Impact Initiation of Reactive Aluminized Fluorinated Acrylic Nanocomposites

13 Pages·2016·3.64 MB·English

by  Bradley W. White

J.dynamicbehaviormater.(2016)2:259–271
DOI10.1007/s40870-016-0065-3
Impact Initiation of Reactive Aluminized Fluorinated Acrylic
Nanocomposites
Bradley W. White1 • Christopher A. Crouse2 • Jonathan E. Spowart3 •
Brady Aydelotte4 • Naresh N. Thadhani5
Received:4February2016/Accepted:31March2016/Publishedonline:18April2016
(cid:2)SocietyforExperimentalMechanics,Inc2016
Abstract The initiation of aluminized fluorinated acrylic Keywords AlFA (cid:2) Taylorimpact (cid:2) Polymer composites (cid:2)
(AlFA) nanocomposites during modified Taylor impact Energetic materials (cid:2) Impact initiation
tests was investigated. Samples were impacted against a
steel orsapphire anvilat a nominal velocity of150 m/s.A
framing camera was used to capture head-on and side- Introduction
profile impact images for the sapphire window and steel
plate rigid anvils, respectively. Correlations were drawn Polymer-based reactive composites are often studied for
between both experimental setups to determine the initia- use as structural energetic materials with proposed appli-
tion locations and reaction times. Reactions were found to cations as munitions in military operations [1] or solid
initiate at an intermediate radius on the impact face of the rocket propellants [2]. These applications often require
pelletatatimenearfullcompaction.Fromsimulations,the detailed knowledge of their mechanical and reactive
higheststrainsandtemperatureswerefoundatradiisimilar behavior under high-rate loading or impact conditions. In
to those observed in experiments at the time of ignition. experiments where a pellet of the reactive composite is
Off-normal impacts produced higher localized straining attached to the front end of a metal projectile and then
and temperatures on one-half of the pellet. The copper impacted against a rigid anvil, reactions have been
projectile,used fordelivery,wasrevealedtoaidinashear observed [3, 4]. However, the initiating reaction locations
assisted reaction by helping to drive the pellet material withinthecompositeandthetimetoreactionfollowingthe
outward as the projectile deformed radially. initial impact are not well known in modified Taylor
impacttests.Thisisinpartduetoobservationalimagedata
obtained from high-speed cameras being limited to side-
profileanglesduringtheimpactprocess.Thisobscuresthe
far side of the sample and metal projectile as well as any
& BradleyW.White processes that occur at the impact surface. Furthermore,
[email protected] reactions may initiate within the interior of the samples
themselves. This work attempts to address these issues by
1 LawrenceLivermoreNationalLaboratory,7000East
identifying likely locations of the reaction initiation sites
Avenue,Livermore,CA94550,USA
using a modified Taylor impact test geometry.
2 AirForceResearchLaboratory,MunitionsDirectorate,
Depending on the nature of the reaction that occurs
EglinAFB,FL32542,USA
during impact, it may be possible to infer what is taking
3 AirForceResearchLaboratory,MaterialsandManufacturing
place on the backside of the projectile-composite sample.
Directorate,Wright-PattersonAFB,OH45433,USA
However,ifthereactionappearstobeverysmallinextent
4 ArmyResearchLaboratory,AberdeenProvingGround,
ornon-existent,thenthereactioneventmaybelocalizedto
MD21005,USA
acertainregionofthecompositeonthefarside,ornottake
5 SchoolofMaterialsScienceandEngineering,Georgia
place, or not be visible due to limited acquisition capabil-
InstituteofTechnology,771FerstDriveNW,Atlanta,
GA30332,USA itiesofthecamera.Toworkaroundtheselimitations,there
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260 J.dynamicbehaviormater.(2016)2:259–271
are options available, such as having mirrors on the
opposite side of the camera to allow an image to simulta-
neously capture both sides of the impact/reaction event.
Examining the impact face itself requires an entirely dif-
ferentsetupinvolvingatransparentwindowthatcanactas
arigidanvil,whilealsoallowingforthehead-onimpactsto
be interrogated [5–7].
