development of a numerical model for an expanding tube with
TRANSCRIPT
Research ArticleDevelopment of a Numerical Model for an Expanding Tube withLinear Explosive Using AUTODYN
Mijin Choi12 Jung-Ryul Lee123 and Cheol-Won Kong4
1 Department of Aerospace Engineering Chonbuk National University 567 Baeje-daero Deokjin-guJeonju 561-756 Republic of Korea
2 LANL-CBNU Engineering Institute Korea Chonbuk National University 567 Baeje-daero Deokjin-guJeonju 561-756 Republic of Korea
3 Department of Mechatronics Engineering Chonbuk National University 567 Baeje-daero Deokjin-guJeonju 561-756 Republic of Korea
4 Structures and Material Department Korea Aerospace Research Institute Daejeon 305-333 Republic of Korea
Correspondence should be addressed to Jung-Ryul Lee leejrrjbnuackr
Received 24 October 2012 Accepted 14 March 2013 Published 24 March 2014
Academic Editor Gyuhae Park
Copyright copy 2014 Mijin Choi et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Pyrotechnic devices have been employed in satellite launch vehicle missions generally for the separation of structural subsystemssuch as stage and satellite separation Expanding tubes are linear explosives enclosed by an oval steel tube and have beenwidely usedfor pyrotechnic joint separation systems A numerical model is proposed for the prediction of the proper load of an expanding tubeusing a nonlinear dynamic analysis code AUTODYN 2D and 3D To compute a proper core load numerical models of the open-ended steel tube and mild detonating tube encasing a high explosive were developed and compared with experimental results2D and 3D computational results showed good correlation with ballistic test results The model will provide more flexibility inexpanding tube design leading to economic benefits in the overall expanding tube development procedure
1 Introduction
Pyrotechnic devices are widely used in many space appli-cations They are used to perform releasing cutting pres-surization ignition switching and other mechanical workto initiate flight sequences during space missions such asthe separation of subsystems boosters fairings stages orpayload satellites Such explosive separation devices generatea shock environment that could have a destructive effect onthe structure and hardware especially on electromechanicaland optical equipment The environment is very complexand studies have revealed that little information is availabledescribing the basic mechanism of shock transmission andpredicting shock response Therefore improved guidelinesfor pyrotechnic design development and qualification areclearly needed [1ndash3]
Pyrotechnic devices may generally be divided into pointsources and line sources Typical point sources includeexplosive bolts separation nuts pin pullers and pushers
and certain combinations of point sources for low explosiveactuation Typical linear sources include flexible linearlyshaped charges mild detonating fuses and SuperlowastZip forhigh explosive actuation [4 5]
An example of line sources is shown in Figure 1 Thepyrotechnic device shown is a high-load-carrying separationsystem that must act without contamination of the payloadand is called an expanding tube in this study The device isone of the greatest shock producers in aerospace separationsystems The detailed components of the expanding tube arealso represented in Figure 1 consisting of an MDF (milddetonating fuse) support and a flattened steel tubeTheMDFis a small diameter extruded tube containing a single strandof explosive cord It is manufactured by filling a tube withexplosive material and extruding the tube using a conven-tional multiple-die cold extrusion process [6ndash9] Structureseparation is accomplished when the MDF is ignited Whenan MDF is initiated the detonation is propagated along
Hindawi Publishing CorporationShock and VibrationVolume 2014 Article ID 436156 10 pageshttpdxdoiorg1011552014436156
2 Shock and Vibration
ESMDC
Shear pin
Bolt
MDF
Oval tubeSupport
ESMDC detail
29
After separation Before separation
Figure 1 A pyro-separation system [9]
For long levels
0000E + 00
1667E minus 01
3333E minus 01
5000E minus 01
6667E minus 01
8333E minus 01
1000E 00
Plastic strains at times 5 10 and 15120583s
+
Figure 2 Numerical simulation of expanding tube free expansion [10]
Main axis
Minor axis
Thickness
+
Figure 3 Geometry of expanding tube
the entire length of the linear explosive at a VOD (velocity ofdetonation) between 60 and 75 kms with very high shockenergy This chemical reaction acts as mechanical loadingwhich allows the elliptical steel tube to expand mainly in the
15 grft
20 grft
25 grft
30grft
Failures
Figure 4 Experimental results of expanding tube
minor-axis direction and fractures pin joints Consequentlythe expanded tube can separate structures according to itsdesign without contamination [8] Since the performanceof expanding tubes is mainly related to the explosive loadinvestigation of the proper explosive load against expandingtube failure and structural damage is important to its design
Shock and Vibration 3
Sheathed HE
Steel tube
Air
Figure 5 Material location of two-dimensional expanding tube
Even if the expanding tube design has to be verified inballistic tests adding a numerical simulation step betweenthe expanding tube sample fabrication and its ballistic testcan be a more effective approach for proper explosive loaddetermination The numerical model can explain the fullphysics of the phenomena by solving the governing equationsthat describe the behavior of the system under consideration
In spite of the advantages of numerical simulation only afew numerical and experimental investigations on pyrotech-nic devices can be found in the literature Quidot [10] adoptedLSDYNA to simulate a pyrotechnic separation system Aline source comprised an expanding tube with a 1mm thickstainless steel case internal synthetic material and a lead-RDX cord with a 2 gm RDX charge Numerical simulationswere performed for this device as shown in Figure 2 How-ever the proper explosive load which is the most importantfactor for real-world applications of expanding tube designwas not addressed under consideration of the detonationwave propagation the fracturemechanism and experimentalvalidation
In this study two- and three-dimensional numericalanalyses of expanding tube were performed in order todevelop a numerical model with high accuracy The explicitdynamic code AUTODYN is adopted to simulate expansionof the tube and compute a proper core load AUTODYN isa hydrocode program that is especially suited to solve theinteraction problems of different systems of structure liquidand gas together as found in many studies of high explosivesimulation [11ndash15] To verify the accuracy of the developedmodel the numerical results were compared to experimentalballistic test results for different explosive load conditions
2 Ballistic Tests of Expanding Tubes
Experiments were performed to properly design a pyrotech-nic device Explosive tests were carried out for differentcore loads of 15 20 25 and 30 grft The expanding tubeis an open-ended cylinder in which an MDF filled withhexanitrostilbene (HNS) explosive is set along the centralaxis of the cylinder All MDF cords were manufactured with3mm diameters regardless of the respective explosive loads
Figure 6 Two-dimensional expanding tube numerical model
t = 000ms t = 002ms
t = 007ms t = 01ms
Figure 7 Expanding tube distortions (explosive load 15 grft)
and the wall thickness of the sheath was 01mm Figure 3represents a section view of an expanding tube with a majoraxis of 20mm a minor axis of 8mm and a thickness of1mm regardless of the core load The tests were carried out4 or 5 times for each core case and the deformed shapeand failure were investigated Figure 4 shows the results ofballistic tests with explosive core loads of 15 20 25 and30 grft Expanding tubes with 15 20 and 25 grft were freelyexpanded without failure In contrast the 30 grft expandingtube failed at both ends of the cylinder as shown in Figure 4The dimensions of each expanding tube were measured andthese measurements were averaged These results are usedto validate the numerical model which will be discussed inSection 3
It can be deduced from the ballistic test results thatthe threshold explosive load of the tested samples mustlie between 25 grft and 30 grft Ballistic tests are a goodapproach to determine a proper explosive load for expandingtubes as well as a better approximation of actual con-ditions However this experimental approach has severaldisadvantages in which ballistic tests typically require manyexpanding tube samples and connected structures which arealso damaged during the test and are nonreusableThe exper-imental method is also not flexible for design change and isexpensive and time consuming Moreover it is difficult toexplain the physical phenomena of structure and detonationinteractions Therefore to mitigate this problem the ballistictest should be the final confirmation test of the expandingtube development procedure after replacing the numerouscase samples with a reliable numerical model
4 Shock and Vibration
Material status
Void
Hydro
Elastic
Plastic
Material status
Void
Hydro
Elastic
Plastic
15 grft
3138
2828
2517
2207
1897
15862121 2471 2821 3171 3521 3871
X
Y
X
20 grft
3211
2860
2510
2160
1809
14592146 2486 2825 3165 3504 3844
Y
25 grft
X
Y
3235
2863
2490
2118
1746
13742135 2479 2823 3167 3511 3855
30grft
X
Y
3269
2868
2466
2065
1663
12622099 2458 2816 3174 3532 3891
Figure 8 Material status of expanded steel tube
3 Numerical Modeling
31 Numerical Model Numerical simulations were per-formed for all the experiments using hydrocode in AUTO-DYN 2D examining the experimental expanding behaviorand numerical stresses The two-dimensional model wasmade of a steel tube support MDF and surrounding airas shown in Figure 5 The surrounding air was modeled asan ideal gas and the area was 400mm times 400mm Sincethe material of the support layer was Teflon and it did notaffect tube expansion significantly it was assumed as air Theexplosive material was HNS 165 where 165 indicates thedensity of HNS which is 165 gcm3 The explosive loads forall cases ranged from 15 to 30 grftThe explosive propagationvelocity for HNS 165 was approximately 7030ms and thedetonation point was set to the center of the MDF
32 Material Description and Boundary Conditions Boththe reacted solid and reacted gaseous products of HNS165 explosive were characterized with the Jones-Wilkins-Lee
180
175
170
165
160145 150 155 160 165 170 175 180 185 190
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft15 grft
20 grft
20 grft
25 grft25 grft
Figure 9 Comparison between the experimental and calculationalresults
Shock and Vibration 5
x
Detonation at t = 000120583s
y
x
y
z
20mm
76mm
Figure 10 Three-dimensional expanding tube
Table 1 Material coefficients in Jones-Wilkins-Lee (JWL) equationfor HNS 165
Parameter Value Unit119860 465 times 10
8 kPa119861 887 times 10
6 kPa1198771
455 mdash1198772
135 mdash120596 035 mdash
equation of state (JWL EOS [16]) The pressure in eitherphase is defined in terms of volume and internal energyindependent of temperature as
119901 = 119860(1 minus
120596
1198771119881
) 119890minus1198771119881+ 119861(1 minus
120596
1198772119881
) 119890minus1198772119881+
120596119890
119881
(1)
where119881 = 120588120588119900is the relative volume 119890 is the internal energy
and 119860 119861 1198771 1198772 and 120596 are empirically determined constants
that depend on the kind of the explosive Table 1 lists theJWL EOS coefficients used for this analysis of the HNS witha density of 165 gcm3
The ideal gas EOS for air is shown as follows
119901 = (120574 minus 1) 120588119890 (2)
where 120574 is the ideal gas constant and 120588 and 119890 are the densityand internal energy of the air The internal energy of air atroom temperature and ambient pressure is 2068 times 105 kJ
Both the tube and sheath were modeled as SS304 steeland AL6061 With the high pressure resulting from explosivedetonation both the tube and sheath undergoing high strainrates were modeled using the shock equation of state [17] andSteinberg-Guinan strength model [18] Both the von Misesyield strength (119884) and the shearmodulus (119866) of the Steinberg-Guinan model are assumed to be described as a function ofpressure (119875) density (120588) and temperature (119879) and in thecase of yield strength the effective plastic strain as well (120576)
119866 = 1198660(1 + (
1198661015840
0
1198660
)
119901
12057813+ (
1198661015840
119879
1198660
) (119879 minus 300))
119884 = 11988401 + 120573 (120576 + 120576
119894)
119899
times (1 + (
1198841015840
119901
1198840
)
119901
12057813+ (
1198841015840
119879
1198840
) (119879 minus 300))
(3)
Shock wave
Reaction zone
Pres
sure
(kPa
)
Time (ms)
Figure 11 Pressure loading profile
where 120573 is the hardening constant and 119899 is the hardeningexponent The subscript 0 refers to the reference state (119879 =300K 119875 = 0 120576 = 0) The primed parameters with thesubscripts 119875 and 119879 indicate the derivatives of the parameterswith respect to pressure or temperature at the referencestate Table 2 summarizes the Steinberg-Guinan strengthparameters used for the numerical model for the SS304 steeland AL6061 used in the present analysis
A flow-out condition was applied to all boundaries ofthe Euler grid This allowed the material to freely leave thegrid and also prevented relief waves from being generatedoff the lateral boundaries of the solid which would reducethe overall strength of the compressive shock and rarefactionwaves
33 Failure Model Spallation (spall-fracture) is a kind offracture that occurs as planar separation of material parallelto the incident plane wave fronts as a result of dynamic tensilestress components perpendicular to this plane [19] The spallstrength for tensile stress generated when a rarefaction wavetravels through material is 21 GPa for the steel tube If thetensile stress of the tube exceeds the predefined spall strength
6 Shock and Vibration
Y
Z
(a)
X
Y
Z
(b)
Figure 12 Three-dimensional model of expanding tube (front view (a) and isotropic view (b))
X
Y
Z
(a)
X
Y
Z
(b)
X
Y
Z
(c)
X
Y
Z
Bulk failBulk faila
(d)
Figure 13 Material status of one-sided detonation expanding tube ((a) 15 grft (b) 20 grft (c) 25 grft and (d) 30 grft)
the material is considered to have ldquofailedrdquo The tensile stressproduced by a rarefaction wave is often shown as a negativepressure [14]
34 Solvers AUTODYN provides various solvers for nonlin-ear problems [11 20 21] Lagrange and Euler solvers wereadopted in these FSI (fluid-structure interaction) simula-tions The Lagrangian representation keeps material in itsinitial element and the numerical mesh moves and deformswith the material The Lagrange method is most appropriate
for the description of solid-like structures Eulerian represen-tation allowsmaterials to flow from cell to cell while themeshis spatially fixed The Eulerian method is typically well suitedfor representing fluids and gases [20ndash23] In this study thesteel tube and sheath were modeled using a Lagrange solverwhile HNS and air were modeled using an Euler solver TheEuler and Lagrange interaction was also implemented to takeinto account the interaction between fluid (explosive and air)and structures (tube and sheath) This coupling techniqueallows complex fluid-structure interaction problems that
Shock and Vibration 7
Table 2 Steinberg-Guinan strength parameters
Parameter SS304 AL6061 Unit119866 77 times 10
8297 times 10
7 kPa119884 34 times 10
55 times 10
4 kPa120573 43 28 mdash119899 035 08 mdash119889119866119889119875 174 14119889119866119889119879 minus35 times 10
4minus129 times 10
4 kPaK119889119884119889119875 768 times 10
minus3235 times 10
minus3 mdashMelting temperature 2380 1604 K
145
180
175
170
165
160150 155 160 165 170 175 180 185
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft
15 grft20 grft
20 grft
25 grft
25 grft
Figure 14 Comparison between the experimental and calculationalresults
include large deformation of the structure to be solved in asingle numerical analysis
4 Results and Discussion
41 Two-Dimensional Numerical Results Figure 6 shows thetwo-dimensional numerical model of an expanding tubeexplosion The cell width was approximately 016mm Thenumber of elements in the tube model was 1404 and thewhole model had 161504 elements A description of thenumerical model is shown in Table 3
To illustrate the expansion process of the steel tube overtime the deformed configurations of a 15 grft expandingtube are depicted in Figure 7 at 119905 = 0ms 002ms 007msand 01ms The calculation was started at time 119905 = 00msand finished at 119905 = 01ms when it could be assumed thatdetonation had been completed It is clearly seen that the tubeis expanded outward radially from the detonation point At119905 = 002ms early in the detonation the minor axis of thetube started to be expanded and the length of the major axiswas becoming shorter over time At a later time the shape ofthe tube sectionwas deformed from elliptical to circular suchthat the shape change might separate a joint
Table 3 Description of numerical model of 2D expanding tube
Part Materials Number of mesh SolverTube SS304 1404 LagrangianSheath AL6061 100Air Air 160000 EulerianHigh explosive HNS 165
A series of computations was performed by varyingexplosive loads to compute the material response of thetube and the deformations are presented in Figure 8 It isapparent that the tube expansion increases as the explosiveload increases For a pressure tube in the plastic deformationregime catastrophic failure is associated with ductile tearingor plastic instability [19 24 25] Rapidly expanding regions(the minor axis of the tube) are accompanied by rapid lossof stress-carrying capability and intense heating due to thedissipation of plastic work and present risks of rupture [26]As shown in Figure 8 the plastic region and computed stresswere increased proportionally to the explosive load As aresult the 30 grft expanding tube shows the largest plasticregion and the greatest stress is on the minor axis dueto energy absorption However the 30 grft expanding tubeexpanded without spallation in the 2D simulation whichdiffers distinctly from the experimental results becausethis FE analysis accounts for only radial expansion Thissuggests that the tube expansion due to the detonation wavepropagation should be considered to develop a more reliablenumerical model
Figure 9 compares the changes of width and height ofthe tube in the FE analysis and experimental results forthree cases with 15 20 and 25 grft Although the calculationresults slightly overestimated the experimental results of eachcore load the overall error of both width (minor axis) andheight (major axis) prediction was less than 10
42 Three-Dimensional Numerical Results Figure 10 illus-trates a three-dimensional expanding tube and detonationdirection The open-ended steel tube was 300mm long andMDF of a 320mm length of MDF was inserted into thecentral bore Its cross section was the same as in the 2D caseDetonation was assumed to be started from the left end of thetube at 119905 = 00ms identically to the experimental conditionsTo describe the 3D detonation propagation a cylindricalblast wave was generated and then remapped in the airThe pressure profile of the detonation wave propagation intothe tube is presented in Figure 11 and its structure consistsof a shock wave and reaction zone where the explosive ischanged into gaseous products at high temperature Thesereaction products act as a piston that allows the shock waveto propagate at a constant velocity [27] Figure 12 shows thenumerical model of the 3D expanding tube A graded gridwas applied to the air and HNS 165 to save computationtime Table 4 summarizes the description of the 3Dnumericalmodel
Figure 13 displays the expansion behaviors and materialstatus of each expanding tube Similar to the 2D results
8 Shock and Vibration
(150 38 0)Gauge number 1 Gauge number 2 Gauge number 3
(75 38 0) (225 38 0)
Detonation at t = 000120583s
y
x
Figure 15 Gauges position
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft27 grft
30 grft
Figure 16 Pressure histories from gauge number 1
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 17 Pressure histories from gauge number 2
Table 4 Description of 3D expanding tube numerical model
Part Materials Number of mesh SolverTube SS304 64800 LagrangianSheath AL6061 13360Air Air 203125 EulerianHigh explosive HNS 165
