energetic material detonation characterization: a laboratory-scale approach

DOI: 10.1002/prep.201300013

Energetic Material Detonation Characterization: ALaboratory-scale ApproachMatthew M. Biss*[a]

1 Introduction

The experimental determination of an energetic material’sdamage potential is characterized by the detonation waveand air shock wave properties produced as a result of itsrapid decomposition. The key detonation wave propertiesneeded for characterization include: detonation or Chap-man-Jouguet (CJ) pressure PCJ, detonation wave velocity D,reaction products particle velocity uCJ, and reaction prod-ucts density 1CJ. The ultra-high-speed nature of the detona-tion event involves chemical reaction timescales down tonanoseconds, producing temperatures upwards of 6000 K,pressures upwards of 50 GPa, and detonation wave veloci-ties ranging from 4–10 mm ms�1 [1–3]. Experimentally meas-uring these properties presents a difficult challenge due tothe severe nature of the environment and the temporalscale on which they occur. Presently, to determine the de-sired detonation wave properties, a multitude of experi-ments and instrumentation are necessary. These can in-clude piezoelectric-pin-instrumented detonation velocityexperiments, plate dent or aquarium experiments, andphoton Doppler velocimetry experiments, to name a few.Thus, the current detonation characterization protocol ulti-mately limits the development of novel energetic formula-tions as it tends to become cost prohibitive.

Early detonation characterization research on the detona-tion wave reaction-zone length and pressure was first sug-gested by Goranson in 1946 [4]. He discovered that the re-action-zone length and CJ pressure for an energetic materi-al could be determined through free-surface velocity meas-urements of metal “flyer plates” positioned adjacent to an

energetic charge. Duff and Houston later tested this theoryby characterizing Composition B using aluminium flyerplates of various thicknesses [5] . Further detonation charac-terization was conducted by Holton, who extrapolated CJpressures using the “aquarium test,“ an extension to Goran-son’s flyer-plate experiment, in which the flyer plate is re-placed by an optically transparent material (most common-ly, water) [6]. In this test, a streak image is taken parallel tothe axis of a sympathetically detonated cylindrical explosivecharge submerged in a container filled with distilled water.The recorded streak record is subsequently analyzed to de-termine the time-dependent position of the outward-prop-agating shock wave. An empirical shock wave distance-vs.-time relationship is applied to the data and from this, theshock wave velocity at the water�charge interface may bedetermined through differentiation and extrapolation tothe interface. From this, a detonation pressure is calculatedusing Goranson’s equation with the known Hugoniot forwater and known energetic material and water densities[7] .

Further aquarium test research was conducted byRigdon and Akst using right-circular cylinder charges to de-termine the optimum procedure for extrapolating the

Abstract : A novel energetic-material detonation and air-blast characterization technique is proposed through theuse of a laboratory-scale-based modified “aquarium test.” Astreak camera is used to record the radial shock wave ex-pansion rate at the energetic material�air interface ofspherical laboratory-scale (i.e. , gram-range) charges deto-nated in air. A linear regression fit is applied to the mea-sured streak record data. Using this in conjunction with theconservation laws, material Hugoniots, and two empiricallyestablished relationships, a procedure is developed to de-termine fundamental detonation properties (pressure, ve-

locity, particle velocity, and density) and air shock waveproperties (pressure, velocity, particle velocity, and density)at the energetic material�air interface. The experimentallydetermined properties are in good agreement with pub-lished values. The theory’s applicability is extended usinghistorical experimental test data due to the limited numberof experiments able to be performed. Predicted detonationwave and air shock wave properties are in good agreementfor a multitude of energetics across various atmosphericconditions.

Keywords: Detonation · Air blast · Shock wave · Laboratory scale · Spherical charges

[a] M. M. BissLethality Division’s Energetic Technology BranchU.S. Army Research LaboratoryAberdeen Proving Ground, MD, USA 21005-5066*e-mail : [email protected]

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shock wave velocity at the material interface, as previousaquarium test detonation pressures were consistently lowerthan published values [8] . A host of empirical curvefittingtechniques were applied to a range of data sets to deter-mine the optimum treatment of the shock wave radius-vs.-time data. They concluded that a linear regression fit to theinitial 2 mm of shock wave travel (7.2 cm charge diameter)yielded the highest-accuracy results when compared topublished values.

