 300 mm×300 mm×300 mm mould.Five pressure gauges were embedded into the liquid gelatin from the top side along the middle plane of gelatin block with the depth of 50 mm. The numbering and positions of the pressure gauges are shown in Fig.2.The filled mould was left to set at room temperature (about 20°C) for 12 h, then it was placed in a refrigerator (4°C) for 24 h. The test was conducted within 3 min after taking the block from the refrigerator to reduce the temperature effect [25].

The NIJ class III bulletproof armor,which is composed of ceramic hard plate and soft body armor (Ningbo Dacheng Advanced Material Co. Ltd., China), was used in the experiments. The ceramic hard plate is consisted of 7 mm thick 99.5%Al2O3ceramic tiles with 11 mm thick UHMWPE fiber-reinforced laminate backing. The soft body armor is a 300 mm × 300 mm panel of 46 UHMWPE-fiber layers, and each layer consists of four plies of UHMWPE fibers which are formed into a [0°/90°/0°/90°] stack. Each sheet is nominally 0.2 mm thick without adhesion between layers. All armors used in the tests were manufactured in the same batch.

2.1.2. Ammunitions

Fig. 2. Schematics of experimental set-up.

The three ammunitions used in the experiment were SS109-5.56×45 mm rifle bullet,Type 87-5.8×42 mm rifle bullet and M43-7.62×39 mm rifle bullet.The basic dimensions and mass of three ammunitions were shown in Table 1.The impact energy of three ammunitions at 25 m (the distance from the muzzle to the striking face of the armor)was adjusted to the same level(ca.1850 J) by changing the amount of the propellant.

2.2. Methods

2.2.1. Experimental set-up and procedures

Three groups of tests were conducted:(1)SS109 group(n=3),(2)Type 87 group(n=3),and M43 group(n=3).The experimental facilities included a launch system, a velocity measuring system,the simulated target and a pressure-measuring system (Fig. 2).Three types of ballistic barrel(5.56 mm,5.8 mm and 7.62 mm)were used and held in place by a special designed fixture to fire the corresponding rifle bullet, respectively.

For every shot, a new gelatin block was used, and so was the body armor.Body armor was placed in front of the gelatin block.To reduce the effect of gap,straps were used to tie the body armor and gelatin block together with no obvious visible gap between them.Then,the simulated target was placed on the test bench 25 m from the end of the muzzle along the positive Z (as shown in Fig. 2, i.e.the designed ballistic direction). The point of bullet impact was aligned with the center of the gelatin block which was marked with red dot by using a laser gun sight. To obtain the desired impact kinetic energy of about 1850 J, the amount of propellant for each type of the ammunition was determined from the speed measurement in the preliminary experiments.The impact velocities of the rifle bullets were measured by an XGK-2002(Manufactured by Xi’an Technological University, China). Five ICP 113B22 pressure sensors (PCB Piezotronics Inc., USA) with a measurement range of 0-34.5 MPa, embedded in the gelatin block at different locations with the spacing of 50 mm along the ballistic line, was used to record the pressure signals. The signals were amplified with a KD 6003 Charge amplifier (Yangzhou KeDong Electronics Co., Ltd.,China) and stored on the NI PXI-6133 data acquisition system(National Instruments, USA) with a 1 MHz sampling frequency.

In addition, assuming the center of the front surface of gelatin block as the origin, the Y axis and Z axis of the right-handed Cartesian coordinates were shown in Fig. 2. Thus, the coordinates of the center of the sensitive surface of each gauge and the impact point for every shot can be determined,and then the distance from the projection point of the impact point along ballistic line on the front surface of the gelatin block to the center of sensitive surface of any pressure sensor can be calculated based on the coordinates.Further, the velocity of pressure wave propagation in the gelatin can be calculated based on the travelled distance and time.

2.2.2. Determination of the parameters of transient pressure wave

From the data of pressure signals, three parameters of the transient pressure wave were determined with FlexPro (Weisang,GmbH, Germany):

1. The maximum pressure(Pmax),corresponding to the maximum value of the first positive phase of the pressure versus time curve recorded after the ballistic impact.

2. The pressure impulse (PI), corresponding to the integral of the pressure-time curve (i.e. the area under the curve). The maximum pressure impulse (PImax) was reached when the pressure curve first crossed the zero line.

3. The third parameter, the duration of the first positive phase(PPD), was also calculated and expressed in the unit of microseconds.

