titanium matrix composite lattice structures · mation was accommodated by elastic buckling of the...

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Composites: Part A 39 (2008) 176–187

Titanium matrix composite lattice structures

Pimsiree Moongkhamklang *, Dana M. Elzey, Haydn N.G. Wadley

Department of Materials Science and Engineering, University of Virginia, 140 Chemistry Way, P.O. Box 400745, Charlottesville, VA 22904-4745, USA

Received 12 June 2007; received in revised form 31 October 2007; accepted 13 November 2007

Abstract

Cellular materials made from high temperature composites with efficient load supporting lattice topologies and small cell sizes wouldcreate new options for light weight, high temperature structures. A method has been developed for fabricating millimeter cell size cellularlattice structures with a square truss topology from 240 lm diameter Ti–6Al–4V coated SiC monofilaments. The compressive stiffness ofthe lattice structures was well approximated by that of the monofilament fraction in the loading direction. The strength of the lattices wascontrolled by elastic buckling and the results were accurately represented by an elastic buckling model. The post peak compressive defor-mation was accommodated by elastic buckling of the SiC fibers and plastic deformation of the titanium coating until the onset of mono-filament fracture. The specific stiffness and strength of the lattices were found to be between 2 and 10 times that of other cellularstructures and thus appear to be promising candidates for high temperature, ultralight weight load supporting applications.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Cellular materials; A. Metal–matrix composites (MMCs); B. Mechanical properties

1. Introduction

Lightweight, multifunctional load supporting structuresbased upon sandwich panel concepts have many applica-tions [1–10]. Their cellular cores usually have either a pris-matic (corrugations) or honeycomb topology and areusually adhesively bonded to the face sheets [2–10]. Thecores are made of very low density materials such asNomex [3,4], polymer foams [5], or light metal construc-tions [6–9] that maintain the face sheet separation neededfor sandwich panel action at minimum parasitic mass [1].Metallic core systems based upon light metals such as alu-minum [6,7] and titanium [8,9] alloys are utilized wherehigh compressive strengths are needed to avoid local inden-tation. They can also be used for higher temperature appli-cations provided metallurgical bonding is used to attachthe core to the face sheets [6–9]. The maximum use temper-ature of these structures is then limited by the creep rate ofthe alloy system.

1359-835X/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compositesa.2007.11.007

* Corresponding author. Tel.: +1 434 982 5035; fax: +1 434 982 5677.E-mail address: [email protected] (P. Moongkhamklang).

While honeycomb topology systems usually offer signif-icantly superior structural performance [1,2,10,11], theirclosed-cell topology limits some potential multifunctionalapplications [10]. They are also susceptible to corrosionand suffer from delamination problems [2,9]. Stochasticmetal foam core systems with fully interconnected poreshave attracted interest because they provide multifunc-tional capabilities such as cross flow heat exchange[11–14], dynamic load protection [11,15–17], and acousticdamping [11,18]. However, their use in structural applica-tions is severely constrained by their low elastic moduliand indentation strengths [1,11].

Methods have recently begun to be developed for fabri-cating millimeter scale, open-cell metallic lattices from arange of light metals and high temperature alloys [19–31].The truss members in lattice materials can be topologicallyconfigured to experience predominantly axial stresses(i.e. tension or compression) when they are used in sand-wich panels that are loaded in bending (i.e. the cores arestretch dominated) [19,32–34]. This results in significantlysuperior mechanical performance compared to stochasticmetal foams whose ligaments deform by bending [35].

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P. Moongkhamklang et al. / Composites: Part A 39 (2008) 176–187 177

These lattice topologies also possess greater compressivestrength and therefore better resistance to indentation.

Numerous cell topologies have been fabricated includ-ing those with tetrahedral [19–23], pyramidal [21, 24–26],3D-Kagome [23,27], woven textile [28,29], and diamondor square collinear [30,31] structures. Examples of theselattices, configured as the cores of sandwich panels, areschematically illustrated in Fig. 1. The textile and collinearlattice structures exploit metallic wires for their fabricationby a simple lay-up and transient liquid bonding process[24,29–31].

