Materials and Design xxx (2010) xxx–xxx

Contents lists available at ScienceDirect

Materials and Design

journal homepage: www.elsevier .com/locate /matdes

Mechanical behavior of sandwich panels with hollow Al–Si tubes core construction

Jian Xiong a, Li Ma a, Linzhi Wu a,⇑, Ming Li a, Ashkan Vaziri b

a Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, PR Chinab Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, USA

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

Article history:Received 2 December 2009Accepted 10 August 2010Available online xxxx

Keywords:B. Sandwich structuresE. MechanicalH. Failure analysis

0261-3069/$ - see front matter Crown Copyright � 2doi:10.1016/j.matdes.2010.08.016

⇑ Corresponding author. Tel.: +86 451 86412549; fE-mail addresses: xiongjian0309@163.com (J. Xion

Please cite this article in press as: Xiong J et al. Mdoi:10.1016/j.matdes.2010.08.016

A new type of lightweight sandwich panels consisting of vertically aligned hollow Al–Si alloy tubes ascore construction and carbon fiber composite face sheets was designed. The hollow Al–Si alloy tubes werefabricated using precision casting and were bonded to the face sheets using an epoxy adhesive. The out-of-plane compression (i.e. core crushing), in-plane compression, and three-point bending response of thepanels were tested until failure. The hollow Ai–Si alloy tubes core configuration show superior specificstrength under crushing compared to common metallic and stochastic foam cores. Under in-plane com-pression and three-point bending, the buckling of face sheets and debonding of hollow cores from theface sheets were observed. Simple analytical relationships based on the concepts of mechanics of mate-rials were provided for the compression tests, which estimate the sandwich panels’ strength with highfidelity. For three-point bending, detailed finite element analysis was used to model the response andinitial failure of the sandwich panels.

Crown Copyright � 2010 Published by Elsevier Ltd. All rights reserved.

1. Introduction

The interest in metallic sandwich panels with cellular cores hasgrown rapidly over the last decade for light weight multi-func-tional structural systems [1–5]. Metallic sandwich panels havebeen traditionally made of stochastic cores such as aluminum alloyfoams [6,7] or micro-architecture lattice materials such as the hex-agonal honeycomb [8,9]. These sandwich panels have superiormechanical properties to their solid plate counterpart (of equalmass); however, their closed-cell configuration limits theirmulti-functional applications [10–14]. On the other hand, open-cell cellular structures and lattices posses mechanical propertiescomparable to most closed-cell cellular structures [15–21]. Inaddition, their open-cell configuration allows heat exchange alongthe panel core, making them attractive candidates for developmentof multi-functional structural systems. This includes three-dimensional periodic truss cores, such as pyramidal, tetrahedralor octet-truss core with high nodal connectivity [22,23].

In the present paper, a new type of light weight sandwich panelwith hollow Al–Si alloy tubes core is designed and manufactured.The Al–Si alloys are widely used in aerospace, marine, automotiveand other engineering applications due to their low weight, excel-lent casting properties and corrosion resistance [24]. The details ofthe fabrication method for the Al–Si alloy tubes and sandwich pan-els are provided in Section 2. In Section 3, we studies the behaviorof the core under crushing (e.g. out-of-plane compression of the

010 Published by Elsevier Ltd. All r

ax: +86 451 86402386.g), wlz@hit.edu.cn (L. Wu).

echanical behavior of sandwic

sandwich panels), as well the mechanical response of the sandwichpanel under in-plane compression and three-point bending. In allexperiments, the specimens were loaded up to large deformationand failure to gain insight into the mechanisms of deformation,failure and fracture of the sandwich panels under differentmechanical loadings.

2. Design and fabrication

The core construction of the sandwich panels consists of Al–Sialloy hollow tubes, made using the precision casting, as shown inFig. 1. The casting process involves a furnace, pattern (A hollowrubber tube), and a sand mold. The pattern has the same dimen-sions as the Al–Si alloy tubes and was used to form the casting cav-ities in the sand mold. The Al–Si alloy was melted in the furnace,ladled and poured into the cavity of the sand mold. After the solid-ification of the alloy, the casted Al–Si tube was removed from thesand mold.