2.2.3. Statistical analysis

Summary statistics (mean (x), standard deviation (s.d.) and coefficient of variation(CV))were calculated for the parameters of the transient pressure wave mentioned above. Analysis of variance(ANOVA) and Tukey analysis were used to determine when significant difference among data set occurred for three ammunitions with Origin (OriginLab, USA). Normality of data and equality of variance were checked for each data set.

3. Results

Results, including the impact velocity, the coordinate of impact point and the pressure signals, were recorded for every shot. The impact velocity (v), impact kinetic energy (KE), the calculated distance from the projection point of the impact point along ballistic line on the front surface of the gelatin block to the center of sensitive surface of any pressure sensor(hereinafter referred to as‘D’,for example the distance from the projection point to the center of the sensitive surface of gauge 3,as shown in Fig.2),Pmax,PImaxand the PPD for all shots were shown in Table 2. In Table 2, it can be found that the impact kinetic energy was basically similar for all shots (average = 1849 J). The average of impact kinetic energy differs from the nine values by a maximum of 1.78%and a minimum of 0.05%. Generally, for the maximum pressure at all measured locations,the values of the M43 group were the highest,followed by the Type 87 group,and those of the SS109 group were the smallest.In contrast,for the PPDs at all measured locations,the values of the SS109 group were the greatest;followed by the Type 87 group,and those of the M43 group were the smallest. Additionally, for the maximum pressure impulse,the values of M43 group were also the highest;most values of the Type 87 group were higher than those of SS109 group.The reasons for the phenomena would be discussed in Section 4.

3.1. Experimental results on the pressure

In this section, the pressure from pressure gauges were presented and analyzed.Since the experiment involved three different rifle bullets, the results obtained for the transient pressure were firstly presented. Fig. 3 showed the pressure-time history profiles obtained from the five gauges for SS109 rifle bullet impacting at 966 m/s. A brief measurement of the pressure signals for the five gauges (Fig. 3) indicated that:

Table 2 Summary of the impact velocity,kinetic energy, D and the parameters of pressure wave.

(a) It can be seen that the waveform obtained by different sensors are similar. The pressure decreased with time and the PPDs ranged from 35 μs to 83 μs for the different gauges.The duration also decreased with the increase of distance between the impact point and the gauges.It could be also found that two peaks obviously appeared on the pressure-time curve. The initial rise measured by the sensors occurred quite sharply;the time to reach the first peak was about 7 μs with a slight delay time about 1-3 μs from gauge 1 to gauge 5. The value of second peak was lower than that of the first peak pressure and it appeared at ca.25 μs after the first peak on the curve for all the five gauges. After this phase, the amplitude of the pressure-time curve decreased rapidly;then the pressure gradually decreased to a negative pressure phase with obvious high frequency oscillation due to various reflection waves from various boundaries of the gelatin block and the vibration after ballistic impact. It was thought that the extent of pressure oscillation was affected by the distance between impact point and the gauge,that is,the farther the gauge from the impact point was, the more obvious the pressure oscillation was.

(b) It can be seen that the values of the first peak measured by the five gauges were significantly different.The values were 0.63,0.48,0.34,0.28,0.18 MPa,respectively,which indicated that the maximum pressure attenuated with the increase of travelled distance.The reason for this phenomenon would be discussed in detail in Section 4.2.

(c) In Fig. 4(a), the pressure wave can be separated into three distinct phases by two peaks and the first trough of the negative pressure:(i)the first phase with a relatively sharply pressure wave associated with 0.63 MPa; (ii) the second phase with a weaker wave with 0.51 MPa;and(iii)the third phase from the second peak to the negative phase.

Fig. 3. Pressure signals for SS109 rifle bullet impacting at 966 m/s.

