failure of sandwich beams consisting of alumina face sheet and aluminum foam core in bending

Materials Science and Engineering A 409 (2005) 292–301

Failure of sandwich beams consisting of alumina facesheet and aluminum foam core in bending

Kapil Mohana, Yip Tick Hona, Sridhar Idapalapatib,∗, Hong Pheow Seowa

a School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singaporeb School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore

Received in revised form 10 June 2005; accepted 21 June 2005

Abstract

Applications of sandwich structures, comprising alumina face sheets and aluminum foam core, depend critically on their mechanical performance.Four point bend tests are performed on sandwich beams with varying geometries to identify competing failure modes, such as core indentation,face sheet cracking and core shear. Analytical formulae for the identified failure modes are obtained. A failure mode map was constructed based onthe analytical calculations in the non-dimensional parameters of beam geometry for a given face sheet to core strength ratio. The tested geometriesare simulated using a finite element program: the beam stiffness and the failure load calculations were found to be in good agreement with thee©

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xperimental and analytical results within experimental scatter.2005 Elsevier B.V. All rights reserved.

eywords: Aluminum foam; Alumina; Beam bending; Failure mode map; Finite element analysis

. Introduction

A range of engineering alloys, such as aluminum, iron, nickel,opper, etc. can be foamed to relatively densities as low as 3% byvariety of manufacturing routes[1]. These metallic foams are

ikely to replace the currently used honeycomb structures andolymeric foams as these are quite anisotropic, creep and noto durable under impact and shock loading[2–5]. Among theetallic foams, aluminum based ones are gaining popularity in

ransport (aerospace, ship building, etc.), sport and biomedicalndustries[2] as they are cost-effective, have high specific stiff-ess and strength, recyclable, good corrosion resistance. Opennd closed cell structure foams can be made by varying the man-facturing techniques both of which favor the usage in differentpplications based on the requirements.

The performance of metallic foams can be enhanced byandwiching it between two strong and stiff face sheets to pro-uce a lightweight structure. Under static loading conditions,

he face sheets carry the axial load or resist against bending,hereas the core bears the shear deformation[5,6]. Sandwichanels with minimal weights, desired stiffness and strength can

be designed specific to suit various applications. This caachieved by optimizing different parameters, such as matof core and face sheets or design geometry of panel witknowledge of operating failure mechanism at the design l[4,7–9]. Sandwich structures with foam core and aluminumsheets were studied extensively by various researchers inof optimum design. In addition to that analytical failure loformulae and modeling based on simulation were develdepending upon the materials used for the sandwich strucSandwich beams having aluminum foam core and alumface sheets, can fail in five modes: face yielding, face wkling, core shear, core indentation and delamination. Delnation can be avoided having the perfect bonding betweensheets and core. Usually, failure due to face wrinkling isfound in sandwich beam with metal foam because load reqfor failure is much higher than other modes[4]. Fleck andSridhar[10] have observed face sheet yield, core shear mbuckling and Euler macro bucking when polymer foam basandwich columns are subjected to edge wise compressiveing.

Sha and Hon[11] have observed core indentation and c

∗ Corresponding author. Tel.: +65 6790 4784; fax: +65 6791 1859.E-mail address: [email protected] (S. Idapalapati).

shear failure of sandwich beams under bending with aluminumfoam core and multiple layers of metallic face sheets. Recently,Gama et al.[12] have showed the potential of aluminum foamin composite armor with different face sheets including ceramic

921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2005.06.070

K. Mohan et al. / Materials Science and Engineering A 409 (2005) 292–301 293

Nomenclature

b width of beamF failure loadFfsc failure load for face sheet crackingFi failure load for core indentationFCSA failure load for core shear in mode-AFCSB failure load for core shear in mode-BGc shear modulus of foam coreH over hang length of the beamIeff effective second moment of area of sandwich

beaml distance between outer or supporting rollersMf maximum working bending moment on the face

sheets distance between inner or loading rollerst thickness of face sheet

Greek symbolsσf

y yield strength of face sheetσc

y compressive yield strength of foam coreδ displacement of loading rollersτc shear strength of foam coreφ yield surfaceα aspect ratio of elliptical yield surfaceυp plastic Poisson’s ratio of foam coreσe Von-mises effective stressσm mean stress

