DTIC ADA588414: Multi-Scale Ballistic Material Modeling of Cross-Plied Compliant Composites

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4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Multi-scale ballistic material modeling of cross-plied compliant W911NF-09-1-0513
composites
5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER
622105
6. AUTHORS 5d. PROJECT NUMBER
M. Grujicic, G. Arakere, T. He, W.C. Bell, P.S. Glomski, B.A.
Cheeseman 5e. TASK NUMBER
5f. WORK UNIT NUMBER
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Clemson University
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The views, opinions and/or findings contained in this report are those of the author(s) and should not contrued as an official Department
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14. ABSTRACT
The open-literature material properties for fiber and polymeric matrix, unit-cell microstructural characteristics,
atomic-level simulations and unit-cell based finite-element analyses are all used to construct a new continuum-type
ballistic material model for 0/90 cross-plied highly-oriented polyethylene fiberbased armor-grade composite
laminates. The material model is formulated in such a way that it can
be readily implemented into commercial finite-element programs like ANSYS/Autodyn [ANSYS/Autodyn
15. SUBJECT TERMS
Polymer-matrix composites (PMCs), Damage tolerance, Finite element analysis (FEA), Armor-grade composites
16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 15. NUMBER 19a. NAME OF RESPONSIBLE PERSON
a. REPORT b. ABSTRACT c. THIS PAGE ABSTRACT OF PAGES Mica Grujicic
UU UU UU UU 19b. TELEPHONE NUMBER
864-656-5639
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Prescribed by ANSI Std. Z39.18
Report Title
Multi-scale ballistic material modeling of cross-plied compliant composites
ABSTRACT
The open-literature material properties for fiber and polymeric matrix, unit-cell microstructural characteristics,
atomic-level simulations and unit-cell based finite-element analyses are all used to construct a new continuum-type
ballistic material model for 0/90 cross-plied highly-oriented polyethylene fiberbased armor-grade composite
laminates. The material model is formulated in such a way that it can
be readily implemented into commercial finite-element programs like ANSYS/Autodyn [ANSYS/Autodyn
version 11.0, User Documentation, Century Dynamics Inc. a subsidiary of ANSYS Inc. (2007)] and ABAQUS/Explicit
[ABAQUS version 6.7, User Documentation, Dessault Systems, 2007] as a User Material Subroutine. Model validation
included a series of transient non-linear dynamics simulations of the transverse impact of armor-grade composite
laminates with two types of projectiles, which are next compared with their experimental counterparts. This comparison
revealed that a reasonably good agreement is obtained between the experimental and the computational analyses with
respect to: (a) the composite laminates’ capability, at different areal densities, to defeat the bullets with different impact
velocities; (b) post-mortem spatial distribution of damage within the laminates; (c) the temporal evolution of composite
armor laminate back-face bulging and delamination; and (d) the existence of three distinct penetration stages (i.e. an
initial filament shearing/cutting dominated stage, an intermediate stage characterized by pronounced filament/matrix
de-bonding/decohesion and the final stage associated with the extensive back-face delamination and bulging of the
armor panel).
The open-literature material properties for fiber and polymeric matrix, unit-cell microstructural characteristics,
atomic-level simulations and unit-cell based finite-element analyses are all used to construct a new continuum-type
ballistic material model for 0/90 cross-plied highly-oriented polyethylene fiberbased armor-grade composite
laminates. The material model is formulated in such a way that it can
be readily implemented into commercial finite-element programs like ANSYS/Autodyn [ANSYS/Autodyn
version 11.0, User Documentation, Century Dynamics Inc. a subsidiary of ANSYS Inc. (2007)] and ABAQUS/Explicit
[ABAQUS version 6.7, User Documentation, Dessault Systems, 2007] as a User Material Subroutine. Model validation
included a series of transient non-linear dynamics simulations of the transverse impact of armor-grade composite
laminates with two types of projectiles, which are next compared with their experimental counterparts. This comparison
revealed that a reasonably good agreement is obtained between the experimental and the computational analyses with
respect to: (a) the composite laminates’ capability, at different areal densities, to defeat the bullets with different impact
velocities; (b) post-mortem spatial distribution of damage within the laminates; (c) the temporal evolution of composite
armor laminate back-face bulging and delamination; and (d) the existence of three distinct penetration stages (i.e. an
initial filament shearing/cutting dominated stage, an intermediate stage characterized by pronounced filament/matrix
de-bonding/decohesion and the final stage associated with the extensive back-face delamination and bulging of the
armor panel).
REPORT DOCUMENTATION PAGE (SF298)
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Continuation for Block 13
ARO Report Number 56526.3-EG
Multi-scale ballistic material modeling of cross-p ...
Block 13: Supplementary Note
© 2009 . Published in Composites Part B: Engineering, Vol. Ed. 0 40, (6) (2009), (, (6). DoD Components reserve a royalty-free,
nonexclusive and irrevocable right to reproduce, publish, or otherwise use the work for Federal purposes, and to authroize
others to do so (DODGARS §32.36). The views, opinions and/or findings contained in this report are those of the author(s) and
should not be construed as an official Department of the Army position, policy or decision, unless so designated by other
documentation.
Approved for public release; distribution is unlimited.