Some magnifications of the pressure profiles were exhibited in Fig.4(a)-(c),which were corresponding to SS109 group at 966 m/s,Type 87 group at 941 m/s and M43 group at 688 m/s. Several interesting features can be observed by comparing these three figures.It can be seen that the profiles of the pressure-time curves were basically similar. The pressure obtained at each location all sharply rose to the maximum value after the initial impact. After this phase, the pressure began to decrease with some inflections.The ‘twin peak’ was observed from the pressure-time history profiles for all three ammunitions,similar observations had been made by van Bree et al. [6-8] and Luo et al. [18] for ballistic impact on gelatin block protected with body armor.It was considered that the‘first peak’was formed due to the shock wave caused by the initial bullet-armor impact and the ‘second peak’ was formed due to the interaction between the deformed armor and gelatin block. As shown in Fig. 4(a), the pressure jump (PA= Pmaxat ta) was commonly termed as the‘first peak’.Similarly,it was interesting to find that the signals obtained from the gauge 5 for all three ammunitions show obvious negative pressure phase,and the absolute value of the first trough of negative pressure was similar to that of maximum positive pressure. After the negative phase, the curves for three ammunitions all showed obvious high frequency oscillation. Because the sizes of gelatin blocks used in the experiments were limited,waves reflected from the free and rigid boundaries of the gelatin block and the vibration after ballistic impact made the analysis of time-profile of pressure wave a formidable task. Thus,this study mainly focuses on the first positive phase of the pressure wave.

Even with all necessary precautions taken to ensure that the bullets impacted at the anticipated point, it may not be the case because of the dispersion of shooting.Moreover,it was also difficult to ensure that the line of impact was perfectly normal to the striking face;the bullet may not travel along the plane located with respect to the five gauges especially after penetrating through the layered armor.Thus,there were some differences in the maximum pressure at the same gauge for the same ammunition,as shown in Table 2. In order to reduce the influence of experimental factors,some values of the experimental results were further summarized in Table 3. In Table 3, for the average of the interval time (tb) between the‘twin peak’at different measured locations,the values of M43 group were the maximum, followed by the SS109 group, and those of Type 87 were the minimum.For the average of PAand PBat different measured locations, the values of M43 group were the highest, followed by the Type 87 group, and those of SS109 group were the lowest. For the average of the interval time (ta-t0) at all measured locations,the values of SS109 group were the maximum,followed by the Type 87 group (except some points), and most values of the M43 group were the minimum.

Fig. 4. (a) Pressure signals for SS109 group impacting at 966 m/s. (b) Pressure signals for Type 87 group impacting at 941 m/s. (c)Pressure signals for M43 group impacting at 688 m/s.

Table 3 Experimental results of the average of PA, PB, ta-t0 and tb.

From Fig. 4(a)-(c), it can be also found that the transient pressure in the ballistic blunt impact can be divided into three distinct phases without relation to the rifle bullet type.The first phase is the initial pressure wave front which had time duration of about 6-19 us from the ambient to peak pressure.The second phase is from the first peak to the second peak with the average time interval of about 17 μs. The second lower peak pressure appeared at ta+ tbafter the initial impact. This second phase was formed when the bullet penetrated the UHMWPE fiber-reinforced laminate backing,and subsequently the soft armor impacted by the deformed laminate backing began to compress the gelatin block.During the initial deformation of soft armor,the face of gelatin block which contacted the soft armor moved along the impact direction. The velocity of armor would grow to compress against the gelatin when the bullet penetrated the armor continuously, and the pressure wave propagated through the gelatin block. The third phase was from the second peak to the first trough of negative pressure which presented at ta+ tcafter the first peak. When the initial wave transmitted down the length of gelatin block, it was reflected back towards the transducers. Thus the reflecting tensile wave was obtained by the gauges.Generally, it can be seen that the tendencies of pressure curves obtained from different sensors were identical for different rifle bullets from Fig. 4(a)-(c).

3.2. Statistical results of the pressure wave’s parameters

The two-way ANOVA was used to investigate the effect of the two factors(bullet types and D)on the parameters of pressure wave(Pmax, PImaxand PPD). The statistical results were listed in Table 4 and discussed below.

3.2.1. Effect of bullet types and D on the Pmax

It can be found that the bullet type had a significant effect on Pmax(F=97.97,P＜0.05),so did the factor of D(F=107.12,P＜0.05).That is, for all three ammunitions, the value of Pmaxat certainlocation was significantly different(e.g.for SS109,Type 87 and M43 at gauge 1: mean = 0.51, s.d. = 0.12; mean = 0.72, s.d. = 0.02;mean = 1.03, s.d. = 0.11, respectively); for the same ammunition,the average of maximum pressure decreased with the increase of the travelled distance (Table 6). It can also be found that the interaction between bullet type and D had a significant influence on Pmax(F = 4.56, P＜0.05).

Table 4 Statistical analysis of Pmax, PImax and PPD for the three ammunitions.

