XVII th World Congress of the International Commission of Agricultural and Biosystems Engineering (CIGR)

Transcription

1 XVII th World Congress of the Internatonal Commsson of Agrcultural and Bosystems Engneerng (CIGR) Hosted by the Canadan Socety for Boengneerng (CSBE/SCGAB) Québec Cty, Canada June 13-17, 2010 SIMULATION OF HEMP FIBRE BUNDLE AND CORES USING DISCRETE ELEMENT METHOD M. AL-AMIN SADEK 1, Y. CHEN 1*, C. LAGUË 2, H. LANDRY 3, Q. PENG 4, W. ZHONG 5 1 Department of Bosystems Engneerng, Unversty of Mantoba, Wnnpeg, Mantoba R3T 5V6, Canada; emal of correspondng author: yng_chen@umantoba.ca 2 Faculty of Engneerng, Unversty of Ottawa, Ottawa, Ontaro, K1N 6N5, Canada 3 Prare Agrcultural Machnery Insttute, Humboldt, Saskatchewan, S0K 2A0, Canada 4 Department of Mechancal and Manufacturng Engneerng, Unversty of Mantoba, Wnnpeg, Mantoba, R3T 5V6, Canada 5 Department of Textle Scences, Unversty of Mantoba, Wnnpeg, Mantoba, R3T 2N2, Canada CSBE Presented at Secton III: Equpment Engneerng for Plant Producton Conference ABSTRACT Demands for hgh-grade hemp fbre are ncreasng for varous ndustral applcatons. To obtan hgh-grade fbre, t s mportant to understand the mechancal behavour of hemp fbre and core. Modellng usng dscrete element method s a promsng approach to smulate mechancal behavour of any materals, ncludng hemp fbre and core. In ths study, a commercal dscrete element software, Partcle Flow Code Three Dmenson (PFC 3D ) was used to smulate hemp fbre and core. Because the basc PFC 3D partcles, named balls, are sphercal. Indvdual vrtual hemp fbres were defned as strngs of balls held together by PFC 3D parallel bonds. The results showed that the resultng vrtual fbre was flexble and could be bended and broken by forces, whch approprately reflect the characterstcs of hemp fbre. Usng the clump logc of PFC 3D, the vrtual hemp core was defned as a rgd and unbreakable body, whch reflect the characterstcs of the core. The vrtual fbre and core were defned wth several mcropropertes, some of whch were prevously calbrated. The fve PFC 3D bond propertes ncludng normal and shear stffness, pb_kn and pb_ks; normal and shear strength, σ c and τ c and bond dsk radus, R of the vrtual fbre were calbrated n ths study. The calbraton started wth developng a PFC 3D model to smulate fbre tensle test. The mcropropertes of vrtual fbre and core were calbrated through runnng the PFC 3D model. The smulatons were compared wth lterature data from fbre tensle tests. The results showed that normal and shear strength of the bond could be consdered equal to the external stress appled on the fbre due to axal load durng tensle test. Shear stffness value could be assumed low to make the fbre flexble. The normal stffness of the bond was determned to be 9e20 N/m by tral and error method. Keywords: hemp fbre and core, dscrete element method, parallel bond, mcropropertes, tensle strength INTRODUCTION The stem of hemp (Cannabs satva) plant conssts of fbre and core. Fbre (Fgure 1a), also called bast fbre, s the surroundng outer layer of bark of the CIGR XVII th World Congress Québec Cty, Canada June 13-17,

