The Geometric Scaling of IMX-104 Explosive: Detonation Velocity versus Charge Size for Cylindrical Rate Sticks and Slab Tests Samuel W. Vincent, Scott I. Jackson, Carlos Chiquete, Mark Short Shock and Detonation Physics Group Weapons Experiments Division Los Alamos National Laboratory Los Alamos, New Mexico, USA Abstract. We report detonation size-effect data for IMX-104, a new insensitive ex- plosive formulation composed of RDX, NTO, and DNAN. The size-effect data in- cludes numerically predicted and experimentally measured diameter-effect curves from cylindrical-geometry rate sticks and thickness-effect curves from slab tests. These results are used to determine the geometric scale factor that relates explosive performance in the cylindrical geometry to that of the slab geometry. A Detona- tion Shock Dynamics calibration curve is also provided for IMX-104 based on the available data. Introduction It has long been known that the detonation phase velocity D 0 of a condensed-phase explo- sive will decrease with increasing flow diver- gence in the detonation reaction zone 1 . This di- vergence occurs when post-shock pressures ex- ceed the yield stress of the explosive confiner and results in a radial flow component behind the shock front (Figure 1). The onset of radial expansion ahead of the sonic locus induces cur- vature of the shock front. As the charge radius R decreases, the relative magnitude of the di- Approved for unlimited release: LA-UR-14-24800 vergence becomes more significant on the det- onation, resulting in a decreased D 0 . In cylin- drical charges, this velocity decrement with di- ameter is referred to as a high explosive’s diam- eter effect. In slab charges, it is referred to as the thickness effect. The combined diameter- and thickness-effect curves are referred to here as the size effect. Comparison of the scaling of the diameter and thickness effect for condensed-phase ex- plosive has recently been a topic of significant interest 3 . Prior comparisons have been made for homogenous liquid explosives 4 , heteroge- nous solid explosives 5 , emulsion explosives 6,7 , and non-ideal blasting explosives 8 . Early In the Proceedings of the 15th International Symposium on Detonation
Transcript
The Geometric Scaling of IMX-104 Explosive:Detonation Velocity versus Charge Size for Cylindrical Rate Sticks and Slab Tests
Samuel W. Vincent, Scott I. Jackson, Carlos Chiquete, Mark ShortShock and Detonation Physics Group
Weapons Experiments DivisionLos Alamos National LaboratoryLos Alamos, New Mexico, USA
Abstract. We report detonation size-effect data for IMX-104, a new insensitive ex-plosive formulation composed of RDX, NTO, and DNAN. The size-effect data in-cludes numerically predicted and experimentally measured diameter-effect curvesfrom cylindrical-geometry rate sticks and thickness-effect curves from slab tests.These results are used to determine the geometric scale factor that relates explosiveperformance in the cylindrical geometry to that of the slab geometry. A Detona-tion Shock Dynamics calibration curve is also provided for IMX-104 based on theavailable data.
Introduction
It has long been known that the detonationphase velocity D0 of a condensed-phase explo-sive will decrease with increasing flow diver-gence in the detonation reaction zone1. This di-vergence occurs when post-shock pressures ex-ceed the yield stress of the explosive confinerand results in a radial flow component behindthe shock front (Figure 1). The onset of radialexpansion ahead of the sonic locus induces cur-vature of the shock front. As the charge radiusR decreases, the relative magnitude of the di-
Approved for unlimited release: LA-UR-14-24800
vergence becomes more significant on the det-onation, resulting in a decreased D0. In cylin-drical charges, this velocity decrement with di-ameter is referred to as a high explosive’s diam-eter effect. In slab charges, it is referred to asthe thickness effect. The combined diameter-and thickness-effect curves are referred to hereas the size effect.
Comparison of the scaling of the diameterand thickness effect for condensed-phase ex-plosive has recently been a topic of significantinterest3. Prior comparisons have been madefor homogenous liquid explosives4, heteroge-nous solid explosives5, emulsion explosives6,7,and non-ideal blasting explosives8. Early
In the Proceedings of the 15th International Symposium on Detonation
Fig. 1. Divergence-induced detonation curva-ture from Ref. 2.
work4–6 measured the critical scale factor, de-fined as the ratio of the failure radius to fail-ure thickness Rc/Rc in cylindrical- and slab-geometry rate sticks, respectively. More recentstudies7–10 have also measured the steady prop-agation scale factor, defined as the ratio of ra-dius to thickness at identical detonation veloc-ity R(D0)/T (D0).
