NON-CRIMP FABRIC PERMEABILITY MODELLING

Transcription

1 FPCM-9 (2008) The 9 th Intenational Confeence on Flow Pocesses in Composite Mateials Montéal (Québec), Canada 8 ~ 0 July 2008 NON-CRIMP FBRIC PRMBILITY MODLLING S.P. Haanappel, 2, R. kkeman Faculty of ngineeing Technology, Chai of Poduction Technology, Univesity of Twente, Dienelolaan 5, P.O. Box , nschede, The Nethelands 2 Coesponding autho s mail: s.p.haanappel@student.utwente.nl SUMMRY: qualitative study to the in-plane pemeability modelling of Non-Cimp Fabics has been caied out. netwok flow model was developed to descibe flow though inte bundle channels (meso level). To impove this model, it was extended with details that conside stitch yan influenced egions. The model pedicts a highly anisotopic pemeability. The pedicted pemeability in the machine diection of the fabic coesponds with the expeimental esults. Howeve, pediction of pemeability pependicula to the fabic s machine diection does not coespond with the expeimental esults. Possibly, flow though fibe filaments (mico level) is significant and the netwok flow model has to be extended to include this type of flow. YWORDS: Non-Cimp Fabic (NCF), in-plane pemeability pediction, netwok flow model, intenal geomety, inte bundle channels, vacuum infusion INTRODUCTION Common poblems that ae encounteed in Liquid Composite Moulding (LCM) pocesses ae non-unifom impegnation, fomation of dy spots, void inclusions and lengthy impegnation cycles. ccuate flow simulations ae essential in finding the optimal pocess paametes. The infusion behaviou is stongly influenced by the fabic s pemeability, which is inhomogeneous in case of a daped fabic. The pemeability depends on the fabic s geomety, which is detemined by positions and diections of fibes and yans. This eseach focuses on the in-plane pemeability pediction of Non-Cimp Fabics (NCFs). The main defomation mechanism duing daping is shea, which influences the positions and diections of fibes and yans. s a consequence, shea influences the fabic s pemeability. shea dependent geometical desciption fo the intenal geomety of NCFs has been poposed by Loendesloot et al. [,2]. Fo this, inte bundle channels wee epesented by Stitch Yan induced fibe Distotions (SYDs). It was assumed that the flow though an NCF is mainly govened by flow though the inte bundle channels. Loendesloot [2] and Nodlund [4] developed a netwok flow model independently. Nodlund [4] analysed the flow in inte bundle channels by using a 3D flow model in nsys CFX. The esults seved as an input fo a netwok model. Loendesloot [2] epesented the inte bundle channels (SYDs) by D finite elements (F), to be assembled in

2 a netwok model as well. Model esults and expeiments [2] did not coespond well. Theefoe, this model will be extended with elements that descibe stitch yan elated egions. Machine diection xtenal channel SYD domain obstacles (a) One laye NCF, consisting of 2 plies. The uppe ply is tanspaent, such that the intesections of SYDs in the uppe ply with the lowe ply can be seen. (b) lemental epesentation of the piece of NCF in Fig. (a). Fig. Piece of unsheaed biaxial NCF, chaacteised by stitch distances 3 and 9B. NTWOR FLOW MODL The F fomulation fo a D element was obtained by using the continuity equation fo an incompessible slow viscous flow, afte which a weak fomulation was applied. Dacy s law fo one spatial dimension was used as a constitutive equation: dp Φ =, () μ dx in which the tems Φ,,, µ, p and x epesent volume flow, coss sectional aea, pemeability, viscosity, pessue and one Catesian coodinate, espectively. Subsequently, assuming a linealy vaying pessue ove an element and choosing the pessue intepolation function equal to the element shape function, esults in the following expession fo a D element: μl p = ϕ, (2) in which p, ϕ ae the nodal pessue and nodal flux vecto, espectively. netwok can be ceated by connecting D elements, which esults in a global system: M p = ϕ, (3) with M the system matix. Fig. (b) shows an elemental epesentation of a piece of NCF.

