Zeitschrift Kunststofftechnik Journal of Plastics Technology

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1 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern Zetschrft Kunststofftechnk Journal of Plastcs Technology engerecht/handed n: angenommen/accepted: Alejandro Londoño-Hurtado, Prof Tm Osswald Department of Mechancal Engneerng, Unversty of Wsconsn, Madson Fber Jammng and Fber Matrx Separaton durng Compresson Moldng Fber jammng s perhaps the least understood defect n moldng of polymer compostes Ths paper presents a descrpton of the problem, ntroduces a mechanstc model and a dmensonal analyss developed to predct fber dstrbuton n rbbed sectons Autor/author Alejandro Londoño-Hurtado, Prof Tm Osswald Department of Mechancal Engneerng, Unversty of Wsconsn-Madson 151 Unversty Avenue Madson, WI 5706 E-Mal-Adresse: osswald@engrwscedu londonohurta@wscedu Herausgeber/Edtor: Europa/Europe Prof em Dr-Ing Dr hc G W Ehrensten, verantwortlch Lehrstuhl für Kunststofftechnk Unverstät Erlangen-Nürnberg Am Wechselgarten 9 D Erlangen Deutschland Phone: +49/(0)911/ Fax: +49/(0)911/ E-Mal-Adresse: ehrensten@lktun-erlangende Berat/Edtoral Board: Professoren des Wssenschaftlchen Arbetsk reses Kunststofftechnk/ Professors of the Scentfc Allance of Polymer Technology Verlag/Publsher: Carl-Hanser-Verlag Jürgen Harth Ltg Onlne-Servces & E-Commerce, Fachbuchanzegen und Elektronsche Lzenzen Kolbergerstrasse 22 D Muenchen Tel: 089/ Fax: 089/ E-mal: harth@hanserde Amerka/The Amercas Prof Dr Tm A Osswald, responsble Polymer Engneerng Center, Drector Unversty of Wsconsn-Madson 151 Unversty Avenue Madson, WI 5706 USA Phone: +1/ Fax: +1/ E-Mal-Adresse: osswald@engrwscedu Wssenschaftlcher Arbetskres der Unverstäts- Professoren der Kunststofftechnk archverte, rezenserte Internetzetschrft des Wssenschaftlchen Arbetskreses Kunststofftechnk (WAK) archval, revewed onlne Journal of the Scentfc Allance of Polymer Technology wwwkunststofftechcom; wwwplastcsengcom Carl Hanser Verlag Zetschrft Kunststofftechnk/Journal of Plastcs Technology 2 (2006) 4

2 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern FIBER JAMMING AND FIBER MATRIX SEPARATION DURING COMPRESSION MOLDING Alejandro Londoño-Hurtado, Prof Tm Osswald Unversty of Wsconsn, Madson Fber jammng s perhaps the least understood defect n moldng of polymer compostes Ths paper presents a descrpton of the problem, ntroduces a mechanstc model and a dmensonal analyss developed to predct fber dstrbuton n rbbed sectons In desem artkel wrd en mechantsches Model der Faser/Matrx-Entmschung entwckelt und ene Ähnlchketsanalyse fur gerpte SMC und GMT Bautelen presentert Faser/Matrx-Entmschung st vellecht ener der am wengsten verstandenem phenomenen n der Faserverbuntwerkstoffe-Verarbetung 1

3 Alejandro Londoño-Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern Compresson moldng of sheet moldng compounds (SMC) and glass mat renforced thermoplastcs (GMT) are common processes used to produce lghtweght nexpensve fber renforced parts, especally for the automotve ndustry Durng the manufacturng process, the materal s squeezed and forced to flow untl the charge covers the whole mold cavty Ths causes materal to flow around sharp corners and nto areas that are dffcult to access by the moldng compound, such as rbs and bosses As the materal s forced to flow, the resn matrx s often squeezed out of the bed of fbers Ths leads to fber densty dstrbutons throughout a part; Fgure 1 depcts ths behavor These varatons affect the mechancal propertes of the fnshed part as well as ther surface fnsh Varatons n fber densty wthn a part wll lead to surface wavness and defects n the fnshed product Fber-matrx separaton s perhaps the least understood and understuded effect n fber renforced materals moldng processes Fgure 1: Uneven fber dstrbuton n a compresson molded part Mechanstc mathematcal models that smulate fber flow have been used for more than four decades The work of Batchelor [1] and hs slender body theory can be hghlghted as one of the precursors n the study of suspended partcles n fluds Jeffery [2,] and Tucker [4,5] provded the foundatons for many of the current models In recent years, Brady et al [6-8] have also made mportant contrbutons n ths area, havng sgnfcant nfluence n later works Phan-Then et al [9] ncorporated long range hydrodynamc nteractons nto Jeffery's model Schmdt et al [10] have done work for flexble fbers at low concentratons Smulatons at hgh fber concentratons are a matter of nterest for polymer processng The work presented n ths paper s part of an effort to characterze the processng of fber renforced compostes 1 CHARACTERIZATION OF FIBER SUSPENSIONS Fber suspensons are classfed accordng to the amount of concentraton of fbers n the matrx A fber suspenson s sad to be dlute f less than one fber on average s found n a sphercal volume of dameter equal to the fber length, nl 1, where n s the number of fbers per unt volume A sem-dlute regme s Journal of Plastcs Technology 2