Researchers have interpreted that curvature-based detonation propagation theories, such asDetonation Shock Dynamics11 (DSD), predictthat all scale factors should be unity5–8 forexplosive propagation where there is a rela-tionship between the normal detonation veloc-ity Dn and the wavefront curvature κ. How-ever, most measured scale factors have not metthat expectation, especially for less ideal ex-plosives4,8,9. This discrepancy has led some8,9
to question the applicability of curvature-basedpropagation theories to non-ideal detonation.
Recently, Jackson and Short12 used a geo-metric proof to analytically demonstrate thatthe scale factor should not, in general, be unity.They12 also demonstrated that DSD was able toproperly predict the diameter effect, thicknesseffect, and a scale factor that was not unity forPBX 9502 cylindrical rate sticks and slab tests.A subsequent experimental study10 further val-
idated their analytical effort12 by measuring av-erage R(D)/T (D) values of 0.98, 0.81, and0.75 for PBX 9501, PBX 9502, and ANFO, re-spectively. These results indicated that increas-ingly non-ideal detonations exhibited scale fac-tors that increasingly deviated from unity.
In the present study, we report the measuredscale factors for the new explosive formulationIMX-104. Diameter- and thickness-effect datafor this material are presented. The results areset in context to the existing scale factor datafrom PBX 9501, PBX 9502, and ANFO.
IMX-104 Formulation and Prior Experi-ment
IMX-104 is an insensitive, melt-castable ex-plosive designed as a direct replacement to thewidely used, more sensitive Composition Bexplosive. Previously referred to as PAX-33MOD, IMX-104 was recently developed15 byARDEC, the U.S. Army Armament Research,Development and Engineering Center and iscomposed of RDX, NTO, and DNAN. Sensitiv-ity testing has shown this energetic material tohave output energy similar to that of Composi-tion B, but with much lower shock and frictionsensitivity. Eight cylindrical rate sticks werepreviously fielded to characterize the diametereffect and Dn–κ relation for IMX-10413. Fiveslab-geometry rate sticks were fielded to mea-sure the thickness effect in this study.
Figure 2 shows the the measured diame-ter effect on a plot of detonation velocity ver-sus inverse charge radius. The black pointsare from our prior measurements (Ref. 13 andmore recent tests). The red points are fromARDEC’s prior work14. The curves are gener-ated from Eyring-form16 fits to different com-binations of the cylindrical rate-stick data usingthe diameter-effect measurements as discussedin Ref. 17.
The Geometric Scaling of IMX-104 Explosive
In the Proceedings of the 15th International Symposium on Detonation
Fig. 2. The diameter-effect curves for IMX-104. Black points are from Ref. 13. Red points arefrom Ref. 14.
Experimental
The slab test geometry is an unconfined vari-ant of the detonation sandwich test18 that gen-erates a region of two-dimensional quasi-steadyflow for measurement of detonation velocityand front shape. Figure 3 is an image of the17.5-mm-thick slab test, which consists of con-sists of a high-aspect-ratio rectangular-cuboidmain charge that was boosted by two pieces ofPBX 9501 and initiated by two detonation linewave generators19,20.
Ionization probes, located in the center ofthe slab, measure the detonation position versustime relationship. As the detonation velocity issteady at the core of this geometry, the slopeof a linear fit to the position-time data yieldsthe detonation velocity. Additional details per-taining to the design and operation of the testare discussed in Ref. 10. Front shapes werealso measured using the mirror turning tech-nique (discussed in Ref. 21) and illuminationvia an Argon flash22.
Slab tests were performed at five thicknessesintended to compare well with the prior cylin-
Fig. 3. The slab test geometry.
drical rate stick data when plotted in size-effectspace (detonation velocity versus the inversecharge radius/thickness). The dimensions ofeach test, resulting detonation velocity, andstandard error are listed in Table 1.
