126June, 2014Agric Eng Int: CIGR JournalOpen access at http://www.cigrjournal.orgVol. 16, No.2 Simulation of tensile tests of hemp fibre using discrete element method M. A. Sadek1, L. Guzman1, Y. Chen1*, C. Lagu2, H. Landry3 (1. Department of Biosystems Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6, Canada; 2. Faculty of Engineering, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada; 3. Prairie Agricultural Machinery Institute, Humboldt, Saskatchewan, S0K 2A0, Canada) Abstract: Tensile strength is an important property of hemp fibre, because it determines the mechanical strength of fibre-based productssuchasbiocomposites.Commercialdiscreteelementsoftware,ParticleFlowCodeinThreeDimensions(PFC3D), wasusedtodevelopanumericalmodelwhichsimulatestensiletestsofhempfibre.Themodelcanpredictthetensile properties(suchasstrengthandelongation)ofahempfibre.Inthemodel,avirtualhempfibrewasdefinedasastringof sphericalballs, heldtogetherbycylindricalbonds implementedinPFC3D.Tocalibrate themodel, tensiledatawascollected for both unretted and retted hemp fibres using a commercial Instron testing system.The average fibre diameter was 0.34 mm for the unretted fibre and 0.30 mm for the retted fibre.The average tensile strength measured was 358 MPa for the unretted fibreand343MPafortherettedfibre.Thecorrespondingaverageelongationsforthetwotypesoffibreswere0.88and 0.80mm,foranoriginalfibrelengthof25mm.Thebondmodulus,themostsensitivemicropropertyofthemodelwas calibrated.The calibrated value was 1.021010 Pa for unretted fibre and 1.051010 Pa for retted fibre.Using the calibrated bondmodulus,elongationsoffibreweresimulatedusingthemodel.Thesimulationresultsshowedthattheelongation increased linearly with the increasing fibre length; whereas the elongation was not affected by the fibre diameter. Keywords: hemp, fibre, PFC3D, tensile, strength, elongation, simulation Citation: Sadek M.A.,L.Guzman,Y.Chen,C.Lagu,H.Landry.2014.Simulationoftensile testsofhempfibre using discrete element method.Agric Eng Int: CIGR Journal, 16(2): 126135. 1Introduction Hempfibreisavaluablesourceformaking environmentallyfriendlyandbiodegradableproducts. Also,hempfibrehasveryhightensilestrengthranging between0.49to1GPa(WilliamsandWool,2000; MunderandFrll,2004;BeckermannandPickering, 2008).Asaresult,hempfibrehasbeenusedinmany applicationssuchastextileproductsandbiocomposites forautomobileindustries.Developmentofanyhemp fibreproductsrequirestheknowledgeofphysicaland mechanicalpropertiesofhempfibre.Hempfibreisthe Received date: 2013-02-21Accepted date: 2014-02-17 Correspondingauthor:YingChen,DepartmentofBiosystems Engineering,UniversityofManitoba,Winnipeg,ManitobaR3T 5V6,Canada.Email:ying_chen@umanitoba.ca.Tel.:1204 474 6292; fax: 1 204 474 7512. outerlayerofthehempstem,alsocalledbastfibre (Garcia et al., 1998; Mediavilla et al., 2001).Bast fibres consist of individual fibres which are bonded together by aninterface,whichcontainsmainlycellulose(67%), hemicelluloses (13%); and lignin (4%) (Bocsa and Karus, 1997; Keller et al., 2001).These groups of joined single fibresareknowncollectivelyasfibrebundles,andare responsibleformakingupthebarktissue.Thisstudy didnotdealwithsinglefibres,butwithfibrebundle (referred to as fibre hereafter for simplicity). Tensilestrengthisoneoftheimportantfibre propertiesbecauseofitsextensiveuseinevaluatingthe strengthoffibreproducts (Bledzki et al., 1996).Tensile strengthofhempfibremaybeaffectedbychemical treatment(BeckermannandPickering,2008)andretting ofthehemp(MunderandFrll,2004).Rettingisa biologicalprocessbywhichpectinandhemicellulosic June, 2014Simulation of tensile tests of hemp fibre using discrete element methodVol. 