10thInternationalMicro-AirVehiclesConference22nd-23rdNovember2018.Melbourne,Australia.

Carbonfibre/PVCfoamsandwichcompositemodelization

forMAVs&longrangedronesstructures

M.LEFEBVRE*,R.KIEFER,M.VEDRINES,andH.CHIBANEIcube,INSA,CNRS,Strasbourg,France

1*contactemail:martin.lefebvre@insa-strasbourg.fr

ABSTRACT

This paper deals with thecharacterization, modelization andsimulationofacompositestructureusedforMAVor generally for dronesdesign.Composite structures are extremelydifficult to simulate due to theanisotropic behaviour. The first part ofthe article is focused on carbonfiber/PVC foam (AIREX) sandwichcomposite characterization with thedesignofexperimentsmethodontensiletests. This method gives equations,which describe thematerial mechanicalbehaviour (Young’s modulus, tensilestrength) depending on factors values.Thesecondpartofthearticledealswiththe improvement of mechanical simu-lationofananisotropicmaterialwiththegoal to get an accurate model and togeneralised properties to an entirestructure. Then, the macroscopicmechanical properties of the mostperforming sandwich will be obtainedwith the global composite behaviourmatrix6x6,inordertobeintegratedintoaFiniteElementAnalysissoftware(CREO/ Simulate) to simulate a fixed wingbehaviour.Finally,comparisonsbetweenexperimentandnumericalsimulationonthewingwillgivepromisingresults,andsimulations will reveal substantialdifferencesbetweentension&compres-sioninaflexuralsolicitation.

1INTRODUCTION

The design of experiments method (Or Taguchimethod)isusedtostudyvariouscombinationsofsandwich composite. Commonly used inaeronautic design, this method can beimplemented in drones design because dronesbecomemoreandmorecompetitive.Thismethodprovides many advantages for drones’ design,suchas leansizingandextraweightavoidancetoincrease drones’ performances and reducemanufacturingcost[4].

Thisapproachpermitstoinvestigatetheeffectofeachfactoronmechanicalproperties,andoffersawaytochoosethebestsandwichmaterialinordertofollowthespecifications.Designofexperimentsfinally gives equations that take design factorsinto account. INSA STRASBOURG team CIGOGNE(https://www.facebook.com/equipecigogne/;https://fondation.unistra.fr/projet/imav2018/)uses this method in the design process of theELCOD project INTERREG in cooperation withGerman and French universities. The objective isto design a low-cost long endurance drone. Bychoosing the correct carbon fibre sandwich forthestructureandknowingthecorrectmechanicalbehaviour of the material, the objective is tochoose the best factors combination thatoptimizescostandhighstrengthofthedrone.

2Thedesignofexperiments

Thedesignofexperimentsusedisathreefactorsgeneralfullfactorialdesign.• Thefirstqualitativefactoriscarbonfibretype

(Fourlevels:A,B,CandD)• The second quantitative factor is fibre

orientation(Twolevels:0°and45°)

10thInternationalMicro-AirVehiclesConference22nd-23rdNovember2018.Melbourne,Australia.

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• The third quantitative factor is PVC foam(AIREX© sheet C70.75 – R&G composite)thickness (Three levels: 1.2mm, 2mm and5mm)

Thus, for this experiments plan, 24 combinationswere tested with tensile tests. Furthermore, foreachcombination, threeexperimentsweremadeto test the repeatability of the measure and tohave a convincing average response. ThoseexperimentswerealsomadeonanarticlefortheIMAV 2015 where the tensile norm andexperimentsprocessareclearlyexplained[1].

Figure1-Sandwichcompositestructure

• The B type is made with two layers of carbon fibre65g/m2(Atype)forthefacesheet.

• 0°istheXXdirection:

F0 F1(θ) F2(c)Carbonfibretype Orientation Foamthickness[mm]

A0° 1,2 2 545° 1,2 2 5

B0° 1,2 2 545° 1,2 2 5

C0° 1,2 2 545° 1,2 2 5

D0° 1,2 2 545° 1,2 2 5

3Results

3.1Effectoffactors

Tensile tests results are analysed to study eacheffectoffactorsonmechanicalproperties:Tensilestrength and Young’smodulus are the responsesstudied.

