Structural imperfections in additive manufacturing perceived from the X-ray micro-tomography perspective

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Structural imperfections in additive manufacturing

perceived from the X-ray micro-tomography perspective

Hedi Nouri, Sofiane Guessasma, Sofiane Belhabib

To cite this version:

Hedi Nouri, Sofiane Guessasma, Sofiane Belhabib. Structural imperfections in additive manufacturing

perceived from the X-ray micro-tomography perspective. Journal of Materials Processing Technology,

Elsevier, 2016, 234, pp.113 - 124. �10.1016/j.jmatprotec.2016.03.019�. �hal-01525748�

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a_Mines_Douai,_Department_of_Polymers_and_Composites_Technology_&_Mechanical_Engineering_(TPCIM),₉₄₁_Rue_Charles_Bourseul,_CS_10838,₅₉₅₀₈_Douai,

France

b_Ecole_Nationale_{d’Ingénieurs}_de_Sfax,_Laboratoires_des_Systèmes_{Electromécaniques,}_Route_Soukra_Km_3,_BPW₃₀₃₈_Sfax,_Tunisia c_INRA,_UR1268_{Biopolymères}_Interactions_Assemblages,_F-44300_Nantes,_France

d_LUNAM_Université_Nantes_Angers_Le_Mans,_CNRS,_GEPEA,_UMR_6144,_IUT_de_Nantes,₂_Avenue_du_Professeur_Jean_Rouxel,₄₄₄₇₅_Carquefou_Cédex,_France

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Articlehistory:

Received13November2015

Receivedinrevisedform17March2016 Accepted20March2016

Availableonline22March2016 Keywords:

Additivemanufacturing AcrylonitrileButadieneStyrene X-raymicro-tomography Fuseddepositionmodelling Structuralanisotropy

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OurconcernistorevealtheextentofstructuralimperfectionsofAdditiveManufacturing(AM)by consid-ering3DimagingtechniquebasedonX-raymicro-tomography.BlocksofAcrylonitrileButadieneStyrene (ABS)polymerareprocessedusingFusedDepositionModelling(FDM)withdifferentprinting orienta-tions.Imageanalysisisappliedtothestacksof3Dprintedblockstoquantifystructuralattributessuch asporositycontentandconnectivity.

TheresultsshowthatporeconnectivityrepresentsthemostimportantstructuralcharacteristicofFDM. Theadoptedcommercialsolutionisabletoproduceacceptableporositycontentsbelow6%regardless oftheprintingorientation.Finiteelementresultsindicatethepresenceofexpectedtransverse symme-try.Theexaminationoftheextentofsuchanisotropyisinwellagreementwiththeobservedstructural imperfectionsmainlytheporositycontent.However,thesepredictionsdonotmatchthewide varia-tionsinmechanicalperformancedescribedintheliterature.Thefiniteelementanalysisguidesthenext researchsteptowardsquantificationoftheimperfectbondingnaturebetweenfilamentsinFDM.

1. Introduction

AdditiveManufacturing(AM)ispresentedby(Zhaietal.,2014)

asthesecondindustrialrevolutionofthisepoch.Theauthorsshow

thatthis termis justiﬁedbythewideimpacttriggeredbysuch

technologyonmodernsociety, allowingmostlyanyone tobea

designer.

AMisnowattractinganimateddebatesindifferentdisciplines

of research.Huang et al. (2013) point out two major concerns

thatneedfurtherinvestigation:energyandhealthfootprints.For

instance,varioushealthcare productscan bepersonalisedusing

additivemanufacturingsuchasimplants, safetyequipmentand

otherproductsrelated to tissue engineering.The sameauthors

(Huang etal.,2013)showthepositive impactofAMonenergy

demandwithtwomaindrivingfactors,namelyreductionand

efﬁ-ciency.Thisimpactisjustiﬁedbytheabilitytodesign products

of alower energy consumption usinglimited amountof

mate-rialsand ﬂuids.All these aspects are expected toimprove the

∗ Correspondingauthor.

E-mailaddress:soﬁ[email protected](S.Guessasma).

environmental impact and product life time. Kietzmann et al.

(2015)showthatsomeofthesedebatesarerelatedtoethicaland

legalissuesdrivenbythenewroleofconsumerinthemarket.This

isillustratedbytheoppositionbetweencompanyinnovationeffort

andconsumercreativityforthedesignproductsthathavecertain

conformity.Versatiletechniquesofadditivemanufacturingareable

toshortenfabricationstepstoonemainbetweentheCADdesign

andtherealpart.AsshowninthereviewworkofPhamandGault

(1998),thereducednumber ofmanufacturingsteps,fora large

numberofAMprocesses,isavectorforenhancingthe

competi-tivenessandanopengatewayforoptimisingmanufacturingcost.

ThiscomeswithacertaincostasdetailedinthesurveybyYanand

Gu(1996),whichpointsoutthelimitedperformance,lackof

accu-racyandshortwindowformaterialselection.Alltheseaspectsare

nowamajorresearchareainAM.Forinstance,recentadvances

in electronbeammelting showa largepotentialtocontrol the

porousstructurein3Dprintedcellularmaterials(Lietal.,2016).

Suchﬁnecontrolofthemicrostructureallowsthedevelopmentof

functionallygradedmaterialsthatpresentadvantageousbiological

functionssuchasosteoblastinbioengineeringapplications(Nune

etal.,2016a,b,2014).

http://dx.doi.org/10.1016/j.jmatprotec.2016.03.019

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Researchliteratureonthesubjectagreesthattheprimary

char-acteristicofadditivemanufacturingistheabilitytodesigncomplex

geometries.Beckeretal.(2005)showthatthisisarealopportunity

torethinkthedesignwithoutbeingboundedbythetooling

con-strain.FuseddepositionmodellingFDMisonethepopularwayof

additivemanufacturing.TheearlyreviewonthesubjectbyPham

andGault(1998)categorisesFDMasliquid-basedadditive

manu-facturing.Turneretal.(2014)describeFDMasatypicalextrusion

process,wheretheﬁlamentofthefeedmaterialisswipedfromthe

supportcartridgeusingdrivingwheels.Thematerialisforcedto

theliquidstateusingaliqueﬁerandthefusedmaterialﬂowsfrom

theprintingtiptothemodellingbase.Thistipisabletomove

rela-tivelytotheprintingbaseinthethreedimensionalspace.Mostof

theprintedmaterialsusingFDMarepolymers(mainlyAcrylonitrile

ButadieneStyreneorABS,PolylacticacidorPLA).Recently,Carneiro

etal.(2015)demonstratethefeasibilityofusingpolypropyleneas

apolymercandidateinFDMstartingfromtheﬁlamentextrusion

stepandendingtothesmallsizepartcharacterisation.