the tubes with explosive loads of 15ndash25 grft freely expandedbut the 30 grft tube failed due to plastic deformation Asshown in Figure 13 there was spallation at 130mm from theside of the 30 grft expanding tube at around 119905 = 007msThis ductile fracture was caused by the significant amount
0 001 002 003 004 005 006 007 008 009 01
Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 18 Pressure histories from gauge number 3
of plastic deformation during tube expansion This failurebehavior in FE analysis was somewhat different from theexperimental failure behavior In experiments two failuresoccurred on the left and right sides of the steel tube whileone bulk failure was found in the numerical simulationEven if the first spallation could be predicted it might beinappropriate to simulate a successive multiple-spallationgeneration mechanism
Figure 14 compares between the numerical simulationand experimental results of each expanding tube deforma-tion The overall error was less than 3 and the agreementwas improved by considering the tube expansion due todetonation wave propagation
To compute a proper core load the internal pressureof the expanding wall of the steel tube was numericallycalculated for explosive loads of 15 20 25 27 and 30 grftThethree points indicated in Figure 15 represent the placementof a gauge for measuring the internal pressure Figures 1617 and 18 plot the time histories of pressure observed bygauges in the middle of the steel tube thickness over timeThe first peak was due to the initial shock wave travelingthrough the tube The rarefaction wave generated due tofree surface interaction is often shown as negative pressurefollowing the first peak and it produces tensile stress onthe tube The maximum pressure of the respective gaugesranged from minus130 to minus520MPa for the various explosiveloads The pressure histories of expanding tubes with loadsof 15ndash25 grft fluctuated and became stable over time Inthe FE analysis the 27 grft expanding tube was able toexpand freely without failure and its maximum pressure was
Shock and Vibration 9
125 times higher than that of the 25 grft expanding tubewhich was found to have a proper explosive load in theballistic test using expanding tube samplesTherefore we canconclude that the proper explosive load in the experimentswas underestimated according to the numerical results Foran explosive load of 30 grft the internal pressure increaseddramatically and reached a value ofminus520MPaThemaximumpressure on the steel tube with the 30 grft load was about 27and 2 times higher than those with the 25 grft and 27 grftloads respectively This means that since the explosive loadof 30 grft was greater than the failure threshold spallationoccurred in the actual expanding tube
5 Conclusions
The development of a numerical model has been presentedfor the free expansion of expanding tubes byMDFdetonationin pyro-separation systems using AUTODYN 2D and 3Dhydrocode Numerical simulations were performed for fourexpanding tube explosive load cases as a verification set forthe numerical model and additional simulation was done tosuggest a more effective explosive load
In the 2D model since the detonation wave propagationcould not be considered the results slightly overestimatedthe shape of the expanded tube To improve the accuracyof the results the 3D model was developed which allowedfor tube expansion due to detonation wave propagationThe developed model was verified with explosive test resultsand showed less than 3 overall error From the results of3D numerical simulation where the Steinberg model wasapplied for the failure criteria of the steel tube 27 grft wasthe proper explosive load and the 30 grft explosive loadexceeded the threshold of expanding tube failure Since thenumerical model verified with ballistic test results allows forvarious design changes the development cost and time can begreatly reduced by minimizing the number of experimentaltests required Therefore it is suggested to add a numericalmodel development step using 3D hydrocode to the overallprocedure of expanding tube development for pyrotechnicseparation systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by the Leading Foreign ResearchInstitute Recruitment Program (2011-0030065) and theBasic Science Research Program (2011-0010489) throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology This studywas also financially supported by the University Collabora-tion Enhancement Project of the Korea Aerospace ResearchInstitute
References
[1] K Y Chang and D L Kern SuperlowastZip (linear separa-tion) shock characteristics 1986 httpntrsnasagovarchivenasacasintrsnasagov19870011172 1987011172pdf
[2] L J Bement and M L Schimmel ldquoA manual for pyrotech-nic design development and qualificationrdquo NASA TechnicalMemerandum 110172 1995
[3] J R Lee CCChia andCWKong ldquoReviewof pyroshockwavemeasurement and simulation for space systemsrdquoMeasurementJournal of the International Measurement Confederation vol 45no 4 pp 631ndash642 2012
[4] K Y Chang ldquoPyrotechnic devices shock levels and theirapplicationsrdquo in Proceedings of the Pyroshock Seminar ICSV92002
[5] NASA ldquoPyroshock test criteriardquo NASA-STD-7003A 2011[6] L H Richards J K Vision and D J Schorr ldquoThrusting
separation systemrdquo US Patent US5372071 1993[7] W C Hoffman III ldquoAge life evaluation of space shuttle crew
escape systempyrotechnic components loadedwith hexanitros-tilbene (HNS) NASArdquo Technical Paper 3650 1996
[8] L J Bement and M L Schimmel ldquoInvestigation of SuperlowastZipseparation jointrdquo NASA Technical Memorandum 4031 1988
[9] MMiyazawa and Y Fukushima ldquoDevelopment status of Japanrsquosnew launch vehicle H-II rocektrdquo in Proceedings of the 40thCongress of the International Astronautical Federation 1989
[10] M Quidot ldquoSome examples of energetic material modelingwith LSDYNArdquo in Proceedings of the 3rd European LS-DYNAConference 2001
[11] G E Fairlie ldquoThenumerical simulation of high explosives usingAUTODYN-2Damp3Drdquo inProceedings of the Institute of ExplosiveEngineers 4th Biannual Symposium (Explo rsquo98) 1998
[12] J K Chen H Ching and F A Allahdadi ldquoShock-induceddetonation of high explosives by high velocity impactrdquo Journalof Mechanics of Materials and Structures vol 2 no 9 pp 1701ndash1721 2007
[13] S M Muramatsu ldquoNumerical and experimental study of apyroshock test set up for small spacecraft componentrdquo ProjectReport UPNA 2010
[14] J Danyluk Spall fracture ofmulti-material plates under explosiveloading [MS thesis] Rensselaser Polytechnic Institute at Hart-ford Hartford Conn USA 2010
[15] RH B Bouma A EDM van derHeijden TD Sewell andDLThompson ldquoChapter2 Simulations of deformation processesin energeticmaterialsrdquo inNumerical Simulations of Physical andEngineering Processes 2011
[16] E L Lee H C Hornig and J W Kury ldquoAdiabatic expansion ofhigh explosive detonation productsrdquo Technical Report UCRL-50422 Lawrence Radiation Laboratory University of CaliforniaLivermore Berkeley Calif USA 1968
[17] M AMeyersDynamic Behavior ofMaterialsWiley NewYorkNY USA 1994
[18] D J Steinberg S G Cochran and M W Guinan ldquoA constitu-tive model for metals applicable at high-strain raterdquo Journal ofApplied Physics vol 51 no 3 pp 1498ndash1504 1980
[19] J N Johnson ldquoDynamic fracture and spallation in ductilesolidsrdquo Journal of Applied Physics vol 52 no 4 pp 2812ndash28251981
[20] ANSYS Workshop 7 Ship Blast ANSYS Training ManualANSYS Cecil Township Pa USA 2010
10 Shock and Vibration
[21] ANSYS Chapter 1 Introduction to AUTODYN AUTODYNTraining Manual ANSYS Cecil Township Pa USA 2010
[22] X Quan N K Birnbaum M S Cowler B I Gerber R AClegg and C J Hayhurst ldquoNumerical simulation of structuraldeformation under shock and impact loads using a coupledmulti-solver approachrdquo in Proceedings of the 5th Asia-PacificConference on Shock and Impact Loads on Structures 2003
[23] Century Dynamics AUTODYN Theory Manual CenturyDynamics Concord Calif USA 2003
[24] J E Shepherd ldquoStructural response of piping to internal gasdetonationrdquo Journal of Pressure Vessel Technology Transactionsof the ASME vol 131 no 3 pp 0312041ndash03120413 2009
[25] J Kanesky J Damazo K Chow-Yee A Rusinek and J EShepherd ldquoPlastic deformation due to reflected detonationrdquoInternational Journal of Solids and Structures vol 50 no 1 pp97ndash110 2013
[26] A J Rosakis and G Ravichandran ldquoDynamic failure mechan-icsrdquo International Journal of Solids and Structures vol 37 no 1-2pp 331ndash348 2000
[27] S Fordham High Explosives and Propellants Pergamon PressElmsford NY USA 2nd edition 1980
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2 Shock and Vibration
ESMDC
Shear pin
Bolt
MDF
Oval tubeSupport
ESMDC detail
29
After separation Before separation
Figure 1 A pyro-separation system [9]
For long levels
0000E + 00
1667E minus 01
3333E minus 01
5000E minus 01
6667E minus 01
8333E minus 01
1000E 00
Plastic strains at times 5 10 and 15120583s
+
Figure 2 Numerical simulation of expanding tube free expansion [10]
Main axis
Minor axis
Thickness
+
Figure 3 Geometry of expanding tube
the entire length of the linear explosive at a VOD (velocity ofdetonation) between 60 and 75 kms with very high shockenergy This chemical reaction acts as mechanical loadingwhich allows the elliptical steel tube to expand mainly in the
15 grft
20 grft
25 grft
30grft
Failures
Figure 4 Experimental results of expanding tube
minor-axis direction and fractures pin joints Consequentlythe expanded tube can separate structures according to itsdesign without contamination [8] Since the performanceof expanding tubes is mainly related to the explosive loadinvestigation of the proper explosive load against expandingtube failure and structural damage is important to its design
Shock and Vibration 3
Sheathed HE
Steel tube
Air
Figure 5 Material location of two-dimensional expanding tube
Even if the expanding tube design has to be verified inballistic tests adding a numerical simulation step betweenthe expanding tube sample fabrication and its ballistic testcan be a more effective approach for proper explosive loaddetermination The numerical model can explain the fullphysics of the phenomena by solving the governing equationsthat describe the behavior of the system under consideration
In spite of the advantages of numerical simulation only afew numerical and experimental investigations on pyrotech-nic devices can be found in the literature Quidot [10] adoptedLSDYNA to simulate a pyrotechnic separation system Aline source comprised an expanding tube with a 1mm thickstainless steel case internal synthetic material and a lead-RDX cord with a 2 gm RDX charge Numerical simulationswere performed for this device as shown in Figure 2 How-ever the proper explosive load which is the most importantfactor for real-world applications of expanding tube designwas not addressed under consideration of the detonationwave propagation the fracturemechanism and experimentalvalidation
In this study two- and three-dimensional numericalanalyses of expanding tube were performed in order todevelop a numerical model with high accuracy The explicitdynamic code AUTODYN is adopted to simulate expansionof the tube and compute a proper core load AUTODYN isa hydrocode program that is especially suited to solve theinteraction problems of different systems of structure liquidand gas together as found in many studies of high explosivesimulation [11ndash15] To verify the accuracy of the developedmodel the numerical results were compared to experimentalballistic test results for different explosive load conditions
2 Ballistic Tests of Expanding Tubes
Experiments were performed to properly design a pyrotech-nic device Explosive tests were carried out for differentcore loads of 15 20 25 and 30 grft The expanding tubeis an open-ended cylinder in which an MDF filled withhexanitrostilbene (HNS) explosive is set along the centralaxis of the cylinder All MDF cords were manufactured with3mm diameters regardless of the respective explosive loads
Figure 6 Two-dimensional expanding tube numerical model
t = 000ms t = 002ms
t = 007ms t = 01ms
Figure 7 Expanding tube distortions (explosive load 15 grft)
and the wall thickness of the sheath was 01mm Figure 3represents a section view of an expanding tube with a majoraxis of 20mm a minor axis of 8mm and a thickness of1mm regardless of the core load The tests were carried out4 or 5 times for each core case and the deformed shapeand failure were investigated Figure 4 shows the results ofballistic tests with explosive core loads of 15 20 25 and30 grft Expanding tubes with 15 20 and 25 grft were freelyexpanded without failure In contrast the 30 grft expandingtube failed at both ends of the cylinder as shown in Figure 4The dimensions of each expanding tube were measured andthese measurements were averaged These results are usedto validate the numerical model which will be discussed inSection 3
It can be deduced from the ballistic test results thatthe threshold explosive load of the tested samples mustlie between 25 grft and 30 grft Ballistic tests are a goodapproach to determine a proper explosive load for expandingtubes as well as a better approximation of actual con-ditions However this experimental approach has severaldisadvantages in which ballistic tests typically require manyexpanding tube samples and connected structures which arealso damaged during the test and are nonreusableThe exper-imental method is also not flexible for design change and isexpensive and time consuming Moreover it is difficult toexplain the physical phenomena of structure and detonationinteractions Therefore to mitigate this problem the ballistictest should be the final confirmation test of the expandingtube development procedure after replacing the numerouscase samples with a reliable numerical model
4 Shock and Vibration
Material status
Void
Hydro
Elastic
Plastic
Material status
Void
Hydro
Elastic
Plastic
15 grft
3138
2828
2517
2207
1897
15862121 2471 2821 3171 3521 3871
X
Y
X
20 grft
3211
2860
2510
2160
1809
14592146 2486 2825 3165 3504 3844
Y
25 grft
X
Y
3235
2863
2490
2118
1746
13742135 2479 2823 3167 3511 3855
30grft
X
Y
3269
2868
2466
2065
1663
12622099 2458 2816 3174 3532 3891
Figure 8 Material status of expanded steel tube
3 Numerical Modeling
31 Numerical Model Numerical simulations were per-formed for all the experiments using hydrocode in AUTO-DYN 2D examining the experimental expanding behaviorand numerical stresses The two-dimensional model wasmade of a steel tube support MDF and surrounding airas shown in Figure 5 The surrounding air was modeled asan ideal gas and the area was 400mm times 400mm Sincethe material of the support layer was Teflon and it did notaffect tube expansion significantly it was assumed as air Theexplosive material was HNS 165 where 165 indicates thedensity of HNS which is 165 gcm3 The explosive loads forall cases ranged from 15 to 30 grftThe explosive propagationvelocity for HNS 165 was approximately 7030ms and thedetonation point was set to the center of the MDF
32 Material Description and Boundary Conditions Boththe reacted solid and reacted gaseous products of HNS165 explosive were characterized with the Jones-Wilkins-Lee
180
175
170
165
160145 150 155 160 165 170 175 180 185 190
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft15 grft
20 grft
20 grft
25 grft25 grft
Figure 9 Comparison between the experimental and calculationalresults
Shock and Vibration 5
x
Detonation at t = 000120583s
y
x
y
z
20mm
76mm
Figure 10 Three-dimensional expanding tube
Table 1 Material coefficients in Jones-Wilkins-Lee (JWL) equationfor HNS 165
Parameter Value Unit119860 465 times 10
8 kPa119861 887 times 10
6 kPa1198771
455 mdash1198772
135 mdash120596 035 mdash
equation of state (JWL EOS [16]) The pressure in eitherphase is defined in terms of volume and internal energyindependent of temperature as
119901 = 119860(1 minus
120596
1198771119881
) 119890minus1198771119881+ 119861(1 minus
120596
1198772119881
) 119890minus1198772119881+
120596119890
119881
(1)
where119881 = 120588120588119900is the relative volume 119890 is the internal energy
and 119860 119861 1198771 1198772 and 120596 are empirically determined constants
that depend on the kind of the explosive Table 1 lists theJWL EOS coefficients used for this analysis of the HNS witha density of 165 gcm3
The ideal gas EOS for air is shown as follows
119901 = (120574 minus 1) 120588119890 (2)
where 120574 is the ideal gas constant and 120588 and 119890 are the densityand internal energy of the air The internal energy of air atroom temperature and ambient pressure is 2068 times 105 kJ
Both the tube and sheath were modeled as SS304 steeland AL6061 With the high pressure resulting from explosivedetonation both the tube and sheath undergoing high strainrates were modeled using the shock equation of state [17] andSteinberg-Guinan strength model [18] Both the von Misesyield strength (119884) and the shearmodulus (119866) of the Steinberg-Guinan model are assumed to be described as a function ofpressure (119875) density (120588) and temperature (119879) and in thecase of yield strength the effective plastic strain as well (120576)
119866 = 1198660(1 + (
1198661015840
0
1198660
)
119901
12057813+ (
1198661015840
119879
1198660
) (119879 minus 300))
119884 = 11988401 + 120573 (120576 + 120576
119894)
119899
times (1 + (
1198841015840
119901
1198840
)
119901
12057813+ (
1198841015840
119879
1198840
) (119879 minus 300))
(3)
Shock wave
Reaction zone
Pres
sure
(kPa
)
Time (ms)
Figure 11 Pressure loading profile
where 120573 is the hardening constant and 119899 is the hardeningexponent The subscript 0 refers to the reference state (119879 =300K 119875 = 0 120576 = 0) The primed parameters with thesubscripts 119875 and 119879 indicate the derivatives of the parameterswith respect to pressure or temperature at the referencestate Table 2 summarizes the Steinberg-Guinan strengthparameters used for the numerical model for the SS304 steeland AL6061 used in the present analysis
A flow-out condition was applied to all boundaries ofthe Euler grid This allowed the material to freely leave thegrid and also prevented relief waves from being generatedoff the lateral boundaries of the solid which would reducethe overall strength of the compressive shock and rarefactionwaves
33 Failure Model Spallation (spall-fracture) is a kind offracture that occurs as planar separation of material parallelto the incident plane wave fronts as a result of dynamic tensilestress components perpendicular to this plane [19] The spallstrength for tensile stress generated when a rarefaction wavetravels through material is 21 GPa for the steel tube If thetensile stress of the tube exceeds the predefined spall strength
6 Shock and Vibration
Y
Z
(a)
X
Y
Z
(b)
Figure 12 Three-dimensional model of expanding tube (front view (a) and isotropic view (b))
X
Y
Z
(a)
X
Y
Z
(b)
X
Y
Z
(c)
X
Y
Z
Bulk failBulk faila
(d)
Figure 13 Material status of one-sided detonation expanding tube ((a) 15 grft (b) 20 grft (c) 25 grft and (d) 30 grft)
the material is considered to have ldquofailedrdquo The tensile stressproduced by a rarefaction wave is often shown as a negativepressure [14]
34 Solvers AUTODYN provides various solvers for nonlin-ear problems [11 20 21] Lagrange and Euler solvers wereadopted in these FSI (fluid-structure interaction) simula-tions The Lagrangian representation keeps material in itsinitial element and the numerical mesh moves and deformswith the material The Lagrange method is most appropriate
for the description of solid-like structures Eulerian represen-tation allowsmaterials to flow from cell to cell while themeshis spatially fixed The Eulerian method is typically well suitedfor representing fluids and gases [20ndash23] In this study thesteel tube and sheath were modeled using a Lagrange solverwhile HNS and air were modeled using an Euler solver TheEuler and Lagrange interaction was also implemented to takeinto account the interaction between fluid (explosive and air)and structures (tube and sheath) This coupling techniqueallows complex fluid-structure interaction problems that
Shock and Vibration 7
Table 2 Steinberg-Guinan strength parameters
Parameter SS304 AL6061 Unit119866 77 times 10
8297 times 10
7 kPa119884 34 times 10
55 times 10
4 kPa120573 43 28 mdash119899 035 08 mdash119889119866119889119875 174 14119889119866119889119879 minus35 times 10
4minus129 times 10
