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Acta Materialia 59 (2011) 6145–6154

Structural ceramic coatings in compositemicrotruss cellular materials

E. Bele, B.A. Bouwhuis, C. Codd, G.D. Hibbard ⇑

Department of Materials Science and Engineering, University of Toronto, 184 College Street, Toronto, Ontario, Canada

Received 15 January 2011; received in revised form 10 June 2011; accepted 18 June 2011Available online 13 July 2011

Abstract

In the present study, anodizing was used to produce Al2O3 coatings in a conventional 3003 aluminum alloy microtruss core; a 38.5 lmthick anodic coating provided a 143% increase in compressive strength. Finite-element analyses were used to illustrate the dependence ofthe compressive strength and failure mechanism on the thickness of the anodic coating. At low thicknesses the microtruss strength isdictated by global bucking of the internal struts. However, at higher thicknesses the compressive strength is controlled by coating frac-ture and local deformation in the hinge region of the struts. Regardless of the failure mechanism, the compressive strength of the com-posite microtruss increased with increasing anodic coating thickness, with very little corresponding weight penalty.� 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Cellular materials; Aluminum alloy; Anodization; Compression test; Buckling

1. Introduction

Microtruss materials possess internal cellular architec-tures which are designed such that externally applied loadsare resolved axially along the constituent structural mem-bers, enabling them to achieve greater weight-specificstrengths and stiffnesses than conventional metal foams[1,2]. The axial failure of microtruss struts is typically con-trolled by the onset of plasticity and/or the occurrence ofstrut fracture (e.g. [3]). For struts in compression, the plasticyielding failure mechanism is often short-circuited by buck-ling; this is especially the case for long and slender struts inarchitectures with low relative densities. For most practicalmicrotruss strut slenderness ratios, inelastic buckling isoften seen as the strength-limiting failure mechanism duringcompression (e.g. [4]) and three-point bending (e.g. [5,6]).When inelastic buckling occurs, the load-bearing capacityis reduced and the governing strength equations dependon the tangent modulus of the strut’s material (ET = dr/de) [7] and the strut’s second moment of area (I).

1359-6454/$36.00 � 2011 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2011.06.027

⇑ Corresponding author. Tel.: +1 416 946 0437; fax: +1 416 978 4155.E-mail address: glenn.hibbard@utoronto.ca (G.D. Hibbard).

Since the surface area of microtruss architectures ishigh and the cross-sectional dimensions of microtrussstruts are small, it is possible to take advantage of whatwould otherwise be considered a surface treatment inorder to strengthen these cellular materials [8]. The sur-face is a particularly important region to reinforce sinceit is by definition optimally positioned away from the neu-tral bending axis of the internal struts. For example, a50 lm thick coating of electrodeposited nanocrystallineNi had the effect of more than doubling the inelasticbuckling resistance of 1.13 mm (w) � 0.63 mm (t) �5. 79 mm (l) plain carbon steel struts in a pyramidalmicrotruss core [8]. Even though the density of the rein-forcing nanocrystalline Ni (8.9 g cm�3) was higher thanthat of the plain carbon steel core (7.8 g cm�3), a 37.5%increase in specific strength was achievable at a coatingthickness of 60 lm. This is primarily due to the combina-tion of strength and second moment of area of the elec-trodeposited nanocrystalline component. In effect,electrodeposition was used to create metal–metal cellularcomposites in which the majority of the load-carryingcapacity was taken up by an interconnected network ofnanocrystalline tubes [8,9].

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Fig. 1. Finite-element model assembly (a) and strut mesh (b), showingplatens P1, P2, strut faces F1, F2, global and local coordination systems(XYZ and 123, respectively), and midstrut locations A, B.

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This study takes a different approach to microtrussstructural coatings, in which a ceramic–metal cellular com-posite is produced by the progressive oxidation of an alu-minum alloy microtruss anode, creating a reinforcingsleeve of Al2O3. Previously, chemical anodizing [10] andoxidizing heat treatments [11] have been applied toclosed-cell aluminum foams. In the case of Ref. [10], anincrease in compressive strength from �7.2 to �9.8 MPawas observed after the application of the anodizing treat-ment, followed by an aging period of 60 days, on an alumi-num foam of density 0.3 Mg m�3 (relative density of �0.1).The oxidizing heat treatment on an ALCAN foam of thesame density produced an oxide thickness of 1–2 lm; thecompressive curves of the oxidized samples were reportedto be essentially the same as those of non-oxidized samples[11]. In addition, plasma electrolytic oxidation has beenused to create oxide coatings on the ligaments of open-cellaluminum foams [12,13]. In the case of Ref. [12], poroussleeves were created on an AA6061 Duocel foam of density0.25 Mg m�3 (relative density of 0.09); the oxidized speci-mens showed nearly the same compressive strength as theuntreated specimens. Alternatively, in Ref. [13], a pure alu-minum foam of density �1.2 Mg m�3 (relative density of�0.4) showed an increase in compressive yield strengthfrom �2 to �12 MPa, after the formation of an oxide layer241 lm thick. Finally, chemical anodizing has been used toreinforce 3003 aluminum alloy honeycombs [14]. In thiscase, a compressive strength increase of 110% was reportedfor honeycombs of web thickness of 40 lm and oxide coat-ing thickness of 10 lm (honeycomb density 0.06 Mg m�3).

