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Dependence of the Mechanical Sensitivity on the Fractal Charac-teristics of Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine Particles

Yi Wang,a, b Xiaolan Song,c Dan Song,d Wei Jiang,a Hongying Liu,a Fengsheng Li*a

a National Special Superfine Powder Engineering Research Center, Nanjing University of Science and Technology,Nanjing 210094, P. R. Chinae-mail: [email protected]

b School of Materials Science and Engineering, North University of China, Taiyuan 030051, P. R. Chinac School of Chemical Engineering and Environment, North University of China, Taiyuan 030051, P. R. Chinad China Ordnance Institute of Science and Technology, Beijing 100089, P. R. China

Received: April 25, 2010; revised version: April 14, 2011

DOI: 10.1002/prep.201000053

Abstract

Three fabrication methods were used to synthesize HMX pow-ders with different particle sizes and microscopic morphologies.All as-prepared samples were characterized by laser granularitymeasurements and scanning electron microscopy (SEM). Themechanical sensitivity and thermal stability of the differentHMX powders were characterized using mechanical sensitivitytests and differential scanning calorimetry (DSC). Size distribu-tion data and SEM images were used to find the size fractal di-mension (D) and surface fractal dimension (Ds) of HMX sam-ples, which were calculated by the least-squares method and frac-tal image processing software (FIPS), respectively. The parame-ters D and Ds quantize two important properties of HMX parti-cles, namely the complexity of the particle size distribution andthe irregularity of the particle surface, which affect the thermalconductivity of the particle group if it is exposed to stimuli suchas impact, friction or heating. The fractal dimensions reveal thedependence of the mechanical sensitivity of HMX on thepowder size, size distribution and microscopic morphology. Theresults indicate that the proportion of fine particles in HMXpowder increases as the D value increases, which causes de-creased impact sensitivity. This occurs because hot spot forma-tion leading to an explosion is more difficult because of the im-proved thermal conductivity of the particle group. Similarly, thesurface roughness of HMX particles increases with an increase inDs, causing an increase in friction sensitivity because of the ex-cessive accumulation of frictional heat. In addition, thermal anal-ysis results indicate that the maximum thermal decompositionrate of HMX decreases with increasing D and Ds.

Keywords: HMX, Energetic Particles Group, FractalCharacteristic, Thermal Conductivity, Mechanical Sensitivity

1 Introduction

The high energy nitramine explosive octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) has been used in nu-clear detonations, anti-tank missile warheads, and highenergy propellants [1–3]. However, there are two prob-lems that must be overcome to allow for more extensiveuse of HMX, i.e., low safety and high cost, with theformer severely restricting the application of HMX inspecial warheads.

Besides the molecular structure, charge diameter andcrystal phases, particle microstructure and size also play asignificant role in the safety of an explosive [4–6]. In ourprevious research, the effects of size and size distributionand microscopic morphology on the safety of HMX andRDX were studied in detail [7,8]. We found that the me-chanical sensitivity of HMX was a function of particlesize, but that the trend of these changes was obviouslyregulated by microscopic morphology. For example, asthe median particle size (d50) of HMX decreased, the fric-tion sensitivity increased for spherical samples and de-creased for needle-shaped ones. Moreover, for two RDXsamples with similar median particle sizes and microscop-ic morphologies, the sample with the broader size distri-bution exhibited a higher apparent activation energyduring thermal decomposition [7].

Previous research has established the relationship be-tween the structural characteristics and mechanical sensi-tivity of HMX powders; however, the exact reason whythe change in particle size and morphology affects thesafety of HMX remained unknown, which is the topic ofthis paper. In classical theory, when energetic materials

Propellants Explos. Pyrotech. 2011, 36, 505 – 512 � 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 505

undergo an action of impact, friction, and electrostaticshock, the energy generated by the stimulus is convertedinto heat, which is conducted among the particles [9, 10].If the effective thermal conductivity of the particle groupis too low to dissipate the heat away from the system intime, initiation is localized in small volumes (hot spots)where the accumulated heat is intense enough to lead toa vigorous reaction. In general, an explosion could be at-tributed to heat conduction and the formation of hot-spots.

