ISSN 0010-5082, Combustion, Explosion, and Shock Waves, 2014, Vol. 50, No. 5, pp. 612–621. c© Pleiades Publishing, Ltd., 2014.

Original Russian Text c© Yu.V. Davydov, A.S. Gubin.

Dependences of the Detonation Velocity

and Propellant Performance of Metallized Explosives

on the Charge Density and Additive Content

UDC 534.222.2Yu. V. Davydova and A. S. Gubina

Published in Fizika Goreniya i Vzryva, Vol. 50, No. 5, pp. 123–133, September–October, 2014.Original article submitted October 16, 2013; revision submitted February 10, 2014.

Abstract: The dependences of the detonation velocity and the propellant performance measuredusing the M-40 technique on the charge density for aluminized explosives with different mass frac-tion of Al were studied. The fractions of the energy of Al combustion utilized during the chemicalreactions and during the acceleration of the flyer plate were estimated. Regression dependences ofthe detonation velocity and the propellant performance on the charge density were obtained. Theeffect of the addition of particulate Al, Ti, Zr, and W in an amount of 5–30% on the detonationvelocity of high-density explosive charges based on plasticized RDX was investigated. It is foundthat the reduction in the detonation velocity with the addition of various metallic additives is de-termined by the longitudinal sound velocity of the additive, and not by its density. Simple formulasfor calculating the detonation parameters of high-density metallized explosives were obtained.

Keywords: detonation velocity, propellant performance, explosives, density, sound velocity, par-ticulate aluminum.

DOI: 10.1134/S0010508214050165

INTRODUCTION

The dependences of the detonation parameters andpropellant performance on the charge density are funda-mental characteristics of explosives (HE). The detona-tion wave velocity has been the subject of many exper-imental studies [1–16]. In high-density charges of mix-tures of powerful explosives with both negative and pos-itive oxygen balance, the detonation velocity (and thepressure and particle velocity of detonation products)has been found to decrease with the addition of partic-ulate metals. It has been established that the additionof smaller-size particles leads to a greater decrease inthe detonation parameters [2]. Furthermore, inert ad-ditives (talc, LiF, and NaCl) often provide a smallerreduction than Al additives.

Various hypotheses have been proposed [1, 3, 17] toexplain the decrease in the detonation velocity. Analysis

aResearch Institute of Mechanical Engineering, Moscow,125212 Russia; vitadavidov@yandex.ru;algoubin@yandex.ru.

of these hypotheses [18] has shown that the physicallyclear reasons for the reduction are the energy losses dueto compression, heating, and acceleration of the additiveparticles. It has been shown [19] that thermal equilib-rium in the chemical reaction zone is established for Aladditives with a particle size of 5 μm. However, it hasbeen found [14] that as the Al particle size decreasesto 0.1 μm, the detonation parameters continue to de-crease, which cannot be explained from the position ofsaid energy losses.

On the other hand, most of the experiments havebeen conducted with aluminized explosives. The effectof particulate metals with widely varying physicochem-ical properties on the detonation parameters of phleg-matized HMX were investigated in [9], but the differentporosity of the charges of metallic mixtures complicatesthe interpretation of the results.

Various methods for predicting the detonation pa-rameters of metallized compounds have been developedassuming that the additive is inert. Some of these meth-ods are based on the assumption of the inversely pro-

612 0010-5082/14/5005-0612 c© 2014 by Pleiades Publishing, Ltd.

Dependences of the Detonation Velocity and Propellant Performance 613

Fig. 1. Schematic of the setup for recording the det-onation velocity: (1) electric detonator; (2) explosivecharge; (3) ionization sensors.

Fig. 2. Detonation velocity versus charge diameter:(1) okfol-3.5 (ρ = 1.77 g/cm3); (2) A-IX-1 (ρ =1.66 g/cm3).

portional relationship between the detonation velocityand the density of the additive [20, 21] and the otheron the assumption that the detonation velocity of themixture is proportional to the sound speed in the addi-tive [18, 22, 23]. At the same time, new experimentaldata frequently conflict with the results of calculations.In this paper, we present new experimental data whichare necessary to refine the computation models.