4 Alejandro Londoño Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern characterzed by 1 < nl < r p and nl 2 << 1 Here L s the fber length and s the aspect rato of a fber of dameter D L r p (1) D In the sem-concentrated regme, fbers are sgnfcantly dsturbed by other fbers durng rotaton and they can no longer rotate smoothly wthout crossng through the excluded volume of another fber [11] A suspenson s sad to be concentrated when nl > r p In ths case, fbers are assumed to be nteractng wth each other and the effect of mechancal contacts becomes domnant The presence of mechancal contacts can sgnfcantly ncrease the stress n a suspenson by changng fber orentaton as well as by transmttng stress through contactng fbers For small aspect ratos, mechancal contacts are the man mechansm causng orentatonal dsperson Far feld hydrodynamcs starts playng a decsve role for hgher aspect ratos As the fber concentraton s ncreased, t s lkely that contact and hydrodynamc forces wll have a jont effect At very hgh concentratons, a state where each fber has several mechancal contacts, mechancal contacts wll preval over far feld hydrodynamc nteractons [12,1] The number of fbers, any gven fber may nteract wth as t rotates, s called the crowdng factor [14] N crowd N crowd 2 2φ crtrp (2) Where φ crt s known as the crtcal concentraton and s defned as one fber, on average, n the sphercal volume wth a dameter equal to the fber length Above ths concentraton, fbers are not able to rotate wthout contactng other fbers The formaton of fber networks s determned by the combnaton of processng parameters and materal propertes, whch wll be covered n the next secton 2 FIBER NETWORK FORMATION When a fber suspenson s drven by a flow, the fbers are subjected to vscous and dynamc forces that cause them to bend When the flow comes to rest, the fbers try to regan ther orgnal unstraned shape Dependng on the concentraton, a fracton of the fbers wll come n contact wth other fbers and they wll come to rest n straned postons where forces wll be transmtted from fber to fber When a fber s locked nto a network n a straned confguraton, t must possess at least three contact ponts wth other fbers [15] These contact ponts must be located on alternate sdes of the fber At low concentratons, there wll Journal of Plastcs Technology r p

5 Alejandro Londoño-Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern be some fbers that do not become entangled n ths manner Fber network formaton and fber jammng s governed by processng and physcal parameters For a specfc process, the effect of a certan parameter may vary n magntude or not have any effect at all, as s the case of magnetc effects n compresson moldng The followng parameters have been dentfed to play a role n fber network formaton [16]: Collodal forces: These forces are caused by the chemcal characterstcs of the fbers and the suspendng flud; they are usually not taken nto account when modelng fber moton n glass fber compostes Surface tenson effects: These are due to entraned gas wthn a fber suspenson Bubbles of gas may appear n fber suspensons due to mxng or other processng factors Bubbles stay n partcle nterstces and create an effectve attractve force between partcles due to free surface effects Mechancal surface lnkages: Its orgn s n contacts nvolvng rregularly shaped fbers wth surface protrusons Also, small fbrous enttes (fbrls) of the fber may extend out from the fber surface In ths case, the fbrls of contactng fber surfaces may become mechancally entangled Elastc fber nterlockng: Ths s found when fbers form an elastc network Flowng fber suspensons may experence suffcent vscous forces to cause fbers to elastcally deform from an equlbrum confguraton As the fbers attempt to relax, they can become locked n elastcally straned confguratons due to contacts wth other fbers The fber surfaces experence frcton forces that are proportonal to the normal force between fbers, and the normal force s a functon of the fber flexblty Flocculaton: Occurs when a dsperson of fbers s dlute enough and fbers tend to aggregate n groups or flocs Ths process s known as flocculaton and only occurs f fbers nteract Expermental studes [14] have shown that although N crowd s drectly related to flocculaton, a hgh value of N crowd doesn't necessarly mply that flocculaton wll take place [12] Other parameters lke r p and the vscosty of the matrx, are also nvolved For example, when the flud 's vscosty s ncreased, the value of the crowdng factor at whch flocculaton occurs s also ncreased MECHANISTIC ANALYSIS OF FIBER SUSPENSIONS In order to study the fber nteractons occurrng n the compresson moldng process, a mechanstc mathematcal model was used to predct the confguraton These knd of models use the classcal equatons of moton, combned wth the momentum equatons for flud flow, to study the movement of Journal of Plastcs Technology 4

