Vacuum infusion of polymer composites

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(1)2001:52. LICENTIATE THESIS. Vacuum Infusion of Polymer Composites. H. Magnus Andersson. Licentiate thesis Institutionen för Maskinteknik Avdelningen för Strömningslära. 2001:52 • ISSN: 1402-1757 • ISRN: LTU-LIC--01/52--SE.

(2) Vacuum Infusion of Polymer Composites by. H. Magnus Andersson. Licentiate Thesis. Division of Fluid Mechanics Department of Mechanical Engineering Luleå University of Technology SE-971 87 Luleå Sweden. Luleå, December 2001.

(3) ABSTRACT The current trend towards an increased use of vacuum infusion for manufacturing of high performance fibre reinforced polymer composites has stressed the necessity of an advanced modelling of the process. Until recent years development in this area has mainly been based on trial and error and the behaviour of the method is therefore not fully understood. The basic principle of the vacuum infusion process is that a stack of dry fabrics is placed between a stiff mould half and a flexible and airtight bag. The bag is sealed to the mould expect at certain positions being open for resin supplies and outlets. Liquid resin then penetrates the stack by a reduction of the pressure at one or several positions in the formed cavity. After complete filling the pressure in the cavity is evened out by retaining the vacuum level at the outlets throughout curing of the resin. The overall goal of this research is to develop tools that ensure optimum and secure processing in practical work with vacuum infusion. The means to achieve this goal has so far been industry scale experiments, simple analysis and numerical simulations. The experimental part comprises fullscale impregnations where thickness variations are measured with an advanced optical metrology system and the out-of-plane flow front is monitored by means of colour marks in the reinforcement stack. Experimental findings are then incorporated in a numerical model including moving boundaries and two-phase flow through porous media based on a commercial software for computational fluid dynamics..

(4) PREFACE This work has been carried out under the supervision of Associate Professor Staffan Lundström and Associate Professor Rikard Gebart at the Division of Fluid Mechanics, Department of Mechanical Engineering, Luleå University of Technology, Sweden. The project is part of a cooperation with the Division of Polymer Engineering, Professor Lars Berglund, at Luleå University of Technology financed by the Swedish Research Council. The research is performed in close collaboration with SICOMP AB, Dr Anders Holmberg. I would like to thank my supervisors Staffan and Rikard for their support and encouragement together with Professor Håkan Gustavsson and my other colleagues at the Division of Fluid Mechanics for sharing the active and creative atmosphere we work in. The experimental parts of this work were realised with the help of Dr. Per Synnergren at the Division of Experimental Mechanics, Luleå University of Technology, and Runar Långström at SICOMP AB. Further invaluable practical help was provided by Allan Holmgren and Tomas Filipsson at Luleå University of Technology. Natalie, you complete me.. Magnus Andersson Luleå, December 2001.

(5) THESIS This thesis consists of the following three papers: Paper A H.M. Andersson, T.S. Lundström, B.R. Gebart and R. Långström, “Flow Enhancing Layers in the Vacuum Infusion Process”, Submitted for publication in: Polymer Composites. Paper B H.M. Andersson, T.S. Lundström, B.R. Gebart and P. Synnergren, “A New Method to Measure Thickness Variations in the Vacuum Infusion Process”, Submitted for publication in: Polymer Composites. Paper C H.M. Andersson, T.S. Lundström and B.R. Gebart, “Numerical Model for the Vacuum Infusion Process”, Submitted for publication in: International Journal of Numerical Methods for Heat & Fluid Flow..

(6) Paper A.

(7) FLOW ENHANCING LAYERS IN THE VACUUM INFUSION PROCESS. H. M. Andersson1,*, T.S. Lundström1, B.R. Gebart1, and R. Långström2. (1): Division of Fluid Mechanics, Luleå University of Technology, SE-971 87 Luleå, Sweden.. (2): Swedish Institute of Composites, P.O. Box 271, SE-941 26, Sweden.. *To whom correspondence should be addressed..

