ISSN 10283358, Doklady Physics, 2012, Vol. 57, No. 7, pp. 288–290. © Pleiades Publishing, Ltd., 2012. Original Russian Text © V.A. Morozov, Yu.V. Petrov, G.G. Savenkov, 2012, published in Doklady Akademii Nauk, 2012, Vol. 445, No. 3, pp. 286–288.
MECHANICS
Criterion of ShockWave Initiation of Detonation in Solid Explosives V. A. Morozov, Corresponding Member of the RAS Yu. V. Petrov, and G. G. Savenkov Received February 21, 2012
DOI: 10.1134/S1028335812070075
The criteria of the shockwave excitation of deto nation in solid explosives existing at present are reduced to experimentally established values of the critical parameters, with achievement of which partial or complete explosive transformation takes place in explosives. Such parameters are determined by fixing the presence or absence of explosive chemical trans formations under the action of shortterm pressures (from submicroseconds to tens of microseconds) on explosives, which substantially exceed both the quasi static and the dynamic durability of the explosives under investigation. Historically, one of the first determining parame ters of the process of shockwave excitation of detona tion is the value of the critical pressure pmcr at the shockwave front entering into the explosive [1]. How ever, it was shown that the critical conditions of exci tation of detonation in solid explosives under shock wave initiation depend also on the duration tin of its action instead of on the pressure amplitude alone. For this reason, the criterion described by the following equation was proposed for short pressure pulses:
pm2 t in = e1cr = const ,
(1)
where pm is the pressure applied to the explosive; e1cr is the constant dependent on the explosive and proper ties of the pulsepressure source (as a rule, the high velocity striker) [2]. Sometimes, criterion (1) is written in a more general form pmn t in = const (n > 0 ) [3]. Under the onedimensional loading with a rectangular pressure pulse acting on the explosivecharge surface, criterion (1) is the work accomplished by this pressure. Because the pulse pressure pm is related to the velocity ui of the pulseapplication surface by the relation
pm = ρ 0ui Di ,
where Di is the shockwave velocity in the explosive, and ρ 0 is the initial density of the explosive, it is possi ble to obtain another form of criterion (1): 2
pmt in (2) = pmuit in = ecr = const . ρ 0 Di However, criteria (1) and (2) approximately coincide with each other only when the initiation occurs before the initial shock wave runs along the explosive charge, or the initiated explosives have small relative volume of pores [4]. It is shown that criterion (2) describes well the experimental results in the region of small values of tin for relatively high values of the critical pressure pmcr [5]. For large tin , the energy criterion is not fulfilled differing appreciably from the experimental data. In addition to the critical value of the pressure and energy criteria (1) and (2), there are also other criteria of initiation of detonation in solid explosives [1, 4]: the value of the increment of the specific internal energy of the explosive compressed by the shock wave, the cri terion of the critical acceleration, the criterion of the minimum initiating pulse, and others. Thus, it is pos sible to ascertain that no unified criterion of shock wave initiation of solid explosives is formulated today. For the characteristic of the explosive sensitivity to the pulse loads, one uses both the depth of excitation of detonation L (the distance from the loading surface on which the normal detonation process arises) and the detonationdelay time tign . These two parameters are related as follows:
t ign = t exp − L , D where texp is the time experimentally measured before the onset of detonation, and D is the velocity of the steady detonation wave. For a charge of an arbitrary length H, the delay time is determined, for example, by the experimental gaptest method [5] with use of the following formula:
St. Petersburg State University, St. Petersburg, 199164 Russia email:
[email protected] 288
t ign = t exp1 − H ; D
CRITERION OF SHOCKWAVE INITIATION OF DETONATION tign, µs
289
tign, µs 5 PBX9407
4
PBX9501 4
3 t ign
3
3 t ign
3 2 2
t pign
1
t pign
1 0
1
2
3
4 p, GPa
tign, µs
2
3
4
5
6 p, GPa
tign, µs PETN
1.6
HMX
0.8
3 t ign
0.6
1.2 0.8
3 t ign
0.4
t pign
t pign 0.2
0.4 0 1.0
1.2
1.4
1.6
1.8 p, GPa
0
4
5
6
7
8
9 p, GPa
Dependence of the detonationdelay time on the initiation pressure for explosive compositions PBX9407, PBX9501, and ex plosives RETN and HMX; curves with points are experimental data, and curves without points are from calculations.