Composites:PartB40(2009)468–482
ContentslistsavailableatScienceDirect
Composites: Part B
journal homepage: www.elsevier.com/locate/compositesb
Multi-scale ballistic material modeling of cross-plied compliant composites
M. Grujicica,*, G. Arakerea, T. Hea, W.C. Bella, P.S. Glomskia, B.A. Cheesemanb
aInternationalCenterforAutomotiveResearchCU-ICAR,DepartmentofMechanicalEngineering,ClemsonUniversity,Clemson,SC29634,UnitedStates
bArmyResearchLaboratory–SurvivabilityMaterialsBranch,Aberdeen,ProvingGround,MD21005-5069,UnitedStates
a r t i c l e i n f o a b s t r a c t
Articlehistory: Theopen-literaturematerialpropertiesforfiberandpolymericmatrix,unit-cellmicrostructuralcharac-
Received2December2008 teristics,atomic-levelsimulationsandunit-cellbasedfinite-elementanalysesareallusedtoconstructa
Receivedinrevisedform21January2009 newcontinuum-typeballisticmaterialmodelfor0(cid:2)/90(cid:2)cross-pliedhighly-orientedpolyethylenefiber-
Accepted7February2009
based armor-grade composite laminates. The material model is formulated in such a way that it can
Availableonline7May2009
bereadilyimplementedintocommercialfinite-elementprogramslikeANSYS/Autodyn[ANSYS/Autodyn
version11.0,UserDocumentation,CenturyDynamicsInc.asubsidiaryofANSYSInc.(2007)]andABA-
Keywords:
QUS/Explicit[ABAQUSversion6.7,UserDocumentation,DessaultSystems,2007]asaUserMaterialSub-
A.Polymer-matrixcomposites(PMCs)
routine.Modelvalidationincludedaseriesoftransientnon-lineardynamicssimulationsofthetransverse
B.Damagetolerance
impactofarmor-gradecompositelaminateswithtwotypesofprojectiles,whicharenextcomparedwith
C.Finiteelementanalysis(FEA)
Armor-gradecomposites theirexperimentalcounterparts.Thiscomparisonrevealedthatareasonablygoodagreementisobtained
betweentheexperimentalandthecomputationalanalyseswithrespectto:(a)thecompositelaminates’
capability,atdifferentarealdensities,todefeatthebulletswithdifferentimpactvelocities;(b)post-mor-
temspatialdistributionofdamagewithinthelaminates;(c)thetemporalevolutionofcompositearmor
laminateback-facebulginganddelamination;and(d)theexistenceofthreedistinctpenetrationstages
(i.e.aninitialfilamentshearing/cuttingdominatedstage, anintermediate stagecharacterized bypro-
nounced filament/matrix de-bonding/decohesion and the final stage associated with the extensive
back-facedelaminationandbulgingofthearmorpanel).
(cid:3)2009ElsevierLtd.Allrightsreserved.
1.Introduction The fiber-reinforced polymer-matrix composites like the one
describedaboveinwhichthemainfiguresofmeritaretheirden-
Fiber-reinforced polymer-matrix composites are among the sity-normalizedstiffness(i.e.specificstiffness)anddensity-normal-
most advanced commercially-available materials. While they are ized strength (i.e. specific strength) are commonly referred to as
widely used in aerospace and defense-related industries, their ‘‘structural-grade”composites.Manyblast-andballistic-protection
applicationinconstruction,automotiveandsporting-goodindus- systemsinmilitaryandcivilianapplicationsare,ontheotherhand,
tries is also quite common. The main reason for the aforemen- madeofanotherclassoffiber-reinforcedpolymer-matrixcompos-
tioned widespread use of the composite materials is their ability ites,theso-called‘‘armor-grade”composites[3,4].Thelatterclass
tosimultaneouslymeetavarietyoffunctionalandmanufacturing ofcomposites generallyis optimized withrespect to itsballistic-
requirements.Forexample,thenewBoeing787Dreamlinerispri- impactprotectionresistance,i.e.withrespecttoitsenergyabsorb-
marily made of carbon-fiber-reinforced epoxy-matrix composites ing capability. Consequently,themost commonlycitedfigures of
which, in addition to having outstanding mechanical properties, meritin these materials are: (a) a critical level of the projectile’s
do notsuffer fromthe similarmanufacturing constraintsas their velocityortheprojectile’skineticenergy(generallyreferredtoas
metallic counterparts/alternatives, allowing a higher degree of the ‘‘ballistic limit”) below which no full perforation takes place
optimizationofthe787aerodynamics.Furthermore,thecomposite [5,6]and(b)anextenttowhichmaterialballistic-protectionresis-
airframesweighlessandarestrongerthanconventionalairframes, tanceiscompromisedinthematerialsystemswhicharepartially
which lead to improvements in the vehicle’s operating efficiency penetratedbyprojectile(s)orwhosestrike-facesurfaceisdamaged
and performance. Lastly, carbon-fiber-reinforced epoxy-matrix bytheprojectile(s).
compositestendtoresistcorrosionandfatigue,thetwophenom- The armor-grade composites are generally constructed using
enawhichare well-establishedtocause gradualdegradationand highspecific-modulus/highspecific-strengthpolymericfiberssuch
ultimatefailureofmetallicairframes. asaramid(e.g.Kevlar(cid:4),Twaron(cid:4),etc.)ororientedpolyethylenefi-
bers (e.g. Spectra(cid:4), Dyneema(cid:4), etc.) with an outstanding impact
resistance [7–11]. The fibers, in the form of either woven fabrics
* Correspondingauthor.Tel.:[phone];fax:[phone].