The strength of lattice core sandwich panels is governedby the stress at which panel failure mechanisms are initi-ated under the various modes of loading (through thick-ness, longitudinal compression, bending, tension etc.)[37–40]. These failure mechanisms are well established formetallic materials and include face sheet yielding[34,36,38], face sheet wrinkling [34,36,38], core shear[28,37,38], core plastic yielding [34,36,38], fracture undertension [33], and plastic buckling [27,33,34] of compres-sively loaded core truss members. Although the most com-mon loading environments for sandwich panels are shearand bending, the practical implementation of sandwichpanels is often limited by concentrated compressive stressesat the loading points. In such cases, the core suffers localyield or crushing (indentation) and can be accompaniedby face sheet stretching/tearing [11,36,37]. These areaffected by the compressive strength of the core and the cellsize (which controls the stretching periodicity) [34].

The compressive stiffness and strength of lattice struc-tures could be significantly increased by the use of stiffer,higher strength core materials. The highest specific strengthlattice structures fabricated to date have utilized Ti–6Al–4V for the truss structures [26]. This alloy has a densityof 4.43 g/cm3, Young’s moduli in the range of 100–120 GPa, and yield strengths of 750–1250 MPa [39]. ATi–6Al–4V coated SCS-6 SiC monofilament developed inthe 1990’s for titanium matrix composite (TMC) manufac-

Fig. 1. Examples of sandwich panel structures with open-cell, lattice core topoloby folding perforated metal sheets or by investment casting. The textile and c

ture [40–42] appears to be an even stronger (but less duc-tile) candidate material for lattice structures. For a 35%fiber volume fraction, the axial Young’s modulus of themonofilament is about 215 GPa and its ambient tempera-ture tensile fracture strength exceeds 1800 MPa. Both areapproximately two times higher than that of Ti–6Al–4Valloy, while the density of such a monofilament would be3.93 g/cm3, roughly 12% less than that of Ti–6Al–4V.These composite materials also offer much better creepresistance than their all-metallic counterparts [43]. Withthese considerations, cellular structures fabricated fromsuch composites might be attractive for high temperatureand/or weight sensitive structural applications.

The aim of the current paper is to report a method forthe fabrication of TMC lattice core sandwich panels. Theout-of-plane compressive behavior of the lattice structureis investigated experimentally and the micromechanismsof lattice deformation as a function of lattice relative den-sity are identified. The mechanical properties are then com-pared to analytic estimates based upon the observed failuremodes. While these materials/structures have limited duc-tility, they appear to be one of the highest specific strengthcellular structures fabricated to date.

2. Lattice truss fabrication

Collinear lattice structures with a square orientation(Fig. 1f) and a relative density, q, in the range of 5–17%were fabricated from Ti–6Al–4V coated SCS-6 SiC mono-filaments supplied by FMW Composite Systems, Inc.(Clarksburg, WV). Each monofilament was approximately240 lm in diameter and consisted of a 140 lm diameter SiC(SCS-6) fiber surrounded by a 50 lm thick physical vapordeposited Ti–6Al–4V coating, Fig. 2. The SCS-6 fibers weremade by chemical vapor deposition on carbon cylindricalsubstrates (33 lm diameter fibers) [44,45]. The densitiesof SCS-6 fiber, Ti–6Al–4V, and the composite monofila-ment are 3.00, 4.43, and 3.93 g/cm3, respectively.

gies. Metallic pyramidal, tetrahedral and kagome core structures are madeollinear core structures are made by wire lay-up and brazing methods.

Fig. 2. (a) Schematic and (b) cross-sectional micrograph of a Ti–6Al–4V coated SCS-6 SiC monofilament (35% fiber volume fraction).

