Research Article Study of Hypervelocity Projectile Impact ... · Research Article Study of Hypervelocity Projectile Impact on Thick Metal Plates ShawoonK.Roy, 1 MohamedTrabia, 1 BrendanO

Research ArticleStudy of Hypervelocity Projectile Impact on Thick Metal Plates

Shawoon K Roy1 Mohamed Trabia1 Brendan OrsquoToole1 Robert Hixson2

Steven Becker2 Michael Pena2 Richard Jennings1 Deepak Somasoundaram1

Melissa Matthes1 Edward Daykin2 and Eric Machorro2

1Department of Mechanical Engineering University of Nevada Las Vegas NV 89154 USA2National Security Technologies LLC Las Vegas NV 89030 USA

Correspondence should be addressed to Mohamed Trabia mohamedtrabiaunlvedu

Received 9 April 2015 Accepted 27 September 2015

Academic Editor Marcello Vanali

Copyright copy 2016 Shawoon K Roy et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Hypervelocity impacts generate extreme pressure and shock waves in impacted targets that undergo severe localized deformationwithin a few microseconds These impact experiments pose unique challenges in terms of obtaining accurate measurementsSimilarly simulating these experiments is not straightforward This study proposed an approach to experimentally measure thevelocity of the back surface of an A36 steel plate impacted by a projectile All experiments used a combination of a two-stagelight-gas gun and the photonic Doppler velocimetry (PDV) technique The experimental data were used to benchmark and verifycomputational studies Two different finite-element methods were used to simulate the experiments Lagrangian-based smoothparticle hydrodynamics (SPH) and Eulerian-based hydrocode Both codes used the Johnson-Cook material model and the Mie-Gruneisen equation of state Experiments and simulations were compared based on the physical damage area and the back surfacevelocity The results of this study showed that the proposed simulation approaches could be used to reduce the need for expensiveexperiments

1 Introduction

Hypervelocity impact events are ubiquitous in many areasincluding micrometeoroid collision with spacecraft projec-tile impacts and when modeling effects of explosives onstructures Consequently researchers have been studyingvarious aspects of this problem for several decades A com-mon technique to study hypervelocity impact in laboratorysettings is the two-stage light-gas gun [1 2] which canaccelerate a projectile to generate shock waves in a targetsimilar to those created by detonating high explosives ormeteorite collisions [3] Swift [4] discussed the historicaldevelopment of this type of gun

Under hypervelocity impact conditions thin metallicplates tend to stretch and bend around the impact areaabsorbing a significant part of the projectilersquos kinetic energybefore perforation occurs On the other hand thick platesexperience several failure modes during impact such as

spalling petalling discing and plugging [5] These failuremodes depend upon several factors such as the impactvelocity the properties of the platematerial and the geometryof the projectile Spalling which is of a particular interestin this study occurs when a triangular-shaped stress wave isreflected from the back of the target plate thereby creating atensile pressure that is greater than the material strength [6]which then results in an internal crack that progresses normalto the direction of the wave

Goldsmith et al [7] studied and developed analyticalmodels for the elastic-plastic plate deformation of aluminumplates impacted by a hard-steel cylindrical-nose projectileFailure modes for rod penetration experiments under hyper-velocity impact conditions have been studied only by arelatively small number of researchers [8] Christman andGehrig [9] studied the penetration mechanics and crateringprocesses in metallic and nonmetallic targets at impactvelocities from 03 to 67 kms Sorensen et al [10] studied

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 4313480 11 pageshttpdxdoiorg10115520164313480

2 Shock and Vibration

penetration mechanics of semi-infinite rolled homogeneousarmor (RHA) steel by monolithic projectiles and segmentedpenetrators at velocities ranging from 25 to 40 kms Sub-sequent studies on spall fracture and dynamic response ofmaterials were reviewed by Oscarson and Graff [6] Shockeyet al [11] reported that different projectile materials causedifferent types of physical damage to steel plates under hyper-velocity impact In addition they reported microstructuralchanges and the pressure induced 120572 999448999471 120576 polymorphictransition of the steel plates during impact The penetrationbehavior of long rod tungsten-alloy projectiles in high-hard armor steel plates was studied by Anderson et al[12] at two impact velocities 125 kms and 170 kms Bond[13] suggested that spallation damage and phase-transitionkinetics were important in damage studies ofmartensitic steelarmor when subjected to hypervelocity impact

Merzhievskii and Titov [14] evaluated the perforation anddeformation of thin steel plates at velocities from 3 to 9 kmsthey developed an analytical method to relate debris particlesto the impact velocity The ballistic limits of aluminum platesof various thicknesses were studied by Boslashrvik et al [15] usinga compressed-air gas gun An analyticalmodel was developedbased on those limits Analytical models were developed topredict the cratering depth of penetration and perforationof semi-infinite target plates by long rod penetrators by Wenet al [16ndash18]

Recent work on impact dynamics and shock physicsof materials has emphasized the use of velocimetry datain flyer plate experiments to characterize the equation ofstate spall strength polymorphic phase transition and theHugoniot elastic limit of materials Velocimetry data canprovide a clear representation of the response of materialsunder high pressure and high strain rates which may leadto developing accurate predictive computational models formaterials The following is a brief overview of velocimetrydiagnostic techniques Barker and Hollenbach developed thehomodyne interferometry technique Velocity Interferom-eter System for Any Reflector (VISAR) system [19] Thistechnique became widely popular within the shock physicscommunity Numerous impact and shock studies have usedVISAR as the primary diagnostic tool [20ndash28] Howevercomplexity cost and various issues that cannot be easilyresolved such as obtaining velocities frommultiple points ona moving surface prompted the development of an alterna-tive diagnostic tool known as photonic Doppler velocimetry(PDV) a displacement interferometer that collects velocitydata based on measuring displacement using optical fiberprobes [29] Advantages of PDV include its relative simplicityrobustness cost accuracy and versatility [30] Chau et al[31] used PDV for shock Hugoniot measurements of a single-crystal copper plate during impact experiments