In previous work by Crouse et al. [8, 9], an aluminized
fluorinated acrylate-based polymer composite (AlFA),
reinforced with nano-sized particles,hasbeen showntobe
highly reactive over a large range of aluminum particle
reinforcement levels. The composite was found to react
reliably inbothairandpartialvacuum atimpactvelocities
greaterthan100m/s[9]forvariousweightpercentages(up
to 60 wt%) of nano-aluminum (80 nm). Thus, this com-
posite system is ideal for the characterization of the reac- Fig. 1 The 7.62 mm (cid:3) 1.8 m Taylor gas gun located at Georgia
Institute of Technology. (1) Laser window mount with lasers. (2)
tion initiation characteristics and behavior under impact
Laserdetectionwindow.(3)Gunbarrelend.(4)Imacon200camera.
conditions using a transparent window and steel anvil (5) Guide rails for holding the anvil and aid in anvil alignment. (6)
setups. In this work we chose to use the formulation con- Observation port with sacrificial windows for image acquisition. (7)
taining50wt%ofnano-aluminum.Additionally,whilethe Catchtankendforaccesstorearofanvil.(8)Secondaryportsforgun
peripherals
modifiedTaylorimpacttestisoftenusedasaninexpensive
screening tool and determining the relative sensitivity of
reactive materials, it also is appropriate for understanding diameter of approximately 20.32 mm. An ultra-high
the behavior of AlFA and similarly related energetic molecular weight polyethylene (UHMWPE) washer loca-
composite materials, due to their applications as a muni- ted between the steel support cylinder and sapphire win-
tionscasingmaterials,pyrotechnicindicatormaterials,and dow acts as a buffer against stress concentrations.
pyrotechnic filament materials [10], where similar loading A UHMWPE sleeve was also used to encase the sapphire
conditions are likely to occur. window. Using this method, the sapphire window was
found to survive multiple lower velocity impacts from a
copper projectile. The velocity was measured using a two-
Experimental Methodology laser interrupt system in conjunction with an up-down
counter (UDC). A schematic of the Taylor gas gun’s key
Oxygen-free high thermal conductivity (OFHC) copper components are shown in Fig. 2. In addition to measuring
wasmachinedintocylindricalprojectiles7.62(diameter)(cid:3)
30 mm (length) to act as a delivery mechanism for the
composite pellets. The pellets were mounted onto one end
IMACON 200
of the copper projectiles using a thin layer of epoxy. Care Camera
was taken to align the center axis of the pellet with the
Primary and
center axis of the copper projectile. The pellets were Secondary Lasers
nominally 3.0 mm diameter (cid:3) 1.5 long and consist of a
fluorinatedpolymermatrixinfiltratedwith50wt%ofnano-
sized aluminum powder. The amount of porosity for this
formulation was measured to be approximately 12 % [8]. 30.0 mm
7.62 mm
Additional details regarding the composite formulation Sapphire
may be found in work by Crouse et al. [8]. 7.62 mm Window Mirror
Barrel
Projectile with
The projectiles with the mounted reactive composite
Mounted UHMWPE Rigid
pelletswerethenloadedintoa7.62mm(cid:3)1.8m(diameter Reactive Pellet Ring and Anvil
Washer
(cid:3) length) Taylor gas gun apparatus as shown in Fig. 1.
Using compressed helium, the projectiles were propelled Primary and
Secondary Beam
towardsasapphirewindoworsteelplateanvilatanominal Detectors
velocity of 150 m/s. The sapphire window was 25.4 mm
Fig.2 SchematicoftheTaylorgasgun’skeycomponents.Therigid
diameter (cid:3) 50.8 mm thick and was supported by a plastic
anvil in this work was either an S7 steel plate (setup not shown) or
buffer and steel cylinder, which has an inner viewing sapphirewindow
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J.dynamicbehaviormater.(2016)2:259–271 261
the precise velocity from the triggering of the two laser compressed’’ to be when there is little, to no visible gap
detectors, the UDC is used to trigger a high-speed camera between the copper projectile and anvil. This is similar to
(Imacon 200) that captures images of the reactive pellet experiments, by Du et al. [3], involving the compaction of
impacting the anvil at specified times. Since the impact metallicpowdermixtures(Al?X)inwhichreactionswere
occurs within an enclosed chamber the energetic response alsofoundtoinitiatenearfullcompaction.Asthisreaction
of the reactive pellets may be captured under ambient or progresses, a mixture of reaction products, unreacted deb-
vacuum environmental conditions. Ambient conditions ris, and gas is expelled in a radial direction away from the
were used for the steel anvil shots and a partial vacuum initial point of impact. Details of the most likely reaction
(145–225mtorr)wasusedforthesapphireanvilshots.The products for this composite system are described in pre-
partial vacuum in sapphire anvil experiments was used to vious work by Crouse et al. [8].
