Composite Structures 108 (2014) 696–710

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Composite Structures

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Hybrid core carbon fiber composite sandwich panels: Fabrication andmechanical response

0263-8223/$ - see front matter Published by Elsevier Ltd.http://dx.doi.org/10.1016/j.compstruct.2013.10.002

⇑ Corresponding author.E-mail address: tg3k@virginia.edu (T. George).

Tochukwu George a,⇑, Vikram S. Deshpande b, Keith Sharp c, Haydn N.G. Wadley a

a Department of Materials Science and Engineering, University of Virginia, 395 McCormick Road, PO Box 400745, Charlottesville, VA 22904-4745, United Statesb Engineering Department, University of Cambridge, Cambridge, UKc 3 TEX Incorporated, Cary, NC, United States

a r t i c l e i n f o a b s t r a c t

Article history:Available online 14 October 2013

Keywords:Lattice structuresPyramidal coresFoam reinforcement

Carbon fiber reinforced polymer (CFRP) composite sandwich panels with hybrid foam filled CFRP pyrami-dal lattice cores have been assembled from a carbon fiber braided net, 3D woven face sheets and variouspolymeric foams, and infused with an epoxy resin using a vacuum assisted resin transfer process. Sand-wich panels with a fixed CFRP truss mass have been fabricated using a variety of closed cell polymer andsyntactic foams, resulting in core densities ranging from 44–482 kg m�3. The through thickness and in-plane shear modulus and strength of the cores increased with increasing foam density. The use of lowcompressive strength foams within the core was found to result in a significant reduction in the compres-sive strength contributed by the CFRP trusses. X-ray tomography led to the discovery that the trussesdevelop an elliptical cross-section shape during pressure assisted resin transfer. The ellipticity of the trusscross-sections increased, and the lattice contribution to the core strength decreased as the foam densitywas reduced. Micromechanical modeling was used to investigate the relationships between the mechan-ical properties and volume fractions of the core materials and truss topology of the hybrid core. The spe-cific strength and moduli of the hybrid cores lay between those of the CFRP lattices and foams used tofabricate them. However, their volumetric and gravimetric energy absorptions significantly exceededthose of the materials from which they were fabricated. They compare favorably with other lightweightenergy absorbing materials and structures.

Published by Elsevier Ltd.

1. Introduction

An ongoing effort to increase the structural efficiency and im-pact energy absorption of weight sensitive structures continuesto motivate interest in ultra-light sandwich panel structures [1].A number of light, stiff, and sometimes strong, concepts haveemerged for such applications. They utilize faces made of materialswith high specific stiffness and strength separated by low densitycellular cores with either a honeycomb topology fabricated fromNomex [2], light metals and composites [3], or a closed cell topol-ogy foam made from rigid polymers [4,5]. Various groups have alsoattempted to use metal foams as a stiffer and stronger replacementfor lower cost polymer foams, and as a less costly alternative tohoneycombs [6,7].

Open cell foams have a low nodal connectivity and are usuallybend-dominated structures. As a result they have low elastic mod-uli and compressive strengths; especially at low density. Gibsonand Ashby [8] have shown that the Young’s elastic modulus, E offoams depends on the foams cell topology (open or closed cell),

its relative density �q defined as the ratio of the density of foamto that of the solid from which it is made, and the elastic modulusof the solid material from which it is made, Es. For open cell foams,the modulus-relative density relationship can be written:

EEs¼ C �q2 ð1aÞ

where C is a cell topology dependent constant (approximately equalto unity for many open cell foams). The inelastic crushing of poly-meric foams usually occurs at a near constant ‘‘plateau’’ stress overa large plastic strain (of order 0.6) terminated by the onset of den-sification at a densification strain, eD ¼ 1� 2�q. For open cell foams,the plateau strength, rpl is proportional to the yield strength of thematerial from which the foam is made, rys but has a power lawdependence upon relative density [8]:

rpl

rys¼ C1 �q3=2 ð1bÞ

where C1 is a constant of proportionality. The energy absorbed perunit volume during crushing of foams to their densification strain, isgiven by the integral of the stress strain response up to the onset ofdensification. For an ideal foam with rectangular stress versus strain

Fig. 1. Hybrid composite core structure consisting of a braided CFRP pyramidallattice with polymer foam inserts configured as the core of a sandwich panel with3D woven carbon fiber composite face sheets.

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relation, the volumetric stored energy is rplð1� 2�qÞ [8,9]. The rapidloss in energy storage as the relative density (and plateau strength)decreases can be mitigated by the use of closed cell foams.

Closed cell foams have cell edges which both bend and stretchduring compression and have cell faces which also stretch. Therelationship between the Young’s modulus and relative densityof closed cell foam includes contributions from the cell edgesand faces, resulting in a foam modulus – relative density relationof the form [8]:

EEs¼ C2/

2 �q2 þ C02ð1� /Þ�q ð2aÞ

where C2 and C02 are the constants of proportionality for the celledges(bending structures) and cell faces (which deform by mem-brane stretching), and / is the fraction of the solid in the cell edges.

The plastic collapse strength of the closed cell foam also con-tains contributions from the stretching of the cell faces and is givenby:

rpl

rys¼ C3ð/�qÞ3=2 þ C03ð1� /Þ�q ð2bÞ

As a result of the stretching, the moduli and plateau strengths ofclosed cell foams are higher than open cell equivalents, and aretherefore preferred for impact protection. While these foams areexcellent impact energy absorbers, the structural efficiency of foamcore sandwich structures are inferior to honeycomb and some othercore topology concepts [10].