Our continued studies have discovered that the thermalconductivity of an HMX particle group is interrelatedwith its size distribution complexity and particle surfaceirregularity. For a particle group, the complexity of thesize distribution and the irregularity of the particle surfa-ces are defined as fractal characteristics quantized by thesize fractal dimension (D) and the surface fractal dimen-sion (Ds), respectively [11–13]. In particular, the depend-ence of the thermal conductivity of an HMX particlegroup on its fractal characteristics is discussed in detail toclarify the mechanism of the influence of particle size andmorphology on the mechanical sensitivity and thermalstability of HMX.

2 Experimental

2.1 Materials, Fabrication, and Sample Testing

Three kinds of HMX samples with spherical, needle andpolyhedral shapes were fabricated by wet milling, solvent/non-solvent and wet riddling methods, respectively [8].Within each kind of HMX, samples with different particlesizes were fabricated [8]. Characterization techniques,mechanical sensitivity testing and thermal analysis meth-ods are described in Ref. [8].

2.2 Calculation of Size Fractal Dimension (D) of HMXParticles

First, the particle size distribution of an HMX sample wasmeasured using a Master Sizer Instrument and the cumu-lative distribution curve (YV, r) was obtained. The relationbetween YV and r is given by Equation 1 [14].

YVðrÞ / r3�D ð1Þ

Those data were converted into dual logarithm data(lnYV, lnr) and fit as a line with a slope b using the least-squares method. Consequently, the D value of an HMXsample is the value (3–b).

2.3 Calculation of Surface Fractal Dimension (Ds) ofHMX Particles

Using Fractal Image Processing Software (FIPS), an origi-nal SEM image of a typical HMX particle sample waspretreated by increasing resolution and removing defectsthen converted into a monochrome bitmap. BOX-arith-

metic was used to calculate the value of Ds, using Equa-tion 2 [15].

Ds ¼ limk!1

lnNek

lnek�1

ð2Þ

With BOX arithmetic, a series of boxes with variablesize e was used to cover the digital image. The amount ofnonzero matrices (Nek

) was recorded according to eachsub-matrix, then the dual logarithm data (lnNek

, lnek�1)

were fit as a line. Consequently, the slope of the line isthe Ds value of the HMX sample.

3 Results

3.1 Size Fractal Characteristic of HMX Particles

The particle size distributions of several HMX sampleswere measured by a Master Size Instrument and are dis-played in Figure 1. The curves indicate that the size distri-butions of four kinds of HMX samples differ from eachother. Raw HMX particles present the broadest size dis-tribution, and the sample prepared by the solvent/non-solvent method exhibits the narrowest size distribution.Comparatively, the particle size distributions of the mill-ing and riddling samples show a major and minor dualpeak, respectively. For the milling samples in Figure 1b,as the median particle size (d50) decreases, the size distri-bution gradually broadens and the major peak shifts tothe left of the minor peak, which indicates that the pro-portion of fine particles increases. In order to accuratelydescribe the change in the size distribution of HMX, thesize fractal dimensions (D) were calculated by the least-squares method, and the results are listed in Table 1. Therepresentative calculations are given in Figure 2.

For HMX samples prepared by milling and solvent/non-solvent methods, the D values increase as the medianparticle size decreases. However, the D values of the rid-dling samples do not follow the same trend but fluctuateirregularly as a function of median particle size. In addi-tion, the average D value of the milled samples (D=2.635) is much higher than that of the riddling samples(D=2.293), and the solvent/non-solvent samples possessan average D value that is quite lower (D=2.178). As weknow, the higher D value means that the particle grouphas a more complex particle size distribution, i.e. , theproportion of fine particles in the group increases [14].Generally, a particle group composed of more fine parti-cles exhibits a higher specific surface area and better ther-mal conductivity [16]. It is inferred that the milling sam-ples may possess the best thermal conductivity for theirhigh D values compared with the other two kinds of sam-ples.

3.2 Surface Fractal Characteristics of HMX Particles

Besides the size fractal characteristic of a group of HMXparticles, the surface fractal characteristic also plays an

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important role in the thermal conductivity. The surfacefractal dimensions (Ds) of all HMX samples were calcu-lated and are listed in Table 1. The Ds calculations are re-corded in Figure 3, Figure 4, and Figure 5, with selectedSEM images, binary bitmaps and fitted regression equa-tions provided.

