Shock WavesDOI 10.1007/s00193-017-0718-8

ORIGINAL ARTICLE

Characterizing the energy output generated by a standard electricdetonator using shadowgraph imaging

V. Petr1 · E. Lozano1

Received: 27 September 2016 / Revised: 14 February 2017 / Accepted: 20 February 2017© Springer-Verlag Berlin Heidelberg 2017

Abstract This paper overviews a complete method for thecharacterization of the explosive energy output from a stan-dard detonator. Measurements of the output of explosivesare commonly based upon the detonation parameters of thechemical energy content of the explosive. These quantitiesprovide a correct understanding of the energy stored in anexplosive, but they do not provide a direct measure of the dif-ferent modes in which the energy is released. This opticallybased technique combines high-speed and ultra-high-speedimaging to characterize the casing fragmentation and thedetonator-driven shock load. The procedure presented herecould be used as an alternative to current indirect methods—such as the Trauzl lead block test—because of its simplicity,high data accuracy, and minimum demand for test repeti-tion. This technique was applied to experimentally measureair shock expansion versus time and calculating the blastwave energy from the detonation of the high explosive chargeinside the detonator. Direct measurements of the shock frontgeometry provide insight into the physics of the initiationbuildup.Because of their geometry, standard detonators showan initial ellipsoidal shock expansion that degenerates into afinal sphericalwave. This non-uniform shape creates variableblast parameters along the primary blast wave. Addition-ally, optical measurements are validated using piezoelectric

Communicated by A. Higgins.

B V. Petrvpetr@mines.edu

E. Lozanojlozanos@mines.edu

1 Colorado School of Mines, 1600 Illinois Street, Golden, CO80401, USA

pressure transducers. The energy fraction spent in the accel-eration of the metal shell is experimentally measured andcorrelatedwith theGurneymodel, aswell as to several empir-ical formulations for blasts from fragmentingmunitions. Thefragment area distribution is also studiedusingdigital particleimaging analysis and correlated with the Mott distribution.Understanding the fragmentation distribution plays a criticalrole when performing hazard evaluation from these types ofdevices. In general, this technique allows for characteriza-tion of the detonator within 6–8% error with no knowledgeof the amount or type of explosive contained within the shell,making it also suitable for the study of unknown improvisedexplosive devices.

Keywords High-speed imaging · Blast wave ·Fragmentation · Energy distribution

List of symbols

a Fragment areaa0 Fragment area scalec0 Local speed of soundC Charge mass of explosivesCEB Equivalent bare mass of explosivesd Distance camera-objectMtot Total mass of casingMcyl Mass of casing cylindrical sectionMtip Mass of casing tipM Shock Mach numberMs Scaled shock Mach numberNTP Normal Temperature and Pressuren Weibull distribution parameterP Peak shock pressurePa Ambient pressure

123

V. Petr, E. Lozano

PETN Pentaerythritol tetranitratePs Scaled peak shock pressureR′ Apparent shock radius from charge axisR Shock radius from charge axisRs Scaled shock radius from charge axisRsph Equivalent spherical shock radiusTa Ambient temperatureTNT Trinitrotoluenet Shock time of arrivalts Scaled shock time of arrivalu Particle velocityU Shock velocityUs Scaled shock velocityVcyl Velocity of casing cylindrical sectionVtip Velocity of casing tipβ Effective charge cone base angleγ Specific heat ratio√2E Gurney constant

1 Introduction

In order to reliably initiate high energetic materials, a strongshock or detonation is required. A capsule of sensitive highexplosives, termed a detonator, can accomplish this. In 1865,Alfred Nobel invented the blasting cap, which consisted of asmall metal cap containing mercury fulminate. Mercury ful-minatewas the only substance known at the timewhich couldbe usedwith reasonable safety formanufacturing. The inven-tion of the blasting capwas the start of themodern era of highexplosives [1]. Since then, there have been many improve-ments in initiation system technology. Presently, standarddetonators have two different explosive materials: a sensi-tive primary explosive (primer charge) and a less sensitive,but more high-powered secondary explosive (base charge).These charges are contained inside ametal cup that is usuallymade of copper, bronze, or aluminumdepending on the appli-cation. Upon initiation, the ignition source sets off the primercharge, which detonates the base charge, which in turn deto-nates themain explosive charge [2]. Depending on the type ofenergetic material that comprises the main charge, differentinitiation energy may be required to achieve a reliable deto-nation. For this reason, conventional detonators are classifiedaccording to their strength. The strength is universally rep-resented by a single number that ranges from 1 to 12, whichis directly related to the net explosive content of the deto-nator. The US Bureau of Mines established the number 8 asthe industry standard from which important definitions, like“blasting agent,” are termed. However, the strength of a det-onator is measured not so much by the net explosive weightbut by the different tests developed over the years (sand test,Trauzl lead block test, etc.). The reason is because the mainfactor affecting the performance is the output of the energy

release. This output is affected not only by the net explosiveweight, but also by the charge geometry, pressing density,casing type and thickness, and even the atmospheric condi-tions. Hence, it is critical to understand how these parametersaffect the generation of the detonator-driven shock load.

High-speed imaging technologies are constantly beingimproved for the study of detonation properties of explosivematerials. Several researchers have reported the use of thesetechnologies for measuring expanding shock waves in theair from bare explosive pellets [3–5]. In addition, Hutchin-son [6] demonstrated how the casing surrounding a particularexplosive charge can be related to an equivalent bare chargeby considering the momentum absorption that takes placeduring the fragmentation.

The goal of this research work was to develop an opticallybased experimental method for characterizing the energyreleased in terms of fragmentation and explosively drivenshock load by a conventional detonator. This techniqueallows studying the performance of these initiation devicesas well as its characterization when its origin is unknown(i.e., IEDs).

2 Theory background

A high explosive material is characterized by a detonationprocess where the front of the chemical reactionmoves fasterthrough the material than the speed of sound. This suddenrelease of energy is usually accompanied by the creation of apropagating disturbance in the surrounding medium knownas a shock or blast wave. By knowing the medium and therate of expansion of this blast wave, one is able to charac-terize not only the explosive shock load, but also the energysource.