eliminatecontributionsofreactionswithairaswellashelp Fromanexaminationofimagesforshot11138,(Fig. 3)
identify reaction initiation sites. between the initial impact and (cid:4)5 ls ((cid:4)8 ls for shots
11139 and 11140), the pellet deforms extensively. During
this time, no indication of media being ejected is visible.
Experimental Results and Discussions This may be due to the high polymer matrix content
allowingforalargeamountofstraintoaccumulatewithout
Impact of Pellets Against a Steel Anvil undergoing extensive fracturing and fragmentation.
and Side-Profile Images Between 5 and 7 ls (8–10 ls for shots 11139 and 11140),
thepelletbecomes’’fully’’compressedbetweenthecopper
In Figs. 3, 4, and 5, sequences of side-profile images are projectileandanvil.Duringthisperiod,thepolymermatrix
shown for experiments in which a steel anvil was used. In and nano-aluminum particles are strained even further
theseimages,theprojectilewithamountedpelletisshown between the copper projectile and anvil. At approximately
to impact the anvil, upon which the pellet begins to com- 7 ls, comminution of the pellet has begun with fragments
pactandstrainradially.Whenthepelletappearstobefully ejected outward. Due to the large increase in surface area
compressed, the beginning of a reaction takes place, indi- of the nano-aluminum and strain-induced mixing with the
cated by the presence of bright regions at the plane of fluorinatedpolymermatrix,andwithoxygenpresentinthe
impact at around 7–10 ls. Here we define ’’fully surrounding environment a reaction initiates. This is
Fig.3 Impactimagesforshot
11138,inambientair.The
projectileimpactvelocityand
verticaltiltweremeasuretobe
145.1m/sand0.9(cid:5)0.25(cid:6)
respectively.Thetimetofirst
observablereactionoccurredat
7lsandisvisibleacrossthe
entireimpactsurface
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262 J.dynamicbehaviormater.(2016)2:259–271
Fig.4 Impactimagesforshot
11139inambientair.The
projectileimpactvelocityand
verticaltiltweremeasuretobe
146.2m/sand1.26(cid:5)0.25(cid:6)
respectively.Thetimetofirst
observablereactionoccurredat
10lsandisvisiblenearthetop
portionoftheimpactsurface
Fig.5 Impactimagesforshot
11140inambientair.The
projectileimpactvelocityand
verticaltiltweremeasuretobe
147.1m/sand0.12(cid:5)0.25(cid:6)
respectively.Thetimetofirst
observablereactionoccurredat
10lsandisvisibleacrossthe
entireimpactsurface
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J.dynamicbehaviormater.(2016)2:259–271 263
indicatedbythepresenceoflightinFigs. 3, 4,and 5,at7, For shot 11139, which impacted at the largest tilt angle
10,and10ls,respectively.Fromthesideprofileimagesit (1.26(cid:6)), the cloud appears to be less uniform, indicating
is unclear if comminution occurs prior to or is induced by that impact angle may have an important role in reaction
the reaction within the pellet. events. Nearertothe anvil there isalsoanappearanceofa
At times greater than 10 ls, the unreacted composite darkring,whichmay beeither previouslyreactedmaterial
material continues to be loaded between the copper pro- (carbonaceous byproducts of the fluorination reaction [8])
jectile and anvil before slowing down and rebounding. or unreacted debris from early pellet fragmentation.