Comparing different HMX samples, the differences insurface roughness are indistinguishable in SEM imagesbut are distinguishable in binary bitmaps. Figure 4 showsthat needle samples have smooth surfaces and sharp out-lines, but the surfaces of spherical samples are unevenand very rough due to the friction action during the longmilling time. Moreover, as the milling time increased, thesurface roughness increased and the median particle sizedecreased. Of course, the calculated results indicate thatthe average Ds values of milled samples (Ds =2.832) arehigher than that of needle (Ds =2.681) and polyhedralsamples (Ds =2.687). The solvent/non-solvent sampleshave the lowest average Ds value due to having thesmoothest surface. For the riddling samples, the Ds valueis independent of median particle size and the average Ds

value is moderate. In fractal theory, the increase of Ds

originates from the increased particle surface irregularity,which implies an increase in surface roughness and specif-ic surface area [17]. Consequently, the milling samplesmay have the highest surface roughness compared withthe other two kinds of samples, which might play a nega-tive role on their friction sensitivity.

3.3 Dependence of Mechanical Sensitivity on the FractalCharacteristics of HMX Particles

In our previous study, within each kind of HMX sample,it was found that the mechanical sensitivity changed regu-larly with a change in median particle size [8]. However,if the microscopic morphology of the HMX particles wasaltered, the above trends showed obvious discrepancies,although the median particle size varied in the same way.For example, for decreasing d50, the impact sensitivity ofspherical HMX samples increases while it decreases forneedle ones. In general, despite the steady trend inmedian particle size, the mechanical sensitivity varies un-predictably. These experimental results strongly suggestthat the dependence of the mechanical sensitivity ofHMX on particle size and microscopic morphologymerely illustrates an ostensible manifestation rather than

Figure 1. Size frequency distribution curve of HMX samples:(a) raw HMX and the three smallest size samples within eachkind of sample; (b) five HMX samples prepared by wet milling.

Table 1. Fractal characteristic of HMX samples fabricated by three methods. d50 is average particle size; D is size fractal dimension;Ds is surface fractal dimension.

Wet milling spherical shaped particles Wet riddling polyhedron shaped particles Solvent/non-solvent needle shaped particles

d50(mm) D Ds d50(mm) D Ds d50(mm) D Ds

0.6 2.911 2.856 3.26 2.308 2.763 2.98 2.277 2.6414.5 2.847 2.848 21 2.360 2.644 4.8 2.166 2.669

10.9 2.528 2.813 63.1 2.395 2.652 10.2 2.198 2.70421.3 2.480 2.839 82.4 2.370 2.606 16.1 2.069 2.71056.1 2.409 2.805 125 2.124 2.710 – – –– – – 230 2.200 2.745 – – –

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Dependence of the Mechanical Sensitivity on the Fractal Characteristics


the actual mechanism. In fact, the fundamental factor ma-nipulating the trends of mechanical sensitivity can be es-sentially ascribed to the complexity of the particle sizedistribution and the irregularity of the particle surface in-stead of the particle size and morphology.

Results displayed in Figure 6 and Table 1 show that anincrease of the D value relates to a reduction of impactsensitivity, and an increase of the Ds value relates to anincrease in the friction sensitivity, no matter how the sizeor microscopic structure of HMX changes. Evidently, forthe riddling samples, the plots of impact and friction sen-sitivity vs. median particle size show no obvious trend;i.e. , the testing data do not increase or decrease regularlyas a function of median particle size. However, substitut-ing Ds for d50, the friction sensitivity shows a monotonicincrease with increasing Ds value.

Comparing the three kinds of HMX samples, sphericalsamples have the largest average D value correspondingto the highest average H50 value (H50 =54.1 cm) and theneedle samples have the lowest H50 value, attributed tothe smallest D value. Moreover, spherical samples havethe largest average Ds value and a highest friction sensi-tivity (P=80%), and the polyhedral samples have thelowest average explosive probability (P =32 %) and thesmallest Ds value of 2.7. In addition, the polyhedral sam-ples exhibit much higher friction sensitivity than theneedle ones although they have the similar average sur-face fractal dimension, which might be mainly attributedto their different crystal phases [8].