Accurate predictive modeling of impact events underhypervelocity conditions can provide a less expensive alter-native to conducting actual experiments However thesenumerical simulations require the identification of a largenumber of parameters that are needed to describe thenonlinearities of the problem In many cases hypervelocityimpact simulation models are based on many simplificationsthat affect the accuracy of these simulations One feature

of hypervelocity impacts is that solid materials behavesomewhat like fluids after the initial elastic-plastic transi-tion Therefore it is appropriate to model plate penetrationusing hydrodynamic techniques having a separately definedstrength model Recently a considerable effort has gone intodeveloping models that deal with perforation and penetra-tion problems For example it was shown that an accuratecomputational model of impact depends on the selection ofthe proper physics models and input parameters [32] Severalconstitutivemodels were developed over the years to simulatehypervelocity impact events Johnson and Cook [33] devel-oped a constitutive model for materials subjected to largestrains high strain rates and high temperatures Two otherflow stress models were developed for plastic deformationof ductile materials Zerilli-Armstrong [34] and Steinberg-Cochran-Guinan-Lund model [35] A comparative study ofall these models was performed by Banerjee [36] Besideall of these constitutive relations equation of state (EOS)models were developed to understand the dynamic behaviorof materials under shock loading and were often used inthis type of simulations Boslashrvik et al simulated perforationphenomena in LS-DYNA [37] using a constitutive materialmodel [38 39] that combined viscosity and ductile damageAdditionally plate perforation with various nose shapesfor projectiles was simulated [40ndash42] using the viscoplasticrelationship described in [39] Eftis and Nemes simulatedductile spall fracture andpostspall behavior of a circular plateusing the PRONTO finite element code where a viscoplasticconstitutive relationship was implemented that included themicrovoid volume fraction as a scalar material damagevariable [43] Recently several computational packages basedon hydrocode methods that simulate events are associatedwith extreme high-pressure dynamics [44] This techniquehas been used for penetration modeling of different steelplates such as Eulerian-based CTH hydrocode [12 45ndash47]All these works [45ndash47] listed Mie-Gruneisen EOS in theirsimulation work

Another simulation approach is to use the Lagrangian-based method of smooth particle hydrodynamics (SPH)technique [48] a meshless Lagrangian numerical methodthat can address the problems associated with the large geo-metric distortions where typical grid-based mesh techniqueshave difficulties The SPH technique has recently gainedpopularity in simulating impact-penetration problems [49ndash53] Johnson-Cook model was used as the primary strengthmodel in [49] and Mie-Gruneisen EOS was listed in [51]

Although numerous studies describe the perforation andpenetrationmechanics of plates during hypervelocity impactonly a few discussed the plastic deformation of plates that donot experience complete penetration under such conditions[13]

This study presents velocimetry data captured by a PDVsystem in experiments using a two-stage light-gas gun tounderstand the plastic-deformation behavior of A36 steelplates that have not had full penetration Two computationalapproaches were developed to simulate the experimentsResultswere comparedwith each other and to the experimen-tal data

Shock and Vibration 3

2 Materials and Methods

21 Materials All gas gun experiments in this study usedLexan projectiles cylinders 56mm in diameter and 86mmin length Depending on the fill pressure of the gas usedthe projectile velocity varied from about 45 to 6 kms Thedimensions of the ASTM A36 steel target plates were 1524 times1524 times 127mm The thickness of the target plates waschosen to prevent their complete penetration due to projectileimpacts at these velocities Youngrsquos modulus (119864) for thisLexan andA36 steel used in all experiments was 254GPa and200GPa respectively

22 Methods A two-stage light-gas gun Figure 1 was usedto perform the hypervelocity impact experiments The maincomponents of the gas gun are the powder breech pump tubecentral breech launch tube blast tank and target chamber

The experiments were conducted according to the follow-ing steps A cartridge filled with gunpowder was fired usinga solenoid pin The resulting explosion propelled a pistonin the pump tube filled with pressurized helium gas As thepiston moved it increased the pressure of the helium whicheventually breaks a petal valve The gas then accelerated theprojectile which was placed immediately behind the petalvalve in the launch tube through the blast tank and thedrift tube until it would impact the target within the targetchamber

The target plates were bolted using four 127mm (1210158401015840)SAE Grade 5 bolts onto a mounting plate that was attached tothe walls of the target chamber Figure 2

The velocity of the projectile was measured by a laserintervalometer system having two stations separated by afixed distance Each station had a laser source that directed abeam through a port to a narrow band-pass filter to ensurethat a 32-photodiode array was free of any contaminationby external light Measuring the time interval was initiatedby the flight of the projectile across the first station andterminated when it passed through the second station Thetime interval was recorded using a digitizer