Throughout the entire captured duration of each shot, the However, there is a minimal amount of the dark ring vis-
back end of copper projectile continued to move towards ibleatearliertimes,anditdoesnotappeartobelessdense
the anvil and had not yet transitioned from a loaded to atlatertimes.This,alongwithapresenceoflightbetween
unloaded (rebounded) state. At these later times the reac- thedarkerringandanvilface,suggeststhatthedarkerring
tioncloudobscurestheimpactendofthecopperprojectile. is primarily comprised of previously reacted material that
However, from our experience with inert experiments and is propelled outward by the expansion of hot gas. The
simulations(withoutareactivepellet)thecopperprojectile darker ring appears to expand radially outward at a higher
plasticallydeformsattheimpactfaceforapproximately30 ratethanthemaincloud.Thismaybeduetoanincreasein
ls following impacts at (cid:4)150 m/s and with the geometry gas pressure generated by reactions taking place in the
used in this work. The overall projectile deformation maincloud,andapartialconfinementeffectcreatedbythe
occurs over a longer period and corresponds to transient steel anvil.
times greater than those captured with the imaging acqui- UsingthediameteroftheprojectilesinFigs. 3, 4,and 5
sition rates chosen for these experiments. This is further asareferencescaleforeachimage,anestimateofthemain
evidenced by the continued translation of the projectiles gas cloud thickness and radial distance from the anvil/
back-end towards the anvil. This continued projectile projectilewereobtainedforeachshot.Similarly,theradial
deformation will cause further mixing and deformation of distance of the darker ring from the projectile was mea-
the nano-aluminum thereby promoting heat generation sured. For this analysis, the reference point on the projec-
through plastic work and increase the propensity for tileforclouddiametermeasurementswaslocatedasnearto
maintaining reactions with faster reaction rates. Moreover, the reacting cloud as possible. The results of the radial
since polymer matrix composites are inherently heteroge- distances for times following the initial observed reaction
neous by their nature, localized increases in temperature are shown in Fig. 6(left) and 6(right) for the main cloud
will develop at the particle scale during dynamic loading and dark ring, respectively. The main cloud and dark ring
events. This can also contribute to enhanced reactions distance profiles for each shot are very similar to one
during the compaction and loading processes. another, indicating that, at a nominal impact velocity of
In the images for times greater than 7 ls, inshot 11138 150 m/s, their reaction mechanisms are dominated by the
and 10 ls in shots 11139 and 11140, a cloud of hot gas is same processes, despite slight differences in their initial
observedtobillowperpendicularlyoutwardfromtheanvil. reaction times. Because of their similar time profiles, the
14 14
12 12
10 10
m) m)
m 8 m 8
e ( sshhoott 1111113389 e ( sshhoott 1111113389
c c
n shot 11140 n shot 11140
a 6 a 6
st st
Di Di
4 4
2 2
0 0
0 5 10 15 20 25 30 0 5 10 15 20 25 30
Time After Ignition (µs) Time After Ignition (µs)
Fig.6 Maincloud(left)anddarkring(right)radialdistancesmeasuredfromouterprojectileradius.Thetimeshavebeenshiftedsothatt=0ls,
isthefirstframewithanobservablereaction.Theerrorindistancemeasurementsisestimatedtobe0.2mm
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264 J.dynamicbehaviormater.(2016)2:259–271
distances were averaged over all three shots (see Fig. 7). ? Teflon mixtures. Depending on the mixture’s composi-
While initially the main cloud and dark ring have similar tion, it was found that the steady-state propagation veloc-
slopes, the dark ring continues to progress at a relatively ities range from 700 to 1300 m/s. The main cloud
constantvelocityof975m/s,whereasthemaincloudslows thicknessesasafunctionoftimefollowingthereactionare
down to approximately 366 m/s. These values are similar approximately equal to the measured main cloud radial
tothedeflagrationvelocitiesfoundbyDolgoborodovetal. distances.