DETONATION VELOCITY

A reliable characteristic of detonation that can bemeasured with maximal accuracy is its velocity. In ourexperiments, steady-state detonation velocity was mea-sured using an electrocontact method according to theRussian State Standard (GOST) No. V3250-75. In allexperiments, except otherwise specified, the detonationvelocity of 20 mm diameter charges was measured ona base of 100 mm using ionization sensors fabricated oftwo strips of copper foil 50 μm thick, which were spaced1 mm apart at the center of the charge. The measure-ment base was monitored with a micrometer. An addi-

tional charge of the test explosive 40 mm high, whichprovided the formation of a steady detonation wave wasplaced between the explosive studied and the first pairof sensors, and another charge, 20 mm high, was placedbehind the second pair of sensors (see Fig. 1).

The time required for the detonation wave to passthrough the measurement base was recorded by an I2-24meter of time intervals with an error of 2 ns. In anothervariant, we used a ChZ3-64 frequency meter, whichrecords time with an accuracy of 1 ns. Thus, the in-strumental (systematic) error of the detonation veloc-ity measurement did not exceed 10 m/s. Each obtainedvalue is the average of three parallel measurements.

Aluminized Pressed Compositions

The dependence of the detonation velocity D onthe density ρ for phlegmatized HMX (okfol-3.5), phleg-matized RDX (A-IX-1), and their mixtures with partic-ulate aluminum of different brands with a mass contentα = 0–20% was determined in a relatively narrow rangeof relative densities of charges of 0.88–0.98. The choiceof high-density charges is due to the fact that for low-density charges of limited diameter (20 mm), the prob-ability of nonideal detonation regimes increases [24].

Curves of detonation velocity versus charge diame-ter presented in Fig. 2 show that the limiting diametersfor okfol-3.5 are d ≈ 15 mm, and those for A-IX-1 ared ≈ 10 mm. Thus, measurements in the range of max-imum charge density were carried out at a diameter ofboth charges higher than the limiting detonation diam-eter.

To verify that the detonation velocity for low-density charges was also measured in the region of thesteady regime, we carried out relevant measurements forokfol-3.5, which has a greater limiting detonation diam-eter. Charges of diameter 20 and 38 mm at a minimumdensity charge ρ = 1.64 g/cm3 were used. The similarityof the obtained velocities (D = 8.39 and 8.34 km/s, re-spectively) confirms that the detonation wave is steadyin the investigated range of density. The dependencesD(ρ) were approximated by linear regression equationswith a correlation coefficient of 0.991–0.999, the stan-dard error of the estimation of D was 4–40 m/s, andthat of the slope ∂D/∂ρ was 1–5%. The results ob-tained and the data of [9] for HMX and the data of [15]for bis-(2,2,2-trinitroethyl)nitramine (BTNEN) and itsmixture with 25% ASD-6 aluminum are shown in Ta-ble 1.

It is known that the addition of low-compressibilityinert additives to explosive increases the slope of the de-pendence D(ρ) due to a decrease in the compressibilityof the mixture [25]. It can be suggested that increasing(within reasonable limits) the mass fraction of the ad-

614 Davydov and Gubin

Table 1. Detonation velocity versus charge density

Explosive compositionD = A+Bρ Correlation

coefficientCharge

diameter, mmA, m/s B, (m/s)/(g/cm3)