Free surface velocity from the target was measured usinga PDV system The basic working principle of a singlechannel PDV system is described in Figure 3 [29] howevera brief overview is presented A laser light is fed into anoptical fiber probe The reference source light (typically ata wavelength 120582 of 1550 nm) is reflected from the measuredmoving surfaceThe resultingDoppler shifted light is sent to adetector to produce fringes each of which corresponds to thedisplacement of the surface by a wavelength difference of 1205822between reflected and reference lights These displacement-time signals are recorded by a high-speed digitizer The PDVwas completely enclosed

In all gas gun experiments the PDV optical fiber probewas placed in a holder and aimed at the center of the backsurface of the target plate Figure 4 The target surface waspolished by using different-grit sand papers and ball rollerbeforehand to reflect light at certain intensity The PDVsystem was triggered few microseconds after the projectilepassed through the second station of the intervalometerThisdelay was based on the projectile velocity and the distance to

Powder breech

Pump tube

Central breech

Launch tube

Blast tank

Drift tube

Target chamber

Figure 1 Two-stage light-gas gun

Figure 2 Target plate bolted inside the gas gun chamber

the target plate was used to initiate the PDV data collectionOnce a digitizer recorded the data a fast Fourier transformwas performed to obtain the measured point velocity basedon the recorded displacement data

Figure 4 shows the layout of the experiment After testingphysical measurements of the impact crater and the resultingback surface bulge were recorded The target plates weresectioned to check for spall damage

3 Experimental Results

In all gas gun experiments the Lexan projectiles disintegratedcompletely A small crater was created as a result of theimpact with a bulge on the back side of the target plate Craterdetails and bulge dimensions are listed in Table 1 In all gasgun experiments the impact location varied within 3mm ofthe geometric center of the plate A typical sectioned targetplate showed that spall had occurred inside the material

4 Shock and Vibration

Table 1 Physical dimensions of the crater and bulge after impact

Test IDImpactvelocity(ms)

Craterdiameter(mm)

Penetration(mm)

Bulge(mm)

1000-016 5338 170 63 231000-017 5063 169 58 23

Laser

Detector

Digitizer

Optical fiber probe

Doppler shifted light

Laser light

Mov

ing

surfa

ce

Lase

r lig

ht

Figure 3 Basic principle of a single channel PDV system (based on[29])

Figure 5 Table 2 summarizes the spall cracking in the twoexperiments

Figure 6 shows typical velocimetry data from a singlechannel PDVTheduration of the projectile-target interactiontypically lasted for 25120583s The first 5 120583s displayed the mostcharacteristic features of the hypervelocity impact namelyelastic precursor wave HEL plastic wave propagation spallsignature and elastic loading and unloading A brief discus-sion of these features follows

When material is loaded in extreme pressure the shock-wave creates an elastic response up to certain limit Thislimit is usually defined by HEL which is usually known asthe elastic precursor wave After this limit material flowsplastically due to the strong shockwave propagation In thecase of uniaxial strain the peak velocity is followed bymultiple loading and unloading phase The first drop fromthe peak velocity and subsequent loading-unloading zonesare associated with the spall signature inmetals Typically thefirst spall signature inmetals is followed by a significant sharpdrop in free surface velocity which is defined as the elasticunloading stage

4 Numerical Simulations

This study described two approaches to simulate the exper-iments described in the previous section a smooth particlehydrodynamics (SPH) solver in LS-DYNA software and thecombined hydro radiation and transport diffusion (CTH)hydrocode The remainder of this section details modeldevelopment

41 Material Model Both the LS-DYNA SPH and the CTHcomputer codes used the Johnson-Cook material model[10] for both the Lexan projectile and A36 steel plate In

the Johnson-Cook material model of plasticity flow stress isexpressed as

120590119910= (119860 + 119861 (120576

119901)

119899

) (1 + 119862 ln (120576sdotlowast)) (1 minus (119879lowast)119898) (1)

where 120590119910is the flow stress 119860 119861 119862 119899 and 119898 were material

constants 120576119901 is the effective plastic strain and 120576sdotlowast is theeffective total strain rate normalized by quasistatic strain rateThe homologous temperature 119879lowast is defined as

119879lowast=

119879 minus 119879119903

119879119898minus 119879119903

(2)

where 119879119903and 119879

119898were room and the melting temperatures in

Kelvin respectivelyAll the parameters of the Johnson-Cook model for Lexan

[54] and A36 steel [55] are listed in Table 3

42 Equation of State (EOS) Materials under shock waveloading needed a shock model that could account for thesudden pressure temperature internal energy and densitychanges that occur in front of the shock waves The equationof state (EOS) of a material is a general thermodynamicrelation that is defined by the code user Various forms ofEOS were used to describe the volumetric compression orexpansion behavior of different types of materials One of themost commonly used EOS is the Mie-Gruneisen equation ofstate which can be expressed [58] as

119875

=

12058801198620

2120583 (1 + (1 minus 120574

02) 120583 minus (1198862) 120583

2)

(1 minus (1198781minus 1) 120583 minus 119878

2(1205832 (120583 + 1)) minus 119878

3(1205833 (120583 + 1)

2

))

2

+ (1205740+ 119886120583) 119864

(3)

where 119875 is the pressure 1198781 1198782 and 119878

3are the coefficients

of slope of shock velocity-particle velocity curve 1205740is the

Gruneisen coefficient 119886 is the volume correction factor 120588 isthe instantaneous density119862

0is the Hugoniot intercept of the

metal 119864 is the internal energy and 120583 = (1205881205880minus 1) where 120588

0

is the reference density For materials under compression atemperature-corrected form of the above equation is given inthe following [59]

119875 =

12058801198620

2120583 (1 + (1 minus 120574

02) 120583)