Conducting the air shock wave characterization of ener-getic materials presents a similarly challenging environmentdue to the pressures and temperatures being transferredinto the surrounding medium. Air shock wave characteriza-tion properties of interest include the shock wave pressureP, shock wave velocity U, particle velocity u, explosive im-pulse I, and more recently of interest, fireball temperaturesT [9] . Air shock wave characterization is traditionally con-ducted using kg-range charges instrumented with piezo-electric or piezoresistive pressure transducers positioned atspecified radial standoff distances. These transducers mea-sure the shock wave time of arrival, peak shock wave pres-sure, explosive impulse, and shock wave velocity, givenmultiple transducers. Due to the harsh nature of the envi-ronment, however, measurements are rarely taken at radialstandoffs of <5 charge diameters, providing little data suit-able towards deriving the detonation wave or air shockwave properties at the energetic material�air interface.

In response to these aforementioned shortcomings, a lab-oratory-scale-based modification of the aquarium test hasbeen developed to allow both the detonation wave andthe air shock wave properties at the energetic material�airinterface to be determined from a single experimentalmeasurement. The optically based method incorporateshigh-speed photography and laboratory-scale (i.e. , gram-range) spherical explosive charges. The detonation waveand air shock wave properties for an energetic material ofinterest may be determined from material Hugoniots, con-servation laws, two empirically established relationships,and a single film-based streak record. The laboratory-scale-based method provides an accurate, cost-effective, charac-terization procedure as a possible alternative to the full-scale characterization experiments currently used for novelenergetic materials.

2 Theory/Methodology

A shock wave is fully defined through knowledge of fivestate variables: shock pressure P, shock velocity U, particlevelocity u, density 1 or specific volume v, and specific inter-nal energy e. These variables are defined by the conserva-tion of mass (Equation (1)), momentum (Equation (2)), andenergy (Equation (3)) jump equations across the shockwave (subscripts 0 and 1 refer to the states before andafter the shock’s passage). In order to solve for the shockwave’s state, two additional relationships are necessary. The

first relationship is an equation of state for the material ofinterest. The desired equation of state would relate thespecific internal energy as a function of pressure and spe-cific volume, i.e. , e = f(P,v). Therefore, by combining thiswith the conservation of energy jump equation (Equa-tion (3)), the specific internal energy is eliminated, leavingthe generic single-variable dependent Hugoniot relation-ship, Equation (4). The Hugoniot relationship describes theloci of pressure states attainable after a shock wave’s pas-sage through a material as a function of the material’s spe-cific volume. This reduces to four variables (P, U, u, and v) inthree equations (Equations (1), (2), and (4)). Thus, if an addi-tional relationship is determinable between the four re-maining variables, the system is closed.

Material Hugoniots are experimentally measured by sub-jecting a material to a series of known shock compressionexperiments. Based on the four remaining state variables,a total of six Hugoniot “planes,“ or pairs, are determinable:P-U, P-u, P-v, U-u, U-v, and u-v. Of these, three planes havebeen found to be of great importance when analyzingshock wave interactions: P-u, P-v, and U-u. Thus, adding theU-u or P-u Hugoniot relationship allows the shock wave’sstate to be fully defined. By extending these equations tothe interaction of an energetic material detonating in a sur-rounding fluid medium, each material’s “shocked“ statemay therefore be determined.

Using these equations, it is proposed to calculate thedetonation wave and transmitted shock wave properties atthe interface of an energetic material detonating in airthrough the sole measurement of the air shock wave veloc-ity U. From this measurement, the following seven proper-ties are to be solved: detonation wave velocity D, detona-tion wave pressure PCJ, reaction products particle velocityuCJ, reaction products density 1CJ, air shock wave pressure P,air shock wave particle velocity u, and air shock wave den-sity 1. Thus, a system of seven equations is necessary todefine the detonation interaction.