4 kPaK119889119884119889119875 768 times 10
minus3235 times 10
minus3 mdashMelting temperature 2380 1604 K
145
180
175
170
165
160150 155 160 165 170 175 180 185
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft
15 grft20 grft
20 grft
25 grft
25 grft
Figure 14 Comparison between the experimental and calculationalresults
include large deformation of the structure to be solved in asingle numerical analysis
4 Results and Discussion
41 Two-Dimensional Numerical Results Figure 6 shows thetwo-dimensional numerical model of an expanding tubeexplosion The cell width was approximately 016mm Thenumber of elements in the tube model was 1404 and thewhole model had 161504 elements A description of thenumerical model is shown in Table 3
To illustrate the expansion process of the steel tube overtime the deformed configurations of a 15 grft expandingtube are depicted in Figure 7 at 119905 = 0ms 002ms 007msand 01ms The calculation was started at time 119905 = 00msand finished at 119905 = 01ms when it could be assumed thatdetonation had been completed It is clearly seen that the tubeis expanded outward radially from the detonation point At119905 = 002ms early in the detonation the minor axis of thetube started to be expanded and the length of the major axiswas becoming shorter over time At a later time the shape ofthe tube sectionwas deformed from elliptical to circular suchthat the shape change might separate a joint
Table 3 Description of numerical model of 2D expanding tube
Part Materials Number of mesh SolverTube SS304 1404 LagrangianSheath AL6061 100Air Air 160000 EulerianHigh explosive HNS 165
A series of computations was performed by varyingexplosive loads to compute the material response of thetube and the deformations are presented in Figure 8 It isapparent that the tube expansion increases as the explosiveload increases For a pressure tube in the plastic deformationregime catastrophic failure is associated with ductile tearingor plastic instability [19 24 25] Rapidly expanding regions(the minor axis of the tube) are accompanied by rapid lossof stress-carrying capability and intense heating due to thedissipation of plastic work and present risks of rupture [26]As shown in Figure 8 the plastic region and computed stresswere increased proportionally to the explosive load As aresult the 30 grft expanding tube shows the largest plasticregion and the greatest stress is on the minor axis dueto energy absorption However the 30 grft expanding tubeexpanded without spallation in the 2D simulation whichdiffers distinctly from the experimental results becausethis FE analysis accounts for only radial expansion Thissuggests that the tube expansion due to the detonation wavepropagation should be considered to develop a more reliablenumerical model
Figure 9 compares the changes of width and height ofthe tube in the FE analysis and experimental results forthree cases with 15 20 and 25 grft Although the calculationresults slightly overestimated the experimental results of eachcore load the overall error of both width (minor axis) andheight (major axis) prediction was less than 10
42 Three-Dimensional Numerical Results Figure 10 illus-trates a three-dimensional expanding tube and detonationdirection The open-ended steel tube was 300mm long andMDF of a 320mm length of MDF was inserted into thecentral bore Its cross section was the same as in the 2D caseDetonation was assumed to be started from the left end of thetube at 119905 = 00ms identically to the experimental conditionsTo describe the 3D detonation propagation a cylindricalblast wave was generated and then remapped in the airThe pressure profile of the detonation wave propagation intothe tube is presented in Figure 11 and its structure consistsof a shock wave and reaction zone where the explosive ischanged into gaseous products at high temperature Thesereaction products act as a piston that allows the shock waveto propagate at a constant velocity [27] Figure 12 shows thenumerical model of the 3D expanding tube A graded gridwas applied to the air and HNS 165 to save computationtime Table 4 summarizes the description of the 3Dnumericalmodel
Figure 13 displays the expansion behaviors and materialstatus of each expanding tube Similar to the 2D results
8 Shock and Vibration
(150 38 0)Gauge number 1 Gauge number 2 Gauge number 3
(75 38 0) (225 38 0)
Detonation at t = 000120583s
y
x
Figure 15 Gauges position
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft27 grft
30 grft
Figure 16 Pressure histories from gauge number 1
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 17 Pressure histories from gauge number 2
Table 4 Description of 3D expanding tube numerical model
Part Materials Number of mesh SolverTube SS304 64800 LagrangianSheath AL6061 13360Air Air 203125 EulerianHigh explosive HNS 165
the tubes with explosive loads of 15ndash25 grft freely expandedbut the 30 grft tube failed due to plastic deformation Asshown in Figure 13 there was spallation at 130mm from theside of the 30 grft expanding tube at around 119905 = 007msThis ductile fracture was caused by the significant amount
0 001 002 003 004 005 006 007 008 009 01
Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 18 Pressure histories from gauge number 3
of plastic deformation during tube expansion This failurebehavior in FE analysis was somewhat different from theexperimental failure behavior In experiments two failuresoccurred on the left and right sides of the steel tube whileone bulk failure was found in the numerical simulationEven if the first spallation could be predicted it might beinappropriate to simulate a successive multiple-spallationgeneration mechanism
Figure 14 compares between the numerical simulationand experimental results of each expanding tube deforma-tion The overall error was less than 3 and the agreementwas improved by considering the tube expansion due todetonation wave propagation
To compute a proper core load the internal pressureof the expanding wall of the steel tube was numericallycalculated for explosive loads of 15 20 25 27 and 30 grftThethree points indicated in Figure 15 represent the placementof a gauge for measuring the internal pressure Figures 1617 and 18 plot the time histories of pressure observed bygauges in the middle of the steel tube thickness over timeThe first peak was due to the initial shock wave travelingthrough the tube The rarefaction wave generated due tofree surface interaction is often shown as negative pressurefollowing the first peak and it produces tensile stress onthe tube The maximum pressure of the respective gaugesranged from minus130 to minus520MPa for the various explosiveloads The pressure histories of expanding tubes with loadsof 15ndash25 grft fluctuated and became stable over time Inthe FE analysis the 27 grft expanding tube was able toexpand freely without failure and its maximum pressure was
Shock and Vibration 9
125 times higher than that of the 25 grft expanding tubewhich was found to have a proper explosive load in theballistic test using expanding tube samplesTherefore we canconclude that the proper explosive load in the experimentswas underestimated according to the numerical results Foran explosive load of 30 grft the internal pressure increaseddramatically and reached a value ofminus520MPaThemaximumpressure on the steel tube with the 30 grft load was about 27and 2 times higher than those with the 25 grft and 27 grftloads respectively This means that since the explosive loadof 30 grft was greater than the failure threshold spallationoccurred in the actual expanding tube
5 Conclusions
The development of a numerical model has been presentedfor the free expansion of expanding tubes byMDFdetonationin pyro-separation systems using AUTODYN 2D and 3Dhydrocode Numerical simulations were performed for fourexpanding tube explosive load cases as a verification set forthe numerical model and additional simulation was done tosuggest a more effective explosive load
In the 2D model since the detonation wave propagationcould not be considered the results slightly overestimatedthe shape of the expanded tube To improve the accuracyof the results the 3D model was developed which allowedfor tube expansion due to detonation wave propagationThe developed model was verified with explosive test resultsand showed less than 3 overall error From the results of3D numerical simulation where the Steinberg model wasapplied for the failure criteria of the steel tube 27 grft wasthe proper explosive load and the 30 grft explosive loadexceeded the threshold of expanding tube failure Since thenumerical model verified with ballistic test results allows forvarious design changes the development cost and time can begreatly reduced by minimizing the number of experimentaltests required Therefore it is suggested to add a numericalmodel development step using 3D hydrocode to the overallprocedure of expanding tube development for pyrotechnicseparation systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by the Leading Foreign ResearchInstitute Recruitment Program (2011-0030065) and theBasic Science Research Program (2011-0010489) throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology This studywas also financially supported by the University Collabora-tion Enhancement Project of the Korea Aerospace ResearchInstitute
References
[1] K Y Chang and D L Kern SuperlowastZip (linear separa-tion) shock characteristics 1986 httpntrsnasagovarchivenasacasintrsnasagov19870011172 1987011172pdf
[2] L J Bement and M L Schimmel ldquoA manual for pyrotech-nic design development and qualificationrdquo NASA TechnicalMemerandum 110172 1995
[3] J R Lee CCChia andCWKong ldquoReviewof pyroshockwavemeasurement and simulation for space systemsrdquoMeasurementJournal of the International Measurement Confederation vol 45no 4 pp 631ndash642 2012
[4] K Y Chang ldquoPyrotechnic devices shock levels and theirapplicationsrdquo in Proceedings of the Pyroshock Seminar ICSV92002
[5] NASA ldquoPyroshock test criteriardquo NASA-STD-7003A 2011[6] L H Richards J K Vision and D J Schorr ldquoThrusting
separation systemrdquo US Patent US5372071 1993[7] W C Hoffman III ldquoAge life evaluation of space shuttle crew
escape systempyrotechnic components loadedwith hexanitros-tilbene (HNS) NASArdquo Technical Paper 3650 1996
[8] L J Bement and M L Schimmel ldquoInvestigation of SuperlowastZipseparation jointrdquo NASA Technical Memorandum 4031 1988
[9] MMiyazawa and Y Fukushima ldquoDevelopment status of Japanrsquosnew launch vehicle H-II rocektrdquo in Proceedings of the 40thCongress of the International Astronautical Federation 1989
[10] M Quidot ldquoSome examples of energetic material modelingwith LSDYNArdquo in Proceedings of the 3rd European LS-DYNAConference 2001
[11] G E Fairlie ldquoThenumerical simulation of high explosives usingAUTODYN-2Damp3Drdquo inProceedings of the Institute of ExplosiveEngineers 4th Biannual Symposium (Explo rsquo98) 1998
[12] J K Chen H Ching and F A Allahdadi ldquoShock-induceddetonation of high explosives by high velocity impactrdquo Journalof Mechanics of Materials and Structures vol 2 no 9 pp 1701ndash1721 2007
[13] S M Muramatsu ldquoNumerical and experimental study of apyroshock test set up for small spacecraft componentrdquo ProjectReport UPNA 2010
[14] J Danyluk Spall fracture ofmulti-material plates under explosiveloading [MS thesis] Rensselaser Polytechnic Institute at Hart-ford Hartford Conn USA 2010
[15] RH B Bouma A EDM van derHeijden TD Sewell andDLThompson ldquoChapter2 Simulations of deformation processesin energeticmaterialsrdquo inNumerical Simulations of Physical andEngineering Processes 2011
[16] E L Lee H C Hornig and J W Kury ldquoAdiabatic expansion ofhigh explosive detonation productsrdquo Technical Report UCRL-50422 Lawrence Radiation Laboratory University of CaliforniaLivermore Berkeley Calif USA 1968
[17] M AMeyersDynamic Behavior ofMaterialsWiley NewYorkNY USA 1994
[18] D J Steinberg S G Cochran and M W Guinan ldquoA constitu-tive model for metals applicable at high-strain raterdquo Journal ofApplied Physics vol 51 no 3 pp 1498ndash1504 1980
[19] J N Johnson ldquoDynamic fracture and spallation in ductilesolidsrdquo Journal of Applied Physics vol 52 no 4 pp 2812ndash28251981
[20] ANSYS Workshop 7 Ship Blast ANSYS Training ManualANSYS Cecil Township Pa USA 2010
10 Shock and Vibration
[21] ANSYS Chapter 1 Introduction to AUTODYN AUTODYNTraining Manual ANSYS Cecil Township Pa USA 2010
[22] X Quan N K Birnbaum M S Cowler B I Gerber R AClegg and C J Hayhurst ldquoNumerical simulation of structuraldeformation under shock and impact loads using a coupledmulti-solver approachrdquo in Proceedings of the 5th Asia-PacificConference on Shock and Impact Loads on Structures 2003
[23] Century Dynamics AUTODYN Theory Manual CenturyDynamics Concord Calif USA 2003
[24] J E Shepherd ldquoStructural response of piping to internal gasdetonationrdquo Journal of Pressure Vessel Technology Transactionsof the ASME vol 131 no 3 pp 0312041ndash03120413 2009
[25] J Kanesky J Damazo K Chow-Yee A Rusinek and J EShepherd ldquoPlastic deformation due to reflected detonationrdquoInternational Journal of Solids and Structures vol 50 no 1 pp97ndash110 2013
[26] A J Rosakis and G Ravichandran ldquoDynamic failure mechan-icsrdquo International Journal of Solids and Structures vol 37 no 1-2pp 331ndash348 2000
[27] S Fordham High Explosives and Propellants Pergamon PressElmsford NY USA 2nd edition 1980
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Shock and Vibration
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Civil EngineeringAdvances in
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DistributedSensor Networks
International Journal of
Shock and Vibration 3
Sheathed HE
Steel tube
Air
Figure 5 Material location of two-dimensional expanding tube
Even if the expanding tube design has to be verified inballistic tests adding a numerical simulation step betweenthe expanding tube sample fabrication and its ballistic testcan be a more effective approach for proper explosive loaddetermination The numerical model can explain the fullphysics of the phenomena by solving the governing equationsthat describe the behavior of the system under consideration
In spite of the advantages of numerical simulation only afew numerical and experimental investigations on pyrotech-nic devices can be found in the literature Quidot [10] adoptedLSDYNA to simulate a pyrotechnic separation system Aline source comprised an expanding tube with a 1mm thickstainless steel case internal synthetic material and a lead-RDX cord with a 2 gm RDX charge Numerical simulationswere performed for this device as shown in Figure 2 How-ever the proper explosive load which is the most importantfactor for real-world applications of expanding tube designwas not addressed under consideration of the detonationwave propagation the fracturemechanism and experimentalvalidation
In this study two- and three-dimensional numericalanalyses of expanding tube were performed in order todevelop a numerical model with high accuracy The explicitdynamic code AUTODYN is adopted to simulate expansionof the tube and compute a proper core load AUTODYN isa hydrocode program that is especially suited to solve theinteraction problems of different systems of structure liquidand gas together as found in many studies of high explosivesimulation [11ndash15] To verify the accuracy of the developedmodel the numerical results were compared to experimentalballistic test results for different explosive load conditions
2 Ballistic Tests of Expanding Tubes
Experiments were performed to properly design a pyrotech-nic device Explosive tests were carried out for differentcore loads of 15 20 25 and 30 grft The expanding tubeis an open-ended cylinder in which an MDF filled withhexanitrostilbene (HNS) explosive is set along the centralaxis of the cylinder All MDF cords were manufactured with3mm diameters regardless of the respective explosive loads
Figure 6 Two-dimensional expanding tube numerical model
t = 000ms t = 002ms
t = 007ms t = 01ms
Figure 7 Expanding tube distortions (explosive load 15 grft)
and the wall thickness of the sheath was 01mm Figure 3represents a section view of an expanding tube with a majoraxis of 20mm a minor axis of 8mm and a thickness of1mm regardless of the core load The tests were carried out4 or 5 times for each core case and the deformed shapeand failure were investigated Figure 4 shows the results ofballistic tests with explosive core loads of 15 20 25 and30 grft Expanding tubes with 15 20 and 25 grft were freelyexpanded without failure In contrast the 30 grft expandingtube failed at both ends of the cylinder as shown in Figure 4The dimensions of each expanding tube were measured andthese measurements were averaged These results are usedto validate the numerical model which will be discussed inSection 3
It can be deduced from the ballistic test results thatthe threshold explosive load of the tested samples mustlie between 25 grft and 30 grft Ballistic tests are a goodapproach to determine a proper explosive load for expandingtubes as well as a better approximation of actual con-ditions However this experimental approach has severaldisadvantages in which ballistic tests typically require manyexpanding tube samples and connected structures which arealso damaged during the test and are nonreusableThe exper-imental method is also not flexible for design change and isexpensive and time consuming Moreover it is difficult toexplain the physical phenomena of structure and detonationinteractions Therefore to mitigate this problem the ballistictest should be the final confirmation test of the expandingtube development procedure after replacing the numerouscase samples with a reliable numerical model
4 Shock and Vibration
Material status
Void
Hydro
Elastic
Plastic
Material status
Void
Hydro
Elastic
Plastic
15 grft
3138
2828
2517
2207
1897
15862121 2471 2821 3171 3521 3871
X
Y
X
20 grft
3211
2860
2510
2160
1809
14592146 2486 2825 3165 3504 3844
Y
25 grft
X
Y
3235
2863
2490
2118
1746
13742135 2479 2823 3167 3511 3855
30grft
X
Y
3269
2868
2466
2065
1663
12622099 2458 2816 3174 3532 3891
Figure 8 Material status of expanded steel tube
3 Numerical Modeling
31 Numerical Model Numerical simulations were per-formed for all the experiments using hydrocode in AUTO-DYN 2D examining the experimental expanding behaviorand numerical stresses The two-dimensional model wasmade of a steel tube support MDF and surrounding airas shown in Figure 5 The surrounding air was modeled asan ideal gas and the area was 400mm times 400mm Sincethe material of the support layer was Teflon and it did notaffect tube expansion significantly it was assumed as air Theexplosive material was HNS 165 where 165 indicates thedensity of HNS which is 165 gcm3 The explosive loads forall cases ranged from 15 to 30 grftThe explosive propagationvelocity for HNS 165 was approximately 7030ms and thedetonation point was set to the center of the MDF
32 Material Description and Boundary Conditions Boththe reacted solid and reacted gaseous products of HNS165 explosive were characterized with the Jones-Wilkins-Lee
180
175
170
165
160145 150 155 160 165 170 175 180 185 190
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft15 grft
20 grft
20 grft
25 grft25 grft
Figure 9 Comparison between the experimental and calculationalresults
Shock and Vibration 5
x
Detonation at t = 000120583s
y
x
y
z
20mm
76mm
Figure 10 Three-dimensional expanding tube
Table 1 Material coefficients in Jones-Wilkins-Lee (JWL) equationfor HNS 165
Parameter Value Unit119860 465 times 10
8 kPa119861 887 times 10
6 kPa1198771
455 mdash1198772
135 mdash120596 035 mdash
equation of state (JWL EOS [16]) The pressure in eitherphase is defined in terms of volume and internal energyindependent of temperature as
119901 = 119860(1 minus
120596
1198771119881
) 119890minus1198771119881+ 119861(1 minus
120596
1198772119881
) 119890minus1198772119881+
120596119890
119881
(1)
where119881 = 120588120588119900is the relative volume 119890 is the internal energy
and 119860 119861 1198771 1198772 and 120596 are empirically determined constants
that depend on the kind of the explosive Table 1 lists theJWL EOS coefficients used for this analysis of the HNS witha density of 165 gcm3
The ideal gas EOS for air is shown as follows
119901 = (120574 minus 1) 120588119890 (2)
where 120574 is the ideal gas constant and 120588 and 119890 are the densityand internal energy of the air The internal energy of air atroom temperature and ambient pressure is 2068 times 105 kJ