Figure 2. Size cumulation distribution curves of raw HMX and the milling samples: (a) raw HMX, d50 =85.9 mm; (b) wet millingsample, d50 =56.1 mm; (c) wet milling sample, d50 =21.3 mm; (d) wet milling sample, d50 =10.9 mm; (e) wet milling sample, d50 =4.5 mm;(f) wet milling sample, d50 =0.6 mm. Inserted graphs show the dual logarithm simulant lines calculated from size cumulating distribu-tion curve respectively.




Figure 3. SEM images of HMX samples prepared by wet mill-ing: (a) after 5 min, d50 =56.1 mm; (b) after 3 hours, d50 =0.6 mm.

Figure 4. Binary bitmaps of part of HMX samples: (a) at select area in Figure 3a; (b) at select area in Figure 3b; (c) by solvent/non-solvent, d50 =16.1 mm; (d) by solvent/non-solvent, d50 =2.98 mm; (e) by riddling, d50 =230 mm; (f) by riddling, d50 =3.26 mm.

Figure 5. Ds calculation of the representative samples: (a) bywet milling, d50 =56.1 mm; (b) by wet milling, d50 =0.6 mm; (c) bysolvent/non-solvent, d50 =16.1 mm; (d) by solvent/non-solvent,d50 =2.98 mm; (e) by riddling, d50 =230 mm; (f) by riddling, d50 =3.26 mm.




4 Discussion

Experimental results reveal that the key factor dominat-ing the mechanical sensitivity of HMX samples is theirfractal characteristics rather than their particle size. Boththe complexity of the particle size distribution and the ir-regularity of the particle surface directly relate to thethermal conductivity of HMX. In terms of the particlesize fractal dimension (D), an increased value indicatesan increased proportion of fine particles in the HMX par-ticle group, which leads to an increased specific surfacearea. Heat accumulation decreases due to a larger contactarea among energetic particles. As a result, if one HMXparticle group has a higher size fractal dimension, theheat generated by an impact action dissipates away in

time, preventing the formation of hot spots which wouldinitiate an explosion.

Furthermore, when HMX undergoes an impact action,adiabatic compression occurs upon the tiny holes scat-tered throughout the sample, which causes the formationof hot spots. The critical size (rc) of a hot spot is inverselyproportional to its critical temperature (Tc) [18]:

T02

ZEexpðE=RTcÞ ¼

0:04Qmrc2

kcRð3Þ

where T0 is the initial temperature, Qm is the reactionheat per unit mass, c is the specific heat capacity, Z is thefrequency factor, E is the activation energy and R is thegas constant. There are numerous tiny holes scatteredamong the compressed particles, and the size of theseholes becomes smaller with an increasing proportion offine particles. The initial explosion is localized at thesetiny holes (hot spots) when HMX undergoes an intenseimpact. A smaller size hole gives a higher critical temper-ature Tc, implied in Equation (3). Therefore, an increasedD value will lead to an increased Tc due to the increasedproportion of fine particles. Combining all of the aboveinformation with our experimental results, it is reasonablethat the milled HMX sample with the highest average Dvalue exhibits the lowest impact sensitivity, and a homol-ogous correspondence also exists for the other two kindsof HMX samples.

Besides the size fractal characteristic, the surface frac-tal characteristic also affects the thermal conductivity of aparticle group because it is related to the specific surfacearea (Sm). The relationship between Ds to Sm is givenbelow [19]:

Sm ¼Ksv

1rDs�1 ð4Þ

where Ksv is a specific shape-dependent constant whichrelates to the particle shape and microscopic morphology,r is the particle size and 1 is the density. Equation 4 indi-cates that the increase of Ds and/or decrease of r willresult in the increase of Sm. For example, because HMXsamples that are prepared by one method should havethe same Ksv and 1, the Sm of the milling sample has amore than 18-fold increase when Ds increase from 2.805to 2.813. In theory, the HMX sample with a higher Ds

value should have shown lower friction sensitivity. How-ever, the experimental results indicate the opposite, i.e. ,the frictional explosion probability rises almost linearlywith an increase in Ds. The frictional explosion mecha-nism is particularly dominated by interfacial frictionamong energetic particles, which is completely differentfrom the impact explosion mechanism, which is predomi-nantly initiated by the adiabatic compression of tiny holeswithin the sample. In terms of a frictional explosion, theformation and growth of hot spots is mainly attributed tothe friction between contacted particle surfaces. Accord-

Figure 6. Plot of mechanical sensitivity of HMX samples to thefractal dimension of HMX particles: (a) the change of impactsensitivity as a function of size fractal dimension D ; (b) thechange of friction sensitivity as a function of surface fractal di-mension Ds. The average particle size d50 of all samples are listedin Table 1.




ingly, the surface roughness will dominate the heat gener-ated by friction (Qf) [20].