[11] for confined linear burn tests conducted on aluminum
Impact of Pellets Against a Sapphire Anvil
and Head-On Images
14
d = 0.975*t+0.7491
R2 = 0.9961 For the sapphire anvil shots, which were used to examine
12 the reaction head-on, the ignition times were found to be
similar to those observed in the side profile images. Two
10 d = 0.3657*t+4.519 shots were conducted with almost identical impact veloc-
m) R2 = 0.9837 ities,shot11211at152.9m/sandshot11212at152.6m/s.
e (m 8 Shot 11211 ignited between 8 and 10 ls following impact
c and shot 11212 at approximately 7.5 ls (see Figs. 8, 9).
n
a 6
st The results from side profile investigations suggest that
Di thereactionappearstoinitiatenearlyuponfullcompaction
4
ofthepellet.However,anyviewoftheignitionlocationis
avg. ring dist.
obscured. From head-on images (Figs. 8, 9), particularly
2 avg. cloud dist.
for shot 11212, the ignition is seen to emanate at an
intermediate radius within the compacted nano-composite.
0
Acontrastandbrightnessenhancedframeimagefromshot
0 5 10 15 20 25 30
Time After Ignition (µs) 11212 showed multiple initiation sites that were arranged
in a crescent shape (see Fig. 10). At later times additional
Fig. 7 Averaged radial distances (over all three shots) for the main initiationsiteswereobservedintheframecorrespondingto
cloud and dark ring. Linear fits to the data were used to obtain
8.75 ls following impact that appear to be distinctly dis-
velocitiesreportedinmaintext.Theerrorindistancemeasurementsis
estimatedtobe0.2mm joint from the nearby reacting material. At 10 ls for shot
Fig.8 Shot11211.Impact
velocityof152.9m/s
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J.dynamicbehaviormater.(2016)2:259–271 265
Fig.9 Shot11212.Impact
velocityof152.6m/s.Camera
timingswereslightlydifferent
forthisshottocapturemore
framesatearliertimesfollowing
impact
11211 and 8.75 ls for shot 11212 there are similar cres- at 10 and 8.75 ls, respectively). This may be due to
cent-shaped reacting regions. In comparison toside profile heterogeneity of the composites leading to heterogeneous
impacts this is believed to correspond to similar extents of initiation.
reactionobservedinFig. 4(shot11139)atatimeof10ls, After initiation, the reaction progresses until a highly
whichhasamorepronouncedstateofreactionnearthetop uniform circular region is burning (within 2–3 ls). This
of the impacted region but has not yet fully evolved to circular region increases in diameter slightly, and the
enclose the whole perimeter of the compacted pellet. The reaction is sustained while under loading. Also of note is
crescent shaped regions were also observed to have vari- thepresenceofadarkerregionnearthecenterofthecircle.
abilityinthesmoothnessoftheirperimeters(seeFigs. 8,9 This darker interior region is relatively large initially and
decreasessizeasmaterialcontinuestobeconsumedbythe
reaction. The reaction itself burns with greatest intensity/
brightness for approximately the first 10 ls, after which it
decreases.Thisisincontrasttotheside-profileimagesthat
showthereactionburningmostintenselyatthelatertimes.
Thissuggeststhematerialburningwithgreatestintensityin
the head on images is continuing to react while jetting
outward.Whiledoingso,itcontributestothemostintense
stages of the reaction seen in the side-profile images. The
jetting of the material is prevalent throughout the entire
reaction, with occasional gaps as seen in the images. This
may lead to some of the cloud variability observed in the
side-profile images.
One surprising observation is the lack of more intense,
brightjetsradiatingawayfromthereactingcenter.Beyond
the extent of the circular reacting region the brightness
Fig.10 Enhancedimageframe,showingthefirstobservedlightfor decreases quickly. This is most likely related to the dark
shot11212.Multipleinitiationsitesarevisible,whicharearrangedin
ring observed in the side-profile images that we suspect is
a crescent shape. At later times these sites coalesced into a single
propagatingreactionzone previously reacted material that is propelled outward.