Both the tube and sheath were modeled as SS304 steeland AL6061 With the high pressure resulting from explosivedetonation both the tube and sheath undergoing high strainrates were modeled using the shock equation of state [17] andSteinberg-Guinan strength model [18] Both the von Misesyield strength (119884) and the shearmodulus (119866) of the Steinberg-Guinan model are assumed to be described as a function ofpressure (119875) density (120588) and temperature (119879) and in thecase of yield strength the effective plastic strain as well (120576)
119866 = 1198660(1 + (
1198661015840
0
1198660
)
119901
12057813+ (
1198661015840
119879
1198660
) (119879 minus 300))
119884 = 11988401 + 120573 (120576 + 120576
119894)
119899
times (1 + (
1198841015840
119901
1198840
)
119901
12057813+ (
1198841015840
119879
1198840
) (119879 minus 300))
(3)
Shock wave
Reaction zone
Pres
sure
(kPa
)
Time (ms)
Figure 11 Pressure loading profile
where 120573 is the hardening constant and 119899 is the hardeningexponent The subscript 0 refers to the reference state (119879 =300K 119875 = 0 120576 = 0) The primed parameters with thesubscripts 119875 and 119879 indicate the derivatives of the parameterswith respect to pressure or temperature at the referencestate Table 2 summarizes the Steinberg-Guinan strengthparameters used for the numerical model for the SS304 steeland AL6061 used in the present analysis
A flow-out condition was applied to all boundaries ofthe Euler grid This allowed the material to freely leave thegrid and also prevented relief waves from being generatedoff the lateral boundaries of the solid which would reducethe overall strength of the compressive shock and rarefactionwaves
33 Failure Model Spallation (spall-fracture) is a kind offracture that occurs as planar separation of material parallelto the incident plane wave fronts as a result of dynamic tensilestress components perpendicular to this plane [19] The spallstrength for tensile stress generated when a rarefaction wavetravels through material is 21 GPa for the steel tube If thetensile stress of the tube exceeds the predefined spall strength
6 Shock and Vibration
Y
Z
(a)
X
Y
Z
(b)
Figure 12 Three-dimensional model of expanding tube (front view (a) and isotropic view (b))
X
Y
Z
(a)
X
Y
Z
(b)
X
Y
Z
(c)
X
Y
Z
Bulk failBulk faila
(d)
Figure 13 Material status of one-sided detonation expanding tube ((a) 15 grft (b) 20 grft (c) 25 grft and (d) 30 grft)
the material is considered to have ldquofailedrdquo The tensile stressproduced by a rarefaction wave is often shown as a negativepressure [14]
34 Solvers AUTODYN provides various solvers for nonlin-ear problems [11 20 21] Lagrange and Euler solvers wereadopted in these FSI (fluid-structure interaction) simula-tions The Lagrangian representation keeps material in itsinitial element and the numerical mesh moves and deformswith the material The Lagrange method is most appropriate
for the description of solid-like structures Eulerian represen-tation allowsmaterials to flow from cell to cell while themeshis spatially fixed The Eulerian method is typically well suitedfor representing fluids and gases [20ndash23] In this study thesteel tube and sheath were modeled using a Lagrange solverwhile HNS and air were modeled using an Euler solver TheEuler and Lagrange interaction was also implemented to takeinto account the interaction between fluid (explosive and air)and structures (tube and sheath) This coupling techniqueallows complex fluid-structure interaction problems that
Shock and Vibration 7
Table 2 Steinberg-Guinan strength parameters
Parameter SS304 AL6061 Unit119866 77 times 10
8297 times 10
7 kPa119884 34 times 10
55 times 10
4 kPa120573 43 28 mdash119899 035 08 mdash119889119866119889119875 174 14119889119866119889119879 minus35 times 10
4minus129 times 10
4 kPaK119889119884119889119875 768 times 10
minus3235 times 10
minus3 mdashMelting temperature 2380 1604 K
145
180
175
170
165
160150 155 160 165 170 175 180 185
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft
15 grft20 grft
20 grft
25 grft
25 grft
Figure 14 Comparison between the experimental and calculationalresults
include large deformation of the structure to be solved in asingle numerical analysis
4 Results and Discussion
41 Two-Dimensional Numerical Results Figure 6 shows thetwo-dimensional numerical model of an expanding tubeexplosion The cell width was approximately 016mm Thenumber of elements in the tube model was 1404 and thewhole model had 161504 elements A description of thenumerical model is shown in Table 3
To illustrate the expansion process of the steel tube overtime the deformed configurations of a 15 grft expandingtube are depicted in Figure 7 at 119905 = 0ms 002ms 007msand 01ms The calculation was started at time 119905 = 00msand finished at 119905 = 01ms when it could be assumed thatdetonation had been completed It is clearly seen that the tubeis expanded outward radially from the detonation point At119905 = 002ms early in the detonation the minor axis of thetube started to be expanded and the length of the major axiswas becoming shorter over time At a later time the shape ofthe tube sectionwas deformed from elliptical to circular suchthat the shape change might separate a joint
Table 3 Description of numerical model of 2D expanding tube
Part Materials Number of mesh SolverTube SS304 1404 LagrangianSheath AL6061 100Air Air 160000 EulerianHigh explosive HNS 165
A series of computations was performed by varyingexplosive loads to compute the material response of thetube and the deformations are presented in Figure 8 It isapparent that the tube expansion increases as the explosiveload increases For a pressure tube in the plastic deformationregime catastrophic failure is associated with ductile tearingor plastic instability [19 24 25] Rapidly expanding regions(the minor axis of the tube) are accompanied by rapid lossof stress-carrying capability and intense heating due to thedissipation of plastic work and present risks of rupture [26]As shown in Figure 8 the plastic region and computed stresswere increased proportionally to the explosive load As aresult the 30 grft expanding tube shows the largest plasticregion and the greatest stress is on the minor axis dueto energy absorption However the 30 grft expanding tubeexpanded without spallation in the 2D simulation whichdiffers distinctly from the experimental results becausethis FE analysis accounts for only radial expansion Thissuggests that the tube expansion due to the detonation wavepropagation should be considered to develop a more reliablenumerical model
Figure 9 compares the changes of width and height ofthe tube in the FE analysis and experimental results forthree cases with 15 20 and 25 grft Although the calculationresults slightly overestimated the experimental results of eachcore load the overall error of both width (minor axis) andheight (major axis) prediction was less than 10
42 Three-Dimensional Numerical Results Figure 10 illus-trates a three-dimensional expanding tube and detonationdirection The open-ended steel tube was 300mm long andMDF of a 320mm length of MDF was inserted into thecentral bore Its cross section was the same as in the 2D caseDetonation was assumed to be started from the left end of thetube at 119905 = 00ms identically to the experimental conditionsTo describe the 3D detonation propagation a cylindricalblast wave was generated and then remapped in the airThe pressure profile of the detonation wave propagation intothe tube is presented in Figure 11 and its structure consistsof a shock wave and reaction zone where the explosive ischanged into gaseous products at high temperature Thesereaction products act as a piston that allows the shock waveto propagate at a constant velocity [27] Figure 12 shows thenumerical model of the 3D expanding tube A graded gridwas applied to the air and HNS 165 to save computationtime Table 4 summarizes the description of the 3Dnumericalmodel
Figure 13 displays the expansion behaviors and materialstatus of each expanding tube Similar to the 2D results
8 Shock and Vibration
(150 38 0)Gauge number 1 Gauge number 2 Gauge number 3
(75 38 0) (225 38 0)
Detonation at t = 000120583s
y
x
Figure 15 Gauges position
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft27 grft
30 grft
Figure 16 Pressure histories from gauge number 1
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 17 Pressure histories from gauge number 2
Table 4 Description of 3D expanding tube numerical model
Part Materials Number of mesh SolverTube SS304 64800 LagrangianSheath AL6061 13360Air Air 203125 EulerianHigh explosive HNS 165
the tubes with explosive loads of 15ndash25 grft freely expandedbut the 30 grft tube failed due to plastic deformation Asshown in Figure 13 there was spallation at 130mm from theside of the 30 grft expanding tube at around 119905 = 007msThis ductile fracture was caused by the significant amount
0 001 002 003 004 005 006 007 008 009 01
Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 18 Pressure histories from gauge number 3
of plastic deformation during tube expansion This failurebehavior in FE analysis was somewhat different from theexperimental failure behavior In experiments two failuresoccurred on the left and right sides of the steel tube whileone bulk failure was found in the numerical simulationEven if the first spallation could be predicted it might beinappropriate to simulate a successive multiple-spallationgeneration mechanism
Figure 14 compares between the numerical simulationand experimental results of each expanding tube deforma-tion The overall error was less than 3 and the agreementwas improved by considering the tube expansion due todetonation wave propagation
To compute a proper core load the internal pressureof the expanding wall of the steel tube was numericallycalculated for explosive loads of 15 20 25 27 and 30 grftThethree points indicated in Figure 15 represent the placementof a gauge for measuring the internal pressure Figures 1617 and 18 plot the time histories of pressure observed bygauges in the middle of the steel tube thickness over timeThe first peak was due to the initial shock wave travelingthrough the tube The rarefaction wave generated due tofree surface interaction is often shown as negative pressurefollowing the first peak and it produces tensile stress onthe tube The maximum pressure of the respective gaugesranged from minus130 to minus520MPa for the various explosiveloads The pressure histories of expanding tubes with loadsof 15ndash25 grft fluctuated and became stable over time Inthe FE analysis the 27 grft expanding tube was able toexpand freely without failure and its maximum pressure was
Shock and Vibration 9
125 times higher than that of the 25 grft expanding tubewhich was found to have a proper explosive load in theballistic test using expanding tube samplesTherefore we canconclude that the proper explosive load in the experimentswas underestimated according to the numerical results Foran explosive load of 30 grft the internal pressure increaseddramatically and reached a value ofminus520MPaThemaximumpressure on the steel tube with the 30 grft load was about 27and 2 times higher than those with the 25 grft and 27 grftloads respectively This means that since the explosive loadof 30 grft was greater than the failure threshold spallationoccurred in the actual expanding tube
5 Conclusions
The development of a numerical model has been presentedfor the free expansion of expanding tubes byMDFdetonationin pyro-separation systems using AUTODYN 2D and 3Dhydrocode Numerical simulations were performed for fourexpanding tube explosive load cases as a verification set forthe numerical model and additional simulation was done tosuggest a more effective explosive load
In the 2D model since the detonation wave propagationcould not be considered the results slightly overestimatedthe shape of the expanded tube To improve the accuracyof the results the 3D model was developed which allowedfor tube expansion due to detonation wave propagationThe developed model was verified with explosive test resultsand showed less than 3 overall error From the results of3D numerical simulation where the Steinberg model wasapplied for the failure criteria of the steel tube 27 grft wasthe proper explosive load and the 30 grft explosive loadexceeded the threshold of expanding tube failure Since thenumerical model verified with ballistic test results allows forvarious design changes the development cost and time can begreatly reduced by minimizing the number of experimentaltests required Therefore it is suggested to add a numericalmodel development step using 3D hydrocode to the overallprocedure of expanding tube development for pyrotechnicseparation systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by the Leading Foreign ResearchInstitute Recruitment Program (2011-0030065) and theBasic Science Research Program (2011-0010489) throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology This studywas also financially supported by the University Collabora-tion Enhancement Project of the Korea Aerospace ResearchInstitute
References
[1] K Y Chang and D L Kern SuperlowastZip (linear separa-tion) shock characteristics 1986 httpntrsnasagovarchivenasacasintrsnasagov19870011172 1987011172pdf
[2] L J Bement and M L Schimmel ldquoA manual for pyrotech-nic design development and qualificationrdquo NASA TechnicalMemerandum 110172 1995
[3] J R Lee CCChia andCWKong ldquoReviewof pyroshockwavemeasurement and simulation for space systemsrdquoMeasurementJournal of the International Measurement Confederation vol 45no 4 pp 631ndash642 2012
[4] K Y Chang ldquoPyrotechnic devices shock levels and theirapplicationsrdquo in Proceedings of the Pyroshock Seminar ICSV92002
[5] NASA ldquoPyroshock test criteriardquo NASA-STD-7003A 2011[6] L H Richards J K Vision and D J Schorr ldquoThrusting
separation systemrdquo US Patent US5372071 1993[7] W C Hoffman III ldquoAge life evaluation of space shuttle crew
escape systempyrotechnic components loadedwith hexanitros-tilbene (HNS) NASArdquo Technical Paper 3650 1996
[8] L J Bement and M L Schimmel ldquoInvestigation of SuperlowastZipseparation jointrdquo NASA Technical Memorandum 4031 1988
[9] MMiyazawa and Y Fukushima ldquoDevelopment status of Japanrsquosnew launch vehicle H-II rocektrdquo in Proceedings of the 40thCongress of the International Astronautical Federation 1989
[10] M Quidot ldquoSome examples of energetic material modelingwith LSDYNArdquo in Proceedings of the 3rd European LS-DYNAConference 2001
[11] G E Fairlie ldquoThenumerical simulation of high explosives usingAUTODYN-2Damp3Drdquo inProceedings of the Institute of ExplosiveEngineers 4th Biannual Symposium (Explo rsquo98) 1998
[12] J K Chen H Ching and F A Allahdadi ldquoShock-induceddetonation of high explosives by high velocity impactrdquo Journalof Mechanics of Materials and Structures vol 2 no 9 pp 1701ndash1721 2007
[13] S M Muramatsu ldquoNumerical and experimental study of apyroshock test set up for small spacecraft componentrdquo ProjectReport UPNA 2010
[14] J Danyluk Spall fracture ofmulti-material plates under explosiveloading [MS thesis] Rensselaser Polytechnic Institute at Hart-ford Hartford Conn USA 2010
[15] RH B Bouma A EDM van derHeijden TD Sewell andDLThompson ldquoChapter2 Simulations of deformation processesin energeticmaterialsrdquo inNumerical Simulations of Physical andEngineering Processes 2011
[16] E L Lee H C Hornig and J W Kury ldquoAdiabatic expansion ofhigh explosive detonation productsrdquo Technical Report UCRL-50422 Lawrence Radiation Laboratory University of CaliforniaLivermore Berkeley Calif USA 1968
[17] M AMeyersDynamic Behavior ofMaterialsWiley NewYorkNY USA 1994
[18] D J Steinberg S G Cochran and M W Guinan ldquoA constitu-tive model for metals applicable at high-strain raterdquo Journal ofApplied Physics vol 51 no 3 pp 1498ndash1504 1980
[19] J N Johnson ldquoDynamic fracture and spallation in ductilesolidsrdquo Journal of Applied Physics vol 52 no 4 pp 2812ndash28251981
[20] ANSYS Workshop 7 Ship Blast ANSYS Training ManualANSYS Cecil Township Pa USA 2010
10 Shock and Vibration
[21] ANSYS Chapter 1 Introduction to AUTODYN AUTODYNTraining Manual ANSYS Cecil Township Pa USA 2010
[22] X Quan N K Birnbaum M S Cowler B I Gerber R AClegg and C J Hayhurst ldquoNumerical simulation of structuraldeformation under shock and impact loads using a coupledmulti-solver approachrdquo in Proceedings of the 5th Asia-PacificConference on Shock and Impact Loads on Structures 2003
[23] Century Dynamics AUTODYN Theory Manual CenturyDynamics Concord Calif USA 2003
[24] J E Shepherd ldquoStructural response of piping to internal gasdetonationrdquo Journal of Pressure Vessel Technology Transactionsof the ASME vol 131 no 3 pp 0312041ndash03120413 2009
[25] J Kanesky J Damazo K Chow-Yee A Rusinek and J EShepherd ldquoPlastic deformation due to reflected detonationrdquoInternational Journal of Solids and Structures vol 50 no 1 pp97ndash110 2013
[26] A J Rosakis and G Ravichandran ldquoDynamic failure mechan-icsrdquo International Journal of Solids and Structures vol 37 no 1-2pp 331ndash348 2000
[27] S Fordham High Explosives and Propellants Pergamon PressElmsford NY USA 2nd edition 1980
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VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
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International Journal of
4 Shock and Vibration
Material status
Void
Hydro
Elastic
Plastic
Material status
Void
Hydro
Elastic
Plastic
15 grft
3138
2828
2517
2207
1897
15862121 2471 2821 3171 3521 3871
X
Y
X
20 grft
3211
2860
2510
2160
1809
14592146 2486 2825 3165 3504 3844
Y
25 grft
X
Y
3235
2863
2490
2118
1746
13742135 2479 2823 3167 3511 3855
30grft
X
Y
3269
2868
2466
2065
1663
12622099 2458 2816 3174 3532 3891
Figure 8 Material status of expanded steel tube
3 Numerical Modeling
31 Numerical Model Numerical simulations were per-formed for all the experiments using hydrocode in AUTO-DYN 2D examining the experimental expanding behaviorand numerical stresses The two-dimensional model wasmade of a steel tube support MDF and surrounding airas shown in Figure 5 The surrounding air was modeled asan ideal gas and the area was 400mm times 400mm Sincethe material of the support layer was Teflon and it did notaffect tube expansion significantly it was assumed as air Theexplosive material was HNS 165 where 165 indicates thedensity of HNS which is 165 gcm3 The explosive loads forall cases ranged from 15 to 30 grftThe explosive propagationvelocity for HNS 165 was approximately 7030ms and thedetonation point was set to the center of the MDF
32 Material Description and Boundary Conditions Boththe reacted solid and reacted gaseous products of HNS165 explosive were characterized with the Jones-Wilkins-Lee
180
175
170
165
160145 150 155 160 165 170 175 180 185 190
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft15 grft
20 grft
20 grft
25 grft25 grft
Figure 9 Comparison between the experimental and calculationalresults
Shock and Vibration 5
x
Detonation at t = 000120583s
y
x
y
z
20mm
76mm
Figure 10 Three-dimensional expanding tube
Table 1 Material coefficients in Jones-Wilkins-Lee (JWL) equationfor HNS 165
Parameter Value Unit119860 465 times 10
8 kPa119861 887 times 10
6 kPa1198771
455 mdash1198772
135 mdash120596 035 mdash
equation of state (JWL EOS [16]) The pressure in eitherphase is defined in terms of volume and internal energyindependent of temperature as
119901 = 119860(1 minus
120596
1198771119881
) 119890minus1198771119881+ 119861(1 minus
120596
1198772119881
) 119890minus1198772119881+
120596119890
119881
(1)
where119881 = 120588120588119900is the relative volume 119890 is the internal energy
and 119860 119861 1198771 1198772 and 120596 are empirically determined constants
that depend on the kind of the explosive Table 1 lists theJWL EOS coefficients used for this analysis of the HNS witha density of 165 gcm3
The ideal gas EOS for air is shown as follows
119901 = (120574 minus 1) 120588119890 (2)
where 120574 is the ideal gas constant and 120588 and 119890 are the densityand internal energy of the air The internal energy of air atroom temperature and ambient pressure is 2068 times 105 kJ