The search for structurally efficient cellular cores has led to thedevelopment of lattice truss structures made from high specificstrength alloys such as titanium [11] and aluminum [12]. They havebeen shown to exhibit superior stiffness and strength to identicaldenzsity closed cell foams made of the same material [13,14]. Thisarises because lattice structures have high nodal connectivity andare fully stretch dominated. Deshpande and Fleck [15] have analyzedthe load redistribution process for tetrahedral and pyramidal trussstructures, and predict a linear relation between the lattice modulusand that of the solid and the relative density of the core given by:

EEs¼ �q sin4 x ð3Þ

where x is the angle of inclination of the truss (typically 45–55�).They also show that for low aspect ratio trusses that do not buckle,the lattice strength was proportional to that of the solid materialused to make the truss, rY, and the lattice relative density:

rrY¼ �q sin2 x ð4Þ

Since the modulus and strength of lattice structures significantlyexceeds those of equivalent foams, a number of fabrication ap-proaches have been devised to utilize lattice structures for the coresof sandwich structures. For instance, aluminum truss cores manu-factured via extrusion or folding have been shown to have goodmechanical performance in both compression and shear [12,16].Titanium alloy lattices have also been shown to have high compres-sive strengths and stiffness’s, and are well suited for use in highertemperature applications [17,18]. Low density carbon fiber rein-forced composite (CFRP) lattices have also attracted significantrecent interest for the cores of ultra-light sandwich structures [19–26]. For example, CFRP honeycomb core sandwich structures havebeen made from 0�/90� fiber reinforced laminates using a slottingand adhesive bonding approach, and have been found to have highcompressive and shear strengths [19]. Carbon fiber truss structureshave also been made by hot-press molding of carbon fiber pre-pregmaterials [20–22] and by a mechanical ‘‘snap-fit’’ method [23,24].

The compressive strength of CFRP lattice structures made fromlaminates is governed by elastic buckling of the struts at low

relative densities, or truss delamination (inter-ply splitting). Inshear, the strength of the adhesive used to attach the truss to theface sheet is also a limiting factor. In addition, the use of 0�/90�laminates results in at most only half of the fibers being orientedin the direction of the load applied to the truss. The strength ofCFRP truss structures could therefore be increased by; (i) increas-ing the fraction of fibers aligned in the loading direction, (ii) creat-ing trusses better able to withstand interplay delamination failure,and (iii) developing a more robust node-face sheet bonding meth-od. However, once a brittle CFRP strut failure occurs, the remnantstrength of the lattices would be low, and so a CFRP core structuremight be ill-suited for impact energy absorption applications.

Here we explore the use of braided carbon fiber approach forfabricating CFRP pyramidal lattice structures that reinforce closedcell polymer foams in a hybrid CFRP truss/foam core sandwich pa-nel. The braided trusses are non-laminated materials. In principlethis eliminates the delamination failure mode. In addition, all thefibers are aligned within a few degrees of the braid axis whichmay increase the axial compressive strength of the strut. We haveinvestigated the effect of varying the foam strength upon mechan-ical response of the hybrid and empty lattice panels in compressionand shear. We find that the hybrid composite/foam structures havea strength that is the sum of the foam and pyramidal lattice. Inter-estingly, we also find that the cross sectional shape, and thus com-pressive strength contributed by the composite struts, is governedby the foams resistance to crushing during the (pressure assisted)resin transfer fabrication process. This led to a synergistic increasein strut strength as the foams compressive strength was increased.The energy absorbed during crushing of these hybrid structuresthen substantially exceeded that of CFRP lattices and the foams.

2. Panel design and fabrication

2.1. Design concept

The sandwich panel concept explored here is schematicallyillustrated in Fig. 1. The panel cores were assembled from a braidedcarbon fiber net and prismatic, closed cell polymer foam inserts to

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form a hybrid CFRP pyramidal lattice/foam core structure. The corematerial was Kevlar fiber stitched to 3D woven carbon fiber facesheets, and the structure then infused with an epoxy resin andcured. The closed cell polymer foam inserts served a number ofpurposes. They (i) provided a means of supporting and definingthe cross-sectional shape of the trusses, (ii) maintained uniformface sheet separation, (iii) increased the area of adhesively bondedinterface with the faces and (iv) provided core strengthening andimpact energy storage during subsequent compression and shearloading.

A variety of foams were used to investigate the effect of foamstrength (at the cost of increased density) on the hybrid cellularmaterials mechanical properties. Table 1 summarizes the densitiesand mechanical properties of the foams used in the study. Theyincluded closed cell PVC Divinycell foams with densities of 80–250 kg m�3 and compressive strengths of 1.6–6.8 MPa, and syntac-tic foams consisting of hollow glass spheres in a polymer matrixwith densities of 320–448 kg m�3 and compressive strengths of10–26 MPa. A very weak, but easily removed polyurethane foamwas also used to fabricate samples so that an empty latticemechanical response could be measured. The foams were CNCmilled to create trapezoidal cross-section prisms with semicircular,2.25 mm radius grooves to contain the carbon fiber braided latticewithin a 4.5 mm diameter channel.

2.2. Braided net fabrication

Three dimensional braiding [27–31] was used to create abraided carbon fiber net in which the trusses contained multidirec-tional fiber reinforcements whose angle of deviation from the lon-gitudinal axis of the truss was up to 11�. The principal advantagesof 3-D braided preforms are that (i) they can be fabricated in var-ious complex (and, if desired continuously variable) shapes[29,30]; (ii) their shear and torsional rigidities are significantlyhigher than those of a traditional laminated structure and (iii)the orientation of the filaments can be controlled. The fiber volumefraction in 3-D braided composite can also be widely varied,depending on the requirements for matrix infiltration, consolida-tion and densification of the various resin types.

The 3BRAID� process used here was developed at 3Tex and in-volved three machine motions [29]. Fig. 2(a) shows a schematic ofthe single 64 carrier braiding module used here. Each of the 16large circles represents a horn gear occupied by 4 braiding carrierscolored in gray, while the smaller circles represent the fork gears.All fork gears in this application are active and so colored green.The horn gear [32], which contained 4 yarn carriers, first com-pleted a 1/4 turn. Fork gears, located at the interstices of the horngears then switch yarn carriers between horn gears by completinga 1/2 turn. Lastly, a take-up system advanced the braid by a prede-termined distance.

Three methods can be used to control the shape of the preformin the 3BRAID� process. These include selective engagement or dis-engagement of individual fork gears, arrangement of the braiding

Table 1Summary of foam properties.