3 FLOW DOMIN Paticula egions in the NCF ae consideed to be a pat of the flow domain. These egions can be descibed by D elements (qn. 2). Finally, the elements may be assembled in a system (qn. 3) that epesents a piece of NCF. The consideed flow domains in the NCF in Fig. (a) ae: The wedge shaped channels (SYDs). SYDs in the uppe ply intesect SYDs in the lowe ply and fom continuous channels. Fig. 2 shows these intesections schematically, chaacteized by intesection distances D. The egion whee the stitch yans penetate the fabic, magnified in the lowe left cone of Fig.. The egions next to the stitch yans, which un fom one stitch yan penetation point to the othe stitch yan penetation point (magnified in the uppe ight cone in Fig. (a)). Stitch Yan Induced Fibe Distotions The connection and numbe of connections of intesecting SYDs depend on stitch yan penetation positions at (a+j, b+k), stitch distances and B, SYD lengths l l and l u and the fibe filament diections θ l and θ u, see Fig. 2. The supescipts l and u coespond to the lowe and uppe ply espectively. t the intesection points, nodes have to be assigned. Continuous egions in SYDs between those nodes can be descibed by a D element (qn. 2). (a) SYD pai of a bi-axial NCF, consisting of a SYD in the lowe and uppe ply. SYD ams ae numbeed fom till 4. The egion within the otated squae is epesented in Fig. 3c. (b) Stitch yan penetation points at (a+j,b+k) fo an unsheaed piece of NCF. Fig. 2 The SYD ams intesect each othe at intesection distances D in which sub and supe scipts efe to associated penetation points and the SYD am numbe espectively. The effective pemeability of an element, will be the effective pemeability of its epesenting pat of the SYD. Fig. 3(a) shows a pat of a SYD, which is assumed to be a wedge shaped channel with a constant height h. It could be consideed as an infinite amount of seially

4 connected channels of length dx with a spatial dependent coss sectional aea (x), such that the effective pemeability of this channel can be detemined with [2]: L d = L x ( ( )) (4) x 0 Results fom Motensen et al. [3] wee used to descibe the pemeability fo the spatial dependent coss section of the channel. These ae elations fo the hydaulic esistance of channels with a ectangula coss section, dependent on the compactness. The compactness is elated to the peimete and the aea of the channel s coss section. SYD Domain Obstacles The magnified egion in the lowe left of Fig. (a) shows a stitch yan that penetates the fabic. The stitch yans in a SYD distub the flow and could influence the oveall pemeability significantly. This egion can be descibed by the domain in figue Fig. 3(c), whee fou opening sufaces ae numbeed fom till 4. ach opening epesents the connection with the SYD-ams (Fig. 2(a)). The connections between the openings till 4 can be descibed by the assembly of six D elements (qn. 2), as is shown in Fig. 3(d). The elements descibe all possible connections between the openings. They contain an individual pemeability, so that each diection has a paticula flow esistance. The pemeability values wee detemined in a paametical study using nsys CFX, fo vaying dimensions b, d c, and h. xtenal Channels The magnified egion in the uppe ight of Fig. (a) shows a stitch yan, which uns fom one stitch yan penetation point to anothe stitch yan penetation point. When the NCF has been positioned between igid mould pats, the compession mechanism pushes this stitch yan in the fabic. s a esult, a channel will be ceated on both sides of this stitch yan and can be descibed by a D element (qn. 2). The coss sectional geomety of the channel in Fig. 3(b) has been idealised in ode to pefom a paametical study. It has been assumed that the coss sectional aea is constant ove the element's length and that pushing the stitch yan in the fibous ply could lead to defomation of the stitch yan's coss section. This leads to an elliptical coss section with majo axis 2e and mino axis 2f. gain, pemeability values wee detemined in a paametical study using nsys CFX, fo vaying dimensions e, f and g.