Both the tube and sheath were modeled as SS304 steeland AL6061 With the high pressure resulting from explosivedetonation both the tube and sheath undergoing high strainrates were modeled using the shock equation of state [17] andSteinberg-Guinan strength model [18] Both the von Misesyield strength (119884) and the shearmodulus (119866) of the Steinberg-Guinan model are assumed to be described as a function ofpressure (119875) density (120588) and temperature (119879) and in thecase of yield strength the effective plastic strain as well (120576)
119866 = 1198660(1 + (
1198661015840
0
1198660
)
119901
12057813+ (
1198661015840
119879
1198660
) (119879 minus 300))
119884 = 11988401 + 120573 (120576 + 120576
119894)
119899
times (1 + (
1198841015840
119901
1198840
)
119901
12057813+ (
1198841015840
119879
1198840
) (119879 minus 300))
(3)
Shock wave
Reaction zone
Pres
sure
(kPa
)
Time (ms)
Figure 11 Pressure loading profile
where 120573 is the hardening constant and 119899 is the hardeningexponent The subscript 0 refers to the reference state (119879 =300K 119875 = 0 120576 = 0) The primed parameters with thesubscripts 119875 and 119879 indicate the derivatives of the parameterswith respect to pressure or temperature at the referencestate Table 2 summarizes the Steinberg-Guinan strengthparameters used for the numerical model for the SS304 steeland AL6061 used in the present analysis
A flow-out condition was applied to all boundaries ofthe Euler grid This allowed the material to freely leave thegrid and also prevented relief waves from being generatedoff the lateral boundaries of the solid which would reducethe overall strength of the compressive shock and rarefactionwaves
33 Failure Model Spallation (spall-fracture) is a kind offracture that occurs as planar separation of material parallelto the incident plane wave fronts as a result of dynamic tensilestress components perpendicular to this plane [19] The spallstrength for tensile stress generated when a rarefaction wavetravels through material is 21 GPa for the steel tube If thetensile stress of the tube exceeds the predefined spall strength
6 Shock and Vibration
Y
Z
(a)
X
Y
Z
(b)
Figure 12 Three-dimensional model of expanding tube (front view (a) and isotropic view (b))
X
Y
Z
(a)
X
Y
Z
(b)
X
Y
Z
(c)
X
Y
Z
Bulk failBulk faila
(d)
Figure 13 Material status of one-sided detonation expanding tube ((a) 15 grft (b) 20 grft (c) 25 grft and (d) 30 grft)
the material is considered to have ldquofailedrdquo The tensile stressproduced by a rarefaction wave is often shown as a negativepressure [14]
34 Solvers AUTODYN provides various solvers for nonlin-ear problems [11 20 21] Lagrange and Euler solvers wereadopted in these FSI (fluid-structure interaction) simula-tions The Lagrangian representation keeps material in itsinitial element and the numerical mesh moves and deformswith the material The Lagrange method is most appropriate
for the description of solid-like structures Eulerian represen-tation allowsmaterials to flow from cell to cell while themeshis spatially fixed The Eulerian method is typically well suitedfor representing fluids and gases [20ndash23] In this study thesteel tube and sheath were modeled using a Lagrange solverwhile HNS and air were modeled using an Euler solver TheEuler and Lagrange interaction was also implemented to takeinto account the interaction between fluid (explosive and air)and structures (tube and sheath) This coupling techniqueallows complex fluid-structure interaction problems that
Shock and Vibration 7
Table 2 Steinberg-Guinan strength parameters
Parameter SS304 AL6061 Unit119866 77 times 10
8297 times 10
7 kPa119884 34 times 10
55 times 10
4 kPa120573 43 28 mdash119899 035 08 mdash119889119866119889119875 174 14119889119866119889119879 minus35 times 10
4minus129 times 10
4 kPaK119889119884119889119875 768 times 10
minus3235 times 10
minus3 mdashMelting temperature 2380 1604 K
145
180
175
170
165
160150 155 160 165 170 175 180 185
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft
15 grft20 grft
20 grft
25 grft
25 grft
Figure 14 Comparison between the experimental and calculationalresults
include large deformation of the structure to be solved in asingle numerical analysis
4 Results and Discussion
41 Two-Dimensional Numerical Results Figure 6 shows thetwo-dimensional numerical model of an expanding tubeexplosion The cell width was approximately 016mm Thenumber of elements in the tube model was 1404 and thewhole model had 161504 elements A description of thenumerical model is shown in Table 3
To illustrate the expansion process of the steel tube overtime the deformed configurations of a 15 grft expandingtube are depicted in Figure 7 at 119905 = 0ms 002ms 007msand 01ms The calculation was started at time 119905 = 00msand finished at 119905 = 01ms when it could be assumed thatdetonation had been completed It is clearly seen that the tubeis expanded outward radially from the detonation point At119905 = 002ms early in the detonation the minor axis of thetube started to be expanded and the length of the major axiswas becoming shorter over time At a later time the shape ofthe tube sectionwas deformed from elliptical to circular suchthat the shape change might separate a joint
Table 3 Description of numerical model of 2D expanding tube
Part Materials Number of mesh SolverTube SS304 1404 LagrangianSheath AL6061 100Air Air 160000 EulerianHigh explosive HNS 165
A series of computations was performed by varyingexplosive loads to compute the material response of thetube and the deformations are presented in Figure 8 It isapparent that the tube expansion increases as the explosiveload increases For a pressure tube in the plastic deformationregime catastrophic failure is associated with ductile tearingor plastic instability [19 24 25] Rapidly expanding regions(the minor axis of the tube) are accompanied by rapid lossof stress-carrying capability and intense heating due to thedissipation of plastic work and present risks of rupture [26]As shown in Figure 8 the plastic region and computed stresswere increased proportionally to the explosive load As aresult the 30 grft expanding tube shows the largest plasticregion and the greatest stress is on the minor axis dueto energy absorption However the 30 grft expanding tubeexpanded without spallation in the 2D simulation whichdiffers distinctly from the experimental results becausethis FE analysis accounts for only radial expansion Thissuggests that the tube expansion due to the detonation wavepropagation should be considered to develop a more reliablenumerical model
Figure 9 compares the changes of width and height ofthe tube in the FE analysis and experimental results forthree cases with 15 20 and 25 grft Although the calculationresults slightly overestimated the experimental results of eachcore load the overall error of both width (minor axis) andheight (major axis) prediction was less than 10
42 Three-Dimensional Numerical Results Figure 10 illus-trates a three-dimensional expanding tube and detonationdirection The open-ended steel tube was 300mm long andMDF of a 320mm length of MDF was inserted into thecentral bore Its cross section was the same as in the 2D caseDetonation was assumed to be started from the left end of thetube at 119905 = 00ms identically to the experimental conditionsTo describe the 3D detonation propagation a cylindricalblast wave was generated and then remapped in the airThe pressure profile of the detonation wave propagation intothe tube is presented in Figure 11 and its structure consistsof a shock wave and reaction zone where the explosive ischanged into gaseous products at high temperature Thesereaction products act as a piston that allows the shock waveto propagate at a constant velocity [27] Figure 12 shows thenumerical model of the 3D expanding tube A graded gridwas applied to the air and HNS 165 to save computationtime Table 4 summarizes the description of the 3Dnumericalmodel
Figure 13 displays the expansion behaviors and materialstatus of each expanding tube Similar to the 2D results
8 Shock and Vibration
(150 38 0)Gauge number 1 Gauge number 2 Gauge number 3
(75 38 0) (225 38 0)
Detonation at t = 000120583s
y
x
Figure 15 Gauges position
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft27 grft
30 grft
Figure 16 Pressure histories from gauge number 1
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 17 Pressure histories from gauge number 2
Table 4 Description of 3D expanding tube numerical model
Part Materials Number of mesh SolverTube SS304 64800 LagrangianSheath AL6061 13360Air Air 203125 EulerianHigh explosive HNS 165
the tubes with explosive loads of 15ndash25 grft freely expandedbut the 30 grft tube failed due to plastic deformation Asshown in Figure 13 there was spallation at 130mm from theside of the 30 grft expanding tube at around 119905 = 007msThis ductile fracture was caused by the significant amount
0 001 002 003 004 005 006 007 008 009 01
Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 18 Pressure histories from gauge number 3
of plastic deformation during tube expansion This failurebehavior in FE analysis was somewhat different from theexperimental failure behavior In experiments two failuresoccurred on the left and right sides of the steel tube whileone bulk failure was found in the numerical simulationEven if the first spallation could be predicted it might beinappropriate to simulate a successive multiple-spallationgeneration mechanism
Figure 14 compares between the numerical simulationand experimental results of each expanding tube deforma-tion The overall error was less than 3 and the agreementwas improved by considering the tube expansion due todetonation wave propagation
To compute a proper core load the internal pressureof the expanding wall of the steel tube was numericallycalculated for explosive loads of 15 20 25 27 and 30 grftThethree points indicated in Figure 15 represent the placementof a gauge for measuring the internal pressure Figures 1617 and 18 plot the time histories of pressure observed bygauges in the middle of the steel tube thickness over timeThe first peak was due to the initial shock wave travelingthrough the tube The rarefaction wave generated due tofree surface interaction is often shown as negative pressurefollowing the first peak and it produces tensile stress onthe tube The maximum pressure of the respective gaugesranged from minus130 to minus520MPa for the various explosiveloads The pressure histories of expanding tubes with loadsof 15ndash25 grft fluctuated and became stable over time Inthe FE analysis the 27 grft expanding tube was able toexpand freely without failure and its maximum pressure was
Shock and Vibration 9
125 times higher than that of the 25 grft expanding tubewhich was found to have a proper explosive load in theballistic test using expanding tube samplesTherefore we canconclude that the proper explosive load in the experimentswas underestimated according to the numerical results Foran explosive load of 30 grft the internal pressure increaseddramatically and reached a value ofminus520MPaThemaximumpressure on the steel tube with the 30 grft load was about 27and 2 times higher than those with the 25 grft and 27 grftloads respectively This means that since the explosive loadof 30 grft was greater than the failure threshold spallationoccurred in the actual expanding tube
5 Conclusions
The development of a numerical model has been presentedfor the free expansion of expanding tubes byMDFdetonationin pyro-separation systems using AUTODYN 2D and 3Dhydrocode Numerical simulations were performed for fourexpanding tube explosive load cases as a verification set forthe numerical model and additional simulation was done tosuggest a more effective explosive load
In the 2D model since the detonation wave propagationcould not be considered the results slightly overestimatedthe shape of the expanded tube To improve the accuracyof the results the 3D model was developed which allowedfor tube expansion due to detonation wave propagationThe developed model was verified with explosive test resultsand showed less than 3 overall error From the results of3D numerical simulation where the Steinberg model wasapplied for the failure criteria of the steel tube 27 grft wasthe proper explosive load and the 30 grft explosive loadexceeded the threshold of expanding tube failure Since thenumerical model verified with ballistic test results allows forvarious design changes the development cost and time can begreatly reduced by minimizing the number of experimentaltests required Therefore it is suggested to add a numericalmodel development step using 3D hydrocode to the overallprocedure of expanding tube development for pyrotechnicseparation systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by the Leading Foreign ResearchInstitute Recruitment Program (2011-0030065) and theBasic Science Research Program (2011-0010489) throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology This studywas also financially supported by the University Collabora-tion Enhancement Project of the Korea Aerospace ResearchInstitute
References
[1] K Y Chang and D L Kern SuperlowastZip (linear separa-tion) shock characteristics 1986 httpntrsnasagovarchivenasacasintrsnasagov19870011172 1987011172pdf
[2] L J Bement and M L Schimmel ldquoA manual for pyrotech-nic design development and qualificationrdquo NASA TechnicalMemerandum 110172 1995
[3] J R Lee CCChia andCWKong ldquoReviewof pyroshockwavemeasurement and simulation for space systemsrdquoMeasurementJournal of the International Measurement Confederation vol 45no 4 pp 631ndash642 2012
[4] K Y Chang ldquoPyrotechnic devices shock levels and theirapplicationsrdquo in Proceedings of the Pyroshock Seminar ICSV92002
[5] NASA ldquoPyroshock test criteriardquo NASA-STD-7003A 2011[6] L H Richards J K Vision and D J Schorr ldquoThrusting
separation systemrdquo US Patent US5372071 1993[7] W C Hoffman III ldquoAge life evaluation of space shuttle crew
escape systempyrotechnic components loadedwith hexanitros-tilbene (HNS) NASArdquo Technical Paper 3650 1996
[8] L J Bement and M L Schimmel ldquoInvestigation of SuperlowastZipseparation jointrdquo NASA Technical Memorandum 4031 1988
[9] MMiyazawa and Y Fukushima ldquoDevelopment status of Japanrsquosnew launch vehicle H-II rocektrdquo in Proceedings of the 40thCongress of the International Astronautical Federation 1989
[10] M Quidot ldquoSome examples of energetic material modelingwith LSDYNArdquo in Proceedings of the 3rd European LS-DYNAConference 2001
[11] G E Fairlie ldquoThenumerical simulation of high explosives usingAUTODYN-2Damp3Drdquo inProceedings of the Institute of ExplosiveEngineers 4th Biannual Symposium (Explo rsquo98) 1998
[12] J K Chen H Ching and F A Allahdadi ldquoShock-induceddetonation of high explosives by high velocity impactrdquo Journalof Mechanics of Materials and Structures vol 2 no 9 pp 1701ndash1721 2007
[13] S M Muramatsu ldquoNumerical and experimental study of apyroshock test set up for small spacecraft componentrdquo ProjectReport UPNA 2010
[14] J Danyluk Spall fracture ofmulti-material plates under explosiveloading [MS thesis] Rensselaser Polytechnic Institute at Hart-ford Hartford Conn USA 2010
[15] RH B Bouma A EDM van derHeijden TD Sewell andDLThompson ldquoChapter2 Simulations of deformation processesin energeticmaterialsrdquo inNumerical Simulations of Physical andEngineering Processes 2011
[16] E L Lee H C Hornig and J W Kury ldquoAdiabatic expansion ofhigh explosive detonation productsrdquo Technical Report UCRL-50422 Lawrence Radiation Laboratory University of CaliforniaLivermore Berkeley Calif USA 1968
[17] M AMeyersDynamic Behavior ofMaterialsWiley NewYorkNY USA 1994
[18] D J Steinberg S G Cochran and M W Guinan ldquoA constitu-tive model for metals applicable at high-strain raterdquo Journal ofApplied Physics vol 51 no 3 pp 1498ndash1504 1980
[19] J N Johnson ldquoDynamic fracture and spallation in ductilesolidsrdquo Journal of Applied Physics vol 52 no 4 pp 2812ndash28251981
[20] ANSYS Workshop 7 Ship Blast ANSYS Training ManualANSYS Cecil Township Pa USA 2010
10 Shock and Vibration
[21] ANSYS Chapter 1 Introduction to AUTODYN AUTODYNTraining Manual ANSYS Cecil Township Pa USA 2010
[22] X Quan N K Birnbaum M S Cowler B I Gerber R AClegg and C J Hayhurst ldquoNumerical simulation of structuraldeformation under shock and impact loads using a coupledmulti-solver approachrdquo in Proceedings of the 5th Asia-PacificConference on Shock and Impact Loads on Structures 2003
[23] Century Dynamics AUTODYN Theory Manual CenturyDynamics Concord Calif USA 2003
[24] J E Shepherd ldquoStructural response of piping to internal gasdetonationrdquo Journal of Pressure Vessel Technology Transactionsof the ASME vol 131 no 3 pp 0312041ndash03120413 2009
[25] J Kanesky J Damazo K Chow-Yee A Rusinek and J EShepherd ldquoPlastic deformation due to reflected detonationrdquoInternational Journal of Solids and Structures vol 50 no 1 pp97ndash110 2013
[26] A J Rosakis and G Ravichandran ldquoDynamic failure mechan-icsrdquo International Journal of Solids and Structures vol 37 no 1-2pp 331ndash348 2000
[27] S Fordham High Explosives and Propellants Pergamon PressElmsford NY USA 2nd edition 1980
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
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Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
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SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
Shock and Vibration 5
x
Detonation at t = 000120583s
y
x
y
z
20mm
76mm
Figure 10 Three-dimensional expanding tube
Table 1 Material coefficients in Jones-Wilkins-Lee (JWL) equationfor HNS 165
Parameter Value Unit119860 465 times 10
8 kPa119861 887 times 10
6 kPa1198771
455 mdash1198772
135 mdash120596 035 mdash
equation of state (JWL EOS [16]) The pressure in eitherphase is defined in terms of volume and internal energyindependent of temperature as
119901 = 119860(1 minus
120596
1198771119881
) 119890minus1198771119881+ 119861(1 minus
120596
1198772119881
) 119890minus1198772119881+
120596119890
119881
(1)
where119881 = 120588120588119900is the relative volume 119890 is the internal energy
and 119860 119861 1198771 1198772 and 120596 are empirically determined constants
that depend on the kind of the explosive Table 1 lists theJWL EOS coefficients used for this analysis of the HNS witha density of 165 gcm3
The ideal gas EOS for air is shown as follows
119901 = (120574 minus 1) 120588119890 (2)
where 120574 is the ideal gas constant and 120588 and 119890 are the densityand internal energy of the air The internal energy of air atroom temperature and ambient pressure is 2068 times 105 kJ
Both the tube and sheath were modeled as SS304 steeland AL6061 With the high pressure resulting from explosivedetonation both the tube and sheath undergoing high strainrates were modeled using the shock equation of state [17] andSteinberg-Guinan strength model [18] Both the von Misesyield strength (119884) and the shearmodulus (119866) of the Steinberg-Guinan model are assumed to be described as a function ofpressure (119875) density (120588) and temperature (119879) and in thecase of yield strength the effective plastic strain as well (120576)
119866 = 1198660(1 + (
1198661015840
0
1198660
)
119901
12057813+ (
1198661015840
119879
1198660
) (119879 minus 300))
119884 = 11988401 + 120573 (120576 + 120576
119894)
119899
times (1 + (
1198841015840
119901
1198840
)
119901
12057813+ (
1198841015840
119879
1198840
) (119879 minus 300))
(3)
Shock wave
Reaction zone
Pres
sure
(kPa
)
Time (ms)
Figure 11 Pressure loading profile
where 120573 is the hardening constant and 119899 is the hardeningexponent The subscript 0 refers to the reference state (119879 =300K 119875 = 0 120576 = 0) The primed parameters with thesubscripts 119875 and 119879 indicate the derivatives of the parameterswith respect to pressure or temperature at the referencestate Table 2 summarizes the Steinberg-Guinan strengthparameters used for the numerical model for the SS304 steeland AL6061 used in the present analysis
A flow-out condition was applied to all boundaries ofthe Euler grid This allowed the material to freely leave thegrid and also prevented relief waves from being generatedoff the lateral boundaries of the solid which would reducethe overall strength of the compressive shock and rarefactionwaves
33 Failure Model Spallation (spall-fracture) is a kind offracture that occurs as planar separation of material parallelto the incident plane wave fronts as a result of dynamic tensilestress components perpendicular to this plane [19] The spallstrength for tensile stress generated when a rarefaction wavetravels through material is 21 GPa for the steel tube If thetensile stress of the tube exceeds the predefined spall strength
