PREDICTION AND CHARACTERISATION OF THE SHEAR BEHAVIOUR OF VISCOUS WOVEN TEXTILE COMPOSITES

Transcription

1 PREDICTION AND CHARACTERISATION OF THE SHEAR BEHAVIOUR OF VISCOUS WOVEN TEXTILE COMPOSITES Jinhuo Wang 1, Philip Harrison 2, Andrew C. Long 1 and Michael J. Clifford 1 1 School of Mechanical, Maerials & Manufacuring Engineering, Universiy of Noingha, Universiy Park, NG7 2RD, U.K. andrew.long@noingha.ac.uk 2 Deparen of Mechanical Engineering, Jaes Wa Building (Souh),Universiy of Glasgow, Glasgow G12 8QQ, U.K. p.harrison@eng.gla.ac.uk ABSTRACT: The objecive of his sudy is o develop a predicive odel of he shear behaviour of exile coposies o replace ie-consuing aerial characerisaion ess. This paper describes an energy iniisaion ehod (EMM) o reduce experienal inpus for a predicive odel developed in previous sudies. The algorih of he EMM is o iniise he suaion of he in-plane shear energy dissipaed a differen regions of he coposie shee. A series of in-plane shear characerisaion ess, Picure Frae (PF) ess, were perfored. In order o validae he es resuls, soe essenial experienal condiions, such as boundary condiions, he direcion of he shearing deforaion, ow-eander and variabiliy, were invesigaed. Coparisons beween predicions and PF es resuls show ha he ipleenaion of he EMM is proising. KEYWORDS: predicive odelling, shear behaviour, ow kineaics, Picure Frae es. INTRODUCTION Predicive odelling of he shear behaviour of viscous woven exile coposies is of ineres o any anufacurers as his can poenially decrease he ie required o characerise aerials and ay also faciliae pre-anufacure aerial opiisaion. Boh hese facors ay produce significan reducions in processing coss. The overriding oivaion is hus o ake viscous exile coposie aerials ore copeiive in ers of boh cos and funcionaliy. Muli-Scale Energy Model (MSEM) ha predics he shear behaviour of viscous woven exile coposies was developed [1]. In he originally published versions of he MSEM [1, 2], cerain experienally deerined inpu were required in he odel. Mos of hese inpus, such as arix rheology and fibre volue fracion of he coposie are easily obained. However, a ore difficul o deerine experienal inpu is he socalled ow kineaics [3]. A ow is a fibre bundle. This er ow kineaics refers o he kineaics ha reflecs differen deforaions beween he ow and he overall

2 aerial. The ow kineaics had o be obained fro experienal saples, and used as inpu for he MSEM before predicions could be ade [1]. In he curren work an energy iniisaion algorih is ipleened ha predics he ow kineaics by iniising he energy conribuions fro ow crossovers, ow regions and iner-ow regions. Hence he inclusion of he energy iniisaion ehod eans ha he MSEM requires less experienal inpu. Fundaenal o he developen and evaluaion of he MSEM are aerial characerisaion experiens. One of he os popular ehods of characerising he inplane shear behaviour of woven exile coposies is he Picure Frae (PF) es [4]. Cerain experienal condiions involved in hese experiens are analysed. Finally, he MSEM based on he energy iniisaion algorih is evaluaed by coparing wih PF es resuls. PREDICTIVE MODELLING The role of he MSEM is o predic he shear force shear angle shear rae behaviour of viscous exile coposies using paraeers supplied readily by aerial anufacurers, such as fibre volue fracion, weave archiecure and arix rheology. The odel has been described in deail previously [2] and so only a brief descripion is given here. The eso-scale kineaics observed in any ypes of viscous exile coposies have oivaed he use of a novel wo-phase aerial odel srucure o analyse he energy dissipaion wihin viscous exile coposies. These kineaics have iporan consequences for he deforaion occurring during shear, boh wihin ow and iner-ow regions, and also beween ow crossovers. Naely, he rae of deforaion ensor us be derived separaely for boh he ow and iner-ow regions and a furher dissipaive energy er us be derived o accoun for viscous energy loss a he ow crossovers. The sress-power in he ow region can be calculaed using he consiuive equaion for a uniaxial ideal fibre reinforced fluid [5]. Wihin his odel appear ers describing he longiudinal and ransverse viscosiies of he ows. These ers describe he dynaic ineracion occurring beween fibres and arix on a icro-scale. Using icroechanical odelling principals [6, 7] reasonable predicions for boh hese viscosiy ers can be ade fro he arix viscosiy and fibre volue fracion wihin he ows. The sress-power in he iner-ow region and also beween crossovers can be calculaed using he arix viscosiy. Thus, given he rae of deforaion and sress ensor for he ow and iner-ow regions, he sress power generaed by hese regions can be deerined. The velociy field beween crossovers is calculaed by analysing he in-plane kineaics of ow deforaion during shear. Using he velociy field and arix fil hickness he shear srain rae in he arix fil separaing ows a crossovers can be esiaed. Fro hese calculaions an esiae of he rae of energy dissipaion can be deerined due o shear beween ow crossovers. By cobining he energy conribuions fro boh ow and iner-ow shear ogeher wih crossover shear, he oal rae of energy dissipaion during shear of he exile coposie can be esiaed and fro his he resisance o shear deforaion can be deerined.