6 Alejandro Londoño Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern the fbers n a suspenson at any tme from the start of the flow untl t has ceased The followng secton descrbes the methodology used to model fber suspensons subject to a shearng flow 1 SIMULATION METHOD The smulaton used n ths work, models fber suspensons as lnked cylnders wth hemsphercal end caps, connected by ball and socket jonts as shown n Fg 2 In the case of polymer processng, some assumptons and smplfcatons are made wthout alterng the accuracy of the results As a frst smplfcaton, fber extensblty s neglected, snce fber length remans vrtually unchanged n polymer processng processes Far feld hydrodynamc nteractons can be neglected for hgh fber concentratons snce frctonal forces domnate the flow Fnally, the fbers are assumed as neutrally buoyant wth no other external felds appled The equatons of moton for a fber nclude the reacton forces between the hnges and contact forces between fbers: F 1 X + F 0 () hyd + X + N c k con IK hyd Where F are the hydrodynamc drag forces, X are the jont forces n the hnges and F are the contact forces The equaton of momentum s, con IK Nc con + 1 Y + Lp X X + Gk Fk k [ ] 0 hyd T + Y (4) Fgure 2: Schematc dagram of a model fber Journal of Plastcs Technology 5

7 Alejandro Londoño-Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern hyd Where T s the hydrodynamc torque, Y the jont torque and the thrd and fourth terms are the torques exerted by the jont forces and the contact forces, respectvely The term G k s the dstance from the segment center to the pont of applcaton of the contact force F hyd hyd The hydrodynamc drag force,, and torque,, are approxmated wth the expressons for an solated prolate spherod wth an equvalent rato, F T hyd hyd 6 πη LA ( U r ) (5) o 8 πη L ( C ( Ω ω ) + H : E ) (6) o Where η o s the vscosty of the flud, L s the length of the fber, T r e s the flud velocty and r s the velocty of the center of mass of the segment The terms Ω and ω are the ambent and segment angular veloctes, respectvely The vortcty of the flud s tensors U E Tensors A, C and, H are the resstance drag The restorng torques Y are used to model dfferent fber flexbltes Fbers can bend and twst snce they are composed by spherods connected by hnges If these torques were not ncluded n the equatons of momentum, the fbers would mmedately bend at the jonts wth the start of the flow Dfferent magntudes of fber flexblty can be modeled by changng the amount of these torques The expresson for the bendng and twstng torque s gven by, b eq b eq t ( θ θ ) e + ( γ γ e ) Y k 0 67 ) (7) eq eq Where and are the bendng and twstng equlbrum angles When a θ eq eq fber s not deformed, θ θ and γ γ, and the resultng torque s zero The constant k s the bendng constant of the fber A hgh k means the fber s rgd whle a low b k b γ means the fber s flexble For a known ntal poston of the fbers, t s possble to ntegrate n tme to a new partcle confguraton at a tme t+dt and the system can be updated Fgure shows smulaton results for an ntally randomly orented fber network subjected to shear flow The unt cell used, employed a perodcty condton, where the fber leavng one sde of the wall enters through the opposte sde The sequence of graphs n the fgure demonstrates that the fbers tend to algn along the plane of shear Ths model works perfectly wth dlute and sem-dlute fber suspensons However, when the fber concentraton s augmented,e, the suspenson s concentrated, t becomes harder to track fber to fber contacts and the fbers are so packed that the smulaton model can no longer correctly descrbe the flow Furthermore, there exsts the possblty of the fbers overlappng f the tme step s too bg The smulaton s then lmted to very small tme steps Journal of Plastcs Technology 6 b