(1 minus (1198781minus 1) 120583)

2+ 1205740119864 (4)

Assuming a negligible change in density and internal energythe above equations can be rewritten as

119875 =

12058801198620

2(2 minus 120574

02)

(1 minus 1198781)2 (5)

Both LS-DYNA and CTH included a Gruneisen EOS forLexan and A36 steel these were used in simulations duringthis study using the input parameters listed in Table 4

Shock and Vibration 5

Table 2 Details of spall crack in sectioned plates

Test ID Impact velocity (ms) Crack diameter (mm) Crack width (mm) Spall crack location withrespect to free surface (mm)

1000-016 5338 185 18 231000-017 5063 185 17 24

PDV oscilloscope

Laser trigger

Intervalometer

Delay generator

Laser probe

Probe attenuator

Processed signal

Figure 4 Layout of the PDV data acquisition

Crater (front side) Bulge (back side) Spall (sectioned)

Figure 5 Typical target plate after an experiment

6 Shock and Vibration

Table 3 Johnson-Cook material properties for the projectile and the target

Material 119860 (MPa) 119861 (MPa) 119862 119872 119899 119879119898(Kelvin) ]dagger EPSO

Lexan [54] 758 689 0 185 1004 533 0344 1A36 steel [55] 2861 5001 0022 0917 02282 1811 0260 1dagger] is Poissonrsquos ratio

Table 4 EOS parameters for the projectile and the target

Material 1205880(kgm3) 119862

0(ms) 119878

11205740

Lexan [56] 1190 1933 142daggerdagger 061A36 steel [57] 7890 4569 149 217daggerdagger1198781value for Lexan is suggested as 142 [55]

Test ID 1000-017

Spall signature

Elastic unloadingRinging in spall

Plastic waveHugoniot elastic

limit (HEL)

Elastic precursor wave

Velo

city

(ms

)

5 10 15 20 250Time (120583s)

0

50

100

150

200

250

Figure 6 Typical free surface velocity data as obtained by a PDVsystem

43 Estimation of theHugoniot Elastic Limit and Spall Strengthof A36 Steel Inmost fundamental shock studies velocimetrydata are obtained from uniaxial strain experiments on theshock HugoniotThis work considered the case of a projectileplate penetration experiment that can be described usingaxisymmetric assumptions The Hugoniot elastic limit andspall strength were calculated based on the uniaxial case inthe absence of axisymmetric data

The approximate Hugoniot elastic limit 120590HEL and spallstrength 120590spall of A36 steel were calculated from this velocityprofile by assuming that the impact was a one-dimensionallocalized phenomenon with the following relations [28]

120590HEL =1

2

Δ1198801198671205880119888119897

120590spall =1

2

Δ119880fs1205880119888119887

(6)

where Δ119880119867was the free surface velocity at elastic precursor

wave Δ119880fs was the pullback velocity of free surface as shownin Figure 7 and 119888

119897and 119888

119887correspond to the longitudinal

and bulk sound speed respectively These speeds depend on

Test ID 1000-017

10 20 300Time (120583s)

0

50

100

150

200

250

Velo

city

(ms

)

ΔUfs

ΔUH

Figure 7 HEL and spall strength calculation for typical test

Youngrsquos modulus 119864 and the bulk modulus 119870 of A36 steelEquations are given as follows

119888119897= radic

119864

120588

119888119887= radic

119870

120588

(7)

where 119888119897and 119888119887were calculated to be 5035ms and 4212ms

respectively for values of 200GPa [60] and 140GPa [60] of 119864and119870 respectively

Based on these equations the Hugoniot elastic limit andthe spall strength of A36 steel were approximated based onthe experiments and the above analysis results are shown inTable 5

Spalling of the material could be defined using either apressure cut-off (Pmin) value in the Johnson-Cook modelor a simple spall threshold parameter independent of theJohnson-Cook material-failure model In this study the firstoption was used to induce the spall in both LS-DYNA andCTH simulations By taking the average of the two spallstrength values of Table 5 a pressure cut-off value of 123GPawas determined

44 Developing Simulation Models The same two-dimen-sional (2D) axisymmetric geometry was used for both theSPH and the CTH simulations The same material modelequations of the state and boundary conditions were usedin the CTH models Because the shock did not reach

Shock and Vibration 7

Table 5 Hugoniot elastic limit and spall strength

Test ID Impact velocity (ms) Δ119880119867(ms) 120590HEL (GPa) Δ119880fs (ms) 120590spall (GPa)

1000-016 5338 6122 122 912 1521000-017 5063 4930 098 57 095

the boundaries during the period of interest it was decidedthat the target plates be modeled as cylindrical plates with aradius of 762mm This assumption allowed the use of a 2Daxisymmetric SPH model

441 SPH in LS-DYNA A body in an SPH model is repre-sented by a set of particles that are placed in interpolationpoints within the bodyThe simulation primarily depends onan interpolation function called the smoothing length [49] Inaddition parameters such as particle density bulk viscosityand scale factors contribute to the quality of the solution

Artificial bulk viscosity was included to dampen thenumerical ringing and oscillations of the shock front Theartificial bulk viscosity parameters Q1 and Q2 are assignedvalues of 15 and 10 respectively [61 62] No boundaryconditions were defined for the model Figure 8 shows theSPH model