here, t exp1 is the experimentally detected time of pas sage of the detonation wave along the entire length of the explosive charge. Taking into account the variety of critical condi tions describing the excitation of detonation in explo sives, the new criterion of initiation of detonation in solid explosives is based on the concept of the “incu bation time” of the process, which has worked well in describing the dynamic transition processes in many divisions of continuum mechanics [6–8]. The proposed criterion in the general form is for mulated as follows: t
∫
t −t inc
α
⎛ p(s) ⎞ ⎜ p ⎟ ds ≤ t inc, ⎝ cr ⎠
(3)
where p(t) is the pulse pressure applied to the initiated explosive; t inc is the incubation time of evolution of the directdetonation process; pcr is the minimum critical pressure of charge initiation for a fixed density and the DOKLADY PHYSICS
Vol. 57
No. 7
2012
average size of explosive particles; t and s are the global and local time; and α is a constant. The incubation time t inc of the detonation process in this case is the parameter determining only the explosive properties and independent of the shock wave loading conditions of the charge. At such an approach to determining the incubation time as this parameter, it seemed to be possible to accept the min imum acoustic time t ac min (the time of motion of a lat eral rarefaction wave to the central charge portion) equal to the characteristic time of the chemicalreac tion development, which is found from the relation
dcr ; (4) 2c here d cr is the critical diameter of the initiated explo sive charge and c is the speed of sound in the detona tion products. However, both the critical diameter and the speed of sound in the detonation products, which amounts to threequarters of the detonation velocity, t inc = t ch = t ac min =
290
MOROZOV et al.
strongly depend on the charge density and dispersibil ity of crystals for the same explosive, while dcr depends additionally on the test conditions [2]. Therefore, the determination of the incubation time is an individual problem, and, in this work, is selected on the basis of the experimental results taken by us for approbation of the proposed criterion. We consider the use of the proposed criterion, for example, for the calculations of the pm − t ign depen dences, which are experimentally determined for many explosive compositions [9] and represent impor tant conditions of comparative shockwave sensitivity. As a rule, the analytical dependences between pm and tign can be presented in the form of ln t ign = A − ξpm as in [10] or log t ign = B − κlog pm as in [9]. Here, A, ξ, B, κ are the experimental constants. As an example, we consider two explosive compo sitions: one based on hexagen, PBX9407, another based on octogen, PBX9501, and also the most sensi tive of brisant explosives, PETN (in the domestic clas sification, tetranitropentaeritrite (TEN)) and HMX (octogen) taken from the handbook [9]. According to the experimental data listed in this handbook, in the case of rectangular loading pulses, we accept pcr = 1.2 GPa for PBX9407, pcr = 2.4 GPa for PBX9501, pcr = 1.2 GPa for PETN, and pcr = 4.4 GPa for HMX. The process incubation times t inc (in μs) are 2.5, 4.14, 1.46, and 1.0 for PBX9407, PBX9501, PETN, and HMX, respectively. These values of t inc are approxi d mately equal to t inc = cr determined for the average c0 bulk speeds of sound in solid explosives and the aver age critical diameters (with the exception of PETN; for it, the critical diameter was chosen equal to d cr ≈ 3.5 mm, to the average value between the critical diameter for the singlecrystal density (5 mm) and the technical density (2 mm) listed in Table 14 from [11]). Substituting the obtained values of the critical pres sure and the incubation time into criterion (3) and accepting α = 2 (the most widespread value for the criterion in the form of pmn t in = const [2, 3, 5]), we
obtain the curves of dependences t ign = f ( pm ), which are shown in the figure. In the same figure, we show the experimental curves constructed from the results of shockwave experiments [9]. It can be seen that the proposed criterion enables us to describe the experiments on the shockwave initia tion of solid explosives with satisfactory accuracy (although a stronger distinction in the left portions of curves is observed for PBX9407; however, taking into account that the spread in experimental data exceeds 16%, even this result can be considered as satisfac tory). Thus, the proposed criterion enables us to avoid carrying out expensive experiments on determining the pm − t ign dependences restricting ourselves to one– two experiments. REFERENCES 1. R. Stresso and J. Kennedy, Detonation and Explosives (Mir, Moscow, 1981) [in Russian]. 2. Physics of Explosion, Ed. by L. P. Orlenko (Fizmatlit, Moscow, 2002) [in Russian]. 3. P. J. Haskins and M. D. Cook, in Proc. XIV Intern. Symp. on Detonation (Idaho, USA, 2010). 4. P. Hove, R. Frey, B. Taylor, and V. V. Boil, in Detonation and Explosives (Mir, Moscow, 1981) [in Russian]. 5. B. L. Glushak, S. A. Novikov, and V. M. Bel’skii, Exci tation of Detonation Process in Solid Heterogeneous Explosives by Pulse Loads (VNIIEF, Arzamas16, 1993) [in Russian]. 6. N. F. Morozov and Yu. V. Petrov, Dokl. Phys. 37 (8), 964 (1992). 7. Yu. V. Petrov, Dokl. Phys. 49 (4), 621 (2004). 8. V. A. Bratov, L. M. Isakov, and Yu. V. Petrov, Dokl. Phys. 53 (10), 612 (2008). 9. Los Alamos Series on Dynamic Material Properties: Last Explosive Property Data, Ed. by I. Gibbs and Al. Popo lato (Los Alamos, 1981). 10. I. Vanpoperuynghe, I. Soret, H. R. Parsons, et al., in Proc. VIII Intern. Symp. on Detonation (Albuquerque, New Mexico, 1985). 11. G. T. Afanas’ev and V. K. Bobolev, Impact Initiation of Solid Explosives (Nauka, Moscow, 1968) [in Russian].
Translated by V. Bukhanov
DOKLADY PHYSICS
Vol. 57
No. 7
2012