Material Density (kg/m3) Compressive strength (MPa) She

Polyurethane foam 32 0.172 0.1Divinycell H80 80 1.3 0.9Divinycell H100 100 2 1.4Divinycell H130 130 2.7 1.9Divinycell H200 200 4.2 3.2Divinycell H250 250 6.8 3.9Synfoam H20 320 10 6.4Synfoam H24 384 16 9.8Synfoam H28 448 26 14.2

carriers on the base of the machine, combined with selective con-trol of individual fork gears, and tailored placement of axial yarns.Selective engagement of individual fork gears controls the ex-change of braiding carriers between horn gears, which can be usedto define the formation of internal openings within the preform, aswell as the outside surfaces of the preform.

In Fig. 2(b), the green colors mark fork gears where an exchangewill occur and red colors mark fork gears where no exchange willoccur. In this example, a single square shaped preform, formed byengaging all of the horn gears and fork gears, is split into 2 smallrectangular shapes formed by disengaging the center fork gearsduring the several machine cycles, and then rejoined by reengagingthe center fork gears. By alternating the splitting and joining fromone section of the braid pattern to another, a truss braid or ‘‘web’’architecture could be produced. Production of the split and joinedsections occurred continuously as the 3D braided preform wasproduced.

The braided net used here was constructed from 24 tows of 12 K(12,000 fibers per tow), Hexcel IM7 carbon fiber. The IM7 fiber hastensile strength of 5.67 GPa, a modulus of 276 GPa, and a density of1800 kg m�3. Fig. 3(a) defines the structural parameters of thisbraid, while Fig. 3(b) shows a section of the braid used here. Thebraid angle, / = 11�, its diameter, d = 4.5 mm and the repeat dis-tance, k = 25 mm. The braided net had a density of 442 kg m�3

and its unit cell geometry is defined in Fig. 3(c).

2.3. Dry panel assembly

The dry assembly of a hybrid foam/CFRP truss core sandwichpanel is schematically illustrated in Fig. 4. The braid was firststitched to the dry face sheet, Fig. 4(a). It was then placed withinthe 2.25 mm radius grooved channels of a foam insert, Fig. 4(b),and an inverted foam mold was inserted to enclose the braidedtruss within a 4.5 mm diameter channel, Fig. 4(c). The braid wasthen stitched to the lower face sheet and the process repeated toform a pyramidal structure, Fig. 4(d). The braid- face sheet nodeswere reinforced using three stitches of Kevlar thread each approx-imately 15 mm in length. The 3Weave™ face sheets were madefrom 12 K Hexcel IM7 Carbon fibers at 3Tex Inc. The sheet consistsof fiber tows running in the x, y and z directions, with 43% x-fibers(warp), 47% y-fibers (weft), and 10% z-fibers. The sheets had athickness of 3.5 mm, prior to infusion, and an areal density of2.08 kg m�2. The 3D woven structure of both the braid and facesheet were selected to increase resistance to delamination.

2.4. Resin infusion process

A SC1A grade epoxy resin with SC1B curing agent (Applied Pole-ramic Inc., Benicia, CA) was used for the polymer matrix. Thisepoxy was selected because of its (i) low viscosity, which allowedcomplete infiltration of the complex shaped panel during the infu-sion process, (ii) moderately high strength, and (iii) high impactresistance. The cured epoxy has a compressive strength of

ar strength (MPa) Compressive modulus (MPa) Shear modulus (MPa)

52 – –5 85 23

115 28145 40265 65350 81360 110460 125575 140

Fig. 2. (a) Schematic of 64 carrier single module used for 3D braiding. (b) Shape control in the 3BRAID� process; disengagement of fork gears (the color red indicates whichgears are disengaged) causes the preform to split. Reengagement of the fork gears rejoins the preform. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

Fig. 3. (a) Schematic illustration of the structure of the braided carbon fiber strut.(b) Photograph of a strut section of the braided net. (c) The braided net structure,with unit cell shape and dimensions identified.

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75 MPa, and a Young’s modulus Eresin = 1.85 GPa. A vacuum as-sisted resin transfer molding (VaRTM) process was used to infusethe assembled carbon fiber structures. The setup prior to infusionis illustrated in Fig. 5. The infusion and cure cycle were performedin an autoclave, which enabled control of the temperature andpressure (vacuum) within the assembly throughout the process.The samples were infused on a wax coated glass substrate to en-able removal of the panel after infusion. A layer of breather mate-rial and a peel ply were then laid over the wax covered glass. Thecarbon fiber panel was then placed on top of the peel ply. A secondlayer of peel ply was used to cover the panel, and a layer of

distribution media was used to ensure even flow of resin through-out the part. A layer of breather material was placed over the dis-tribution media, and finally, a nylon vacuum bag was used toenclose and seal the part. Inlet and an outlet tubes were also in-serted in the vacuum bag. The outlet tube was connected to a resintrap, and could be separately evacuated from the autoclave. The in-let tube was connected to the resin container.

The panels were infused using an epoxy to curing agent ratio of100:22. The vacuum bagged parts were placed in the autoclave,and the outlet line evacuated to a vacuum pressure Pv = �3.6 kPa,with the resin inlet line sealed. The inlet line was then opened,and resin allowed to flow through the part and began to exitthrough the outlet tube. The inlet tube was then closed, and the re-sin cure cycle program was executed within the autoclave. The partwas first externally pressurized to 0.1 MPa, while maintaining theinternal vacuum pressure. The vacuum line was then released toatmospheric pressure, and the external pressure increased to0.17 MPa to eliminate resin vapor voids. The part was then heatedup to 71 �C, and the pressure and temperature maintained for a 4 hcuring period.

After cure, the panels were removed from the infusion toolingand machined to the appropriate dimensions needed for testing.Each compression test panel comprised of four unit cells, in a2 � 2 unit cell array. The shear test panels were 6 unit cells longand two unit cells wide. The foam was mechanically removed fromsome samples in order to ascertain the empty lattice mechanicalresponse. We note that small gaps between the prismatic foam in-serts resulted in a thin layer of resin being retained in the hybridcore panels. Fig. 6 shows a photograph of a finished hybrid core pa-nel, as well as an X-ray computed tomographic (X-CT) reconstruc-tion. The retained corrugated resin layer can be clearly seen in thereconstructed image. The X-CT characterization also revealed thatthe trusses had an elliptical cross section that is discussed below.