Theresultoflyingdownofthefusedmatterinsuccessive

lay-ersisthedevelopmentofanisotropicstructuring.Ahnetal.(2002)

showastrongcorrelationbetweentherasterangleandthetensile

propertiesofABS.Theauthorsshowthattensilestrengthcanvary

inawiderange(from2.5to20MPa)dependingoninter-ﬁlament

crossingandorientation.Leeetal.(2007)showthatfailuremodes

undercompressionaredistinct dependingonthechoiceofAM

technology.Shafferetal.(2014)showthatimproved

macromolecu-larcrosslinkinginFDM-basedthermoplasticsystemsisachievable

usinggammaradiation.Theauthorshighlightadirectconsequence

onincreasedtoughnessof studiedpolymers.Thesecontributors

(Shaffer et al.,2014)conﬁrmthat tensile responsesof PLA and

ABS samples are sensitive to printing orientation. The optimal

responsecorrespondstothemaximumalignmentofﬁlamentin

theloadingdirection.Inaddition,theresultsofthesameauthors

indicatehighersensitivityofABScomparedtoPLAtomechanical

anisotropy.Theliteratureworkisconstantlyexhibitingattempts

toreduceanisotropyissuesby,forexample,optimisingthepart

orientationorapplyingpost-processingtoimprovecross-linking.

Carneiroetal.(2015)showthat,besidesthepartorientation

pre-vailingeffect,theinﬁlldegreehasalsoastrongeffectontensile

properties of PP and PP based composites.Thrimurthulu et al.

(2004)suggesttheuseofoptimisationstrategybasedongenetic

algorithmtoachieveoptimaldepositionorientationwithreduced

stair-caseeffectandminimumsupportmaterial.Strategiesalsoare

appliedtoreducediscontinuitiesbyconsideringmorecontinuous

modesofprinting.Chakrabortyetal.(2008)argueonthe

bene-ﬁtsofusingcurvedlayerFDMtoimprovetheprocessingofcurved

structuressuchasthin shell-typeparts. Theauthorsshow that

thereductionofthestair-caseeffectandsmoothﬁnishingsurface

stateareimportantoutcomesoftheproposedFDMstrategy.Choi

etal.(2011)presentamodiﬁedcommercialset-upwith

capabili-tiesofverticallayering.Theauthorsclaimthatthismodiﬁedset-up

allowsmoreﬂexibilitybyreducingthedependencetothebuilding

direction.Foralargenumberofthesecontributions,theoptimal

designinAMisconductedfromanengineeringviewpoint,by

focus-ingonprocessparameterdriveneffects.Forinstance,Galantucci

etal.(2008)focusonoptimisingmanufacturingtimeandcostwith

respecttoshapefactorssuchastheinternalangle,rasterandshell

width.Inareviewpaper,Mohamedetal.(2015)showthattheFDM

optimisationreliesonbuildingorientation,layerthicknessandtool

pathparameters.Theauthorsrefertotheliteratureworktorelate

theseinﬂuentialparameterstosurfaceroughness,partdeposition

imprecision,buildingtime,andpartperformance.

Betteractionstowardstheoptimaldesigncanbedrivenbymore

fundamentalunderstandingofthenatureandextentofthedefects

inducedbyAM.Thankstotherecentadvancesin3Dimage

tech-niques,itisnowpossibletoachieveaclearpictureofthetextureand

defectextentatthemicrostructurescale(Bakeretal.,2012;Maire

andWithers,2014;MizutaniandSuzuki,2012).Thisisillustratedin theworkofMostefaietal.(2015),whichsuggeststheuseofX-ray

micro-tomographytoachievemicrostructuralarrangementin

het-erogeneouscementiteouscomposite.Thispicturecanbeevenmore

accurateifananticipationofthemicrostructuralperformanceis

includedthroughcomputationalanalysis(Moreno-Atanasioetal.,

2010).ThisisconductedintheworkofAyadietal.(2015),where

theauthorsareabletocombineﬁniteelementanalysisandX-ray

micro-tomographyimagingtopredicttheelasticitybehaviourof

polymericcomposites.Thesetwotypesofanalysis,namelyX-ray

micro-tomographyand ﬁnite elementcomputation arebrought

togetherinthisresearchcontributiontogainmorefundamental

knowledgeabouttheprocess-induceddefects.

Indeed,X-raymicro-tomographyisused,inthisstudy,to

quan-tifythedefectsinthethree-dimensionalspace.Partoftheanalysis

isthedeterminationoftheporousstructureandrelatedattributes.

The3Dimagesareconvertedintoﬁniteelementmodeltocapture

theeffectofprocess-induced defectsonthemechanical

perfor-manceoftheprinted parts.Thisstudyfocuses onABSpolymer

blocksthatareprintedusingacommercialFDMsolution.

2. Experimentallayout

TheABSpolymerisdeliveredbyCADvisioncompany

(Guyan-court, France) under the reference P430XL ABS. The additive

manufacturingisbasedoncommercialsolutionoffuseddeposition

modellingmanufacturing.ProcessingisperformedusinguPrintSE

3Dprinter fromStratasys.Thisprinting technologyisequipped

withtwotipsof254␮mindiametereachforthedepositionofABS

andadissolvablesupport.CuboidsofABS(30×30×30)mm3_are

printedusingdifferentorientationswithrespecttothemodelling

base.Orientationisrepresentedbytheangle␪,wherethe

follow-ingchoicesaremade0◦,30◦,45◦,60◦,and90◦(Fig.1).TheStlﬁles

oftheCADmodelsaretransformedintotoolpathsusingbuilt-in

software(CatalystEX).DuetothesimplicityoftheCADmodel,the

softwareplanssolublesupportattheﬁrstlayerstopreventstrong

bondingtothebase.

X-raymicro-tomographycharacterisationoftheprinted

sam-ples is conducted using an UltraTom X-ray ␮-CT system. The

acquisition parameters are: voltage 60KV, current intensity

480␮A,voxelsize30␮m,continuousmodeacquisition,resolution

of2DradiographicImages1920×3536pixelswithvariandetector

focusedonascintillatingmaterial,1440radiographicimages.

Weneedtomentionthattheaccuracyof3Dimaging

acquisi-tionreliesonthevoxelsizewhichiseighttimessmallerthanthe

printingtipdiameter.Stacksrepresentingtheacquiredvolumesare

builtfromthecollectionofradiographicimagesusingtheﬁltered

back-projectionalgorithm(X-ActsoftwarefromRx-Solutions).The

imageacquisitionandthestackassemblingrequirelessthan30min

percondition.Thevoxelnumberperstackvariesisoftheorderof

onebillion.

Theclearseparationbetweenthesolid andairphasesallows

thesuccessfulapplicationofvarietiesofimageoperators,which

arecodedusingtheprogrammingenvironmentofImageJ(http://

imagej.nih.gov/ij/,NationalInstituteofHealth)softwarefromthe

publicdomain.Inparticular,automaticthresholdingisappliedto

greylevel stackstoachieve binaryimagesrepresentingair and

densephases.Floodingisappliedtoseparatethebackgroundfrom

theairphase.Floodingisbasedontheﬂoodﬁllingtoolavailablein

ImageJ.SincethecontouroftheacquiredABSblockisclosed,wedid

notusesophisticatedcontourdetectionalgorithmssuchlike

wrap-pingdeveloped in(Mamloukand Guessasma,2013)toseparate

accuratelythebackgroundfromthefeatureofinterest.Flooding

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Fig.1.Illustrationofthepartorientationanddeﬁnitionoftheprintingangle␪.

neighbouringpixelswhichhavethesamegreylevelareattributed

anintermediategreylevelof128.Theprocessisextendedtoall

slicesoftheimage.Asaresult,thebackgroundappearsdistinctfrom

theporousandsolidphases.Notethatthisoperationispossible

becauseprintingofABSisrealisedusingaﬁlledcontour.

