In the test, the charges were placed vertically on a trestle in the air 1.5m above the ground. The booster used was JH-14, and the initiating agent was 8# detonator. Two lines of pressure transducers with an angle of 60° were distributed around the blast center. Each line had nine measuring points designated as No.1-9 to monitor the shock wave pressure-time history. The stand-off distance of two lines from the measuring points to the explosion center are 2.73,3.62, 4.54, 5.5, 6.36, 7.3, 9.1, 11.0 and 12.8m, respectively. The high speed camera and infrared thermometer were placed 100 meters away from the explosion center, to record fireball evolutions and its surface temperature. Fig.1 shows the layout between experimental device and explosion center.
2.1 Shock wave parameters
The pressure transducers measure the voltage value ΔU, which is converted into the peak air pressure Δp by Eq.(1), and then calculates the impulse I with Eq.(2). Values of Δp and I determined on the basis of two pressure histories are summarized in Table 1. Fig.2 shows the blast wave pressure-time curves of TNT at stand-off distance of 3.62m and 6.36m on two contrast lines. It can be seen that the arrival times of the blast wave peak pressure at the same distance are basically the same, and the peak pressures are in slightly different, which may be caused by the flatness of the ground in the experimental site.
Δp=(ΔU)/s(1)
I=∫t1t0Δpdt(2)
Where s is the transducer sensitivity; t0 and t1 are start time and end time of positive pressure, respectively; Δ p is the peak air pressure.
From Table 1, we see that the peak pressure and impulse of AE at different stand-off distances are both significantly higher than those of TNT. The peak pressure Δp and impulse I improved by 33.1% and 28.9% at No.1 position(2.73m), respectively. The results of experimental overpressure and impulse data in Table 1 are shown in Figs.3(a)and(b). As shown, the fitted curves in each figure have the similar trends. The overpressure Δp and impulse I of AE are always higher than those of TNT in the near field, however, the gap is very small in the far field. This is because the shock wave is a spherical wave, which is gradually clouded and rapidly attenuated during propagation.
Fig.2 The shock wave pressure-time curves at stand-off distance of 2.73m and 5.5m on two contrast lines
Table 1 Values of Δp and I obtained from the overpressure histories
Fig.3 The fitted curves of shock wave data along the stand-off distance
2.2 Heat effect parameters
For most objects, heat effect may change properties of the targets as theirs internal temperature rise, even creep orbuckling[21-22]. Obtaining the heat effect data is of great importance to study the power of AE. The infrared thermometer was used to measure the surface brightness of the fireball, and its surface temperature could be evaluated by means of the following expression[23].
L=ε(T)T4σ/π(3)
Where L stands for the brightness of the object; ε(T)means the total emissivity of the object, generally is among 0.3-0.45, which was taken 0.35 here [23-24]; Stephen boltzmann's constant 5.67×10-8 W/(m2·K4). T refers to the absolute temperature of the object.
Temperature higher than 1000℃ were plotted in Fig.4.
Fig.4 The fitted curves of temperature histories
From Fig.4 we can see that duration is 320ms for AE, but 260ms for TNT. When temperature higher than 2000 ℃, the duration is 140ms for AE, but only 20ms for TNT, the former value is 7 times that of the latter, AE are more effective at high temperatures. Besides, after the temperature reaches its maximum value, it begins to decay, but the attenuation curve of AE is slower than that of the examined TNT charge due to the combustion of Al particles included only in AE. The set of images captured by the high speed camera are presented in Fig.5. The image analysis was employed to quantify the fireball size, as well as its characteristic features with time. It could be seen that the fireball shape of AE is flatter than TNT, and AE owning a larger fireball volume at the same moment. Both fireball temperatures of the two explosives have the feature of high center temperature and low surrounding temperature, even though there are also differences, the TNT fireball temperature decays monotonously from the center to the periphery, and there are several high temperature zones scattered in AE explosive fireball. After 100ms, under the action of ground reflected pressure and rarefaction wave, the fireball begins to gradually exhibit ineffectiveness. When the fireball temperature decay to 1000℃, the size of the fireball of AE attained its maximum diameter 4.8m, and TNT is only 4m, the former is 1.2 times the latter.