2.5. Core geometry

A unit cell of the pyramidal lattice is shown in Fig. 7 with ellip-tical cross section trusses with a minor axis width d1 and majoraxis length d2. The angle of inclination of the trusses to the baseof the unit cell x = 54�. The truss-face sheet node in both caseswas assumed to have a width equal to the major axis diameter ofthe truss, and a length b that was set equal to 2 times the woven

Fig. 4. The hybrid CFRP pyramidal lattice core sandwich panel assembly sequence.

Fig. 5. Setup used for the vacuum assisted epoxy resin infusion process.

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diameter of the braid (d = 4.5 mm). The length of the truss,l = 41 mm.

The relative density of the CFRP empty lattice unit cell �q wasfound by calculating the ratio of the truss volume to that of the unitcell. One quarter of a node can be assigned to each lower corner ofthe unit cell, and a full node volume to the top face. For the mostgeneral case of an elliptical truss:

�q ¼ pd1d2ðlþ bÞl sinxð

ffiffiffi2p

l cos xþ 4d2Þðffiffiffi2p

l cos xþ 2bÞð5Þ

In the special case where a truss was not deformed during resininfiltration, d1 = d2 = d.

The measured values of d1 and d2 were determined from X-CTreconstructions of the as fabricated samples, Table 2.

The total density of the hybrid core, q, is found by accountingfor the masses of the foam and resin sheets. The volume, vrs occu-pied by a resin sheet of thickness t within the unit cell was esti-mated by calculating the volume of the corrugated resin sheet:

mrs ¼ 2tðlþ bÞðffiffiffi2p

l cos xþ 4dÞ ð6aÞ

The volume fraction of the resin sheet vfr is found by dividing Eq.(6a) by the volume of the unit cell:

mfr ¼2tðlþ bÞ

l sinxðffiffiffi2p

l cos xþ 2bÞð6bÞ

The thickness of the resin sheet varied in thickness from 0.2 to1.0 mm and was assigned an average value tavg = 0.5 mm. It was as-sumed that the volume within the unit cell which was not occupiedeither by the truss or the resin sheet was occupied by foam. The vol-ume fraction of the foam vff can then be estimated as:

mff ¼ ð1� ð�qþ mfrÞÞ ð7Þ

The total density of the hybrid core, q can then be expressed as:

q ¼ ð�qqccÞ þ ðqrsmrsÞ þ ðqf mff Þ ð8Þ

where qcc is the density of the braided CFRP trusses (1450 kg m�3),qrs is that of the cured epoxy resin (1100 kg m�3), and qf is the den-sity of the foam given in Table 2.

Fig. 6. a) Photograph of a completed hybrid panel with CFRP pyramidal lattice and H250 Divinycell foam core. (b) X-CT image of the sample shown in (a) revealing the interiorstructure of the finished panel with the foam digitally filtered out.

Fig. 7. Pyramidal CFRP unit cell with elliptical cross section trusses. The minor axisof the truss cross-section was perpendicular to the trapezoidal side face of the foamcore (not shown) used to support the truss.

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3. Braided CFRP truss properties

3.1. Compression

The compressive strength of a circular cross section CFRP braidwas first determined. Samples were prepared by flowing resinthrough a length of the braid, confined within a circular glass tubewith an inner diameter d = 4.5 mm equal to that of the braid. The

Table 2Summary of core properties.

Foam type None (Empty) H80 H100

Core density (kg m�3) 44 120 141Compressive strength (MPa) 1 4.2 5.2Compressive modulus (MPa) 50.7 172 251.5Shear strength (MPa) 0.5 1.7 3.2Shear modulus (MPa) 20.7 77 123Ellipticity (d1/d2) (mm/mm) 2.1/5.3 2.75/5.1 2.9/5.1a

a Indicates interpolated data.

resin was cured, and the tubing removed, leaving behind the cylin-drical braided composite sample with a fiber volume fraction of52%. These samples were cut into 12.5 mm long pieces, and theirends coated with SC1 epoxy to prevent brooming failure [33] andglued to the platens. They were then tested in compression asshown in Fig. 8(a) taking care to ensure the two platens were par-allel, and the cylindrical axis of the CFRP braids was normal to theplatens. The samples were tested in compression at ambient tem-perature (23 �C) at a strain rate of 2 � 10�4 s�1.

The compressive stress–strain response of a typical sample isshown in Fig. 9(a). The average compressive strength for 5 testsrmax = 540 ± 40 MPa, and the Young’s modulus (measured duringunloading) Etruss = 28 ± 2 GPa. The braided CFRP struts failed mac-roscopically in shear, Fig. 8(b). Fig. 9(b) shows an X-CT cross sec-tional reconstruction of a failed truss. It can be seen that theinitial failure occurred by microbuckling within one of the tows.This occurred on a plane at approximately 45� to the loading axisand displaced the ends of the tow in the struts radial direction. Thisresulted in cracks forming in adjacent tows and macroscopic fail-ure propagating at an angle to the direction of applied load.

3.2. Tension

The tensile strength of the truss was determined in accordancewith the ASTM D3039 standard for composite tensile testing. Thesamples were made by the same method as the samples for com-pressive testing (with d = 4.5 mm). The samples are securelyclamped within the grips and had a 50.8 mm gauge length. Thesamples were then strained at a constant rate of 2 � 10�4 s�1, atambient room temperature (23 �C). A typical stress – strain

H130 H200 H250 HP20 HP24 HP28

171 239 288 356 418 4826 8.1 12.5 16 22.5 34.5315 402.8 477.1 485 564 755– – – – – –– – – - – –3.0/5.0a 3.2/4.9 3.9/4.5 3.6/4.5 4.1/4.5a 4.3/4.5

Fig. 8. (a) Schematic illustration showing setup used to determine compressivestrength of the braided composite strut, and (b) the orientation of the strut fracturesurface.

Fig. 9. (a) Axial compressive stress–strain response of a braided truss. (b) X-CTcross sectional image of a failed truss specimen showing damage initiating bymicrobuckling in one of the tows and shear crack propagation across the truss. (c)Axial tension test response of a braided truss.