16, No.2127 compounds between the individual fibre cells are degraded. Although fibre properties have beenmeasured by several researchers(Rowelletal.,2000;Hobsonetal.,2001; MunderandFrll,2004),littleworkhasbeendoneto numerically simulate fibre tensile properties (Sadek et al., 2011). Thisstudyusedthediscreteelementmethod(DEM) tosimulatetensiletestsofhempfibretopredictthe tensilepropertiesof the fibre.The DEM is a numerical method tomodel amaterial as an assemblage ofdiscrete particles.The DEM was first introduced by Cundall and Strack(1979)foranalyzinggeologicalmaterials(rocks andsoils).Sincethen,theDEMhasbecomea promisingtooltosimulatemechanicalbehavioursof various other materials, including hemp fibre (Sadek et al., 2011).However,nosimulationshavebeencarriedout on tensile tests of hemp fibre using the DEM. Commonly used DEM software is Particle Flow Code inThreeDimensions(PFC3D)(ItascaConsultingGroup, Inc.,Minneapolis,MN).InPFC3D,thebasicparticles are spherical and they are referred to as balls.Materials tobesimulatedarerepresentedbyassembliesof individualballs.PFC3Dprovidesuserswithdifferent contactmodelsamongparticles,whichallowstomodel differentparticleinteractionbehaviours,forexample, free-flowing granular material, such as powder and grains (Djordjevic, 2003;Sakaguchietal.,2001),cohesiveand frictionalmaterials,suchassoilandmanure(Maketal., 2012;Landryetal.,2006),andsolidmaterials,suchas rock(PotyondyandCundall,2004;Pierce,2004). PFC3Disconsideredtobeoneoftheeffectivetoolsfor the simulation of hemp fibres. Regardlessofthetypeofmaterialtobesimulated,a set ofmicroproperties is required as inputparameters for anyDEMmodels.Micropropertiesdefineamodelat theparticlelevel,andtheysignificantlyaffectthemodel outputs.Most microproperties are not measurable at the currenttime,andtheyaredeterminedeitherusing analyticalassumptionsorinversecalibrationmethods. Inanalyticalassumptionmethods,micropropertiesare determinedusingexistingtheoryofthematerial.For example,YoungsmodulusandPoissonsratioofbulk material were used to determine particle normal and shear stiffness of the material (Cundall and Strack, 1982; Chang etal.,2003).Ininversecalibrationmethods, microparemetersaredeterminedbymatchingthe simulatedresultswithexperimentaldata.Forexample, directsheartestswereusedtocalibratemodel microproperties of a material through matching simulated friction angles with measured ones (Coetzee and Els, 2009; Sadeketal., 2011).Similarly Tanakaetal. (2000) and Asaf et al. (2007) used penetration test data for calibrating a soil model, and Vu-Quocetal.(2000) used drop weight test data for calibrating a model for soybean grains. Insummary,understandingthetensilepropertiesof hempfibreisimportanttoindustrieswhichusehemp fibrefortheirproducts.Todate,nodiscreteelement modelshavebeendevelopedforsimulationsofthefibre tensileproperties.Theobjectivesofthisstudywereto (1) measure tensile properties of hemp fibres, (2) develop adiscreteelementmodeltosimulatethetensiletestsof hempfibreusingPFC3D,and(3)calibratethemodel usingmeasurements,andsimulatethetensileproperties of hemp fibres of different diameters and lengths. 2Mesurements of fibre tensile properties 2.1Materials and methods 2.1.1Tensile testing system TheInstronelectromechanicaltestingsystem(3366, Instron Corporation, MA, USA) was used for fibre tensile tests.The testing system (Figure 1) consisted of a frame, a crosshead, two clamps, a load cell, a drive system, and a controller.The bottom clamp was stationary and affixed to the base of the frame, and the top clamp was connected tothecrossheadthroughtheloadcell(2kNcapacity). The test fibre sample was secured using the clamps.As thedrivesystemmovedthecrossheadup,itapplieda tensileloadonthesample.Thesystemwascontrolled viaInstronproprietarysoftware(Bluehill2)which alloweduserstosetthetestparametersandanalysethe data. 2.1.2Fibre sample preparation Hempfibresamplesusedfortensiletestswerefrom twotypesoffibre:unrettedandrettedhemps.The unrettedhempwas baled shortly after being swathed and therettedhempwaslefttoretinthefieldfor 128JuneAgric Eng Int: CIGR JournalOpen access at http://www.cigrjournal.orgVol. 