In this paper, an electrochemical anodizing process isused to oxidize the surface of 3003 aluminum alloy micro-truss structures possessing a relative density of �0.07. TheAl2O3 provides nearly the same strength increase per unitcoating thickness to the starting microtruss as was seen inthe case of nanocrystalline Ni [9]. However, unlike nano-crystalline electrodeposition, the strength increase in thepresent case is accomplished at virtually no additionalweight penalty.

2. Experimental

The metal–ceramic composite microtruss materials of thepresent study were fabricated from a perforated aluminumalloy 3003 (AA3003) sheet (initial thicknesst0 = 0.78 ± 0.01 mm). The 25.81 mm2 square perforationswere punched on a two-dimensional square lattice of unitcell size 6.35 mm � 6.35 mm, creating an open area fractionof / = 0.64 (the same as in Ref. [8]). The pyramidal coreswere fabricated by deforming alternating nodes aboveand below the starting plane using a modified stretch-bend-ing process (see Refs. [8,15] for details). A fixed out-of-plane forming displacement of 3.50 mm was used, leadingto a truss height h of 4.13 ± 0.06 mm, strut length l of5.30 ± 0.06 mm, strut width w of 1.06 ± 0.03 mm, and strutthickness t of 0.68 ± 0.05 mm, which corresponded to atruss angle x of 33� and relative density qR of �6.6%.

The Al2O3 surface layer was created using a four-step pro-cess. The first three steps (surface cleaning, etching and de-smutting) were used to prepare the microtruss surfaces foranodizing. Of the three, the etching step (2 min in 5 wt.%NaOH at 55–60 �C) was the only one that removed a sig-nificant amount of the starting microtruss substrate; thestrut width and thickness after this step were 1.03 ± 0.02and 0.66 ± 0.02 mm, respectively. The final anodizing stepwas performed after the Hard Anodize Alumilite 225/226Method [16], with a DC current density of 28 mA cm�2.Anodizing times were set at 10 min intervals for up to60 min.

For each anodizing time, the thickness of the sleeve tS

was measured from strut cross-sections using standardmetallographic techniques and scanning electron micros-copy (SEM). The mechanical properties of the anodic coat-ing were evaluated by Vickers microhardness measurements at a load of 0.25 N. The Al2O3/Al microtruss coreswere tested in compression using confinement plates, i.e.recessed channels in steel plates that rigidly lock the trussnodes in place (see Refs. [17,18] for details). This testmethod can be used to simulate the mechanical perfor-mance that microtruss sandwich cores would exhibit in asandwich structure [17,18]. Failure mechanisms in the com-posite microtruss cores were investigated by pre-loadingsamples to characteristic strain values and examining themby SEM.

The failure mechanisms and strengthening potential ofthe Al2O3 coating were also investigated by finite-element

Fig. 2. Sleeve thickness (tS) and core thickness (t) as a function ofanodizing time (a), and cross-section of an Al2O3–Al composite microtrussstrut with a sleeve thickness tS = 35.3 ± 2.5 lm (b).

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(FE) analyses. Al2O3 sleeves with uniform thicknesses of0.01, 0.02, 0.03, 0.04 and 0.05 mm were modeled on a singlestrut with the geometry of the pyramidal truss cores studiedhere. A schematic of the assembly is shown in Fig. 1a. Thecompression platens were modeled as analytical rigid sur-faces; platen P2 was constrained in all degrees of freedomof the global XYZ coordinate system, whereas platen P1was prescribed a vertical displacement in the �Y directionto simulate compression. To reproduce the symmetry con-ditions of the pyramidal unit cell, faces F1 and F2 of thestrut and coating were constrained from displacement inthe global X axis and rotation about the Y and Z axes; fur-thermore, no vertical displacement was allowed for faceF2.