face sheets in ballistic application. Additionally, Ashby andBrechet [13] have also envisaged that better design perfor-mance could be achieved withhybrid sandwich constructionsby employing non-traditional combination of materials. To theauthors knowledge, there are no reported results high-lightingthe failure mechanisms of sandwich beams having a brittleceramic face sheet and metal foam core, which is a hybridconstruction. Sandwich beams comprising alumina face sheeimparts good stiffness, wear resistance and fire retardation whecompared to aluminum face sheets. So detailed study on sanwich structure constituting aluminum foam core and aluminaface sheets should be carried out in order to optimize theimechanical performance.

In this present work, bending studies were carried out onbeams consisting of alumina (Al2O3) face sheets and Alpo-ras (an Al alloy of Mn and Si) foam core to find variouscompeting failure modes. For the identified failure modes,equations for the failure load are provided. Failure mode mapis constructed showing all possible failures in terms of non-dimensional geometrical parameters of the beam for a givenface sheet to core yield strength ratio. Numerical simulationswere carried out to verify the analytical solutions and to com-pare with the experimental measurements of stiffness and failurload.

2. Analysis of sandwich beams under four point bending

Consider a sandwich beam of widthb and lengthl, comprisingtwo identical face sheets of thicknesst and foam core of thicknessc. The beam is subjected to four point bending load as shownin Fig. 1: the outer rollers acts as supports and the inner rollersload the specimen. Both the supporting and loading rollers havea diameter of 10 mm. The loading indenters are separated by adistances.

2.1. Elastic stiffness

The maximum deflection of the beam is due to both flexuraland shear deformations. It was noted that the shear deformationis predominated in the core and hence, the approximate expres-sion for the elastic deflection can be expressed as[6]:

δ = F (l − s)2(l + 2s)

48(EI)eq+ F (l − s)

4(AG)eq(1)

wherel is the distance between supporting rollers,s the innerloading span and (EI)eq is the equivalent flexural rigidity of thesandwich beam. The equivalent flexural rigidity is given by:

(EI)eq = Efbtd2

2+ Efbt3

6+ Ecbc3

12≈ Efbtd2

2(2)

a

(

wm lio

2

red tal oft fort y ten-s as ar

2nsile

s

F geo-m

tnd-

r

e

nd the equivalent shear rigidity (AG)eq is given by:

AG)eq = bd2

cGc ≈ bcGc (3)

hereGc is core shear modulus and the spacingd = c + t of theid plane of the face sheets.Ef andEc are the Young’s moduf the face sheet and foam core materials, respectively.

.2. Estimation of failure loads

Analytical formulae for the different failure modes weeveloped and discussed in the following paragraphs. To

hree possible mutually competing modes were identifiedhe sandwich beams: the face sheet is assumed to fail bile fracture in a linear elastic manner and the foam coreigid-perfectly plastic material.

.2.1. Face sheet crackingAlumina ceramic face sheet is brittle and possesses te

trength approximately 10–15% of compressive strength[14].

ig. 1. Schematic of a sandwich beam under four point bending showingetrical and material parameters.

294 K. Mohan et al. / Materials Science and Engineering A 409 (2005) 292–301

Therefore, tensile strength of the ceramic material was consid-ered to be the failure strength for the face sheets of the sandwichbeams. It is known that for a sandwich beam under four pointbending, upper face sheet is under compression and lower facesheet is in tension and hence, the failure initiates in the bot-tom face sheet. It was assumed that the face sheet start crackingwhen the lower face sheet of the sandwich beam attains the fail-ure strength ofσf

y. The failure load for face sheet cracking iscalculated by equating the moments within the sandwich beam(summation of the moments due to elastic brittle face sheet andrigid–plastic foam core) to the external bending moment appliedto sandwich beam.