6 Shock and Vibration
Y
Z
(a)
X
Y
Z
(b)
Figure 12 Three-dimensional model of expanding tube (front view (a) and isotropic view (b))
X
Y
Z
(a)
X
Y
Z
(b)
X
Y
Z
(c)
X
Y
Z
Bulk failBulk faila
(d)
Figure 13 Material status of one-sided detonation expanding tube ((a) 15 grft (b) 20 grft (c) 25 grft and (d) 30 grft)
the material is considered to have ldquofailedrdquo The tensile stressproduced by a rarefaction wave is often shown as a negativepressure [14]
34 Solvers AUTODYN provides various solvers for nonlin-ear problems [11 20 21] Lagrange and Euler solvers wereadopted in these FSI (fluid-structure interaction) simula-tions The Lagrangian representation keeps material in itsinitial element and the numerical mesh moves and deformswith the material The Lagrange method is most appropriate
for the description of solid-like structures Eulerian represen-tation allowsmaterials to flow from cell to cell while themeshis spatially fixed The Eulerian method is typically well suitedfor representing fluids and gases [20ndash23] In this study thesteel tube and sheath were modeled using a Lagrange solverwhile HNS and air were modeled using an Euler solver TheEuler and Lagrange interaction was also implemented to takeinto account the interaction between fluid (explosive and air)and structures (tube and sheath) This coupling techniqueallows complex fluid-structure interaction problems that
Shock and Vibration 7
Table 2 Steinberg-Guinan strength parameters
Parameter SS304 AL6061 Unit119866 77 times 10
8297 times 10
7 kPa119884 34 times 10
55 times 10
4 kPa120573 43 28 mdash119899 035 08 mdash119889119866119889119875 174 14119889119866119889119879 minus35 times 10
4minus129 times 10
4 kPaK119889119884119889119875 768 times 10
minus3235 times 10
minus3 mdashMelting temperature 2380 1604 K
145
180
175
170
165
160150 155 160 165 170 175 180 185
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft
15 grft20 grft
20 grft
25 grft
25 grft
Figure 14 Comparison between the experimental and calculationalresults
include large deformation of the structure to be solved in asingle numerical analysis
4 Results and Discussion
41 Two-Dimensional Numerical Results Figure 6 shows thetwo-dimensional numerical model of an expanding tubeexplosion The cell width was approximately 016mm Thenumber of elements in the tube model was 1404 and thewhole model had 161504 elements A description of thenumerical model is shown in Table 3
To illustrate the expansion process of the steel tube overtime the deformed configurations of a 15 grft expandingtube are depicted in Figure 7 at 119905 = 0ms 002ms 007msand 01ms The calculation was started at time 119905 = 00msand finished at 119905 = 01ms when it could be assumed thatdetonation had been completed It is clearly seen that the tubeis expanded outward radially from the detonation point At119905 = 002ms early in the detonation the minor axis of thetube started to be expanded and the length of the major axiswas becoming shorter over time At a later time the shape ofthe tube sectionwas deformed from elliptical to circular suchthat the shape change might separate a joint
Table 3 Description of numerical model of 2D expanding tube
Part Materials Number of mesh SolverTube SS304 1404 LagrangianSheath AL6061 100Air Air 160000 EulerianHigh explosive HNS 165
A series of computations was performed by varyingexplosive loads to compute the material response of thetube and the deformations are presented in Figure 8 It isapparent that the tube expansion increases as the explosiveload increases For a pressure tube in the plastic deformationregime catastrophic failure is associated with ductile tearingor plastic instability [19 24 25] Rapidly expanding regions(the minor axis of the tube) are accompanied by rapid lossof stress-carrying capability and intense heating due to thedissipation of plastic work and present risks of rupture [26]As shown in Figure 8 the plastic region and computed stresswere increased proportionally to the explosive load As aresult the 30 grft expanding tube shows the largest plasticregion and the greatest stress is on the minor axis dueto energy absorption However the 30 grft expanding tubeexpanded without spallation in the 2D simulation whichdiffers distinctly from the experimental results becausethis FE analysis accounts for only radial expansion Thissuggests that the tube expansion due to the detonation wavepropagation should be considered to develop a more reliablenumerical model
Figure 9 compares the changes of width and height ofthe tube in the FE analysis and experimental results forthree cases with 15 20 and 25 grft Although the calculationresults slightly overestimated the experimental results of eachcore load the overall error of both width (minor axis) andheight (major axis) prediction was less than 10
42 Three-Dimensional Numerical Results Figure 10 illus-trates a three-dimensional expanding tube and detonationdirection The open-ended steel tube was 300mm long andMDF of a 320mm length of MDF was inserted into thecentral bore Its cross section was the same as in the 2D caseDetonation was assumed to be started from the left end of thetube at 119905 = 00ms identically to the experimental conditionsTo describe the 3D detonation propagation a cylindricalblast wave was generated and then remapped in the airThe pressure profile of the detonation wave propagation intothe tube is presented in Figure 11 and its structure consistsof a shock wave and reaction zone where the explosive ischanged into gaseous products at high temperature Thesereaction products act as a piston that allows the shock waveto propagate at a constant velocity [27] Figure 12 shows thenumerical model of the 3D expanding tube A graded gridwas applied to the air and HNS 165 to save computationtime Table 4 summarizes the description of the 3Dnumericalmodel
Figure 13 displays the expansion behaviors and materialstatus of each expanding tube Similar to the 2D results
8 Shock and Vibration
(150 38 0)Gauge number 1 Gauge number 2 Gauge number 3
(75 38 0) (225 38 0)
Detonation at t = 000120583s
y
x
Figure 15 Gauges position
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft27 grft
30 grft
Figure 16 Pressure histories from gauge number 1
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 17 Pressure histories from gauge number 2
Table 4 Description of 3D expanding tube numerical model
Part Materials Number of mesh SolverTube SS304 64800 LagrangianSheath AL6061 13360Air Air 203125 EulerianHigh explosive HNS 165
the tubes with explosive loads of 15ndash25 grft freely expandedbut the 30 grft tube failed due to plastic deformation Asshown in Figure 13 there was spallation at 130mm from theside of the 30 grft expanding tube at around 119905 = 007msThis ductile fracture was caused by the significant amount
0 001 002 003 004 005 006 007 008 009 01
Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 18 Pressure histories from gauge number 3
of plastic deformation during tube expansion This failurebehavior in FE analysis was somewhat different from theexperimental failure behavior In experiments two failuresoccurred on the left and right sides of the steel tube whileone bulk failure was found in the numerical simulationEven if the first spallation could be predicted it might beinappropriate to simulate a successive multiple-spallationgeneration mechanism
Figure 14 compares between the numerical simulationand experimental results of each expanding tube deforma-tion The overall error was less than 3 and the agreementwas improved by considering the tube expansion due todetonation wave propagation
To compute a proper core load the internal pressureof the expanding wall of the steel tube was numericallycalculated for explosive loads of 15 20 25 27 and 30 grftThethree points indicated in Figure 15 represent the placementof a gauge for measuring the internal pressure Figures 1617 and 18 plot the time histories of pressure observed bygauges in the middle of the steel tube thickness over timeThe first peak was due to the initial shock wave travelingthrough the tube The rarefaction wave generated due tofree surface interaction is often shown as negative pressurefollowing the first peak and it produces tensile stress onthe tube The maximum pressure of the respective gaugesranged from minus130 to minus520MPa for the various explosiveloads The pressure histories of expanding tubes with loadsof 15ndash25 grft fluctuated and became stable over time Inthe FE analysis the 27 grft expanding tube was able toexpand freely without failure and its maximum pressure was
Shock and Vibration 9
125 times higher than that of the 25 grft expanding tubewhich was found to have a proper explosive load in theballistic test using expanding tube samplesTherefore we canconclude that the proper explosive load in the experimentswas underestimated according to the numerical results Foran explosive load of 30 grft the internal pressure increaseddramatically and reached a value ofminus520MPaThemaximumpressure on the steel tube with the 30 grft load was about 27and 2 times higher than those with the 25 grft and 27 grftloads respectively This means that since the explosive loadof 30 grft was greater than the failure threshold spallationoccurred in the actual expanding tube
5 Conclusions
The development of a numerical model has been presentedfor the free expansion of expanding tubes byMDFdetonationin pyro-separation systems using AUTODYN 2D and 3Dhydrocode Numerical simulations were performed for fourexpanding tube explosive load cases as a verification set forthe numerical model and additional simulation was done tosuggest a more effective explosive load
In the 2D model since the detonation wave propagationcould not be considered the results slightly overestimatedthe shape of the expanded tube To improve the accuracyof the results the 3D model was developed which allowedfor tube expansion due to detonation wave propagationThe developed model was verified with explosive test resultsand showed less than 3 overall error From the results of3D numerical simulation where the Steinberg model wasapplied for the failure criteria of the steel tube 27 grft wasthe proper explosive load and the 30 grft explosive loadexceeded the threshold of expanding tube failure Since thenumerical model verified with ballistic test results allows forvarious design changes the development cost and time can begreatly reduced by minimizing the number of experimentaltests required Therefore it is suggested to add a numericalmodel development step using 3D hydrocode to the overallprocedure of expanding tube development for pyrotechnicseparation systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by the Leading Foreign ResearchInstitute Recruitment Program (2011-0030065) and theBasic Science Research Program (2011-0010489) throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology This studywas also financially supported by the University Collabora-tion Enhancement Project of the Korea Aerospace ResearchInstitute
References
[1] K Y Chang and D L Kern SuperlowastZip (linear separa-tion) shock characteristics 1986 httpntrsnasagovarchivenasacasintrsnasagov19870011172 1987011172pdf
[2] L J Bement and M L Schimmel ldquoA manual for pyrotech-nic design development and qualificationrdquo NASA TechnicalMemerandum 110172 1995
[3] J R Lee CCChia andCWKong ldquoReviewof pyroshockwavemeasurement and simulation for space systemsrdquoMeasurementJournal of the International Measurement Confederation vol 45no 4 pp 631ndash642 2012
[4] K Y Chang ldquoPyrotechnic devices shock levels and theirapplicationsrdquo in Proceedings of the Pyroshock Seminar ICSV92002
[5] NASA ldquoPyroshock test criteriardquo NASA-STD-7003A 2011[6] L H Richards J K Vision and D J Schorr ldquoThrusting
separation systemrdquo US Patent US5372071 1993[7] W C Hoffman III ldquoAge life evaluation of space shuttle crew
escape systempyrotechnic components loadedwith hexanitros-tilbene (HNS) NASArdquo Technical Paper 3650 1996
[8] L J Bement and M L Schimmel ldquoInvestigation of SuperlowastZipseparation jointrdquo NASA Technical Memorandum 4031 1988
[9] MMiyazawa and Y Fukushima ldquoDevelopment status of Japanrsquosnew launch vehicle H-II rocektrdquo in Proceedings of the 40thCongress of the International Astronautical Federation 1989
[10] M Quidot ldquoSome examples of energetic material modelingwith LSDYNArdquo in Proceedings of the 3rd European LS-DYNAConference 2001
[11] G E Fairlie ldquoThenumerical simulation of high explosives usingAUTODYN-2Damp3Drdquo inProceedings of the Institute of ExplosiveEngineers 4th Biannual Symposium (Explo rsquo98) 1998
[12] J K Chen H Ching and F A Allahdadi ldquoShock-induceddetonation of high explosives by high velocity impactrdquo Journalof Mechanics of Materials and Structures vol 2 no 9 pp 1701ndash1721 2007
[13] S M Muramatsu ldquoNumerical and experimental study of apyroshock test set up for small spacecraft componentrdquo ProjectReport UPNA 2010
[14] J Danyluk Spall fracture ofmulti-material plates under explosiveloading [MS thesis] Rensselaser Polytechnic Institute at Hart-ford Hartford Conn USA 2010
[15] RH B Bouma A EDM van derHeijden TD Sewell andDLThompson ldquoChapter2 Simulations of deformation processesin energeticmaterialsrdquo inNumerical Simulations of Physical andEngineering Processes 2011
[16] E L Lee H C Hornig and J W Kury ldquoAdiabatic expansion ofhigh explosive detonation productsrdquo Technical Report UCRL-50422 Lawrence Radiation Laboratory University of CaliforniaLivermore Berkeley Calif USA 1968
[17] M AMeyersDynamic Behavior ofMaterialsWiley NewYorkNY USA 1994
[18] D J Steinberg S G Cochran and M W Guinan ldquoA constitu-tive model for metals applicable at high-strain raterdquo Journal ofApplied Physics vol 51 no 3 pp 1498ndash1504 1980
[19] J N Johnson ldquoDynamic fracture and spallation in ductilesolidsrdquo Journal of Applied Physics vol 52 no 4 pp 2812ndash28251981
[20] ANSYS Workshop 7 Ship Blast ANSYS Training ManualANSYS Cecil Township Pa USA 2010
10 Shock and Vibration
[21] ANSYS Chapter 1 Introduction to AUTODYN AUTODYNTraining Manual ANSYS Cecil Township Pa USA 2010
[22] X Quan N K Birnbaum M S Cowler B I Gerber R AClegg and C J Hayhurst ldquoNumerical simulation of structuraldeformation under shock and impact loads using a coupledmulti-solver approachrdquo in Proceedings of the 5th Asia-PacificConference on Shock and Impact Loads on Structures 2003
[23] Century Dynamics AUTODYN Theory Manual CenturyDynamics Concord Calif USA 2003
[24] J E Shepherd ldquoStructural response of piping to internal gasdetonationrdquo Journal of Pressure Vessel Technology Transactionsof the ASME vol 131 no 3 pp 0312041ndash03120413 2009
[25] J Kanesky J Damazo K Chow-Yee A Rusinek and J EShepherd ldquoPlastic deformation due to reflected detonationrdquoInternational Journal of Solids and Structures vol 50 no 1 pp97ndash110 2013
[26] A J Rosakis and G Ravichandran ldquoDynamic failure mechan-icsrdquo International Journal of Solids and Structures vol 37 no 1-2pp 331ndash348 2000
[27] S Fordham High Explosives and Propellants Pergamon PressElmsford NY USA 2nd edition 1980
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 Shock and Vibration
Y
Z
(a)
X
Y
Z
(b)
Figure 12 Three-dimensional model of expanding tube (front view (a) and isotropic view (b))
X
Y
Z
(a)
X
Y
Z
(b)
X
Y
Z
(c)
X
Y
Z
Bulk failBulk faila
(d)
Figure 13 Material status of one-sided detonation expanding tube ((a) 15 grft (b) 20 grft (c) 25 grft and (d) 30 grft)
the material is considered to have ldquofailedrdquo The tensile stressproduced by a rarefaction wave is often shown as a negativepressure [14]
34 Solvers AUTODYN provides various solvers for nonlin-ear problems [11 20 21] Lagrange and Euler solvers wereadopted in these FSI (fluid-structure interaction) simula-tions The Lagrangian representation keeps material in itsinitial element and the numerical mesh moves and deformswith the material The Lagrange method is most appropriate
for the description of solid-like structures Eulerian represen-tation allowsmaterials to flow from cell to cell while themeshis spatially fixed The Eulerian method is typically well suitedfor representing fluids and gases [20ndash23] In this study thesteel tube and sheath were modeled using a Lagrange solverwhile HNS and air were modeled using an Euler solver TheEuler and Lagrange interaction was also implemented to takeinto account the interaction between fluid (explosive and air)and structures (tube and sheath) This coupling techniqueallows complex fluid-structure interaction problems that
Shock and Vibration 7
Table 2 Steinberg-Guinan strength parameters
Parameter SS304 AL6061 Unit119866 77 times 10
8297 times 10
7 kPa119884 34 times 10
55 times 10
4 kPa120573 43 28 mdash119899 035 08 mdash119889119866119889119875 174 14119889119866119889119879 minus35 times 10
4minus129 times 10
4 kPaK119889119884119889119875 768 times 10
minus3235 times 10
minus3 mdashMelting temperature 2380 1604 K
145
180
175
170
165
160150 155 160 165 170 175 180 185
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft
15 grft20 grft
20 grft
25 grft
25 grft
Figure 14 Comparison between the experimental and calculationalresults
include large deformation of the structure to be solved in asingle numerical analysis
4 Results and Discussion
41 Two-Dimensional Numerical Results Figure 6 shows thetwo-dimensional numerical model of an expanding tubeexplosion The cell width was approximately 016mm Thenumber of elements in the tube model was 1404 and thewhole model had 161504 elements A description of thenumerical model is shown in Table 3
To illustrate the expansion process of the steel tube overtime the deformed configurations of a 15 grft expandingtube are depicted in Figure 7 at 119905 = 0ms 002ms 007msand 01ms The calculation was started at time 119905 = 00msand finished at 119905 = 01ms when it could be assumed thatdetonation had been completed It is clearly seen that the tubeis expanded outward radially from the detonation point At119905 = 002ms early in the detonation the minor axis of thetube started to be expanded and the length of the major axiswas becoming shorter over time At a later time the shape ofthe tube sectionwas deformed from elliptical to circular suchthat the shape change might separate a joint
Table 3 Description of numerical model of 2D expanding tube
Part Materials Number of mesh SolverTube SS304 1404 LagrangianSheath AL6061 100Air Air 160000 EulerianHigh explosive HNS 165
A series of computations was performed by varyingexplosive loads to compute the material response of thetube and the deformations are presented in Figure 8 It isapparent that the tube expansion increases as the explosiveload increases For a pressure tube in the plastic deformationregime catastrophic failure is associated with ductile tearingor plastic instability [19 24 25] Rapidly expanding regions(the minor axis of the tube) are accompanied by rapid lossof stress-carrying capability and intense heating due to thedissipation of plastic work and present risks of rupture [26]As shown in Figure 8 the plastic region and computed stresswere increased proportionally to the explosive load As aresult the 30 grft expanding tube shows the largest plasticregion and the greatest stress is on the minor axis dueto energy absorption However the 30 grft expanding tubeexpanded without spallation in the 2D simulation whichdiffers distinctly from the experimental results becausethis FE analysis accounts for only radial expansion Thissuggests that the tube expansion due to the detonation wavepropagation should be considered to develop a more reliablenumerical model
Figure 9 compares the changes of width and height ofthe tube in the FE analysis and experimental results forthree cases with 15 20 and 25 grft Although the calculationresults slightly overestimated the experimental results of eachcore load the overall error of both width (minor axis) andheight (major axis) prediction was less than 10