Qf ¼mWn

4aJðK1 þK2Þð5Þ

where W is the load, v is the relative velocity, a is the con-tact radius, K1 and K2 are the thermal conductivity coeffi-cients and J is the mechanical equivalent of heat. A highDs value of HMX implies a considerably rough particlesurface. In this case, the heat cannot be dissipated awayin time to prevent explosion, because the frictional heatis much greater than that radiated by thermal conduction.Consequently, experimental results confirm a direct ratioof Ds to the friction sensitivity. Comparing HMX samplesprepared by different methods, the milled samples havethe highest average Ds value and average value of explo-sive probability (P=80 %) due to the intrinsic friction be-havior of milling. In addition, riddling samples presentthe lowest friction sensitivity (P=31) owing to the small-est average Ds value, i.e. the smoothest surface.

Nevertheless, the above experimental results can notconceal the improvement in thermal conductivity result-ing from the increase of Ds and Sm. This improvementwas observed via exerting another kind of action onHMX samples instead of friction. Thermal analysis of themilled samples was conducted, and their TG curves andthe derivative of the TG curves as a function of tempera-ture are presented in Figure 7. Because the temperature(T) corresponds to the testing time (t) during the TGanalysis, i.e. T=at+b, the ratio of mass loss (Dm) to thechange of temperature (DT) is the slope of the line, andgives the thermal decomposition rate of the HMX sam-ples. Figure 7 indicates that the final weight loss of fiveHMX samples do not show any obvious differences, butthe maximum thermal decomposition rate (jdm/dT jmax)falls as the Ds and D values rise. In particular, the samplewith D of 2.911 and Ds of 2.856 had the lowestjdm/dT jmax, simply due to having the best thermal con-ductivity.

5 Conclusion

The size, size distribution and microscopic morphology ofHMX particles play significant roles in the safety of thematerial. Our previous study presented the dependenceof the mechanical sensitivity and thermal stability ofHMX on particle size and microscopic morphology. How-ever, because of the uncertainty of defining trends inthose experimental data, we concluded that the mecha-nism of the influence of particle size and microscopicmorphology on the safety of HMX had not been clarified.In this paper, it is suggested that the essential factor af-fecting the mechanical sensitivity is the different thermalconductivities of HMX particle groups, which is relatedto their size distribution complexity and the irregularityof the particle microscopic morphology.

To quantize the complexity and the irregularity of anHMX particle group, fractal theory was introduced andthe size fractal dimension (D) and surface fractal dimen-sion (Ds) were calculated, by which some important andimplicit characteristics of an HMX particle group, such assize distribution width, proportion of fine particles, sur-face roughness and specific surface area, can be depictedclearly. These features are directly correlated with thethermal conductivity of the energetic particle system.

HMX samples with higher D values show less sensitivi-ty to impact action, which is attributed to the increasingproportion of fine particles. An increase in the proportionof fine particles means an improvement of the thermalconductivity of an HMX particle group because the spe-cific surface area increases. Accordingly, it is hard to formhot spots under impact action. However, HMX sampleswith larger Ds values exhibit higher friction sensitivity.

Figure 7. Thermal decomposition of HMX samples fabricatedby wet milling: (a) typical TG curves; (b) the derivative of TGcurves as a function of temperature. Average particle size d50 ofabove the samples are listed in Table 1.




Although their specific surface area also increases, higherfriction sensitivity results from the rapid accumulation offrictional heat from higher surface roughness. Moreover,as the D and Ds values increase, the maximum thermaldecomposition rate of HMX decreases due to the im-proved thermal conductivity. In conclusion, introducingfractal characteristics bridges the gap between the phe-nomena and the underlying mechanisms, by which we caninterpret the experimental data in depth.