(8) ABSTRACT The current trend towards increased use of vacuum infusion moulding for large surface area parts has increased the interest for an advanced modelling of the process. Because the driving pressure is limited to 1 Atmosphere it is essential to evaluate possible ways to accelerate the impregnation. One way of doing this is to use layers of higher permeability within the reinforcing stack, i.e. flow enhancing layers. We will here present an experimental investigation of the flow front shape when using such layers. The through-thickness flow front was observed by making a number of colour marks on the glass-mats forming the reinforcing stack, which became visible when the resin reached their position. The in-plane flow front was derived from observations of the uppermost layer. It turned out that existing analytical models agree very well with the experiments if effective permeability data is used, that is, permeability obtained from vacuum infusions. However the fill-time was nearly twice as long as predicted from permeability data obtained in a stiff tool. This rather large discrepancy may be due to certain features of a flexible mould half and is therefore a topic for further research. The lead-lag to final thickness ratio is dependent on the position of the flow front and ranges from 5 to 10 for the cases tested. Interestingly the lead-lag has a maximum close to the inlet..

(9) INTRODUCTION The vacuum infusion moulding process has a high potential for manufacturing of high performance fibre reinforced polymer composites at a reasonable price. The process offers an excellent repeatability and it is cost effective for production of large surfacearea components in smaller series and prototype manufacturing (1, 2). In addition, by means of the closed moulding technique, environmentally harmful discharges are reduced almost completely compared to open methods, such as spray-up. Another advantage, as compared to open methods, is that the fibre content is generally higher and the void content lower, which result in better mechanical properties of the part manufactured. The basic principle of the method is that a stack of dry fabrics is placed between a stiff mould half and a flexible and airtight bag. The bag is sealed to the mould except at certain positions being open for resin supplies and outlets. Liquid resin is then forced into the stack by a reduction of the pressure at the outlets, while keeping the pressure atmospheric at the resin inlets. The difference between the ambient pressure and the resulting pressure gradient within the cavity will also result in a compaction force and a corresponding height variation of the stack. After complete filling the pressure in the cavity is evened out by retaining the vacuum level at the outlets when the resin supplies are closed.. The vacuum infusion technique is renowned and established since long. One version of this process was, for instance, patented already in 1950 (3). However, process development has until recent years mostly been based on trial and error. Hence, the behaviour of the process is not fully understood and the modelling is so far not sufficient (4, 5). It is obvious that an increase in part size and the corresponding increase in material value stresses the risk of severe economic losses in the case of an unsuccessful charge. A fundamental issue is therefore the development of tools that can guide the processing engineers in the choice of reinforcements, flow enhancing technique, injection strategy, injection parameters, etc for an optimum and reliable processing. One such tool is rule-of-thumb expressions. These kinds of expressions have been derived in connection to Resin Transfer Moulding (RTM) where the dry. A-1.

(10) reinforcement is placed in a rigid cavity. For instance, the time to impregnate a square shaped plate with side L can be found from (6):. t =C. L2 µ (1 − f ) ∆pK tot. (1). where C is a constant dependent on the injection strategy, µ the viscosity of the resin, f the fibre volume fraction, ∆p the driving pressure and Ktot the permeability of the reinforcement. If the perform consists of several layers with different permeability, the total permeability may be derived from (7, 8):. K tot =. K1 h1 + K 2 h2 + ....... + K n hn htot. (2). where h is the height and the subscripts 1, 2 and n denote first, second and final layer, respectively. Although Eq. 1 is derived for square shaped plates it is a valuable tool also for other geometries. Hence, on the first hand it can be observed that Eq. 1 and 2 are simple rule-of-thumb expressions that work well with RTM. On the other hand there are significant differences between RTM and vacuum infusion, e.g.:. i). The permeability varies considerably in the through-thickness direction due to flow enhancing layers/systems.. ii). The cavity thickness changes both in time and space due to the flexibility of the bag.. Also, preform permeability is often anisotropic in the plane, both in vacuum bag infusion and in RTM. With this in mind we have conducted an experimental study on the vacuum infusion process. The study comprises measurements of the flow front position and shape as a function of time and also measurements of the height of the cavity as a function of time and spatial coordinate (9). In addition to the actual interpretation of the equations above it is our hope that the work presented increases the overall understanding of the vacuum infusion process.. A-2.