Several SPH particle spacing arrangements were testedwhile ensuring that the mass of each projectile particlewas approximately equal to the mass of each target plateparticle All the simulation models were tested in a 46-coreCentOS 56 system having LS-DYNA R 70 MPP (massivelyparallel processing) version A summary of the free surfacevelocity profiles for different particle spacingwas presented inFigure 9The results showed that increasing the particle den-sity resulted in a better representation of the elastic precursorwave However it was observed that increasing the particledensity increases the peak velocity when compared with theexperimental curve Additionally increasing the particle inthe SPH model required significantly more computationaltime Therefore a particle spacing of 010mm was selectedfor all subsequent SPH simulations

442 CTH Model A typical CTH model with a 010mm times010mm zone is shown in Figure 10 Zone-size studies rec-ommended an optimal zone size of 010mm times 010mm forall CTH models (Figure 11) as this zone density reasonablydescribed the elastic wave and the sharp rise of the plasticwave

45 Comparison of Simulation Results Simulation results forLS-DYNA and CTH are shown in Figure 12 The resultswere compared with the experiments in terms of craterdimensions spall details and free surface velocity profiles

As Table 6 shows both techniques accurately capturedthe dimensions of the crater The shorter simulation timewithin CTH (10 120583s) may explain the larger difference inthe length of the back surface bulge dimension LS-DYNAsimulations showed higher magnitude of crater diameter andbulge for both experiments compared to CTH simulationsBut LS-DYNA simulations underpredicted the crater depth

ProjectilePlate

Figure 8 A typical SPH model (zoomed in) with 005mm particlespacing

Ve

loci

ty (m

s)

05 1 15 2 25 30Time (120583s)

0

50

100

150

200

250

Test ID 1000-017

025mm SPH spacing050mm SPH spacing 005mm SPH spacing

010mm SPH spacing

Figure 9 Typical SPH particle sensitivity study

Projectile

Plate

Figure 10 A typical CTH model with 010mm times 010mm zone(zoomed in)

in case of 5063 kms impact experimentThe exact reason forthis anomaly is yet to be understood both codes captured thephysical damage reasonably

8 Shock and Vibration

Table 6 Physical comparison of the impact craters

Impactvelocity(ms)

Test IDCrater

diameter(mm)

difference Crater depth(mm) difference Back side bulge

(mm) difference

53381000-016 170 NA 63 NA 23 NALS-DYNA 171 +06 59 minus71 21 minus81

CTH 157 minus76 57 minus93 20 minus195

50631000-017 169 NA 58 NA 24 NALS-DYNA 159 minus59 50 minus138 22 minus78

CTH 157 minus71 57 minus17 19 minus129

1 2 3 4 50Time (120583s)

0

50

100

150

200

250

Velo

city

(ms

)

Test ID 1000-017050 times 050mm zone 010 times 010mm zone

025 times 025mm zone

Figure 11 A typical CTH zone-sensitivity study with a 1200MPaspall strength

Additionally spall damage was monitored in both sim-ulations These simulations were able to capture the spallbehavior in the material (Figure 12) the location of the spallplane is compared in Table 7 As simulation models were notrun for longer times spall cracks did not develop completelyLocation of the spall plane was measured from the backsurface of the target plate to the start of spall crack plane

Comparison of the free surface velocity profiles for thefirst 5 120583s of both tests is presented in Figures 13 and 14 Freesurface velocity profiles of the simulations and experimentswere compared in terms of (a) elastic precursor wave andHEL (b) plastic wave rise (c) peak velocity and (d) spallsignatures which were defined in Section 3 The values ofthese variables are listed in Table 8 The results show thatboth LS-DYNA and CTH simulations captured the elasticprecursor However both of these simulations showed lowerHEL Both LS-DYNA and CTH simulation showed sharperrise in the plastic wave The slope of the simulation curveswas steeper than that of the experimental velocity profileBoth LS-DYNA and CTH simulations were able to capturethe pullback velocity signal after the second peak velocitywhich determines spall strength of thematerial However themagnitude of the pullback velocity signal was significantlydifferent from what was observed in the experiment whichmay be due to the fact that the spall strength values usedin both CTH and LS-DYNA simulations were based on

Table 7 Comparison of spall crack in simulations

Impactvelocity(ms)

Test ID

Spall crack locationwith

respect to freesurface (mm)

difference

53381000-016 23 NALS-DYNA(10120583s) 28 minus196

CTH (10120583s) 26 130

50631000-017 24 NALS-DYNA(10120583s) 23 minus33

CTH (10120583s) 21 minus125

the assumed similarity with the one-dimensional flier plateexperiments In both cases CTH overestimated second peakin velocity profiles when compared to the correspondingLS-DYNA simulations This difference can be explained bythe fact that Eulerian-based hydrocode often had issuesmodeling broader set of physical behaviors and Lagrangian orcoupled Eulerian-Lagrangian method was preferred in thosecases [63] though both of these codes had their limitationscomparing to the experimental velocity profiles

5 Conclusion

Gas gun experiments were performed to measure the plasticdeformation of A36 steel plates during hypervelocity impactsThe velocity of the back surface of plates was measuredusing a PDV system Simulation models were developed inthe LS-DYNA SPH solver and the CTH hydrocode Bothmodels used Johnson-Cook material model and the Mie-Gruneisen equation of state A procedure for identifying theHugoniot elastic limit and spall strength of A36 steel waspresented A study was conducted to determine SPH particlesensitivity and CTH zone spacing studies were conducted toidentify the best meshing strategy The results showed thatboth simulation approaches were able to accurately matchthe physicalmeasurements of impact crateringMoreover thesimulations were able to predict the velocity profiles in thePDV experiments however some differences were observedAdditional experiments and fine-tuning of the simulation