2 stems and core (Fgure 1b), also called hurd, s the nner layer wth hollow pth (Garca et al., 1998; Medavlla et al., 2001). The core s responsble for provdng stffness to the hemp stem whle the fbre provdes tensle and flexural strength. Hemp fbre s extracted from hemp plants through decortcaton. Decortcaton s a mechancal process that separates fbre and core. Fbre bundles are the man product of decrotcaton and cores are the by-product. (a) (b) Fgure 1. Hemp materal; (a) sngle fbre bundle, (b) cores. Hemp fbre consttutes a valuable source for the manufacturng of envronmentally frendly and renewable products. Hemp fbre has been used for textle for a long tme. Lately hemp fbres have been used for bo-compostes for automoble and many other ndustral applcatons. Cores have also many uses, such as for anmal beddng and constructon materals. The qualty of these materals hghly depends on the physcal and mechancal propertes of the hemp fbre or core. Thus, studyng propertes of hemp fbre and cores s very mportant for the qualty of these products. Exstng data showed that hemp fbre bundle has a very hgh strength. Its hgh value of Young s modulus wth a hgh aspect rato (length/wdth) gves an ndcaton of ts hgh strength (Rowell et al., 2000). The tensle strength of hemp fbre bundle s as good as that of hgh-tensle steel (Munder and Fürll, 2004). Hgher tensle strength was also reported by Wllams and Wool (2000), Munder and Fürll (2004), Beckermann and Pckerng (2008). Lmted data could be found n the lterature for core propertes. To the knowledge of the authors, no research work has been done on the modelng of both fbre and core. Ths study used an nnovatve numercal modelng approach, the dscrete element method (DEM), to smulate the propertes of fbre bundle and core. DEM s a numercal approach to model a materal usng dscrete assemblages of partcles. DEM was frst ntroduced by Cundall and Strack (1979) for analyzng geologcal materals (rocks and sols). More recently, DEM has been appled to many other materals and t has become a promsng tool to smulate the bulk behavour varous materals through ther consttuent of ndvdual partcles. A wdely used commercal DEM software s Partcle Flow Code Three Dmenson (PFC 3D ) developed by Itasca Consultng Group, Inc., Mnneapols, MN (Itasca, 2008). In PFC 3D, materals to be smulated are represented by assembles of ndvdual partcles, or balls. The surroundng envronments n whch the materals are placed, such as CIGR XVII th World Congress Québec Cty, Canada June 13-17,

3 boundares and machne surfaces, s smulated by walls. The basc partcles n PFC 3D are sphercal (.e. balls). The recent verson of PFC 3D can be used to model materal partcles wth any arbtrary shape by attachng a group of sphercal partcles together. The group of sphercal partcles can be defned ether as an autonomous object or a brttle sold. PFC 3D has been used n smulatng not only free-flowng granular materals, such as grans (Lu et al., 1997 and Sakaguch et al., 2001), but also cohesve materals, such as sol (van der Lnde, 2007) and manure (Landry et al., 2006), and sold materals, such as rock (Potyondy and Cundall, 2004 and Perce, 2004). In a hemp decortcaton process, hemp plant stems are subjected to external forces, whch separate fbre and core. Then the decortcated materal goes through a cleanng process n whch core materals wll be further removed to obtan clean fbre. All these processes encounter flows of fbre buddle and cores around wthn the decortcator. Thus, PFC 3D has hgh potental to be used as a tool to smulate hemp fbres and cores. PFC 3D provdes users wth dfferent contact models among partcles and a correspondng set of mcroscopc parameters of partcles at the contact between partcles. Regardless of type of materal to be smulated, the bottom lne s to select the approprate PFC 3D contact model and mcroscopc parameters at the partcle level, whch best descrbes the macro behavour at the materal level. In summary, understandng the propertes of hemp fbre and core s mportant to ndustres that use hemp fbre and core. It wll also lead to mprovement on the desgn of hemp processng and other handlng machnes, due to the fact that t wll be possble to desgn these machnes accordng to the materal to be handled. No DEM models have been prevously developed for hemp fbre and core. The purpose of ths study was to use PFC 3D to smulate fbre bundle and core. The specfc objectves were a) to examne how hemp fbre bundle and core could be defned wth PFC 3D partcles; b) to develop a PFC 3D model to smulate the tensle test of fbre; c) to calbrate the mcropropertes of hemp fbre bundle wth exstng data from tensle tests. METHODOLOGY Vrtual fbre bundle and core PFC 3D contact model To construct vrtual fbre bundle and core wth PFC 3D partcles (balls), one needs to determne what knd of nteractons should occur between balls. PFC 3D provdes three dfferent models: stffness model, slp model and contact model. In the stffness model, there are no bonds between ndvdual balls and the contact force and deflecton between balls are governed by the stffness of the balls. The slp model s smlar to stffness model, but t takes nto account frcton among balls. The stffness and slp models are more sutable for smulatons of free flow granular materals. Whereas the contact model allows users to add bonds between balls to connect them together. Ths model s more sutable for the smulaton of cohesve materals. Wthn the contact model, PFC 3D allows for two dfferent bondng among balls: contact bond and parallel bond. Both bonds are envsoned as a knd of glue jonng the balls. The glue of the contact bond acts only at the contact pont, whle the glue of the parallel-bond acts over a CIGR XVII th World Congress Québec Cty, Canada June 13-17,