The primary shock front of a blast wave is, in many ways,a determining factor in its behavior [7]. The goal is then tocharacterize the detonator-driven shock load from its perfor-mance in air, which for present purposes may be consideredas an ideal gas. According to Needham [8], the ideal gasassumption is accurate at 99% for incident blast overpres-sures up to 2000 kPa.

Using a Lagrangian coordinate system, the basic param-eters in air before and after the passage of the shock wavecan be described. Several relations are then obtained for thedifferent blast parameters from the fact that mass, momen-tum, and energy must be conserved across the shock front.Therefore, shock wave velocity U , shock wave Mach num-ber M , particle velocity u, incident shock wave pressureP , etc., can be calculated from the sole measurement ofthe air shock expansion rate and the Rankine–Hugoniotrelations.

When the primary interest is to study the output of theenergy released by an explosive charge, the most reliable

123

Characterizing the energy output generated by a standard electric detonator using shadowgraph…

method is to measure the distance from the center of theexplosion atwhich a specific blastwave property occurs. Thisvalue is then related to thedistance atwhich the samepropertyis produced by a reference explosion using the cube rootscaling law [3]. This reference is usually the TNT standardfor chemical explosions. On the other hand, conventionaldetonators have their base charge and components allocatedwithin a light to moderate case. The PV energy available inthe explosive charge has to work on the casing before it isable towork on the air. Therefore, the amount of energy givenup to the metal is no longer available for the air blast wave[9].

A small fraction of the energy is also expected to bereleased in other forms such as radiation [3]. The type ofdetonator referred to in this manuscript is limited to chemi-cal explosive charges. Thus, this energy fraction is expectedto be negligible compared to the one associated with the gen-eration and expansion of detonation products.

2.1 Air shock characterization

The primary shockwave expansion rate in air from a standardnumber 8 electric detonator is measured in two directions.The directions correspond with the longitudinal and trans-verse axes of the detonator (Fig. 1). The elliptical expansionof the shock wave is a result of the charge geometry. As theblast wave expands, it decays in strength, lengthens in dura-tion, and slows down, both because of the spatial divergenceand because of the medium attenuation [8].

Most of the sources of compiled data for air blast wavesfrom high explosives are limited to bare, spherical chargesin free air. However, different experiments conducted withalternative charge geometries show how explosive materialstend to drive their energy to the larger area of their outer sur-face. This behavior is critical because if the initial expansionwave has a shape different than spherical, the blast parame-ters will decay at a different rate than that of the referenceexplosion [9].

Esparza [10] presented a spherical equivalency of cylin-drical charges in free air where a higher explosive yield isreached at 90◦ from the longitudinal charge axis. The differ-ence in the shock wave magnitude in the different directionswill decrease as the shock expands through the air, adopt-ing a final spherical shape. This is the case for conventionaldetonator geometries where the shock travels faster in thetransverse direction.

The blast wave expansion rate in atmospheric air is exper-imentally measured by using retroreflective shadowgraphy.Because the shock front is recorded in an object plane con-taining the charge center, the apparent radius measured in theimage plane does not correspond to the actual shock radius[11]. The recorded radius must be corrected for the non-parallel light using the following geometric relation:

Fig. 1 Approximated initial blast wave generated from a standard det-onator and axes locations

R = R′(1 +

(R′d

)2)1/2 (1)

where R represents the actual shock wave radius, R′ is theapparent shock radius, and d is the distance from the camerato the center of the charge. Note that (1) is only validwhen theoptical axis of the camera is aligned with the charge center.Dewey [11] includes a more general trigonometrical expres-sion for nonzero offset angles.

The blast wave expansion is obtained along the longitudi-nal and transverse axes of the detonator providing two sets ofdata. Themeasured values are also corrected to Normal Tem-perature and Pressure (NTP) by using the scaling approachpresented by Kleine et al. [3]. The scaling is as follows:

Rs = R

(Pa

101.325

) 13

(2)

ts = t

(Ta

288.16

) 12(

Pa101.325

) 13

(3)

The subscript “s” refers to scaled values toNTP conditions. Rrepresents the shock wave radius from the center of the blastand t is the recorded time. Pa and Ta are the ambient pres-sure and ambient temperature at the time of the experiment.Finally, the shock wave radius versus time in the transverse

123

V. Petr, E. Lozano

and longitudinal directions is fitted to an empirical equationdeveloped by Dewey [11] and reported in references [3] and[4]. This empirical correlation is as follows:

Rs (ts) = A + Bc0ts + C ln (1 + c0ts) + D√ln (1 + c0ts) (4)

where Rs represents scaled shockwave radius from the centerof the blast, ts represents scaled time of arrival of the shockwave, c0 is the local speed of sound at NTP (340.29m/s), andA, B, C , and D are the yielding coefficients. B should be setto 1 to guarantee an asymptote to the speed of sound for largetimes [4]. The calculation of the parameters A, B, C , and Dwas done by least-squares curve-fit through a computationalcode written in MATLAB®.

A relation between shock waveMach number versus timecan be obtained by differentiation of (4) and dividing theresulting value by the local speed of sound:

Ms (ts) = 1

c0

dRs (ts)

dts= B + C

1 + a0ts

+ D

2 (1 + a0ts)√ln (1 + a0ts)

(5)

At this point, an analytical expression for the shock Machnumber versus radius is derived for the two main expandingshock directions. The next stepwill be to quantify the yield ofthe detonation by the analysis of this shock wave expansion.As previously mentioned, the energy released can be relatedto that of another reference high explosive of the same mass;in this case TNT [3]. Therefore, the measured shock Machnumber versus radius is fitted to the high explosive blaststandard. This standard is established for thewidely acceptedKingery and Bulmash (K–B) curves [12] for spherical free-air TNT bursts. The K–B curves can be obtained from (6)and (7):

X = K0 + K1 log

(Rs

CEB1/3

)(6)

Ps = 10C0+C1X+C2X2+...+C8X8(7)

where Rs represents scaled shock wave radius, CEB is themass of explosive, Ps is the scaled peak shock pressure, andCi and Ki represent the empirical coefficients. These coeffi-cients vary for spherical and hemispherical TNT bursts andcan be found in multiple references including [12]. Sincethe data collected is in terms of shock Mach number Ms,the parameter peak shock pressure Ps is converted to shockMach number using the Rankine–Hugoniot relations and theideal gas assumption (γ = 1.4). This leads to a nonlinearanalytical expression of the K–B curves where the shockMach number is only a function of the shock wave radiusand the mass of explosive. The data collected can be then fit-ted in a least-squares sense using the Levenberg–Marquardt

algorithm where the mass of explosive CEB becomes the fit-ting parameter. The algorithm can be found implemented incommercial software such as MATLAB®.