Pore size distribution is obtained using granulometry

tech-nique(Guessasmaetal.,2008).Thesizedistributiondetermination

is based on a growingstructural element that scans the stack

with a regular step. Each time a feature of size less than the

sizeofthestructuringelementisdetected,itiseliminatedfrom

theforeground.Thiscorrespondingsizefrequencyisincremented

accordingly.Thecomputationtimemaybesigniﬁcanttoassessthe

poresizedistribution.Indeed,a largenumberof scanningsteps

isneededtoscanthestack.Thisprocessisrepeatedforeachsize

increment(onevoxel)ofthestructuringelement,whichrequires

additional savingof intermediate stacks.The last iteration

cor-respondstothelargestdetectedfeaturein theforeground.This

algorithmworksthusasanumericalsievingtechnique.

Granulom-etrytechniqueisefﬁcienttomeasuretheporepolydispersitybut

ithardlyestimatesporeconnectivity.Thislastfeatureiscaptured

from3Dlabellingtechnique.Sinceporesareviewedascollection

ofvoxels,theyareconnectediftheysharecommonfaces,edgesor

corners.Poreconnectivitycanbeassessedfromanalysisofporosity

volumedistribution.3Dlabelling techniqueallowsthe

determi-nationofthelargestconnectedfeatureusingface,edgeorcorner

connectivitydeﬁnedbytheoperator.Iftwovoxelsbelongingtotwo

globularporosities(oridentiﬁedasdistinctfeaturesfrom

granu-lometryanalysis)shareafaceoranedge,theseareconsideredas

partofthesamefeature.Ameasureofporeconnectivitywouldbe

toscalethelargestconnectedfeaturewithrespecttothesumof

alllabelledfeatures.Theratio(largestfeaturevolume/totalpore

networkvolume)islargeforahighlyconnectedporenetwork.One

maynoticethatthisratioisaboundedquantity(between0and

1),whichmakesiteasiertorankporeconnectivityofprintedABS

blocksasfunctionofprintingangle␪.

Labellingisperformedusing26connectivityschemeinwhich

voxelsbelongtothesamefeatureiftheysharefaceorcornerin

common.Withthislastprocess,informationaboutpore

connectiv-itycanbegainedbyscalingthelargestporevolumewithrespectto

thetotalvolumeofavailableporosity.Itiscommontoﬁndinthe

literaturepercolationanalysisbasedonlowerconnectivityscheme

suchasfaceconnectivity.Fromtheperspectiveofrelatingpore

con-nectivityresultstoelasticityconstants;suchschemewillbetoo

restrictive.Indeed,iftwoporesareconnectedthroughanedge,

openingandthuslocalisationoccursevenifloadingislimited.The

useoffaceconnectivityreducestheconnectivitytotheﬁrst

neigh-boursandobviouslyaffectsthemagnitudeofporepercolation.This

effectisfurtherinvestigated.Granulometryand3Dlabellingare

timeconsumingtechniqueespeciallyforlargestacks.Thesize

dis-tributiondeterminationoftheporousnetworkisthemostresource

consumingtechniqueevenifthedevelopedalgorithmisoptimised

intermsofmemoryandCPU(CentralProcessingUnit)

manage-ment.Indeed,thedurationofprocessingvariesfrom2daysto5

daysperstackonworkstationequippedwith24-coreXeonCPU

E5-2620and192GBofRAM.

Severalstructuralattributesaremeasuredfromtheprocessed

images.Theporositycontentisdeterminedusingtheexpression

f (%)=100×

n×m×l i=1 ı 1 i(gi) /

n×m×l i=1 ı 2 j

gj

(1) where ı1_i(0)=1;ı1_i (128)=0;ı1_i(255)=0 (2) and ı2 j(0)=1;ı2j (128)=0;ı2j(255)=1 (3)

andf (%) is theporosity volumepercentage,ıi istheKronecker

function,whichdependsonthegreylevelg_iassociatedtovoxeli;

n,mandlarethedimensionsoftheX-rayimageinX,YandZ

direc-tions,respectively.Z-axisisthebuilding-updirectionassociatedto

the3DprintedABSsamples.

Inadditiontotheoverallporositycontentf (%),theaxial

con-tributionsareaccountedtomeasuretheanisotropyinferredtothe

process.Theaverageporositycontentpercross-sectionareais

plot-tedagainsttheslicenumber.Forexample,theporositycontentin

thedirectionofsamplegrowthf_z(i) ataparticularslicenumberi

reads f_z(i)=100×

(i)×n×m j=(i−1)×n×m+1ı 1 j

gj

/

(i)×n×m k=(i−1)×n×mı 2 k(gk)

(4)

Thescatteroftheporositycontentinthesamedirectionıfzis

calculatedusingthedeﬁnitionofthestandarddeviation

ıfz(%)=

1/l

×

l i=1

f_z(i)−

l i=1fz(i) /l

2 (5)

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Thelargest porosity levelMxf is alsomeasured in allspace

directionsfromthestatisticsonallavailablecross-sections.In

Z-direction,thisimplies

Mxfz=Maxli=1(fz(i)) (6)

where Mxfz is the peakporosity level measuredin Z-direction.

EquivalentexpressionscanbederivedforMxfxandMxfy.

Poreconnectivityismeasuredusing

(%)=100×MaxN

i=1

V_p(i)

/

N

i=1Vp(i) (7)

where istheporeconnectivitypercentage,V_p(i) isthevolume

associatedtothelabelledporei,Nisthetotalporenumber.

Weperformboth26-connectivity(26)and6-connectivity(6)

analysistocomparethelossofporeconnectivitywhenonlyﬁrst

nearestvoxelneighboursareused.

3. Modellingtechnique

ThepurposeoftheFiniteelementanalysisistoquantifythe

effectofmicrostructuralimperfectionsbylookingatthestressand

strainﬁeldsfordifferentprintingorientations.Ansysmulti-physics

commercialpackage(ANSYSInc.,Canonsburg,PA,USA)isusedfor

allﬁniteelementcomputations.Theacquiredstacksareimported

asregularmeshesusingvoxeltoelementconversion(Ayadietal.,

2015).Themodelsizeisproportionaltotheimageresolution.Itis

adaptedtoallowcomputationstobeperformedunderhundredsof

millionsofdegreesoffreedom.Thelimitedcomputationresources

(timeandmemoryrequirement)imposetheloweringoftheimage

resolutionbyafactor3_such_that

3₌_N

/N0 (8)

whereN0andNarethetotalnumberofvoxelsintheoriginaland

newimages.

Theresolutioncoarseningcanbefurtherdeﬁnedusing

dimen-sionsn,mandloftheX-rayoriginalimages

N=

n/

×

m/

×

l/

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Finiteelementcomputationsareconductedusingacoarsening

fac-torof0.25(3₌_1/64).