The first two equations implemented are the conserva-tion of mass and momentum equations across the detona-tion wave. Here, the equations are written for the case ofa one-dimensional planar detonation wave. Conservation ofmass (Equation (1)) is rewritten for the detonating energeticmaterial, yielding Equation (5). For this, the density ratio isthe reaction products density 1CJ divided by the energeticmaterial pressing density 1e, detonation velocity D is substi-

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tuted for the shock wave velocity U, and the reaction prod-ucts particle velocity uCJ replaces the particle velocitybehind the detonation wave u1. The particle velocity aheadof the detonation wave u0 is zero as the material is yet tobe affected by the detonation.

1CJ

1e¼ D

D�uCJð5Þ

Detonation wave property variables are additionally sub-stituted into the conservation of momentum equation(Equation (2)). The previous conservation of mass substitu-tions remain valid and the pressure ahead of the detona-tion wave P0 is assumed to be zero as P0 ! PCJ. Thus, con-servation of momentum across the detonation wave is rep-resented by

PCJ ¼ 1euCJD ð6Þ

When the outward-propagating detonation wave reachesthe energetic material�air interface, a transmitted shockwave is produced and driven radially outward through theair by the expanding energetic material reaction products[10]. As a result of this interaction, a rarefaction wave isdriven rearward through the reaction products toward thepoint of initiation [2] . To satisfy the laws of conservation,the pressure and particle velocity at the energetic materi-al�air interface must be equal for the forward propagatingtransmitted shock wave and the rearward propagating rare-faction. Thus, if a pressure�particle velocity (P-u) Hugoniotis known for both the energetic material reaction productsand air, a solution for the pressure and particle velocity atthe interface is determinable.

Presently, there exists a limited collection of Hugoniotdata for energetic material reaction products due to thenumerous existing explosives and their multiple densitiesincorporated throughout the field. In response to this,Cooper developed a non-dimensional empirical relationshipfrom published P-u Hugoniot data for energetic material re-action products [2] . He discovered that if the compilationof existing Hugoniot data are plotted in a reduced form,i.e. , reduced pressure P/PCJ and reduced particle velocity u/uCJ, they collapse to a single profile, represented by twoempirical relationships [2]. This profile is divided into twoequations based upon the reduced pressure value. For re-duced pressures greater than 0.08, the reduced reactionproducts Hugoniot is represented by Equation (7) and hasa coefficient of determination of 0.987.

For reduced pressures less than 0.08, the reduced reac-tion products Hugoniot is represented by Equation (8) andhas a coefficient of determination of 0.898.

For the present case, the reduced pressure is anticipatedto be extremely low due to the large shock impedance dis-crepancy between the energetic material and air. Shock im-pedance Z is defined as the product of a material’s densityand shock wave velocity [2], Equation (9). The energeticmaterial impedance Ze is defined as the product of itspressing density 1e and its detonation velocity D (Equa-tion (10)), whereas air’s shock impedance Zair is defined asthe product of its ambient density 1air and the transmittedshock wave velocity U (Equation (11)). The energetic materi-al pressing density is approx. 1500 times greater than thedensity of air. If it is assumed that the detonation wave ve-locity and air shock wave velocity are of approximately thesame order of magnitude, the detonation wave interactionwith air results in a transmitted shock wave having a pres-sure less than the detonation pressure PCJ and a particle ve-locity greater than uCJ, according to the material Hugoniots(Figure 1). Knowledge of the air shock wave�particle veloci-ties relationship is required to determine how low this re-duced pressure will be. It should be noted that each mate-rial’s impedance is not constant and that both will increaseslightly with increasing pressure. However, for practical pur-poses, the shock impedances may be considered constantacross a reasonable range of interest [2].

Previous research has shown that, for most materials,a linear relationship exists between the shock wave andparticle velocities, or the U-u Hugoniot [2] . The linear rela-

Figure 1. Schematic of shock wave interaction between energeticmaterial reaction products and air on the P-u Hugoniot plane.