Acknowledgments

The authors would like to thank Prof. James Short (deputy direc-tor of Center for Energetic Concepts Development of U.S.A.)and Dr. Haridwar Singh of the High Energetic Materials Re-search Lab of India, who provided many helpful suggestions forour experiments.

References

[1] R. R. Sanghavi, P. J. Kamale, M. A. R. Shaikh, HMX-basedEnhanced Energy LOVA Gun Propellant, J. Hazard. Mater.2007, 143, 532.

[2] M. L. Hobbs, HMX Decomposition Model to CharacterizeThermal Damage, Thermochim. Acta 2002, 384, 291.

[3] L. Qiu, H. M. Xiao, Molecular Dynamics Study of BindingEnergies, Mechanical Properties and Detonation Perform-ances of Bicyclo-HMX-based PBXs, J. Hazard. Mater. 2009,164, 329.

[4] C. R. Siviour, M. J. Gifford, S. M. Walley, Particle Size Ef-fects on the Mechanical Properties of a Polymer BondedExplosive, J. Mater. Sci. 2004, 39, 1255.

[5] J. H. ter Horst, R. M. Geertman, G. M. van Rosmalen, TheEffect of Solvent on Crystal Morphology, J. Cryst. Growth2001, 230, 277.

[6] P. Karakaya, M. Sidhoum, C. Christodoulatos, Aqueous Sol-ubility and Alkaline Hydrolysis of the Novel High Explo-sive Hexanitrohexaazaisowurtzitane (CL-20), J. Hazard.Mater. 2005, 120, 183.

[7] X. L. Song, F. S. Li, Dependence of Particle Size and SizeDistribution on Mechanical Sensitivities and Thermal Sta-bilities of Hexahydro-1,3,5-trinitro-1,3,5-triazine, Def. Sci. J.2009, 59, 37.

[8] X. L. Song, Y. Wang, C. W. An, Dependence of ParticleMorphology and Size on the Mechanical Sensitivity andThermal Stability of Octahydro-1,3,5,7-tetranitro-1,3,5,7-tet-razocine, J. Hazard. Mater. 2008, 159, 222.

[9] M. J. Gifford, W. G. Proud, J. E. Field, Development of aMethod for Quantification of Hot-spots, Thermochim. Acta2002, 384, 285.

[10] R. W. Armstrong, H. L. Ammon, W. L. Elban, Investigationof Hot-spot Characteristics in Energetic Crystals, Thermo-chim. Acta 2002, 384, 303.

[11] R. Jahn, H. Truckenbrodt, A Simple Fractal AnalysisMethod of the Surface Roughness, J. Mater. Process. Tech.2004, 145, 40.

[12] A. Tasdemir, Fractal Evaluation of Particle Size Distribu-tions of Chromites in Different Comminution Environ-ments, Miner. Eng. 2009, 22, 156.

[13] A. Billi, F. Storti, Fractal Distribution of Particle Size inCarbonate Cataclastic Rocks from the Core of a RegionalStrike-Slip Fault Zone, Tectonophysics 2004, 384, 115.

[14] K. Yu, Z. S. Zheng, Fractal Study on Granularity Distribu-tion of Powder, Mater. Sci. Eng. 1995, 13, 30.

[15] Z. G. Feng, H. W. Zhou, Computing Method of Fractal Di-mension of Image and its Application, J. Jiangsu Univ. Sci.Technol. 2001, 22, 92.

[16] Y. Shi, J. S. Xiao, S. H. Quan, Fractal Model for Predictionof Effective Thermal Conductivity of Gas Diffusion Layerin Proton, Exchange Membrane Fuel Cell, J. Power Sources2008, 185, 241.

[17] Y. T. Wang, S. Diamond, A Fractal Study of the FractureSurfaces of Cement Pastes and Mortars Using a Stereoscop-ic SEM Method, Cement Conc. Res. 2001, 31, 1385.

[18] C. G. Feng, Thermal Explosion Theory, 1, Science Press,Beijing, 1988.

[19] H. P. Xie, Fractal Pores and Fractal Particles of Rock andSoil Materials, Adv. In Mech. 1993, 23, 145.

[20] F. H. Chen, Principle and Design of Pyrotechnics, 1,Weapon Industry Press, Beijing, 1990.




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