The K–B curves provide an accurate representation ofthe peak blast parameters as a function of the range forranges greater than about three charge radii [8]. However, theoverpressure as a function of the range is a strong functionof the detonation energy of the explosive which can intro-duce large errors when comparing different solid explosives.Needham [8] shows that this dependence vanishes for scaledistances larger than approximately 1 m/kg1/3 where theoverpressure–distance curves converge for chemical explo-sions.

A critical aspect must be taken into consideration at thispoint. The K–B curves are expressed for spherical free-airexpanding shocks, while the blast waves from conventionaldetonators will show an ellipsoidal expansion due to theirexplosive charge geometry (Fig. 1).

This challenge is overcome by applying the basic lawsto the blast wave expansion. An equivalent spherical shockwave is then considered by specifying that the volume ofair being compressed by the ellipsoidal shock wave is thesame as the one compressed by an equivalent sphere of radiusRsph. Next, the equivalent spherical shock wave Mach num-ber versus distance data is fitted to the reference sphericalfree-air burst yielding a single coefficient. The obtained valuerepresents the equivalent spherical mass of TNT that wouldproduce the measured blast wave properties in atmosphericair. This explosive yield is expected to be lower than the totalenergy content of the detonator since only the blast wave inair is being accounted for.

It must be mentioned that the classic similarity solutionsolution for a point energy release and strong shock waveformation by Taylor [13] predicts the motion of the shockwave and the resulting physical property distributions usingdimensional analysis. This ideal prediction, however, cannotbe directly applied to typical explosions where the energy isreleased over a finite time. Chemical explosions are betteranalyzed experimentally by measuring shock propagation orproperty variations rather than applying scaling laws [14].Here, the shock propagation is measured from the center ofthe explosion as a function of time and becomes the primarydata for developing the blast wave characterization in the air.

2.2 Fragmentation characterization

A significant part of the energy released by a conventionalexplosive detonator is spent during the fragmentation processof the casing. The energy is transferred to the metal in threemodes: shock heating, strain and fracture, and kinetic energyof the fragments [9]. The energy released in the form of ablast wave is thereby reduced, since the expanding explosiveproduct gases will have to expend part of their energy to

123

Characterizing the energy output generated by a standard electric detonator using shadowgraph…

overcome the strength of the metal shell and accelerate thegenerated fragments. Hutchinson [6] developed a detailedanalysis of the escape of blast from fragmenting munitions,which departs from the physically valid initial assumptionprovided by Gurney [15].

Three different equations presented in [6] regarding frag-menting casings are compared in order to better estimatethe energy partition during the fragmentation. Each equationrepresents the ratio of the equivalent bare explosive mass tothe actual mass as a function of the ratio between the massof casing and the mass of explosives contained within thecasing. The mentioned equations are as follows:

Fisher: CEB = C

(0.2 + 0.8/

(1 + Mtot

C

))(8)

Modified Fisher: CEB = C

(0.6 + 0.4/

(1 + Mtot

C

))(9)

Hutchinson: CEB = C

(1

2/

(1

2+ Mtot

C

))1/2

(10)

where C is the mass of explosives in the base charge, Mtot

represents the total mass of the casing surrounding the baseexplosive charge, and CEB is the equivalent bare charge. (9)is an empirically adjusted version of (8) assuming early frag-mentations of the casings while the pressure of the explosiveproducts within them is still high. The explosive productscan then escape through the fragmented casing, taking themomentum theywould otherwise have to impart to the casingmaterial [6]. However, this modified equation is more rep-resentative of brittle casings rather than ductile metals suchas the aluminum shell studied in this paper. Alternative waysfor calculating blast impulse reduction due to encased explo-sive charges has been also studied by Hutchinson [6]. (10) ispresented as an alternative to Fisher’s formula since the latterdoes not provide good approximation forMtot/C > 5. Fisher(8), Modified Fisher (9), and Hutchinson (10) are acceptedas valid approaches that account for the energy absorptionduring the fragmentation process.

Equations (8) through (10) consider exclusively the frac-tion of the energy from fragmenting cylindrical shells.However, part of the explosive energy is exerted on the tipof the casing, imparting high velocities to this small area. Inorder to validate the results and applicability of these threeformulations (8) to (10) for this particular experiment, thecasing expansion and accelerationwill be opticallymeasuredusing ultra-high-speed imaging (Figs. 6, 10) and correlatedwith the well-known Gurney model.

Overall, this fragmentation phenomenon can be dividedinto two separate problems: the acceleration of the cylindri-cal mass of metal that surrounds the base charge Mcyl andthe acceleration of the mass of the tip at the end of the shellMtip. Gurney [15] developed a model that correlates termi-

nal fragment velocities from explosive/metal systems basedon energy and momentum balances and without consideringshock mechanics:

Vcyl = √2E

[Mcyl

C+ 1

2

]−1/2

(11)

where Vcyl is the velocity of the corresponding acceleratedmetal, C is the total mass of explosives, Mcyl representsthe mass of the cylinder casing, and

√2E is the Gurney

constant for the given explosive. Benham [16] extended theGurney model for the acceleration of barrel-tamped explo-sive propelled plates, which departs from the relation for theunsymmetrical sandwich configuration. However, for massratios lower than 1/3 in non-symmetric configurations, thegas-dynamics behavior dominates during the expansion lead-ing to an alternative expression for the motion of the tip[17]:

VtipD

= 1 − 27

16

Mtip

Ctip

[(1 + 32

27

Ctip

Mtip

)1/2

− 1

](12)

where Vtip is the velocity of the tip,Ctip is the effective chargeweight, Mtip represents the mass of the tip, and D is thevelocity of detonation for the given explosive. The mass ofthe effective charge that exerts energy on the tip is the onecontained within a cone with base angle β and base diam-eter equal to the charge diameter. Benham [16] shows thatthe base cone angle β is only a function of the ratio betweenthe full charge mass C and the mass of the tamping cylinderMcyl:

β = 90 − 30√2McylC + 1

(13)

Therefore, the effective charge mass that accelerates thetip can be calculated from the cone volume and the densityof the explosive. By knowing the mass of casing and thecasing initial velocity (experimentally measured), the abso-lute mass of explosives contained in the base charge can becalculated and correlated with the values obtained in (8)–(10). This analysis will assist to validate which of the threeformulations (8)–(10) better represents the energy partitionresulting from standard detonators.

The fragmentation phenomenon is further characterizedby the investigation of the fragment areas resulting from thedetonation. The dynamic fragmentation of a rapidly expand-ing metal casing involves a complexity of opening fissuresand cracks that results in a variety of fragments that followthe linear Mott distribution. Grady [18] developed an analyt-ical approach to approximate this variation of fragment sizesin terms of a Weibull distribution of parameter n = 3.45:

123

V. Petr, E. Lozano

h(a) = 2n

a0

(a

a0

)n−1

K0

(2

(a

a0

)n/2)

(14)

where h is the frequency, n is the distribution parameter set to3.45, a represents the fragment area, a0 is the fragment areascale, and K0 represents the modified Bessel function of thesecond kind. The results from (14) will be compared to theexperimental fragment areas collected from the detonation.

3 Experimental procedure

3.1 Number 8 detonator

The detonator studied in this paper is a number 8 mining andconstruction detonator, the Dyno Nobel’s Electric SuperTM

SP [19]. It can be described as a metal shell that contains aPETN base charge positioned on one end of the shell. Adja-cent to this, there is a highly sensitive primer charge housedin a heavy steel sleeve. Next, a fuse head embedded with abridge wire connects the two leg wires, thus forming ameansof electrical ignition. If a firing current is applied to the legwires, the bridge wire becomes incandescent, and the fusehead is initiated. This initiation sets off the very sensitiveprimer charge and subsequently the base charge.

The manufacturer reports a net explosive content of885 mg of which 555 mg is the PETN base charge. Whilethe primer charge is protected by a relatively heavy steel cas-ing for safety reasons, the secondary explosive base chargeis in direct contact with the outer aluminum shell. The alu-minum shell has a measured thickness of 0.42±0.01mm,while the steel sleeve has a thickness of 1.60±0.01mm.From the design alone, it is expected that the air shockwill be essentially generated by the lightly cased basecharge. This argument will be discussed in the later sections.Figure 2 shows the different components of the electric det-onator Dyno Nobel’s Electric SuperTMSP [19].

3.2 Camera setups

The direct shadowgraph technique requires a light source, acamera, and a screen on which to create a shadow. The lightsource is placed at an optimum distance from the screenand from refractive disturbances in the Schlieren object.A shadow is then projected at a certain height onto thescreen. The retroreflective shadowgraph technique, specif-ically, requires the use of a retroreflective screen and arod mirror, which is aligned with the camera axis, illumi-nating the retroreflective screen with a significant amountof light, and thus providing a high-quality image. A high-speed camera, collimated strobe lighting system (AlienBees),plano-convex lens with a rod mirror, and a retroreflective

Fig. 2 Internal view of a standard electric detonator (courtesy of DynoNobel)

screen are required for the execution of the retroreflectiveshadowgraphy. This method was introduced by Hargather etal. [20] and is effective for the visualization of blast wavesand, in general, any other variation of flow density in the air.This experimental setup is shown in Fig. 3.

The high-speed camera used for blastwave visualization isVision Research’s Phantom v.711. The retroreflective screenis made of 3M Scotchlite TM 7610 with a surface area of2.4m2. In addition, a Specialized Imaging SIM X16 ultra-high-speed camera is used for themeasurements of the casingexpansion. The setup was similar to the one shown in Fig. 3but without the rod mirror or the Plano-Convex lens and withthe strobe light aiming directly at the object.

3.3 Pressure transducers

Two PCB Piezotronics model 137A23 pressure sensors wereplaced in the measurement plane of the expanding shockwave for the validation of the shock parameters measured byoptical methods. Both sensors were mounted on a steel stand

Fig. 3 Retroreflective shadowgraphy setup

123

Characterizing the energy output generated by a standard electric detonator using shadowgraph…

pointing in an axial direction to the detonator. Standoff dis-tances from the energy source varied from 420 to 460mm.The sensitivity of the sensor is 14.5 mV/kPa±15% depend-ing on the calibration. The diaphragm was insulated usingcommon black vinyl electrical tape to minimize thermaliza-tion of the transducer from the passing of the shock front.Additionally, the bodies of the gauges were isolated from theground by placing vinyl electrical tape in contact with thesurface of the steel stand.

The two pressure sensors were connected by coaxialcables to a PCB sensor signal conditioner model 482C05.Both outputs were also connected to a Tektronix DPO3014oscilloscope where the signal provided by each gauge wasrecorded. The triggering was implemented from an ScorpionHB-SBS electric firing system and a digital delay/pulse gen-erator Stanford DG535, which provides a 2 V output to thelighting system, the high-speed camera, and the oscilloscope.

4 Results and discussion

4.1 Camera results

A total of nine tests were conducted in air. Tests 1 through 6were captured using the Phantom v.711 and the goal was tomeasure the blast wave propagation in different directions.Tests 7 through 9 were recorded using the SIMX16 and thegoal was to determine the expansion rate of the metal shell ofthe detonator. The main camera settings for each individualtest are summarized in Table 1.