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Energetic Material Detonation Characterization: A Laboratory-scale Approach


tionship is composed of two empirically measured coeffi-cients: C0, defined as the bulk sound speed and s, corre-sponding to the U-u Hugoniot slope, Equation (12). The U-u Hugoniot coefficients for air are well established fromprevious research by Deal who conducted plate impact ex-periments using explosively driven flyer plates [11]. In hisresearch, he determined air’s Hugoniot coefficient C0 to be0.2375 mm ms�1 and s to be 1.0575 for measured shockwave velocities up to 4.5 mm ms�1. A higher shock wave ve-locity is expected here, however, air’s Hugoniot is assumedto remain linear throughout the measurement regime.Given that the air shock wave velocity is linearly related tothe particle velocity and the energetic material pressingdensity is approx. 1500 times greater than the density ofair, an extremely large impedance mismatch between ma-terials results, and ultimately, a much lower pressure is pro-duced [2]. Thus, the reduced pressure is anticipated to fallbelow the 0.08 established threshold, and Equation (8) isused for solving the system. If, however, the reduced pres-sure were to fall above the 0.08 threshold, a solution is at-tainable using Equation (7). Lastly, it should be noted thatthe U-u Hugoniot for air is used in place of the P-v Hugo-niot as it has been previously well characterized [11].

U ¼ C0 þ su ð12Þ

As shown by Figure 1, an equation representing the P-u Hugoniot plane for air is required to determine the shockwave pressure and particle velocity solution to the energet-ic material�air interaction. This is obtained by combiningthe conservation of momentum equation (Equation (2))and air’s U-u Hugoniot relation, yielding Equation (13). Aswith conservation of momentum across the energetic ma-terial detonation wave (Equation (6)), the shock wave pres-sure and particle velocity ahead of the shock wave (P0, andu0 in Equation (2), respectively) are zero, as the air is yet tobe affected by the detonation and P0 ! P. Thus, given Equa-tion (8) and (13), a solution for the shock wave pressureand particle velocity at the energetic material�air interfaceis determinable by plotting the two P-u Hugoniots.

P ¼ 1airC0uþ 1airsu2 ð13Þ

The final equation required to define the air shock waveis the conservation of mass across a shock wave, Equa-tion (14). For this, the density ratio is the air shock wavedensity 1 divided by the atmospheric density 1air, the shockwave particle velocity u is the particle velocity behind theair shock wave u1, and the shock wave velocity U remains.As before, the shock wave pressure and particle velocityahead of the shock wave (P0 and u0) are zero, as the air isyet to be affected by the shock wave and P0 ! P.

1

1air¼ U

U�uð14Þ

The final equation required to close the system is an em-pirical relationship developed by Cooper [2] that relates thereaction products density to the energetic material pressingdensity, Equation (15). This is chosen in place of a P-v Hugo-niot for the reaction products as no all-energetic-material-encompassing Hugoniot exists. Equation (15) is shown tobe valid for densities ranging between 0.002–9 g cm�3.

1CJ ¼ 1:3861e0:96 ð15Þ

By solving the above-outlined system of equations, thedesired detonation wave properties (D, PCJ, uCJ, and 1CJ) andair shock wave properties (P, u, and 1) at the energetic ma-terial�air interface are determinable for an energetic mate-rial of interest by measuring the air shock wave velocity U.The system solution is represented by Equations (16)–(22):

u ¼ U�C0

sð16Þ

P ¼ 1air C0uþ 1air su2 ð17Þ

1CJ ¼ 1:3861e0:96 ð18Þ

D ¼ uCJ1CJ

1CJ�1eð20Þ

PCJ ¼ 1euCJD ð21Þ

1 ¼ U1air

U�uð22Þ

3 Experimental Methods

3.1 Spherical Charges

Centrally initiated laboratory-scale spherical charges havingshort reaction zones are chosen to eliminate both diver-gence and critical diameter effects associated with energet-ic-material detonations [12–15]. As previously mentioned,the conservation equations developed are written for thecase of a planar shock wave interaction. However, previousresearch has demonstrated that the radial divergence ef-fects associated with spherical detonation waves are insig-nificant for shock wave curvatures that are orders-of-magni-tude larger than the detonation-reaction-zone thickness[12, 14–16]. Thus, the planar equations are valid for thepresent explosive charge configuration.