(11) In this paper we focus on the experiments done on flow enhancing layers/resin distribution systems. The effect of flow layers was studied by Sun, et al. (11) by recording of the in-plane flow front position on both sides of a parallel plate tool (for vacuum assisted RTM). Naturally, the front took the lead on one side of the mould while on the other side the front lagged. With their lay-up the flow front lead-lag was less than expected and it remained close to constant during the filling of the mould. Diallo, et al. (12) observed both in-plane and through-thickness flow by means of electrically conductive wires inserted in the stack. They studied parallel flow under pressure between two stiff mould halves and observed that after a certain time, the shape of the through-thickness flow front remained fairly constant. In our experiments we use a typical vacuum bag infusion set-up with a stiff lower mould half and a flexible bag on top. By studying the in-plane and the through-thickness flow we are able to draw conclusions on the possible validity of Eq. 1 and 2 when applied to vacuum infusion.. EXPERIMENTAL PROCEDURES The experimental study is divided into three parts. In the first part, the used materials are characterized by permeability and viscosity measurements. In the second and third part the characterized materials are used to form a plate with the vacuum infusion process. In the second part the focus is on the position and shape of the in-plane flow front while the third part deals with the position and shape of the through-thickness flow front. The materials under consideration are the non-crimp stitch bonded (ncf) reinforcement Devold DBT-800-E06 and the continuous strand mat (csm) Vetrotex Unifilo U813 300, used as flow enhancing layers. The resin is the polyester Synolite 6811-N-1 from DSM Resins.. The in-plane permeability data was obtained with the multi-cavity parallel flow tool (13). The procedure is that samples, taken in three directions of the fabric, are loaded into three cavities. These cavities are coupled in parallel and consequently, the test liquid (a paraffin oil) can be driven in parallel through the samples with one pressure source. The flow rate through respective sample is then measured as a function of time and the permeability in each direction is obtained from Darcy’s law. From these three. A-3.

(12) values the principal permeability values and the principal direction of the permeability tensor can be calculated. The technique has been proven to produce stable and reliable results when the measurements are carefully performed (14, 15). This was also confirmed through repeatable measurements and comparison to data obtained earlier on the same fabric. The through-thickness tool and measuring procedure used has also been evaluated with good results for the case of cloths used in papermaking (16). Here the sample is compressed between two parallel plates. The liquid is then forced through a large number of capillaries drilled in the lower compression plate, through the sample and into capillaries drilled in the upper plate. In order to minimize the effect of edge flow, the permeability value is based on the flow through the centre of the sample. It must be noticed that although this is not in general the principal through-thickness permeability value it is often a very good estimate since most layers in the fabrics have a morphological symmetry about their surface plane. To ensure that the viscosity of the resin stayed constant it was measured as a function of time simultaneously with the injection experiments. This was done with a concentric cylinder geometry rheometer (Bohlin Visco-88BV). The basic lay-up for the study of the flow front shape is a 0.8 by 0.8 m2 large 8-layer stack of ncf and on top of this 0, 1, 2 or 3 layers of csm used as flow enhancing layers (see Fig. 1). The adopted injection strategy was point injection and radial flow, which means that resin is injected through the thickness at some central location of the stack while the pressure is reduced along the perimeter of the stack. In this set-up a circular hole was cut in the stack in order to obtain well defined in flow conditions and thereby simplifying the interpretation of the results. The diameter of the vertical hole going through all layers, including flow enhancing layers, was 12 mm. To achieve isotropic in-plane permeability each layer of reinforcement was shifted 90° with respect to the previous one. To minimize possible effects of pre-compaction, all pieces were taken randomly from the fabric-roll. When the layers had been properly placed on a glass plate, a transparent bag was sealed around the stack, the inlet was connected to resin and vacuum was applied to the outlets. With this set-up the in-plane flow could be monitored directly by observations of the actual flow front visible through the bag (see Fig. 2).. A-4.