The chemical composition (wt.%) of the Al–Si alloy is as follows:Mg (0.8–1.2%), Si (0.4–0.8%), iron (0.7%), copper (0.15–0.4%), zinc(0.25%), titanium (0.15%) and manganese (0.04–0.35%). The mate-rial properties of the Al–Si alloy depend the solidification parame-ters (e.g. the crystallization rate and the temperature gradient)[25–27]. Here, the Al–Si alloy has the Young’s modulus of E = 72GPa and the tensile strength, rs = 251 MPa [28]. The flat face sheetswere made of continuous carbon fiber reinforced epoxy resin com-posite prepreg sheets with thickness 0.175 mm. The tubes werebonded to the face sheets using an adhesive (08–57, Heilongjiang

ights reserved.

h panels with hollow Al–Si tubes core construction. J Mater Design (2010),

Fig. 1. Casting processing for hollow Al–Si alloy tubes.

Fig. 2. (a) Sketch of the unit cell of sandwich panels with hollow Al–Si alloy tubescore. (b) A sandwich panel with �q ¼ 3:35% .

2 J. Xiong et al. / Materials and Design xxx (2010) xxx–xxx

Institute of Petrochemical) and were aligned at constant distancesin the two in-plane direction of sandwich panels, denoted by a andb, in both in-plane directions of the panel. Table 1 gives the mate-rial properties of the Al–Si alloy, the carbon fiber-reinforced com-posite and adhesive used in the fabrication of the sandwich panel.

Fig. 2a shows the schematic of a unit cell of the sandwich panel,where r, R, and h are the inner radius, outer radius and height ofeach Al–Si hollow tube, respectively, d and L are the thicknessand radius of the rings at the two ends of the tube. The relativedensity of the core �q is given by

�q ¼ p½ðR2 � r2Þhþ 2ðL2 � R2Þd�abh

ð1Þ

In our study, the tube’s geometry was constant with r = 2 mm,R = 3 mm, h = 10 mm, d = 1 mm and L = 4 mm and a and b are vary-ing in this study to obtain different core densities. The relative den-sity of the sandwich core was varied by changing the number oftubes per unit surface area of panel (i.e. changing the unit celldimensions, a and b). Fig. 2 shows a sandwich panel with a core rel-ative density �q ¼ 3:35% and face sheet thickness 1 mm. In this casethe unit cell of the sandwich panel has the dimensions, a = 20 mmand b = 30 mm.

3. Core behavior and strength

Out-of-plane compression tests were performed to determinethe compressive stiffness and strength of the Al–Si tubes core con-struction, using a screw-driven testing machine (INSTRON 5569).The sandwich panels tested were 80 mm � 80 mm, with a totalheight of 12.8 mm. Each face sheet was a composite laminate with8 plies with a sequence [0/45/-45/0]s and thickness 1.4 mm. Fig. 3shows the crushing response of two sandwich panels with�q ¼ 2:83% (a = 26.67 mm and b = 26.67 mm) and �q ¼ 5:03%

(a = 20 mm and b = 20 mm). A simple analytical relation for a tubecores Young’s modulus gives

Ec ¼pR2 � pr2

a� bE ð2Þ

which yield the Young module, Ec = 133.0 MPa and 236.4 MPa,for the core relative densities, �q ¼ 2:83% and �q ¼ 5:03%, respec-tively. Based on the measured unloading curves, Young’s moduleof the same sandwich cores are 115.1 MPa and 211.5 MPa, respec-

Table 1Properties of the materials used in manufacturing the sandwich panels.