3 The eso-scale kineaics were obained by easureens in he previous papers [1, 2]. In order for he MSEM o require less experienal inpu, an energy iniisaion ehod has been aeped o predic he eso-scale kineaics and is described in he following secion. Energy Miniisaion Mehod (EMM) The acual ow kineaics are deerined by iniising he energy generaed due o inplane ow shear, in-plane iner-ow shear and crossover shear. For exaple, a low degree of in-plane ow shear generaes a relaively sall aoun of energy due o inplane shearing of ows bu a relaively large energy conribuion due o in-plane inerow shear and crossover shear. Alernaively, a high degree of in-plane ow shear generaes a relaively large aoun of energy due o in-plane shearing of ows bu a relaively sall energy conribuion due o in-plane iner-ow shear and crossover shear. The aoun of energy dissipaed by he in-plane ow shear, Eqn (1), is direcly relaed o he longiudinal viscosiy of he ows, η L. The aoun of energy dissipaed by iner-ow regions, Eqn (2), and crossovers, Eqn (3), is direcly relaed o he arix viscosiy, η. The ow angular shear rae, χ, deerines he in-plane shear rae of he ow and inerow regions as well as he crossover shear rae. Thus, by increasing χ fro o θ (aerial angular shear rae) he iniu energy dissipaion during any sall angular increen can be deerined. In his way he ow angular shear rae corresponding o iniu energy can be deerined. The process is deonsraed in Fig. 1. Calculaions were ade for auooive prepreg (4x4 will weave, carbon/epoxy) using he following experienal paraeers: eperaure = 23 o C, θ =3 o, aerial shear angular velociy θ =.26 rad/s, he ow shear angle for his sep χ = 3 o. where a is he disance increen of ow regions a sall increen of θ, (1) wo is he iniial widh of ow regions, T is he hickness of he coposie shee and γ is he siple shear rae in he ow region. (2) Ein er ow = bqη γ T / cosθ where b is he disance increen of iner-ow regions a sall increen of θ, q is a facor accouning for weave archiecure, γ is he siple shear rae in he iner-ow region and η is he arix viscosiy (a funcion of γ ). (3) Ecrossover = ca e η * γ f where c is he disance increen of a sall eleen a crossovers a sall increen of θ, Ae is he area of he sall eleen, γ f is he siple shear rae a his sall eleen a crossovers and awotη L γ ow = 2 θ cosθ * η is he arix viscosiy (a funcion of E γ ). f

4 5.E-11 4.E-11 Zero ow-shear poin A 4.E-11 3.E-11 Hoogeneous shear poin 3.E-11 2.E-11 2.E-11 1.E-11 B 5.E-12 C Free odel.e (Tow angular velociy)/(maerial angular velociy) Fig. 1 Scheaic of energy iniisaion ehod o predic he ow kineaics. Energy increen (J) Fro Fig. 1, χ can be prediced by iniising he oal energy increen, which is a poin C. Then χ can be calculaed analyically. By increasing he aerial shear angle ( θ ), he corresponding χ and χ can be deerined, which induces a for of χ versusθ, i.e. prediced ow kineaics. Maerial CHARACTERISATION TESTS The aerial used in his sudy is a 4x4 will weave, carbon/epoxy auooive prepreg, provided by Hexcel Coposies in he UK, and is aerial code is M47N/42%/28T4X4/CHS-3K/1. Speciens were cu ino a shape wih he ows parallel or perpendicular o he ouer edges. The hickness of he un-esed shee is.36. Tes Procedure Picure frae es apparaus coprises of four-bar linkage loaded by a Hounsfield Universal Tesing achine hrough a load cell conneced o he crosshead. Four bars are joined such ha he iniially square frae becoes a rhobus. An environenal chaber was used o es aerials a elevaed eperaures. To iniise hea-up ie he picure frae rig and claps are heaed o he required eperaure in he chaber prior o ouning he saple. Once saples are claped wihin he frae, hea-up ies us be sufficienly shor o avoid epoxy resin cure during esing. During he es, a consan displaceen rae is applied o he crosshead and he axial picure frae force ( F pf ) and he displaceen ( d pf ) of he crosshead are easured. If