All ﬁnite element computations are conducted exclusively

usingtheabovementionedcoarseningfactor.However,structural

attributessuchasphasecontentandporeconnectivityare

deter-minedforalargeintervalofcoarseningfactors(≥0.025)upto

theoriginalresolution(=1).Changeofthephasecontentand

poreconnectivitymayoccurasaresultoftheresolution

degrada-tion.Theaccuracyofthevoxeltoelementconversionischecked

bymonitoringphasecontentandporeconnectivityvariationfora

decreasingresolution.

Meshingreliesonstructuralelementsdeﬁnedby8nodesand

threestructuraldisplacementspernodeinX,YandZdirections.The

elementsizeof120␮misstillsmallerthanthetipdiameterofthe

3Dprinter.Computationsareperformedbasedonafullstackforall

orientationsbutalsoonsubstacksrepresentingfractionsfromthe

fullvolume.Croppingisrealisedinbothlateral(X,Y)andbuilding

(Z)directions.Thenewz-dimensioninnormalsamplingusing

z=˛×Z|˛=0.1,...,1.0 (10)

Tenlevelsareused,andthesecorrrespondto30ﬁniteelement

evaluations per orientation. In these computations, remaining

dimensionsXandYofeachdomainarekeptatthefullscale.

Forlateralsampling,asimilarexpressionisused

x=ˇ×X|ˇ=0.1,...,1.0

y=ˇ×Y|ˇ=0.1,...,1.0 (11)

ThesamenumberoflevelsisusedandtheZdimensioniskept

atfullscale.

Themodelsizevariesdependingonsamplingfromfew

thou-sandstofewdozensofmillionsofdof(i.e.,degreesoffreedom).

Isotropicelasticmaterialmodelisimplementedforthedense

ABSphase(ES=1.54GPa,␯S=0.35,whereESisYoung’smodulus

and␯SisPoisson’scoefﬁcient).

Periodicboundary conditions are usedto predictstress and

straindistributionsintheprintedblocksinthreeloadingdirections

X,YandZ.

Regularmeshingallowsusinghomologuenodestoapply

peri-odic boundary conditions. Homologue nodes are identiﬁed for

opposedfacesas

Ri1j1k1=Ri2j2k2+D|D=Dx,Dy,Dz (12)

whereRandDarevectors,themagnitudeandorientationofD

areassociatedtooneofthephysicaldimensionsoftheacquired

volume,i1,j1,k1,i2,j2,k2areindicesrelatedtovoxellocationsR

intheimage.

Constraintsequationscanbeexpressedusing

Ui1j1k1=Ui2j2k2+U (13)

whereUrepresentsnodaldisplacementvector,Uisaconstant

vec-tor,nodessatisfyingtheconstraintequationsaredeterminedusing

equation(12).

Sinceboundaryconditionsareappliedasconstrainequations

(couplingequations),thestrainand displacementﬁeldsarenot

knowninadvanceatlateralfaces.Whensolvingtheelasticity

prob-lem,thesequantitiesbecomeavailableforallnodesincludingthose

belongingtothelateralfaces.Theaverageoflateraldisplacements

forallnodesbelongingtotheexternalsurfaces(thoseassociated

tothecroppedvolume)isusedtocomputePoisson’sratiosatany

samplingratio.

In addition,Young’smoduliare derived fromnodalreaction

forcesknowingtheimposeddisplacementwhereasPoisson’sratios

are determinedfrom theaveragedisplacement oflateral faces.

ThreeYoung’smoduli(EX,EYandEZ)andsixPoisson’sratios(␯yx,

␯zx,␯xy,␯zy,␯xz,and␯yz.where␯ijreferstothelateralexpansion

ini-directionforanimposedcompressioninj-direction)are

com-putedforeachrun.Thecomputationdurationperloadingpoint

reaches2hperformedon24-coreXeonCPUE5-2620workstation

equippedwith192GBofRAM.

4. Resultsanddiscussion

Fig.2showsqualitativelythetypeofdefectsidentiﬁedfrom

X-raymicro-tomographyanalysis.Onthetoprightside,typical

poremorphologyisshown.Dimensionsoftheorderofhundreds

of microns and even millimetric scale porosities are identiﬁed.

Thesearecharacterisedbylargearmsrepresentingthe

connec-tivitysharedwithotherglobularporosities.Onthebottomright

side,topographyofexternalsurfacesisexposed.Bothaverageand

maximumroughnessarealsogiven.

ThecentralviewsareinnerandouterperspectivesoftheABS

block.The leftside shows closeviews ofthe ﬁlament

arrange-ments.Twodistinctdimensionsarehighlightedfortheﬁlament

arrangementinFig.2:out-of-plane(Z-axis)isthebuilding

direc-tionassociatedtotheverticalsampling.Thein-planedimension

(XYplane)isrelatedtothelayingdownplane,whichisrepresented

inmanystudiesbytherasterangleor,inthisstudy,referredbythe

printingangle␪.

Despite removalefforts, someresidualsupportmaterial still

adherestothe3DABSstructure.Theresidualrepresentsfew

per-centoftheacquired volumebut coversa largesurfacearea. In

thebuilding direction,the boundingbox created at the

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Fig.2.Characteristicdimensionsofmicrostructuraldefectsinducedby3Dprinting.

in Fig.2)formbecause of theabrupt change in pathdirection

anddeceleration oftheprintingtip.Thealternation ofﬁlament

pathsrevealsdifferentcrossingsituationswherelargeconnectivity

betweenporositiesislikelytoappear(centralporeinFig.2).The

mismatchbetweensuccessivecontours(lackofcohesionbetween

successivelayers)isthecauseoftheobservedsurfacetopography,

whichistypicalofpartsrealisedusingFDM.Bothaverageand

max-imumroughnessvaluesarewellbelowtheprintingtipsize.This

issymptomaticofthelackofcohesionbetweencontiguous

ﬁla-ments(out-of-planeviewofﬁlamentinFig.2).Thein-planeview

oftheﬁlamentarrangement(leftuppersketchinFig.2)showsthat

thelateralﬁlamentexpansiondoesnotguaranteelateralcontinuity

overtwoorthreetypicaldimensions(threetimesthediameterof

theprintingtip).Discontinuityisthendrasticallyenhancedbythe

successivelayerscreatingconnectedporositiesalongthebuilding

direction(centralviewinFig.2).Theout-of-planeviewofthe

lay-ingdownshowsmorphologicalmodiﬁcationsexperiencedbythe

ﬁlament.Thechangeconcernsthecircularsectionwhichappears

aselliptical.Thesmallesttransversedimensioniscapturedinthe

buildingdirection,which meansthat theshape modiﬁcation is

drivenbythestretchingoftheﬁlamentcombinedtothe

gravita-tionalactionofthefollowinglayers.Theaverageratiobetweenthe

transversedimensionsoftheellipticalﬁlamentis326±17␮mfor

out-of-planeover586±80␮mforin-plane,whichiscloseto0.56.