16, No.2 approximatelysixweekspriortobeingbaled.Intotal 30rettedand30unrettedsampleswerepickedupfrom processedhemp(Figures2aand2b).Selectedfibres werecuttoalengthofapproximately45mm,andthey wereassignedanidentificationnumberfrom1to30 (Figure2c)forthepurposeofrandomizingthetests. Thehumidityoftheenvironmentwherethe measurementsaretakenhasasignificanteffectonthe strengthandstrainoftextilematerials(Saville,1999). Therefore,beforetensiletests,allfibresampleswere exposed to a relativehumidityof 65% and a temperature of21C(CGSB,2001)inanenvironmentalchamberfor three days. Figure 1The Instron testing system and its components a. Processed unretted hempb. Processed retted hemp c. Hemp fibre samples prepared for the tensile tests Figure 2Hemp materials 2.1.3Tensile tests Priortothetest,eachfibresamplewasattachedtoa thincardboardframe(Figure3a)toavoidslippagefrom theclampsofthetestingsystemduringpulling. Sampleswerestraightenedwithoutpullingtoohardand weresecuredinsidethecardboardwindowusing polyepoxide(Epoxy)glue.Thewindowgavean effective testing fibre length of 25 mm.To start testing, thecardboardframewasfittedintothegrips.Thenthe sidesofthecardboardframewerecutsothatonlythe fibrewaspulledduringthetest.Theclampswere attachedattheinneredgeofthecardboard,thusthe gluedfibredidnotcontributetothemeasuringoffibre properties.Tensionwasappliedtothefibrebymoving thecrossheadupat2mm/minandcontinueduntilthe sample broke as shown in Figure 3b. a. A fibre sample on a cardboard frame before test b. A broken fibre sample after test Figure 3Tensile testing samples 2.1.4Measurements The unit of fibre fineness is expressed as tex which is equaltoamassof1gramperkilometreoffibrelength (Kymlnen,2004).Themassofthefibreswas measuredusingahigh-precisionanalyticalscale (SymmetryPA220,QC,Canada),andthelengthwas measuredusingaruler.Themassandthelengthwere usedtodeterminethefineness.Then,fibrediameter wasestimatedusingthefollowingequation,assuming that fibre had a circular cross-section (Munder andFrll, 2004) and a uniform section along the length. 4 fd (1) where, d = fibre diameter, m; f = fibre fineness, tex; = fibre particle density, kg/m3. June, 2014Simulation of tensile tests of hemp fibre using discrete element methodVol. 16, No.2129 Particledensityofhempfibrewastakenas 1,480 kg/m3.This density value was reported by Lilholt and Lawther (2000). TheBluehill2softwareoftheInstrontestingsystem recordedtheload-extensioncurveduringatest.The sensitivityofthesoftwarewasadjustedtodeterminethe maximumloadat10%afterdropinmaximumforce. Consequently, the software detected the maximum load at thefibrefailure.Severalparameterswerederivedto characterizethefibrepropertieswiththerecorded load-extensioncurve.Thefibrestrengthwasdescribed instressformat.Themaximumstresswastheratioof maximumtensileforceandthecross-sectionarea.The specific stress was the ratio of maximum tensile force and thefinenessofthefibre(Khanetal.,2011).This parameterprovidesthemeansofcomparingindividual fibresinequivalenttermsandmethodology.The maximumstrainwastherelativechangeinlengthofthe sampleatthemaximumtensileforce,recordedbythe Bluehill2software.Theelongationatthefibrefailure was determined from the maximum strain, given the initial fibre length of 25 mm.The software used a least square fitalgorithmtodeterminethemodulusofelasticityfrom the load-extension curve.The criteria formeasuring the modulusofelasticitywasimplementedbyanalgorithm builtwithintheBluehill2software.Themodulusof elasticity in this study was expressed in the same units as the specific stress.To determine the work of rupture, the Bluehill2softwaremeasuredtheamountofenergy requiredtoreachtheyieldpoint;thisenergywas calculatedbydeterminationoftheareaunderthe load-extensioncurvebeforetheyieldpoint.Theyield pointisthepointwheretheslopeoftheload-extension curve is zero. 2.2Data processing Outof30fibresamplestested,thedataconsidered valid included 21 samples for the unretted fibres and nine samplesonlyfortherettedsamples.In instances where thegluewasnotabletomaintainthesampleattachedto thecardboardframe,thedatawerediscarded.Itis importanttonotethatthemainobjectiveofthetensile testsinthisstudywastosupportmodeldevelopment. Therefore, in spite of the limited number of fibre samples, thedatawasdeemedsufficientforthepurposeofmodel calibration.Studentst-testswereusedtoexamine differencesinthosemeasuredvariablesbetweenthe retted and unretted fibres at the probability of 0.05. 