4 crcular cross-secton (dsk) lyng on the contact plane between the balls. The contact bond can transmt only forces, whle the parallel bond can transmt both forces and moments. Defnton of vrtual core Vrtual core was created usng the clump logc of PFC 3D. A clump conssts of a set of balls beng rgdly bonded together to behave as a rgd body. PFC 3D slp model was used for the contact between balls to smulate the frctonal nature of hemp core. Balls wthn a PFC 3D clump may overlap to any extent. A clump wll not break apart, regardless of the force actng on t. Ths means that the vrtual core s rgd and unbreakable. Dfferent shapes of core were constructed wth dfferent arrangement of balls. Fgure 2(a, b) shows two dfferent shapes of core, rectangular and semcrcular. Any other arbtrary shapes can be constructed by changng ball arrangement usng the PFC 3D clump logc. The wall thckness of core (unbroken hemp stem has a cylndrcal and hollow core) vared from 3 to 9 mm (Khan et al., 2009), whch s a small dmenson. Thus, core was defned to have one layer of balls n the drecton of wall thckness, regardless of the shape and the other dmensons of core. Thus, the dameter of the balls was set to be equal to the wall thckness. The number of partcles requred for a core clump depends on the wdth and length of the core as follows: where n c = (2b/D c 1) (2c/ D c 1) (1) n c = number of partcles n a vrtual core. D c = dameter of ball, equal to the wall thckness of the core (mm). b, c = wdth and length of core (mm). (a) (b) Fgure 2. Vrtual core; (a) rectangular shape, (b) sem-crcular shape Defnton of vrtual fbre bundle The vrtual fbre bundle was created by the cluster logc of PFC 3D. The cluster conssted of a seres of balls. Between balls, the radus (R) of the parallel bond was set to be equal to the ball radus, the mum radus allowed by PFC 3D. Ths mum value was chosen to ncrease the bond strength and reduce the roughness of the vrtual fbre bundle. Fgure 3(a, b) shows two dfferent shapes of vrtual fbre: straght and S-shaped. Any other arbtrary shapes of fbre can be constructed by changng the arrangement of the balls. CIGR XVII th World Congress Québec Cty, Canada June 13-17,