Contiguousﬁlamentsformalsoaneck.Thelimitedextensionof

theneckisthesourceoftheporousmorphologyhighlightedinthe

sameﬁgure.Neckingrepresentstheconnectingpartbetween

ﬁla-ments.Theresultofthelackofcohesion,whichcanbeestimatedby

theextensionoftheneck,createstheroughnessdiscussedearlier.

Fig.3showsperspectiveviewsoftheporousnetworkinABS

blocksasfunctionofprintingorientation.Thelightgreylevel

rep-resentstheporosityarrangementintheprintedABSblock.3Dviews

areillustratedasfunctionoftheprintingangle(␪).Ontheleftside,

perspectiveviewsareorganisedtoillustratetheporosity

arrange-mentthroughtheverticaldirection(buildingdirection).Theimages

ontherightsidearetopviewsthatillustratethein-plane

arrange-mentoftheporosity network.Thisporousnetworkreﬂectsthe

quality of adhesionbetween contiguous ﬁlaments described in

Fig.2.

Indeed,theregulararrangementofporosityfollowsthepath

crossingofﬁlamentasfollows:+45◦/−45◦_,₊₇₅◦_/₋₁₅◦_,₊₉₀◦_/+0◦_,

Table1

PorositystatisticsfromanalysisofX-ray␮-tomographyofprintedABSsamplesas functionofprintingangle.

␪(◦) f (%) ıfx ıfy ıfz Mxfx Mxfy Mxfz 26(%) 6(%) 0 5.07 3.01 2.95 0.97 20.94 18.78 10.39 85.04 79.54 30 4.57 2.21 2.24 1.09 20.13 23.69 9.87 76.60 75.10 45 6.12 7.04 6.33 1.11 45.29 44.84 11.13 62.11 61.84 60 4.51 2.26 2.32 1.00 17.09 18.70 9.41 71.68 69.32 90 4.84 1.97 2.70 1.16 11.68 15.23 9.82 78.33 74.49

+15◦/−75◦_,_and_again₊₄₅◦_/₋₄₅◦ _for_␪₌₀◦_,₃₀◦_,₄₅◦_,₆₀◦ _and₉₀◦_,

respectively.Thechangeoforientationoftheporousnetwork coin-cideswiththeangleincrement.

Thealternationofthelayersfollowsalogicof45◦/−45◦_for_␪₌₀◦_.

Layersrotateby30◦ aboutthebuildingdirectionforeachangle increment.

Resolutioncoarseningeffectsonbothporecontentand connec-tivityareexploredinFig.4.

Porecontentisstableupagainstresolutionloweringdownto

acoarseningfactorof0.1.Thismeansthatscalingeachdimension

oftheoriginalimagetoitsonetenthdoesnotaffectthe

predic-tionofelasticityconstants.Theseareexclusivelydependentonthe

phasecontent.Poreconnectivityresitsresolutionloweringdown

toacoarseningfactorof0.4.Sinceallcomputationsofstructural

attributes areconducted at full resolution ( =1), connectivity

resultsarerepresentativeofthe3Dprintingeffect.

Theexaminationoftheporositylevelasfunctionofsample

ori-entationindicatesslightdifferences(standarddeviationof0.66%)

betweenstudiedconﬁgurations(Table1).

Thelargestporositylevelisobtainedfor3Dprinting

conﬁgura-tionswith␪=45◦.TheresultssummarisedinTable1demonstrate

thattheporositylevelisacceptable(<6.2%)forallsituations.

How-ever,thescatterinporositylevelsmeasuredinallspacedirections

(ıfx,ıfy,ıfz)indicatesa stronganisotropy(Table1).The largest

scatterinporosity levelisobserved inx-and y-directions.This

scatter represents, in the average or irrespective of the

orien-tation, 63%, 64% and 22% of the average porosity level in X-,

Y-andZ-directions,respectively.Thesmallﬂuctuationof

poros-ity measured in the building direction (22%) compared to the

remainingdirectionsis anevidenceofahigherhomogeneityin

(7)

conﬁgurationcorrespondsto␪=45◦,wheretheporosity

ﬂuctua-tionsinx-andy-directionsarethelargestones.

Fig.5depictstheaxialproﬁlesofporositycontentinmainspace

directionsasfunctionoforientationangle(␪).Theseproﬁlesdepict

howtheporousnetworkisarrangedinparticulardirection.These

Fig.3.3Dviewsshowingtheporousnetworkasfunctionofprintingangle␪. Poros-ityislabelledwithalightgreylevel.

Fig.4.Effectsofresolutioncoarseningonporeconnectivityandcontent.

Fig.5. Axialporositylevelsasfunctionofsampleorientationangle(␪)in(a)X-,(b) Y-and(c)Z-directions.

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Fig.6.ToolpathgenerationlogicillustratingtheclosecontourinXYplane(perponducilartothebuildingdirection)incomparisonwiththemicrostructuralrenderingatthe borderoftheprintedABS.

Fig.7.Relationshipbetweenporeconnectivityandporositycontent.

proﬁlesarethusinformativeofanyanisotropytakingplaceacross

thelayersofprintedABS.

Thisinformation isnotaccessiblethroughaveragequantities

depictedinTable1.Inaddition,axialproﬁlesallowtherankingof

suchanisotropybecauseofmarkeddifferencesbetweenprinting

anglesindifferentspacedirections.Fig.5ashowstheporosity

con-tentproﬁleinX-directionforallprintingangles.AtypicalU-form

illustratesthetypeofanisotropyexhibitedbytheaxialporosity

distribution(Fig.5a). Theaxialproﬁleofporosity contentin

Y-directionlookssimilarfromtheheterogeneityviewpoint(Fig.5b).

Bothproﬁlesrepresentinsomewaythein-planeporosity

arrange-ment,which is differentfromtheout-of-plane proﬁle(Fig. 5c).

Thedifferenceisrelatedtothefactthatporositycontentislarger

than3% atmost Zpositions (Fig.5c)while porosity contentin

anyin-planepositionalternates betweentheground valueand

largerlevels(Fig.5aandb).Despitethesedifferences,allproﬁles

presentlimitedporositylevelsatbothends,whicharefollowed

bylargepeaks.Thecorrespondingabscissapositionscorrespond

totheprintedpartskinorenvelope.Theabsenceofporosityat

theseparticularpositionsindicatesthepresenceofathin dense

bandsurroundingtheprintedfeature.Thegenesisofthisbandis

relatedtothelogicbehindthetoolpathgeneration(Fig.6).Indeed,

Fig.6designatesqualitativelythetypeofgeometricalanisotropy

associatedtotheporousnetwork.Withinthisband(markedwith

dashlinesinFig.6),noporosityisdetectedinatypicalthickness

varyingbetween360␮mand780␮m.Theclosecontourconfersto

theprintedstructuremechanicalstabilitytotheskinandensures

compactness.This comesat a costascan bededucedfromthe

microstructuralanalysis(Fig.6).Filamentpathmismatchcreates

alackofspaceﬁllingrepresentedbylimitedextensionofﬁlament

necking.Thus,largeporositiesfollowimmediatelythedense

con-tour,whose effectisreﬂectedbytheobservedporosity content

peaksinFig.5.These peaksvaryinintensitydependingonthe

printingangle␪.Theformedporosityundertheskinhasalarge

connectivityandatypicalformshowninFig.2(edgeporosity).