Front Curvature Analysis
To obtain a representation of the shock frontshape in the shock height z versus radius r
The Geometric Scaling of IMX-104 Explosive
In the Proceedings of the 15th International Symposium on Detonation
Table 1. Slab test thickness t, length L, width w, initial density ρ0, detonation velocity D0, andstandard error SE.
plane, a digitized image of the front breakoutis produced and reduced according to magnifi-cation factors obtained from the axial detona-tion velocity and included fiducial in the im-age. To determine a base representation of thecrucial normal velocity-curvature relation thatinvolves derivatives of the front, experimentalfront shapes were fit using the form used dis-cussed in Hill23. It is a series function formbased on the work of Bdzil24,
z(r) = −n∑
i=1
Ai
[ln
(cos
(πη
2Rer
))]i, (1)
where r is the local radius and the parametersAi and η are fitting constants such that 0< η <1 and n = 1 except for the smallest test (8-1850, T = 9.99 mm) where it was necessary touse n = 3 for fitting the slab front shape data.
The normal velocity Dn and the front cur-vature κ can then be found from the curvaturerelations,
Dn =D0√
1 + (z′)2, (2a)
κ =z′′
[1 + (z′)2]3/2+ α
z′
r√1 + (z′)2
, (2b)
where z′ = dz/dr, z′′ = d2z/dr2 and α deter-mines whether the underlying test geometry iscylindrical (α = 1) or slab (α = 0). Use of atwice continuously-differentiable (C2) analyticfunction for z(r) yields smooth values of thefirst and second derivatives (z′(r) and z′′(r))and avoids the significant noise that would begenerated in the numerical differentiation of theraw wave front data.
The Geometric Scaling of IMX-104 Explosive
In the Proceedings of the 15th International Symposium on Detonation
0 2 4 6 8 10r (mm)
−2.0
−1.5
−1.0
−0.5
0.0
0.5
z(m
m)
8-1849
8-1848
8-1847
8-1846
8-1850
Fig. 4. The produced detonation front shapesfor the slab tests in circles. Additionally, log-form fits to the front shapes appear as lines.
The variation of the normal detonation ve-locity and total curvature κ appear in Figures 5and 6 for all the tests carried out in this series.The circle and triangle symbols in these seriesof plots represent the 90% and 99% extent ofeach detonation front shape. These are para-metrically plotted in Figure 7. The central threefront shapes overlapped very well when plottedinDn-κ space, but the largest and smallest testssignificantly diverged from the central core.
DSD Calibration
To calibrate an explosive for DSD, a func-tional form for theDn–κ relation must be spec-ified and its parameters systematically variedto optimally fit the available experimental datawithin the calibration procedure. To quantifythe quality of a particular fit, a merit func-tion must be defined that incorporates the errorin the DSD-calculated detonation velocity andfront shapes into a single metric. Here it is de-
0 2 4 6 8 10r (mm)
5.5
6.0
6.5
7.0
7.5
8.0
Dn
(mm
/µs)
Fig. 5. The variation of the normal detonationvelocity Dn vs. r produced from the log-formfits to the front shapes.
fined as
M = w∑
i=1,NDE
(Fi(Dcalc0,i −Dexp
0,i ))2+ (3)
(1− w)∑
i=1,NFS
Ei
∑j=1,N i
r
((zi,calcj − zi,expj ))2.
(4)
The merit function is structured into a size ef-fect component and a front shape error compo-nent. The scaling factor between the two setsof data is determined by w. In the calibrationsdescribed below, w = 0.999 (a value close to1 since there are many more front point errorpoints than size effect velocity error). The op-timized parameters or parameterization of theDn–κ relation is obtained by numerically min-imizing the defined multivariable merit func-tion. With this choice, the final shock front er-ror was 10% of the total merit function value.The calibration procedure used here is based onthe approach of Bdzil et al.25.
The specific functional form utilized in this
The Geometric Scaling of IMX-104 Explosive
In the Proceedings of the 15th International Symposium on Detonation
0 2 4 6 8 10r (mm)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
κ(1
/mm
)8-1849
8-1848
8-1847
8-1846
8-1850
Fig. 6. The variation of the curvature κ vs.r produced from the log-form fits to the frontshapes.
work is as follows:
Dn
DCJ= 1− α1κ
1 + α2κ+ α3κ2
1 + α4κ+ α5κ2(5)
where the parameters αi for i = 1, ..., 5 wereoptimized in the minimization of the meritfunction. The results are plotted in Dn − κspace in Figure 8 and the parameters are listedin Table 3.