2.3Results and discussion 2.3.1Load-extension curve Load-extension(elongation)curvesfromthetensile tests could be classified into three typesof curves.One type showed the brittle behaviour of hemp fibre.As the fibre was extended, the load increased in a linear fashion; at a certainpointofextension, the load reached itspeak, and the fibre sample suddenly broke and the load dropped tozero(Figure4a).Fortheparticularfibreshownin Figure4a,thetensilestrengthandtheelongationofthe fibrewere30Nand0.65mm,respectively.Another type of curve also showed the brittle behaviour; however, theincreasingloadportionofthecurvewasnotlinear, but polynomial (Figure 4b).The third type of curve had thesimilarincreasingportion(ineitherlinearor polynomial fashion), but a gradual failure pattern (Figure 4c).In the last case, the fibre must be split into multiple thinnerfibreswhichbrokeatdifferenttimesduring testing, and the incompletely broken fibre could still carry some load until being completely broken. Fortheunrettedfibres,themajority(approximately 80%)ofthesamplesbehavedlikeeitherFigure4aor Figure4b,andtheother20%behavedmorelikeFigure 4c.Fortherettedfibres,approximately50% experiencedaformofbehaviourlikeFigure4a,andthe other 50% behaved like Figure 4c.One can say that the unrettedfibresweremorebrittlethantherettedfibres. However,thiswillneedtobeverifiedfurtherwitha larger number of samples. 2.3.2Fibre properties The results of statistical analysis showed that none of themeasuredvariablesweresignificantlydifferent between the retted and unretted fibres at the probability of 0.05.This was due to the highly variable nature of fibre properties, as indicated by the high standard deviations of the measurements shown in Table 1.However, the data showedsomeimportanttrendsintheeffectsofretting conditions on fibre properties. 130JuneAgric Eng Int: CIGR JournalOpen access at http://www.cigrjournal.orgVol. 16, No.2 a b c Figure 4Typical results of load-extension curves from the tensile tests: (a) linear curve and sudden failure, (b) polynomial curve and sudden failure, (c) gradual failure; the triangle sign on the figure stands for the point where the maximum load and strain were taken Table 1Summary of measured properties of the unretted and retted fibres Unretted fibreRetted fibre Property MeanSD[1] MeanSD[1] Fineness, tex13959.610739.0 Diameter, mm0.340.0710.300.057 Maximum load, N31.615.624.515.9 Maximum stress, MPa358173343157 Specific stress, cN/tex 24.211.723.210.6 Maximum strain, %3.551.783.202.34 Elongation, mm0.880.440.800.58 Work of rupture, mJ17.114.412.914.6 Modulus, cN/tex 11366511397603 Note: [1]SD is standard deviation. Therettedfibrehadapproximately23%lower finenessand35%lowerstandarddeviationthanthe unrettedfibre(Table1).Thisindicatedthatretting hempcouldimprovethefinenessandtheuniformityof fineness.Accordingly,thediametersoftherettedfibre weresmallerandlessvariablethanthoseoftheunretted fibre.On an average, the retted fibre carried 22% lower loads than the unretted fibre, the corresponding maximum loadswere24.5and31.6Nrespectively.Althoughthe retted fibre had smaller diameter and lower fineness, only 4%lowermaximumstressand8%lowerspecificstress wereobservedfortherettedfibre.Similarspecific stresseswerereportedbyKhanetal.(2011)forunretted fibres.MunderandFrll(2004)foundthatthe maximumtensilestressesofhempfibrevariedfrom0.5 to0.9GPa,whichwereslightlyhigherthanthose observedinthisstudy.Higherspecificstresseswere alsoreportedbyHobsonetal.