The truss core was modeled with linear hexahedral ele-ments with reduced integration and enhanced hourglasscontrol, whereas shell elements having one in-plane andfive through-thickness integration points were used tomodel the Al2O3 sleeves. The mesh of the strut and sleeveis shown in Fig. 1b; mesh convergence studies showed thatthis level of refinement was satisfactory. To simulate theinterfacial conditions between the Al2O3 sleeve and under-lying AA3003 truss core, tie constraints were used to con-nect the contacting sleeve–truss surface nodes, preventingrelative displacement. The commercial ABAQUS packagewas used to execute the FE simulations. Due to the largenumber of elements (5.2 � 104 in the core and 1.1 � 104

in the sleeve) a quasi-static explicit analysis was performedto speed up the analysis. An artificial increase of the com-pression velocity to 1500 mm s�1 was found to be satisfac-tory, producing no change in the load–displacement curvecompared to static analyses, and maintaining a negligibleratio of kinetic to internal energy (i.e. <10�6).

To model the material properties of the core, an ASM-published stress–strain curve of AA3003 aluminum alloy inthe fully softened O-temper [19] was fitted to the Hollomonpower law r ¼ Ken

P , where r and eP represent the true stressand plastic strain, respectively, and K and n are the Hollo-mon fitting parameters (here K = 201 MPa and n = 0.27).In order to examine the effect of coating stiffness, the sleevematerial was modeled to have elastic modulus values in therange 50–130 GPa (typical values of anodized Al2O3 coat-ings [20–26]). Local coordinate systems that follow thedeformation of elements were defined to capture the stressstate of the model during buckling. The local coordinatesystem of the Al2O3 sleeve is shown in Fig. 1a: axis 3 is nor-mal to the surface of shell elements, axis 2 follows the out-line of the length of the strut, and axis 1 follows thecircumference of the sleeve.

To illustrate material failure in the sleeve, fracture wassimulated using Hilleborg’s model [27]. This model is typi-cally used in concrete [28] and ceramics [29,30], where frac-ture occurs in tension due to Mode I crack initiation [27].The material is assumed to have elastic properties up to amaximum tensile stress, when microcracks coalesce aheadof the crack tip. Typical tensile strengths of Al2O3 coatingsfabricated using the same processing methods as the

present study are in the range 108–228 MPa [26]; a valueof 150 MPa was chosen for the present study. The tensilestress degradation after the initiation of damage was pro-vided using a bilinear stress–COD (crack opening displace-ment) relationship [28], which minimizes mesh sensitivity.A fracture energy of 100 J m�2 was used to specify the areaunder the stress–COD curve, which is typical of concretesand Al2O3 composites [29]. Mode II crack propagationwas defined by a linear degradation of shear stiffness tozero at a fracture strain of w2/50 lm, where w2 is theCOD when the uniaxial stress is degraded to zero, and50 lm is the average element size in the hinge. Finally, ele-ment removal was specified when the stiffness degraded tozero from the stress degradation criterion of Mode I.

3. Results

The Al2O3 sleeve thickness (tS) and AA3003 corethickness (t) are shown as a function of anodizing time inFig. 2a. The anodic film thickness increased fromt = 4.8 ± 0.4 lm after 10 min of anodizing to t = 38.5± 2.7 lm after 60 min (an average rate of 0.62 ±0.08 lm min�1 over all samples). The cross-section of a typ-ical 50 min anodized microtruss strut (t = 35.3 ± 2.5 lm) isshown in Fig. 2b. An average microhardness of410 ± 10 HV over 10 measurements was obtained in the

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anodic film; while the hardness depends greatly on the anod-izing parameters (e.g. [31]), the average obtained here fallswithin the range of 350–600 HV typically seen for anodicAl2O3 (e.g. [22,31–33]). The coating discontinuity at the cor-ners of the cross-section corresponded to cracks runningalong the length of the strut edges. These cracks formbecause the volume expansion associated with anodizationat the Al2O3–Al interface results in tensile stresses buildingup at regions of large convex curvature—an issue thatbecomes more significant with greater anodic layer thickness[32]. It is worth noting that this non-uniformity in structuralreinforcement is different than that found during microtrussreinforcement by electrodeposition, where the amount ofelectrodeposited metal is greatest at the strut corners, sincethe rate of metal ion reduction is highest at regions of largeconvex curvature [34].