5 (a) (b) Fgure 3. Vrtual fbre; (a) straght, (b) S-shaped In the vrtual fbre, balls were overlapped by 50% (Fgure 4) whch s the mum overlap allowed by PFC 3D. Ths mum value was used to reduce the surface roughness of the vrtual fbre. All balls had a unform dameter whch was equal to the dameter of the real fbre to be smulated. The number of partcles requred for a vrtual fbre bundle depends on the length of the fbre and can be calculated as where n f = 2l/D -1 (2) n f = number of balls n a vrtual fbre bundle. D = dameter of ball, equal to the dameter of fbre (mm). l = length of fbre (mm). D 6(D/2) Fgure 4. A fbre wth fve balls overlapped by 50% and the correspondng dmensons The PFC 3D parallel bond model was used to descrbe the contact between balls n the vrtual fbre, wth the ntenton that the balls were held by the bond (the glue), provdng both strength and flexblty to the vrtual fbre to smulate the real fbre. The parallel bond model s defned by mcropropertes of both ball and bond. Ball propertes nclude normal and shear stffness, kn and ks (stress/dsplacement) and frcton coeffcent, µ. Bond propertes are descrbed by fve parameters, ncludng normal and shear stffness, pb_kn and pb_ks; normal and shear strength, σ c and τ c (stress) and bond dsk radus, R. Fgure 5(a, b) depcts the parallel bond as a cylnder of elastc materal and forcedsplacement behavours. The bond radus was set to be equal to the partcle radus to ncrease the bondng strength between balls. The mum tensle ( ) σ and shear ( τ ) stresses actng on the bond perphery are calculated usng the followng equatons (Itasca, 2008): n s F M σ = + R (3) A I CIGR XVII th World Congress Québec Cty, Canada June 13-17,

6 where s n F M τ = + R (4) A J A = area of the bond dsk, J = polar moment of nerta of the dsk cross-secton and I = moment of nerta of the dsk cross-secton about an axs through the contact pont s F, F = normal and shear component vectors of force M, M = normal and shear component vectors of moment n n s The parallel bond breaks f the mum tensle stress exceeds the normal strength ( σ σ c ), or the mum shear stress exceeds the shear strength ( τ τ c ) (Potyondy and Cundall, 2004). A B [ A] x [C] x [B] x 2R Fgure 5. Parallel bond between two balls and force-dsplacement behavor. n = unt normal of the contact plane; x [A] [B] and x = the poston vectors of the centres of Ball A [C] and Ball B; x = locaton of the contact pont; F, M and F, M = normal and shear component vectors of force and moment respectvely; R = bond dsc radus (Itasca, 2008). Model development for tensle test of fbre bundle The vrtual tensle test model was developed usng PFC 3D for a sngle fbre bundle. One end of the fbre was fxed and the other end was free (Fgure 6). The fxed end was at the orgn of the coordnate system and the x-axs was drected toward the tp and les along the axs. Ths setup was smlar to a tp-loaded cantlever beam test n PFC 3D. The fbre was pulled wth an axal force, P from the free end of the fbre. The model allows alterng magntudes of fbre dameters and external force. n n s s CIGR XVII th World Congress Québec Cty, Canada June 13-17,

7 Z D X P L Fgure 6. Fbre for tensle test and for parallel bond The model was cycled untl statc equlbrum reached. At the ntal condton the dsplacements of all balls were zero (Fgure 7a). Then, P was added to the free end of the fbre, causng ncreasng dsplacement of fbre. The fbre may break or may not, dependng on the magntude of the tensle force, P, fbre dameter and the strength of the bond, σ c. Break would occur when the nternal stress exceeds the σ c. The break was physcally reflected by the detachment between any of two balls and recorded by fsh command n PFC 3D. Fgure 7 shows ntal state (Fgure 7a) and fnal state (Fgure 7b) of the vrtual tensle test for a sngle fbre bundle n PFC 3D. The break occurred between the frst and the second ball. The dsplacement of the fbre was consdered as the dsplacement of the last ball along the x drecton at the tme of parallel bond breaks. Thus, the dsplacement of the last ball at the breakng pont can be montored as the elongaton of the fbre. PFC3D 4.00 Settngs: ModelPerspectve 21:48:06 Wed Feb Center: X: 2.400e-001 Y: 0.000e+000 Z: 0.000e+000 Rotaton X: Y: Z: Dst: 1.532e+000 Mag.: 1 Ang.: Ball Axes Lnestyle PBond Locatons Dsplacement *** All Values Zero Z Y X (a) CIGR XVII th World Congress Québec Cty, Canada June 13-17,