HMX∗ 2438 3542± 573 0.9403

Okfol-3.5 1513 4081± 113 0.9984 20

Okfol-5.5 −655 5229± 221 0.9938

Okfol-5.5 −1774 5994± 110 0.9988 10

Okfol-3.5 + 14% ASD-1 −2827 6121± 295 0.9988

Okfol-5.5 + 10% ASD-1 −2722 6274± 305 0.9953

Okfol-5.5 + 15% ASD-1 −3378 6453± 225 0.9982 20

Okfol-5.5 + 20% ASD-1 −1580 5315± 481 0.9840

A-IX-1 1983 3750± 722 0.9820

Gekfol-5.5 (A-IX-10) 1854 3871± 49 0.9999 15

RDX + 30% ligaments 2182 3395± 46 0.9999

A-IX-1 + 10% PAP-2 −706 5083± 61 0.9995

A-IX-1 + 10% ASD-4 −2964 6469± 383 0.9914

A-IX-1 + 14% ASD-1 −3028 6396± 313 0.9964

A-IX-1 + 20% ASD-1 −2353 5826± 72 0.9999 20

BTNEN 4226 2178± 79 0.9987

BTNEN∗∗ 1793 3592± 35 0.9999

BTNEN + 10% PAP-2 3213 2509± 22 0.9999

BTNEN + 25% ASD-6∗∗ −1489 4760± 165 0.9994

Notes: ∗Data of [9], relative densities of 0.840–0.998. ∗∗Data of [15], relative densities of 0.974–0.995.

ditive α leads to a monotonic increase in ∂D/∂ρ. How-

ever, as can be seen from Fig. 3, the dependences∂D

∂ρ(α)

have a maximum at α ≈ 10–15%.Note that the position of the maxima in Fig. 3 coin-

cide with the maxima of the propellant performance forthese mixtures determined for expansion of steel tubesand models by flash radiography in the middle section ofthe shells [12] (see Fig. 4). A ∅20× 120 mm charge witha steel plate 2 mm thick disposed at its end was placed ina tube with a wall thickness of 5 mm. The shell models6 mm thick had a cavity of size ∅35× 80 mm; the thick-ness of the bottom and cover of the model was 10 mm.

This fact and an increase in ∂D/∂ρ with the ad-dition of particulate Al to 15% suggest that partial ox-idation of Al may occur even in the chemical reactionzone of powerful explosives, i.e., with 10–100 ns [26].This may be associated not only with an increase inthe elasticity of the mixture with the addition of Al,but also with the participation of the Al additive inthe physicochemical processes occurring in the chemi-

cal reaction zone. Among these processes are the loss ofenergy in compression, heating, and acceleration of theadditive [19], energy release due to partial combustionof the additive, and the redistribution of the elastic andthermal energy of the detonation products in favor ofthe latter [27]. Increasing α increases the elasticity ofthe explosive (detonation products) and, probably, theamount of the energy released during combustion of Al(especially with increasing density), i.e., the pressure ofthe detonation products. However, the energy losses,in particular those relating to its redistribution also in-crease. The ratio of the negative and positive factors islikely to determine the rise and subsequent descent of

the curves of∂D

∂ρ(α) in Fig. 3.

The addition of 3.5% phlegmatizer to HMX in-creases the value of ∂D/∂ρ by 15%, and the increasein the amount of phlegmatizer from 3.5% (okfol-3.5) to5.5% (okfol-5.5) leads to a further 28% increase in theslope of the dependences D(ρ) (see Table 1 and Fig. 5).This may be due to two factors. First, increasing the

Dependences of the Detonation Velocity and Propellant Performance 615

Fig. 3. Dependence of the slope of the lines ofD(ρ) on the mass fraction of Al in mixtures withA-IX-1 (1) and okfol-3.5 (2).

Fig. 4. Dependence of the expansion velocity of theshells on the mass fraction of Al in the explosive:(1) model, A-IX-1 + PAP-2; (2) tube, okfol-3.5 +ASD-1; (3) tube, A-IX-1 + ASD-1.

amount of the inert impurity can increase the limitingdetonation diameter, especially for low-density charges.In other words, the points inn the curve of D(ρ) forlow-density charges of okfol-5.5 can be underestimated.Second, more likely, the effect reported in [28] takesplace. In the detonation wave, the inert additives candecompose to an additional amount of C and N atomsin the chemical reaction zone. The excessive concentra-tion of the fuel shifts the equilibrium of the formationreactions of oxides to the right:

C + O2 → CO2 +Q1;

H2 + 0.5O2 → H2O+Q2.

Fig. 5. Detonation velocity versus charge density forA-IX-1 and its mixtures with aluminum: (1) HMX;(2) okfol-3.5; (3) okfol-5.5.

As a result, additional energy is released, which is thegreater the higher the pressure in the detonation prod-ucts (i. e., the higher the charge density) and the higherthe concentration of the phlegmatizer in the mixture.As seen from Table 1 and Fig. 5, the value of ∂D/∂ρincreases in the series HMX–okfol-3.5–okfol-5.5.