702 T. George et al. / Composite Structures 108 (2014) 696–710

response is shown in Fig. 9(c). The trusses are found to have anaverage tensile strength (from 5 tests) of rtensile = 640 ± 30 MPa,and a Young’s modulus (measured during unloading) Etruss = 32 ±4 GPa.

4. Hybrid core testing

4.1. Out of plane compression

The through thickness compressive response of the panels wasmeasured with a screw-driven universal testing machine (Model4208 Instron Corporation, Canton, MA) with a 300 kN load cell inaccordance with ASTM C-365, using the same method describedby Finnegan et al. [23]. Retro-reflective tabs were attached to thetop and bottom face sheets, and strain measurements were takenusing a laser extensometer. The samples were compressed at anominal strain rate of 2 � 10�4 s�1 at 23 �C. The elastic modulusfor each sample was measured by unloading within the nominallyelastic region of the stress–strain curve.

Compressive stress strain responses for the hybrid compositecores constructed with Divinycell and syntactic foams are shownin Figs. 10 and 11, and compared with those of the foams used tofabricate each hybrid core. The compressive strength (the fracturestress) and modulus for each of the hybrid cores are summarized inTable 2. The stress strain curves for all the samples were initiallylinear, followed by yielding and a sample dependent drop instrength that was followed by a stress plateau before the stressrose as the core densified. It can be seen that the difference be-tween the strength of the hybrid core and that of the foam, de-creased as the foams compressive strength decreased. Thereasons for this are investigated in Section 5.

X-ray computed tomography was performed on compressedhybrid core specimens in order to identify the failure mechanismscontrolling the cores peak strength. Scans were first performed onunstrained specimens and then repeated after the specimens hadbeen loaded to strain levels of 10%, 20%, and 40%. Three dimen-sional reconstructions were performed using volume graphics soft-ware (VG Studio 2.0). The reconstructed images at the variousstrain levels for a hybrid CFRP truss/H250 foam core are shownin Fig. 12. The shape and position of the trusses, as well as the resinsheet can be clearly seen in the unstrained sample, Fig. 12(a).The foam has been digitally filtered from the image to allow an

unimpeded view of the trusses and resin sheet. From the stress–strain curve, it can be seen that the panel yielded at a strain ofabout 5%. The reconstruction of a panel compressed to 10% strainis shown in Fig. 12(b). It can be seen that the panel yield corre-sponded to fracture of the trusses near the nodes with the crackplane at an acute angle with respect to the truss axis. This was sim-ilar to the mode observed for a single compressed CFRP braidedstrut. The resin sheets began to buckle at a strain of 20%,Fig. 12(c). The onset of densification (strain of 40%), Fig. 12(d), coin-cided with contact of the buckled resin sheets with the face sheets.

The compressive stress versus strain response of an empty lat-tice made using a low strength (but easily removed) polyurethanefoam is shown in Fig. 13a. The trusses within the empty latticefracture at the same location as those within the hybrid core. In

Fig. 10. Compressive stress–strain responses for the hybrid CFRP pyramidal lattice/foam core panels constructed using Divinycell foams of different strengths (anddensities). The response of just the foams is also shown.

Fig. 11. Compressive stress–strain responses for the hybrid composite core panelsconstructed from syntactic foams of different strengths.

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compression, the empty lattice yielded at a stress of 1 MPa. Themeasured modulus was 50.7 MPa. Further straining led to a rapid,progressive drop in strength.

4.2. Role of resin sheet on panel strength

During the infusion process for the panel, a thin layer of resinformed between the foam molds. The thickness of this layer

typically varied between 0.2 and 1 mm. Given the high strengthof the epoxy used, it is necessary to determine the contributionof this resin sheet to the strength of the hybrid core. In order todo this, panels were assembled using polymer foam molds as be-fore, but contained no grooves or braided trusses. These panelswere infused in the same manner and the compressive stress–strain responses of these ‘‘no-CFRP truss’’ cores were measuredfor the H80, H200, and HP20 foams, Fig. 14. It can be seen thatthe resin sheets add about 1 MPa to the compressive strength ofthe panel, and was independent of the density of the foam. It istherefore reasonable to conclude that about 1 MPa of the strengthdifference between the hybrid and foam only cores described inSection 4.2 can be attributed to the presence of the resin sheets.

4.3. In-plane shear

The in-plane shear response of the panels was measured withthe same screw driven universal testing machine using a compres-sion shear plate setup previously described by George et al. [24].The shear testing was performed in accordance with ASTM C273,

Fig. 12. Reconstructed X-CT images of a hybrid composite panel with H250 foam core; (a) as fabricated and at various levels of strain (b–d). The trusses fail by microbucklingand shear fracture near the nodes while the resin sheets fail by buckling.

704 T. George et al. / Composite Structures 108 (2014) 696–710

which dictated that the sample length was twelve times its thick-ness and the width was two times the thickness. These specifica-tions were satisfied by preparing samples that were two unitcells wide and six unit cells in length. The samples were attachedto the shear plates using a high strength Redux epoxy adhesive(Hexcel Corporation, Stamford, CT), as well as a set of screws thatpenetrated the face sheets. The shear plates also had edge stops toprovide additional sliding restraint. The testing was performed at23 �C and at an angle of g = 0 (in the x-direction) as defined inFig. 7. This orientation places two trusses of each unit cell in axialcompression, and two in axial tension. Tests in shear were success-ful for the empty lattice (polyurethane foam removed), H80 foam,and the H100 foam hybrids. Efforts to test panels with denser foamcores resulted in failure of the adhesive bond between the compos-ite and the shear plates.

The shear stress-shear strain curves for the successfully testedhybrid core panels are shown in Fig. 15, along with the curvesfor the corresponding foams. In shear, the empty lattice failed ata peak strength of 0.5 MPa, and had a measured shear modulusof 20.7 MPa, Fig. 13(b). Failure first occurred within the trussesloaded in tension; a consequence of the larger tensile stress in

the tensile loaded struts of a pyramidal lattice with inclination an-gle x = 54� [23,24]. Fig. 15 shows a summary of the measuredcompressive and shear strengths of the composite cores, as wellas the foams.