Figure3-Effectofeachfactorsonaveragetensilestrength

Figure4-EffectofeachfactorsonaverageYoung'smodulus

When PVC foam thickness increases, averagemechanical properties decrease, becausesandwichpropertiesconvergetofoamproperties.That is adequately explained with the sandwichruleofmixture[3].Off-axisorientationdecreasesalsomechanicalproperties[2,5].Withthismethod,aselectioncanbedone:• Atypehasn’tgotenoughmechanicalstrength• B type is too expensive in a low-cost design

(thecarbon fibre surface isdoubledcomparetotheothertypes)

• 80g/m2and160g/m2carbon(C&Dtype)haveto be preferably considered in terms ofmechanical properties. In the following, acomplete analysis will be done.Table2-Designofexperiments;factors’values

CarbonfibretypeA C D

65g/m2

Plainweave(60tex)

80g/m2

SpreadtowfabricTeXtrem(800tex)

160g/m2

Plainweave(200tex)

Table1-Carbonfibretype

Figure2-Fibreorientation

Facesheet(Carbonfibre/epoxy)Factor:Type&orientationA,C&Dtype:1layerBtype:2layers

Core(Polyvinylchloridefoam(PVC)orAIREX)Factor:Thickness

XY

Z

(t)(l)

10thInternationalMicro-AirVehiclesConference22nd-23rdNovember2018.Melbourne,Australia.

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3.2Compositebehaviourequations

3Dplots give visual results on thebest sandwichmaterial composition. The comparison betweensandwich C and D is done on the Figures 5 & 6.Behaviourequationsaregivenon theEquation1&2.

Figure5-CarbonfibreCtype;factors3Dplot

Figure6-CarbonfibreDtype;factors3Dplot

Equation 1 & 2 gives theoretical tensile strengthfor this factors combination. It is an importanttimesavinginthedesignstep.

Example: For the carbon fibre C, with θ=0° andfoamthickness=3mm:!!"# = 122,1 − 1,23×0 − 45×3 + 4,76×3!

+ 0,21×0×3 = !",!"#$%Design experiments method can be use forstructuresizing.Bychoosingfactorsvaluesforthecomposite, it is possible to evaluate thetheoreticalYoung’smodulusandtensilestrength.

4Flexuralmodels

Theobjective is todetermine themostadequateflexuralmodel touse in the followingstudy.A3-pointsbendingtestwillbedonetostudyflexuralbehaviour.Assample,a2mmthicknesssandwichbeamCtypewillbetested.

4.1Castiglianomodel

Equations 3& 5 give the deflection Δ [mm] of acomposite sandwich beam for a 3-point bendingtestunderaloadF[N]:

• ∆= !"!!" !" é!

+ !"!

!!" (eq.3)[2]

With !" !" =!!!!!! + !!!!!

!" + !!!"!!! (eq.4)[6]

Figure7-Sandwichcompositethicknessdata

This model takes the separate layers and theshear contribution (second term of Equation 3)intoaccount.Forthebendingtest,propertiesofthesampleare:o !! = 49 and!! = 0,066 [GPa]o ! = 50 , ! = 600, ! = 2and! = 0,22[mm]o ! = 1Note:!!and!!aredeterminedwithsuppliers’dataandruleofmixture for!!withepoxyresin.Theerror isquantifiedto+/-5%.

4.2Homogeneousbeammodel(Voigtmodel)

• ∆= !"!!" !" !"#$%"

(eq.5)The term !" !"#$%" is determined with thetensiletestfromthedesignofexperiments.

4.3Experimental3-pointsbendingtest

Figure8-3-pointbendingtestonsandwichsample(Ctype)

SandwichC!!"# = 122,1 − 1,23×!1 − 45,0×!2 +4,76×!2! + 0,21×!1!×2 (!".1)

SandwichD!!"# = 135,5 − 1,23×!1 − 45,0×!2 +4,76×!2! + 0,21×!1×!2 (!".2)

Table3-Compositebehaviourequations(R2=81,04%)

F1:Orientation(θ)-F2:Foamthickness(c)

core

fibre

CarbonfibretypeC

CarbonfibretypeD

Fibreorientation(°)AIREXthickness(mm)

Tensile

stren

gth(M

Pa)

Fibreorientation(°)AIREXthickness(mm)

Tensile

stren

gth(M

Pa)

10thInternationalMicro-AirVehiclesConference22nd-23rdNovember2018.Melbourne,Australia.