As the charge diameter is decreased to 10 mm, thevalue of ∂D/∂ρ for okfol-5.5 increases by ≈15% (seeTable 1). This is probably due to an increase in thenonideality of the detonation of charges of 10 mm di-ameter with decreasing density [24].

It is important that for a mixture of A-IX-1 with10% ASD-4, the slope of the dependence D(ρ) is 27%larger than that for a mixture with 10% PAP-2 (seeTable 1 and Fig. 6). It has been shown [29] that in testsusing a ballistic pendulum, the effect of the addition ofASD-4 was twice the effect of the addition of PAP-2.Thus, the dependences D(ρ) can serve as a qualitativecharacteristic of the effectiveness of additives.

Measurements of ∂D/∂ρ for BTNEN and its mix-tures with talc and PAP-2 particulate aluminum wereperformed in [11]. The choice of BTNEN is due tothe fact that for this explosive oxidizer, the heat of ex-plosive conversion does not depend on the charge den-sity [30], so that conversion of the dependence D(ρ)into the dependence of D (or D2) on the volume heatof explosion reduces to the multiplication of the val-ues of the abscissa by a constant—the specific heat ofexplosion of BTNEN. Note that the constructed depen-dences D(ρ) are much more flatter than those in [15] forboth BTNEN and its mixtures with Al.

The obtained results were used to calculate thefraction of the energy of Al combustion released in thechemical reaction zone, which was 3–15%, dependingon the charge density. It is important to emphasize

616 Davydov and Gubin

Fig. 6. Detonation velocity versus charge density forA-IX-1 and its mixtures with aluminum: (1) A-IX-1;(2) A-IX-1 + 10% PAP-2; (3) A-IX-1 + 10% ASD-4.

the physical meaning of these estimates. We have ac-tually neglected the complex processes of conversion ofthe stored energy of the charge into the energy releasedunder the specific gas-dynamic conditions (in this case,the chemical reaction zone). In addition, we do nottake into account the energy redistribution between theelastic and thermal components [27] and the transferof the released energy to the detonation wave front. Inthis approach, we estimate not the actual portion of theburnt Al, which can be much higher, but that fractionof the energy of Al combustion that is perceived by aparticular response function, in this case, the velocityof the detonation wave.

Metallized CompositionsBased on a Thermoplastic Binder

Mixtures with particulate metal additives were pre-pared on the basis of an explosive containing RDX and30% active thermoplastic binder. Mixtures with 5, 10,20, and 30% particulate additives of Al (PAP-2), Ti,Zr, and W, with a particle size of 10–50 μm, wereinvestigated. The high binder content provided suffi-ciently high density of the charges produced by thermalpressing. The detonation velocity was measured by themethod described above.

The results are shown in Fig. 7. It can be seenthat the detonation velocity of the mixtures Dmx is notinversely proportional to the density of the metal addi-tive ρm, as suggested, for example, in [20] since tung-sten (ρ = 19.35 g/cm3) has a greater density than Zr(ρ = 6.51 g/cm3) and decreases the detonation veloc-ity to a lesser extent. According to [9], the additionof 10% Nb (ρ = 8.57 g/cm3), whose density is greater

Fig. 7. Detonation velocity versus mass fraction ofthe additive in the explosive.

than that of Zr, also reduces the detonation velocity ofokfol-3.5 to a lesser extent than the addition of 10% Zr.

CALCULATIONOF THE DETONATION VELOCITY

OF METALLIZED EXPLOSIVES

The relative position of the curves of Dmx(α) inFig. 7 is largely determined by the longitudinal velocityof sound in the additive (cm) [18]. Indeed, the metalis generally an elastic–plastic medium in which a shockwave of two-wave configuration propagates [31]. In thiscase, the velocity of propagation of the elastic precur-sor can be estimated with high accuracy as cm. At thesame time, in [18], the formula for calculating the deto-nation velocity of metallized explosives, which was usedto calculate the other detonation parameters, was notvalidated:

Dmx = Dex(1− α) + cmα. (1)

Here Dex is the detonation velocity of velocities at thenominal density of ρex, which can be calculated fromthe well-known dependences D = A + Bρ experimen-tally established for many explosives. The nominal den-sity of the explosive in the charge is given by the equa-tion ρex = (1 − α)/(1/ρmx − α/ρm), where ρmx is thedensity of the mixture and ρm is the initial density ofthe metallic additive.