Moment due to face sheet is:

Mf

Ieff= σf

y(t + c

2

) (4)

where the moment of inertiaIeff having considered the tensilefailure of the lower face sheet is:

Ieff =(

bt3

12

)+(

bt(c + t)2

4

)(5)

Now, equating the internally resisting moment to the maximumexternally applied bending moment we obtain:

F (l − s) {(bt3/12)+ (bt(c + t)2)/4}σf

F

e tot coret

2g

m isa ressivef s at earsw entersw heta -l icallyd n to

Fig. 3. Two competing core shear failure modes of sandwich beam: (a) mode-Aand (b) mode-B.

initiate indentation failure in the foam core.

Fi = bt

(π2(t + c)Ef (σc

y)2

3(l − s)

)1/3

(8)

2.2.3. Core shearThe complaint core in the sandwich construction carries the

shear load under bending. When the transverse shear stressexceeds the core shear strength, the sandwich beam fails in shearmode. Two competing shear failure mechanisms are identifieddepending upon the beam overhang length[8]. Fig. 3 showsthese two possible failure mechanisms termed as mode-A and -B. Failure loadFcswas calculated by equating the external workdone by the sandwich beam to the internal work done by facesheets and core.

In collapse mode-A, the face sheets on the right hand side ofthe sandwich panel rotates through an angleθ whereas the leftside rotate through−θ. Hence, the foam core shears by an angle2θ. At the same instant of core shear we assume that the bottomface sheet gets subjected to tensile fracture.

External work done by the applied forces is, Wb = F (l − s)θ

2(9)

Internal work done by the core and face sheets is:

W

wi rittlefi for

2 2= y

t + (c/2)(6)

ailure loadFfsc = 2{bt3 + (3bt(c + t)2)}σfy

3(2t + c)(l − s)(7)

Ceramics have conventionally higher Young’s moduli duheir stiff covalent bonds and hence, here the contribution ofo the bending moment is neglected.

.2.2. Core indentationThe applied transverse loadF induces a uniform bendin

omentM = F(l − s)/4 between the loading rollers and itssumed that the upper face sheet is subjected to a comp

orce of P = M/(c + t) while the lower face sheet experienceensile force of equal magnitude. Indentation failure apphen foam core is compressed beneath the upper indithin a region of2λ in a rigid-ideally plastic manner, so that t

ransverse load on the sandwich face from the core isq = bσcy

s shown inFig. 2. Recently, Steeves and Fleck[15] have anayzed the indentation failure as an elastic beam on a plasteforming foundation and obtained the following expressio

Fig. 2. Indentation zone beneath a loading indenter.

i = 4Mfθ + [bcτyc (2H + l − s)θ] (10)

hereτcy is the shear strength of the foam core andMf = bt2

6 σfy

s the working bending moment in the face sheet to initiate bracture. Equating the external work done by the forceF to thenternal work done, we obtain the core shear failure load


mode-A as:

FCSA = 2bcτcy(2H + l − s)

l − s+ 4[bt2σf

y]

3(l − s)(11)

In core shear mode-B, it was assumed that there is no defor-mation in the core beyond the overhang length. Similar to coreshear mode-A, failure load for core shear mode-B was calculatedby equating the work done and is expressed as:

FCSB = 2bcτcy + 8bt2σf

y

3(l − s)(12)

The overhang lengthH decides the transition from mode-A toMode-B. By equating the two failure loads, the critical overhanglength was estimated as:

H = t2

3c

σfy

τcy

(13)

If the overhang length is more than the aforementioned value,sandwich beam fails under mode-B and vice-versa.

3. Experimentation

In this section, we briefly explain the materials used in thisexperimental study and their mechanical characterization. Thep ned.

3

3s

c e thema lls is3 tio oft ate-r laps to thet DM)t tingM peedo po-r wn inF -s rength( vely.A earr ed fors -v de int s oft

b

Fig. 4. Stress–strain response of Alporas foam under: (a) tension and compres-sion and (b) double-lap shear.

Table 1Material properties of Alporas foam and alumina sheet of 2 mm thickness

Property Material

Alporas foam Alumina

Density (kg/m3) 256 3960Young’s modulus (GPa) 0.5 349Elastic Poisson’s ratio 0.35 0.22Bending strength (MPa) – 192Failure strain (%) – 0.055Compressive yield stress ratio 1.1 –Plastic Poisson’s ratio 0.03 –

3.1.2. Details of face sheet materialAlumina (Al203)2 was used as face sheets for the construction

of sandwich beams. It is well known that the failure strength andmodulus of ceramics is strongly influenced by their inherentporosity and Weibull statistics is commonly employed to studythe statistical variation in strength with material volume[14,25].