(13) A most convenient material property made observation of the through-thickness flow front possible, namely that the used reinforcement and flow enhancing layers both become transparent when wetted by the resin. Colour marks were made on every second layer of the ncf, starting with the lowest one. Distributed in radial direction in four sets (60, 120, 180 and 240 mm from the inlet) and within each set slightly displaced in angular direction, not to obscure the view of each other, these marks gradually became detectable as the flow front advanced (see Fig.1 and 2). The requirements of maximum visibility and minimum disturbance of the flow was fulfilled by acrylic touch-up paint (for cars) in different colours. As a further improvement, a 12 mm thick glass plate, with adjustable illumination from below, was used as lower, stiff mould half. The glass plate considerably increased the transparency of the wetted parts of the stack. Video recording of the process also turned out to be most useful in the evaluation phase.. EXPERIMENTAL RESULTS. Following the outline in the previous section, the outcome of the characterization of the materials will be presented first, followed by the results from the in-plane measurement and ditto from the through-thickness flow front measurements. The three main results from the permeability measurements are (cf. Table 1): i) The permeability of the fabrics considered is nearly two orders of magnitude lower in the through-thickness direction as compared to the principal in-plane permeability values. This is a striking difference that naturally will influence the impregnation through the thickness. ii) The in-plane permeability of the csm is close to isotropic, while for the ncf the resistance to flow is about twice as high in the production direction of the fabric. iii) The permeability of the csm is about 10 times higher than for the ncf at the evaluated fibre volume fractions. These are similar to the average values from the experiments, which are 59% for the ncs and 21% for the csm. Consequently a stack of the two materials will have great variation in permeability both in direction and position. In contrast to the permeability the variation in viscosity of the resin as a function of time was only a few percent. Hence, most of the cross-linking started subsequent to complete filling. Also the alteration of the resin viscosity between the injections was fairly small (values between 170-190 mPas) where the differences could be traced to variations in temperature.. A-5.

(14) The in-plane flow front is in all cases close to circular, which is expected for the isotropic lay-up used. The actual radial flow front position as a function of time is however strongly dependent on the number of flow layers, see Fig. 3 and please notice that this is the position in the uppermost layer. Adding one and two layers considerably decrease the filling time, while the additional gain from a third layer is rather small.. As previously explained, the through-thickness flow front profiles were derived from measurements of the time when the colour marks became visible from the topside of the stack. This data, for the case with 3 layers of csm on top of 8 layers of ncf, is shown by the symbols in Fig. 4. From power functions fitted to the data, showed as curves in Fig. 4, the flow front position throughout the thickness, and thereby its shape, could then be found as a function of time, see Fig. 5 where the flow front profiles are shown for the cases of 1, 2 and 3 flow layers. The profiles are computed at a fill length of 240 mm but their shape is typical for all radial positions. Naturally, the three fronts will reach this position at different times since the number of flow layers strongly influence the filling time (cf. Fig. 3). The leading dot in each curve of Fig. 5 is the flow front position in the uppermost flow layer and the second dot is the position in the uppermost ncf, etc, cf. Fig. 1. It is evident that the lead-lag increases with the number of flow layers and that most of the lag from the top to the bottom takes place in the low permeability layers. Interestingly the lead-lag decreases with the radial position of the flow front cf. Fig. 6. This is somewhat surprising since at the inlet the lead-lag is zero and it must therefore have a maximum somewhere between the inlet and the first point of our measurement.. DISCUSSION: TOWARDS DEVELOPMENT OF GUIDELINES FOR THE VACUUM INFUSION PROCESS The work in our group is aimed at developing a set of guidelines for practical work based on sound scientific principles. So far we have obtained high-resolution data for the flow front shape with one material combination. Principally it is necessary to investigate other material combinations and to generalize the data before it is possible to approach the goal. However we may already at this stage scrutinize the results obtained and let us start with the actual flow front position in the uppermost layer. Interestingly. A-6.