The relationship between Dmx and cm can be es-tablished using the well-known formula for the detona-tion velocity obtained from the laws of conservation ofmass and momentum. For a mixture of an explosivewith metal, assuming that the pressures in the explo-sive and additive are equal and neglecting the initial

Dependences of the Detonation Velocity and Propellant Performance 617

pressure, we write this formula as

Dmx = V0mx

(p

V0mx − Vmx

)1/2

,

where V0mx is the initial specific volume of themixture, Vmx is the specific volume of the shock-compressed mixture, and p is the pressure at the frontof the detonation wave.

Expressing the specific volume of the mixture interms of the specific volumes of the explosive (Vex) andmetal (Vm)

Vmx = (1 − α)Vex + αVm,

we obtain

Dmx = [(1− α)V0ex + αV0m]

(p

1− αΔVex

)1/2

×(1 +

α

1− α

ΔVm

ΔVex

)−1/2

, (2)

where ΔVm and ΔVex are the differences between thespecific volumes ahead of the front and at the frontof the detonation wave for the metal and explosive,respectively.

In (2), we replace the ratio of the compressibilitiesof the explosive and additive by the ratio of their waveimpedances (ρexDex/ρmcm)2 and rewrite the formula as

Dmx = Dex(1− α)1/2(1 +

αρex1− α

ρm

)

×[1 +

α

1− α

(ρexDex

ρmcm

)2]−1/2

. (3)

Comparison of the calculations with experiment (78 val-ues) shows that formula (3) is only 0.1% (RMS error≈3%) more accurate that the previously proposed for-mula (1). Table 2 compares the results of calculationwith those of our experiments.

Formulas (1) and (3), together with the expres-sion of [18] for the polytropic index of the mix-tures nmx = nex + 2.5α, allows calculating the otherparameters of the detonation mixture. The accuracy ofthe estimation of detonation pressure (60 experimentalvalues) was ≈7%.

For physical validation of formula (1), we ex-pand expression (2) in a series in the parame-ter α/(1− α)(ΔVm/ΔVex), which is substantially lessthan 1 for all investigated mixtures (except for the mix-tures with Mg), and drop terms of order higher than 1.Then,

Dmx = [(1− α)V0ex + αV0m]

×(

p

1− αΔVex

)1/2(1− α

1− α

ΔVm

ΔVex

).

Separating the terms at Dex and cm, we obtain

Dmx = Dex

[(1− α)1/2 − α

2(1− α)1/2

ΔVm

ΔVex

]

+ cm

[α

(1− α)1/2

(ΔVm

ΔVex

)1/2

− α2

2(1− α)3/2

(ΔVm

ΔVex

)3/2].

Estimates show that for α � 0.3, the numerical val-ues of the expressions in square brackets at Dex andcm practically coincide with the coefficients 1 − αand α in formula (1). The natural limitations ofthe computation scheme follows from the requirementα/(1 − α)(ΔVm/ΔVex) < 1: α < 0.5 and ρmcm >ρexDex. The requirement for the lower compressibil-ity of the additive compared to the explosive (ρmcm >ρexDex) is not satisfied for Mg. We also note that, ac-cording to the physicochemical model of the detonationof metallized explosives [27, 32], confirmed by experi-mental results [28] and numerical calculations [33], it isassumed that cm < Dex, which is not valid for additivesof Be and crystalline boron.

In the above scheme for calculating the detonationparameters, as in other computation schemes [18–23], itis assumed that metallic additives are inert in the chem-ical reaction zone. At the same time, some papers [8–11]reported on the possibility of partial combustion of Alwithin the chemical reaction zone. This is also indi-cated by the graphs in Fig. 8, which shows the dataof Fig. 7 as a function of the partial density of the ex-plosive in the mixture charge, defined by the formulaρpartial = (1 − α)ρmx. The graph in these coordinatesclearly shows the effect of various additives placed in theair pores of the explosive charge. As can be seen fromFig. 8, the introduction of metallic additives into thepores of the explosive can totally have both a negativeand positive effect on the detonation velocity.