42 Three-Dimensional Numerical Results Figure 10 illus-trates a three-dimensional expanding tube and detonationdirection The open-ended steel tube was 300mm long andMDF of a 320mm length of MDF was inserted into thecentral bore Its cross section was the same as in the 2D caseDetonation was assumed to be started from the left end of thetube at 119905 = 00ms identically to the experimental conditionsTo describe the 3D detonation propagation a cylindricalblast wave was generated and then remapped in the airThe pressure profile of the detonation wave propagation intothe tube is presented in Figure 11 and its structure consistsof a shock wave and reaction zone where the explosive ischanged into gaseous products at high temperature Thesereaction products act as a piston that allows the shock waveto propagate at a constant velocity [27] Figure 12 shows thenumerical model of the 3D expanding tube A graded gridwas applied to the air and HNS 165 to save computationtime Table 4 summarizes the description of the 3Dnumericalmodel
Figure 13 displays the expansion behaviors and materialstatus of each expanding tube Similar to the 2D results
8 Shock and Vibration
(150 38 0)Gauge number 1 Gauge number 2 Gauge number 3
(75 38 0) (225 38 0)
Detonation at t = 000120583s
y
x
Figure 15 Gauges position
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft27 grft
30 grft
Figure 16 Pressure histories from gauge number 1
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 17 Pressure histories from gauge number 2
Table 4 Description of 3D expanding tube numerical model
Part Materials Number of mesh SolverTube SS304 64800 LagrangianSheath AL6061 13360Air Air 203125 EulerianHigh explosive HNS 165
the tubes with explosive loads of 15ndash25 grft freely expandedbut the 30 grft tube failed due to plastic deformation Asshown in Figure 13 there was spallation at 130mm from theside of the 30 grft expanding tube at around 119905 = 007msThis ductile fracture was caused by the significant amount
0 001 002 003 004 005 006 007 008 009 01
Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 18 Pressure histories from gauge number 3
of plastic deformation during tube expansion This failurebehavior in FE analysis was somewhat different from theexperimental failure behavior In experiments two failuresoccurred on the left and right sides of the steel tube whileone bulk failure was found in the numerical simulationEven if the first spallation could be predicted it might beinappropriate to simulate a successive multiple-spallationgeneration mechanism
Figure 14 compares between the numerical simulationand experimental results of each expanding tube deforma-tion The overall error was less than 3 and the agreementwas improved by considering the tube expansion due todetonation wave propagation
To compute a proper core load the internal pressureof the expanding wall of the steel tube was numericallycalculated for explosive loads of 15 20 25 27 and 30 grftThethree points indicated in Figure 15 represent the placementof a gauge for measuring the internal pressure Figures 1617 and 18 plot the time histories of pressure observed bygauges in the middle of the steel tube thickness over timeThe first peak was due to the initial shock wave travelingthrough the tube The rarefaction wave generated due tofree surface interaction is often shown as negative pressurefollowing the first peak and it produces tensile stress onthe tube The maximum pressure of the respective gaugesranged from minus130 to minus520MPa for the various explosiveloads The pressure histories of expanding tubes with loadsof 15ndash25 grft fluctuated and became stable over time Inthe FE analysis the 27 grft expanding tube was able toexpand freely without failure and its maximum pressure was
Shock and Vibration 9
125 times higher than that of the 25 grft expanding tubewhich was found to have a proper explosive load in theballistic test using expanding tube samplesTherefore we canconclude that the proper explosive load in the experimentswas underestimated according to the numerical results Foran explosive load of 30 grft the internal pressure increaseddramatically and reached a value ofminus520MPaThemaximumpressure on the steel tube with the 30 grft load was about 27and 2 times higher than those with the 25 grft and 27 grftloads respectively This means that since the explosive loadof 30 grft was greater than the failure threshold spallationoccurred in the actual expanding tube
5 Conclusions
The development of a numerical model has been presentedfor the free expansion of expanding tubes byMDFdetonationin pyro-separation systems using AUTODYN 2D and 3Dhydrocode Numerical simulations were performed for fourexpanding tube explosive load cases as a verification set forthe numerical model and additional simulation was done tosuggest a more effective explosive load
In the 2D model since the detonation wave propagationcould not be considered the results slightly overestimatedthe shape of the expanded tube To improve the accuracyof the results the 3D model was developed which allowedfor tube expansion due to detonation wave propagationThe developed model was verified with explosive test resultsand showed less than 3 overall error From the results of3D numerical simulation where the Steinberg model wasapplied for the failure criteria of the steel tube 27 grft wasthe proper explosive load and the 30 grft explosive loadexceeded the threshold of expanding tube failure Since thenumerical model verified with ballistic test results allows forvarious design changes the development cost and time can begreatly reduced by minimizing the number of experimentaltests required Therefore it is suggested to add a numericalmodel development step using 3D hydrocode to the overallprocedure of expanding tube development for pyrotechnicseparation systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by the Leading Foreign ResearchInstitute Recruitment Program (2011-0030065) and theBasic Science Research Program (2011-0010489) throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology This studywas also financially supported by the University Collabora-tion Enhancement Project of the Korea Aerospace ResearchInstitute
References
[1] K Y Chang and D L Kern SuperlowastZip (linear separa-tion) shock characteristics 1986 httpntrsnasagovarchivenasacasintrsnasagov19870011172 1987011172pdf
[2] L J Bement and M L Schimmel ldquoA manual for pyrotech-nic design development and qualificationrdquo NASA TechnicalMemerandum 110172 1995
[3] J R Lee CCChia andCWKong ldquoReviewof pyroshockwavemeasurement and simulation for space systemsrdquoMeasurementJournal of the International Measurement Confederation vol 45no 4 pp 631ndash642 2012
[4] K Y Chang ldquoPyrotechnic devices shock levels and theirapplicationsrdquo in Proceedings of the Pyroshock Seminar ICSV92002
[5] NASA ldquoPyroshock test criteriardquo NASA-STD-7003A 2011[6] L H Richards J K Vision and D J Schorr ldquoThrusting
separation systemrdquo US Patent US5372071 1993[7] W C Hoffman III ldquoAge life evaluation of space shuttle crew
escape systempyrotechnic components loadedwith hexanitros-tilbene (HNS) NASArdquo Technical Paper 3650 1996
[8] L J Bement and M L Schimmel ldquoInvestigation of SuperlowastZipseparation jointrdquo NASA Technical Memorandum 4031 1988
[9] MMiyazawa and Y Fukushima ldquoDevelopment status of Japanrsquosnew launch vehicle H-II rocektrdquo in Proceedings of the 40thCongress of the International Astronautical Federation 1989
[10] M Quidot ldquoSome examples of energetic material modelingwith LSDYNArdquo in Proceedings of the 3rd European LS-DYNAConference 2001
[11] G E Fairlie ldquoThenumerical simulation of high explosives usingAUTODYN-2Damp3Drdquo inProceedings of the Institute of ExplosiveEngineers 4th Biannual Symposium (Explo rsquo98) 1998
[12] J K Chen H Ching and F A Allahdadi ldquoShock-induceddetonation of high explosives by high velocity impactrdquo Journalof Mechanics of Materials and Structures vol 2 no 9 pp 1701ndash1721 2007
[13] S M Muramatsu ldquoNumerical and experimental study of apyroshock test set up for small spacecraft componentrdquo ProjectReport UPNA 2010
[14] J Danyluk Spall fracture ofmulti-material plates under explosiveloading [MS thesis] Rensselaser Polytechnic Institute at Hart-ford Hartford Conn USA 2010
[15] RH B Bouma A EDM van derHeijden TD Sewell andDLThompson ldquoChapter2 Simulations of deformation processesin energeticmaterialsrdquo inNumerical Simulations of Physical andEngineering Processes 2011
[16] E L Lee H C Hornig and J W Kury ldquoAdiabatic expansion ofhigh explosive detonation productsrdquo Technical Report UCRL-50422 Lawrence Radiation Laboratory University of CaliforniaLivermore Berkeley Calif USA 1968
[17] M AMeyersDynamic Behavior ofMaterialsWiley NewYorkNY USA 1994
[18] D J Steinberg S G Cochran and M W Guinan ldquoA constitu-tive model for metals applicable at high-strain raterdquo Journal ofApplied Physics vol 51 no 3 pp 1498ndash1504 1980
[19] J N Johnson ldquoDynamic fracture and spallation in ductilesolidsrdquo Journal of Applied Physics vol 52 no 4 pp 2812ndash28251981
[20] ANSYS Workshop 7 Ship Blast ANSYS Training ManualANSYS Cecil Township Pa USA 2010
10 Shock and Vibration
[21] ANSYS Chapter 1 Introduction to AUTODYN AUTODYNTraining Manual ANSYS Cecil Township Pa USA 2010
[22] X Quan N K Birnbaum M S Cowler B I Gerber R AClegg and C J Hayhurst ldquoNumerical simulation of structuraldeformation under shock and impact loads using a coupledmulti-solver approachrdquo in Proceedings of the 5th Asia-PacificConference on Shock and Impact Loads on Structures 2003
[23] Century Dynamics AUTODYN Theory Manual CenturyDynamics Concord Calif USA 2003
[24] J E Shepherd ldquoStructural response of piping to internal gasdetonationrdquo Journal of Pressure Vessel Technology Transactionsof the ASME vol 131 no 3 pp 0312041ndash03120413 2009
[25] J Kanesky J Damazo K Chow-Yee A Rusinek and J EShepherd ldquoPlastic deformation due to reflected detonationrdquoInternational Journal of Solids and Structures vol 50 no 1 pp97ndash110 2013
[26] A J Rosakis and G Ravichandran ldquoDynamic failure mechan-icsrdquo International Journal of Solids and Structures vol 37 no 1-2pp 331ndash348 2000
[27] S Fordham High Explosives and Propellants Pergamon PressElmsford NY USA 2nd edition 1980
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 7
Table 2 Steinberg-Guinan strength parameters
Parameter SS304 AL6061 Unit119866 77 times 10
8297 times 10
7 kPa119884 34 times 10
55 times 10
4 kPa120573 43 28 mdash119899 035 08 mdash119889119866119889119875 174 14119889119866119889119879 minus35 times 10
4minus129 times 10
4 kPaK119889119884119889119875 768 times 10
minus3235 times 10
minus3 mdashMelting temperature 2380 1604 K
145
180
175
170
165
160150 155 160 165 170 175 180 185
Width (mm)
Numerical resultsExperimental results
Hei
ght (
mm
)
15 grft
15 grft20 grft
20 grft
25 grft
25 grft
Figure 14 Comparison between the experimental and calculationalresults
include large deformation of the structure to be solved in asingle numerical analysis
4 Results and Discussion
41 Two-Dimensional Numerical Results Figure 6 shows thetwo-dimensional numerical model of an expanding tubeexplosion The cell width was approximately 016mm Thenumber of elements in the tube model was 1404 and thewhole model had 161504 elements A description of thenumerical model is shown in Table 3
To illustrate the expansion process of the steel tube overtime the deformed configurations of a 15 grft expandingtube are depicted in Figure 7 at 119905 = 0ms 002ms 007msand 01ms The calculation was started at time 119905 = 00msand finished at 119905 = 01ms when it could be assumed thatdetonation had been completed It is clearly seen that the tubeis expanded outward radially from the detonation point At119905 = 002ms early in the detonation the minor axis of thetube started to be expanded and the length of the major axiswas becoming shorter over time At a later time the shape ofthe tube sectionwas deformed from elliptical to circular suchthat the shape change might separate a joint
Table 3 Description of numerical model of 2D expanding tube
Part Materials Number of mesh SolverTube SS304 1404 LagrangianSheath AL6061 100Air Air 160000 EulerianHigh explosive HNS 165
A series of computations was performed by varyingexplosive loads to compute the material response of thetube and the deformations are presented in Figure 8 It isapparent that the tube expansion increases as the explosiveload increases For a pressure tube in the plastic deformationregime catastrophic failure is associated with ductile tearingor plastic instability [19 24 25] Rapidly expanding regions(the minor axis of the tube) are accompanied by rapid lossof stress-carrying capability and intense heating due to thedissipation of plastic work and present risks of rupture [26]As shown in Figure 8 the plastic region and computed stresswere increased proportionally to the explosive load As aresult the 30 grft expanding tube shows the largest plasticregion and the greatest stress is on the minor axis dueto energy absorption However the 30 grft expanding tubeexpanded without spallation in the 2D simulation whichdiffers distinctly from the experimental results becausethis FE analysis accounts for only radial expansion Thissuggests that the tube expansion due to the detonation wavepropagation should be considered to develop a more reliablenumerical model
Figure 9 compares the changes of width and height ofthe tube in the FE analysis and experimental results forthree cases with 15 20 and 25 grft Although the calculationresults slightly overestimated the experimental results of eachcore load the overall error of both width (minor axis) andheight (major axis) prediction was less than 10
42 Three-Dimensional Numerical Results Figure 10 illus-trates a three-dimensional expanding tube and detonationdirection The open-ended steel tube was 300mm long andMDF of a 320mm length of MDF was inserted into thecentral bore Its cross section was the same as in the 2D caseDetonation was assumed to be started from the left end of thetube at 119905 = 00ms identically to the experimental conditionsTo describe the 3D detonation propagation a cylindricalblast wave was generated and then remapped in the airThe pressure profile of the detonation wave propagation intothe tube is presented in Figure 11 and its structure consistsof a shock wave and reaction zone where the explosive ischanged into gaseous products at high temperature Thesereaction products act as a piston that allows the shock waveto propagate at a constant velocity [27] Figure 12 shows thenumerical model of the 3D expanding tube A graded gridwas applied to the air and HNS 165 to save computationtime Table 4 summarizes the description of the 3Dnumericalmodel
Figure 13 displays the expansion behaviors and materialstatus of each expanding tube Similar to the 2D results
8 Shock and Vibration
(150 38 0)Gauge number 1 Gauge number 2 Gauge number 3
(75 38 0) (225 38 0)
Detonation at t = 000120583s
y
x
Figure 15 Gauges position
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft27 grft
30 grft
Figure 16 Pressure histories from gauge number 1
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 17 Pressure histories from gauge number 2
Table 4 Description of 3D expanding tube numerical model
Part Materials Number of mesh SolverTube SS304 64800 LagrangianSheath AL6061 13360Air Air 203125 EulerianHigh explosive HNS 165
the tubes with explosive loads of 15ndash25 grft freely expandedbut the 30 grft tube failed due to plastic deformation Asshown in Figure 13 there was spallation at 130mm from theside of the 30 grft expanding tube at around 119905 = 007msThis ductile fracture was caused by the significant amount
0 001 002 003 004 005 006 007 008 009 01
Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 18 Pressure histories from gauge number 3
of plastic deformation during tube expansion This failurebehavior in FE analysis was somewhat different from theexperimental failure behavior In experiments two failuresoccurred on the left and right sides of the steel tube whileone bulk failure was found in the numerical simulationEven if the first spallation could be predicted it might beinappropriate to simulate a successive multiple-spallationgeneration mechanism
Figure 14 compares between the numerical simulationand experimental results of each expanding tube deforma-tion The overall error was less than 3 and the agreementwas improved by considering the tube expansion due todetonation wave propagation
To compute a proper core load the internal pressureof the expanding wall of the steel tube was numericallycalculated for explosive loads of 15 20 25 27 and 30 grftThethree points indicated in Figure 15 represent the placementof a gauge for measuring the internal pressure Figures 1617 and 18 plot the time histories of pressure observed bygauges in the middle of the steel tube thickness over timeThe first peak was due to the initial shock wave travelingthrough the tube The rarefaction wave generated due tofree surface interaction is often shown as negative pressurefollowing the first peak and it produces tensile stress onthe tube The maximum pressure of the respective gaugesranged from minus130 to minus520MPa for the various explosiveloads The pressure histories of expanding tubes with loadsof 15ndash25 grft fluctuated and became stable over time Inthe FE analysis the 27 grft expanding tube was able toexpand freely without failure and its maximum pressure was
Shock and Vibration 9
125 times higher than that of the 25 grft expanding tubewhich was found to have a proper explosive load in theballistic test using expanding tube samplesTherefore we canconclude that the proper explosive load in the experimentswas underestimated according to the numerical results Foran explosive load of 30 grft the internal pressure increaseddramatically and reached a value ofminus520MPaThemaximumpressure on the steel tube with the 30 grft load was about 27and 2 times higher than those with the 25 grft and 27 grftloads respectively This means that since the explosive loadof 30 grft was greater than the failure threshold spallationoccurred in the actual expanding tube
5 Conclusions
The development of a numerical model has been presentedfor the free expansion of expanding tubes byMDFdetonationin pyro-separation systems using AUTODYN 2D and 3Dhydrocode Numerical simulations were performed for fourexpanding tube explosive load cases as a verification set forthe numerical model and additional simulation was done tosuggest a more effective explosive load
In the 2D model since the detonation wave propagationcould not be considered the results slightly overestimatedthe shape of the expanded tube To improve the accuracyof the results the 3D model was developed which allowedfor tube expansion due to detonation wave propagationThe developed model was verified with explosive test resultsand showed less than 3 overall error From the results of3D numerical simulation where the Steinberg model wasapplied for the failure criteria of the steel tube 27 grft wasthe proper explosive load and the 30 grft explosive loadexceeded the threshold of expanding tube failure Since thenumerical model verified with ballistic test results allows forvarious design changes the development cost and time can begreatly reduced by minimizing the number of experimentaltests required Therefore it is suggested to add a numericalmodel development step using 3D hydrocode to the overallprocedure of expanding tube development for pyrotechnicseparation systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by the Leading Foreign ResearchInstitute Recruitment Program (2011-0030065) and theBasic Science Research Program (2011-0010489) throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology This studywas also financially supported by the University Collabora-tion Enhancement Project of the Korea Aerospace ResearchInstitute
References
[1] K Y Chang and D L Kern SuperlowastZip (linear separa-tion) shock characteristics 1986 httpntrsnasagovarchivenasacasintrsnasagov19870011172 1987011172pdf
[2] L J Bement and M L Schimmel ldquoA manual for pyrotech-nic design development and qualificationrdquo NASA TechnicalMemerandum 110172 1995
[3] J R Lee CCChia andCWKong ldquoReviewof pyroshockwavemeasurement and simulation for space systemsrdquoMeasurementJournal of the International Measurement Confederation vol 45no 4 pp 631ndash642 2012
[4] K Y Chang ldquoPyrotechnic devices shock levels and theirapplicationsrdquo in Proceedings of the Pyroshock Seminar ICSV92002
[5] NASA ldquoPyroshock test criteriardquo NASA-STD-7003A 2011[6] L H Richards J K Vision and D J Schorr ldquoThrusting
separation systemrdquo US Patent US5372071 1993[7] W C Hoffman III ldquoAge life evaluation of space shuttle crew