Spherical charges possessed a centrally positioned right-circular-cylinder void to accommodate an RP-3 explodingbridgewire (EBW) detonator (29 mg pentaerythritol tetrani-trate [PETN]), Figure 2. Charges are composed of Class VRDX pressed to a density of 1.77 or 1.63 g cm�3. The chargemasses m and their respective densities 1e are tabulated inTable 1.

3.2 Charge Imaging

3.2.1 Film-based Streak Camera

A Cordin Model 132B synchronized film-based streakcamera was used to record the explosively driven air shockwave radial expansion. The streak camera had a slit widthof 0.1 mm and write speed of 8 mm ms�1. A 90 cm f/6.3field lens was used to relay a focused image onto thestreak camera film plane. Figure 3 shows the experimentalsetup used for the present experiments. An FS-43 EBW (Tel-edyne Risi, Inc.) firing system charged to 4.2 kV was usedfor detonator initiation. A xenon flash bulb and Fresnel lenswere used to backlight the charge prior to detonation. Thisprovided a charge edge fiducial on the streaked film imageand allowed the charge orientation and position to be de-

termined between static and streak images. The explosivefireball and ionization of the surrounding air (due to theshock wave) provided self-illumination of the record, fromwhich, radial expansion rates were measured. A geometriccorrection factor was not implemented into the presentmeasurements as the angles associated with the radial ex-pansion measurements were extremely small (i.e. ,O(mrads)), therefore allowing the small-angle approxima-tion.

3.2.2 Intensified Camera

A PCO-TECH Inc. model HSFC Pro intensified camera wasused to image the sphericity of the detonation wave trans-ferring into air near the energetic material�air interface.Images were gathered to ensure the absence of “jetting”within the air blast wave as a result of the RP-3 detonatorand small-diameter charge incorporated. The experimentswere conducted in the same blast chamber with setup sim-ilar to that of Figure 3, however, the gated intensifiedcamera replaced the streak camera, the relay lens was re-placed with a 80–400 mm f/4.5–5.6 Nikon zoom lens, andthe xenon flash bulb was repositioned to front illuminatethe detonating charge. Images were captured at 1 Millionframes per second with a 40 ns exposure time, 400 mmfocal length, and f/8 aperture.

4 Results and Discussion

4.1 Experimental Results

4.1.1 Film-based Streak Camera Results

Prior to conducting an experiment, a static image of a cali-bration object (here, a dimensional scale) was recorded todetermine image magnification, and ultimately, a calibrationlength scale. Spherical charges were oriented with the cy-lindrical detonator axis collinear to the slit to ensure thetransferred air shock wave measured was produced bya steady-state detonation normal to the slit axis (Figure 4).The explosive fireball and air shock wave ionization pro-duced an acceptable streak record (50 ms total), as only the

Figure 2. Spherical energetic material charge with centrally posi-tioned RP-3 EBW detonator.

Table 1. Experimental charges detonated.

Charge Density, 1e Mass, mg cm�3 g

11318-3 1.77 1.80911318-4 1.77 1.81412040-2 1.63 1.77912040-4 1.63 1.74912052-1 1.63 1.72612052-3 1.63 1.758

Figure 3. Experimental imaging setup.

Figure 4. Static image of the charge�slit orientation (bottom) andstreak record at 8 mm ms�1 writing speed with time = ordinate andradius = abscissa (top).





initial 130 ns were necessary for the present research(Figure 4).