E-mailaddress:[email protected](M.Grujicic). or in the form of 0(cid:2)/90(cid:2) cross-plied collimated continuous
1359-8368/$-seefrontmatter(cid:3)2009ElsevierLtd.Allrightsreserved.
doi:10.1016/j.compositesb.2009.02.002
M.Grujicicetal./Composites:PartB40(2009)468–482 469
filaments, are embedded in the resin/polymer matrix. To attain shearing/cutting and fiber tensile failure. In the cross-plied lami-
maximum utilization of the inherently-high transverse-impact nates, fibers in the top plies are typically found to fail by shear-
resistance of the fibers, the polymer-matrix content does not ing/cutting, primarily along the edges of the projectile. Fibers
typicallyexceed20%byvolume.Asaresultoftheverylowresin locatedinthebacklayersofthelaminates,ontheotherhand,gen-
content, these composites remain flexible/compliant to relatively erallyfailintensionalthoughinthinlaminates,thelateralmotion
high laminate thicknesses. Penetration resistance of the armor- offibersand/orfiberpull-outratherthanfibertensilestrainingto
gradecompositesisfrequentlyincreasedthroughtheuseofhybrid fractureissometimesobserved.
structures in which a hard metallic or ceramic strike-plate is (e)Thedelaminationinthecross-pliedSpectrafiber-reinforced
attachedtothefrontofanarmor-gradecompositelaminate. compositelaminatesistypicallyfoundtoresemblethe‘‘generator
Armor-gradecompositelaminatesbasedonaramidfiber-rein- strip” phenomenon [22] seen in glass fiber-reinforced epoxy-ma-
forcedphenolic-poly-vinyl-butyralresinandon0(cid:2)/90(cid:2)cross-plied trixstructural-gradecomposites.Thatis,undertransverseimpact,
orientedpolyethylenefiber-reinforcedvinyl-esterarewidelyused theprojectilepushesastripofthefirstlaminatowardtherearof
inhardpersonnel-armorsystems(e.g.protectivehelmets)forpro- thelaminatewhichinducesshearcracksintheresinmatrixparal-
tection against fragments from exploding munitions [10–15]. leltothefibersandappliesatransverseloadtothesecondlamina.
These armor-grade composites are also increasingly being used This,inturn,causesseparationbetweenthefirsttwolaminae,i.e.
for ballistic protection in light-weight armored vehicles, helicop- delamination.Aftertheaforementioneddelaminationprocesshad
ters, patrol boats and transportable shelters (e.g. command shel- takenplacesuccessivelythroughtheentirethicknessofthelami-
ters) [10]. Over the past decade, considerable efforts have been nate via the same mechanism and penetration of the laminate
investedincarryingoutvariousexperimentalinvestigationsinor- hasoccurred,narrowstripsofdamagezoneremainvisibleunder
der to identify and elucidate various penetration-failure mecha- transmitted light and the strips are found to tend to follow the
nisms of the armor-grade fiber-reinforced composites under respectivefiberorientationinthepanel.Thesestripstypicallycon-
transverse impact loading and to compare and contrast these tainnumerousmatrix/fiberinterfacecracks.Inaddition,acircular
mechanismswiththoseoperatingintherelatedresin-freefabrics delaminationzoneisgenerallyseenaroundtheperforationhole.
and resin-rich structural-grade composites. The main results ob- (f) In contrast to the case of cross-plied fiber-reinforced com-
tainedintheseinvestigationscanbesummarizedasfollows[16– positelaminates, fabric-reinforced laminatesarefoundtoexhibit
23]: muchlesslateralmovementsofreinforcingfibersduringthepen-
(a) In sharp contrast to the penetration of resin-free fabrics etration of the projectile [3,4]. Even in thin panels, fibers appar-
whichisdominatedbythesuccessivefractureofindividualyarns ently failed due to shearing/cutting in the laminae near the
along the periphery of the penetrator head and by the side-way/ strike-faceandintensionattherearofthecompletelypenetrated
lateralmovementoftheyarnswhichenablesthemtoslipofffrom laminates.Thepresenceofanarrowstripofthefirstlaminapushed
the penetrator, the penetration of armor-grade composites is forward by the penetrator is generally not observed. Instead, the
mainlygovernedbythefailureofprincipalyarns(theyarnswhich delaminationzonesareobservedpreferentiallyalongthetworein-
areindirectcontactwiththepenetratorhead).Thisobservationis forcement directions of woven fabric. However, these damage
attributedtotheeffectofresinmatrixonreducingyarnmobility zones are closely integrated with the circular delamination zone
whichpreventsthemfromslippingofffromthepenetrator.Ingen- aroundtheperforationhole.Theoccurrenceoflessanisotropicpat-
eral,stifferresinmatrices(e.g.vinyl-estervs.polyurethane)tendto tern of delamination was linked with the presence of resin-rich
constraintheyarnmovementtoagreaterdegreeandtoforcethe pockets between the reinforcing layers and with a greater con-
penetratortoengageandfracturemoreyarnsduringpenetration. strainttomatrixcrackpropagationparalleltothefibers/yarns.