8 Alejandro Londoño Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern Smulatons where the fber concentraton by volume s more than 1 % become mpractcal The neglecton of the hydrodynamc effects n concentrated suspensons s based n the dea that the flud between fbers does not cause a hydrodynamc effect [17,18] The hydrodynamc force s based on the deal stuaton where a fber of a gven geometry s mmersed n a free flowng flud Ths mght be true for dlute and sem dlute suspensons, where the fber nteractons are mnmum However, n the case of a concentrated suspenson, ths s not the case snce fbers are constantly n contact wth each other, and the nteracton wth the flow s far from the deal case It has been suggested that for the case of concentrated suspensons, the force of frcton, the normal force and a lubrcaton force are orders of magntude greater than the hydrodynamc force The lubrcaton force replaces the hydrodynamc force snce, n realty, there s only a thn flm of flud that lubrcates the movement between fbers [19,20] The followng secton presents a dmensonal analyss created to evaluate the relevance of each of the competng forces n the processng of fber renforced compostes Fgure : Fber matrx smulaton for a fber concentraton of 1% 4 DIMENSIONAL ANALYSIS FOR COMPRESSION MOLDING OF A RIBBED SECTION Fundamental dmensonal analyss was conducted on mechanstc models of fber suspensons to study the nfluence of processng varables on the fnal qualty of the part Fgure 4 shows a schematc of the compresson moldng of a rbbed part An upper platen s lowered wth a force F whch exerts a pressure p Journal of Plastcs Technology 7

9 Alejandro Londoño-Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern on the charge The charge s squeezed at a closng speed completely flled wth a fnal flange thckness h Fgure 4: Schematc of compresson moldng of a rbbed part h untl the mold s The fbers have a length L, area moment of nerta I, Young's modulus E and dameter D The fber bed has a permeablty K whch s expressed n terms of D'Arcy's Law Bakharev and Tucker [21] used ths law to descrbe flow through a porous medum The flow of the resn through the fber bed s modeled as one dmensonal flow of a Non-Newtonan flud through a porous materal, K dp V η dy K D φ (9) where V s the velocty of the resn, η the vscosty of the resn, D the fber dameter and φ the volume fracton of fbers Wth a mold cover charge of about 50%, the velocty V can be assumed to be equal to the closng speed of the compresson moldng machne The relevant parameters for the dmensonal analyss are summarzed as follows: Process varables: closng speed h, pressure p, mold closng force F, average fber dstance δ o Geometrc varables: fber length L, fber dameter D, flange thckness h, fber's area moment of nerta I Journal of Plastcs Technology 8 (8) h

10 Alejandro Londoño Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern Physcal or materal propertes: matrx vscosty η, permeablty K and Young's modulus of the fber E It should be noted that the volume fracton, φ, s already a dmensonless number From the dmensonal analyss, the followng Π -groups are obtaned: L Π 1 (10) 1/ 4 I D Π 2 (11) 1/ 4 I h Π (12) 1/ 4 I η h Π 4 (1) 1/ 4 EI K Π 5 (14) 1/ 2 I F Π 6 (15) 1/ 2 EI p Π 7 (16) E The Π -groups can be rearranged to obtan the followng dmensonless numbers: 2 2 Π 4Π1 Π η h h L ℵ 1 (17) Π KEI 5 η h h ℵ 2 Π 4Π (18) EI 2 Π L 2 1 ℵ (19) Π K L D δ o ℵ 4 (20) 4 h Each of these numbers have a physcal sgnfcance They can be expressed n terms of D'Arcy's forces FD hydrodynamc forces FH and fber bendng forces F B Journal of Plastcs Technology 9

11 Alejandro Londoño-Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern The dmensonless number forces, ℵ 1 s the rato between D'Arcy's and fber bendng D ' Arcy' s Forces ℵ 1 (21) Fber Bendng Forces A value of ℵ 1 less than one, s an ndcator of fber bendng forces beng greater than D'Arcy's forces, leadng to sgnfcant fber matrx separaton or fber jammng When ℵ > 1 1, the force needed to bend the fbers s lower than the force needed to make the matrx flow through the fber bed In ths case, fbers wll also be dragged nto the rb, dmnshng the effects of fber matrx separaton The hgher the values of ℵ 1, the less the chance of fber matrx separaton Fgure 5 shows the behavor of ℵ 1 for dfferent fber concentratons and dfferent fber dameters The graph shows that for a gven fber concentraton, lower fber dameters have hgher ℵ 1 In other words, fbers wth lower dameter requre less bendng force to flow nto the rb and decrease the chance of fber matrx separaton Fgure 5: ℵ1 Vs φ for dfferent fber dameters Journal of Plastcs Technology 10