2 Supplied byPI-KEM, UK.

rocedure followed for the four point bending is also explai

.1. Materials

.1.1. Details of metal foam coreAlporas® (trade name) closed cell Al foam1 was used a

ore material for sandwich structures as it is reported to bost isotropic and homogenous cellular structure[16,17]. The

verage cell size of Alporas foam measured from 220 ce.5 mm and the average relative density (defined as the ra

he apparent density of foam to the density of cell wall mial) is 9.5%[18]. Uniaxial tensile, compression and double-hear tests are conducted on the foam specimens (cutest standard dimension by electron discharge machine (Eo minimize cell wall damage) using Instron Universal Tesachine5567 under displacement control at a cross-head sf 0.1 mm/min.[19–24]. The stress–strain responses of Alas foam under tensile and compressive loading are shoig. 4(a) and discussed elsewhere[18]. In summary, the meaured tensile strength, compressive strength and shear stfor 20 mm foam) were 1.51, 1.85 and 1.01 MPa, respectis shown inFig. 4(b), there is an effect of core thickness on sh

esponse: uniform shear strength and modulus were obtainpecimens of thickness greater than 20 mm[18]. Similar obserations on the effect of foam size on its properties were mahe literature[8,20]. Other measured mechanical propertiehe Alporas foam are summarized inTable 1.

1 Suppliedby Gleich Gmbh Metallplatten-service, Germany produced byatch casting process.


Table 2Geometry of sandwich beams under four point bending (all dimensions are in millimeters)

Specimen (geometry) Core thickness,c Face thickness,t Outer roller span,l Inner roller span,s Overhang length,H Failure mode

1 3 2 80 20 15 FSC2 3 1 100 25 17.5 FSC3 3 0.5 100 25 17.5 FSC4 20 0.5 100 25 17.5 CI5 50 0.5 100 25 17.5 CI6 20 1.0 100 25 17.5 CS7 30 2 80 20 15 CS8 50 2 80 20 15 CS

Where FSC: face sheet cracking; CI: core indentation; CS: core shear.

Fig. 5. Effect of alumina sheet thickness under four point bending tests.

Uniaxial tension tests on alumina sheets are ruled out due tothe premature failure at the grip portion of the specimen whileloading. Hence, we have conducted bending tests on aluminaface sheets of varying thicknesses and taken the average modulusand strength from three specimens each.Fig. 5shows the averagestress–strain response under four point bend tests for variousspecimen thicknesses. The measured properties of these aluminaface sheets are listed inTable 1.

3.2. Sandwich beam

In order to identify all possible failure modes, maximum prac-tically possible geometries of the sandwich beams were testewith the help of alumina face sheets of different thicknesses. Inthe present work, alumina face sheet of thickness of 0.5, 1.0 an2.0 mm and Alporas core of 9.5% relative density with varyingthickness are employed to fabricate the beams. Fuller details obeam geometries are listed inTable 2.

Sandwich beams of 25 mm width were prepared by bond-ing alumina face sheets to Alporas foam core using Redux-32adhesive3. Foam core specimens of required geometry were cufrom a panel of 300 mm× 300 mm× 50 mm by electron dis-charge machining, to minimize cell wall damage. Foam blocks

3 Supplied by Hexel Composites, Australia.

and alumina plates were degreased and cleaned with acetoneusing white cotton cloth. Foam specimens were then adhered toalumina plates using Redux-322 epoxy adhesive on a nylon car-rier mesh. The sandwich beams were air cured in oven at 175◦Cfor 1 h under a nominal contact pressure of 0.1 MPa[18]. It isto be noted from suppliers data sheet that the shear strength ofRedux adhesive is about 20 MPa, which is much higher thanthat of foam core specimen’s shear strength. Hence, the bondinterface failure is not expected.

All the tests were conducted under displacement control bysetting a cross-head displacement of 1.0 mm/min. Surface dis-placement analysis (SDA) was employed for continuous moni-toring of deformed geometry. Snapshots of the loaded sandwichbeams were taken at every significant change in the beam geom-etry.