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266 J.dynamicbehaviormater.(2016)2:259–271
Reactions are clearly taking place away from the main Zerilli–Armstrong constitutive model [12, 13], which has
impact location (i.e. the billowing cloud observed in side- been used for PTFE [12–14] and composites with PTFE
profile images) as well as the within the circular region. and Al [15], and is well suited for describing the behavior
Depending on the availability of environmental oxygen of strain hardening polymeric materials at high rates of
and/orfluorinefromthepolymermatrixthatcanreactwith strain. For modeling purposes we chose to use PTFE as a
the nano-aluminum, either a fluorination or oxidation representative matrix material since limited strength data
reaction is most likely to occur. exists for the fluorinated acrylate matrix and AlFA com-
The footprint of the reacting region increases only posites.Whileitwouldbeidealtohaveconstitutivemodels
slightly in diameter within the measured time. Shown in describing the behavior of the fluorinated acrylate (FA)
Fig. 11, is an outline of the approximate viewing area used in this work, the quasi-static strengths for PTFE (10–
visible from the backside of the sapphire window. This 20MPa)[14,16]andFA(\15MPa)[8]forastrainrateof
outline is determined from the halo/brighter region sur- (cid:4)0.001 s(cid:7)1 are fairly close. The acrylate-containing
rounding the main reacting material in the center. This is polymer, PMMA, was also considered. However, PMMA
most easily visible in Fig. 8 for the frames corresponding hasamuchhigherquasi-staticcompressivestrengththatis
to 26, 28, and 30 ls after the initial impact. Using the greater than 70 MPa [17, 18] for the same strain rate.
knownvisiblewindowsize(20.32mm)asascalingfactor, For a composite comprised of 26.5/73.5 wt% of Al and
measurements were taken of the reacting footprint’s size PTFE, Casem et al. applied the Zerilli–Armstrong (Z–A)
for shot 11211. The footprint increased in diameter from model to experimental data for uniaxial compression
7.5(cid:5)0.5to8.65(cid:5)0.5mmbetween12and16lsatarate
of 288 m/s and at a rate of 144 m/s between 16 and 22 ls
(9.52 (cid:5) 0.5 mm). The final observable diameter for this 200
shot was 9.8 (cid:5) 0.5 mm, giving a rate of expansion for the Al (S-G)
PTFE (Z-A)
footprint of approximately 35 m/s. From the individual 73.5/26.5 PTFE/Al (Z-A)
frames the reaction light had the highest intensity during 175 73.5/26.5 PTFE/Al (lb-ROM)
73.5/26.5 PTFE/Al (up-ROM)
the period of 12–22 ls, correlating with the duration of 50/50 PTFE/Al (Z-A)
highest rates of the footprint’s expansion. 50/50 PTFE/Al (lb-ROM)
150 50/50 PTFE/Al (ub-ROM)
Computational Studies of Impact Ignition 125
in Modified Taylor Impact Tests a)
P
M
Modeling Setup gth ( 100
n
e
r
To model the early impact stages of high deformation that St
75
lead uptoinitiationofthecomposite, we implemented the
50
25
0
0 0.1 0.2 0.3 0.4 0.5
Plastic Strain (--)
Fig. 12 The modeled constitutive behavior of the constituents
(black), composite containing 73.5/26.5 wt% PTFE/Al (red), and
composite containing 50.0/50.0 wt% PTFE/Al (blue). Using the
Zerilli–Armstrong(ZA)modelparametersdeterminedbyCasemetal.