T700/TDE85 E11 (GPa) E22 (GPa) G12

132 10.3 6.5Al–Si alloy (6061) Tensile modulus (GPa) Shear modulus (GPa) Ten

72 27 25108–57 Adhesion Young’s modulus (GPa) Pois

3.0 0.38

Please cite this article in press as: Xiong J et al. Mechanical behavior of sandwicdoi:10.1016/j.matdes.2010.08.016

tively, which demonstrates a relatively good agreement with theanalytical estimates.

For both sandwich cores, the initial linear response is followedby a nonlinear response regime, which is associated with the plas-tic deformation of the hollow tubes. Generally, the peak stress(marked by the arrows in Fig. 3) occurs when the failure of tubesis originally observed. The measured peak stresses of 5.46 MPaand 9.38 MPa were measured for tube cores with �q ¼ 2:83% and�q ¼ 5:03%, respectively. Fig. 4 displays an image of a failed hollowAl–Si alloy tubes under crushing, showing cracks at approximately45� that extend between the two ends of the tubes. The analyticalrelations of the maximum strength can be obtained as follows,

(GPa) G23 (GPa) m12 q (gm/cm3)3.91 0.25 1.57

sile (compressive) strength (GPa) Poisson’s ratio Density (g/cm3)0.33 2.658

son’s ratio Room temperature shear strength (MPa)86.83

h panels with hollow Al–Si tubes core construction. J Mater Design (2010),

Fig. 3. Out-of-plane compression curves of sandwich panels with hollow Al–Si alloytubes core.

J. Xiong et al. / Materials and Design xxx (2010) xxx–xxx 3

Material failure : rt ¼pR2 � pr2

a� brs

Euler buckling : re ¼p3EðR4 � r4Þ

16abðh� 2dÞ2ð3Þ

For the hollow Al–Si tubes with a low relative density, rt� re.The analytical values of the peak stress are somewhat higher thanthe measured values, which are given above, possibly due to man-ufacturing variations and formation of defects (e.g. cracks andvoids) in the tubes during the manufacturing.

In Table 2, we have compared the specific crushing strength ofthe manufactured Al–Si tube core constructions with stochasticcarbon foams and aluminum lattices. In Fig. 5, the modified Ash-by’s strength–density chart [29] for variety of materials with den-sity 61000 g/cm3 is given, including natural materials, stochasticmetallic and polymer foams, aluminum lattices, the Al–Si tubescore construction developed in this study, and novel fiber-rein-forced composite cellular structures from [30–33]. The hollowAl–Si allow tubes core construction is located in the low-den-sity–high strength region of the chart and has specific strengthhigher than most stochastic foams and metallic lattices and is com-parable to fiber-reinforced composite cellular structures. The prop-erties of the tubes core construction studied here, makes it apromising design for ultra lightweight sandwich structures.

Fig. 4. Failure of hollow tubes und

Table 2Mechanical properties of stochastic foam [15], aluminum lattice [16] and hollow Al–Si alpresented for two different densities.

Carbon foam

Density (g/cm�3) 0.71 0.45Relative density 0.507 0.321Strength (MPa) 39.7 10.3Specific strength (103 m2 s�2) 55.92 22.89

Please cite this article in press as: Xiong J et al. Mechanical behavior of sandwicdoi:10.1016/j.matdes.2010.08.016

4. In-plane compression of sandwich panels

In this section, we studied the response and failure of the sand-wich panels with a hollow Al–Si tube core construction under in-plane compression using a screw-driven testing machine (IN-STRON 5569). The axial compression tests were carried out in thequasi-static regime with a nominal displacement rate of 0.5 mm/min. Fig. 6a shows the load–displacement response of a sandwichpanel with h = 10 mm, width, w = 60 mm, length, L = 210 mm andcore relative density �q ¼ 3:35%. Each face sheet had 8 compositesplies with the ply sequence [0/0/90/0]s and thickness 1.4 mm. Thein-plane effective stiffness of the panel is 5.81 MPa and the effec-tive in-plane strength of the panel, calculated based on the mea-sured peak load of 21451.6 N, is �21.7 MPa. Fig. 6b shows thesandwich panel before and after loading.