5. Micro-mechanical modeling

To interpret the experiments above, analytical expressions arederived for the compressive and shear moduli and strengths ofboth the empty CFRP lattice and foam filled hybrid cores. We uti-lize a local Cartesian coordinate system, with the axes x, y, and zin the length, height, and width directions of the unit cell, Fig. 7.

5.1. Core compression

5.1.1. Compressive modulusWhen an out of plane compressive force is applied to the top of

a rigidly supported empty lattice unit cell with oval cross sectiontrusses, Fig. 7, axial, FA, and shear, FS forces are created in each ofthe trusses. Using the approach developed by Finnegan et al.[23], these forces can be related to geometric parameters of the

Fig. 13. The mechanical response of the empty CFRP lattice in (a) compression and(b) shear.

Fig. 14. Core compressive stress – strain response in the absence of a truss core for3 foam densities.

T. George et al. / Composite Structures 108 (2014) 696–710 705

unit cell and the material used to make it. The axial force, FA isdependent on the cross-sectional area of the truss, and the shearforce, FS, is also dependent on the second moment of the cross-sectional area of the beam. These truss supported forces are given by:

FA ¼Etrusspr1r2d sin x

lð9aÞ

and

Fs ¼Etrusspr3

1r2d cos xl3 ð9bÞ

where r1 = d1/2 and r2 = d2/2 and d is the unit cell displacement inthe y direction (recall that the trusses are bending about the d2

axis). In the limit of a circular cross section truss, these expressionsreduce to:

FA ¼Etrusspr2d sinx

lð10aÞ

and

Fs ¼Etrusspr4d cos x

l3 ð10bÞ

The total force supported by each truss, F is the sum of the axial andshear forces:

F ¼ FA sin xþ FS cos x

¼ Etrusspr1r2dl

sin2 xþ r21

l2

� �cos2 x

� �ð11Þ

Since there are four struts within a CFRP pyramidal unit cell, eachsupporting an applied force F (Eq. (11)), and the base area of theunit cell is known, the stress supported by an empty lattice is givenby:

r ¼ 8F

ðffiffiffi2p

l cos xþ 4d2Þðffiffiffi2p

l cos xþ 2bÞð12aÞ

The compressive strain of the unit cell is given by:

e � dl sin x

ð12bÞ

The compressive modulus of the pyramidal lattice, Elattice = r/e, andit follows from Eqs. (12a) and (12b) that:

Elattice

Etruss¼

8pr1r2 sin x sin2 xþ r21

l2

� �cos2 x

h iðffiffiffi2p

l cos xþ 4d2Þðffiffiffi2p

l cos xþ 2bÞð13Þ

where Etruss is the compressive elastic modulus of the truss, as mea-sured in Section 3.1.

Assuming the strains in the foam, resin sheet and trusses of thecompressed hybrid core to be identical, the compressive modulusof the foam filled hybrid, Ec, can be determined using a rule ofmixtures:

Ec ¼ Elattice þ mff Efoam þ mfrEre sin sin4 h ð14Þ

where vfr is the volume fraction and Eresin the elastic modulus of theresin and vff is the volume fraction, h is the angle of inclination ofthe resin sheet with respect to the x–z plane, and Efoam is the elasticmodulus of the foam. Fig. 16(a) shows that the predicted and mea-sured moduli are in reasonable agreement, while Fig. 16(b) showsthe contribution of each of the components within the hybrid core

Fig. 15. Shear stress versus shear strain curves for the hybrid composite coresandwich panels made using (a) H80 and (b) H100 foam. The stress strain curves forthe foams used are also shown.

Fig. 16. Barcharts showing: (a) the measured compressive modulus compared tothe predicted modulus for select foam densities, and (b) the individual moduluscomponents combined for the cumulative prediction (Ecore) for each of the specifiedcore densities.

706 T. George et al. / Composite Structures 108 (2014) 696–710

system (truss, resin sheet and foam) to the total predicted modulus.The sources of the systematic over predicted modulus are discussedbelow.

5.1.2. Compressive strengthFor low aspect ratio trusses, axial loading of braided CFRP strut

in the axial direction results in either Euler elastic or plastic micro-buckling. For microbuckling failure, Argon [34] has argued that thecompressive strength, rmax of an axially loaded composite made upof fibers within a plastic matrix with shear yield strength sy is gi-ven by:

rmax ¼sy

uð15Þ

where u is the axial misalignment angle of the fibers. In a pyrami-dal lattice loaded in through thickness compression the struts areloaded in both axial compression and in-plane shear [23]. Whenan in-plane shear stress is superimposed on the axial compressivestress, Fleck and Budiansky [35] have shown that the critical micro-buckling stress rc can be approximated by:

rc ¼sy � s1

uð16Þ

where s1 < sy, is the in-plane shear stress which reduces the criticalaxial stress required to cause microbuckling. Since s1 and rc are gi-ven by Eq. (10a) and b divided by the truss cross sectional area, theratio of s1/rc = (r/l)2 cotx. Upon substitution for s1 in Eq. (16) andrearranging gives, we find that the critical buckling strength undercombined axial compression and in-plane shear can be written as:

rc ¼sy

uþ r1l

2 cotx¼ rmax

1þ r1l

2 cotxu

h i ð17Þ

From Eq. (11), the critical buckling force supported by a single in-clined strut is:

F ¼ rcpr1r2 sinx sin2 xþ r1

l

� �2cos2 x

� �ð18Þ

Since there are four trusses per unit cell, and the area of the unit cellis known, the microbuckling strength of the pyramidal lattice canbe written as:

rp �8rcpr1r2 sin x

ðffiffiffi2p

l cos xþ 4d2Þðffiffiffi2p

l cos xþ 2bÞsin2 xþ r1

l

� �2cos2 x

� �

ð19Þ

From Eq. (17), it can be seen that this expression for the peakstrength of the core can be rewritten as:

rp

rmax¼ 8pr1r2 sinx

ðffiffiffi2p

lcosxþ4d2Þðffiffiffi2p

lcosxþ2bÞ 1þ r1l

2 cotxu

h i sin2 xþ r1

l

� �2cos2 x

� �

ð20aÞ

In the special case of a cylindrical truss; r1 = r2 = r, this expressionreduces to:

rp

rmax¼ 8pr2 sinx

ðffiffiffi2p

lcosxþ4dÞðffiffiffi2p

lcosxþ2bÞ 1þ rl

2 cotxu

h i sin2 xþ rl

� �2cos2 x

� �

ð20bÞ

Eqs. (20a) and (20b) are evaluated using the compressive strengthof the truss rmax determined in Section 3.1, as well as unit cellparameters x, l, b, and d listed in Section 2.5. In addition r1 and r2

were determined from the d1 and d2 values listed in Table 2. The fi-ber misalignment angle is taken to be the braid angle 11�.