(2001)forrettedand unretted hemp fibre. The maximum strain and elongation of the retted fibre werealsoslightlylower,whencomparedtothoseofthe unrettedfibre.Asaresultoftheirlowerloadsand strains,therettedfibrehadlowerworkofruptureand highermodulus.Sankari(2000)studiedtheproperties of 14 varieties of hemp fibres and reported higher specific stressesrangingfrom41to74cN/tex,butthereported maximumstrains(3.3%to5.0%)weresimilartothis study. 3Simulations of fibre tensile properties 3.1Model development 3.1.1Construction of virtual fibre Forsimulationsoftensiletests,avirtualfibrewas constructedwithasetofPFC3Dbasicparticles(balls). InPFC3D,particlescanbeconnectedtogetherinto clusters or clumps.Cluster is a group of balls which are connected by bonds, and they are breakable with external forces.Clumps are also groupof balls, but they are not breakableunderexternalforces.Therefore,clumpsdo notreflectmodelledfibrematerials.Inthisstudy,a virtualfibrewasrepresentedbyaclusterofballswhich were arranged like a string (Figure 5a).All the balls had thesamediameter.Theballdiameterandnumberof ballscanbevariedtomatchthediameterandlengthof thefibretobesimulated.Thenumberofballsrequired forafibrewithagivenlengthandagivendiameteris calculated by the following equation: June, 2014Simulation of tensile tests of hemp fibre using discrete element methodVol. 16, No.2131 1lnD (2) where,n=numberofballsinthevirtualfibre;D= diameterof balls, equal tothediameteroffibre,mm; l = length of virtual fibre, mm. a b Figure 5Virtual fibres: (a) dimensions of a virtual fibre, l is fibre length, and D is fibre diameter; (b) examples of PFC3D virtual fibres The next step was to define the contact between balls inthevirtualfibre,sothatthevirtualfibrecould withstandtensileloadlikearealfibre.ThePFC3D parallel bond models (PBM) are suitable for this purpose, becausethebondatthecontactbetweenballsprovides certaininter-particletensilecapacity.Examplesof virtualfibreswiththePBMareshowninFigure5b. Bond acts over a circular cross section at the contact point oftwoballs,andtheradiusofthecylindricalbondis equaltotheradiusoftheball.Thecylindricalbond withstandstensileload,andthebondbreaksifthe maximumexternalloadexceedstheprescribedstrength of the bond (Potyondy and Cundall, 2004).Breaking of anybondsinavirtualfibremeansthefailureofthe virtualfibre.Therefore,thestrengthofthevirtualfibre is determined by the properties of the bond to be specified by users. 3.1.2Microproperties of virtual fibre When using the PFC3D PBM, material to be modelled isdefinedbythreeballmicroproperties:normalstiffness (kn),shearstiffness(ks),andfrictioncoefficient(),and fivebondmicroproperties:theradiusofthecylindrical bond (R), normal and shear stiffness (nk and sk ), normal andshearstrength(candc).Inthecaseofafibre subjectedtoatensileload,thebondmicropropertiesare morerelevantthantheballmicropropertiesastheballs are connected with bonds only, and there is no interaction among the balls under tensions.Thevalue of R was set tobeequaltotheballradius,asillustratedinFigure5b. Toreducethenumberofbondmicropropertiestobe calibrated, c was set to be equal to c, and nk was set to be equal to sk .The same assumptions have been made in the literature formodellingothermaterials (Asaf et al., 2007;McDowellandHarireche,2002).Ontheother hand,cand sk arenotcriticalinthisparticularcase havingtensileloadonly.Thestiffnessoftheisotropic linear elastic material is related to the modulus and varies with the particle size.Then, the stiffness was calculated fromtherelationshipbetweenelasticmodulusand particle size given below (Itasca, 2008). 4n ck RE (3a) nc EkL (3b) where,kn=ballstiffness,N/m;R=ballradius,m;Ec= ball elastic modulus, Pa; nk = bond stiffness, Pa/m; cE = bond elastic modulus, Pa; L = centre to centre distance of two balls in contact, m. Inthisstudy,thepreviouslycalibratedball microproperties(KN=5104N/m,kn/ks =1,=1.0)by Sadeketal.(2011)wereused.Astheelasticityisthe intrinsic property of the material, it is more appropriate to usethemodulusinsteadofthestiffness.Theball normalstiffnessvaluefromSadeketal.(2011)was obtainedforauniformparticlesizeof2mm.This stiffnesswasconvertedtoelasticmodulus:Ec= 1.25107PaaccordingtoEquation(3a).Thus,onlyc and cE were unknown and were to be calibrated. 