Theporositypeakisassociatedtothelayingdownmismatch

whentheprintingtipchangesrapidlythepathdirectiontowards

thenextpass.So,thelargestporositylevelsinaxialproﬁles

corre-spondtothealterationofmaterialdepositionattheboundaries.The

peakofporositycontentcanbeaslargeas45%(Fig.5aandb)asalso

showninTable1.InX-andY-directions,similarhighﬂuctuations

ofporosityproﬁlesareobserved(Fig.5aandb).Thelowest

ﬂuctua-tionsinporosityareobservedinthebuildingdirection(Fig.5c).

For allcases,axial ﬂuctuationsinporosity areassociatedtothe

defectsinducedbycrossedoralignedﬁlaments.Amongallstudied

conﬁgurations,␪=45◦achievesthehighestlevelsofporosity

ﬂuc-tuations.Indeed,thecorrespondingaxialproﬁleofporositycontent

inFig.5apresentspeaksofabout20%(ifexcludingthelargestpeaks

associatedtotheskin).Thelargestlevelsdonotexceed10%for

theremainingprintingangles. Asimilarcommentgoesalsofor

theotherin-planeaxialproﬁlesshowninFig.5b.Theout-of-plane

proﬁles(Fig.5c)stillshowthesamerankingbutthedifferenceis

secondarycomparedtothein-planeaxialproﬁles.Mostofthese

peaksarebelow8%for␪=45◦whereasthesearesmallerthan6%

fortheremainingprintingangles.

Thelargeﬂuctuations inporosityproﬁleobservedfor␪=45◦

contrast with the results of pore connectivity summarised in

Table1.Indeed,theformerorientationiscorrelatedtothe

low-estporeconnectivityamongallpossibleorientations.Thelargest

poreconnectivityisobtainedfortheangles0◦and90◦.Eq.(7)

sug-geststhatporeconnectivityresults(Table1)canbeduetoeither

achangeofthevolumeofthelargestpore,ortoadifferent

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Fig.8. Stresscomponent␴YYcontourplotsofatfullscale(␣=1.0)asfunctionofprintingangle␪.

edges.Ifporeconnectivityisonlydrivenbytheincreaseofporosity

content,alineardecreasingtrendshouldbeobtained.Theplotof

theporeconnectivityasfunctionofporositycontent(Fig.7)shows

thatthisisnottrueforalmostprintingangles.Thetrendismore

paraboliceveniffaceconnectivity(6)isused.Thistrendsuggests

thatporeconnectivityismorerelatedtothevolumevariationof

thelargestconnectedpore.

Theresultsoffaceconnectivity(6)showthatthisschemeis

responsibleforthelossofabout2.69%ofporeconnectivityasshown

inTable1.Thisresultindicatesthatthislossisminorandconﬁrms

thatmostoftheporositiesareconnectedthroughvoxelfaces.

Fig.8 illustrates thenodal solutions correspondingtostress

component␴YYrelatedtofullscale(␣=␤=1)loadedinthebuilding

direction.Thewaytheporousnetworkaffectsthestress

distribu-tionis,atthesametime,qualitativeandquantitativeinformation.

Thisinformationisretrievablethroughthemagnitudeand

distribu-tionofstressinthecontourplots(Figs.8and9).Ifthisinformation

isretrievedasfunctionofprintingangleandsamplingratio,the

effectofprocessinducedimperfectionsonelasticitybehaviourof

printedABSiscaptured.

Thestressﬁeldsrevealheterogeneousdistributionaffectedby

(10)

Fig.9.Effectofverticalsamplingonstresscomponentcontourplots(ontheright␴ZZforloadinginlateraldirection−Yand␣=0.7)fordifferentprintingangles␪.Onthe

leftstresscomponent␴XXatfullscale(␪=60◦,␣=1.0,loadinginbuildingdirection−Z)isalsoillustrated.

Table2

Statisticalanalysisofelasticityresponseof3DprintedABS.Min,AVE,STDareminimum,averageandstandarddeviationoperators.

␪(◦₎ _Lateral_{sampling—␤} _Vertical_{sampling—␣}

0 30 45 60 90 0 30 45 60 90 (EX) 0.97 0.94 0.96 0.96 0.96 0.99 0.99 0.99 0.99 0.99 (EY ) 0.96 0.94 0.96 0.96 0.97 0.99 0.99 0.99 0.99 0.99 (EZ) 0.98 0.97 0.97 0.98 0.99 0.99 0.99 0.99 0.99 0.99 ı (EX) 1.13 1.88 1.06 1.18 1.21 0.43 0.29 0.36 0.22 0.25 ı (EY ) 1.21 1.76 0.93 1.36 1.09 0.43 0.35 0.29 0.28 0.25 ı (EZ) 0.63 0.99 0.66 0.58 0.48 0.49 0.36 0.28 0.27 0.24

ω (EX,EY,EZ) 1.04 1.04 1.03 1.03 1.04 1.02 1.01 1.02 1.01 1.02

(EX,EY ) 0.13 0.38 0.23 0.50 0.27 0.05 0.23 0.10 0.36 0.09 (xy,yx) 0.13 0.38 0.20 0.50 0.27 0.03 0.24 0.10 0.41 0.09 (xz,yz) 0.04 0.14 0.04 0.16 0.02 0.00 0.03 0.04 0.02 0.02 (zx,zy) 0.12 0.35 0.21 0.54 0.27 0.03 0.24 0.16 0.48 0.09 ı(xy) 0.09 0.75 0.48 0.52 0.20 0.05 0.19 0.19 0.15 0.06 ı(zy) 0.51 0.76 0.41 0.63 0.40 0.21 0.29 0.21 0.24 0.18 ı(yx) 0.20 0.83 0.64 0.35 0.19 0.05 0.14 0.25 0.10 0.04 ı(zx) 0.43 0.88 0.55 0.48 0.52 0.20 0.17 0.29 0.18 0.20 ı(xz) 0.16 0.24 0.22 0.22 0.15 0.08 0.07 0.06 0.04 0.04 ı(yz) 0.12 0.27 0.25 0.20 0.14 0.09 0.04 0.04 0.05 0.05

revealeddistributionsshowalternationofcompressiveand ten-sionstresses(Figs.8and9).Whensubjectedtouniaxialloading,

compressivestressesdeveloparoundporeedgesalignedwiththe

loadingdirectionandtensilestresseselsewhere.Crackinitiation

islikelytooccurfromtheporositycontoursundertensionasa

resultoflocalisation.Sinceﬁniteelementcomputationisbasedon

meshingofX-raystacks,thestressdistributionhighlightsthusthe

signatureofporositymorphologyandconnectivity.

The alternation of compressive and tensile stresses differs

signiﬁcantlydependingontheprintingorientationbutmarked

dif-ferencesintermsofmagnitudearenotobserved.Stresslocalisation

isexpectedtoinducesigniﬁcantdamagepercolation.Thisis

evi-dencedbythealigneddomainsofisostressinparticulardirections.