3.3. Finite element modeling

All the test geometries were simulated numerically usingABAQUS® commercial finite element program. The aluminaface sheet is assumed to be perfectly bonded to the core, elimi-nating the delamination failure mode. The foam core is com-pletely constrained by the face sheets, also the face sheetsare much wider than their thickness and hence a plane-strainanalysis is justified on the sandwich beams. Four nodded bilin-e egra-t try ass or-p Loadw pperl inedc

igid-b n-l . Them ecka teda

φ

wa tion

d

d

f

2t

ar plane strain quadrilateral elements with reduced intion (CPE4R) are used to discretize the sandwich geomehown inFig. 6. For improved accuracy, fine mesh was incorated in the regions of high stress or strain gradient.as applied in terms of displacement through the two u

oading indenters while two lower indenters are constraompletely.

The loading and supporting rollers are modeled as rodies. A contact algorithm within ABAQUS models frictio

ess contact between the rollers and the sandwich beamsultiaxial failure of metallic foams was investigated by Flnd co-workers[26] and the failure surface can be approximas:

≡[

9

9 + α2

] [σ2

e + α2σ2m

]−(σc

y

)2 = 0 (14)

hereσcy is the uniaxial compressive strength of foam,α is the

spect ratio of the elliptical yield surface (which is a func


Fig. 6. Typical finite element mesh showing the geometry, loading and boundary conditions.

of foam plastic Poisson’s ratio),σe is the Von-misses effectivestress andσm is the mean stress.

A brittle cracking failure model is used to identify failure inthe alumina face sheet. According to this model, crack appearsat any element only when the maximum principal tensile stressexceeds the material tensile strength in that region[27]. In thenext load increment, the stresses applied to it are rotated nor-mally for closing the crack in order to give a flexibility to studythe behavior of brittle material which experiences the crackopening and closing together. Here, the brittle material is lin-

F(f

ear elastic in compression and failure behavior is dominated bytensile cracks.

Both the metal foam constitutive model of Deshpande andFleck[26] and brittle cracking model of alumina face sheet arein-built in ABAQUS explicit solver and hence it was used forsimulation purposes.

ig. 7. Failure mechanisms map for sandwich beam having foam core thicknessa) 3 mm and (b) greater than or equal to 20 mm. In both case effect of aluminaace sheet thickness is shown on map for a fixeds̄ of 0.25.

FawtT

:

ig. 8. (a) Load and displacement curves derived from analytical, experimentalnd numerical analysis for the sandwich beam having geometry no. 2 (Table 2)hich failed under face sheet cracking. (b) Effect of face sheet thicknesst on

he face sheet cracking failure for sandwich beams having geometries (1,2,3)able 2.


3.4. Failure mechanisms map for sandwich beam underfour point bending

For a given sandwich beam geometry and material systemthe dominating failure mode is the one, which requires the low-est load to fail among all possible modes. A failure mechanismmap (pioneered by Gibson and Ashby[28]) is drawn inFig. 7in terms of non-dimensional parameters ¯c = c/l and t̄ = t/c

based on the analytical formulae presented in Section2. It showsan overview of all possible failure modes with the locations ofthe selected geometry of sandwich beams in the region of eachfailure mode. In the present investigation, due to the limitedquantity of materials available in standard geometries, experi-mented beam geometries are carefully chosen to identify all thecompeting failure mechanisms.

The failure load given by Eqs.(7), (8), (12)contain fracturestress of face sheet and core shear strength, and both of these arefunctions of their respective thicknesses. Therefore, the bound-aries corresponding to different failure modes depend upon thethickness of face sheet and its influence is as shown inFig. 7(aand b). Effect of core thickness is represented by the shrinkageof domain of the core shear failure in the failure mechanism mapof Fig. 7(a) (3 mm thick core) as compared toFig. 7(b) (20 mmcore thickness). This is due to the increment in load require-ment to fail under core shear as the core thickness decreases(seeFig. 4(b)). For all the geometries selected, the beam over-h q.( ortee p inc

4. Results and discussion

Three competing failure modes, namely core shear, coreindentation and face sheet cracking were identified under fourpoint bending of sandwich beams consisting of alumina facesheet and Alporas foam core. In the following paragraphs,the measured load–displacement responses are compared withnumerical simulations. Also, the elastic stiffness of the beam andfailure load values is compared with the analytical formulae.