5 daa of shear force versus shear angle is required, hen F pf and d pf need o be convered hrough Eqns (4) and (5). Fpf Fs = (4) 2cosΦ where Φ is he frae angle, and can be relaed o he shear angle ( θ ) hrough θ = π 2 2Φ. where L is he side lengh of he picure frae. Resuls and Discussions Effec of boundary condiions π θ = 2 cos d pf 2L (5) As he es boundary condiion is a criical facor in obaining reliable daa [8, 9], wo boundary condiions were invesigaed, claped (four edges of PF are claped) and pinned (hree pins a each claping edge provide shear force o aerial shee during esing). I had been found ha he pinned case is ore suiable for Twinex (a 2x2 will weave, glass/polypropylene heroplasic coposie) [4]. Three ess for each case were perfored. Sligh wrinkling occurred in only one es for he claped case, whereas serious wrinkling happened a he sar of all ess for he pinned case. This suggess ha he claped case should be used in he PF ess for he auooive prepreg used. Influence of direcion of he shearing deforaion There are wo direcions of shear deforaion, posiive and negaive. A posiive shearing deforaion is defined wih he warp fibre direcions a an angle of + 45 o wih he axis of loading, as viewed fro he fron of he PF apparaus. PF es resuls for a 1/7 sain weave (glass fibre reinforced Nylon 12) showed ha he force required o shear he coposie shee in posiive shear was nearly double he corresponding force in negaive shear [1]. A heory developed in [11, 12] gives predicions consisen wih he resuls of his es. To invesigae is influence, hree ess for each case were perfored. The resuls sugges ha he direcion of shearing deforaion for his prepreg has a negligible effec on he PF resuls, copared o variabiliy of PF ess (see he following analysis). Influence of ow-eander Ideally, he ows of speciens in he wef direcion are sraigh and perpendicular o hose in he warp direcion. However, in pracice, he ows are no exacly sraigh and perpendicular o each oher, as shown in Fig. 2(a). In order o invesigae he influence of ow-eander, hree ess were perfored wih saples aken direcly off-he-roll. Fro Fig. 2(b), he resuls for off-he-roll speciens are uch higher han hose for he case of sraighened speciens (i.e. where he aerial was sraighened o iprove ow alignen), and show poor repeaabiliy. This suggess ha es speciens should be sraighened prior o esing in order o reduce he influence of ow-eander on es daa.

6 (a) (b) Noralised axial force (N/) off-he-roll specien sraighened specien Noralised displaceen Fig. 2 (a) The profile of ows in he warp and wef direcion in he aerial roll. (b) PF resuls wih he cases of ow-eander and sraighened speciens. Noe ha PF resuls are noralised by he side lengh of he picure frae [4], e.g. he noralised displaceen equals o he recorded displaceen divided by he side lengh. Variabiliy of Picure Frae ess The repeaabiliy of ess can be used o easure he accuracy of he es. The experienal errors involved during he ess ay be due o isalignen due o cuing aerial shees fro he aerial roll, aligning shees, claping of he aerial, saple isalignen ec. Soe PF ess were discarded due o preaure wrinkling. Fig. 3 shows he PF resuls a hree noralised crosshead speeds. 7 Noralised axial force (N/) per in.44 per in.11 per in Noralised displaceen Fig. 3 PF es resuls a differen noralised crosshead speeds o invesigae he variabiliy of experiens. COMPARISONS BETWEEN PREDICTIONS AND CHARACTERISATION Predicions fro he MSEM using he EMM were ade o copare wih PF resuls. Wihin experienal variabiliy, a good agreeen beween force predicions and experienal resuls is found (Fig. 4(a)), alhough he shape of prediced curve of he ow kineaics does no confor o he easureens (Fig. 5). MSEM predicions a a higher rae, 1.74 in -1, were also ade o copare wih PF es resuls, shown in Fig. 4(b). The agniude of force predicions increases rapidly as he rae increases, bu he shape reains siilar. The discrepancies beween predicions and easureens are hough o be ainly due o he accuracy of longiudinal/ransverse viscosiies used in he MSEM. An suggesion on he iproveen of hese wo viscosiies was given by [13]. These probles will be addressed fuure work.