Fig.9 showsthepredictedstressdistributionsfora constant

verticalsamplingalongthebuildingdirection(␣=0.7).

Ontherightside,stresscomponent␴ZZiscomparedfordifferent

printinganglesforthesameverticalsampling(␣=0.7).Alternation

ofcompressiveandtensionstressesareevidencedforallprinting

angles.Themagnitudesoftheminimumandmaximumstress

lev-elsareadaptedtoshowthespatialperiodicityoftheheterogeneous

stressﬁeld.Thestressheterogeneityismarkedbyaregular

alter-nationoflowandlargestresslevels,whichisacharacteristicof

theprintingprocess.Theselevelsfollowtheporousarrangement

sincetheporositycontoursareregionsoflargerstresslevelsand

stresslocalisation.Thisconﬁrmstheroleoflocalheterogeneities

thataffectthespatialdistributionofstressﬁeld.Periodicityofthe

stressﬁeldiscorrelatedtotheorientationoftheprintedblockand

variesdependingontheprintingangle.Theperiodicityofthestress

distributionisalsopreservedthroughalargerangeofvertical

sam-pling.OntherightsideinFig.9,stresscomponent␴XXissuedfora

loadinginZ-directionatthefullscale(␣=1)exhibitsimilar

charac-teristicswiththestressdistributionsontherightside(␪=30◦and

␪=60◦).Thehighestheterogeneityisthusobtainedequivalentlyby

loadingthesampleinXorYdirectionsandissuingthecomponent

␴ZZorbyloadingthesamestructureinZ-directionandissuingthe

components␴XXor␴YY.Allstressdistributionsconﬁrmalsothat

theaverageintensitydoesnotdiffertoomuchfromoneprinting

angletoanother.Thisisalsoexpectedfromtheanalysisofporosity

contentinTable1.

Fig.10comparesthepredictedtendenciesforYoung’s

modu-lusinallspacedirectionsasafunctionoforientationandsampling

foranincreasinglateral(␤)directions.Young’smodulitrendsare

scaledwithrespecttoYoung’s modulusof theas-receivedABS

material.Anoveralltrendshowingalternationoflowerandhigher

Young’smoduliishighlighted.Thisjaggedvariationofall

inves-tigatedYoung’smodulicomponentsistobecorrelatedwiththe

spatialperiodicityofthedefectsasattestedbytheporosity

pro-ﬁlesinFig.5.However,suchalternationappearstobeoflimited

magnitudeasattestedbythequantity (−)

(11)

Fig.10.Effectoflateralsamplingratio(␤)onYoung’smoduliforallprintingangles (␪).

wherethesubscriptsreferstoanysamplinginlateral(_␤)orvertical

(␣)directions.

SimilarexpressionsarederivedforEYandEZforbothlateral

andnormalsamplingratiosasfollows

(EY )=Min (EY_∀s) /Max (EY∀s) (15)

(EZ)=Min (EZ_∀s) /Max (EZ∀s) (16)

wheretheintensitiesof (EX), (EY ) and (EZ) areshown in

Table2.

InFig.10,thepredictedtendenciesshowqualitatively

similar-itiesbetweentendenciesinXandYdirections,whichmeansthat

reasonablytherelationship(EX≈EY )holdsforanyorientationand

samplingsituation.

Qualitativeanalysisoftheseresultsshowsatransverseisotropy

perceivable for all orientations more particularly for ␪=45◦

( (EX,EY ) inTable2).Indeed,Fig.10cshowsthatYoung’s

mod-uliEXandEYhave theclosesttrends.For theremainingcurves

(Fig.10aandb),thetendenciesexhibitedbyEZisdistinctforall

lateralsamplingratios.Thepredictedtransverseisotropyis

quan-titativelyconﬁrmedfromthesmallscatter(≤0.40%)betweenEX

andEYexpressedusingthequantity (EX,EY )

(EX,EY )=100×STD (EX_∀s,EY∀s) /AVE (EX∀s,EY∀s) (17)

Theextentofthetransverseisotropyisalsolimitedforallstudied

cases,whichisrevealedfromthequantity

ω (EX,EY,EZ)=AVE (EX_∀s,EY∀s) /EZ∀s (18)

Inthefullrangeofsampling,thevariationofallengineering

constantsincluding Young’s moduliis expressed usinganother

quantityıwhichwritesasfollows

ı()=100×STD(_∀s)/AVE(∀s)|=EX,EY ,EZ,

xy,zy,vyx,zx,xz,yz (19)

Thisquantityseemstobealsolimited(␦<2%)forall

compo-nentsEX,EYandEZirrespectiveoforientationandtypeofsampling

(Table2).

SimilarresponsesareshowninFig.11forPoisson’sratios(␯yx,

␯zx,␯xy,␯zy,␯xz,and␯yz)resultingfromthecombinationoflateral

samplingandorientation.

Theexaminationofalltrendsconﬁrmsminorjaggedvariations

ofPoisson’scoefﬁcientswithrespecttolateralsamplingratiolike

intheformercase(Fig.10).Similarlytotheformerexpression

relat-ingin-planeYoung’smodulicomponentsEXandEY,thepredicted

transverseisotropyisalsoquantiﬁedusingthequantities

(xy,yx)=100×STD(_xy∀s,yx∀s)/AVE(xy∀s,yx∀s) (20)

(xz,yz)=100×STD(_xz∀s,yz∀s)/AVE(xz∀s,yz∀s) (21)

And

(zx,zy)=100×STD(_zx∀s,zy∀s)/AVE(zx∀s,zy∀s) (22)

ThetrendsinFig.11showthatthefollowingrelationshipscan

bededuced

xy≈yx;xz≈yz;zx≈zy (23)

ThevalidityofallequalitiesinEq.(23)againstsample

orienta-tionisillustratedinTable2bytheanalysisofthequantities(xy,

yx),(xz,yz)and(zx,zy)forbothsamplingtypes.These

quan-titiesarebelow0.60%, conﬁrmingthetransverseisotropy inall

casesirrespectiveofsamplingratios(␣and␤).

IntensityofPoisson’scoefﬁcientsshowninFig.11areoflimited

variationasconﬁrmedbythequantitiesı(xy),ı(yx),ı(xz),ı(zx),

ı(yz)andı(zy).

5. Conclusions

X-raymicro-tomographyrevealsthat fuseddeposition

mod-ellingresultsinlargemodiﬁcationofABSﬁlamentgeometry.The

in-planelayingdownofthefusedmaterialisnotcontinuous.

Con-tiguousﬁlamentsexhibitevidentlackofcohesionrunningthrough

themillimetrescale.Thisisalimitingfactoragainstgeometry

accu-racy.Thecircularcross-sectionofABSﬁlamenttransformstoan

(12)

Fig.11.Effectoflateralsampling(␤)onPoisson’sratiosforallprintingangles(␪).

amountofporosityoflessthan6.2%isnotlimitingforthedesign

rather than poreconnectivity which is, inthe bestcase, above

62%.Thiscanbeaseriousissueforthemechanicalperformance

atrupturepoint.Therelativestabilityofallcomputedengineering

constantsagainstsamplingresultsfromthecombinationofsmall

porositycontentandregularityofitsspatialarrangement.Thisis

supportedbythesimilaritiesoftheheterogeneousstress

distri-butionsandlowscatterofengineeringconstants(lessthan1%for

bothYoung’smoduliandPoisson’sratios)predictedforlargerange

oflateralandverticalsamplings.