The error of the detonation parameters estimatedby the proposed method increases significantly withincreasing charge density and increasing oxygen con-tent in the explosive. The detonation velocity andpressure of aluminized explosives-based mixtures withvarious oxygen balances (OB) were measured by amagnetoelectric method to determine the role of theoxygen content in the explosive. As such explosives,in addition to okfol-3.5 (OB = −22%), we investiga-ted N,N-bis(2,2,2-trinitroethyl)ethylenedinitrodiamine(BTNEEDND, OB = 0) [34], which contains the sameamount of phlegmatizer as okfol (3.5%), and BTNEN(OB = +16.5%). In mixtures based on explosives withnegative OB (RDX and HMX), containing 27–30% Al,the calculated detonation velocities coincided with the

618 Davydov and Gubin

Table 2. Detonation velocity of plasticized RDX with metallic additives

Explosive Additive cm, m/s α, % ρmx, g/cm3

Detonation velocity, m/s

experimentcalculation

formula (1) formula (3)

— — 0 1.720 8020 — —

Al(PAP-2)

6400

5 1.741 7920 7905 7912

10 1.774 7910 7825 7839

20 1.841 7760 7657 7683

30 1.917 7620 7500 7534

RDXwith 30% active

binder

W 5320

5 1.796 7860 7867 7831

10 1.890 7750 7743 7669

20 2.097 7450 7466 7301

30 2.346 7080 7173 6894

Zr 4360

5 1.737 7650 7688 7725

10 1.828 7630 7573 7646

20 1.965 7230 7164 7295

30 2.050 7085 6609 6756

5 1.711 7785 7734 7721

Ti 6163 10 1.780 7700 7690 7665

30 1.999 7300 7249 7142

Table 3. Detonation parameters of aluminized explosives

Explosive Additive α, % ρmx, g/cm3Experiment Calculation

Dmx, m/s p, kbar Dmx, m/s p, kbar

Okfol-3.5 ASD-4

0 1.724 8660 294 — —

10 1.817 8480 296 8515 286

20 1.878 8230 292 8269 265

30 1.923 7980 273 7970 240

Phlegmatized BTNEEDND PP-1

5 1.774 8610 304 8593 290

10 1.801 8530 298 8466 278

20 1.852 8420 288 8197 254

27 1.889 8300 282 8007 239

BTNEN PP-10 1.920 8800 — — —

27 2.033 8340 — 7870 —

experimental values or were lower by less than 100 m/c,whereas in mixtures based on explosives with zero OB,the underestimation of the calculated values comparedwith the experimental results increased to 300 m/s, andfor mixtures with a positive OB, to 450 m/s (Table 3).This is further indirect evidence of partial combustion ofAl in the chemical reaction zone of powerful explosives.Other evidence of the possibility of partial combustion

of particulate metal additives to the Jouguet plane canbe obtained by examining the dependence of the deto-nation velocity on the charge density [11].

At the same time, analysis [18, 35] of the causesof the reduction in the detonation parameters with theaddition of particulate metals has shown that this effectis largely due to a decrease in the elastic energy and anincrease in the thermal energy during formation of poly-

Dependences of the Detonation Velocity and Propellant Performance 619

Table 4. Flyer plate velocity versus charge density

Explosive compositionW40 = A+Bρ Correlation

coefficientNumber of pointsversus W40(ρ)A, m/s B, (m/s)/(g/cm3)

Okfol 128.7 1086.4 ± 43 0.997 4

Okfol + 15% ASD-4 −334.3 1307.2 ± 155 0.975 4

TNETNB 123.7 1096.9 ± 2.4 0.999 3

TNETNB+ 15% ASD-4 33.5 1101.1 ± 0 1 2

BTNEN 212.6 985.3 ± 55 0.994 4

BTNEN + 15% ASD-4 −1673.7 1967.3 ± 203 0.990 3

Fig. 8. Detonation velocity versus partial density ofthe explosive in the charge.

atomic molecules of oxides, especially pentahydric oxideAl2O3. This conclusion is confirmed by calculations ofthe change in the covolumes of the molecules of thedetonation products due to combustion of Al [35] andexperiments showing that the addition of Al reduces thepressure and increases the detonation temperature [14].