Some frame sequences are presented in Figs. 4, 5, and 6.As shown, the initial blast wave presents a sharp ellipticalshape in the two-dimensional plane due to charge geometry.The ellipsoidal shock generated by the explosive charge pro-duces higher shock velocity values in the transverse plane ofthe charge versus those recorded along the longitudinal axis.As the shock expands, the spatial divergence and medium

Table 1 Camera settings for each test

Test Camera Resolution Interframe (µs) Exposure

1 Phantom 608×600 56 0.294µs

2 Phantom 608×600 56 0.294µs

3 Phantom 512×656 53 0.294µs

4 Phantom 512×656 53 0.294µs

5 Phantom 512×656 53 0.294µs

6 Phantom 912×848 110 0.294µs

7 SIM 1280×960 4.27 400ns

8 SIM 1280×960 0.27 100ns

9 SIM 1280×960 0.27 100ns

Fig. 4 Sample images from test 5, frames are 53µs apart

Fig. 5 Sample image from test 6 (330µs after initiation), the tips ofthe pressure sensors appear on the right part of the image

attenuation cause a gradual change in shape, ending as aspherical shock wave.

Figure 6 shows the casing expansion and subsequent frac-ture during the acceleration process due to the expandingdetonation products. Only three frames are displayed forcompactness.

123

V. Petr, E. Lozano

Fig. 6 Sample images from test 8, the last two frames displayed are2.7µs apart

4.2 Gauge measurements

Two piezolelectric pressure transducers were placed in themeasurement plane at a distance of 460mm from the centerof the explosion for tests 3 through 6. The top and bottomgaugeswere placed at−4◦ and−20◦ from the transverse axisof the detonator, respectively. The sample length was 10,000samples with a sample rate set to 500K samples per second.Figure 7 shows the pressure-time signal recorded in test 6 bythe top gauge and the smoothed profile.

The signal exhibits noise during a certain period of timebefore the shock arrival. This noise is due to the shock wavesproduced by the primary fragments from the aluminum cas-ing as they fly by the diaphragm of the transducer. Somediscussion of this noise in the gauge signal follows: Initially,an experimentalist may think that this noise is attributed todirect fragment impact and subsequent ringing of the gaugefixture. However, a direct fragment impact was observedduring the experimentation. Such an impact produces a high-frequency noise that invalidates the entire record.

Relating to the data analysis, it must also be taken intoconsideration that the maximum value recorded in the oscil-

Fig. 7 Overpressure–time record (black) and smoothed profile (red)for test 6

loscope does not match exactly with the peak incidentoverpressure because of sensor overshoot [21]. In order toobtain the actual peak overpressure, the overpressure–timerecord must be smoothed. This is done using the analyti-cal methodology presented by Kinney et al. [7] where peakoverpressure, positive duration, and wave form parameterare determined and inserted into the Friedlander equation. Inthis case, a peak overpressure of 25.02kPa was obtained fortest 6 with a positive duration of 272.5µs and a wave formparameter of 0.9 (Fig. 7). The values obtained for the tests3, 4, and 5 varied by no more than 0.04 kPa for the peakoverpressure.

4.3 Blast wave analysis

The shock wave expansion in each direction within a two-dimensional plane was experimentally measured for the firstsix tests. Two directions were recorded corresponding tothe longitudinal and transverse axes of the detonator. Thesame behavior observed for the transverse direction wasassumed for the third dimension due to the charge axialsymmetry.

From first principles, it was calculated that the volume ofair being compressed by the ellipsoidal shock wave was thesame as the one that is compressed by an equivalent sphereof radius Rsph; therefore, an estimation of the expansion ratefor an equivalent spherical shock wave was obtained. Thisargument seems convenient for explosive yield determina-tion sincemost of the data from high explosives are presentedfor spherical charges. As previously mentioned, this ini-tial ellipsoidal blast wave will end up adopting a sphericalshape due to geometrical expansion andmedium attenuation.Figure 8 compiles the shock wave radius versus time mea-sured in longitudinal and transverse directions and correctedfor the non-parallel light using (1).

The uncertainty associated with these measurements is±0.25 mm due to the resolution of the camera images. Theerror in the apparent radius due to the geometric distortionreaches a maximum of 1.89% for the last data point in thetransverse direction. Such error would increase even morefor larger radii, which reveals the importance of correctingthe measured shock wave data using (1). Shock wave radiusand time of arrival were scaled using (2) and (3). By applyingleast-squares regression, coefficients A, B, C , and D weredetermined for the use of Dewey’s equation (4). Table 2 sum-marizes the obtainedfitting coefficients for eachdirection andthe equivalent sphere.

Although an empirical correlation (4) does satisfy theappropriate physical condition as the time tends to infinity,ensuring that the shock wave velocity approaches the atmo-spheric speed of sound. By differentiating (4) and dividing bythe local speed of sound, an expression for the shock Machnumber versus time was obtained.

123

Characterizing the energy output generated by a standard electric detonator using shadowgraph…

Fig. 8 The shock wave expansion rate in transverse direction, longi-tudinal direction, and equivalent sphere

From the Rankine–Hugoniot relations, the blast incidentoverpressure was then calculated in the transverse direc-tion and validated with the data recorded by the pressuregauges. A peak pressure of 25.02±0.04 kPa was recordedby the transducer at 460mm from the center of the explo-sion. Conversely, a value of 25.92kPa was obtained from theshadowgraph measurements. Therefore, a good agreementwas observed with a maximum 7.5% difference for the peakoverpressure.

The next step consisted of quantifying the energy releaseby the detonator-driven blast wave. Starting from the Machnumber versus time for the equivalent sphere, a relation-ship between Mach number versus distance can be found.By taking discrete points from this analytical relationshipand fitting them to the high explosive blast standard (K–Bcurves), a single yielding coefficient was retrieved in termsof mass of TNT. The nominal value obtained was 543 mgfor the number 8 electric detonator studied. Physically, thismass represents the equivalent sphere of bare TNT thatwouldrelease the same amount of blast wave energy into the atmo-spheric air. Figure 9 shows the shock Mach number versusdistance in the different directions, the equivalent sphericalblast wave, and the fitted K–B curve.