178 P. Moongkhamklang et al. / Composites: Part A 39 (2008) 176–187

Lattice structures were assembled from the monofila-ments using a simple fixture (constructed of stainless steeland spray coated with BN to prevent sticking) to alignthe monofilaments in collinear layers, Fig. 3a. The orienta-tion of consecutive layers was alternated to create a squarelattice truss topology structure. Fig. 4 shows a stackingsequence and a unit cell of the lattice structure. Onceassembly of the TMC filament lay-up was complete, a deadweight was used to apply a force of 3.7 � 10�2 N (equiva-

Fig. 3. Fabrication of a TMC square lattice core sandwich panel: (a) assembly(c) sandwich panel lay-up; and (d) brazing of face sheets to the square orienta

lent to an applied pressure of 1.5–5 MPa) to each contact(truss–truss node). The assembly was diffusion bonded byplacing it in a vacuum furnace at a base pressure of10�7 Torr. It was heated at 20 �C/min to 900 �C and thenheld for 4 h under pressure, Fig. 3b. The lattice structureswere then removed from the tooling and cut, using wireelectro-discharge machining, to create samples that werefour cells high and six cells in length, Fig. 3c. The samplewidth was approximately the same as the sample height,

sequence to make a TMC lattice; (b) vacuum diffusion bonding of the core;ted core.

Fig. 4. Representative unit cells of a square lattice: (a) three layer lattice;(b) unit cell before diffusion bonding; and (c) unit cell of the diffusionbonded structure (w < wo).


i.e. W � H = 4l, where l, W, and H are the unit cell length,the lattice width, and the lattice height, respectively.

The relative density of the as laid-up lattice,qo, is simplythe volume fraction of the unit cell occupied by solid trussmaterial:

qo ¼V s

V c

¼ 2pa2l

wol2¼ 2pa2l

4al2¼ pa

2l; ð1Þ

where Vc, Vs, wo, a, and l are the unit cell volume, the vol-ume occupied by the solid trusses, the cell width, the fila-ment radius, and the cell length, respectively.

Fig. 5 shows nodal regions of the lattice structure afterthe diffusion bonding step. It can be seen that excellentmetallurgical uniformity was achieved in the bondedregion. Equiaxed a-grains and an intergranular b-phasemicrostructure was observed with an average grain size of8 lm. During diffusion bonding, the spacing between con-secutive layers and hence the macroscopic lattice widthdecreased as the titanium alloy coating at the contactpoints deformed and interdiffused. Fig. 4 schematicallyshows a unit cell of the square lattice before and after dif-fusion bonding.

A diffusion bonding coefficient, b, can be introduced byassuming the titanium alloy coating was redistributed sim-ilarly in each collinear layer (see Fig. 4). The b coefficient isdefined as w/wo, where w and wo are the unit cell widthsprior to and after the diffusion bonding process (Figs. 4band c), correspondingly. The unit cell volume of the diffu-sion bonded lattice can then be written:

V c ¼ wl2 ¼ bwol2 ¼ b4al2: ð2Þ

Even though the titanium alloy coating is deformed at thecontacts, the volume occupied by the solid composite in theunit cell remains the same as for the as laid-up unit cell.The relative density of the diffusion bonded square latticestructure, q, is therefore:

q ¼ V s

V c

¼ 2pa2l

b4al2¼ 1

bpa2l

� �¼ qo

b: ð3Þ

Table 1 summarizes cell parameters and corresponding rel-ative densities of the square lattices prior to and after dif-fusion bonding. For the diffusion bonding conditionsused here, b was 0.9–0.92, and the relative density of thelattices therefore increased by 8–10% during the bondingprocess.

After being cut to size, the lattices were brazed to 2 mmthick Ti–6Al–4V face sheets using a TiCuNi-60� pastebraze alloy supplied by Lucas-Milhaupt, Inc. (Cudahy,WI), Figs. 3c–d. This alloy powder had a nominal compo-sition of Ti-15Cu-25Ni (wt%) and was held in a polymerbinder. The solidus and liquidus temperatures of the braz-ing alloy are 890 �C and 940 �C, respectively. The sandwichpanel samples were vacuum brazed by heating at 20 �C/minto 550 �C, holding for 5 min (to volatilize and remove thepolymer binder), and finally heating to 975 �C for 30 minat a base pressure of �10�7 Torr. Micrographs of a truss-face sheet node made by the brazing technique are shownin Fig. 6. It can be seen that the TiCuNi-60� braze pro-vided good wettability to the SCS-6 fiber surface as wellas good penetration to the Ti–6Al–4V alloy coating andface sheet. Photographs of sandwich panel samples of eachcore relative density are shown in Fig. 7.