Shock and Vibration 9

Table 8 Comparison of free surface velocities in simulations

Impactvelocity(ms)

Test ID HEL (GPa) difference 1st peakvelocity (ms) difference 2nd peak

velocity (ms) difference

53381000-016 122 NA 2430 NA 1950 NA

LS-DYNA (5120583s) 064 minus475 2320 minus45 2200 128CTH (5 120583s) 057 minus533 2472 17 2565 315

50631000-017 095 NA 2050 NA 1710 NA

LS-DYNA (5120583s) 064 minus326 2289 117 1951 141CTH (5 120583s) 057 ndash400 2248 97 2402 405

Spall plane(a) LS-DYNA at 10120583s (b) CTH at 10120583s

Figure 12 Spall plane in Test 1000-017 simulations

Test ID 1000-016LS-DYNACTH

Velo

city

(ms

)

1 2 3 4 50Time (120583s)

0

100

200

300

Figure 13 Free surface velocity comparison of Test 1000-016(impact velocity 5338 kms)

models were needed including the use of more accuratematerial models and simulation parameters Furthermorestudies were needed on the effect of the pressure induced120572 harr 120576 phase transition that is known to occur in pure iron

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Test ID 1000-017LS-DYNA CTH

Velo

city

(ms

)

1 2 3 4 50Time (120583s)

0

50

100

150

200

250

300

Figure 14 Free surface velocity comparison of Test 1000-017(impact velocity 5063 kms)

Acknowledgments

This study was conducted by National Security TechnologiesLLC under Contract no DE-AC52-06NA25946 with the USDepartment of Energy and supported by the Site-DirectedResearch and Development Program The United StatesGovernment retains and by accepting the article for pub-lication the publisher acknowledges that the United StatesGovernment retains a nonexclusive paid-up irrevocableworldwide license to publish or reproduce the published formof this work or allow others to do so for United StatesGovernment purposes (DOENV25946mdash2392)

10 Shock and Vibration

References

[1] L C Chhabildas and M D Knudson ldquoTechniques to launchprojectile plates to very high velocitiesrdquo in High-Pressure ShockCompression of Solids VIII L C Chhabildas LDavidson andYHorie Eds High-Pressure Shock Compression of CondensedMatter pp 143ndash199 Springer Berlin Germany 2005

[2] C Doolan A Two-Stage Light Gas Gun for the Study of HighSpeed Impact in Propellants Department of Defence SalisburyUK 2001

[3] N Holmes ldquoShockingrdquo Gas-Gun Experiments STR13ndash9 2000[4] H F Swift ldquoLight-gas gun technology a historical perspectiverdquo

in High-Pressure Shock Compression of Solids VIII L C Chha-bildas L Davison and Y Horie Eds High-Pressure ShockCompression of Condensed Matter pp 1ndash35 Springer BerlinGermany 2005

[5] Z Rosenberg and E Dekel Terminal Ballistics Springer 2012[6] J H Oscarson and K F Graff Spall Fracture and Dynamic

Response of Materials Battelle Memorial Institute ColumbusOhio USA 1968

[7] W Goldsmith T W Liu and S Chulay ldquoPlate impact andperforation by projectilesrdquo Experimental Mechanics vol 5 no12 pp 385ndash404 1965

[8] G G Corbett S R Reid and W Johnson ldquoImpact loading ofplates and shells by free-flying projectiles a reviewrdquo Interna-tional Journal of Impact Engineering vol 18 no 2 pp 141ndash2301996

[9] D R Christman and J W Gehrig ldquoAnalysis of high-velocityprojectile penetration mechanicsrdquo Journal of Applied Physicsvol 37 article 1579 1966

[10] B R Sorensen K D Kimsey G F Silsby D R Scheffler T MSherrick andW S de Rosset ldquoHigh velocity penetration of steeltargetsrdquo International Journal of Impact Engineering vol 11 no1 pp 107ndash119 1991

[11] D A Shockey D R Curran and P S De Carli ldquoDamage in steelplates fromhypervelocity impact I Physical changes and effectsof projectile materialrdquo Journal of Applied Physics vol 46 no 9pp 3766ndash3775 1975

[12] C E Anderson Jr V Hohler J D Walker and A J StilpldquoTime-resolved penetration of long rods into steel targetsrdquoInternational Journal of Impact Engineering vol 16 no 1 pp 1ndash18 1995

[13] J W BondHypervelocity Impact Shock Induced Damage to SteelArmor Defense Technical Information Center Fort Belvoir VaUSA 1976

[14] L A Merzhievskii and V M Titov ldquoPerforation of platesthrough high velogity impactrdquo Journal of AppliedMechanics andTechnical Physics vol 16 no 5 pp 757ndash764 1975

[15] T Boslashrvik A H Clausen O S Hopperstad and M LangsethldquoPerforation of AA5083-H116 aluminium plates with conical-nose steel projectilesmdashexperimental studyrdquo International Jour-nal of Impact Engineering vol 30 no 4 pp 367ndash384 2004

[16] HMWen and B Lan ldquoAnalyticalmodels for the penetration ofsemi-infinite targets by rigid deformable and erosive long rodsrdquoActa Mechanica Sinica vol 26 no 4 pp 573ndash583 2010

[17] H Wen Y He and B Lan ldquoAnalytical model for cratering ofsemi-infinite metallic targets by long rod penetratorsrdquo ScienceChina Technological Sciences vol 53 no 12 pp 3189ndash3196 2010