12 Alejandro Londoño Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern Fgure 6 shows the varaton of ℵ 1 wth fber concentratons for dfferent resn matrx vscostes The hgher the vscosty of a charge, the more dffcult t s for the charge to flow through the fber bed Ths explans why, for a gven fber concentraton, hgher vscostes have hgher values of ℵ 1 Fgure 7 shows the nfluence of the closng speed n the fnal part dstrbuton on fber matrx separaton A hgher closng speed ncreases the D'Arcy forces, draggng the fbers nto the rbbed secton, and therefore reducng fber matrx separaton effects The dmensonless number ℵ 2 s the rato between hydrodynamc forces and fber bendng forces The dmensonless number ℵ s the rato between D'Arcy's forces and hydrodynamc forces, Hydrodynamc Forces ℵ 2 (22) Fber Bendng Forces D ' Arcy' s Forces ℵ (2) Hydrodynamc Forces A hgh value of ℵ 2 s ndcatve of hydrodynamc forces prevalng over bendng forces Ths s usually not the case n compresson moldng, snce the fber bendng forces are orders of magntude hgher than the hydrodynamc forces Fgure 8 shows the the behavor of ℵ versus fber concentraton for dfferent fber dameters It can be observed that D'Arcy's forces are orders of magntude hgher than hydrodynamc forces Only for very low fber concentratons, hydrodynamc forces play an mportant role For a gven fber concentraton, a smaller radus means a lower hydrodynamc force and therefore hgher ℵ The dmensonless number hydrodynamc forces ℵ 4 s the rato between lubrcaton forces and Lubrcaton Forces ℵ 4 (24) Hydrodynamc Forces Fgure 9 shows the dmensonless number for dfferent average fber separatons At low fber concentratons, the hydrodynamc forces domnate the lubrcaton forces As the fber concentraton ncreases, the lubrcaton forces start playng the domnant role, to the pont that hydrodynamc forces can be neglected These results are n accordance wth the observatons made n expermental results [18,19] and rase the possblty of smplfyng the smulaton algorthm The suspenson nter-fber frcton can be expressed n terms of known forces Typcal Coulombc frcton s gven by F f µ F N (25) Journal of Plastcs Technology 11

13 Alejandro Londoño-Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern Fgure 6: Fgure 7: ℵ1 ℵ1 Vs φ for dfferent resn vscostes Vs φ for dfferent mold closng veloctes Journal of Plastcs Technology 12

14 Alejandro Londoño Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern Where F f and µ are the force and the coeffcent of frcton, respectvely The force F N s the normal force between contactng fbers Ths normal force can be assumed equal to the sotropc pressure appled to the charge tmes the projected surface area of the fber A f F N PA f (26) Where A f DL (27) Expressng the pressure n terms of D'Arcy's forces and fndng the rato wth respect to hydrodynamc forces, a fnal dmensonless number s obtaned Frcton Forces L ℵ µ µ Hydrodynamc Forces K 2 5 ℵ Ths result suggests that D'Arcy's and lubrcaton forces have the same behavor when compared to hydrodynamc forces In other words, Fgure 8 s equvalent to plottng ℵ 5 versus fber dameter wthout the dampenng ntroduced by the coeffcent of frcton µ It s then concluded that frcton forces domnate over hydrodynamc forces at hgh fber concentratons Fgure 8: ℵ Vs φ for dfferent fber dameters (28) Journal of Plastcs Technology 1

15 Alejandro Londoño-Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern Fgure 9: ℵ4 5 CONCLUSIONS Vs φ for dfferent fber separatons The dmensonal analyss presented n ths paper s amed at verfyng that hydrodynamc forces may be neglected and at mantanng the physcal connecton of an ndustral process wth a complex mathematcal smulaton Wth the help of dmensonal analyss t s possble to refne the computer smulatons and optmze computatonal tme otherwse spent n unrealstc processes Dmensonal analyss supports and valdates smulaton results that otherwse mght lose touch wth realty By conductng a smple dmensonal analyss, t was found that at hgh fber concentratons, the effect of the hydrodynamc forces can be neglected and replaced by a lubrcaton effect Ths result s n accordance wth the behavor found n experments The mportance of ths result should not be overlooked snce for concentrated fber suspensons, most of the problems encountered n the smulatons are caused by ncreasng fber to fber contact and trackng the hydrodynamcs of the flow The lubrcaton smplfcaton could lead to successful smulatons of hghly concentrated fber suspensons Journal of Plastcs Technology 14