3. Experimental compressive response

The square lattice structures were tested at ambient tem-perature in compression with a displacement rate of

Table 1Cell/lattice parametersa and corresponding relative densities prior to and after core diffusion bonding (T = 900 �C, t = 4 h, P = 1.5–5 MPa)

Center-to-center celllength, l (mm)

Prior to diffusion bonding After diffusion bonding b (w/w0)

Relative density, qo ð%Þ Core width, Wo (mm) Core width, W (mm) Relative density, q ð%Þ1.26 15.0 6.03 5.43 ± 0.015 16.7 ± 0.05 0.90 ± 0.0031.88 10.0 9.05 8.35 ± 0.025 10.8 ± 0.03 0.92 ± 0.0032.51 7.5 12.06 10.91 ± 0.043 8.3 ± 0.03 0.90 ± 0.0043.77 5.0 18.10 16.75 ± 0.147 5.4 ± 0.05 0.92 ± 0.008

a The monofilament diameter was 240 lm for all samples. The center-to-center cell length l is unaffected by diffusion bonding.

Fig. 6. Truss-face sheet interface for a square oriented lattice structure after the brazing treatment: (a) SEM micrograph; (b) optical microscope cross-sectional micrograph; and (c) SEM cross-sectional micrograph.

Fig. 5. Diffusion bonded truss–truss nodes: (a) exterior deformation of the metal coating at the nodes; (b) cross-section of a pair of nodes; and (c) diffusionbonded region between a pair of monofilaments.

Fig. 7. Photographs showing TMC square lattice core sandwich structures.


0.02 mm/min (see Table 2 for corresponding strain rates).The measured load cell force was used to calculate thenominal stress applied to the sandwich, and the nominalthrough thickness strain was obtained from a laser exten-someter positioned about the sample centerline. The gagelength for strain measurement for the compression sampleswas the core height, H (see Table 2).

The through thickness, compressive stress–strainresponses for square lattice structures at each q are shownin Fig. 8. All the cellular structures deformed in an elastic–brittle manner with a variable degree of post peak strengthretention that decreased with increasing relative density.The stiffnesses and peak strengths are plotted against q inFigs. 9a and b. The stiffness exhibited a linear dependence

Table 2Compression test parameters

Sample relative density,q ð%Þ

Core height,H (mm)

Strain rate,_e (10�5 s�1)

16.7 6.20 ± 0.031 5.38 ± 0.02710.8 9.38 ± 0.010 3.56 ± 0.0048.3 12.66 ± 0.015 2.68 ± 0.0035.4 19.26 ± 0.022 1.73 ± 0.002

Fig. 9. Experimental data for (a) out-of-plane compressive stiffness and(b) out-of-plane compressive strength of the TMC square truss cores.

Fig. 8. Compressive stress–strain response for square lattice truss struc-tures with q ¼ 16:7; 10:8; 8:3; and 5:4%.


upon q, while the strength appeared to depend on ðqÞ3.Figs. 10 and 11 show stress–strain responses and photo-graphs of the lattice taken during the compression of sam-ples with high (q ¼ 16:7%) and low (q ¼ 5:4%) latticerelative densities, correspondingly. As the samples werecompressed, trusses parallel to the loading directiondeformed elastically and then buckled cooperatively as aconsequence of being joined by the horizontal trusses.The peak stress in the stress–strain curve coincided withthe onset of this buckling instability. Unload/reload testsindicated that prior to the peak compressive strength thestrain was fully recoverable, indicating that the strengthof these structures is controlled by elastic buckling of thevertical trusses. Note that Fig. 8 indicates that the lowerthe relative density (the more slender the trusses) the lowerthe strength and the smaller the core strain at the onset ofelastic buckling.