This typically results in improved ballistic-protection resistance (g) Up to the thickness of (cid:2)3mm, the kinetic energy for full
of armor-grade composites and is the reason that armor-grade perforationofarmor-gradecompositeshasbeenfoundtodepend
compositesreinforcedwithwoven-yarnfabricaregenerallyfound onthelaminatethicknessinawaysimilartothatobservedinduc-
to possess a higher energy-absorption potential than their resin- tilemonolithicmaterials(e.g.poly-carbonateoraluminum).
free fabric counterparts. However, excessive confinement of the Thefull-perforationkineticenergyvs.laminatethicknessrela-
yarns/filaments due to overly-high matrix stiffness and/or exces- tionship, however, was found to be somewhat non-linear. This
sive amounts of the matrix may have a deleterious effect on the finding has been attributed to the unique mode of tensile failure
ballistic-protection performance of this class of composites. The seeninthesematerialsforwhichthecriticallevelofkineticenergy
latter effect is related to the fact that highly confined fibers are forfullperforationisloweredbythefiber/yarnmobility.
morelikelytofailintransverseshearbeforeexperiencinganysig- Thefirstuseoffiber-basedcomposites(primarilynylon(poly-
nificantextensionsinthelongitudinaldirection. amide)fabricandE-glassfiber/ethylcellulosecomposites)inbody
(b)Sincetheenergyabsorbedbythearmor-gradecompositeis armorsystemsinplaceofthetraditionallyusedmetallicsolutions
foundtoscalewiththenumberofbrokenyarnsinitsfabriccon- canbetracedbacktotheKoreanWar[24].Although,primarilydue
stituent, fiber tensile straining and ultimate fracture is believed totheirlowcost,nylonandE-glassfibersarestillbeingusedtoday,
tobethedominantmechanismforabsorptionoftheprojectileki- high-performancepolymericfibersarenowthestandardinmost
neticenergy. fiber-reinforced body-armor applications. The high-performance
(c) In addition to fiber fracture, both woven-fabric-reinforced polymericfibersusedtodayarecharacterizedbysubstantiallyim-
andcross-pliedfiber-reinforcedcompositelaminatesaregenerally proved strength, stiffness and energy-absorbing capacity. Among
foundtoincludeadditionalcomplexfailureprocessessuchas:(i) thesehigh-performancefibersthemostnotableare:(a)poly-ara-
delamination, (ii) a plug punch out, (iii) resin matrix cracking, mids(e.g.Kevlar(cid:4),Twaron(cid:4),Technora(cid:4));(b)highly-orientedultra
and (iv) fiber pull-out. These failure modes are also typically ob- high molecular weight polyethylene, UHMWPE (e.g. Spectra(cid:4),
served in conventional structural-grade composites reinforced Dyneema(cid:4)); (c) poly-benzobis-oxazole, PBO (e.g. Zylon(cid:4)); and (d)
withglassorcarbonfibers. poly-pyridobisimi-dazole, PIPD (e.g.M5(cid:4)). Whentested in tension,
(d) In the case of multi-ply armor-grade composite laminates allthesematerialsdiffersignificantlyfromthenylonfibers,having
reinforcedwitheithercross-pliedcollimatedSpectrafibersorwith veryhighabsolutestiffness,extremelyhighspecificstrength,and
wovenSpectrafabrics,thefollowingfracturemodesaremostoften quitelow(<4%)strains-to-failure.Thesefibersessentiallybehave,
observed [1]: (i) sequential delamination, (ii) plug punch out in- in tension, as rate-independent linear elastic materials. When
ducedbythethrough-the-thicknessshear,and(iii)combinedfiber testedintransversecompression,however,thesefibersaresimilar
470 M.Grujicicetal./Composites:PartB40(2009)468–482
tonylonandcanundergolargeplasticdeformationwithoutasig- Areviewofthepublic-domainliteraturecarriedoutaspartof
nificantlossintheirtensileload-carryingcapacity.Thisbehavioris thepresentworkrevealedtheexistenceofseveralmaterialmodels
quitedifferentfromthatfoundincarbonorglassfibers,whichtend forarmor-gradecomposites[25–30].Whilesuchmodelshavepro-
toshatterundertransversecompressionloadingconditions. vided an important insight into the roles of a number of factors
Theballisticperformanceofhigh-performancepolymericfibers mentionedabove,theysufferfromthreemajorshortcomings:(a)
is,ingeneral,quantifiedwithrespecttotheirabilityto:(a)absorb some are more phenomenological, i.e. less physically-based in
the projectile’s kinetic energy locally and (b) spread out the ab- their character; (b) others require the knowledge of a relatively
sorbedenergyfastbeforelocalconditionsforthefailurearemet. largenumberofparameters;and(c)maynotveryefficientcompu-
In simple terms, the ability of high-performance fibers to absorb tationally.Inadditiontothemodelsmentionedabove,purelyphe-
energypertheirunitmass,E ,isrelatedtothefibertenacity/fail- nomenological models [e.g. 31] also exist in the literature. Such
sp
urestrength,r ,thefiberstrain-to-failure,e ,andthefiberden- models are the result of extensive experimental efforts and typi-
fail fail
sity,q,as: cally have, within the same family of armor-grade composite
E ¼0:5r e =q ð1Þ materials,ahighpracticalutility.However,theyprovidenoinsight
sp fail fail into the complicated physics of projectile/armor interactions and
The ability of fibers to spread out energy is governed by their cannotbeusedacrosstheboundariesofdifferentarmor-typecom-
speedofsound,v ,whichisdefinedintermsoftheiraxialmod- positefamilies.