(15) the experimental flow front position follows neatly (cf. Fig. 7) the by Adams, et al. (17) analytically derived expression:. r (R f ) =. R 2f  R  2 ln f 2  R R0   0.   4 K∆p  − 1 + 1 = t 2  ( 1 − ) µ f R 0  . (3). Eq. 3 describes the flow front position Rf as a function of time, t, for a Darcian and radial flow through a porous media with knowledge of the inner radius R0. Experimental data is expected to agree with Eq. 1 when a rigid mould is used, but in the current experiments one of the mould halves was flexible. The good fit to Eq. 3 consequently indicates that the flexibility of the mould can be unimportant and that Eq. 1 can be used to predict the time to fill certain geometries. The results from such an estimate for the experiments presented here are shown in Table 2. Apparently the resistance to flow is much larger than predicted from theory and the deviation increases with the number of flow layers. Hence it is reasonable to believe that the flexibility of the bag, to a large extent, influence on the results. Except for the actual movement of the bag during injection, see (9), it has been observed that the bag is drawn into the hole made in the middle of the fibre stack. In addition the bag may move into larger channels in the uppermost layer and therefore partly blocking the flow. There is also an uncertainty in the thickness of the reinforcing stack since the estimates in Table 2 are based on the final thickness of the part.. The filling time is strongly dependent on the number of flow enhancing layers. This was clearly seen from the experiments and is also obvious from a study of Eq. 2 which is reduced to:. K tot =. K f h f m + K r hr n h f m + hr n. (4). for a stack of uniform thickness consisting of m flow enhancing layers, each of thickness hf and permeability Kf, and n reinforcing layers, each of thickness hr and permeability Kr. Eq. 4 can be made even simpler if the permeability of the reinforcing fabrics is much less than that of the flow enhancing layers and if their total thickness is similar, i.e.: A-7.

(16) K tot =. Kf 1 + hr n. (5) hf m. Hence adding extra flow enhancing layers is unmistakably most efficient when m is small. It is also interesting to check the validity of Eq. 4 and 5. This is best done by calculating the actual averaged permeability of each fabric from the injections without flow layers and that with one flow layer. The obtained values can then be used to approximate the permeability of the injections with 2 and 3 flow layers, cf. Table 3. The overall good agreement indicates that we can predict the effect of any number of flow layers from just two vacuum infusions. It is also obvious that Eq. 4 gives a much better estimate than Eq. 5.. It is likely that a too large lead-lag may result in void formation and a poor quality of the laminate produced. In addition the resin will reach the outlet long before the whole stack is impregnated and a lot of resin must be used in order to get a perfect filling of the mould. There exists no criteria deciding when this may occur and the actual lead-lag is not a good measure of this. It is more likely that the ratio between the lead-lag and the thickness of the preform is the most critical parameter. This ratio is rather large but comparable for all injections performed, cf. Fig 8. Also, the measurements showed that the lead-lag decreases with the fill length, cf. Fig 5 and Fig 8. This is in agreement with the observations made by Sun, et al. (11). However the lead-lag is zero at the onset of impregnation and consequently a maximum must have been reached before the observations started. The maximum cannot be explained with existing theory developed for the RTM-process (18). Hence it is crucial that new models are derived that can predict the most critical position for the void formation.. A-8.