7 (a) Noralised axial force (N/) MSEM predicions a.44 per in PF ess a.44 per in Noralised axial force (N/) MSEM predicions a 1.74 per in PF ess a 1.74 per in (b) Noralised displaceen Noralised displaceen Fig. 4 Coparisons beween force easureens fro Picure Frae ess and force predicions based on he EMM for auooive prepreg shee a differen noralised displaceen raes of (a).11 in -1 (b) 1.74 in -1 Tow shear angle ( o ) Hoogeneous Shear Measured Tow Kineaics Prediced Tow kineaics based on EMM Polynoial fi o Measured Tow Kineaics Maerial shear angle ( o ) Fig. 5 Coparisons beween easureens and predicions of ow kineaics based on he EMM a a noralised displaceen rae of.11 in -1 for auooive prepreg shee. Measureens were obained fro fored heispheres. The error bars indicae he sandard deviaion. CONCLUSIONS A predicive odel wih less experienal inpu, based on he uniaxial coninuu heory for ideal fibre-reinforced fluids bu applied o woven exile coposies, has been developed. The eso-scale kineaics for ow deforaion ha in he original MSEM had o be obained fro experienal easureens, such as fored heisphere, can be prediced by an energy iniisaion algorih. PF ess have been perfored and sugges ha he claped boundary condiion should be used for his paricular prepreg, and he effec of direcion of he shearing deforaion for his prepreg can be negleced. The influence of ow-eander is significan, which suggess ha es speciens should be sraighened prior o esing. A reasonable agreeen beween MSEM predicions and PF es resuls encourages he developen of he energy iniisaion ehod.

8 ACKNOWLEDGEMENTS We would like o hank he following organisaions for heir suppor: EPSRC, Minisry of Defence, Universiy of Cabridge, ESI Sofware, Ford Moor Copany Ld., Grana Design Ld, Hexcel Coposies, MSC Sofware Ld, Polynor Plasics (UK) Ld and Sain Gobain Veroex. REFERENCES 1. Harrison, P., Clifford, M.J., Long, A.C., and Rudd, C.D., A consiuen-based predicive approach o odelling he rheology of viscous exile coposies. Coposies: Par A, : p Harrison, P., Clifford, M.J., Long, A.C., and Rudd, C.D., Consiuive odelling of ipregnaed coninuous fibre reinforced coposies: a icro-echanical approach. Pas Rubber Copos, (2): p Hive, G., Duon, F., Launay, J., Maurel, V., Vacher, P., and Boisse, P. Opical analysis of woven fabric's shear behaviour. in 7h Inernaional ESAFORM Conference on Maerials Foring. 24. Trondhei, Norway. 4. Harrison, P., Clifford, M.J., and Long, A.C., Shear characerisaion of viscous woven exile coposies: a coparison beween picure frae and bias exension experiens. Coposies Science and Technology, : p Rogers, T.G., Rheological characerisaion of anisoropic aerials. Coposies, (1): p Chrisensen, R.M., Effecive viscous flow properies for fibre suspensions under concenraed condiions. Journal of Rheology, (1): p Coffin, D.W., Pipes, R.B., and Siacek, P., Firs-order approxiaions for he effecive shearing viscosiies of coninuous-fiber suspensions. Journal of Coposie Maerials, (9): p Milani, A.S., Nees, J.A., Pha, X.-T., and Lebrun, G. The effec of fibre isalignen on paraeer deerinaion using picure frae es. in 14 h Inernaional Conference on Coposie Maerials (ICCM) h July, 23. San Diego, California. 9. Peng, X.Q. and Cao, J., A coninuu echanics-based non-orhogonal consiuive odel for woven coposie fabrics. Coposies: Par A, : p McGuiness, G.B. and O'Bradaigh, C.M., Developen of rheological odels for foring flows and picure-frae shear esing of fabric reinforced heroplasic shees. Journal of Non-Newonian Fluid Mechanics, : p Spencer, A.J.M., Theory of fabric-reinforced viscous fluid. Coposies: Par A, 2. 3: p Spencer, A.J.M., A heory of viscoplasiciy for fabric-reinforced coposies. Journal of The Mechanics and Physics of Solids, : p Harrison, P., Haylock, T. and Long, A.C. Measureen of he Transverse and Axial Viscosiies of Coninuous Fibre Reinforced Coposies. in 8h Inernaional ESAFORM Conference on Maerials Foring. 25. Cluj-Napoca, Roania.