8 PFC3D 4.00 Settngs: ModelPerspectve Step :10:52 Fr Feb Center: X: 1.657e-002 Y: 0.000e+000 Z: 0.000e+000 Rotaton X: Y: Z: Dst: 1.055e-001 Mag.: 1 Ang.: Ball Axes Lnestyle PBond Locatons Z Y X (b) Fgure 7. Tensle strength test for calbratng fbre bundle mcropropertes n PFC 3D ; (a) Intal state, (b) Fnal state. Calbraton of bond mcropropertes of vrtual fbre Mcropropertes (kn, ks and µ) of ball for both fbre and core have been calbrated by Sadek and Chen (2009). Thus, only the bond propertes of vrtual fbre were requred to calbrate n ths study. Source of data for calbratons To defne the PFC 3D partcles for fbre bundle and to calbrate the mcropropertes of fbre, exstng data from tensle tests of hemp fbre (Belsham, 2000) were used. The setup of the test s brefly summarsed here for the nformaton of the readers. In Belsham (2000), test samples of fbre bundle were obtaned from manual decortcaton of unretted hemp. Samples were prepared to have a length of 50 mm, whch gave an effectve length of 35 mm after beng mounted on the tensle machne. An INSTRON machne was used for the tensle tests. Pror to the tests, the dameter of each specmen was measured. The measured dameters vared from 0.03 to 0.33 mm. Durng the test, the force-elongaton curve was recorded wth a computersed data acquston system. The peak force,.e. the force at the break was read from the curve. Ths force, together wth the fbre dameter, was used to determne the mum tensle stress,.e. tensle strength of fbre. Selecton of some mcropropertes As mentoned above, for the parallel bond model of fbre, there are several mcropropertes: bond normal and shear strength, σ c and τ c (stress), bond normal and shear stffness, pb_kn and pb_ks and radus multpler. Only one mcroproperty can be calbrated, the others have to be selected based on the logcal aspects (Potyondy and Cundall, 2004). As dscussed n the prevous secton, the parallel bond breaks when the external stress exceed the bond normal strength. Thus, t would be logcal to let the value of σ c be equal to the external stress, P/A. The shear strength τ c was consdered equal to σ c. Snce the bond radus of the vrtual fbre was set to be equal to the CIGR XVII th World Congress Québec Cty, Canada June 13-17,

9 partcle radus, the radus multpler was 1. The shear stffness was assumed to have a lower value (1e4 N/m, equal to the ball shear stffness) to make the fbre as flexble as possble and the normal stffness (pb_kn) was calbrated usng the tensle test data from (Belsham, 2000). Calbraton of the bond normal stffness of fbre (pb_kn) Vrtual tensle tests were performed usng the aforementoned model. The values of balls stffness, kn and ks were chosen as 1e4 N/m and the frcton, and µ was chosen as 0.2, based on the result from Sadek and Chen (2009). As n the real tests, all vrtual fbres were 35 mm n length whch were the same as those n Belsham (2000). The number of balls for each vrtual fbre was determned usng equaton (2), gven the constant length of 35 mm. Data of fbre dameters (D), tensle strengths and elongatons at break from Belsham (2000) were used for calbraton. The calbraton followed the tral and error method, as descrbed below. The vrtual tensle test was run by assgnng the measured tensle strength as the bond normal strength, σ c of the vrtual fbre and a set of assumed values of bond normal stffness; then compared the smulated elongaton wth the measured one; the calbrated value of the bond normal stffness was the one whch resulted n the best match between the smulated and measured elongatons. The vrtual tests were repeated for 11 fbres and t was found that the value of normal stffness of the fbre, 9e20 N/m, resulted n the best match between the smulated and measured elongatons. The results are shown n Fgure 8. 2 Elongaton, mm test model Dameter, mm Fgure 8. Comparson of test and model results for dfferent fbre. CONCLUSION In PFC 3D, fbre bundle could be defned usng the PFC 3D cluster logc and core could be defned usng the PFC 3D clump logc. Usng these two dfferent logcs, dfferently shaped vrtual fbre bundle and core were obtaned. The PFC 3D parallel bond was used for the vrtual fbre, so that the vrtual fbres were flexble. The vrtual cores were rgd and the smple PFC 3D slp model was used. A vrtual tensle test model was CIGR XVII th World Congress Québec Cty, Canada June 13-17,