Under in-plane compression, the skins remain intact but tend tobuckle and bend outward. By neglecting the contribution of thehollow Al–Si alloy tube core, the Euler buckling load PE can be ex-pressed as

PE ¼k2p2D

L2 ð4Þ

where k = 2 for a panel with built-in ends to prevent rotation, and Dis the flexural rigidity of the panel. Assuming that the Poisson ratiosof the core in the in-plane direction are negligible, the equivalentflexural rigidity of the composite column can be estimated fromthe classical laminate composite beam [34], as

ðEIÞeq ¼w3

XN

k¼1

Ek1

1� mk12mk

21

ðz3k � z3

k�1Þ þw12

EPh3 ð5Þ

where the first term is the contribution of face sheets to the flexuralrigidity of the composite column and the last term is the contribu-tion of the core, where N is the number of laminate plies, Ek

1 is theYoung’s modulus of ply k in the direction of loading, mk

12 and mk21

are the Poisson’s ratio of ply k and zk and zk�1 are the distances ofthe outer and inner surface of the laminate from the panel neutralaxis (the middle height of the panel due to symmetry). EP is theYoung’s modulus of the core in the direction of loading. For sand-wich panels with a low core density, the contribution of the corein the overall flexural rigidity of the panel is negligible and can beignored.

When the flexural and shear rigidities are of the same order ofmagnitude, the interaction between the Euler and shear bucklingmodes must be taken into consideration for the prediction of thecritical load and strength of the sandwich panel. The shear

er out-of-plane compression.

ly tubes core construction. The properties for the carbon foam and hollow tubes are

Aluminum lattice Hollow tubes core

0.367 0.138 0.0740.136 0.050 0.0287.10 9.38 5.4619.34 67.97 73.78

h panels with hollow Al–Si tubes core construction. J Mater Design (2010),

Fig. 5. Modified Ashby’s strength–density chart for a wide range of materials with alow relative density. We have added to this chart, the measured properties of theAl–Si hollow tubes core construction.

4 J. Xiong et al. / Materials and Design xxx (2010) xxx–xxx

buckling load PC of the core construction can be estimated byneglecting the shear stiffness of the face sheets (assuming thatthe sandwich panel shear rigidity is approximately equal to thecore shear rigidity), PC = whGc, where Gc is the out-of-plane effec-tive shear modulus of the core and was obtained from a three-point bending experiment according to ASTM standard [35], Gc

�42 MPa. The critical buckling load, PCr, can be estimated from[36]:

1PCr¼ 1

PEþ 1

PCð6Þ

0.0 0.2 0.4 0.6 0.8 1.0 10

5000

10000

15000

20000

25000

Small amounts of debonding

Load

(N)

Displacement (mm)

Max=21451.6

Complete debo

(a)

Fig. 6. In-plane compression of sandwich panels: (a) load–displacement response up to faapplied and after failure. The deformed panel shows overall buckling and also debondin

Please cite this article in press as: Xiong J et al. Mechanical behavior of sandwicdoi:10.1016/j.matdes.2010.08.016

According to Eq. (7), the critical load of the panel under in-planecompression is 25.2 MPa, about 13.9% larger than the measuredstrength. The occurrence of the buckling mode at the lower com-pression load suggests the weakness of the bonding – see Fig. 6b. Ini-tially, the debonding occurs between a few tubes and the face sheets,which results in a small reduction in the load-carrying capacity ofthe panel, as observed in the force–displacement response shownin Fig. 6a. As the compression test proceeds, the complete debondingof the core from the face sheet occurs abruptly, the face sheet burstapart with a sharp sound and the load–displacement curve dropssharply. The hollow tubes stay intact with no apparent fracture orsignificant plastic deformation.