3.1.3Virtual tensile test Avirtualfibrewiththedesireddiameterandlength wasfirstconstructedusingballsandbondsasdescribed above.Thecentreofthefirstballofthevirtualfibre wassetastheoriginofthecoordinatesystemandthe x-axiswasalongthecentrelineofthevirtualfibre (Figure6).Tosimulateatensiletest,theballatthe originwasfixedbyapplyingazerovelocityboundary condition.Allotherballsinthevirtualfibrearefreeto 132JuneAgric Eng Int: CIGR JournalOpen access at http://www.cigrjournal.orgVol. 16, No.2 move.A tensile load along the x-axis was applied at the freeendofthevirtualfibrebypullingthelastballata constantvelocity.Thismodelsimulatesthelaboratory testsconductedwiththeInstrontestingsystem,andit allowsalteringmagnitudesoffibrediameter,length, pullingvelocity,andmicropropertiesoftheballand bond. Figure 6A virtual fibre subjected to a pulling action at a constant velocity During thevirtual testing, thevelocity of the last ball willcauseincreaseinthetensilestresswithinthevirtual fibre,morespecificallywithinthecylindricalbonds. Thevirtualfibrewillfailifthemaximumtensilestress exceedsthetensilestrengthofthebond.Thisconcept hasbeenverifiedinPFC3Dusinganexampleofa cantilever beam subjected to a tensile load (Itasca, 2008). Giventhesefacts,thebondstrength,c,wasenvisioned tobeequivalenttothemaximumstressmeasuredinthe tensiletests,whilethebondmodulus, cE ,wasbeing calibrated,asdescribedinthemodelcalibrationsection below. 3.2Simulation results 3.2.1Model behaviour Beforecalibrations,thebehaviourofthemodelwas observedwithassumedbondparameters.Whena tensile load is applied to a virtual fibre, i.e. when the ball atthefreeendofthefibreisbeingpulledataconstant velocity,thevirtualfibreisextended.Asthevirtual fibre continues to bepulled, the stress of the virtual fibre is increasing in a linear fashion and fails suddenly.The extensionofthevirtualfibreisconsideredasthe displacementofthelastballalongthex-axisdirection. Thisdisplacementandthestressofvirtualfibrewere monitoredandplottedinFigure7.Althoughnotall load-extensioncurvesfromthevirtualtestswerelike thosefromthelaboratorytestsshowninFigure4,the generalbehaviouroftheloadincreasingwithextension andthesuddenfailurepatternweresimilarbetweenthe virtualandlaboratorytests.Thevirtualfibreis consideredtobebrokenwhenthedetachmentbetween balls within the virtual fibre occurs. Note: X-Axis is fibre extension, m and Y-Axis is maximum stress, Pa. Figure 7A typical load-extension curve from a virtual tensile test 3.2.2Model calibration Themodelinputparametersfortherettedand unrettedfibres are listed in Table 2, and the valueof cEwasassumed.Inrunningthemodelforcalibrationsof cE ,comparisonsinstressweremadebetweensimulated andmeasuredfibrestressesateverycomputingcycle. When the stress of the virtual fibre reaches the maximum stressmeasured,theextensionofthevirtualfibrewas recordedastheelongationofthevirtualfibre,andthe simulationwasended.Thesimulatedelongationwas recorded for each of the assumed cE values.To assess whichassumedvalueof cE resultedintheelongation whichbestmatchedthemeasuredelongation,relative errorsbetweensimulationsandmeasurementswere calculated using the following equation: Table 2Model input parameters for simulations Model parametersUnrettedRettedSource Length of the fibre, mm2525 Same as the fibre samples tested Diameter of the fibre, mm0.340.30 Average of all the fibre samples Number of balls in the fibre7484 Determined using Equation (2) Ball elasticity modulus, Pa1.251071.25107Sadek et al. (2011) Ball friction1.01.0Sadek et al. (2011) Bond normal and shear strength, Pa 3.581083.43108Average maximum stress measured Diameter of the cylindrical bond, mm 0.340.30 Equal to the fibre diameter June, 2014Simulation of tensile tests of hemp fibre using discrete element methodVol. 