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Figure9-Beamcomparisonbetweenflexuralmodels

Model RelativeerrorCastigliano 20%Voigt 166%

In flexural solicitation, it’smore adequate to usetheCastiglianomodel (Sandwichmodel): To takethe distinct layers into account with the !" é! term. The theoretical result will be closer to thereality with this model. For tensile, themacroscopicmodelcanbeused;itisbydefinitionthe behaviour of a composite with the rule ofmixture.However, for flexuralsolicitationamoreelaborate bending theory is needed [2, 7]. Thisaccurate theory takes behaviour of heterogeniclayers and the shear contribution into account.Thatiswhytherelativeerrorislessimportant.

5Bestfactorcombination

Low foam thickness means high tensile strengthand high Young’s modulus. And high foamthickness means high rigidity (high secondmoment of inertia). The objective is to find acompromise between high tensile strength andhighrigidity.

Thanks to the experiments, the optimizationprocess gives a thickness between 1.8mm and2,5mm (white area on the Figure 10) with thecarbon fibre C and 0° orientation to insure best

compromise between high bending stiffness andhightensilestrength:

Figure10-Compositethicknessoptimization

In the followingparts,acomparisonwillbedonebetween a real bending test and a numericalsimulationonaCtypecarbonfibresandwichwing(NACA MH 32 wing profile) with a carbon fibresandwich spar. The objective is to study theaccuracy of a numerical simulation on complexfixed wing geometry. Thanks to the previousresults,thechoiceofa2mmfoam,CarbonfibreCtype is done forthe analysis. Themulti-layersmodelwill be used toincrease the ac-curacy of thesimulation.

6Sandwichmechanicalbehaviour

The following equations are used for input allmaterialdataonCREOSimulate.

!! ! = !!!!!!!

!!!!!!!! !

!!"!!!!"!!

!! ! = !!!!!!!!!!!!

!!! !!!"

!!!!"!!

!!" ! = !

!!!!! !!!! !!!!!!!"!! ! !!!!! !

!!"

(eq.6)[2]

Equations 6 can give !!" thanks to the tests at! = 45°. Thus, all coefficients of stiffnessmatrix! canbedeterminedforeachlayer:

y=3,3479x

y=2,6675x

y=8,9015x

0

10

20

30

40

50

60

70

0 2 4 6 8

Defl

ecgon

Δ(m

m)

Force(N)Δexperimental

Δtheoreqcal(Casqglianomodel)

Δtheoreqcal(Voigtmodel)

Table4-Relativeerrorcomparisonbetweenflexuralmodels

Figure11-ExperimentalwingMH32+sparCompositesandwichstructureC

10thInternationalMicro-AirVehiclesConference22nd-23rdNovember2018.Melbourne,Australia.

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! !"#$%!!!! =58,47 14,03 014,03 58,47 00 0 30,47 !° !"°

! !"#$ =0,073 0,022 00,022 0,073 00 0 0,028

(UnitsinGPa)

Distinct layers have to be integrated into thebehaviourmatrix6x6,inordertogetmacroscopicsandwichcompositebehaviour:

! =

!!! !!" 0!!" !!! 00 0 !!!

|!!! !!" 0!!" !!! 00 0 !!!

— —!!! !!" 0!!" !!! 00 0 !!!

|!!! !!" 0!!" !!! 00 0 !!!

(eq.7)

With:

!!" = !!"!!!!!!! (8)

!!" = !! !!"! ℎ!! − ℎ!!!!!

!!! (9)

!!" = !! !!"! ℎ!! − ℎ!!!!!

!!! (10)

Note:Forasymmetriccomposite:! = 0

Figure12-Sandwichcompositelayersthickness

Finally, the carbon fibre/foam 2mm sandwichcomposite macroscopic behaviour can beexpressedwiththismatrix:

! =

13009 3131 03131 13009 00 0 6759

| 0— —

0 |14379 3453 03453 14379 00 0 7486

(AmatrixinN/mm;DmatrixinN.mm)

7Sandwichsimulations

Aftercomputingmatrixbehaviourdata (Equation7) into CREO Simulate, flow stress and beam iscalculated with a 10N load at the edge of thetestedwing:

Figure13–FlowstressXX(N/mm)simulationonsandwich

compositeC;wing+spar(Displaybeamscale:10%)

The upper side of thewing is in tension and thelowersideincompression.Themaximumstressisreachinthesparofthewing.Itisthispartonthewingwhichtakesupefforts.