5. Three-point bending of sandwich panels

Three-point bending experiments were carried out for sandwichpanels using the same test machine as previous sections under thedisplacement controlled condition. Fig. 7a shows the load–displace-ment responses obtained in two different trails for a sandwich panelwith L = 210 mm, the span length 150 mm, w = 60 mm, height12.8 mm and relative density �q ¼ 1:26%. Each face sheet was a com-posite laminate with eight plies with a sequence [0/45/-45/0]s andoverall thickness 1.4 mm. Two test results are presented in Fig. 7aand labeled as curve A and curve B, respectively. At the initial stageof deformation, the response curves approximately coincide and theslope of the load–deflection curve is �600 N/mm. The initial elasticresponse is followed by a nonlinear regime, where debonding, facewrinkling, delamination and core shearing were observed – seeFig. 7b.

After the initial elastic behavior, the adhesion strength betweenface sheets and the core is insufficient to sustain the completeintegrity of the sandwich panel, and the tubes debond from thetop face sheet as it undergoes compression during bending. Thisdebonding is the first apparent failure in the panel and results ina sudden drop in the load-carrying capacity of the panels (at901.5 N and 1080 N in the two trials of Fig. 7a), while the lowerface sheet and the core are still adhered together. As the experi-ment proceeds, the top face sheet buckles and delamination occursand propagates between tubes and the shearing force increases inthe core. At final stage of the experiment, several cracks were ob-served in the Al–Si alloy tubes and the tubes completely debond

.2

N

nding

Debondin

(b)

ilure and (b) a sandwich panel with the relative density �q ¼ 3:35% before the load isg of the hollow tubes from the composite face sheets.

h panels with hollow Al–Si tubes core construction. J Mater Design (2010),

Fig. 7. Bending behavior of the sandwich panel: (a) load–displacement response under three-point bending for two different specimens and (b) the deformed configuration in(top) in the elastic regime and (bottom) at the final stage of experiment (deflection = 7 mm, curve B), showing buckling and delamination of the top face sheet, debonding,delamination and core shear.

Fig. 8. (a) Finite element mesh for a sandwich panel with hollow tubes core; (b) deformed configuration and the distribution of von-Mises stress for a sandwich panel with�q ¼ 1:26% subjected to P = 1080 N in three-point bending.

J. Xiong et al. / Materials and Design xxx (2010) xxx–xxx 5

Please cite this article in press as: Xiong J et al. Mechanical behavior of sandwich panels with hollow Al–Si tubes core construction. J Mater Design (2010),doi:10.1016/j.matdes.2010.08.016

6 J. Xiong et al. / Materials and Design xxx (2010) xxx–xxx

from the top face sheets. The observed failure mode of the sand-wich panel combines debonding, delamination, core shearing andface wrinkling.

The total elastic displacement of the mid-span of a s sandwichbeam in three-point bending, d is the sum of the flexural and sheardeflections [36],

d ¼ PL3

48ðEIÞeqþ PL

4ðAGÞeqð7Þ

where P is the applied load, (EI)eq the equivalent flexural rigidity ofthe sandwich panel, Eq. (6) and (AG)eq is the equivalent shear rigid-ity, which is dictated by the core shear stiffness [37] and is in theorder of whGc. The deformation of the sandwich panel is mainlydue to core shear deflection. Assuming (AG)eq = whGc, the slope ofthe load–deflection curve is �434 N/mm, which is smaller thanthe experimental value. As the next step, we carried out detailed fi-nite element calculations to simulate the behavior of the sandwichpanel subjected to three-point bending. The calculations were car-ried out using commercial software, ANSYS. In our model, the facesheets were modeled using 8-node shell elements. The tubes weremodeled as three-dimensional parts and meshed using 20-nodebrick solid elements. We also modeled the adhesive layer using8-node quad solid elements. The mesh size was refined systemati-cally to obtain reliable convergence and mesh size independency.Fig. 8a shows a typical finite element mesh used in our calculations.The boundary condition in the finite element calculations is thesame as experiments and discussed above. Fig. 7b shows the de-formed configuration and the distribution of the von-Mises stressfor a sandwich panels subjected to P = 1080 N – which was themaximum load measured in our experiment, see Fig. 6a. This loadresults in the displacement of 1.68 mm in the middle of the top face,which is comparable with the measured value of 1.7 mm. To esti-mate the failure load of the sandwich panel under three-pointbending, we monitored the maximum shear stress in the adhesivelayer. At P = 1182 N, the maximum shear stress reaches the failureshear strength of the adhesive, given in Table 1. The response ob-tained from the finite element calculation is shown in Fig. 7a,which, in general, is in a good agreement with the experimentalresults.