5 Channel (d) Channel with linea vaying width (SYD). (a) xtenal channel, ceated by pushing the stitch yan in the fabic. (c) Flow domain aound the penetating stitch yan. (b) D elemental epesentation of Fig. 3(c). Fig. 3 Flow domains fo which individual pemeability elations wee detemined. MODL IMPLMNTTION The netwok flow model was obtained by assembling all elements that descibe the diffeent flow domains, with a typical esult depicted in Fig. b. The popeties of the fabic unde consideation ae listed in Table. Table Popeties of the biaxial NCF that was used fo the infusion expeiments To detemine the pemeability of the fabic in the machine diection, a pessue diffeence was ceated by applying bounday conditions at the sides I and II (Fig. b). To detemine the pemeability of the fabic pependicula to the machine diection, a pessue diffeence was ceated by applying bounday conditions at the sides III and IV (Fig. b). Fo the intenal domain, nodes fulfil the estictionϕ = 0. Once the system is solved fo the unknown pessues, the effective pemeability can be detemined with:

6 = μl ϕ o Δp = μ L h ϕ (5) Δp l in which L is the length between sides with low and high pessue bounday conditions, Δ p the pessue diffeence between the applied high and low pessue and summation will be done ove all nodal fluxes ϕ, at nodes with high pessue bounday conditions o nodes with low pessue bounday conditions. The coss sectional flow aea is detemined by V / L, in which V is the total volume of the elements, i.e. the volume of the inte bundle channels. Results The model was solved seveal times, in which the fabic s height 2h (twice the height of a SYD in case of a biaxial NCF) and the maximum width b of the SYDs (Fig. 2a) wee vaied. The SYD lengths l wee 8, [mm]. The dimensions of the extenal channels wee detemined by micoscopic analyses and wee pocessed in the model. The esults in Fig. 4 show that the pemeability is vey dependent on the width of the SYDs. The height of the fabic influences the pemeability less. This height is elated to the height of the SYDs. The height h of the wedge shaped channel in Fig. 3a influences its effective pemeability less, compaed to the channel s widths b. Since the SYDs influence the effective pemeability of the fabic much, this behaviou is seen at this scale as well. (a) Pessue gadient diection in the fabic s machine diection. (b) Pessue gadient diection pependicula to the fabic s machine diection. Fig. 4 Results of a netwok as in Fig. b with the dimensions 0 and 25B (Fig. 2b). The model pedicts a highly anisotopic pemeability. Compaing Fig. 4a with Fig. 4b, the anisotopy is chaacteised by a diffeence of fou odes of magnitude. The pedicted anisotopic chaacte is mainly caused by the SYD intesection points, which ae moe ideally located fo infusion in the machine diection (Fig. 2b). The oientation of the elements that descibe the extenal channels (Fig. and Fig. 3b), influences the anisotopy as well.

7 XPRIMNTL VLIDTION To validate the netwok flow model, liquid infusion expeiments wee pefomed. simple vacuum infusion set-up was developed. The set-up oughly consists of two glass plates, within between the fabic to be infused (Fig. 5) with a viscous, Newtonian and incompessible liquid (maple syup). To seal the infusion domain, tacky tape has been positioned aound the infusion domain, afte which a tanspaent foil was timmed ove the uppe glass plate. The pessue diffeence was ceated by attaching a vacuum pump at the outlet tube. x = L (a) The fabic was infused between two glass plates. (b) Flow font and its position, visualized by using a fluoescent. Fig. 5 xpeimental set-up. Since no space o clamping system was used, the cavity height vaies along the infusion diection. Since the fibe volume faction is dependent on the cavity height 2h(x) and thus on the pemeability, the cavity height was measued duing the expeiments by using two height sensos. fomulation, based on seially connected pemeabilities was used to detemine the effective pemeability at the flow font position x=l (Fig. 5b): = = Δ Δ L Δx Δx L + L x x x= L Δx x (6) with the following effective coss sectional aeas: ( L ) = L L 0 ( x)dx ( L Δx) = L Δx L Δx 0 ( x)dx Δx = Δx L L Δx ( x) dx (7) Repeatedly applying qn. 6 fo evey flow font position L with a esolution that is detemined by Δx, esults in a position dependent pemeability. Diffeent elations fo wee used, i.e.:

8 ΦμL ( L ) = (8) Δp x= L fo which it was assumed that a steady state (qn. ) situation fo evey flow font position L was obtained. nothe elation is based on the flow font position L and its associated infusion time: 2 μl ( L ) = 2 tδp x= L (9) Only esults that wee obtained by combining qn. 6 and qn. 9 ae shown in this pape (Fig. 6). ll vaiables in qn. 8-9, wee acquied by sensos duing the infusion expeiments. Results Fo each fabic oientation (infusion in the machine diection and infusion pependicula to the machine diection), thee eliable expeiments wee executed. Fig. 6 shows the esults, in which a shaded aea with a single colou efes to one paticula expeiment. Duing the infusion expeiments, the cavity height was time dependent as well. Theefoe, the pemeability deteminations fo one expeiment wee done by using the initial cavity 2 h(x,t=t) and the final cavity 2 h(x,t=t2), which ae chaacteised by open en filled makes espectively in Fig. 6. The pemeability (x) as a function of the fabic s position x was obtained by using qn. 6. The (h) plots in Fig. 6 wee obtained by combining (x) and 2 h(x). The figues show a slightly inceasing pemeability, as the fabic s height inceases (fo a deceasing fibe volume faction). The vaiation between the diffeent expeiments and the time dependent cavity height ae the souces of the scatte. Howeve, these esults indicate in which ode ange, pemeability values of this biaxial NCF lie. Compaing Fig. 6a and Fig. 6b, the fabic s pemeability is nealy isotopic. (a) Pessue gadient diection along the fabic s machine diection. (b) Pessue gadient diection pependicula to the fabic s machine Fig. 6 Results fom infusion expeiments detemined by using qn. 6 and qn. 9.

9 CONCLUSIONS The netwok flow model poposed by Loendesloot [2] was extended by including stitch elated featues. The netwok flow model pedicts an anisotopic pemeability, while infusion expeiments show an isotopic pemeability. Howeve, fo the expeiments with infusion in the machine diection, Fig. 4a and Fig. 6a show good ageement in pemeability values (consideing the ode of magnitude). Since the netwok flow model is based on flow though inte bundle channels, the pedicted anisotopy of the pemeability and the isotopic pemeability fom the expeiments, indicate that flow between the fibe filaments (at mico level) is significant. Theefoe, it is needed to extend the netwok flow model, to account fo this type of flow. The model pedicts that the effective pemeability depends stongly on the mico geomety, in paticula on the width of the SYDs. Theefoe, when vaying the fabic s height, it is necessay to elate the netwok model to compaction mechanisms of an NCF that could descibe the dimensions of the SYDs. Some wok [, 2] was aleady done, which elated the size of the stitch yan and the shea angle of the fabic to the SYD dimensions. RFRNCS. R. Loendesloot, S.V. Lomov, R. kkeman and I. Vepoest, Cabon Composite based on Multiaxial Multiply Stitched Pefoms. Pat V: Geomety of Sheaed Biaxial Fabics, Composites Pat, Volume 37, pages 03 3 (2006). 2. R. Loendesloot, The Stuctue Pemeability Relation of Textile Reinfocements, PhD thesis, Univesity of Twente (2006). ISBN N.. Motensen, F. Okkels and H. Buus, Reexamination of Hagen-Poiseuille Flow: Shape Dependence of the Hydaulic Resistance in Micochannels, Physical Review, Volume 7, Numbe (2005). 4. M. Nodlund, Pemeability Modelling and Paticle Deposition Mechanisms Related to dvanced Composites Manufactuing, PhD thesis, Leleå Univesity of Technology (Octobe 2006).