4.1. Face sheet cracking

The load versus displacement curve for sandwich beamgeometry 2 (Table 2), failed experimentally by face sheet crack-ing was compared with analytical calculations and simulationresults as shown inFig. 8(a). It is a typical example of thegeometries failed by face sheet cracking. Load increases mono-tonically with displacement in a linear elastic manner and dropssuddenly indicating catastrophic failure, when the lower facesheet cracked under tensile fracture. The deflection for failurewas very low because of very high Young’s modulus of aluminaface sheet. This failure mode was dominant when the span length(l) was large and face sheet thickness,t, was small with respectto core thickness,c. It agrees with the findings on the sandwichbeam made with aluminum foam core and ductile aluminumf

thatt of thef s ont good

F(

ang length (H) was more than the critical value given by E13). Hence, we observed core shear mode-B in the repxperiments and only this mode was plotted in failure maore shear category.

ig. 9. In situ picture of the sandwich beam specimens expected to fail by: (a)geometry 7).

d

ace sheets[8].Analytical Eq.(7) for face sheet cracking failure suggests

he face sheet cracking load increases with the thicknessace sheets.Fig. 8(b) shows the effect of face sheet thickneshe failure load for the three tested geometries. There is

face sheet cracking (geometry 1), (b) core indentation (geometry 4) and (c) core shear


agreement between the experimentally measured failure loadvalues with numerical and analytical predictions.

Cracking of lower face sheet was observed in snapshots ofgeometry 2 (Table 2) taken at failure as shown inFig. 9(a).It shows a location of typical failure, which was observed inalmost all the sheets failed under this mode. The normal stresscontours obtained from the numerical simulation confirmed thatthe failure was initiated in the lower face sheet (seeFig. 10(a)).It was confirmed that the maximum principal tensile stress inthe lower face sheet exceeded the failure limit and at this stagethe shear stresses in the core and the compressive stresses in thetop face sheet are within their design limits.

4.2. Core indentation

Core indentation failure mode was experimentally observedfor smaller values oft/c and large values ofc/l. Failure mapsuggests that the beam having equal dimensions of length, facesheet thickness and core thickness will also fail under this cat-egory, which is not a practically feasible design (see the upperright hand side ofFig. 7(a)).

Two geometries were tested to check the validity of analyticaland numerical simulations. The load–displacement observationsare shown inFig. 11(a and b). It is clear from the figure thatthe loads for indentation drop after initiation of indentation,which correspond to the reduction in cross-sectional area. Minorwiggles in the load–displacement curve, were found due to thecracking of the face sheet beneath the loading rollers, whichis highlighted inFig. 11. Here, prediction for failure loads byanalytical solution(8) was found to be in agreement with thesimulation and experiments. Stiffness of the sandwich beamspredicted by Eq.(1) was also found to be in good agreementwith the simulation and experimentally measured values. Thereason for a sudden fall in the load values in the experimentalcurve for geometry 4 (Table 2) at around 4.5 mm displacementwas due to the cracking of lower face sheet. This could havebeen triggered by core shear, as this geometry lies in the regionnear to boundary between core indentation and core shear fail-ure in failure mechanism map ofFig. 7(b). Predominant crushingof foam takes place beneath the loading rollers and also slightindentation at the supporting rollers is noticed (seeFig. 9(b)).The stress contours predicted by the finite element simulations

Fp(o

ig. 10. Stress contours (in MPa) in the sandwich beam at the failure. (a) Noortion of the face sheet of the sandwich beam with compressive stress (S22S22) contours showing core indentation underneath the upper indenters (geof the foam core within the loading and supporting indenter (geometry 7).

rmal tensile stress (S11) contours showing face sheet cracking at the lowermiddle) contours in upper face sheet (geometry 1), (b) through thickness compressive stressmetry 4), and (c) shear stress (S13) contours showing shear failure in the middle portion


Fig. 11. Load vs. displacement responses under core indentation as derivedfrom analytical, experiments and numerical analysis for (a) geometry 4, (b)geometry 5.

shown inFig. 10(b) also reveal a tiny region of indentation atthe supporting roller.