6. Conclusions

Light weight sandwich panels with hollow Al–Si alloy tubescore and carbon fiber reinforced laminated panels were manufac-tured. The mechanical behavior and failure of the sandwich panelwere studied under out-of-plane compression, in-plane compres-sion, and three-point bending tests. The tube core offers high spe-cific strength compared to stochastic and metallic cellular coresand thus, can be used to design light weight multi-functionalstructures.

Acknowledgements

This work was supported by the National Science Foundation ofChina under Grant Nos. 90816024 and 10872059, the Major StateBasic Research Development Program of China (973 Program)under Grant No. 2006CB601206, the Program of Excellent Teamin Harbin Institute of Technology and by the Department ofMechanical and Industrial Engineering at Northeastern (AV). LMacknowledges the Program for New Century Excellent Talents inUniversity under Grant No. NCET-08-0152.

Please cite this article in press as: Xiong J et al. Mechanical behavior of sandwicdoi:10.1016/j.matdes.2010.08.016

References

[1] Gibson LJ, Ashby MF. Cellular solids: structure andproperties. Cambridge: Cambridge University Press; 1997.

[2] Evans AG, Hutchinson JW, Fleck NA, Ashby MF, Wadley HNG. The topologicaldesign of multifunctional cellular metals. Prog Mater Sci 2001;46(3–4):309–27.

[3] Deshpande VS, Fleck NA. Energy absorption of an egg-box material. Int J SolidStruct 2003;51:187–208.

[4] Fleck NA, Deshpande VS. The resistance of clamped sandwich beams to shockloading. J Appl Mech 2004;71:386–401.

[5] Hutchinson RG, Wicks N, Evans AG, Fleck NA, Hutchinson JW. Kagome platestructures for actuation. Int J Mech Sci 2003;40:6969–80.

[6] Ashby MF, Evans AG, Fleck NA, Gibson LJ, Hutchinson JW, Wadley HNG. Metalfoams: a design guide. London: Butterworth/Heinemann; 2000.

[7] Smith BH, Hutchinson JW, Evans AG. Measurement and analysis of thestructural performance of cellular metal sandwich construction. Int J Mech Sci2001;43(8):1945–63.

[8] He MF, Hu WB. A study on composite honeycomb sandwich panel structure.Mater Des 2008;29:709–13.

[9] Nia AA, Sadeghi MZ. The effects of foam filling on compressive response ofhexagonal cell aluminum honeycombs under loading experimental study.Mater Des 2010;31:1216–30.

[10] Charles J. Heat pipe honeycomb panel. Patent application (NASA).[11] Camarda CJ, Basiulis A. Radiant heating tests of several liquid metal heat-pipe

sandwich panels. NASA-TM 85669.[12] Tanzer HJ. Fabrication and development of several heat pipe honeycomb

sandwich panel concepts. NASA-CR-165962.[13] Fleischman GL, Tanzer HJ. Advanced radiator concepts utilizing honeycomb

panel heat pipe (stainless steel), NASA-CR-171979.[14] Queheillalt DT, Carbajal G, Peterson GP, Wadley HNG. A multifunctional heat

pipe sandwich panel structure. Int J Heat Mass Transfer 2008;51:312–26.[15] Sihn S, Rice BP. Sandwich construction with carbon foam core materials. J

Compos Mater 2003;37:1319–36.[16] Deshpande VS, Fleck NA, Ashby MF. Effective properties of the octet-truss

lattice material. J Mech Phys Solid 2001;49(8):1747–69.[17] Wadley HNG, Fleck NA, Evans AG. Fabrication and structural performance of

periodic cellular metal sandwich structures. Compos Sci Technol2003;63:2331–43.