Streak records were analyzed on a vertical-beam opticalcomparator (S-T Industries, Inc. Model 4600 [0.001 mmlinear stage resolution]) with 20X objective lens. Measure-ments were taken at 0.05 mm intervals along the temporalaxis, corresponding to a radial shock wave measurementtaken every 6.25 ns. Data were subsequently transformedinto dimensional shock wave radius and time coordinatesusing the calibration length scale and known write speed.A best-fit linear correlation was determined for each dataset according to Equation (23), which consists of the shockwave radius R, air shock wave velocity U, time t, and thespherical charge radius r0. Only the initial 1.2 mm of radialshock wave travel were measured. Resulting data and anaverage linear regression fit are shown in Figure 5 andFigure 6.

R ¼ Ut þ r0 ð23Þ

The air shock wave velocity U was determined from thebest-fit linear correlation to the data and input intoa MATLAB script written to calculate the desired characteri-zation properties. The script allows the user to input theenergetic material pressing density 1e and the ambient

density of air 1air at the time of experiment. Detonationwave and air shock wave properties were subsequentlysolved for each experiment according to Equation (16)–(22).Experimental results are tabulated in Table 2 and Table 3.

The percent deviation between average and publishedvalues was determined using Equation (24). As shown byTable 2 and Table 3, the detonation wave properties (D, PCJ,and 1CJ) were all within 3 % of their published values withthe exception of the detonation pressure for the1.63 g cm�3 charges, which was found to be 10.2 %. Itshould be noted, however, that the published detonationpressure for RDX pressed to 1.63 g cm�3 was an empiricallyderived value, as an experimentally measured value wasunavailable [17]. Thus, the presently calculated deviationwould be affected by the inherent empirical error associat-ed with the published value.

An analysis was performed according to Moffat to deter-mine the inherent uncertainty within the calculated data asa result of the experimental uncertainty present and empir-ical relationships employed [18]. Tabulated uncertaintieswere derived from the experimental uncertainties intro-

Figure 5. Shock wave radius-vs.-time data for Class V RDX at1.77 g cm�3 with average linear regression fit.

Figure 6. Shock wave radius-vs.-time data for Class V RDX at1.63 g cm�3 with average linear regression fit.

Table 2. Calculated detonation wave and air shock wave properties for RDX at 1.77 g cm�3.

Charge 1air U D PCJ 1CJ uCJ P 1 ug cm�3 mm ms�1 mm ms�1 GPa g cm�3 mm ms�1 MPa g cm�3 mm ms�1

Published – – 8.69 [21] 33.6 [21] 2.34 [2] – – – –11318-3 1.202e-3 9.18 8.73 35.3 2.40 2.28 93.3 1.532e-2 8.4611318-4 1.202e-3 8.96 8.51 33.6 2.40 2.23 88.9 1.517e-2 8.25Average 1.202e-3 9.07 8.62 34.4 2.40 2.26 91.1 1.524e-2 8.36Uncertainty 8.298e-6 0.04 0.07 0.5 0.01 0.02 1.21 1.370e-4 0.03

– – 0.81 2.38 2.56 – – – –





duced as a result of measuring the initial charge radius(Dr0 = 0.005 mm), shock wave radius (DR = 0.005 mm), time(Dt = 6.25 e�5 ms) and atmospheric density at the time oftest. For all properties calculated, the experimental uncer-tainty was determined to be less than 2 % of their respec-tive values.

4.1.2 Intensified Camera Results

A static image of the charge orientation was captured priorto conducting the experiments. Shown below in Figure 7 isthe static image for one of the three experiments conduct-ed along with the image series capturing the detonationwave breakout and transfer into air. As shown, the airshock wave is spherical in nature and exhibits no form ofjetting as a result of the RP-3 detonator. All three experi-ments produced identical results.