escape systempyrotechnic components loadedwith hexanitros-tilbene (HNS) NASArdquo Technical Paper 3650 1996
[8] L J Bement and M L Schimmel ldquoInvestigation of SuperlowastZipseparation jointrdquo NASA Technical Memorandum 4031 1988
[9] MMiyazawa and Y Fukushima ldquoDevelopment status of Japanrsquosnew launch vehicle H-II rocektrdquo in Proceedings of the 40thCongress of the International Astronautical Federation 1989
[10] M Quidot ldquoSome examples of energetic material modelingwith LSDYNArdquo in Proceedings of the 3rd European LS-DYNAConference 2001
[11] G E Fairlie ldquoThenumerical simulation of high explosives usingAUTODYN-2Damp3Drdquo inProceedings of the Institute of ExplosiveEngineers 4th Biannual Symposium (Explo rsquo98) 1998
[12] J K Chen H Ching and F A Allahdadi ldquoShock-induceddetonation of high explosives by high velocity impactrdquo Journalof Mechanics of Materials and Structures vol 2 no 9 pp 1701ndash1721 2007
[13] S M Muramatsu ldquoNumerical and experimental study of apyroshock test set up for small spacecraft componentrdquo ProjectReport UPNA 2010
[14] J Danyluk Spall fracture ofmulti-material plates under explosiveloading [MS thesis] Rensselaser Polytechnic Institute at Hart-ford Hartford Conn USA 2010
[15] RH B Bouma A EDM van derHeijden TD Sewell andDLThompson ldquoChapter2 Simulations of deformation processesin energeticmaterialsrdquo inNumerical Simulations of Physical andEngineering Processes 2011
[16] E L Lee H C Hornig and J W Kury ldquoAdiabatic expansion ofhigh explosive detonation productsrdquo Technical Report UCRL-50422 Lawrence Radiation Laboratory University of CaliforniaLivermore Berkeley Calif USA 1968
[17] M AMeyersDynamic Behavior ofMaterialsWiley NewYorkNY USA 1994
[18] D J Steinberg S G Cochran and M W Guinan ldquoA constitu-tive model for metals applicable at high-strain raterdquo Journal ofApplied Physics vol 51 no 3 pp 1498ndash1504 1980
[19] J N Johnson ldquoDynamic fracture and spallation in ductilesolidsrdquo Journal of Applied Physics vol 52 no 4 pp 2812ndash28251981
[20] ANSYS Workshop 7 Ship Blast ANSYS Training ManualANSYS Cecil Township Pa USA 2010
10 Shock and Vibration
[21] ANSYS Chapter 1 Introduction to AUTODYN AUTODYNTraining Manual ANSYS Cecil Township Pa USA 2010
[22] X Quan N K Birnbaum M S Cowler B I Gerber R AClegg and C J Hayhurst ldquoNumerical simulation of structuraldeformation under shock and impact loads using a coupledmulti-solver approachrdquo in Proceedings of the 5th Asia-PacificConference on Shock and Impact Loads on Structures 2003
[23] Century Dynamics AUTODYN Theory Manual CenturyDynamics Concord Calif USA 2003
[24] J E Shepherd ldquoStructural response of piping to internal gasdetonationrdquo Journal of Pressure Vessel Technology Transactionsof the ASME vol 131 no 3 pp 0312041ndash03120413 2009
[25] J Kanesky J Damazo K Chow-Yee A Rusinek and J EShepherd ldquoPlastic deformation due to reflected detonationrdquoInternational Journal of Solids and Structures vol 50 no 1 pp97ndash110 2013
[26] A J Rosakis and G Ravichandran ldquoDynamic failure mechan-icsrdquo International Journal of Solids and Structures vol 37 no 1-2pp 331ndash348 2000
[27] S Fordham High Explosives and Propellants Pergamon PressElmsford NY USA 2nd edition 1980
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 Shock and Vibration
(150 38 0)Gauge number 1 Gauge number 2 Gauge number 3
(75 38 0) (225 38 0)
Detonation at t = 000120583s
y
x
Figure 15 Gauges position
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft27 grft
30 grft
Figure 16 Pressure histories from gauge number 1
0 001 002 003 004 005 006 007 008 009 01Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 17 Pressure histories from gauge number 2
Table 4 Description of 3D expanding tube numerical model
Part Materials Number of mesh SolverTube SS304 64800 LagrangianSheath AL6061 13360Air Air 203125 EulerianHigh explosive HNS 165
the tubes with explosive loads of 15ndash25 grft freely expandedbut the 30 grft tube failed due to plastic deformation Asshown in Figure 13 there was spallation at 130mm from theside of the 30 grft expanding tube at around 119905 = 007msThis ductile fracture was caused by the significant amount
0 001 002 003 004 005 006 007 008 009 01
Time (s)
Pres
sure
(kPa
)
minus6
minus5
minus4
minus3
minus2
minus1
0
1
2
3times105
15 grft
20 grft
25 grft
27 grft30 grft
Figure 18 Pressure histories from gauge number 3
of plastic deformation during tube expansion This failurebehavior in FE analysis was somewhat different from theexperimental failure behavior In experiments two failuresoccurred on the left and right sides of the steel tube whileone bulk failure was found in the numerical simulationEven if the first spallation could be predicted it might beinappropriate to simulate a successive multiple-spallationgeneration mechanism
Figure 14 compares between the numerical simulationand experimental results of each expanding tube deforma-tion The overall error was less than 3 and the agreementwas improved by considering the tube expansion due todetonation wave propagation
To compute a proper core load the internal pressureof the expanding wall of the steel tube was numericallycalculated for explosive loads of 15 20 25 27 and 30 grftThethree points indicated in Figure 15 represent the placementof a gauge for measuring the internal pressure Figures 1617 and 18 plot the time histories of pressure observed bygauges in the middle of the steel tube thickness over timeThe first peak was due to the initial shock wave travelingthrough the tube The rarefaction wave generated due tofree surface interaction is often shown as negative pressurefollowing the first peak and it produces tensile stress onthe tube The maximum pressure of the respective gaugesranged from minus130 to minus520MPa for the various explosiveloads The pressure histories of expanding tubes with loadsof 15ndash25 grft fluctuated and became stable over time Inthe FE analysis the 27 grft expanding tube was able toexpand freely without failure and its maximum pressure was
Shock and Vibration 9
125 times higher than that of the 25 grft expanding tubewhich was found to have a proper explosive load in theballistic test using expanding tube samplesTherefore we canconclude that the proper explosive load in the experimentswas underestimated according to the numerical results Foran explosive load of 30 grft the internal pressure increaseddramatically and reached a value ofminus520MPaThemaximumpressure on the steel tube with the 30 grft load was about 27and 2 times higher than those with the 25 grft and 27 grftloads respectively This means that since the explosive loadof 30 grft was greater than the failure threshold spallationoccurred in the actual expanding tube
5 Conclusions
The development of a numerical model has been presentedfor the free expansion of expanding tubes byMDFdetonationin pyro-separation systems using AUTODYN 2D and 3Dhydrocode Numerical simulations were performed for fourexpanding tube explosive load cases as a verification set forthe numerical model and additional simulation was done tosuggest a more effective explosive load
In the 2D model since the detonation wave propagationcould not be considered the results slightly overestimatedthe shape of the expanded tube To improve the accuracyof the results the 3D model was developed which allowedfor tube expansion due to detonation wave propagationThe developed model was verified with explosive test resultsand showed less than 3 overall error From the results of3D numerical simulation where the Steinberg model wasapplied for the failure criteria of the steel tube 27 grft wasthe proper explosive load and the 30 grft explosive loadexceeded the threshold of expanding tube failure Since thenumerical model verified with ballistic test results allows forvarious design changes the development cost and time can begreatly reduced by minimizing the number of experimentaltests required Therefore it is suggested to add a numericalmodel development step using 3D hydrocode to the overallprocedure of expanding tube development for pyrotechnicseparation systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by the Leading Foreign ResearchInstitute Recruitment Program (2011-0030065) and theBasic Science Research Program (2011-0010489) throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology This studywas also financially supported by the University Collabora-tion Enhancement Project of the Korea Aerospace ResearchInstitute
References
[1] K Y Chang and D L Kern SuperlowastZip (linear separa-tion) shock characteristics 1986 httpntrsnasagovarchivenasacasintrsnasagov19870011172 1987011172pdf
[2] L J Bement and M L Schimmel ldquoA manual for pyrotech-nic design development and qualificationrdquo NASA TechnicalMemerandum 110172 1995
[3] J R Lee CCChia andCWKong ldquoReviewof pyroshockwavemeasurement and simulation for space systemsrdquoMeasurementJournal of the International Measurement Confederation vol 45no 4 pp 631ndash642 2012
[4] K Y Chang ldquoPyrotechnic devices shock levels and theirapplicationsrdquo in Proceedings of the Pyroshock Seminar ICSV92002
[5] NASA ldquoPyroshock test criteriardquo NASA-STD-7003A 2011[6] L H Richards J K Vision and D J Schorr ldquoThrusting
separation systemrdquo US Patent US5372071 1993[7] W C Hoffman III ldquoAge life evaluation of space shuttle crew
escape systempyrotechnic components loadedwith hexanitros-tilbene (HNS) NASArdquo Technical Paper 3650 1996
[8] L J Bement and M L Schimmel ldquoInvestigation of SuperlowastZipseparation jointrdquo NASA Technical Memorandum 4031 1988
[9] MMiyazawa and Y Fukushima ldquoDevelopment status of Japanrsquosnew launch vehicle H-II rocektrdquo in Proceedings of the 40thCongress of the International Astronautical Federation 1989
[10] M Quidot ldquoSome examples of energetic material modelingwith LSDYNArdquo in Proceedings of the 3rd European LS-DYNAConference 2001
[11] G E Fairlie ldquoThenumerical simulation of high explosives usingAUTODYN-2Damp3Drdquo inProceedings of the Institute of ExplosiveEngineers 4th Biannual Symposium (Explo rsquo98) 1998
[12] J K Chen H Ching and F A Allahdadi ldquoShock-induceddetonation of high explosives by high velocity impactrdquo Journalof Mechanics of Materials and Structures vol 2 no 9 pp 1701ndash1721 2007
[13] S M Muramatsu ldquoNumerical and experimental study of apyroshock test set up for small spacecraft componentrdquo ProjectReport UPNA 2010
[14] J Danyluk Spall fracture ofmulti-material plates under explosiveloading [MS thesis] Rensselaser Polytechnic Institute at Hart-ford Hartford Conn USA 2010
[15] RH B Bouma A EDM van derHeijden TD Sewell andDLThompson ldquoChapter2 Simulations of deformation processesin energeticmaterialsrdquo inNumerical Simulations of Physical andEngineering Processes 2011
[16] E L Lee H C Hornig and J W Kury ldquoAdiabatic expansion ofhigh explosive detonation productsrdquo Technical Report UCRL-50422 Lawrence Radiation Laboratory University of CaliforniaLivermore Berkeley Calif USA 1968
[17] M AMeyersDynamic Behavior ofMaterialsWiley NewYorkNY USA 1994
[18] D J Steinberg S G Cochran and M W Guinan ldquoA constitu-tive model for metals applicable at high-strain raterdquo Journal ofApplied Physics vol 51 no 3 pp 1498ndash1504 1980
[19] J N Johnson ldquoDynamic fracture and spallation in ductilesolidsrdquo Journal of Applied Physics vol 52 no 4 pp 2812ndash28251981
[20] ANSYS Workshop 7 Ship Blast ANSYS Training ManualANSYS Cecil Township Pa USA 2010
10 Shock and Vibration
[21] ANSYS Chapter 1 Introduction to AUTODYN AUTODYNTraining Manual ANSYS Cecil Township Pa USA 2010
[22] X Quan N K Birnbaum M S Cowler B I Gerber R AClegg and C J Hayhurst ldquoNumerical simulation of structuraldeformation under shock and impact loads using a coupledmulti-solver approachrdquo in Proceedings of the 5th Asia-PacificConference on Shock and Impact Loads on Structures 2003
[23] Century Dynamics AUTODYN Theory Manual CenturyDynamics Concord Calif USA 2003
[24] J E Shepherd ldquoStructural response of piping to internal gasdetonationrdquo Journal of Pressure Vessel Technology Transactionsof the ASME vol 131 no 3 pp 0312041ndash03120413 2009
[25] J Kanesky J Damazo K Chow-Yee A Rusinek and J EShepherd ldquoPlastic deformation due to reflected detonationrdquoInternational Journal of Solids and Structures vol 50 no 1 pp97ndash110 2013
[26] A J Rosakis and G Ravichandran ldquoDynamic failure mechan-icsrdquo International Journal of Solids and Structures vol 37 no 1-2pp 331ndash348 2000
[27] S Fordham High Explosives and Propellants Pergamon PressElmsford NY USA 2nd edition 1980
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 9
125 times higher than that of the 25 grft expanding tubewhich was found to have a proper explosive load in theballistic test using expanding tube samplesTherefore we canconclude that the proper explosive load in the experimentswas underestimated according to the numerical results Foran explosive load of 30 grft the internal pressure increaseddramatically and reached a value ofminus520MPaThemaximumpressure on the steel tube with the 30 grft load was about 27and 2 times higher than those with the 25 grft and 27 grftloads respectively This means that since the explosive loadof 30 grft was greater than the failure threshold spallationoccurred in the actual expanding tube
5 Conclusions
The development of a numerical model has been presentedfor the free expansion of expanding tubes byMDFdetonationin pyro-separation systems using AUTODYN 2D and 3Dhydrocode Numerical simulations were performed for fourexpanding tube explosive load cases as a verification set forthe numerical model and additional simulation was done tosuggest a more effective explosive load
In the 2D model since the detonation wave propagationcould not be considered the results slightly overestimatedthe shape of the expanded tube To improve the accuracyof the results the 3D model was developed which allowedfor tube expansion due to detonation wave propagationThe developed model was verified with explosive test resultsand showed less than 3 overall error From the results of3D numerical simulation where the Steinberg model wasapplied for the failure criteria of the steel tube 27 grft wasthe proper explosive load and the 30 grft explosive loadexceeded the threshold of expanding tube failure Since thenumerical model verified with ballistic test results allows forvarious design changes the development cost and time can begreatly reduced by minimizing the number of experimentaltests required Therefore it is suggested to add a numericalmodel development step using 3D hydrocode to the overallprocedure of expanding tube development for pyrotechnicseparation systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by the Leading Foreign ResearchInstitute Recruitment Program (2011-0030065) and theBasic Science Research Program (2011-0010489) throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology This studywas also financially supported by the University Collabora-tion Enhancement Project of the Korea Aerospace ResearchInstitute
References
[1] K Y Chang and D L Kern SuperlowastZip (linear separa-tion) shock characteristics 1986 httpntrsnasagovarchivenasacasintrsnasagov19870011172 1987011172pdf
[2] L J Bement and M L Schimmel ldquoA manual for pyrotech-nic design development and qualificationrdquo NASA TechnicalMemerandum 110172 1995
[3] J R Lee CCChia andCWKong ldquoReviewof pyroshockwavemeasurement and simulation for space systemsrdquoMeasurementJournal of the International Measurement Confederation vol 45no 4 pp 631ndash642 2012
[4] K Y Chang ldquoPyrotechnic devices shock levels and theirapplicationsrdquo in Proceedings of the Pyroshock Seminar ICSV92002
[5] NASA ldquoPyroshock test criteriardquo NASA-STD-7003A 2011[6] L H Richards J K Vision and D J Schorr ldquoThrusting
separation systemrdquo US Patent US5372071 1993[7] W C Hoffman III ldquoAge life evaluation of space shuttle crew
escape systempyrotechnic components loadedwith hexanitros-tilbene (HNS) NASArdquo Technical Paper 3650 1996
[8] L J Bement and M L Schimmel ldquoInvestigation of SuperlowastZipseparation jointrdquo NASA Technical Memorandum 4031 1988
[9] MMiyazawa and Y Fukushima ldquoDevelopment status of Japanrsquosnew launch vehicle H-II rocektrdquo in Proceedings of the 40thCongress of the International Astronautical Federation 1989
[10] M Quidot ldquoSome examples of energetic material modelingwith LSDYNArdquo in Proceedings of the 3rd European LS-DYNAConference 2001
[11] G E Fairlie ldquoThenumerical simulation of high explosives usingAUTODYN-2Damp3Drdquo inProceedings of the Institute of ExplosiveEngineers 4th Biannual Symposium (Explo rsquo98) 1998
[12] J K Chen H Ching and F A Allahdadi ldquoShock-induceddetonation of high explosives by high velocity impactrdquo Journalof Mechanics of Materials and Structures vol 2 no 9 pp 1701ndash1721 2007
[13] S M Muramatsu ldquoNumerical and experimental study of apyroshock test set up for small spacecraft componentrdquo ProjectReport UPNA 2010
[14] J Danyluk Spall fracture ofmulti-material plates under explosiveloading [MS thesis] Rensselaser Polytechnic Institute at Hart-ford Hartford Conn USA 2010
[15] RH B Bouma A EDM van derHeijden TD Sewell andDLThompson ldquoChapter2 Simulations of deformation processesin energeticmaterialsrdquo inNumerical Simulations of Physical andEngineering Processes 2011
[16] E L Lee H C Hornig and J W Kury ldquoAdiabatic expansion ofhigh explosive detonation productsrdquo Technical Report UCRL-50422 Lawrence Radiation Laboratory University of CaliforniaLivermore Berkeley Calif USA 1968
[17] M AMeyersDynamic Behavior ofMaterialsWiley NewYorkNY USA 1994
[18] D J Steinberg S G Cochran and M W Guinan ldquoA constitu-tive model for metals applicable at high-strain raterdquo Journal ofApplied Physics vol 51 no 3 pp 1498ndash1504 1980
[19] J N Johnson ldquoDynamic fracture and spallation in ductilesolidsrdquo Journal of Applied Physics vol 52 no 4 pp 2812ndash28251981
[20] ANSYS Workshop 7 Ship Blast ANSYS Training ManualANSYS Cecil Township Pa USA 2010
10 Shock and Vibration
[21] ANSYS Chapter 1 Introduction to AUTODYN AUTODYNTraining Manual ANSYS Cecil Township Pa USA 2010
[22] X Quan N K Birnbaum M S Cowler B I Gerber R AClegg and C J Hayhurst ldquoNumerical simulation of structuraldeformation under shock and impact loads using a coupledmulti-solver approachrdquo in Proceedings of the 5th Asia-PacificConference on Shock and Impact Loads on Structures 2003
[23] Century Dynamics AUTODYN Theory Manual CenturyDynamics Concord Calif USA 2003
[24] J E Shepherd ldquoStructural response of piping to internal gasdetonationrdquo Journal of Pressure Vessel Technology Transactionsof the ASME vol 131 no 3 pp 0312041ndash03120413 2009
[25] J Kanesky J Damazo K Chow-Yee A Rusinek and J EShepherd ldquoPlastic deformation due to reflected detonationrdquoInternational Journal of Solids and Structures vol 50 no 1 pp97ndash110 2013
[26] A J Rosakis and G Ravichandran ldquoDynamic failure mechan-icsrdquo International Journal of Solids and Structures vol 37 no 1-2pp 331ndash348 2000
[27] S Fordham High Explosives and Propellants Pergamon PressElmsford NY USA 2nd edition 1980
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 Shock and Vibration
[21] ANSYS Chapter 1 Introduction to AUTODYN AUTODYNTraining Manual ANSYS Cecil Township Pa USA 2010
[22] X Quan N K Birnbaum M S Cowler B I Gerber R AClegg and C J Hayhurst ldquoNumerical simulation of structuraldeformation under shock and impact loads using a coupledmulti-solver approachrdquo in Proceedings of the 5th Asia-PacificConference on Shock and Impact Loads on Structures 2003
[23] Century Dynamics AUTODYN Theory Manual CenturyDynamics Concord Calif USA 2003
[24] J E Shepherd ldquoStructural response of piping to internal gasdetonationrdquo Journal of Pressure Vessel Technology Transactionsof the ASME vol 131 no 3 pp 0312041ndash03120413 2009
[25] J Kanesky J Damazo K Chow-Yee A Rusinek and J EShepherd ldquoPlastic deformation due to reflected detonationrdquoInternational Journal of Solids and Structures vol 50 no 1 pp97ndash110 2013
[26] A J Rosakis and G Ravichandran ldquoDynamic failure mechan-icsrdquo International Journal of Solids and Structures vol 37 no 1-2pp 331ndash348 2000
[27] S Fordham High Explosives and Propellants Pergamon PressElmsford NY USA 2nd edition 1980
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of