[18] Kooistra GW, Wadley HGN. Lattice truss structures from expanded metalsheet. Mater Des 2007;28:507–14.

[19] Queheillalt DT, Murty Y, Wadley HNG. Mechanical properties of an extrudedpyramidal lattice truss sandwich structure. Scripta Mater 2008;58:76–9.

[20] Queheillalt DT, Wadley HNG. Titanium alloy lattice truss structures. Mater Des2009;30:1966–75.

[21] Lee BK, Kang KJ. Compression strength of tube-woven Kagome truss core.Scripta Mater 2008;58:76–9.

[22] Deshpande VS, Ashby MF, Fleck NA. Foam topology bending versus stretchingdominated architectures. Acta Mater 2001;49(6):1035–40.

[23] Wallach JC, Gibson LJ. Mechanical behavior of a three-dimensional trussmaterial. Int J Solid Struct 2001;38:7181–96.

[24] Courbiere M, Mocellin A. Spray cast Al–Si base alloys for stiffness and fatiguestrength requirements. J de Physique IV 1993;3:207–13.

[25] Nikanorov SP, Volkov MP, Gurin VN, Burenkov YA, Derkachenko LI, KardashevBK, et al. Structural and mechanical properties of Al–Si Al–Si/Ge alloysobtained by fast cooling of a levitated melts. Mater Sci Eng A 2005;390:63–9.

[26] Nikanorov SP, Peller VV, Totten GE, Mackenzie DS. Handbook of aluminum:physical metallurgy and processes, vol. 1. New York: Marcel Decker; 2003. p.81–211.

[27] Li PJ, Nikitin VI, Kandalova EJ, Nikitin KV. Effect of melt overheating, coolingand solidification rates on Al–16 wt.% Si alloy structure. Mater Sci Eng A2002;332:371–4.

[28] Totten GE, Xie L, Funatani K. Handbook of mechanical alloy design (mechanicalengineering). New York: CRC Press; 2003.

[29] Ashbly MF, Brechet YJM. Designing hybrid material. Acta Mater2003;51(19):5801–21.

[30] Xiong J, Ma L, Wu LZ, Wang B, Vaziri A. Fabrication and crushing behavior oflow density carbon fiber composite pyramidal truss structures. Compos Struct2010;92:2695–702.

[31] Wang B, Wu LZ, Ma L, Sun YG, Du SY. Mechanical behavior of the sandwichstructures with carbon fiber-reinforced pyramidal lattice truss core. Mater Des2010;31:2659–63.

[32] Finnegan K, Kooistra G, Wadley HNG, Deshpande VS. The compressiveresponse of carbon fiber composite pyramidal truss sandwich cores. Int JMater Res 2007;98:1264–72.

[33] Zupan M, Deshpande VS, Fleck NA. The out of plane compressive behaviour ofwoven-core sandwich plates. Eur J Mech A/Solids 2004;23(3):411–21.

[34] Jones RM. Mechanics of composite materials. Int StudentEdition. Tokyo: McGraw-Hill Kogakusha, Ltd; 1975.

[35] ASTM D7250-06. Standard practice for determining sandwich beam flexuraland shear stiffness[S]. Philadelphia, USA: ASTM; 2006.

[36] Allen AG. Analysis and design of structural sandwich panels. Oxford:Pergamon; 1969.

[37] Deshpande VS, Fleck NA. Collapse of truss core sandwich beams in 3-pointbending. Int J Solid Struct 2001;38:6275–305.

h panels with hollow Al–Si tubes core construction. J Mater Design (2010),