If the statistical processing includes the data of [9],in particular, those for low-density charges and the dataof Table 3 for explosives with zero and positive oxygenbalance, the errors of the calculated values will increasemarkedly to ≈5% for the detonation velocity and ≈8%for the detonation pressure.

PROPELLANT PERFORMANCE

Results of investigation of the dependences of thepropellant performance determined by the M-40 tech-nique [36] on the charge density for okfol-3.5, 2′,2′,2′-trinitroethyl-4,4,4-trinitrobutirate (TNETNB) [34],BTNEN and their mixtures with 15% Al are shown in

Table 4. The acceleration time of the plate in the M-40technique is ≈20 μs, which is much larger than thetime of the chemical reactions. It is seen that for theplate acceleration, the addition of Al also increases theslope of the dependences W40(ρ) for all the investigatedexplosives. In this case, the effect is most pronouncedfor the mixture of BTNEN with Al, which is obviouslydue to the higher heat effect of the reaction of Al withfree oxygen and to the higher rate of this reaction.

Analysis of the obtained dependences for explosivesnot containing Al shows that the slope of the curve ofW40(ρ) for BTNEN is significantly lower than that forokfol and TNETNB, for which the dependences prac-tically coincide. This may be due to the presence offree oxygen in the detonation products of BTNEN andthe absence of the dependence of the heat of explosionon density for BTNEN [30]. According to Le Chate-lier’s principle, increasing the charge density, i.e, thepressure should speed up the reactions proceeding inthe products and resulting in a decrease in the volume,in particular, the endothermic reaction of formation ofnitrogen oxides.

Plotting the curves of W40(ρ) in the coordinatesW 2–ρQ for BTNEN and its mixture with 15% Al andusing the approach described in [11, 32], we can showthat for a mixture of BTNEN with ASD-4 Al underthese conditions, the fraction of the energy of Al com-bustion converted to the energy of the plate, is 20–40%.

CONCLUSIONS

1. For HMX, the value of ∂D/∂ρ increases withthe addition of 3.5 and 5.5% phlegmatizer as well aswith the addition of up to 15% particulate aluminum ofdifferent brands.

2. The curves of ∂D/∂ρ on the mass fraction ofthe Al additive (ASD) to okfol-3.5 and A-IX-1 has amaximum at α = 10–15%. The positions of these peakscoincide with the positions of the maxima of the curves

620 Davydov and Gubin

of the propellant performance on the mass fraction ofthe additive in these mixtures.

3. Addition of 10% ASD-4 aluminum to A-IX-1leads to a 27% larger increase in the value of ∂D/∂ρ,than the addition of 10% PAP-2 aluminum. This isindicated by the results of measurements in the testsusing a ballistic pendulum.

4. According to the estimates based on the mea-sured dependences D(ρ) for BTNEN and its mixtureswith 10% PAP-2 aluminum, 3–15% of the energy ofAl combustion can be released in the chemical reactionzone.

5. Measurements of the propellant performance us-ing the M-40 technique showed that the slope of thecurve of the plate velocity versus charge density in-creases with the addition of Al to okfol-3.5, TNETNB,and BTNEN, which is particularly pronounced in mix-tures with BTNEN.

6. Estimates obtained using the curves of the platevelocity versus charge density showed that in the caseof mixtures of BTNEN with 15% ASD-4 aluminum un-der the gas-dynamic conditions of the M-40 technique,20–40% of the energy of Al combustion can be expendedin the acceleration of the plate.

7. A method for calculating the detonation param-eters of high-density metallized explosives was proposedwhich is based on the relationship between the detona-tion velocity and the longitudinal velocity of sound inthe additive and which provides correct estimates of theeffect of the additives in a wide range of their physico-chemical properties. The prediction accuracy decreaseswith decreasing charge density and increasing oxygencontent in the explosive.

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