4.2 Historical Data

The proposed theory was applied to previous research thatincorporated variants of the aquarium test to determinethe detonation wave and air shock wave properties for anenergetic material. The research allowed the presentmethod to be applied to a range of full-scale (i.e. , kg-range) right-circular-cylinder energetic charges across vari-ous atmospheric conditions [10,19,20]. These tests consist-ed of experimentally measuring multiple variables fora given explosive as well as having a priori knowledge ofthe energetic material’s reaction products Hugoniot or det-onation variables. For each replicated experiment, the ener-

getic material pressing density 1e, measured air shock wavevelocity U at the interface, and atmospheric density 1air

were input into the MATLAB script. All other detonationwave and air shock wave properties were subsequently cal-culated from these three input values. The results for sever-al cases are reported in Table 4. Air shock wave density atthe interface was not reported in any references and wastherefore disregarded in the present results. The developedtheory was able to predict the published values within 6 %(Equation (25)) for all properties, while the majority waspredicted within 3 %, as shown by the tabulated results.Thus, the theory’s accuracy was extended using historicalcharacterization research. This also demonstrates the theo-ry’s utility as the only properties required to perform a fun-damental detonation characterization on an energetic ma-terial of interest are the energetic material pressing density,atmospheric air density, and the initial shock wave velocity.

5 Conclusions

A laboratory-scale-based modification of the aquarium testhas been provided for the detonation wave and air shockwave characterization of energetic materials. The techniquemeasures the radial shock wave expansion rate producedat the energetic material�air interface from the detonationof laboratory-scale spherical charges. Air shock wave veloci-ties were measured by fitting a regression line to the first1.2 mm of streak record data. From this measurement,

Figure 7. Static and intensified image series of detonating spherical charge illustrating the transferred air shock wave’s sphericity (inter-frame time is 1 ms).

Table 3. Calculated detonation wave and air shock wave properties for RDX at 1.63 g/cm3.

Charge 1air U D PCJ 1CJ uCJ P 1 ug cm�3 mm ms�1 mm ms�1 GPa g cm�3 mm ms�1 MPa g cm�3 mm ms�1

Published – – 8.34 [21] 28.3 [17] 2.16 [2] – – – –12040-2 1.207e-3 8.85 8.40 30.4 2.22 2.22 87.0 1.504e-2 8.1412040-4 1.207e-3 9.06 8.61 31.9 2.22 2.28 91.2 1.519e-2 8.3412052-1 1.213e-3 9.16 8.71 32.7 2.22 2.31 93.7 1.543e-2 8.4412052-3 1.206e-3 8.74 8.30 29.7 2.22 2.19 84.8 1.506e-2 8.04Average 1.208e-3 8.95 8.51 31.2 2.22 2.25 89.2 1.518e-2 8.24Uncertainty 8.146e-6 0.04 0.07 0.46 0.01 0.02 1.17 1.340e-4 0.03% Deviation – – 2.04 10.2 2.78 – – – –





a procedure was developed to determine fundamental det-onation wave and air shock wave properties for an energet-ic material of interest through use of conservation laws,material Hugoniots, and two empirically established rela-tionships. The theory was verified using pressed RDXspheres and historical test data.

The developed theory allows a fundamental characteriza-tion to be performed from a single laboratory-scale experi-ment requiring minimal energetic material, and possibly of-fering a highly advantageous, cost-saving approach for thescreening of novel energetic formulations. Thus, it couldprovide an alternative to the multitude of full-scale experi-mental characterization techniques currently employedduring the developmental phase of novel energetic formu-lations. Presently, to determine the desired detonationwave (velocity D, pressure PCJ, particle velocity uCJ, and den-sity 1CJ) and air shock wave (velocity U, pressure P, particlevelocity u, and density 1) properties, a multitude of experi-ments and instrumentation are necessary. However, asshown by the experimental and historical data, the presenttheory only requires a single experimental measurement toobtain all of the above-named properties. The theory’s utili-ty is apparent as it provides fundamental energetic materialcharacterization properties from only a few grams of mate-rial. Lastly, it is recommended that numerical modelling beperformed to ensure that the assumed second-order spher-ical divergence effects are indeed negligible for the pro-posed laboratory-scale charges.