sound
ulusofelasticity,E,andtheirdensityas: Toovercometheaforementionedlimitationsofthetwogroups
ofmaterialmodels,anewmulti-scalephysically-basedcomputa-
v ¼ðE=qÞð1=2Þ ð2Þ
sound tionally-efficientmaterialmodelforUHMWPE-filament(e.g.Spec-
InFig.1,thetwoaforementionedballisticperformanceparam- tra(cid:4),Dyneema(cid:4),etc.)basedarmor-gradecompositesisdeveloped,
etersaredisplayedforthemost-commonlyusedhigh-performance parameterized and validated in the present work. A preliminary
fibers. A summary of the key properties of the same set of high- version of this model without details regarding the atomic-level
performancefibersisprovidedinTable1. analysis of the filament/matrix interfacial bonding/de-bonding
While the results displayed in Fig. 1 clearly reveal a high bal- and without detailed validation was previously reported Grujicic
listic potential of the high-performance fibers in general (and etal.[32].Sinceitisgenerally-establishedthatfortheUHMWPE
specificallyofthehighly-orientedUHMWPEfibers,thetypeoffi- fiber-basedarmor-gradecomposites,asubstantiallyhigherballis-
ber-reinforcements considered in the present work), full utiliza- tic-protectionperformanceisobtainedwhensuchfibersareused
tion of this potential in armor-grade composites turned out to as 0(cid:2)/90(cid:2) cross-plied layers of highly-oriented filaments rather
beaformidablechallengebecauseanumberofadditionalfactors thanwovenfabrics,onlytheformercomposite-laminatearchitec-
(e.g. fabric/ply structure/architecture, ply areal density, fiber-to- turewillbeaddressedinthepresentwork.Inpassing,itshouldbe
fiber/yarn-to-yarn and fiber/yarn-to-projectile friction, type of mentionedthatitisbelievedthatthedeflectionofstresswavesat
polymeric matrix, composite processing and fabrication condi- theyarn/yarnorfiber/fibercross-everpointsinwovenfabric(the
tions, shape, mass and mechanical properties of the projectile process which lowers the ability of fibers to spread out energy
to be defeated, etc.) become important. To overcome these chal- along their axis) is the main reason for their inferior ballistic
lenges, the development of flexible-armor systems has started to performance.
relyincreasinglymoreontheuseoftransientnon-lineardynam- Asstatedabove,themainobjectiveofthepresentworkwasto
ics computational analyses of the ballistic response of armor develop, parameterize and validate, (against the relevant experi-
when impacted with high-speed projectiles. For these analyses mental results), a simple physically-based computationally-effi-
to yield reliable predictions and for them to be used as comple- cient continuum-level material model for a prototypical 0(cid:2)/90(cid:2)
ments to the accompanying experimental investigations, high- cross-plied oriented polyethylene fiber-based armor-grade com-
fidelity physically-based material models for the armor-grade posite material. While developing this model, unit-cell level fi-
composite materials must be available. nite-element analyses of the meso-scale material mechanical
response and properties and atomic-level simulations of the fila-
ment/matrix bonding/de-bonding had to be employed giving the
presentapproachamulti-lengthscalecharacter.
14 Itshouldbenotedthatwithinafullymulti-scalecomputational
PIPD PBO
approach, the underlying boundary-value problem is set-up and
12 simultaneously solved at several length scales (e.g. at atomistic,
s HMWPE
m/10
k
d, Table1
n Typicalmechanicalpropertiesofhigh-performancefibers.
u 8 Aramid
o
S Fiber Failurestrength Failure Axialmodulus Density
of LCP type (GPa) strain (GPa) ðkg=m3Þ
d 6
e Aramid 2.8–3.2 0.015– 60–115 1390–1440
e S2-Glass
p 0.045
S 4 HMWPE 2.8–4.0 0.029– 90–140 970–980
0.038
LCP 2.7–2.9 0.033– 64–66 1400–1420
2 Nylon 0.035
PBO 5.4–5.6 0.024– 270–290 1540–1560
0.026
0
0 10 20 30 40 50 60 70 PIPD 3.9–4.1 0.011– 320–340 1690–1710
Mass-basedEnergyAbsorptionCapacity,kJ/kg 0.013
Nylon 0.06–0.08 1.5–2.5 1.0–1.5 1070–1170
S-glass 4.64–4.66 0.053– 82–92 2470–2490
Fig.1. Soundspeedvs.mass-basedenergyabsorptioncapacityforanumberof 0.055
high-performancefibers.