thebehaviorofthecompositecontaining73.5/26.5wt%(19.65/80.35
vol.%)PTFE/Alwasfoundtoliemorecloselytothelowerboundrule
ofmixtures.TheZAmodelparametersforcompositecontaining50.0/
Fig. 11 Subsample of shot 11211 at a time of 30 ls following the 50.0 wt% PTFE/Al were modified to have a response similar to the
initialimpactwiththeapproximateboundaryofthesapphireanvil’s lower bound rule of mixtures for that formulation (Color
viewingregion(20.32mmdiameter) figureonline)
123
J.dynamicbehaviormater.(2016)2:259–271 267
experiments at a strain rate of 2500 s(cid:7)1, and obtained fair behavior of the composite are plotted along-side those of
agreementbetweentheexperimentsandmodeling[15].We pure aluminum and PTFE in Fig. 12. In this figure the
compared this composite’s response to the Steinberg– stressvs.plasticstrainresponseofthecompositewith26.5/
Guinan (S–G) strength model for pure aluminum [19] and 73.5 wt% Al/PTFE more closely follows the response
Zerilli–Armstrong model for pure PTFE. We found the predicted by the lower-bound mixture. Thus, we applied
strengthbehavior ofthe compositeof Casem etal. tohave the same approach for a composite containing 50/50 wt%
amoresimilarresponsetothatofPTFEthanaluminumata Al/PTFE using the lower bound response as an idealized
strain rate of 2500 s(cid:7)1. This can be seen in Fig. 12, which reference high-rate stress-strain response for the surrogate
shows the stress-strain response of each material. This AlFA composite. We then used the reference curve to
observation is logical, based on the relative proportions of calibrate a new set ofZ–Amodelparameters (see Fig. 12)
PTFE and Al in this material. To further understand the at a strain-rate of 2500 s(cid:7)1, which were then used in our
behavior of the types of composites in this study we also simulations.Duetothefairlysmallsamplesizeusedinthe
used the following lower- [20] and upper-bound [21] rule modified Taylor impact tests we expect the strain-rates to
of mixtures relationships shown in Eqs. 1 and 2, respec- varyduringimpactandbenolargerthanoneortwoorders
tively, to determine the composite stress for the 26.5/73.5 of magnitude larger. The Z–A model has strain rate
wt% Al/PTFE composite. We then compared the result dependency built into the model, which for higher strain-
with the response found by Casem et al. [15] using the rates results in a shift of the stress-strain response of the
Zerilli–Armstrong model. AlFA composite upwards. For constant strain-rates of
25,000 and 250,000 s(cid:7)1 the initial strength is calculated to
(cid:2)1(cid:3) XN /
¼ i ð1Þ increasefrom39MPa,atastrainof2500s(cid:7)1,to50and64
X X
i¼1 i MPa, respectively. The Z–A model parameter values for
N each Al/PTFE composite, and 100 wt% PTFE are listed in
X
\X[ ¼ /X ð2Þ Table 1 and the S-G strength model parameters used for
i i
i¼1 aluminum are listed in Table 2. For the Gru¨neisen equa-
tion-of-state of each material a seven-term polynomial is
Here, / and X are the volume fraction and stress (deter-
i i
used [22], in which the pressure (P) is related to the
mined fromeither theS-Gmodelfor AlorZ–A model for
compression (l) and energy per reference volume (E) of
PTFE) at a particular overall composite strain level, e, of
the material through the relation:
each constituent, i. These bounds on the mechanical
Table1 Zerilli–ArmstrongstrengthparametersvaluesforPTFE[13],73.5/26.5wt%PTFE/Al[15],and50.0/50.0wt%PTFE/Al
Model PTFE 73.5/26.5wt% 50.0/50.0wt% Parameter
Parameter PTFE/Al PTFE/Al Units
b 0.0201 0.011672 0.012 1/K
0
b 0.000264 0.000139 0.00037 1/K
1
a 0.00478 0.0 0.00478 1/K
0
a 0.0000502 0.0 0.0000502 1/K
1
x0 (cid:7)3.6 (cid:7)3.0 (cid:7)3.0 –
x1 (cid:7)0.625 (cid:7)0.5 (cid:7)0.5 –
xp (cid:7)40.0 0.0 (cid:7)31.0 1/GPa
B 4.016 0.55 0.55 1/GPa
pa
B 20.0 0.0 20.0 1/GPa
pb
B 0.714 0.0 0.714 –
pn
B 0.0724 0.025 0.1 1/GPa
0pa
B 22.0 0.0 22.0 1/GPa
0pb
B 0.5 0.0 0.5 –
0pn
Table2 Steinberg–Guinan
A B G Y n b
strengthparametersvaluesfor 0 0
(1/GPa) (1/K) (GPa) (GPa) (–) (–)
aluminum(1100-O)[19]
0.0652 0.00616 27.1 0.04 0.27 400
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268 J.dynamicbehaviormater.(2016)2:259–271
P¼a þa lþa l2þa l3þ(cid:4)b þb lþb l2(cid:5)E ð3Þ
0 1 2 3 0 1 2
where a is a pressure constant, a , a , and a the bulk
0 1 2 3
moduli coefficients, b the Gru¨neisen coefficient, and b
0 1
and b corrections to the Gru¨neisen coefficient. However,
2
in the present work, a , b , and b were set to zero, sim-
0 1 2
plifying Eq. 3.