Despite the longitudinal cracks in the metal–ceramiccomposite struts, significant strength and modulusincreases were seen with increasing coating thickness. Typ-ical compression stress–strain curves of the as-formed, pre-anodized and anodized microtrusses are shown in Fig. 3. Itis important to note that the peak compressive strength ofthe pre-anodized microtrusses (i.e. after the surface prepa-ration steps, but without the ceramic reinforcement) was9.4% lower than the peak compressive strength of the as-formed starting structure. This decrease in strength is dueto the removal of material during the etching stage:approximately 2.5% of the aluminum microtruss weightwas lost after 2 min in the NaOH solution. The cross-sec-tional dimensions of the strut after the etching stage corre-spond to a �10% reduction in the second moment of areaI, which is consistent with the 9.4% reduction in peak com-pressive strength. Despite the material loss during the pre-anodizing stages, the strength of the starting microtrusswas completely recovered with an anodic sleeve thicknessof less than 4.8 lm. With greater coating thickness themicrotruss strength and modulus also increased: at a thick-ness of 12.4 lm, the compressive strength was approxi-mately 60% greater than the as-formed microtruss; at the

Fig. 3. Typical uniaxial compression stress (rMT)–strain (e) curves of as-formed, pre-anodized and anodized microtruss cores with sleeve thickness4.8 lm 6 tS 6 38.5 lm.

greatest thickness, 38.5 lm, the compressive strength wasapproximately 140% greater than the as-formed micro-truss. Over this same range, the compressive modulusincreased by approximately 40% over that of the as-formedmicrotruss.

Fig. 4a presents an SEM micrograph of a typicalmicrotruss strut (pre-anodized, loaded past the peakstrength at e = 0.36), exhibiting a mid-strut plastic hingedue to inelastic buckling failure. This failure mechanismwas also observed for ceramic–metal microtrusses withtS = 4.8 and 12.4 lm. Note that for these samples, sleevefracture was eventually observed at comparatively large

Fig. 4. Low-magnification SEM micrographs showing the overall strutfailure mode for a pre-anodized aluminum core (a) and Al2O3–Al corewith sleeve thickness tS = 38.5 lm (b) loaded to just after the initial peakstress. The higher-magnification SEM image (c) of the Al2O3–Al coreshows the progression of coating fracture above the hinge-front.

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post-buckling strains (e.g. e > 0.04) in the convex side ofthe buckled strut as a result of the induced tensile stresses.At greater coating thicknesses, however, the failure mecha-nism changed: there was no evidence of buckling failure,and collapse was localized to the strut ends. An exampleof a strut undergoing this failure mechanism is shown inFig. 4b (sample with sleeve thickness tS = 38.5 lm, com-pressed to e = 0.36). Progressive failure was observed inthe form of sleeve fracture (Fig. 4c) that spread along thestrut length in a series of waves; the onset of sleeve fractureand the accompanying loss of load-carrying capacity thateach of these failure events indicates is the likely cause ofthe serrated stress–strain curve. From an energy absorptionperspective, this failure mechanism may be desirable sincethe failure zone moves progressively along the strut, akinto a “travelling knuckle” mechanism (e.g. [35]), and a largeamount of new surface area is created within the frag-mented Al2O3 coating.

The difference between the two strut failure mechanismscan also be seen when the slope of the stress–strain curves isplotted as a function of strain (Fig. 5). The thinnest coat-ings exhibited a smooth transition from the initial elasticregion through a peak buckling stress, which was compara-ble to what is seen in conventional aluminum alloy micro-truss materials. On the other hand, for Al2O3 coatingthicknesses of �20 lm and greater, a series of small loaddrops could be seen in the stress–strain curve (Fig. 3),which correspond to sharp valleys in the slope–strain plotof Fig. 5.

4. Discussion

Some insight into the overall failure mechanisms of theceramic–metal microtruss can be obtained by FE simula-tions of individual struts having the same geometry asthe experimental microtrusses. Upper- and lower-boundestimates for the elastic modulus of the oxide layer canbe taken from previous studies of anodized Al2O3, whichtypically fall in the range 30–150 GPa [20–26]. FE simula-

Fig. 5. The instantaneous slope to the stress–strain curve (drMT/de)plotted as a function of strain (e) for the pre-anodized microtruss cores,and Al2O3–Al hybrid cores with sleeve thicknesses tS = 4.8 and 38.5 lm.

tions of strut collapse for coating thicknesses of 10, 20,30, 40 and 50 lm with elastic modulus values of 50, 90and 130 GPa were studied. Fig. 6 shows compressionstress–strain curves of hybrid struts with a sleeve modulusof 50 GPa and thicknesses between 10 and 50 lm. Thestress–strain curves exhibit an initial elastic region followedby non-linear deformation when the stress in the aluminumcore exceeds the proportional limit. At continued deforma-tion, strut bending is initiated at the onset of bucklinginstability. The strut continues to support increasing com-pressive loads as it starts to bend, before finally exhibiting apeak strength in the overall stress–strain curve. In the finalstage of compression, the models display a softeningbehavior which is caused by a loss in load-carrying capabil-ity due to continued buckling.