[18] Y He and H M Wen ldquoA note on the penetration of semi-infinite metallic targets struck by long rods at high velocitiesrdquoin Proceedings of the International Conference on Mechanical

Engineering and Material Science (MEMS rsquo12) pp 550ndash552Atlantis Press Shanghai China December 2012

[19] L M Barker and R E Hollenbach ldquoLaser interferometer formeasuring high velocities of any reflecting surfacerdquo Journal ofApplied Physics vol 43 no 11 pp 4669ndash4675 1972

[20] L M Barker and R E Hollenbach ldquoShock wave study of the120572 999448999471 120576 phase transition in ironrdquo Journal of Applied Physics vol45 article 4872 1974

[21] G F Kuscher V Hohler and A J Stilp ldquoHigh-resolutionvelocity interferometer system for any reflector (VISAR) laserinterferometer measurements of the rear side response ofimpact loaded steel platesrdquo in Proceedings of the 15th Interna-tional Congress on High Speed Photography and Photonics vol0348 of Proceedings of SPIE pp 508ndash518 March 1983

[22] J L Wise and L C Chhabildas ldquoLaser interferometer mea-surements of refractive index in shock-compressed materialsrdquoin Proceedings of the 4th American Physical Society TopicalConference on Shock Waves in Condensed Matter Y M GuptaEd pp 441ndash454 PlenumPress SpokaneWash USA July 1986

[23] M J Forrestal L M Lee and B D Jenrette ldquoLaboratory-scale penetration experiments into geological targets to impactvelocities of 21 kmsrdquo Journal of Applied Mechanics vol 53 no2 pp 317ndash320 1986

[24] Z Rosenberg and S J Bless ldquoDetermination of dynamic yieldstrengths with embedded manganin gages in plate-impact andlong-rod experimentsrdquo Experimental Mechanics vol 26 no 3pp 279ndash282 1986

[25] A K Zurek W R Thissell J N Johnson D L Tonks andR Hixson ldquoMicromechanics of spall and damage in tantalumrdquoJournal of Materials Processing Technology vol 60 no 1ndash4 pp261ndash267 1996

[26] M D Knudson C A Hall J R Asay D L Hanson J E BaileyandWW Anderson ldquoEquation of statemeasurements in liquiddeuterium to 70GPardquo Physical Review Letters vol 87 no 22Article ID 225501 2001

[27] T J Vogler and J D Clayton ldquoHeterogeneous deformation andspall of an extruded tungsten alloy plate impact experimentsand crystal plasticity modelingrdquo Journal of the Mechanics andPhysics of Solids vol 56 no 2 pp 297ndash335 2008

[28] D Mukherjee A Rav A Sur K D Joshi and S C GuptaldquoShock induced spall fracture in polycrystalline copperrdquo AIPConference Proceedings vol 1591 pp 608ndash610 2014

[29] O T Strand D R Goosman CMartinez T LWhitworth andW W Kuhlow ldquoCompact system for high-speed velocimetryusing heterodyne techniquesrdquo Review of Scientific Instrumentsvol 77 no 8 Article ID 083108 2006

[30] B Jilek ldquoHistory of velocimetry technologyrdquo in Proceedings ofthe 7th Annual Photonic Doppler Velocimetry Workshop (PDVrsquo12) Sandia National Laboratory Albuquerque NM USAOctober 2012

[31] R Chau J Stolken P Asoka-Kumar M Kumar and N CHolmes ldquoShock hugoniot of single crystal copperrdquo Journal ofApplied Physics vol 107 no 2 Article ID 023506 2010

[32] J A Zukas High Velocity Impact Dynamics vol 1990 Wiley1990

[33] G R Johnson and W H Cook ldquoA constitutive model and datafor metals subjected to large strains high strain rates and hightemperaturesrdquo in Proceedings of the 7th International Sympo-sium on Ballistics pp 541ndash547 The Hague The Netherlands1983

Shock and Vibration 11

[34] F J Zerilli and R W Armstrong ldquoDislocation-mechanics-based constitutive relations formaterial dynamics calculationsrdquoJournal of Applied Physics vol 61 no 5 pp 1816ndash1825 1987

[35] D J Steinberg and C M Lund ldquoA constitutive model for strainrates from 10minus4 to 106 sminus1rdquo Journal of Applied Physics vol 65 no4 pp 1528ndash1533 1989

[36] B Banerjee ldquoAn evaluation of plastic flow stressmodels for thesimulation of high-temperature and high-strain-rate deforma-tion of metalsrdquo httparxivorgabscond-mat0512466

[37] T Boslashrvik O S Hopperstad T Berstad and M LangsethldquoNumerical simulation of plugging failure in ballistic penetra-tionrdquo International Journal of Solids and Structures vol 38 no34-35 pp 6241ndash6264 2001

[38] T Boslashrvik M Langseth O S Hopperstad and K A MaloldquoBallistic penetration of steel platesrdquo International Journal ofImpact Engineering vol 22 no 9 pp 855ndash886 1999

[39] T Boslashrvik O S Hopperstad T Berstad and M LangsethldquoA computational model of viscoplasticity and ductile damagefor impact and penetrationrdquo European Journal of MechanicsASolids vol 20 no 5 pp 685ndash712 2001

[40] X W Chen and Q M Li ldquoPerforation of a thick plate by rigidprojectilesrdquo International Journal of Impact Engineering vol 28no 7 pp 743ndash759 2003