Additional testing is necessary to validate the theory fora wider range of energetic formulations. Energetics exhibit-ing large reaction-zone thickness, critical diameter, and

energy fluence should be tested to verify the technique’svalidity. Explosives having a larger reaction zone and higherenergy fluence than fine RDX will require a booster chargefor proper detonation initiation. Work is currently underwayto investigate this aspect as well as the effect of under- orover-boosting the test explosive.

Symbols and Abbreviations

C0 Air bulk sound speedD Detonation wave velocityEBW Exploding bridgewiree Specific internal energyHBX-1 Pourable explosive mixtureHMX Cyclotetramethylene tetranitramineI Explosive impulsem Explosive charge massP Air shock wave pressurePCJ Detonation wave pressurePETN Pentaerythritol tetranitratePo Atmospheric pressureRDX Cyclotrimethylene trinitramines Air’s U-u Hugoniot slope_0 Properties in front of shock wave_1 Properties behind shock waveT TemperatureT0 Atmospheric temperatureTNT TrinitrotolueneU Shock wave velocityu Particle velocity

Table 4. Calculated detonation wave and air shock wave properties from previous experimental research.

INPUT OUTPUT

Charge 1e 1air U D PCJ 1CJ P ug cm�3 g cm�3 mm ms�1 mm ms�1 GPa g cm�3 MPa mm ms�1

HMX/Inert [19] 1.781 1.068e�2 7.42 8.73 33.5 2.34 53.0 6.53Calculated – – – 8.60 34.5 2.41 53.8 6.79% Deviation – – – 1.5 3.0 2.9 1.5 4.0HMX/TNT/Inert[19] 1.776 3.785e�3 7.84 8.21 31.2 2.40 21.2 7.13Calculated – – – 8.26 31.7 2.41 21.3 7.18% Deviation – – – 0.6 1.7 0.4 0.5 0.7TNT [10] 1.636 0.971e�3 7.34 6.93 20.7 2.15 47.8 6.71Calculated – – – 6.80 20.0 2.22 47.8 6.71% Deviation – – – 1.9 3.4 3.2 0 0Comp. B [10] 1.717 0.947e�3 8.67 7.98 29.5 2.34 65.5 7.97Calculated – – – 8.05 29.2 2.33 65.5 7.98% Deviation – – – 0.9 1.0 0.4 0 0.1Cyclotol [10] 1.752 0.936e�3 8.64 8.27 31.3 2.38 64.2 7.94Calculated – – – 8.01 29.5 2.37 64.2 7.95% Deviation – – – 3.1 5.8 0.4 0 0.1Octol [10] 1.821 0.943e�3 8.86 8.49 34.2 2.46 68.1 8.14Calculated – – – 8.23 32.2 2.46 68.1 8.15% Deviation – – – 3.1 5.8 0 0 0.1HBX-1 [20] 1.712 1.253e�3 7.61 7.31 22.0 2.18 67.0 6.97Calculated – – – 7.22 22.4 2.21 66.5 6.97% Deviation – – – 1.2 1.8 1.4 0.7 0





uCJ Reaction products particle velocityv Specific volume1air Ambient air density1CJ Reaction products density1e Energetic material pressing densityWs Streak camera writing speedZ Shock impedanceZair Air shock impedanceZe Energetic material shock impedance

Acknowledgments

I would like to acknowledge the U.S. Army Research Laboratory’sLethality Division Innovation Program and the National ResearchCouncil Postdoctoral Fellowship Program for funding of this re-search. I am greatly appreciative to Dr. Thuvan Piehler, Dr. LarryVan de Kieft, Mr. Gerrit Sutherland, and Mr. Vincent Boyle for theirthoughtful discussions, Mr. Roy Maulbetsch, Mr. Terry Piatt, andMrs. Lori Pridgeon for pressing of the energetic samples, and totechnicians Mr. Ronnie Thompson, Mr. William Sickels, Mr. RichardBenjamin, Mr. Ray Sparks, and Mr. Gene Summers for their assis-tance in conducting these experiments.

References

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Received: January 31, 2013Revised: March 7, 2013

Published online: && &&, 0000





energetic material detonation characterization: a laboratory-scale approach

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