M.Grujicicetal./Composites:PartB40(2009)468–482 471
meso,macro).Thisapproachwillbeadoptedinourfuturework.In basedmulti-scalematerialmodelforaprototypicalsingle-lamina
the present investigations, a simpler, and computationally more 0(cid:2)/90(cid:2) cross-plied uni-directional UHMWPE-filament based ar-
efficient yet less accurate approach was adopted. That is, results mor-grade composite. Also details regarding the implementation
from the experimental investigation of Iremonger [36] are used of the model into a material-user subroutine suitable for use in
to infer the main deformation and fracture mechanisms of the commercialfinite-elementpackagesarepresented.Thebasicidea
composite material under investigation and a coupled meso- behind the unit-cell based approach is that the mechanical re-
scale/continuumlevelmodelisconstructed.However,criticalfila- sponse of the unit-cell (consisting of high-stiffness/high-strength
ment/matrix de-bonding parameters needed in this model were polymeric filament segments and a compliant polymeric matrix)
determinedinaseparateatomiclevelcomputationalinvestigation, can be smeared out (homogenized) into an equivalent response
describedinAppendixA. of a (anisotropic) continuum material. A simple schematic of the
The organization of the paper is as follows: Details regarding unit cell which is used to represent 0(cid:2)/90(cid:2) cross-plied unidirec-
thecomputationalproceduresemployedtodevelopanewunit-cell tional UHMWPE-filament based armor-grade composites allotted
continuum-damagebasedmaterialmodelforaprototypical0(cid:2)/90(cid:2) to a single filament crossover is depicted in Fig. 2(a). Its contin-
cross-plieduni-directionalUHMWPE-filamentbasedarmor-grade uum-level material point counterpart is represented in Fig. 2(b).
composite and the implementation of this model into a material Withinthecontinuum-materialframework,filamentsarenotrep-
usersubroutinesuitableforuseincommercialfinite-elementpro- resented explicitly but rather by two material directions whose
gramsarepresentedinSection2.Theformulationofasimplepro- orientations are denoted in terms of material vectors, g and g .
1 2
jectile-target impact problem used to validate the new material (Pleasenotethatvectorsaredenotedusingaboldlower-casefont,
modelisdescribedinSection3.Mainresultsobtainedinthecur- tensorsusingaboldupper-casefontwhilescalarsusinganon-bold
rentworkarepresentedanddiscussedinSection4.Themainsum- font.) The ‘‘unit-cell” term is used to denote the basic structural
marypointsandconclusionsresultingfromthepresentworkare block so that a piece of the armor-grade composite material can
listed in Section 5. A brief discussion regarding the atomic-scale
computationalanalysisusedtoinvestigatefilament/matrixbond-
ing/de-bondingbehaviorispresentedinAppendixA.
2.Materialmodelformulationandimplementation
Inthissectionanditssubsections,adetailedaccountisgivenof
theprocedureusedtodevelopanewunit-cellcontinuum-damage
Fig.2. Therelationshipbetweenaunitcellandthecorrespondingmaterialpointin Fig.3. Typicalfinite-elementmeshesusedintheunit-cellcomputationalanalyses
ananisotropiccontinuum. todiscretize:(a)thetwofilamentsand(b)thematrix.
472 M.Grujicicetal./Composites:PartB40(2009)468–482
Table2 Anexampleofthefinite-elementmeshesusedintheunit-cell
TheorthotropiclinearelasticmaterialdataforUHMWPEfilaments[31]. computationalanalysesisdisplayedinFig.3(a)and(b).20,847first
E11 E22 E33 G12 G13 G23 m12 m13 m23 order tetrahedron elements (ABAQUS/Explicit designation C3D4)
(GPa) (GPa) (GPa) (GPa) (GPa) (GPa) are used to discretize each of the two filament segments,
118.0 6.0 6.0 6.0 6.0 6.0 0.3 0.3 0.4 Fig.3(a),while21,606elementsofthesametypeareusedtodis-
cretizethematrix,Fig.3(b).Bondingbetweenthematrixandthe
Axialfailurestrain=0.05;transverseshearstrength=350MPa.
filaments is represented using 7056 ‘‘cohesive” elements, (ABA-
QUS/ExplicitdesignationCOH3D6).
The polymeric filaments (assumed to be based on the
be considered as a result of the repetition of this block in three
UHMWPE) are modeled as orthotropic (more precisely as planar
orthogonaldirections.
isotropic)linearelasticmaterials(uptothepointoffailureunder
Couplingbetweenthecontinuummaterialformulationandthe
axialtensionortransverseshear)withtheuniquematerialdirec-
unit-cellgeometryandmechanicalresponseisdoneinthefollow-
tionbeingalignedwiththefilamentaxis.Asummaryoftheelastic
ingway:(a)thedeformationstateofacontinuummaterialpoint
andfailurepropertiesofthefilamentmaterialisprovidedinTable
(asquantifiedbythecorrespondingdeformationgradient)isused
2.
toupdatetheunit-cellgeometry;(b)theupdatedunit-cellgeom-
The polymeric matrix (assumed to be based on styrene–iso-
etryandthestateofthecontinuummaterialattheendofthepre-
prene–styrenetri-blockcopolymer[33])ismodeled,duetoatten-
vious time increment are used to update the extent of structural
dant high-deformation rate conditions, as a linear isotropic
damage in the unit cell; and (c) the updated material state ob-
materialwithaYoung’smodulusof3GPaandaPoisson’sratioof
tainedinpoint(b)isthenusedtocomputethestressstateatthe
0.4.
endofthecurrenttimeincrement.