P¼a lþa l2þa l3þb E ð4Þ
1 2 3 0
Fig.13 Initialsetupofhalf-symmetrythree-dimensionalsimulations
Using the same approach implemented for the consti- andpelletmeshforanimpactangleof2(cid:6)
tutive behavior we defined a set of elastic and equation of
state model parameters to create a full set of parameters
that describe a surrogate composite material. This is used 2(cid:6), and 4(cid:6) andat 6 (left) and 8 ls(right)following impact
tointerrogatetheimpactinitiationmechanismsofanAlFA against the rigid steel anvil. The temperature and plastic
composite containing 50 wt% of nano-sized aluminum strain are plotted on the left- and right-hand sides of each
particles. The equation-of-state and elastic parameters for subfigure, respectively. Throughout this elapsed duration
each material are given in Table 3 along with their elastic the diameter of the pellet did not strain beyond the diam-
and shear moduli. eterofthecopperprojectile(outlinedinFig. 14).Atearlier
These parameters were implemented in three dimen- times (\6 ls), the regions of highest plastic strain and
sional Lagrangian simulations using the arbitrary Lagran- temperature were located in the interior and rear of the
gian–Eulerian hydrocode, ALE3D [23], to examine the pellet. Between 6 and 8 ls these regions moved forward,
state of the composite pellet at initiation times found in towards the impact face of the sample, with increasing
modifiedTaylorimpactexperiments.Thecopperprojectile velocity as the impact angle was increased. At impact
and composite pellet had the same geometry as experi- durations later than 9.4 ls, the pellet strained beyond the
ments, and an impact velocity of 146 m/s. Simulations copper projectile and the simulations became unstable.
varied the impact angle up to five degrees, which exceeds Results are not reported for these final stages of the
the observed range of angles, found in side-profile experi- simulations.
mentalimagesandincludedtheuseofafrictioncoefficient During a normal impact angle initiation event, the
of 0.2 between the anvil face, pellet, and projectile. The regionsofhigheststrainandtemperaturewerelocatedina
anvil’s constitutive behavior was modeled using the Stein- narrow ring on the impact face at an intermediate radius.
berg–Guinan strength model with parameters for 4340 Rc As the tilt angle is increased the region is more concen-
38 steel [19]. Figure 13 shows the initialization of a simu- trated towards the side of the pellet that first impacts the
lation with an impact tilt angle of two degrees. The axial anvil. Rather than taking on a ring appearance, as shown
andradialmeshsizesusedintheseriesofcalculationswere for the zero to very small tilt angle cases, the footprint of
15and30zones/mm,respectively.While,pelletfracturing this region is crescent-shaped and resembles that of the
andpost-reactioneffectsmaybeimportant,simulationsdid initial reaction zones in the sapphire anvilexperiments. At
notinclude any failure or chemistry models. 6ls,(see Figs. 8,9)the simulated increaseintemperature
((cid:4)416 K) is higher than the reported decomposition
Modeling Results and Discussions temperature of 357Kfor the fluorinated acrylate [8].By 8
lsthemaximumtemperatureincreasedto518K,however
In Fig. 14, the impact face of three-dimensional simula- there were only slight differences in the maximum
tions are shown for impacts with tilt angles of 0, 0.5(cid:6), 1(cid:6), observedtemperatureswithchangesinimpactangle.These
Table3 Elasticandseven-term
Materials q E G a a a b
polynomialEOSmodel 1 2 3 0
(g/cm3) (GPa) (GPa) (GPa) (GPa) (GPa) (–)
parametersforpolymerbinders
PTFE 2.15 1.02 0.36 1.5 0.5 35.0 0.59
26.5/73.5wt%Al/PTFE 2.29 1.26 0.45 1.2 0.36 68.0 0.86
50/50wt%Al/PTFE 2.40 1.81 0.64 1.53 0.005 71.0 1.20
TheEOSa ,b ,andb wereallsettozero.ParametersforPTFEweretakenfromWhiteandSpringer[24]
1 1 2
123