Figure 9 shows good agreement between the measuredshock Mach number versus distance and the K–B curve forthe obtained yielding coefficient. The data are representedusing logarithmic scales starting from a shock radius of 5 cm.As previously mentioned, the reference explosion does notapply well for small radii if the explosives are other thanTNT, and therefore, a maximum 5% error is measured at5 cm. However, the error is reduced to only 1.5% (circu-lar markers in Fig. 9) after the shock wave has expanded

Fig. 9 Mach number as a function of the radius and fitted referencespherical standard for high explosives. The radius of the circularmark-ers represents 1.5% error

7.5 cm (approximately 0.95 m/kg1/3), which is consistentwith the convergence at 1 m/kg1/3 that Needham [8] refersto. Thus, the measured shock data must be spatially reducedin order to obtain an accurate fitting parameter using the K–Bcurves.

It must be remarked that the 1.5% error measured betweenthe experimental and the K–B curves does not correspond tothe uncertainty associated with the fitting coefficient. Theradius at which a given blast wave parameter occurs for aparticular charge mass scales with the cube root of the explo-sive mass, and so from error propagation rules, the resultantrelative uncertainty will increase up to 4.5%. At this point,the obtained yielding coefficient corresponds to the mass ofexplosive that actively contributes to the blast wave gener-ation. The next step will be to evaluate the energy partitionthat goes into the fragmentation of the casing.

4.4 Fragmentation analysis

In Sect. 2.2, three different equations for cased explosiveswere presented for the estimation of the momentum absorp-tion of the metal casing. The twomagnitudes required for theapplication of these formulations are the mass of the casingand the equivalent mass of bare explosive. For the calculationof the mass of casing, cylinder length and cylinder thicknessare required. The length considered is the one surroundingthe explosive base charge. The mass of the casing is obtainedfrom the dimensions of the cylinder metal shell surround-ing the explosive charge and the volumetric mass density ofthe shell. Next, the total explosive mass contained inside thedetonator is determined from (8), (9), and (10). Notice themass will be in terms of the reference explosive, in this case

123

V. Petr, E. Lozano

Table 2 Curve fitting coefficients for Equation (4)

Direction A B C D

Transverse 3.575 1 38.815 −16.884

Longitudinal 3.634 1 43.305 −49.641

Equ. sphere 3.596 1 41.679 −31.339

Table 3 Energy values for bare and cased charge

Equivalent barecharge (kJ)

Mass of casing(mg)

Cased explosiveenergy (kJ)

2.50±5.4% 290 Eq. (8): 3.26±5.4%

Eq. (9): 2.87±5.4%

Eq. (10): 3.35±5.4%

TNT. As it was mentioned in Sect. 2.2, the main differencebetween (8), (9), and (10) is that the latter considers earlyfragmentation of the casing [6].

From the total explosive mass in TNT, the total energy interms of kJ is calculated by multiplying this term by the heatof detonation for TNT. The heat of detonation is the energyrelease at theChapman–Jouguet (C–J) condition and refers tothe change in enthalpy [22]. This value can be obtained fromnumerous references for different types of explosives withina 3% difference. In this case, the adopted value for this heatof detonation for TNT is 4.61MJ/kg [7]. Table 3 summarizesthe energy values in kJ obtained from (8–10) for the equiv-alent bare charge and the actual cased charge. The relativeuncertainty for the equivalent bare charge (5.4%) considersthe accumulated error from the blast wave analysis and thediscrepancies for value of the heat of detonation for TNT.The systematic error from the mass of casing is negligiblecompared to the dominant error attributed to the blast waveanalysis.

As given in Table 3, a percentage difference of up to16% is obtained by the three different formulations (8) to(10). In order to determine the formulation that best modelsthe energy partition from these types of detonators, furtheranalysis was performed using the Gurney model. From thecylinder casingmass and terminal velocity, themass of explo-sive that accelerates the shell can be obtained using (11).This was done using the SIM Control 1.0.5.23 (Special-ized Imaging camera software package) for tests 7 and 8,where the nominal value of the terminal velocity measuredalong the transverse axis of the detonator was 2.87 mm/µs(Fig. 6). The uncertainty associatedwith themeasurements is±0.03mmdue to the image pixelation. From the velocity andthe mass of the cylinder section of the casing, (11) yieldeda nominal mass of PETN of 532 mg and a correspondingenergy value of 3.32 kJ ± 3.7% (considering a heat of det-onation for PETN of 6.24MJ/kg [22]). The actual mass of

Fig. 10 Sample images of the tip expansion from test 9, the last twoframes displayed are 0.54µs apart

PETN contained in the base charge (i.e., 555mg) falls withinthe experimental error.

The explosive energy obtained from theGurneymodel liesbetween the values obtained from (8) and (10) showing thatthe Fisher and Hutchinson equations provide a good estima-tion for gram-scale cased explosive charges. A significantlylower energyvaluewas obtained from theModifiedFisher (9)due to the high ultimate strain of the aluminum casing. How-ever, asmentioned in Sect. 2.2, (8) through (11) are not able toevaluate the fraction of the energy that is exerted on the shell’stip. In order to evaluate the energy transmitted to this region,one-dimensional measurements of the tip free-surface veloc-ity along the detonators centerline were performed using theSIM Control 1.0.5.23 for test 9 (Fig. 10).

A tip terminal velocity of 3.51±0.03mm/µswas recordedin test 9.This value is in goodagreementwith the3.45 mm/µsobtained by the gas-dynamic solution (12) considering aneffective conical charge Ctip with a 68◦ base cone angle.Therefore, the kinetic energy imparted to this region is0.22 kJ± 1.7% for one-dimensional motion of the tip. Simi-larly, the kinetic energy transmitted to the cylindrical sectionwas calculated, which yields a value of 0.70 kJ±2.1%.Mur-phy et al. [24] perform an alternative 1-D analysis of the tipof a prototype detonator where the free-surface position ver-sus time of the nickel cup is fitted to a power-law relationand compared to PDV measurements. General quantitativeagreement was found between the imaging and the PDV fits,suggesting that the tip is accelerated as an explosively drivenflyer.