3.2.2. Effect of bullet types and D on the PImax

From Table 4, it can be seen that the PImaxwas significantly affected by both the bullet type and D(F=13.26,P＜0.05;F=66.38,P＜0.05, respectively) with the maximum PImax(28.1 MPa μs at gauge 1) for M43 group. However, PImaxwas not affected by the interaction between bullet type and D (F= 2.09, P＞0.05).

3.2.3. Effect of bullet types and D on the PPD

It can be found that PPD was significantly affected by both the bullet type and D(F = 5.06, P＜0.05; F = 38.28, P＜0.05, respectively)with the longest PPD(82.67 μs at gauge 1)for SS109 group.However, the PPD was not influenced by the interaction between bullet type and D (F = 1.51, P＞0.05).

4. Data analysis and discussion

4.1. Pressure wave velocity

To determine the velocity of pressure wave,the beginning of the pressure signal was determined for all tests. This beginning was defined as the time when the pressure amplitude exceeded 0.1 MPa. In Fig. 5(a)-(c), the starting times were plotted as a function of the distance from the projection point of the impact point along ballistic line on the front surface of the gelatin block to the center of sensitive surface of each pressure sensor for SS109 group,Type 87 group,M43 group,respectively.A straight line was fitted through the points for every shot with the function as below.

Where t presents the time with the unit of second;D presents the distance of pressure wave propagation with the unit of meter; A presents the velocity of pressure wave propagation in the gelatin with the unit of m/s;B presents the intercept with the Y axis when the time equals zero.

The fitting results of the velocity of pressure wave for all shots were presented in Table 5 and Fig. 5. As shown in Fig. 5(a)-(c), it can be found that the fitting straight line of every shot was basically parallel to each other for the same ammunition,and these indicated that the experimental results were in good agreement.The average velocity of the pressure wave for all shots was 1343 m/s;and it was 7.38%smaller than Liu’s experimental result(1450 m/s in the 4°C/10 wt%ballistic gelatin)[19]due to the armor and ammunition used in the corresponding test,the measurement errors,non-uniformity of gelatin block and other factors. Thus, the method used to measure the pressure signals at different locations was considered to be reasonable and the data obtained from the experiment can be used to further analyze the characteristics of the pressure wave propagation in the gelatin block for different ammunitions.

4.2. Effect of bullet type on the pressure attenuation

Fig.5. Time that pressure wave reaches different pressure transducers as a function of travelled distance and the fitting curves: (a) SS109 group; (b) Type 87 group; (c) M43 group.

Table 5 Fitting results of the velocity of pressure wave for three ammunitions.

Table 6 Mean amplitude μ(Pmax),standard deviation σ(Pmax)and coefficient of variation of the pressure signals for three ammunitions.

To get some insight in the pressure attenuation, the maximum pressures of all shots were determined. The mean amplitude,standard deviation and coefficient of variant of maximum pressure of the five gauges were presented in Table 6. The pressure was caused by the local compression in the gelatin under ballistic blunt impact. Pmaxis the maximal instantaneous pressure recorded at each gauge in the gelatin. This important parameter has already been used in other studies on behind armor blunt trauma[6-9,14-18]. As shown in Table 6, it can be found that the largest differences in the amplitude are presented in the SS109 group.The amplitudes differ more than 20%at different sensors,which is twice as large as those of the other two groups. Moreover, it can be also seen that the pressure amplitude decreased from gauge 1 to gauge 5 for the same ammunition.From gauge 1 to gauge 5,the distance was a factor 2.87 as large,while the pressure amplitude decreased a factor 3.33. This decrease was faster than in the case of a point source with theoretical pressure attenuation proportional to the inverse of the travelled distance. Thus, it can be concluded that except for geometrical attenuation, the viscoelastic property of gelatin also decreased the pressure amplitude during the pressure wave propagation in the gelatin block.

Generally, the attenuation of the maximum pressure in the gelatin block can be assumed to be governed by Eq. (2) [26]:

Where,P（r）is the maximum pressure at an arbitrary location r;Pr0is the maximum pressure at a reference location r0;here,r0equals 3.16 mm, the average of the caliber of three ammunitions; α represents the attenuation coefficient of pressure wave propagation in the gelatin block.The value of Pr0and α could be obtained by fitting the data in Table 6 with Eq.(2).The fitting results of the maximum pressure for three ammunitions were presented in Fig. 6 and Table 7.