10 developed for determnng the mcropropertes of fbre bundle. The mocropropertes of the fbre bundle were calbrated through the vrtual tensle test usng the lterature data. In the calbraton, the normal strength of the bond was consdered equal to the external stress (P/A) appled on the fbre durng tensle test. The approprate normal stffness of the bond was found to be 9e20 N/m by the calbraton. The results from ths study were obtaned based on lmted number of runs of the PFC 3D model, further tests are requred to confrm the results. Also, the calbraton was based on the tensle strength and elongaton of fbre and whether the vrtual fbre reflects the flexblty of a real fbre was not studed. REFERENCES Beckermann, G.W. and K.L. Pckerng Engneerng and evaluaton of hemp fbre renforced polypropylene compostes: Fbre treatment and matrx modfcaton. Compostes: Part A. 39, Belsham, T The effect of seedng rate on the fbre tensle strength. Graduaton project, Unversty of Mantoba, Canada. Cundall, P.A. and O.D.L. Strack A dscrete numercal model for granular assembles. Geotechnque, 29: Garca, C., D. D. Jaldon and M.R.Vgnon Fbres from sem-retted hemp bundles by steam exploson treatment. Bomass and Boenergy 14(3): Itasca PFC 3D partcle flow code n 3 dmensons, theory and background. Itasca Consultng Group, Inc. Mnneapols, Mnnesota, USA. Khan, M. M. R., Y. Chen, O. Wang, J. Raghavan Compressve behavor of hemp fber (Cannabs satva L.) stalks. In CSBE/SCGAB 2009 Annual Conference. CSBE Paper No Landry, H., F. Thron, C. Laguë and M. Roberge Numercal modelng of the flow of organc fertlzers n land applcaton equpment. Computers and Electroncs n Agrculture. 51: Lu, Z., S.C. Neg and J.C. Jofret A numercal model for flow of granular materals n slos. Part 1: model development. Journal of Agrcultural Engneerng Research. 68: Medavlla, V., M. Leupn and A. Keller Influence of the growth stage of ndustral hemp on the yeld formaton n relaton to certan fbre qualty trats. Industral Crops and Products. 13: Munder, F. and C. Fürll Effectve processng of bast fber plants and mechancal propertes of the fbers. ASAE/CSAE Annual Internatonal Meetng, Ottawa, Ontaro, Canada. Perce, M.E PFC 3D modelng of nter-partcle percolaton n caved rock under draw numercal modelng n mcromechancs va partcle methods. 1(6): Potyondy, D.O. and P.A. Cundall A bonded-partcle model for rock. Internatonal Journal of Rock Mechancs & Mnng Scences. 41(8): Rowell, R.M., J.S. Han and J.S. Rowell Characterzaton and Factors Effectng Fber Propertes. Natural Polymers and Agrofbers Compostes ISBN: X. Sadek, M. A. and Y. Chen Characterzaton of the shear propertes of hemp usng dscrete element method. ASABE/CSBE Paper No. SD ASABE, MI: St. Joseph. Sakaguch, F., M. Suzuk, J.F. Faver and S. Kawakam Numercal smulaton of the shakng separaton of paddy and brown rce usng the dscrete element method. Journal of Agrcultural Engneerng Research. 79(3): Van der Lnde, J Dscrete element modelng of a vbratory subsoler. Mateland, South Afrca: department of mechancal and mechatronc engneerng, Unversty of Stellenbosch. Wllams, G.I. and R.P. Wool Compostes from natural fbers and soy ol resns. Appled Composte Materals. 7: CIGR XVII th World Congress Québec Cty, Canada June 13-17,