One last step in the characterization of the detonatorwas done by analyzing the fragment area distribution. Anumber 8 electric detonator was detonated in a cylindricalaluminum container with a capacity of 3.8 L. The containerwas filled with shock absorbing foam with dynamic vis-cosity of 1 kPa·s. The main purpose of the foam was toabsorb most of the kinetic energy of the fragments beforethey impact the container’s walls. After detonation, the con-tent of the aluminum cylinder was filtered through two metalsieves with openings corresponding to 1.81 mm and 850µm(Fig. 11). The fragments from the detonator’s shell were thencollected and digitally analyzed using ImageJ. ImageJ is anopen-source image-processing program designed for scien-tific multidimensional images.

123

Characterizing the energy output generated by a standard electric detonator using shadowgraph…

Fig. 11 Fragments recovered from the detonator (negative image) anddigital particle size analysis

Fragments from the different parts of the detonator weredispersed in all directions. A wide variety of fragment sizesare observed in Fig. 11. However, those from the casingin contact with the base charge are of main interest (pri-mary fragmentation). Some internal components, such as thebridge plug or the steel sleeve that houses the primer charge,can be also observed.

The particle analysis performed in Fig. 11 reveals theexperimental fragment area distribution of the primary frag-mentation. As shown in Fig. 12, the majority of the primaryfragmentation has an area ranging from 1 to 12 mm2. Thehighest frequency is reached for fragment areas between 2and 3mm2. The histogram bin width, that ultimately revealsthe statistical features of the data, was calculated using theFreedman–Diaconis rule. Figure 12 also plots the area dis-tribution from the Weibull approximation to the linear Mottstatistical fracture spacing distribution from (14). The theo-retical distribution is in good agreement with the measuredexperimental distribution. A total of 6 fragments out of the144 lay outside the area distribution based on the Mott the-ory. Similar agreement was reported by Grady [18] based onfragmentation experiments on uranium-6%-niobium (U6Nb)tubes.

The fragment area distribution presented here is particu-larly interesting for the discretization of the detonator casingand the application of computational methods. Additionally,and in combination with the velocities obtained, it providesvaluable information for hazard evaluation in case of acci-dental detonation.

Fig. 12 Fragment area distribution of primary fragmentation

4.5 Explosive energy partition

The total energy released by the detonation can be obtainedby multiplying the explosive masses of the primer and basecharges by their heat of detonation. These quantities pro-vide a correct understanding of the energy stored in thedetonator, but they do not provide a direct measure of thedifferent modes in which the energy is released. Since theprimer charge is housed in a heavy steel casing and hasa very low heat of detonation—about 25% of the heat ofdetonation of the PETN—its contribution to the final shockoutput is expected to be less than 3% of the free-air energyreleased by the base charge. This assumption is evaluated byusing the Hutchinson equation since Fisher’s formula failsfor M/C > 5 [6]. The steel sleeve has a total mass of 7.77g,while the associated section of the shell is 980mg of alu-minum. For the 330mg of primer charge, this correspondsto an M/C equal to 26.5. By applying (10), the resultantmass of equivalent bare charge is 47.6mg, which multipliedby the heat of detonation for Lead Azide (1.638 kJ/kg [25])yields approximately 78J. This value lies within the totalerror associated with the work presented here and thereforeis neglected regarding the energy output of the detonator. Asimilar argument could be made for the electrical energy thatis applied to the bridgewire. This energy usually ranges from5 to 10mJ for standard electric detonators [23], which meansthat the electrical energy is five orders of magnitude lowerthan the energy coming from the explosive base charge.

Based on the analysis performed in this paper with 6%cumulative error, the explosive energy partition for the stud-

123

V. Petr, E. Lozano

ied number 8 electric detonator is as follows: 70% of theenergy content goes into the blast wave formation, 25% intothe kinetic energy of the casing, and the remainder uncertainfractions partitioned between radiation, strain, and fractureenergy, along with incomplete energy release of the explo-sive itself. From the total kinetic energy transmitted to thecasing, 75% is spent on accelerating the cylindrical section,while 25% is directed on the tip of the detonator.

5 Conclusions

The retroreflective shadowgraph technique has proven tobe a fast and accurate tool for characterizing the strengthof detonators compared to the traditional indirect methods.Additionally, it allows for the study of different modes inwhich the chemical energy is converted and how it is dis-tributed.

A total of nine electric detonators were tested usinghigh-speed and ultra-high-speed imaging techniques. Bymeasuring the shock wave expansion rate, the primary blastwave in the air was characterized. Shock wave parame-ters were successfully calculated versus distance and timescales. Optical measurements were additionally validatedusing piezoelectric pressure gauges that recorded overpres-sure versus time histories at specific locations.

Because of their geometry, standard detonators show aninitial ellipsoidal shock expansion that degenerates into afinal spherical wave. This non-uniform shape creates vari-able blast parameters along the primary blast wave. For thisreason, transverse and longitudinal directions were studiedas well as the equivalent geometric sphere. From the shockMach number versus distance, a total energy of 2.50 kJ wasassessed to the air shock load with 5.4% uncertainty.

The fraction of the energy spent in the fragmentation of thecasing was also accounted for using three different empiricalformulations: Fisher, Modified Fisher, and Hutchinson. Theresults obtained from each of them varied by 16%; therefore,the casing expansion and acceleration was experimentallymeasuredusingultra-high-speed imaging and correlatedwiththe Gurney model. The terminal velocity was optically mea-sured at the tip and at the cylindrical section of the casing.These velocities yielded values of kinetic energy from thedifferent sections in good agreement with the existing for-mulations. Nominal values of 0.22 and 0.70kJ were obtainedfor the kinetic energies of the tip and cylinder, respectively.This revealed that Hutchinson’s equation provides the bestresults within an 8% range versus the other formulations.

The fragment area distribution was also studied usingparticle imaging analysis, showing that the majority of theprimary fragmentation has an area ranging from 1 to 12 mm2

with the greatest frequency for fragment areas between2 and 3mm2. Good agreement was found between the

experimental and theMott fragment area distribution. Under-standing the fragment density distribution plays a criticalrole when performing hazard evaluation from these types ofdevices.