In the highest relative density lattice (with q ¼ 16:7%),the trusses had a relatively low aspect ratio, and fractureof the monofilament was observed instantaneously withbuckling (Fig. 10). Fig. 11 shows clearly that for the latticeswith lower relative densities (more slender trusses), thetrusses continued to buckle cooperatively as the strainprogressed beyond the load peak. The buckling halfwavelength was equal to the core height. This buckling-accommodated straining was accompanied by a significantdecrease in applied stress, i.e. core softening. As compres-

sion continued, the truss nodes were subjected to increas-ingly significant shear forces and eventually debonded.Fig. 12 shows micrographs of a vertical truss after the com-pression test where shear debonding has occurred. In addi-tion to debonding at the nodal contact, fracture of themetallic coating and fiber also occurred in this case.

While the peak compressive strengths appear to be sim-ply controlled by the elastic buckling instability, the postpeak stress behavior is controlled by less obvious mecha-nisms. From Fig. 11, it is clear that the unloading pathswere not parallel to the initial elastic response and didnot return to zero strain. This is indicative of inelasticdeformation of the metallic coating. It appears that afterthe onset of the buckling instability, the SCS-6 fiber contin-

Fig. 10. Compressive stress–strain response and corresponding photographs of a square lattice truss structure with q ¼ 16:7%: (a) prior to initial loading;(b) prior to peak load; (c) immediately after the peak load; and (d) after the peak load. Events (b)–(d) occurred within a few seconds.

Fig. 11. Compressive stress–strain response and corresponding photographs of a square oriented lattice truss structure with q ¼ 5:4%: (a) prior to initialloading; (b) after the peak load and prior to first unloading; (c) following first unloading; (d) prior to second unloading; (e) following second unloading; (f)prior to third unloading; (g) following third unloading; (h) prior to fourth unloading; and (i) following fourth unloading.


Fig. 13. Analytical prediction and experimental data for (a) dimensionlessstiffness and (b) strength of TMC square lattices.

Fig. 12. Nodal shear and coating/fiber fracture near the nodes of acompressively loaded square lattice truss structure with q ¼ 10:8%.


ued to buckle elastically, while Ti–6Al–4V coatingdeformed plastically to accommodate the bending strainand node shear. At the highest core strains, beyond theelastic limit of the SCC-6 fiber and ductility of the Ti alloycoating, truss node debonding, coating fracture, and even-tually SCS-6 fiber fracture accommodated the imposedstrain and were responsible for the core softening.

The reloading behavior of these structures also revealedinteresting effects, Fig. 11. In particular, it can be seen thatwhen the lattice structure was reloaded, it followed a differ-ent stress–strain path to that during unloading. Duringunloading, the applied stress at a fixed core strain was lessthan that during the subsequent reloading cycle. Thisappears to be a result of elastic SiC fiber spring back andthe release of the stored elastic energy in the fiber.

4. Discussion

Simple micromechanical arguments can be used to ratio-nalize the initial loading modulus and peak strength of thecomposite cellular materials tested here.

4.1. Compressive stiffness

Under out-of-plane compression, only half of the trusses(the vertical trusses) carry load. Prior to buckling of thecompressively loaded columns, the elastic modulus, Ec, ofthe collinear lattice is simply [46]:

Ec ¼1

2Esq; ð4Þ

where Es is the axial Young’s modulus of the parent mate-rial. The axial Young’s modulus of the TMC monofilamentcan be estimated by the rule of mixtures:

Es ¼ ð1� f ÞEm þ fEf ; ð5Þwhere f is the volume fraction of the SCS-6 fiber, and Em

and Ef are the Young’s moduli of the Ti–6Al–4V matrixand SCS-6 fiber, respectively. For Ef = 400 GPa [44,45],Em = 115 GPa [39], and f = 0.35, Eq. (5) gives Es =215 GPa.