8Sandwichexperimentaltest

Theobjectiveistocomparesimulationwithanexperimentalbendingtest:

Figure14-ExperimentalZwickRoellbendingtestbench

Strain is measured in three points with straingauges:Pt1:Upperside,closetorigidlinkPt2:Lowerside,closetorigidlinkPt3:Upperside,middleofthewing

Figure15-Experimentalwingstrainon3points

Intheexperimentaltest,thetensilestressontheupper side of the wing is the same than thecompressivestressonthelowersideofthewing.

y=-59,061x

y=28,007x

y=59,1x

-1500

-1000

-500

0

500

1000

1500

0 5 10 15 20Strain(x10

-6)

Load(N)

εPt2

εPt3

εPt1

0

1

2 h3h2

h1 h02 2,22

10thInternationalMicro-AirVehiclesConference22nd-23rdNovember2018.Melbourne,Australia.

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For compression the relative error is moreimportant because it is difficult to predictcompressive behaviour for fibre due to crushing,bucklingandfibredelamination.ThoseresultsareshowedintheTable5.

Table5-Relativeerroronstressandbeamcomparison

9CONCLUSION

Design of experiments has made possible thechoice the best sandwich composite for thecorrespondingapplicationandgivesequations tocorrectly design the composite structure. Thismethodhas tobeused todesigndrones; it is animportant timesavingtocomparestructuresandtochoosethebestfactors’values.

Afterchoosingtheadequatesandwichcomposite,numerical simulations show that compositebehaviour is not the same in tension orcompression for high deformations. Even if themodelwith distinct layers ismore accurate thanthe homogeneous model, investigation can bedone to improve this theory. Buckling and fibredelamination can occur for compression, and amoreexhaustivetheorythattakeslayersslippageand plastic deformation into account has to beused.Theflexuralbehaviourisnon-linearforhighcompressive deformations [7]; and for theexperiment of the present article, increasing theloadtoproducehigherdeformationscouldpermitto studyamoreaccuratenon-linear compressivebehaviourandrevealbuckling[7,8].Togofurtherwith simulation, Tsai-Wu failure criterion can beused to study the limit of the composite, plusobservation on sample have to be done toinvestigatedamageand failure [8].Fornumericalsimulation, it is possible to be confident withtension, because the behaviour is linear-brittle

and error is under 5%. However, it is highlyrecommended to be careful when localcompression appears. Indeed, the currentmodelis neither accurate nor optimal and simulationerrorishigherthan25%becauseofbuckling.

REFERENCES

[1] Renaud K., Marc V., Proposition of designmethod and optimization of multirotorscompositestructures,ICubeUMR7357,2015.

[2] D. Gay, Matériaux composite (CompositeMaterials). Paris: Lavoisier Hermes, 6th revisededition,2015.687p.(ISBN978-2-7462-4707-9)

[3]CESEduPack,SandwichPanel:Assumptionandcalculations,Granta,85p.2017.

[4] R. Rikards, A. Chate, Optimal design ofsandwich and laminated composite plates basedon the planning of experiments, StructuralOptimization,RigaTechnicalUniversity,1995.

[5] KawaiM.,MorishitM., SatohH., Tomuras S.,Effect of end-tape shape on strain field ofunidirectionalcarbon/epoxycompositespecimenssubjecttooff-axistension,CompositePartA,Vol.28A,pp267-275,1997.

[6] K. Joon Yoon, C.K. Kim and Hoon C. Park,Nonlinear flexural deflection of thermoplasticfoam core sandwich beam, Journal of CompositeMaterial,Vol.36,No13/2002,2001.

[7]I.M.Daniel,J.L.Abot,K.A.Wang,Testingandanalysis of composite sandwich beams, ICCM,1999.

[8] E.E. Gdoutos, I.M. Daniel, Failure modes ofcompositesandwichbeams,Thoeret.Appl.Mech.,Vol.35,No.1-3,pp.105-118,Belgrade2008.

ACKNOWLEDGEMENTS

The ELCOD project (www.elcod.eu) is co-fundedby the European Regional Development Fund(ERDF) and the co-financed project partnersRegion Grand Est and the countries of Baden-Württemberg and Rhineland-Palatinate in theframework of the INTERREG V Upper Rhineprogram.

Numerical Experimental StressXX(MPa) ErrorPt1 3,83 3,95 3,1%Pt2 -3,15 -3,94 25%Pt3 1,66 1,63 1,8% BeamUY(mm) ErrorMax 10,31 13,62 25%