The onset point of buckling (critical or bifurcationstress) can be determined in FE models by monitoringthe longitudinal stress on opposing surfaces of the sleeveon the bending plane, i.e. points A and B in Fig. 1a. Inthe initial stage of compression, the strut remains straightand the longitudinal stress is uniformly distributed acrossa cross-sectional area perpendicular to the length of thestrut, i.e. r2,A = r2,B, where subscript 2 refers to the direc-tion of the local coordinate system aligned with the lengthof the strut (see Fig. 1a). The critical buckling strength rep-resents the initiation of bending: at continued deformation,the stress perpendicular to the cross-section increases fasteron the concave side than the convex side, i.e. r2,B > r2,A.The critical stress and strain in the FE model can thus beobserved by detecting the instant at which stress bifurcateson the opposite surfaces of a cross-sectional area located atmid-length. The simulated critical buckling stress for thepresent microtruss strut geometry is plotted as a functionof sleeve thickness in Fig. 7. For each simulated modulusvalue, the critical buckling stress increased with Al2O3

coating thickness: for instance, at a thickness of 10 lm,the critical buckling stress of the hybrid increased over thatof the uncoated model by factors of 2.8, 5.9 and 6.9 forsleeve modulus values of 50, 90 and 130 GPa, respectively.

Fig. 6. FE simulated stress (rMT)–strain (e) curves for the startingaluminum strut and Al2O3–Al composite struts with sleeve elastic modulusES = 50 GPa and thickness 10 lm 6 tS 6 50 lm.

Fig. 7. FE predicted critical microtruss stresses (rMTCR ) for Al2O3–Al

composite struts with sleeve elastic moduli (ES) of 50, 90 and 130 GPa andsleeve thicknesses 0 lm 6 tS 6 50 lm (the dashed lines are visual guides).

Fig. 8. Analytical model predictions of the microtruss stress (rMT) atbifurcation in an Al2O3–Al hybrid with sleeve modulus ES = 50 GPa, forstrut end constraint values k = 1.0, 1.4 and 2.0. Also shown are the FEpredictions of the critical stress, and the value of the microtruss stress atthe first appearance of longitudinal tensile stresses in the sleeve (rMT atrT).

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The increased critical buckling stress is not unexpected forES = 90 and 130 GPa since these values are higher than theYoung’s modulus of the core material (69 GPa). However,at first sight it might be somewhat unexpected that a sleevewith modulus of ES = 50 GPa, i.e. 27% smaller than that ofthe core material, could also increase the critical bucklingstress.

The mechanism by which a sleeve with a lower elasticmodulus can increase the critical buckling stress of a strutcan be understood by examining the values of tangentmodulus and stress of each material at the critical strain.The dimensions of the composite struts (slenderness ratioof 25.6) are such that buckling occurs inelastically. Forthe present uncoated strut, ET,C is calculated as 1.7 GPa.As the sleeve thickness (tS) increases, the tangent modulusof the core at buckling (ET,C) further decreases below theelastic modulus of the sleeve, from 591 to 360 MPa fortS = 10 and 50 lm respectively. Furthermore, the additionof the sleeve increases the critical strain in the aluminumcore component, also raising its stress above that possiblein the absence of the sleeve; e.g. from 56.0 MPa (uncoatedcore) to 84.8 and 102.2 MPa (tS = 10 and 50 lm, respec-tively). As a result of these stress magnitudes, anodizedsleeves can provide a reinforcing role in Al2O3–Al compos-ite struts even if the sleeve modulus is at the low end of therange of reported values.