A comparison between the measured and predicted stiff-ness (plotted as non-dimensional compressive stiffness,P ¼ Ec=ðEsqÞÞ as a function of the lattice relative densityis shown in Fig. 13a. While most of the experimental datalie within 30% of the predicted value, some data lie well


below the prediction. Such discrepancies have been fre-quently reported for cellular materials [20–31] and the ori-gin of the effect appears to result from imperfectionsintroduced in the fabrication process. The discrepancyobserved here is believed to be a consequence of small vari-ations in the length of the load–carrying trusses (coreheight) due to the cutting process. During initial loadingthe applied load would then be disproportionately sharedbetween the trusses. The compressive platen would applythe load onto longer trusses first. Because the platen movedwith a constant rate, lower load would then be required thanif all the trusses were load carrying. As compression pro-ceeds, the load would be applied onto more and eventuallyall trusses. This makes the initial slope of the stress–strainplot (where a constant load supporting area is assumed) rel-atively low, but it continues to increase until the appliedload is proportionately shared among all the trusses.

4.2. Compressive strength

The peak compressive strengths of the TMC square col-linear cores can be estimated by analyzing the failuremodes of truss members as individual axially loaded col-umns. It is assumed that the lattice collapses by elasticbuckling of the constituent struts over the full height ofthe sandwich core as schematically illustrated in Fig. 14.If the vertical trusses are not joined together by horizontaltrusses, the buckling stress acting on each vertical truss canbe described by the elastic bifurcation stress, rcr, of a com-pressively loaded circular column [47,48]:

rcr ¼p2k2Es

4

alb

� �2

; ð6Þ

Fig. 14. Sketches of (a) an undeformed square lattice core and (b) itsexpected buckling mode under compression.

where Es is the column elastic modulus, a the column ra-dius and lb the length of the column between two support-ing ends. The factor k depends upon the rotational stiffnessof the end nodes with k = 1 corresponding to a freely rotat-ing pin-joint and k = 2 corresponding to built in nodeswhich cannot rotate [47,48]. For the square lattices, thetrusses length was H (the core height) and we assumek = 2. Using this expression for the predicted criticalstrength of individual truss members, the mechanical prop-erties of the sandwich panel that has no interaction amongthe truss members can be globalized and the compressivecollapse strength of a core structure, r0pk, can be expressedby [21]:

r0pk ¼ Rrcrq; ð7Þ

where R is a lattice topology dependent scaling factor.The scaling factor R = 1/2(sin2x1 + sin2x2) accounts forthe fact that trusses oriented in the loading direction arethe most efficient for load bearing, while those that areinclined are limited by force resolution considerations[49]. For square truss samples, half of the trusses havex1 = 0� and another half have x2 = 90� so the effectivevalue of R ¼ 0:5.

By substituting Eq. (6) into Eq. (7), the peak compres-sive strength of a square lattice truss structure failing byelastic buckling is then:

r0pk ¼p2Es

2

aH

� �2

q: ð8Þ

Substituting H = nl (where n = number of unit cells alongthe height of the core), Eqs. (1) and (3) into Eq. (8) givesa relation between core strength, lattice relative density,and the number of cells in the principle loading direction:

r0pk ¼2Es

n2bq3

o ¼2Esb

2

n2q3: ð9Þ

However, since the vertical trusses are joined together andhence are forced to buckle cooperatively, an additionalshear stress at the truss nodes is also present (as suggestedby experiment, see Fig. 12). This cooperative bucklingmode is similar to the shear buckling mode of a fiber com-posite material modeled by Rosen [50]. In Rosen’s model,adjacent fibers buckle with the same wavelength and inphase with one another. The deformation of the matrixmaterial between adjacent fibers is assumed to be primarilya shear deformation. Rosen found that the compressivestrength of a fiber composite rc due to (cooperative) shearbuckling is:

rc ¼Gm

1� vf

þ vfrcr; ð10Þ

where Gm, vf, and rcr are the shear modulus of the matrix,the volumetric fraction of the fibers, and the bucklingstrength of the fibers. The first term on the right-hand sideof Eq. (10) is the contribution to the composite compres-sive strength from matrix shear and the remaining term isthe contribution to the compressive strength associated


with the finite-bending resistance of the fibers. Fleck [51]subsequently argued that the matrix shear contribution,Gm/(1�vf), should be replaced by the in-plane shear modu-lus of the composite when the compressive strength of thecomposite material is to be estimated.