Fig. 6. Relation between average Pmax versus distance and fitting curves for the three ammunitions.

Table 7 Fitting results of the parameters for Eq. (2).

The fitting curves in Fig. 6 showed that the attenuation of maximum pressure propagation in the gelatin block could be accurately described by Eq. (2). As shown in Table 7, the fitting results indicated that the value of Pr0was also significantly affected by bullet type. The value of Pr0for the M43 group, Type 87 group and SS109 group were 28.17 MPa, 21.45 MPa and 17.76 MPa,respectively. The investigation of Crouch [27] indicates that the hardness of the core materials of the bullet and the sharpness of the nose(blunt,ogival,or conical)would affect the bullet’s penetration capability on the armor.As addressed in Section 2.1.2,the structure of SS109 is obviously different from those of Type 87 and M43;the mass of steel core of Type 87 is about 2.3 times heavier than that of SS109 (1.5 g vs. 0.66 g). Additionally, although Type 87 and M43 share the similar structure(that is,copper jacketed,lead sheath and steel core), the mass of the steel core of M43 is obviously heavier than that of Type 87. Since the three ammunitions used in the experiment are all cylindrical with an ogive-shaped nose and the impact kinetic energy was adjusted to the same level(ca.1850 J),it can be considered that the hardness of the core materials and the mass of the core would affect the bullet’s penetration behavior and the transient pressure wave propagation in the gelatin behind the armor.

For the influence of the hardness of the core materials,the lead core of SS109 is soft and deformable with relative low strength.When the lead core started to impact the ceramic composite plate at high speed,it deformed significantly on impact which made the kinetic energy of the bullet distribute in larger area; more energy would be absorbed by the abruption and deformation of the fibers during the penetrating process. However, the hardness and strength of the steel core of Type 87 and M43 are higher than those of lead.Thus,the extent of deformation or erosion of the steel core during the penetrating process would be lower than that of lead core,which made the kinetic energy distribute in smaller area;less energy would be absorbed by the deformation of fibers, and the dynamic deformation and speed of the body armor for Type 87 and M43 may be greater than those for SS109. Therefore, the energy transferred to gelatin for Type 87 and M43 would be more than that for SS109 and the pressure in gelatin for Type 87 and M43 would be higher than that for SS109.

As presented in Tables 1 and 6, it can be concluded that the heavier the steel penetrator was,the higher Pr0was.The small steel penetrator of the SS109 would erode quickly as it came into contact with the ceramic plate.Moreover,the mass of M43 steel cores was about 2.4 times heavier than that of Type 87, which made the velocity of M43 decay slower than that of Type 87, that is, the penetration ability of M43 would be stronger than that of Type 87.Thus,the energy transferred to gelatin through the body armor for M43 would be more than that for Type 87,and the pressure in gelatin for M43 was also relatively higher than that for Type 87.

In Fig. 6, it can be seen that the fitting curves for the three ammunitions were basically parallel to each other. Thus, it can be thought that the pressure-distance curve could be further characterized by the dimensionless pressure P/Pmax1and dimensionless distancer/r1, where Pmax1represents the average of maximum pressure at gauge 1 for the same ammunition; r1represents the average of the distance from the projection point of the impact point along ballistic line on the front surface of the gelatin block to the center of sensitive surface of gauge 1 for the same ammunition.

Fig. 7. Dimensionless curve of the mean amplitude for the three ammunitions.

The dimensionless pressure P/Pmax1and dimensionless distance r/r1are shown in Fig. 7. It can be found that the points for different rifle bullet at the same gauge were very close and can be fitted by the function:

Where, y = P/Pmax1, x = r/r1. The fitting curve is also plotted in Fig.7 with a=1.02,b=-1.012.This may further indicated that the tendencies of pressure propagation in the gelatin block were identical without relation to the bullet type.

Moreover,Courtney et al.[28]reviewed that pressure wave near 0.2 MPa can cause immediate incapacitation in laboratory animals and mild or moderate injuries may occur with local pressure levels in the range of 0.1-0.3 MPa. In our experiment, the maximum pressure at the position 260 mm away from the impact point was still greater than 0.2 MPa.Thus,it can be concluded that the ballistic blunt impact may cause mild or moderate injuries to the armored targets for the three ammunitions.