The final explosive energy partition for the studied deto-nator resulted in 70% of the energy content going into theairborne shock wave, 25% into the kinetic energy of thecasing, and the remainder comprised of uncertain fractionspartitioned between radiation, strain, and fracture energy,along with incomplete energy release of the explosive itself.75% of the kinetic energy is spent on accelerating the cylin-drical section, while 25% is directed on the tip of thedetonator. Additionally, it has been proven that the energycontribution from the primer detonator charge and the elec-tric bridgewire are negligible in relation to the shock andprimary fragmentation.

In general, this paper has demonstrated a method to relatethe strength of a detonator to a value of energy in kilojouleswith 6% cumulative error if the casing acceleration is directlymeasured. The uncertaintywould increase to 8% if the energyspent in the fragmentation is evaluated using Hutchinson’sempirical relation.

Understanding how the energy is released and in whatquantities is critical for the performance evaluation of detona-tors and other similar devices. Future workwill be performedby AXPRO at the Colorado School of Mines for the char-acterization of the energy output for different types andstrengths of commercial detonators using advanced imagingtechniques.

Acknowledgements We would like to thank the Colorado School ofMines, Mining Engineering Department for the use of the ExplosivesResearch Laboratory. We would also like to thank JonathanMace, fromLos Alamos National Laboratory, for providing us with the knowledgeand equipment to develop our shadowgraph research capabilities. Aswell, we would like to acknowledge the support of Vision Researchand Specialized Imaging, specifically Frank Mazella, Rick Robinson,and Frank Kosel for their encouragement of the advancement of ourexperimentation.

References

1. Bigg-Wither, H.: Notes on detonators. Trans. Inst. Min. Eng. 21,442 (1900)

2. Environmental Protection Agency: AP 42, 5th Edition, Vol. I, Ord-nance Detonation 15.9: Blasting Caps, Demolition Charges, andDetonators (2009)

3. Kleine, H., Dewey, J.M., Ohashi, K., Mizukaki, T., Takayama, K.:Studies of the TNT equivalence of silver azide charges. ShockWaves 13(2), 123–138 (2003)

4. Hargather, M.J., Settles, G.S.: Optical measurement and scalingof blasts from gram-range explosive charges. Shock Waves 17(4),215–223 (2007)

5. Biss, M.: Energetic material detonation characterization: Alaboratory-scale approach. Propellants Explos. Pyrot. 38(4), 477–485 (2013)

123

Characterizing the energy output generated by a standard electric detonator using shadowgraph…

6. Hutchinson,M.D.: The escape of blast from fragmentingmunitionscasings. Int. J. Impact Eng. 36(2), 185–192 (2009)

7. Kinney, G.F., Graham, K.J.: Explosive Shocks in Air. Springer,New York (1985)

8. Needham, C.E.: Blast Waves. Springer, Berlin (2010)9. Cooper, P.W.: Comments on TNT equivalence. In: 20th Interna-

tional Pyrotechnics Seminal, pp. 215–226 (1994)10. Esparza, E.D.: Spherical equivalency of cylindrical charges in free-

air. In: 25th Explosives Safety Seminar, pp. 403–428 (1992)11. Dewey, J.M.: Expanding spherical shocks (Blast Waves). In: Ben-

Dor, G., Igra, O., Elperin, T. (eds.) Handbook of ShockWaves, vol.2, pp. 441–481. Academic Press, Boston (2001)

12. Kingery, C.N., Bulmash, G.: Air blast parameters from TNT spher-ical air burst and hemispherical burst. Report ARBRL-TR-02555,Army Ballistic Research Laboratory, Aberdeen Proving Ground,MD (1984)

13. Taylor, G.I.: The formation of a blast wave by a very intense explo-sion. Proc. R. Soc. Ser. A 201(1065), 159–174 (1950)

14. Hargather, M.J.: Scaling, characterization, and application ofgram-range explosive charges to blast testing of materials. Ph.D.Dissertation, Pennsylvania State University (2008)

15. Gurney, G.W.: The initial velocities of fragments from bombs,shells, and grenades. Tech. Rep. BRL-405, Army BallisticResearch Laboratory, Aberdeen Proving Ground, MD (1943)

16. Benham, R.A.: Analysis of themotion of a barrel-tamped explosivepropelled plate. Report SAND78-1127, Sandia National Laborato-ries, NM (1978)

17. Kennedy, J.E.: The Gurney model of explosive output for drivingmetal. In: Zukas, J.A., Walters, W. (eds.) Explosive Effects andApplications, Ch. 6, pp. 221–257. Springer, New York (1998)

18. Grady, D.: Fragmentation of Rings and Shells: The Legacy of N.F.Mott. Springer, Berlin (2006)

19. Dyno Nobel.: Electric SuperTM SP Technical Information.http://www.dynonobel.com/~/media/Files/Dyno/ResourceHub/Technical%20Information/North%20America/Initiation%20Systems/Electrics/ElectricSuperSP.pdf. Accessed 10 Aug2016

20. Hargather, M.J., Settles, G.S.: Retroreflective shadowgraph tech-nique for large-scale visualization. Appl. Opt. 48(22), 4449–4457(2009)

21. Rigby, S.E., Tyas, A., Fay, S.D., Clarke, S.D., Warren, J.A.: Val-idation of semi-empirical blast pressure predictions for far fieldexplosions—is there inherent variability in blast wave parameters?In: 6th International Conference on Protection of Structures againstHazards, pp. 16–17 (2014)

22. Weinheimer, R.: Properties of selected high explosives. In: 27thInternational Pyrotechnics Seminar, pp. 13–17 (2000)

23. Cooper, P.W.: Explosives Engineering. Wiley, New York (1996)24. Murphy, M.J., Clarke, S.A.: Simultaneous photonic doppler

velocimetry and ultra-high speed imaging techniques to char-acterize the pressure output of detonators. In: AIP ConferenceProceedings 1426, 402 (2012)

25. Meyer, R., Köhler, J., Homburg, A.: Explosives. Wiley, Weinheim(2007)

123