4.3. Core shear

The load versus displacement response of beams failed incore shear are shown inFig. 12(a–c) and the response is com-pared with numerical and analytical predictions. For each beam,overhang length was chosen to be more than the critical oneso that the failure would appear in core shear mode-B. Cer-tain serrations in the experimental response, near the peak load,represent the local contact failure of face sheet underneath theindenters. Failure load measurements for core shear by simula-tion agreed well, but deviated from analytical Eq.(12)by 20%.But the stiffness predicted by Eq.(1) was found to be in goodagreement with the simulation and experimentally measuredvalues.

The snapshot inFig. 9(c) clearly reveals the mode-B shearfailure in the sandwich beam (geometry 7). Shearing of the core

Fig. 12. Load vs. displacement responses under core shear as derived fromanalytical, experiments and numerical analysis for (a) geometry 6, (b) geometry7, and (c) geometry 8.

occurs between upper loading indenter and lower supportingindenters and is confirmed from FE simulations (seeFig. 10(c));within this domain shear stress contours exceed the core shearstrength. Cracking of lower face sheet was observed with furtherloading as the tensile stress exceeds the rupture strength of theface sheet in the lower region.


5. Conclusions

Sandwich beam comprising aluminum foam core and alu-mina face sheets with different geometries have been testedunder four point bending and three failure modes, namely facesheet cracking, core indentation and core shear were identified.Local cracking was found in many specimens, in the region nearto upper indenters because the local stress exceeds the tensilestrength of face sheet. Contact failure was not accounted as afailure mode because even after exceeding this limit, beam wasable to take further load. The analytical equations for elasticstiffness and failure loads for various failure modes are in goodagreement with the prediction by FE simulation and experimen-tally measured values within material and numerical scatter. Ourobservation further verifies the validity of the phenomenologi-cal metal foam constitutive model developed by Deshpande andFleck[26].

The failure mode map in terms of non-dimensional geo-metrical parameters(c̄, t̄) of the sandwich beam for a givencore and face sheet strength ratio will help in identifyingexpected failure mode for a given design geometry. Furtherwork needs to be carried out to identify beam geometry andcore density selection to minimize beam weight for a givenstructural load. Also in the current analytical models size depen-dent strength of ceramics should be including using statisticalmethods.

A

in-g Stu-d alia)f e.

R

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[20] E.W. Andrews, G. Gioux, P.R. Onck, L.J. Gibson, Int. J. Mech. Sci. 43

[ 00)

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cknowledgements

Kapil Mohan thanks Nanyang Technological University, Sapore for the financial support in the form of a Graduateentship. Authors are grateful to Hexcel composites (Austr

or providing the Redux-322 Adhesive for research purpos

eferences

[1] G.J. David, S. Zhen, J. Mater. Sci. 18 (1983) 1899–1911.[2] J. Banhart, Prog. Mater. Sci. 46 (2001) 559–632.

(2001) 701–713.21] G. Gioux, T.M. McCormack, L.J. Gibson, Int. J. Mech. Sci. 42 (20

1097–1117.22] Y. Sugimura, J. Meyer, M.Y. He, H. Bart-Smith, J. Grenstedt, A

Evans, Acta Mater. 45 (12) (1997) 5254–5259.23] A.E. Simone, L.J. Gibson, Acta Mater. 46 (11) (1998) 3929–393524] A.E. Simone, L.J. Gibson, Acta Mater. 46 (6) (1998) 2139–2150.25] W.D. Callister Jr., Material Science and Engineering—1: An Intro

tion, John Willey & Sons, Inc., 1994.26] V.S. Deshpande, N.A. Fleck, J. Mech. Phys. Sol. 48 (2000) 1253–27] ABAQUS theory manual Version 6.3, Hibbit, Karlsson & Sorensen,

USA, 2002.28] L.J. Gibson, M.F. Ashby, Cellular Solids—Structure and Properties,

ond ed., Cambridge University Press, Cambridge, 1997.

failure of sandwich beams consisting of alumina face sheet and aluminum foam core in bending

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