4.3. Effect of bullet type on the PImax

The mean amplitude, standard deviation and coefficient of variant of PImaxfor three ammunitions were presented in Table 8.Generally, in Table 8, it can be seen that the PImaxalso decreased with the increase of the distance from the impact point to the gauges for the same ammunition.At any measurement location,the average of PImaxfor the SS109 group was the minimum;from gauge1 to gauge 3 the values of M43 group were the maximum;however,from gauge 4 to gauge 5, the values for Type 87 group and M43 group were close to each other. The reason for this phenomenon may be that PImaxnot only depends on Pmaxbut also on the duration of the pressure applied. In addition, the coefficients of variant of PImaxat all measured locations were obviously higher than those of Pmaxfor M43 group and Type 87 group.PImaxcan be compared with the momentum, and refers to the amount of energy transferred to gelatin. The energy of pressure wave was mainly concentrated in the positive pressure zone during the impact process, and the pressure and pressure impulse are related to the energy. Thus,the coefficients of variation of Pmaxand PImaxbetween each measuring point for all three ammunitions were compared, as shown in Table 9.

Table 8 Mean amplitude μ(PImax),standard deviation σ(PImax)and coefficient of variation of the PImax for three ammunitions.

Table 9 Comparisons of the coefficients of variation of pressure attenuation.

In Table 9, it can be seen that the attenuation rate of Pmaxand PImaxof the wave front decreased with the increase of distance from 90 mm to 210 mm. The reason for this phenomenon may be that the pressure wave propagated in gelatin block with the form of spherical wave, and the energy per unit area decreased with the increase of propagation radius and wave front area,which led to the rapid attenuation of maximum pressure and impulse during propagation in the gelatin block. However, from 210 mm to 260 mm, the attenuation rate restarted to increase for both the maximum pressure and maximum pressure impulse.

4.4. Effect of bullet type on the PPD

Table 10 summaries the mean value, the standard deviations and the coefficient of variation of the PPD for all shots.In Table 10,it can be seen that the PPDs at different gauges were obviously different for the same ammunition, and the duration gradually decreased with the increase of travelled distance due to the geometrical effect and the viscoelastic property of gelatin. Moreover, at the same measurement location, it can be found that the PPDs of SS109 group were the longest,followed by Type 87 group,and those of M43 group were the shortest. The reasons for thisphenomenon may be that PPD not only depends on the initial velocity of bullet but also on the interaction time between armor and gelatin. On the one hand, the impact velocity of SS109 was the highest among three ammunitions, followed by Type 87 and the velocity of M43 was the lowest. On the other hand, because the steel penetrator of SS109 is the lightest and the strength of lead is lower than that of steel, the resistance of SS109 rifle bullet during penetrating the armor may be weaker than those for the other two groups; then the interaction time between soft body armor and gelatin was longer for SS109 group than those for the other two groups.

Table 10 Mean positive pressure duration(PPD)μ(T),standard deviation σ(T)and coefficient of variation of the PPDs for three ammunitions.

5. Conclusions

The transient pressure wave in the ballistic gelatin behind the NIJ class III body armor induced by ballistic blunt impact for three ammunitions was investigated experimentally. The pressure-time history profiles at different locations were recorded by five pressure gauges along the ballistic direction.The conclusions are listed below.

1.For the non-penetration impact on the armored gelatin block by rifle bullet, the pressure signals showed that twin peak and negative phase existed in the experiment.The twin peak appeared as the same as‘twin peak’in the soft armor,and the negative phase may be produced by the first shock wave reflection.

2. It can be found that the waveform and the twin peak of transient pressure wave appeared in the ballistic blunt impact were not related to the bullet type.However,the values of peak pressure at the same location for three ammunitions were significantly different,that is,the parameters of the pressure wave(Pmax,PImax,PPD) were significantly affected by bullet type and the travelled distance of pressure wave.

3. It can be concluded that the pressure amplitude decreased with the increase of travelled distance due to both geometrical effect and the viscoelastic property of gelatin. For the three ammunitions, the attenuation of maximum pressure at different locations in the gelatin block followed the similar law,which can be accurately described by P（r） = Pr0（r0/r）α.

Acknowledgment

This study is supported by the National Basic Scientific Research Project(Grant NO. JCKYS2019209C001),National Key Research and Development Program of China (Grant NO. 2017YFC0822301& Grant NO. 2018YFC0807206), National Natural Science Foundation of China (Grant NO.11772303).