The microbuckling mechanism competes with an Euler (elastic)buckling mode. The critical Euler buckling load, PE is given by:

Fig. 17. The micromechanical predictions for both the elastic and microbucklingstrengths plotted as a function of the ellipticity ratio d1/d2. The compressivestrength contribution of the CRFP lattice deduced by subtracting the contributionsof the foam and resin sheets from the measured strength are also shown for thedifferent foams (open circles).

T. George et al. / Composite Structures 108 (2014) 696–710 707

PE ¼p2EI

L2 ð21aÞ

where E is the Young’s modulus of the beam, I is the second areamoment, and L is the length of the beam. For an elliptical cross-sec-tion truss, the second area moment, I � pr3

1r2=4, where r1 and r2 arethe short and long radii of the elliptical. In this case, the criticalbuckling stress is given by:

rel ¼p2r3

1r2Etruss

4l2 ð21bÞ

For a cylindrical truss, I � pr4/4, and the elastic buckling stress re-duces to:

rel ¼p2r4Etruss

4l2 ð21cÞ

The peak elastic buckling strength of the core can then be found bysubstituting rel for rmax in Eq. (20).

The predicted microbuckling and elastic buckling strengths ofan empty CFRP pyramidal lattice are plotted as a function of thed1/d2 ratio for d2 = 4.5 (core with strongest foam) and 5.3 mm(weakest polyurethane foam) in Fig. 17. It can be seen that as thetruss became more oval (decreased d1/d2), the elastic bucklingstress becomes lower than the microbuckling stress and thestrength of lattices made using the polyurethane, H80 and H200foams is predicted to be governed by elastic buckling. However,as d1/d2 approached unity, the plastic microbuckling stress becamelower than the elastic buckling stress, and failure is predicted tooccur by microbuckling for the lattices fabricated with syntacticfoams (HP series of foams). The deduced lattice contribution1 tothe compressive strength is overlaid on the predictions in Fig. 17.The trends with d1/d2 ratio are similar to that predicted, but thestrength levels are lower consistent with the imperfection sensitivityof the failure modes.

The compressive strength of the foam filled hybrid core can bepredicted by assuming iso-strain conditions in the lattice, foamand polymer corrugation. The rule of mixtures compressivestrength of the hybrid core rhc can then be written as:

rhc ¼ mff rf þ mfrrr sin2 hþ rp ð22Þ

where vff is the volume fraction of the foam within the compositecore unit cell, vfr and is the volume fraction of the resin sheets, his the angle of inclination of the resin sheets with respect to thedirection of compression, and rf and rr are the compressivestrengths of the foam and resin, respectively. Fig. 18 compares themeasured compressive strength of the hybrid composite core andthe micromechanical predictions for the three contributions to thepredicted strength (Eq. (22)). The upper bound micromechanicalpredictions are in good agreement with the measurements.

5.2. Core shear

5.2.1. Shear modulusExamination of the unit cell in Fig. 7, shows that an applied

shear force along the x-axis at a shearing angle g = 0, would resultin a deflection d of the top face of the unit cell and a tensile force ontwo of the trusses and a compressive force on the remainingtrusses. Following an approach proposed by George et al. [24],the unit cell deflection can be resolved into axial and shear dis-placements da and ds of the trusses given by:

da ¼ d cos x ð23aÞ

1 Obtained by subtracting the strength of the foam and resin sheet from themeasured strength of the hybrid core.

ds ¼ d sinx ð23bÞ

Since the direction of the applied shear force is perpendicular to y–zplane of the unit cell, Fig. 7, the force is symmetrically distributedamong the trusses within the unit cell. The axial and shear forceson each of the trusses are then given by:

FA ¼Etrusspr1r2da sin x

lð24aÞ

and

Fig. 18. Barcharts showing (a) the measured core compressive strength comparedto the micromechanical predictions, and (b) the individual components of thecompressive strength prediction.

708 T. George et al. / Composite Structures 108 (2014) 696–710

Fs ¼Etrusspr3

1r2ds cos xl3 ð24bÞ

The total applied force applied to each truss, F is given by:

F ¼ FA cos xþ FS sin x

¼ Etrusspr1r2dl

cos2 xþ r1

l

� �2sin2 x

� �ð25Þ

The shear stress, s supported by the four trusses is then:

s � 4F

ðffiffiffi2p

l cos xþ 4d2Þðffiffiffi2p

l cos xþ 2bÞð26Þ

The engineering shear strain c is given by:

Fig. 19. (a) The measured shear modulus of the composite cores compared to the micrcompared to the micromechanical predictions.

Fig. 20. Material property chart showing (a) compressive strength, (b) shear strength, (truss structures. The hybrid CFRP lattice/foam results of this study are also shown toget

c � dl sin x

ð27Þ

The shear modulus G of the truss-only structure can then be writtenas:

Glattice

Etruss¼

4pr1r2 sin x cos2 xþ r1l

2 sin2 xh i

ðffiffiffi2p

l cos xþ 4d2Þðffiffiffi2p

l cos xþ 2bÞð28Þ

The shear modulus of hybrid core should also include contributionsfrom the foam and resin corrugations. Assuming their contributionis given by the rule of mixtures, the hybrid core shear modulus, Gc isgiven by:

Gc ¼ �qGlattice þ mff Gfoam þ mfrEre sinsin2 2h

4ð29Þ

omechanical predictions. (b) The measured shear strength of the composite cores

c) compressive modulus and (d) shear modulus of CFRP honeycomb and pyramidalher with that of the foams.