This critical buckling strain (and therefore the geome-tries over which a lower-modulus anodized coating mightstrengthen an aluminum alloy microtruss) can be predictedanalytically by using a composite strut buckling approach,after Ref. [36]. Using an isostrain assumption, the averageaxial stress of the composite column is given by:

rAxial ¼rSAS þ rCAC

AS þ AC; ð1Þ

where rS and rC are the stresses in the reinforcing Al2O3

sleeve and aluminum core, respectively, and AS and AC

are the cross-sectional areas of the sleeve and core, respec-tively. According to the inelastic buckling theory [7,37], the

composite column will start to bend at a critical axial stress(rCR) determined by [9,38]:

rAxial ¼ rCR ¼k2p2ðESIS þ ET ;CICÞðAS þ ACÞL2

; ð2Þ

where ES and IS are the elastic modulus and second mo-ment of area of the Al2O3 sleeve, ET,C and IC are the tan-gent modulus and second moment of area of the aluminumcore, L is the length of the column, and k is a constantdescribing the rotational stiffness of the ends (k = 1 forpin ends and k = 2 for rigid ends). Finally, the critical com-pressive stress of the microtruss (rMT

CR ) is obtained by forceresolution in a unit cell of the architecture [38]:

rMTCR ¼ ðN sin xÞAS þ AC

AMT rCR; ð3Þ

where N, x and AMT are the number of struts in a unit cell,strut angle and unit cell area, respectively.

The analytically predicted critical buckling stresses of acomposite strut are plotted in Fig. 8, using the theoreticallimits k = 1 and k = 2 and sleeve elastic modulusES = 50 GPa. As expected, these k limits bracket the criti-cal stress obtained by the FE simulations. The actual endconstraint of the starting aluminum strut can be estimatedby using the critical buckling stress from the FE model tosolve for k in Eq. (2), giving a value of k = 1.4. There is rea-sonable agreement between the analytical and FE-pre-dicted critical buckling stresses of the Al2O3–Alcomposite struts using k = 1.4 (see Fig. 8), but this agree-ment decreases with increasing sleeve thickness.

The effectiveness of Eq. (2) breaks down at higher sleevethicknesses because local shell buckling is initiated in thehinge regions of the struts. Shell buckling occurs duringthe uniaxial compression of thin-walled hollow columnswhen energy loss can occur more readily (i.e. at lower stres-ses) by local bending of the section’s faces rather than by

Fig. 9. Distribution of longitudinal stress (r22; values in Pa) in the outersurface of shell elements representing an Al2O3 sleeve with thicknesstS = 30 lm and elastic modulus ES = 50 GPa, at the first appearance oftensile stresses (positive in this coordinate system).

Fig. 10. Compressive stress (rMT)–strain (e) curve of an FE simulationwith a sleeve thickness of 50 lm and activated material fracture [27]model. Points 1–4 correspond to the stress states illustrated in Fig. 11.

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global bending of the column [39–42]. If the sleeves that arebeing considered here were compressed in the absence ofthe aluminum core, the material properties and dimensionswould dictate local buckling as the preferred failure mech-anism for all thicknesses. However, the aluminum core actsas a medium that provides resistance to the creation oflocal folds. Thus, the critical strength of the struts is ulti-mately determined by a complex interaction between theglobal bending of the composite strut and the local foldingdeformation near the hinge.

Localized folds are regions of concentrated deformationwhere longitudinal tensile and compressive stresses create ahigh stress gradient. Fig. 9 shows the distribution of longi-tudinal stresses in the outer shell surface of a FE modelwith a sleeve thickness t = 30 lm and elastic modulusES = 50 GPa, at the stage of compression when tensilestresses are first developed in the sleeve. Notice that thelocation of the maximum tensile stress is in the same regionthat fracture and failure of the Al2O3 coating was seenexperimentally (Fig. 4b). These tensile stresses are devel-oped at the hinge due to the development of local bucklingfolds, thus they can appear before or after stress bifurca-tion (i.e. global buckling) occurs in the strut.

Some insight into the initiation of fracture in the Al2O3

sleeves can be obtained from the FE model. The microtrussstress at the stage of deformation in which tensile stressesare first observed in the hinge region of the sleeve is plottedas a function of coating thickness in Fig. 8. Among the sim-ulations of composite struts with ES = 50 GPa, modelswith sleeve thicknesses of 10 and 20 lm showed tensilestresses only after the critical inelastic buckling stress hadbeen achieved (i.e. global buckling had been initiated),whereas in all other models tensile stresses were developedin the hinge before the initiation of global buckling. In thelatter models, distinct folds were observed in the hinge, andtheir progression led to the sudden drops in the microtrussstress–strain curves shown in Fig. 6.

Of these two competing failure mechanisms, the domi-nant one will be that which is activated at a lower stress.The interaction between buckling and sleeve fracture thusdefines two failure regimes. At low sleeve thicknesses (e.g.t 6 0.02 mm in these simulations), the stress and strainrequired for inelastic buckling is small, and tensile stressesin the hinge are developed after the critical strain isreached. Thus, in this regime strut buckling is the predom-inant failure mode, and the critical stress and strain of thecomposite strut is modeled well by the analytical inelasticbuckling model (see Fig. 8). As the coating thicknessincreases (e.g. t > 0.02 mm in these simulations), the stressand strain required for strut buckling also increases. In thisregime, local buckling in the hinge can be activated beforethe necessary deformation for global buckling is reached(see Fig. 8).