[41] X W Chen Y B Yang Z H Lu and Y Z Chen ldquoPerforationof metallic plates struck by a blunt projectile with a soft noserdquoInternational Journal of Impact Engineering vol 35 no 6 pp549ndash558 2008

[42] XW Chen X Q Zhou and X L Li ldquoOn perforation of ductilemetallic plates by blunt rigid projectilerdquo European Journal ofMechanicsmdashASolids vol 28 no 2 pp 273ndash283 2009

[43] J Eftis and J A Nemes ldquoModeling of impact-induced spallfracture and post spall behavior of a circular platerdquo InternationalJournal of Fracture vol 53 no 4 pp 301ndash324 1992

[44] J Zukas Introduction to Hydrocodes Elsevier 2004[45] D E Grady and M E Kipp ldquoExperimental and computational

simulation of the high velocity impact of copper spheres on steelplatesrdquo International Journal of Impact Engineering vol 15 no5 pp 645ndash660 1994

[46] G T Camacho and M Ortiz ldquoAdaptive lgrangian modelling ofballistic penetration of metallic targetsrdquo Computer Methods inApplied Mechanics and Engineering vol 142 no 3-4 pp 269ndash301 1997

[47] D J Gee ldquoPlate perforation by eroding rod projectilesrdquo Interna-tional Journal of Impact Engineering vol 28 no 4 pp 377ndash3902003

[48] R A Gingold and J J Monaghan ldquoSmoothed particle hydrody-namics theory and application to non-spherical starsrdquoMonthlyNotices of the Royal Astronomical Society vol 181 no 3 pp 375ndash389 1977

[49] J L Lacome C Espinosa and C Gallet ldquoSimulation ofhypervelocity spacecrafts and orbital debris collisions usingsmoothed particle hydrodynamics in LS-DYNArdquo inProceedingsof the 5th Dynamics and Control of Systems and Structures inSpace Conference p 9 Cambridge UK 2002

[50] V Mehra and S Chaturvedi ldquoHigh velocity impact of metalsphere on thin metallic plates a comparative smooth particlehydrodynamics studyrdquo Journal of Computational Physics vol212 no 1 pp 318ndash337 2006

[51] F Plassard J Mespoulet and P Hereil ldquoHypervelocity impactof aluminium sphere against aluminium plate experiment andLS-DYNA correlationrdquo in Proceedings of the 8th European LS-DYNA Conference pp 1ndash11 Strasbourg Germany May 2011

[52] H A Kalameh A Karamali C Anitescu and T RabczukldquoHigh velocity impact of metal sphere on thin metallic plateusing smooth particle hydrodynamics (SPH)methodrdquo Frontiersof Structural andCivil Engineering vol 6 no 2 pp 101ndash110 2012

[53] K Loft M C Price M J Cole and M J Burchell ldquoImpactsinto metals targets at velocities greater than 1 km sminus1 a newonline resource for the hypervelocity impact community andan illustration of the geometric change of debris cloud impactpatterns with impact velocityrdquo International Journal of ImpactEngineering vol 56 pp 47ndash60 2013

[54] D J Littlewood ldquoSimulation of dynamic fracture using peridy-namics finite element modeling and contactrdquo in Proceedings ofthe ASME International Mechanical Engineering Congress andExposition pp 1ndash9 Vancouver Canada November 2010

[55] J D Seidt A Gilat J A Klein and J R Leach ldquoHigh strainrate high temperature constitutive and failure models for EODimpact scenariosrdquo in Proceedings of the SEMAnnual Conferenceamp Exposition on Experimental and Applied Mechanics p 15Society for Experimental Mechanics Springfield Mo USAJune 2007

[56] D J Steinberg Equation of State and Strength Properties ofSelected Materials Lawrence Livermore National LaboratoryLivermore Calif USA 1996

[57] T Elshenawy and Q M Li ldquoInfluences of target strength andconfinement on the penetration depth of an oil well perforatorrdquoInternational Journal of Impact Engineering vol 54 pp 130ndash1372013

[58] Livermore Software Technology Corporation (LSTC) LS-DYNA Keyword Userrsquos Manual vol 1 Livermore SoftwareTechnology Corporation (LSTC) 971st edition 2007

[59] M A Zocher P J Maudlin S R Chen and E C Flower-Maudlin ldquoAn evaluation of several hardening models usingtaylor cylinder impact datardquo in Proceedings of the EuropeanCongress on Computational Methods in Applied Sciences andEngineering (ECCOMAS rsquo00) vol 53 pp 1ndash20 Barcelona SpainSeptember 2000

[60] ASTM A36 Steel Plate March 2015 httpwwwmatwebcomsearchdatasheetaspxmatguid=afc003f4fb40465fa3df05129f0-e88e6ampampckck=1x26ckck=1

[61] R Panciroli ldquoHydroelastic impacts of deformable wedgesrdquoin Dynamic Failure of Composite and Sandwich Structures SAbrate B Castanie and Y D S Rajapakse Eds vol 192 of SolidMechanics and Its Applications pp 1ndash45 Springer DordrechtThe Netherlands 2013

[62] M Selhammar ldquoModified artificial viscosity in smooth particlehydrodynamicsrdquoAstronomy andAstrophysics vol 325 no 2 pp857ndash865 1997

[63] A J Ward R P Nance X Xiao A D Shirley and J R Cogarldquo10+ kmsec hypervelocity impact modeling with a lagrangiansolverrdquo in Proceedings of the IMPLAST Conference ProvidenceRI USA October 2010

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