Using this composite analogy, the cooperative bucklingstrength of a square lattice is then controlled by the resis-tance to lattice buckling (Eq. (9)) and the resistance to lat-tice shear given by the in-plane shear modulus of the latticestructure, G:

rpk ¼ Gþ r0pk: ð11Þ

An analytical expression of the in-plane shear modulus ofsquare lattice G has been recently derived by Hutchinson[52]. He finds that the structure investigated here has ashear modulus:

G ¼ 1

16Esq

3: ð12Þ

By substituting Eqs. (12) and (9) into Eq. (11), the peakcompressive strength of a square lattice truss structure thatfails by cooperative elastic buckling then becomes:

rpk ¼1

16þ 2b2

n2

� �Esq

3: ð13Þ

A comparison between the measured and predicted com-pressive peak strength (plotted as non-dimensional peakcompressive strength, R ¼ rpk=ðEsq3Þ against qÞ of theTMC square collinear cores is shown in Fig. 13b. The coop-

erative elastic buckling model is seen to capture the peakcompressive strengths of these square lattices well. Theanalytically predicted strength coefficient is 0.13. Most ofthe experimental data lie within 20% of this estimate.

Fig. 15. (a) Stiffness and (b) compressive strength versus density for TMCand stainless steel collinear lattice structures. Data for ceramic foamshaving service temperature of 500 �C and above is also included.

4.3. Comparisons with other cellular structures

The highest specific strength lattice structures previouslyreported [19–31] utilized a Ti–6Al–4V alloy for the trussstructure. The specific strength of such lattices was foundto be approximately 100 kN m/kg [26]. The specificstrength of the titanium composite lattices studied herewas 185 kN m/kg. These TMC lattices therefore appearto be the highest specific strength cellular materialsreported to date.

The titanium composite lattices investigated here areexpected to retain good dimensional stability during load-ing at temperature up to 500 �C (above this, creep of themetallic component becomes significant). The stiffnessand peak strength of the square TMC lattice structurescan be compared with those of similar lattices made fromstainless steel [30] and ceramic foams [53–62] whose servicetemperatures also extend to 500 �C and above, Fig. 15.Examination of the figure indicates that the higher relativedensity TMC lattices possess a higher specific stiffness andstrength than any of the other structures/materials. Thesematerials may therefore provide interesting high tempera-

ture multifunctional opportunities provided their limitedductility is not a significant constraint.

5. Conclusions

1. A method for making titanium sandwich panels withmillimeter-scale titanium matrix composite (TMC) lat-tice cores has been developed. The method involves lay-ing up linear arrays of TMC monofilaments, alternatingthe direction of consecutive layers, and using diffusionbonding to join the nodes. The relative density of the


lattice was controlled by the diameter of the TMCmonofilaments, the spacing between the filaments ineach collinear layer (cell length), and the degree of diffu-sion bonding.

2. The out-of-plane modulus of square TMC lattice struc-tures has been shown to scale linearly with q. The com-pressive peak strength was controlled by cooperative

elastic buckling and varied with ðqÞ3.3. The specific strength and stiffness of the lattices signifi-

cantly exceeds that of other lattice structures fabricatedto date.

4. These TMC lattices appear promising candidates for ele-vated temperature, multifunctional applications.

Acknowledgements

The authors are grateful to Norman Fleck at the Uni-versity of Cambridge and Vikram Deshpande at the Uni-versity of California at Santa Barbara for helpfuldiscussions of the interpretation of this work. The studywas supported by the Office of Navel Research (ONR)and monitored by Drs. David Shifler and Steve Fishmanunder Grant Number N00014-01-1-1051.

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titanium matrix composite lattice structures · mation was accommodated by elastic buckling of the...

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