In experimental samples, however, the sleeves are notcapable of supporting large tensile stresses, due to the lim-ited ductility of the ceramic coating. As a result, local buck-ling and the resultant formation of tensile stresses coincide

with the development of cracks in the hinge region; subse-quent deformation occurs by way of progressive crackpropagation. An illustration of this failure propagationmechanism can be provided by the FE simulation of a strutwith a 50 lm sleeve thickness, where the sleeve elements areassigned crack initiation and propagation propertiesaccording to the Hilleborg model [27].

The compressive stress–strain curve of this model(Fig. 10) exhibits numerous load drops before and afterthe peak strength, similar to the experimental curves ofFig. 3. These load drops correspond to element deletions,which occur when stiffness is lost due to the stress degrada-tion from the opening of the simulated cracks, resulting inan overall peak strength reduction of 42% when comparedto the FE model without a fracture criterion. Notice alsothat due to the element deletion, the peak strain is 0.14,i.e. 0.53% lower than the corresponding peak strain ofthe model without a fracture criterion.

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The fracture propagation mechanism can be illustratedthrough sequential plots of the maximum principal stressdistribution in the sleeve elements (Fig. 11). The principalstress first exceeds the prescribed tensile strength of thesleeve at a strain of 0.016 (Fig. 11a, corresponding to point1 in Fig. 10a), due to the tendency of the sleeve to fail bythe formation of localized folds. Because the hinge rotatesabout its center of curvature, these maximum tensile stres-ses are first formed on the convex surface. Elements with amaximum principal stress equal to the prescribed tensilestrength of the material (150 MPa) satisfy the conditionfor the coalescence of microcracks ahead of the crack tip,and their load-carrying capacity progressively degrades.Fig. 11b shows the stress state of the sleeve at a strain of0.07 (point 2 in Fig. 10). At this stage, the first elementshave been removed because of a complete loss of stiffness(i.e. degradation of the principal stress to a value of zero).The distribution of the maximum principal stress at thepoint of peak strength is shown in Fig. 11c (strain of0.14; point 3 in Fig. 10), and Fig. 11d shows the stress stateat a post-peak strain of 0.25 (point 4 in Fig. 10). The

Fig. 11. Maximum principal stress states at strains of 0.016 (a), 0.06 (b), 0.14 (shown. Elements that are shaded in gray have failed and experience brief stre

removed elements have been predominantly localized inthe near-hinge region; it is significant to note that whenthe axial stresses were tracked at the mid-section of thestrut (points A and B in Fig. 1a), there was no indicationof stress bifurcation either before or after the peak stresshad been reached (i.e. no appreciable buckling hadoccurred). By contrast, in the FE model without the sleevefracture criterion, stress bifurcation was observed at astrain of 0.28; this strain was smaller than the peak strainby 0.01. The FE models therefore suggest that the peakstrength of these composite microtruss cores is controlledby localized material fracture in the hinge rather than glo-bal buckling instability, in agreement with the experimentalmicrographs of Fig. 4b and c.

The activation and evolution of failure within the sleeveelements and its propagation down the length of the strutcan be tracked by plotting the maximum principal stressas a function of nominal compressive strain in a series ofelements along the length of the strut (I–V in Fig. 11a).Fig. 12 shows that elements within the strut connectiveregion (e.g. element I) never achieve the maximum tensile

c) and 0.25 (d) (points 1–4 in Fig. 10). For clarity, only half of the model isss instabilities before being removed.

Fig. 12. Maximum principal stress (r1) as a function of strain (e) inelements I–V (see Fig. 11a) of the FE model with a sleeve thickness of50 lm and activated material fracture [27] model.

Fig. 13. Experimentally measured compressive peak strength (rMTPK ) as a

function of coating thickness (tS) for n-Ni–Al [9] and Al2O3–Al hybrids(a), and strength (rMT

PK )–density (q) property map (b).

E. Bele et al. / Acta Materialia 59 (2011) 6145–6154 6153

stress of the material, and thus the failure criterion is notactivated. By contrast, elements located in the hinge andits proximity (elements II–V), satisfy the fracture initiationcriterion at successively larger deformation. Stress degrada-tion corresponding to microcrack coalescence begins at theelements that are closest to the hinge and progressivelymoves down the length of the strut as the overall compres-sive strain increases (e = 0.033, 0.041, 0.050 and 0.057 forelements II, III, IV and V, respectively).