Bondingbetweenthefilamentsandthematrixismodeledusing
It must be recognized that in order for the aforementioned
traction vs. interfacial displacement–discontinuity relations (one
approach to be valid (i.e. in order for homogenization of the ar-
for the normal and one for the tangential displacements). These
mor-grade composite unit-cell response to be justified), the
two relations are characterized by a linear traction vs. displace-
characteristiclengthsinthenumericalanalysisinwhichthemodel
ment/discontinuity relation unto the point of damage initiation
isused(e.g.theprojectileandthetargetdimensionsinaprojectile/
and with a linear ‘‘Downhill” post damage relationship. Conse-
targetimpactproblemanalyzedinthepresentworkandtheasso-
quentlythetwomodes‘‘NormalandShear”ofinterfacial-bonding
ciatedstress/straingradientranges)must belargein comparison
damage are each characterized by three parameters: (a) critical
totheunit-celledgelengths.Inmostpracticalsituations,thisap-
normalorshearinterfacial-displacementdiscontinuitiesatwhich
pearstobethecasesincetheunitcelledgelengthisintherange
damage initiation begins; (b) the corresponding normal or shear
between10and30lm.
interfacialstrengths;and(c)normalorshearinterfacial-displace-
ment discontinuities at which complete filament/matrix decohe-
2.1.Meso-scaleunit-celllevelfinite-elementanalyses sion takes place. A summary of the interfacial cohesion
parameters used in the present work is given in Table 3. These
Thesalientfeatureoftheproposedcomputationalapproachis parametersweredeterminedinaseparatemolecular-staticsbased
thatthemechanicalresponseofacontinuum-levelmaterialpoint investigationofatomic-levelmechanicalpropertiesofthecompos-
(corresponding to a unit cell in the armor-grade composite) and ite materials consisting of the unidirectional UHMWPE filaments
the accompanying changes in constituent materials (primarily and an amorphous polymeric matrix. Few details regarding the
thoseassociatedwiththefilament/matrixinterfacialde-bonding) atomic-levelanalysiscarriedoutandtheresultsobtainedarepre-
can be inferred by carrying out a series of meso-scale finite-ele- sentedinAppendixA.Theprocedureusedcloselyfollowsthatpre-
ment analyses pertaining to relatively simple mechanical tests sentedinourrecentwork[34]inwhichatomiclevelpropertiesof
of the unit cell. In these analyses, a detailed representation of composite materials consisting of multi-walled carbon nanotube
the unit-cell microstructure is considered. In this section, details reinforcements and a poly-vinyl-ester-epoxy matrix were
are presentedregarding the geometrical models usedin the con- investigated.
struction of the unit cell, material properties/models assigned to Interactionsbetweenthefilamentsandthematrixafterdecohe-
thefilamentsegments,matrixandthefilament/matrixinterfacial sionareaccountedforthrougha‘‘Hard”pressurevs.overclosure
bonding/de-bonding, and the finite-element analyses used to algorithmwithinwhichtheinteractingbodiesmustbeincontact
determine the mechanical response and the material evolution beforetheycaninteractandthepressurelevelsthatcanbetrans-
under different loading conditions. As will also be shown in this mitted through the contact interactions are unbounded. Relative
section,toobtainquantitativeinformationaboutthefilament/ma- sliding of the contacting bodies is opposed by a frictional force
trix interfacial bonding/de-bonding, atomic-level simulations basedonaconstantfrictioncoefficient.
were employed. This portion of the work is covered in more de- The following simple mechanical tests were carried out using
tails in Appendix A. It should be noted that, as correctly themeso-scale unit-cellbasedfinite-elementapproachdescribed
pointedoutbyoneofthereviewersofthepresentwork,interfa- above: (a) uniaxialtension along the axis of one of the filaments
cialde-bondingparameterscanbealsomeasuredexperimentally (i.e.alongthedirections1or2);(b)uniaxialtensioninadirection
using one of the methods such as the so-called ‘‘fiber push-out” normaltothesingle-laminasurface(direction3);(c)in-plane1–2
method. shear;and(d)thetransverseshear.
Table3
Normalandshearfilament/matrixde-bondingparametersusedinthepresentwork.
Normalde-bonding Shearde-bonding
Initiationdisplacement– Bond Completede-bondingdisplacement– Initiationdisplacement– Bond Completede-bondingdisplacement–
discontinuity(lm) strength discontinuity(lm) discontinuity(lm) strength discontinuity(lmÞ
(MPa) (MPa)
0.05 18.0 1.1 0.9 23.0 2.1
M.Grujicicetal./Composites:PartB40(2009)468–482 473
It is well-established that the presence of free surfaces (along
which loading is applied) in isolated unit cells, like the one used
inthepresentwork,canaltertheunitcellmechanicalresponserel- γ12/γ12,init
ative to the one displayed by ‘‘bulk” unit cells subjected to the
same mode of loading. To provide the first-order assessment of
these effects, few mechanical-test simulations were carried out γ12,fail/γ12,init
usingablockof3(cid:3)3(cid:3)3=27unitcells.Theresultsobtainedshow
that the ‘‘surface-loading effects” can be significant. However,
these effects were not included in the current rendition of the D=1.0
material modelsince thiswould have required thelevel of effort D=0.0 1,0
notavailableinthepresentwork.