16, No.2133 100m sme eREe (4) where, RE = relative error, %; em = elongation measured, mm; es = elongation simulated, mm. Some of the simulation results are listed in Table 3 to demonstratehowthecalibrated cE wasselected.As can be seen, fibre elongations were extremely sensitive to cE ,andincreasing cE resultedinincreasingofthe elongationforboththefibres.Amongtheassumed valuesof cE ,thethebestmatchtothemeasured elongationwas1.021010Paforunrettedhempand 1.051010Paforrettedfibres.Thecorresponding relative errors were 1.14% and 1.25%.Either increasing or decreasing cE value resulted in a greater relative error. Table 3Summary of calibration results using the data from the unretted and retted fibres UnrettedRetted Bond modulus, cE /PaMeasured elongation /mm Simulated elongation /mm Relative error /% Measured elongation /mm Simulated elongation /mm Relative error /% 9.01090.880.9811.360.800.9518.75 9.51090.880.935.680.800.8911.25 1.0210100.880.871.140.800.845 1.0510100.880.853.410.800.811.25 1.1010100.880.817.950.800.773.75 3.2.3Effectsoffibrelengthanddiameteronfibre elongation Themodelcanbeusedtopredictelongationsfor fibreswithanylengthsanddiameters.Here,virtual tensiletestswereperformedwiththecalibratedbond modulus.Theothermodelparameterswerethosefor the unretted hemp listed in Table 2.The testing velocity was2mm/min,thesameasthetensiletests.To examineeffectsoffibrelengthonelongation,thevirtual tensiletestswereperformedforfivedifferentfibre lengths:20,25,30,35,and40mmwithaconstantfibre diameterof0.30mm.Similarly,virtualtestswere performedforfivedifferentdiameters:0.20,0.25,0.30, 0.35, and 0.40 mm with a constant fibre length of 30 mm to examine effectsof fibrediameter on elongation.The simulationresultsshowthatelongationisincreased linearly(R2=0.99)withtheincreaseoffibrelength (Figure8a).Thesimulatedelongationsrangedfrom 0.69to1.39mmwhenfibrelengthvariesfrom20to 40mm.Whentheseelongationsweretranslatedto strains,theaveragestrainwas3.48%withaverysmall standarddeviation:0.02,demonstratingtheconsistency of thevirtual testsover the studied range offibre length. This result supports the hooks law where the strain rate is constantforamaximumelasticstrengthofmaterial. Simulationresultsalsoshowedthattheelongation remainsfairlyconstantforalldiameters(Figure8b). Thisimpliesthatthesimulatedfibrebehavedas anisotropic linear elastic material independent of the fibre diameter.Insummary,theresultsrevealthatthe calibrated model is reliable for simulating tensile strength of fibre with variable lengths and diameters. a. Effect of fibre length b. Effect of fibre diameter Figure 8Simulated elongations for unretted fibre Intheliterature,testedfibresusedbydifferent researchersweredifferentinlengthanddiameter.As 134JuneAgric Eng Int: CIGR JournalOpen access at http://www.cigrjournal.orgVol. 16, No.2 theelongationoffibrevarieswiththefibrelength,the simulatedstrainwascomparedwiththeliteraturedata. The simulated strain (3.48%) was higher than the average strain for hemp fibre (1.6%) reported by Khan et al. (2011) andthat(3.0%)byDuvaletal.(2011).However,the simulatedstrainwaswithintherange(1.3%-5.0%) observed by Munder and Frll (2004) and Sankari (2000). 4Conclusions Hempfibrescanbesimulatedwiththenumerical modeldevelopedusingPFC3D,commercialdiscrete elementsoftware.Avirtualfibre,formedusing sphericalparticlesconnectedwithbondsimplementedin the PFC3D parallel bond model, reflects tensile behaviours of a real fibre.Specifying a given velocity to one end of thevirtualfibrerepresentstensileloadadequately,while theotherendofthevirtualfibreisaffixed.Amongthe severalmicropropertiesforparticlesandbondsofa virtualfibre,thebondmicropropertiesinthenormal directionaremorecriticalastheydeterminethetensile strengthofthevirtualfibre.Thecalibratedbond modulususingthelaboratorytensiletestdatawas 1.021010Paforunrettedfibreand1.051010Pafor rettedfibre.Thesimulatedresultshowedthatundera tensileload,elongationofafibreincreaseslinearlywith theincreaseofthefibrelength,whiletheelongation remainsnearlyconstantfordifferentfibrediameters. 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