Fig.5 Flame propagation after explosion of TNT and AE in the open field before 100ms by a high speed camera
2.3 Power evaluation of the AE
Through experiments presented in the previous section and analysis, one can observe that the main destructive effects of AE in the free field are shock wave and heat effect[15-16,18]. When assessing the power of AEs, it is inaccurate to take blast pressure or detonation heat as the object of comparison. As we had confirmed when assessing the power of AE only with detonation heat, the calculated overpressure data was 48% higher than the experimental data[20]. On the other hand, a large proportion of Al power included in AE are used to generate the heat, the explosion characteristics of AE cannot be fully manifested only by the comparison of overpressure.
Theblast wave effects are not only related to the magnitude of peak air pressure, but also to the impulse. p-I damage criterion is applicable to most of the impacted targets. So, the shock wave power of non-ideal explosive(Eq.(4))is expressed as a function of the overpressure and impulse.
Heat effects are mainly reflected in diameter, duration and surface temperature of the fireball. If we agreed the diameter and duration data of the fireball are those of the surface temperature higher than a certain value(take 1000℃ here), the parameters of the heat effects could be reduced to two reference values(diameter and duration). The power of the heat effects of AE can be expressed by Eq.5.
qshock=α1qΔp+α2qI(4)
qheat=β1qD+β2qt(5)
where qΔp,qI,qD and qt stand for TNT equivalent of overpressure, impulse, fireball diameter and fireball duration, respectively. qshock and qheat refer to TNT equivalent of shock wave and heat effect, respectively. α1, α2, β1, β2 are weight coefficients.
According tothe dimensional analysis[25], the shock wave overpressure and impulse of TNT can be described as Eqs.(6)and(7), the diameter and duration of the fireball can be fitted by using the following Eqs.(8)and(9)[26].
Δp=a(m3)/r+b((m3)/r)2+c((m3)/r)3(6)
I=A(m2/3)/r(7)
D=d·m0.32(8)
t=f·m0.32(9)
Where m and r refers to the quality of TNT and the distance from the measuring points to the blast center, kg and m; D and t stand for the diameter and duration of the fireball, m and s; a, b, c, A, d, f are correction factors.
The shock wave data and fireball data of TNT obtained from the experiments were substituted into Eqs.(6)-(9)respectively. The coefficients contained in the Eqs. were determined by fitting with the software of Matlab, and the results are as follows:
Δp=-0.44×(m3)/r+3.9×((m3)/r)2-2.36×((m3)/r)3 (10)
I=280.6×(m2/3)/r(11)
D=2.255×m0.32(12)
t=0.147×m0.32(13)
The overpressure and impulse data of AE obtained from the experiment were put into Eqs.(10)and(11), respectively, the value of m inverse solved were then divided by the quality of AE, the corresponding TNT equivalents of shock wave overpressure and impulse of AE at different measuring points were gained. And then, with Eqs.(14)and(15), the averaging TNT equivalent of overpressure and impulse were solved, the results are1.38 and 1.37 respectively. Bring the maximum fireball diameter of AE into Eq.(12), the TNT equivalent qD converted from the maximum diameter of the fireball was obtained 1.76. The fireball duration of AE was substituted into Eq.(13), and the TNT equivalent qt embodied the fireball duration equals to 1.88.
qΔP=1/n∑ni=1qΔPi(14)
qI=1/n∑nj=1qIj(15)
where qΔPi and qIj stand for TNT equivalent of overpressure and impulse at different gauge points. n refers to the total gauge numbers, here, it equals to 9.
The comprehensive explosion power of AE should be the weighted average of TNT equivalent of shock wave effect and heat effect, described as Eq.(16).
qTNT=ε1qshock+ε2qheat(16)
Where qTNT stands for the power of AE; ε1,ε2 are weight coefficients.
When we use Eqs.(4)-(16)to evaluate the blast power of AE, considering the damage effects are attributes of AE itself, ignoring the diversity of damage modes sensitiveness to different targets, the shock wave overpressure, impulse, diameter and duration of fireball are on equal footing. So, we take α1, α2, β1, β2, ε1, ε2 all equal to 0.5. By calculating with the above Eqs., we finally get the explosive power of this kind AE is 1.56 times TNT.