(17) CONCLUSIONS To conclude: •. Based on data from previous vacuum infusion mouldings, simple equations (Eq. 4 and 5) can be used to predict the effect of adding extra flow enhancing layers.. •. Predictions based on permeability data agree qualitatively to experimental result, however, to get quantitatively conformity new models must be developed.. •. The lead-lag to final thickness ratio is dependent on the position of the flow front and ranges from 5 to 10.. •. The lead-lag has a maximum close to the inlet.. ACKNOWLEDGEMENTS This work was supported by the Swedish Research Council for Engineering Sciences (TFR). The authors would like to thank the staff at the Swedish Institute of Composites where the experiments were done. Special thanks to Allan Holmgren at Luleå University of Technology for technical support.. A-9.

(18) REFERENCES 1. P. Lazarus, International SAMPE Symposium and Exhibition, Anaheim CA, USA (1996). 2. K. Bernetich, D. Briggs, and S. Viskocil, International SAMPE Technical Conference, Seattle WA, USA (1996). 3. Marco method, US Patent No 2495640 (1950). 4. C. Williams, J. Summerscales, and S. Grove, Composites Part A, 27A (1996). 5. F. C. Smith, Mat Tech, 14 (1999). 6. B. R. Gebart, C. Y. Lundemo, and P. Gudmundsson, Proceedings of the 47th Annual Conference of the Society of Plastics Institute, Cincinnatti, USA (1992). 7. J. Bear, Dynamics of Fluids in Porous Media, Dover Publications Inc. New York (1972). 8. B. R. Gebart, P. Gudmundsson, L. A. Strömbeck, and C. Y. Lundemo, Proceedings of the 8th International Conference on Composite Materials, Honolulu, USA (1991). 9. H. M. Andersson, T. S. Lundström, B. R. Gebart, and P. Synnergren, In preparation. 10. A. Hammami, and B. R. Gebart, Polymer Composites, 21 (2000). 11. X. Sun, S. Li, and L. J. Lee, Polymer Composites, 19 (1998). 12. M. L. Diallo, R.Gauvin, and F. Trochu, Polymer Composites, 19 (1998) 13. B. R. Gebart, and P. Lidström, Polymer Composites, 17 (1996). 14. T. S. Lundström, B. R. Gebart, and E. Sandlund, Polymer Composites, 20 (1999). 15. T. S. Lundström, R. S. Stenberg, R. Bergström, H. Partanen, and P-A. Birkeland, Composites: Part A, 31 (2000). 16. T. S. Lundström, S. Toll, and J. Håkanson, Submitted for publication, Transport in Porous Media. 17. K. L. Adams, W. B. Russel, and L.Rebenfeld, Int. J. Multiphase Flow, 14 (1988). 18. B. R. Gebart, Journal of Composite Materials, 26 (1992).. A - 10.

(19) TABLES. Table 1. Principal permeability values as derived from measurements. Fabric. f (%). Kx *10. -11. θ1). Ky 2. [m ]. *10. -11. 2. [m ]. (˚). Kz *10. -11. (m2). ncf. 52.5. 9.20. 5.06. -3.8. -. ncf. 57.2. 5.03. 2.31. -6.6. -. ncf. 58.5. -. -. -. 0.081. ncf. 64.6. -. -. -. 0.019. csm. 26.2. 90.6. 84.1. 16.4. -. csm. 28.6. 63.8. 59.7. 39.9. -. csm. 26.3. -. -. -. 3.0. csm. 29.1. -. -. -. 1.5. 1) Angle between the production direction of the fabric and the direction of Ky.. A - 11.

(20) Table 2. Comparison between model and experiments. Final h csm/ncf. Kmod1). Kexp2). *10-3 [m]. *10-11 [m2]. *10-11 [m2]. 0. 0.0/4.35. 3.40. 2.01. 1.7. 1. 0.59/4.21. 23.6. 12.0. 2.0. 2. 1.10/4.35. 32.1. 17.6. 1.8. 3. 1.75/4.25. 50.9. 22.7. 2.2. No. of csm. 1) Eq. 2, Tab. 1, 2) Eq. 3, R0 = 0.006. Table 3. Applicability of Eq. 4 and Eq. 5. No. of csm. Kexp *10. -11. Kmod2 2. [m ]. *10. -11. Kmod3 2. [m ]. *10-11 [m2]. Eq. 3. Eq. 4. Eq. 5. 0. 2.01. 2.01. 2.01. 1. 12.0. 12.0. 12.0. 2. 17.6. 18.4. 19.7. 3. 22.7. 25.7. 28.5. A - 12. Ratio.