16 Alejandro Londoño Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern 6 REFERENCES [1] G K Batchelor Slender-body theory for partcles of arbtrary cross-secton n stokes flow Journal of Flud Mechancs, 44 part :419440, 1970 [2] GB Jeffery Proc Roy Soc, 111:110, 1926 [] GB Jeffery The moton of ellpsodal partcles mmersed n a vscous flud Proc Roy Soc, A102:161, 1922 [4] FP Folgar and C L Tucker [5] TA Osswald and C L Tucker [6] G Bosss and JF Brady [7] Ivan L Claeys and John F Brady [8] Ivan L Claeys and John F Brady [9] XJ Fan, N Phan- Then, and R Zheng Orentaton behavor of fbers n concentrated suspensons Renf Plast Comp, :98, 1984 Compresson mold fllng smulaton for nonplanar parts Internatonal Polymer Processng, 5(2):7987, 1990 Dynamc smulaton of sheared suspensons l general method Journal of Chemcal Physcs, 80: , 1984 Suspensons of prolate spherods n stokes flow part 2 statstcally homogeneus dspersons J Flud Mech, 251:44477, 1992 Suspensons of prolate spherods n stokes flow part hydrodynamc transport propertes of crystallne dspersons J Flud Mech, 251:479500, 1992 A drect smulaton of fbre suspensons J Non-Newtonan Flud Mech, 74:1115, 1998 Journal of Plastcs Technology 15

17 Alejandro Londoño-Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern [10] Chrstan F Schmdt, LH Swtzer, and DJ Klngenberg [11] B Herzhaft and E Guazzell Smulatons of fber flocculaton:effects of fber propertes and nterfber frcton J Rheology,44:781809, 2000 Expermental study of the sedmentaton for dlute and sem-dlute suspensons of fbres Journal of Flud Mechancs,84:1158, 1999 [12] L Swtzer Smulatng Systems of Flexble Fbers PhD thess, Unversty of Wsconsn- Madson, 2002 [1] RR Sundararajakumar and DL Koch [14] RJ Kerekes and CJ Schell Structure and propertes of sheared fber suspensons wth mechancal contacts Journal of Non-Newtonan Flud Mechancs, 7:20529, 1997 Characterzaton of fbre flocculaton regmes by a crowdng factor Journal of Pulp and Paper Scence, 18:28, 1992 [15] D Wahren Fber network structures n papermakng operatons In Paper Scence and technology,the Cuttng edge, 1979 [16] RJ Kerekes, R M Soszynsk, and P a Tam Doo [17] A Moghaddam and Staffan Toll [18] J E Manson K A Ercsson, S Toll [19] Coln Servas, Andre Lucan, Jan The flocculaton of pulp fbres In Transactons of the eghth fundamental research symposum held at Oxford, 1985 Fbre suspenson rheology: effect of concentraton, aspect rato and fbre sze Rheologca Acta, 45:1520, 2006 The two-way nteracton between ansotropc flow and fber orentaton n squeeze flow J Rheol, 41(): , 1997 Fber-fber nteracton n concentrated suspensons: Dspersed fber bundles J Journal of Plastcs Technology 16

18 Alejandro Londoño Hurtado, Tm Osswald Fber Jammng 2006 Carl Hanser Verlag, München wwwkunststofftechcom Ncht zur Verwendung n Intranet- und Internet-Angeboten sowe elektronschen Vertelern Anders, and J E Manson [20] Coln Servas, Andre Lucan, Jan- Anders, and JE Manson [21] AS Bakharev and C L Tucker Rheol,4(4):991100, 1999 Squeeze flow of concentrated long fbre suspensons: experments and model J Non-Newtonan Flud Mech, 104: , 2002 Predctng the effect f preformng on rtm mold fllng In Socety of Plastc Engneers Inc, Techncal Papers Volume XLII,1996 Keywords: Fber jammng, fber matrx separaton, computer smulatons, dmensonal analyss Contact: Prof Tm Osswald (osswald@engrwscedu) Alejandro Londoño-Hurtado (londonohurta@wscedu) Department of Mechancal Engneerng, Unversty of Wsconsn, Madson 151 Unversty Avenue, 17 Mechancal Engneerng Buldng Journal of Plastcs Technology 17