Theauthorsbelievethatthelargeconnectivityintheporous

networkand thelackof cohesionbetweenﬁlamentsin printed

materialsneedtoberelatedtostressand strainlocalisationfor

acknowledgetheInternationalCampusonSafetyand

Intermodal-ityinTransportation(CISIT),theNord-Pas-de-CalaisRegionandthe

EuropeanCommunity(FEDERfunds)forpartlyfundingtheX-ray

tomographyequipment.

References

Ahn,S.H.,Montero,M.,Odell,D.,Roundy,S.,Wright,P.K.,2002.Anisotropic materialpropertiesoffuseddepositionmodelingABS.RapidPrototyp.J.8, 248–257.

Ayadi,A.,Nouri,H.,Guessasma,S.,Roger,F.,2015.Anoriginalapproachtoassess elasticpropertiesofashortglassﬁbrereinforcedthermoplasticcombining X-raytomographyandﬁniteelementcomputation.Compos.Struct.125, 277–286.

Baker,D.R.,Mancini,L.,Polacci,M.,Higgins,M.D.,Gualda,G.A.R.,Hill,R.J.,Rivers, M.L.,2012.AnintroductiontotheapplicationofX-raymicrotomographytothe three-dimensionalstudyofigneousrocks.Lithos148,262–276.

Becker,R.,Grzesiak,A.,Henning,A.,2005.Rethinkassemblydesign.Assembly Autom.25,262–266.

Carneiro,O.S.,Silva,A.F.,Gomes,R.,2015.Fuseddepositionmodelingwith polypropylene.Mater.Des.83,768–776.

Chakraborty,D.,Reddy,B.A.,Choudhury,A.R.,2008.Extruderpathgenerationfor curvedlayerfuseddepositionmodeling.Comput.AidedDes.40,235–243.

Choi,J.W.,Medina,F.,Kim,C.,Espalin,D.,Rodriquez,D.,Stucker,B.,Wicker,R., 2011.Developmentofamobilefuseddepositionmodelingsystemwith enhancedmanufacturingﬂexibility.J.Mater.Process.Technol.211,424–432.

Galantucci,L.M.,Lavecchia,F.,Percoco,G.,2008.Studyofcompressionproperties oftopologicallyoptimizedFDMmadestructuredparts.CIRPAnn.Manuf. Technol.57,243–246.

Guessasma,S.,Babin,P.,DellaValle,G.,Dendievel,R.,2008.Relatingcellular structureofopensolidfoodfoamstotheirYoung’smodulus:ﬁniteelement calculation.Int.J.SolidsStruct.45,2881–2896.

Huang,S.H.,Liu,P.,Mokasdar,A.,Hou,L.,2013.Additivemanufacturingandits societalimpact:aliteraturereview.Int.J.Adv.Manuf.Technol.67,1191–1203.

Kietzmann,J.,Pitt,L.,Berthon,P.,2015.Disruptions,decisions,anddestinations: entertheageof3-Dprintingandadditivemanufacturing.BusHoriz.58, 209–215.

Lee,C.S.,Kim,S.G.,Kim,H.J.,Ahn,S.H.,2007.Measurementofanisotropic compressivestrengthofrapidprototypingparts.J.Mater.Process.Technol. 187,627–630.

Li,S.,Zhao,S.,Hou,W.,Teng,C.,Hao,Y.,Li,Y.,Yang,R.,Misra,R.D.K.,2016.

FunctionallygradedTi-6Al-4Vmesheswithhighstrengthandenergy absorption.Adv.Eng.Mater.18,34–38.

Maire,E.,Withers,P.J.,2014.QuantitativeX-raytomography.Int.Mater.Rev.59, 1–43.

Mamlouk,H.,Guessasma,S.,2013.Finiteelementsimulationofthecompression behaviourofairybreakfastcereals.InnovFoodSci.Emerg.19,190–203.

Mizutani,R.,Suzuki,Y.,2012.X-raymicrotomographyinbiology.Micron43, 104–115.

Mohamed,O.A.,Masood,S.H.,Bhowmik,J.L.,2015.Optimizationoffused depositionmodelingprocessparameters:areviewofcurrentresearchand futureprospects.Adv.Manuf.3,42–53.

Moreno-Atanasio,R.,Williams,R.A.,Jia,X.,2010.CombiningX-ray microtomographywithcomputersimulationforanalysisofgranularand porousmaterials.Particuology8,81–99.

Mostefai,N.,Hamzaoui,R.,Guessasma,S.,Aw,A.,Nouri,H.,2015.Microstructure andmechanicalperformanceofmodiﬁedhempﬁbreandshivmortars: discoveringtheoptimalformulation.Mater.Des.84,359–371.

NationalInstituteofHealth.NIH,MD,USA.http://imagej.nih.gov/ij/. Nune,K.C.,Misra,R.D.K.,Gaytan,S.M.,Murr,L.E.,2014.Biologicalresponseof

next-generationof3DTi-6Al-4Vbiomedicaldevicesusingadditive manufacturingofcellularandfunctionalmeshstructures.J.Biomater.Tissue Eng.4,755–771.

(13)

Nune,K.,Kumar,A.,Misra,R.,Li,S.,Hao,Y.,Yang,R.,2016a.Osteoblastfunctionsin functionallygradedTi-6Al-4Vmeshstructures.J.Biomater.Appl.30(8), 1182–1204.

Nune,K.C.,Kumar,A.,Murr,L.E.,Misra,R.D.K.,2016b.Interplaybetween self-assembledstructureofbonemorphogeneticprotein-2(BMP-2)and osteoblastfunctionsinthree-dimensionaltitaniumalloyscaffolds:stimulation ofosteogenicactivity.J.Biomed.Mater.Res.A104,517–532.

Pham,D.T.,Gault,R.S.,1998.Acomparisonofrapidprototypingtechnologies.Int.J. Mach.ToolManuf.38,1257–1287.

Shaffer,S.,Yang,K.J.,Vargas,J.,DiPrima,M.A.,Voit,W.,2014.Onreducing anisotropyin3Dprintedpolymersviaionizingradiation.Polymer55, 5969–5979.

Thrimurthulu,K.,Pandey,P.M.,Reddy,N.V.,2004.Optimumpartdeposition orientationinfuseddepositionmodeling.Int.J.Mach.ToolManuf.44,585–594.

Turner,B.N.,Strong,R.,Gold,S.A.,2014.Areviewofmeltextrusionadditive manufacturingprocesses:I.Processdesignandmodeling.RapidPrototyp.J.20, 192–204.

Yan,X.,Gu,P.,1996.Areviewofrapidprototypingtechnologiesandsystems. Comput.AidedDes.28,307–318.

Zhai,Y.W.,Lados,D.A.,Lagoy,J.L.,2014.AdditiveManufacturing:Making ImaginationtheMajorLimitation.JOM66,808–816.