(21) FIGURES. flow front. wetted material. bag. 11. csm. 9 flow. 7 5. ncf. 3 glass table. 1 colour marks. Figure 1. Schematic side view of lay-up with three layers of csm on top of eight layers. of ncf. Resin flow from left to right. The four color marks in the wetted region behind the flow front are visible from above, while the four color marks in the dry region still are invisible.. A - 13.

(22) Figure 2. Flow front observations by color marks in stacking on illuminated glass table.. Radial distance between each set of marks is 60 mm. The quarter-circle shaped lines are instantaneous in-plane flow fronts marked with a pen on the bag during injection.. A - 14.

(23) Fill length (mm). 25 20 15 No. of csm 0 1 2 3. 10 5 0 0. 500. 1000. 1500. 2000. 2500. Time (s) Figure 3. Fill time dependence when changing the number of flow layers.. A - 15.

(24) 300. Fill length (mm). 250 200 Layer No. 11 7 5 3 1. 150 100 50 0 0. 100. 200. 300. 400. 500. 600. 700. Time (s). Figure 4. Results from tracking of color marks for stack with 3 flow layers (layers 9, 10. and 11) on top of 8 reinforcement layers (layers 1 to 8). Symbols are experimental times, curves are power functions fitted to data. The curve through the solid squares show the fill length vs time for the lowest layer of ncf (layer 1) and the curve through the solid circles show the fill length vs time for the top layer of csm (layer 11). The remaining curves show fill length vs time for the intermediate layers of ncf (layers 3, 5 and 7).. A - 16.

(25) 11. Layer No.. 9 7. No. of csm 1 2 3. 5 3 1 230. 240. 250. 260. 270. 280. Fill length (mm) Figure 5. Steady state flow front profiles for 1, 2 and 3 flow layers, 240 mm from the. inlet.. A - 17.

(26) 60. Lead-lag (mm). 50 40 30 20 10. No. of csm 1 2 3. 0 100. 150. 200. Fill length (mm) Figure 6. Flow front lead-lag vs fill length.. A - 18. 250. 300.

(27) No. of csm 0 1 2 3. 10000. r 5000. 0 0. 600. 1200. 1800. t (s) Figure 7. Experimental data plotted according to Eq. 3.. A - 19. 2400.

(28) 12 10. Ratio. 8 6 No. of csm. 4. 1 2 3. 2 0 50. 100. 150. 200. Fill length (mm) Figure 8. Lead-lag to final thickness ratio.. A - 20. 250. 300.

(29) Paper B.

(30) A NEW METHOD TO MEASURE THICKNESS VARIATIONS IN THE VACUUM INFUSION PROCESS. H. M. Andersson1,*, T.S. Lundström1, B.R. Gebart1, and P. Synnergren2. (1): Division of Fluid Mechanics, Luleå University of Technology, SE-971 87 Luleå, Sweden.. (2): Division of Experimental Mechanics, Luleå University of Technology, SE-971 87 Luleå, Sweden.. *To whom correspondence should be addressed..

(31) ABSTRACT A new method to measure the movement of the flexible bag used in vacuum infusion is presented. The method is based on an in-house developed stereoscopic digital speckle photography system (DSP). The advantage with this optical method, which is based on cross-correlation, is that the deflection of a large area can be continuously measured with a great accuracy (down to 10 µm). The method is at this stage most suited for research but can in the long run also be adopted in production control and optimisation. By use of the method it was confirmed that a ditch is formed at the resin flow front and that there can be a considerable and seemingly perpetual compaction after complete filling. The existence of the ditch demonstrates that the elasticity of the reinforcement can be considerably reduced when it is wetted. Hence, the maximum fibre volume fraction can be larger than predicted from dry measurements of perform elasticity. It is likely that the overall thickness reduction after complete filling emanates from lubrication of the fibres combined with an outflow of the resin. Besides the cross-linking starts and the polymer shrinks. Hence, the alteration in height will continue until complete cross-linking is reached..