Fig. 21. (a) The energy absorbed per unit volume and (b) energy absorbed per unitmass both plotted against density for low density cellular materials. The hybridcomposites compare favorably with the other materials.

T. George et al. / Composite Structures 108 (2014) 696–710 709

where Gfoam is the shear modulus of the foam.

5.2.2. Shear strengthFailure within the specimens tested in shear occurred within

the trusses loaded in tension. Thus, the tensile strength of the trussis used to predict the shear strength. It follows from Eqs. (25) and(26) that the shear strength, sL of the (empty) lattice core can beexpressed as:

sL

rtensile¼

pr1r2 cos2 xþ r1l

2 sin2 xh i

ðffiffiffi2p

l cos xþ 4d2Þðffiffiffi2p

l cos xþ 2bÞð30aÞ

where rtensile is the tensile strength of the truss, as determined inSection 3. In the special case where the trusses are cylindrical,r1 = r2 = r, the above equation can be rewritten as:

sL

rtensile¼

pr2 cos2 xþ rl

2 sin2 xh i

ðffiffiffi2p

l cos xþ 4dÞðffiffiffi2p

l cos xþ 2bÞð30bÞ

The shear strength sc of the foam filled hybrid core can be deter-mined by accounting for the individual components using the ruleof mixtures:

sc ¼ mff sf þ mfrrtr cos2 hþ sL ð31Þ

where sf is the shear strength of the foam, and rtr is the tensilestrength of the cured resin. Fig. 19 compares the measured shearmodulus and strength of the cores to the micromechanical predic-tions. The modulus is slightly over predicted, due to truss wavinesseffects from the VaRTM process, as explained earlier. The strengthpredictions are in pretty reasonable agreement with the measuredvalues.

As the density of the foam decreases, there is a significantknockdown in the measured empty lattice strength of the core,while cores made using stronger foams have higher measuredempty lattice strengths. This knockdown is explained by the factthat the weaker foams allow significant deformation of the shapeof the trusses during the pressure assisted consolidation process(vacuum and pressure cycle within the autoclave), causing thecross-section of the truss to become more oval, and the d1/d2 ratiosmaller.

6. Discussion

Compressive and shear moduli and strengths of the hybrid CFRPlattices are plotted against density on modified Ashby charts inFig. 20 and compared with the foams used here and other CFRP lat-tices and honeycombs discussed in the introduction. It can be seenthat the strength and moduli of the hybrid cellular structures liebetween those of the foams and CFRP lattices/honeycombs. Thespecific strength and modulus of the CFRP lattices with circularcross section struts exceed those of the foams, and so as the massfraction of the hybrid devoted to the foam increases, the mechan-ical properties converge to those of the foam and vice versa. A com-plicating discovery here was that partial compression of the foaminserts during pressure assisted resin transfer caused the originallycircular trusses to assume an elliptical cross sectional shape, withthe ellipticity increasing as the foams compressive strength wasdecreased. The reduced resistance of the elliptical shaped CFRPtruss to elastic bending led to a significant reduction in the CRFPlattice contribution to the hybrid structures strength as the foamdensity was decreased.

The compressive stress versus strain responses of the hybridcores exhibited a foam-like behavior with a well-developed pla-teau stress that continued to onset of densification, Figs. 10 and11. They therefore appear well suited for impact energy absorptionapplications. To investigate this further, the energy absorbed per

unit volume, Wv was determined by integrating the stress straincurve to the onset of densification:

Wm ¼Z ed

0rde ð32Þ

where ed is the densification strain. The densification strain wasdetermined by the point where the stress at the end of the plateauregion exceeded the initial peak stress, or in the absence of a sharpinitial peak, was defined as the inflection point where the tangent ofthe plateau region of the stress strain curve intersected the tangentto the densification region [9]. The energy absorbed per unit mass,Wm, was obtained by dividing Wv by the core density.

Fig. 21(a) shows a plot of the volumetric energy absorption as afunction of the density, while Fig. 21(b) shows a plot of the gravi-metric energy absorbed per unit mass, again as a function of thecore density. It can be seen that the hybrid core significantly ex-ceeds that absorbed by foams and CFRP lattices and honeycombs.This suggests that for applications where high crush strength andimpact energy absorption are required, these hybrid structures of-fer an interesting alternative to honeycombs and other core struc-tures. The micromechanical models developed in Section 5 providea simple means for designing structures that meet specified de-mands for strength and modulus.

7. Conclusions

We have developed a novel process for the fabrication of CFRPsandwich structures and used 3D X-ray tomography in conjunction

710 T. George et al. / Composite Structures 108 (2014) 696–710

with micromechanical modeling and experimental testing to ex-plore the factors governing the mechanical properties of the core.We find that:

1. A CFRP pyramidal lattice structure can be fabricated from abraided IM7 carbon fiber net using pre-machined polymer foaminserts and a pressure assisted SC 1 resin transfer moldingprocess.

2. Sandwich panels with robustly bonded hybrid CRP/foam core-3D weave IM7 face sheets can be fabricated using Kevlar fiberreinforcement at the nodes.

3. The strength and moduli of the hybrid cores are found toincrease with foam density due to a combination of increasein foam strength and modulus, and retention of a more circularcross section CFRP truss which is less susceptible to elasticbuckling.

4. The moduli and strengths of the hybrid cellular materials devel-oped here are well predicted by micromechanical models thatdecompose the applied stresses into axial and shear loads onthe CFRP trusses and calculate the global (Euler) elastic andplastic microbuckling stresses for the struts.

5. The strength and moduli of the hybrid material lie betweenthose of foams and CFRP lattices, but their volumetric and gravi-metric energy absorptions up to the onset of densification sig-nificantly exceed those of either material from which they arecomposed.

Acknowledgements

We are grateful to the Office of Naval Research (Grant NumberN00014-07-1-0114) and the Defense Advanced Research ProjectsAgency (Grant Number W91CRB-10-1-005) for the financial sup-port for this research.

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