A transition in microtruss strut failure mechanism wasalso seen in nanocrystalline nickel (n-Ni)-reinforced alumi-num microtrusses [9]. In the case of n-Ni–Al microtrusscores with the same starting geometry as that used in thepresent study, the compressive peak strength of the hybridwas determined by global strut buckling at small coatingthicknesses (t = 17.1 lm), a combination of strut bucklingand hinge failure at intermediate coating thicknesses (27.2and 36.8 lm), and only hinge failure at large coating thick-nesses (t P 48 lm). However, there is an important differ-ence in the onset of these failure mechanisms. In the n-Ni–Al composites, hinge failure started as delaminationof the sleeve from the aluminum substrate, which resultedin comparatively few larger cracks within the coating nearthe hinge. Because of the intrinsic ductility of the n-Nimaterial, the hinge-dominated failure was only possibledue to the imperfect adhesion between the two components[9]. By contrast, the present Al2O3 sleeves adhere firmly tothe underlying Al substrate, but their limited ductility givesrise to crack initiation almost as soon as tensile stresses aredeveloped in the newly created fold, and crack propagationoccurs in the form of a moving fracture front along thestrut length.

One measure of the effectiveness of a structural coatingis the strength increase provided per unit of layer thickness;Fig. 13a plots the n-Ni–Al and Al2O3–Al microtruss peakstrengths as a function of their respective coating thickness.For this particular type of architecture, n-Ni is more effec-tive than Al2O3 at increasing the strength: the measuredrates are �90 kPa lm�1 for n-Ni and �70 kPa lm�1 forAl2O3. However, on a weight-specific basis the Al2O3 sleeve

provides a significantly greater property enhancement; thiscan be seen in Fig. 13b, which plots the overall microtrussstrength (rMT

PK ) against density (q) for the Al2O3–Al and n-Ni–Al hybrids. For example, at a n-Ni coating thickness of37 lm, the n-Ni–Al trusses in Ref. [9] possessed a strengthof �5.2 MPa at a density of 0.25 Mg m�3 (specific strengthof �21 MPa (Mg/m3)–1). By contrast, the microtruss rein-forced with a 38 lm thick anodized sleeve had a strengthof �4.6 MPa at a density of 0.17 Mg m�3 (specific strengthof �27 MPa (Mg/m3) –1); the density of this metal–ceramiccomposite was only 3% higher than the density of the start-ing core.

5. Conclusions

Metal–ceramic composite microtruss materials were cre-ated by anodizing a structural Al2O3 coating around anAA3003 aluminum alloy starting microtruss core. Thisapproach increased the compressive strength and elasticmodulus of the cellular material considerably. Comparedto the case of electrodepositing high-strength nanocrystal-line Ni sleeves on the same type of aluminum microtrusscore, the strength increase per unit sleeve thickness pro-vided by anodizing was lower. However, because anodizingis a transformative surface treatment, the Al2O3 coatingwas able to achieve these performance increases with little

6154 E. Bele et al. / Acta Materialia 59 (2011) 6145–6154

overall weight penalty. With this processing approach, anearly vertical path can be traced upwards through thestrength–density material property space.

SEM characterization revealed that the peak compres-sive strength of structures with very thin (<20 lm) ceramicsleeves was determined by inelastic strut buckling; at largerthicknesses, however, the struts exhibited progressive frac-ture of the ceramic sleeve near the hinge region. The inter-action between these competing failure mechanisms andtheir effect on compressive strength was elucidated withthe use of FE analyses. The preferred failure mechanismof the high-strength Al2O3 sleeve is local shell buckling.However, the encapsulated aluminum substrate withinthe microtruss hybrids inhibits the cross-sectional deforma-tion required for local folding, thus the composite strutinstead fails by global buckling. At higher sleeve thick-nesses, the deformation required for global bucklingincreases rapidly, thus localized folding at the hinges canshort-circuit global buckling as the strut failure mecha-nism. Due to the limited tensile ductility of the ceramiccomponent, the formation of a local fold is associated withthe initiation of tensile cracks in the hinge and the propa-gation of cracks in the form of a moving fracture frontalong the length of the strut.

Acknowledgements

This work was supported by the Natural Sciences andEngineering Research Council of Canada (NSERC). Oneof the authors (E.B.) was also supported by an OntarioGraduate Scholarship in Science and Technology(OGSST). The authors would also like to acknowledgethe contributions of Mr. Sal Boccia at the University ofToronto.

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