For each of the aforementioned tests, a series of loading–
unloading–reloadingcycleswasappliedinordertodetecttheon- NNoo 1,0 ε33,fail/ε33,init
setofinterfacialde-bondingandtheresultingdegradationinthe DDaammaaggee ε33/ε33,init
correspondingcontinuum-materialstiffnessparameters.Todeter- A
minehowonemodeofloadingmayaffectalltheunit-cellstiffness
parameters,loadingisdoneinonemodewhilesubsequentreload- Damage B
ingisdoneinallthemodes(oneatatime).Itshouldbenotedthat C
simulations of the mechanical test mentioned above were done
underloadingratescomparabletothosetypicallyencounteredin
Complete
the bullet/target impact problems. Consequently, the inertial ef-
Failure
fects were accounted for, at least to the first order of
approximation.
The results obtained suggest that interfacial de-bonding is
mainlycausedbythethrough-the-thicknesstension(indirection Fig.4. Aschematicofthecomputationalprocedureusedtodeterminetheonset
3) and by the in-plane shear (1–2 shear) and that E ; G ; G andtracktheprogressofmaterialdamage(interfacialde-bonding)withintheunit
33 12 23
andG aremostlydegradedbyinterfacialde-bonding.Inaddition, cell.
31
these four stiffness parameters are found to degrade essentially
linearlywiththeextentofinterfacial-bondingdamage,D.
present model is not suitable for use in the calculations dealing
In accordance with the aforementioned observations and the
withlowloading-ratestructuralresponseofthesematerials.
atomic-levelinterfacialde-bondinginitiationparameterslistedin
Table 3, the following strain-based damage initiation criterion
2.2.Determinationoftheunit-cellcurrentgeometryandarchitecture
wasderived:
(cid:2) e (cid:3)2 c !2 As discussed earlier, a critical step in the development of the
33 þ 12 ¼1 ð3Þ present continuum-damage material model is establishment of
e c
33;init 12;init the relationship between the continuum-level material-point
wheree andc arepurenormalandshearstrainsatwhich deformationstateandthemeso-scaleunit-cellgeometry.Thisto-
damage3i3n;iintitiationi1s2;fiinritstobserved.Ina e33 vs. c12 plot,Eq.(3)de- piciscoveredinthepresentsection.
e33;init c12;init Ingeneralsixindependentgeometricalparametersareneeded
finesaunit(failure-initiation)circle.Withinthesameplane,thecon-
to fully describe the current geometry of the unit cell. These
ditionatwhichcompletedamage-induceddegradationtakesplace
parameters include: (a) The three unit-cell edge lengths,
isdefinedbyanellipseintheform:
a ði¼1—3Þ;(b)thein-planeshearinter-filamentincludedangle,
i
h;and(c)thetwoout-of-planeshearangles,/andw.Inthissection
(cid:2) e (cid:3)2 c !2
33 þ 12 ¼1 ð4Þ itisshownhowtheseparametersarerelatedtothecontinuum-le-
e33;fail c12;fail vel deformation state of the material point corresponding to the
unitcellinquestion.
At the continuum level, the state of deformation at a given
wheree andc arepurenormalandshearstrainsatwhich
33;fail 12;fail materialpointisdescribedbythedeformationgradient,F,whose
completedegradationðD¼1Þtakesplace.
components in a Cartesian coordinate system are defined in Eq.
Whentheðe ;c Þstrainstateofamaterialpoint(e.g.pointB
33 12 (5)inRef.[32]:Next,alsoatthecontinuumlevel,the0(cid:2)and90(cid:2)
inFig.4)liesbetweenthedamageinitiationcircleandthefailure
filamentscanbedescribedusingvectorsa ði¼1;2Þalignedwith
ellipse, the corresponding extent of material damage is defined i
astheratiooflinesegmentsABandACindicatedinFig.4.Thefour
continuumleveldamageparameterse ; e ; c andc
33;init 33;fail 12;init 12;fail Table4
are determined using the unit-cell finite-element analyses de- Experimental [36] and the corresponding computational [Present Work] results
scribed in this section. The values of these four parameters are: pertainingtothesuccessofarmor-gradecompositetestpaneltostopaM855bulletat
0.01,0.04,0.01and0.04,respectively. differentinitialbulletvelocities.
Itshouldbenotedthat,ascorrectlypointedoutbyoneofthe Test-panel Arealdensity Bulletvelocity(m/s)
reviewersofthepresentwork,themechanicalresponse(including thickness(mm) (kg=m2)
600 700 800 900
thefailurebehavior)ofcompositematerialsisloading-ratedepen-
4.2 4 – – – G/G
dent.Sincethepresentmaterialmodelisintendedtobeusedonly
11 10.5 G/G G/G G/G G/G
inthehighloading-rateregime(theregimewhichdominatesbul- 15 13.7 – O/O O/O G/G
let/target interaction conditions), under which the constituent 22 21 U/U U/U U/U U/U
materials tend to behave essentially as linear elastic with weak 32 31 U/U U/U U/U U/U
rate dependency, the material model parameters utilized in the
Nomenclature:U –undermatched, O – overMatched, G – grossly overmatched;
present work are treated as rate independent. Consequently, the Experiment/Computation.