The comparison of this calibration in termsof the thickness curve appears in Figure 9 andthe front shapes appear in Figure 10. The rootmean square (RMS) error for the thickness ef-fect data was 32.9 m/s but this is biased by thedifficulty of matching the smallest test veloc-ity point (for T = 9.99 mm). If one removesthat point from consideration, the RMS errorbecomes 17.2 m/s. The RMS error across allthe front shape fits was 0.0638 mm.
0.0 0.1 0.2 0.3 0.4κ (1/mm)
5.5
6.0
6.5
7.0
7.5
8.0
Dn
(mm
/µs)
8-1849 (19.31 mm)
8-1848 (17.51 mm)
8-1847 (15.06 mm)
8-1846 (12.55 mm)
8-1850 (9.99 mm)
Fig. 7. The experimental Dn-κ data resultingfrom the log-form fits of the slab front shapes.
DSD calibration prediction of rate-stickdata
The series of slab tests shared a consis-tent bulk or initial density of 1.755 ± 0.002g/cm3. As a result the slab-derived fit producedhere did not incorporate density dependence inany of the Dn(κ) functional form parameters.However, the rate-stick tests for this explosiveshowed a large range of densities in the explo-sive segments for each test13 and the averagedensities were generally lower than the currentslab test average.
Low-density explosive generates less energyrelease per unit volume and exhibits lower D0
values. These density-induced velocity vari-ations can overwhelm the size-effect velocityvariations and must be corrected for when com-paring experiments performed at varying den-sities. To leading order, density correction isachieved with a linear correction parameter β,such that
D0(ρ0) = D0(ρnom)× [1 + β (ρ0 − ρnom)] .
The Geometric Scaling of IMX-104 Explosive
In the Proceedings of the 15th International Symposium on Detonation
Table 3. Optimized fit parameters produced inthe calibration of the slab data.
Parameter Values Units
DCJ 7.714 mm/µsα1 1.491 mmα2 0.004 mmα3 134.4 mm2
α4 9.034 mmα5 216.3 mm2
φe 35.29 deg
(6)
Parameter β is determined from analysis ofthe experimental measurements and was deter-mined to be 0.802 from the slab test results.
Figure 11 compares the current calibrationprediction of the diameter effect data for a cal-culation at a nominal density ρnom of 1.755g/cm3 to a “density-corrected” set of the exper-imental rate-stick velocities (using β = 0.802)to the slab density.
Geometric Scale Factor for IMX-104
The geometric scale factor R/T (D0) is plot-ted in Figure 12 for IMX-104 as computed fromthe DSD calibration curve. The size effectdata indicates a steady detonation scale fac-tor R/T (D0) of approximately 0.82, but thatvaries with D0. This measurement is consis-tent with other explosive measurements10 andalso with theory12 as it lies below unity. Asmentioned, previous measurements10 indicatedaverage R(D)/T (D) values of 0.98, 0.81, and0.75 for PBX 9501, PBX 9502, and ANFO, re-spectively.
Conclusions
Five slab tests were performed with IMX-104 explosive to measure the detonation veloc-ity as a function of charge thickness. The re-sulting calibration data set consisting of thick-
Fig. 8. The experimentalDn-κ data of Figure 7is compared to the calibrated Dn(κ) function(black).
ness effect and slab front data has been usedto characterize the explosive’s Dn-κ propaga-tion law necessary for the application of theDSD methodology. In addition, this propaga-tion law was used to generate the correspond-ing diameter-effect curve. The slab-derivedDSD calculation of the diameter effect curveshowed some agreement (for the larger tests inthat series) with the previously obtained exper-imental diameter effect data (corrected to ac-count for the higher initial density seen in theslab tests). When combined with prior cylin-drical diameter-effect data13, the slab thick-ness effect data shows a geometric scale factorthat is approximately 0.82, which is consistentwith prior measurements10 for PBX 9501, PBX9502, and ANFO in that it is below unity12.
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The Geometric Scaling of IMX-104 Explosive
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0.00 0.02 0.04 0.06 0.08 0.10 0.121/R, 1/T (mm−1)
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