(32) INTRODUCTION In vacuum infusion a dry and elastic reinforcement is put between a stiff mould half and an airtight and flexible bag. Resin is then forced into the reinforcement by a reduction of the pressure at one or several positions in the formed cavity. A combination of the elasticity of the reinforcement and a variation in pressure inside the cavity results in a deformation of the bag during processing and the volume available for the resin to flow will change accordingly. The motion of the bag has been observed (1) and measured (2) in earlier work. The LVDT-technique used in (2) works well for point wise measurements of the deformation at single positions. It can, however, be more important to continuously measure the deformation of the whole bag as a function of time, in research projects and during production. This is certainly necessarily for process control.. There are a several non-contact optical methods being used to measure surface displacements. For vacuum infusion the method should be designed to measure the out-of-plane motion, with an accuracy of hundreds of a millimetre but with the possibility to measure deflections up to a few millimetres. Besides, it should be possible to measure on a opaque or semi-opaque surface. If the sensitivity required is in the order of a few hundreds nanometers, interferometer methods such as electronic speckle pattern interferometry (ESPI) (3) is adaptable. The drawback, when it comes to vacuum infusion, is that the largest displacement measurable with a typical ESPI is in the order of a few microns. Another method, scanning laser triangulation, has two drawbacks making it inappropriate for vacuum infusion. First, the sensor moves over the surface measuring one point at the time. Consequently, measurements of moving object will be contaminated with systematic errors. Secondly, most bags used in vacuum infusion are semi-opaque for laser radiation even if they are colored. This result in volume scattering of the reflected laser light and it is therefore difficult to, with high accuracy, measure the position of the bag. All these problems can be avoided by usage of stereoscopic digital speckle photography (DSP) (4). This is an image processing technique, which is field measuring and uses just white light to illuminate the object surface (5-9). In essence, a random pattern is produced on the. B-1.

(33) surface of the specimen and the motion of this pattern is photographed. By crosscorrelating small sub-images of ‘before’ and ‘after’ images of the random pattern, deformation maps can be deduced.. We will here show that it is possible to continuously measure the deformation of a bag used in vacuum infusion with DSP. We will also use the method to measure the deformation taking place during filling and post compaction.. METHODS AND MATERIALS Measuring method The basic principles of stereoscopic DSP will here be outlined and the special solutions for vacuum infusion will be described. In standard DSP two digitised images are captured of a random intensity pattern (speckled images) under motion. The immediate in-plane displacement between the exposures is then derived by usage of a filter proposed by Sjödahl (5). The filter divides each image into sub-images and respective sub-image is compared to its counterpart in the other image by crosscorrelation. The correlation is carried out in the spectral domain by multiplying the conjugate of the spectrum of one of the sub-images, HS1* for instance, by the spectrum of the other sub-image, HS2 , according to: c ( p, q ) = F. where F. −1. −1. ( H S*1 H S 2 ) ,. (1). is the inverse Fourier transform operator and c(p,q) is the resulting discrete. cross-correlation between the sub-images. The 2-D translation between the two exposures is then ideally given by the location of the maximum correlation peak in c(p,q). In reality additional operations are required to get the in-plane motion. It may, for instance, be required to add correction operations to take care of poor overlap between the images (5).. In this particular case we are mainly interested to measure height variations or out-ofplane movements. We therefore need to apply a stereoscopic imaging system B-2.

(34) consisting of two cameras (4, 9). Stereovision is then achieved by a translated lens method meaning that: i) The cameras are aligned so that the object plane, the lens planes and the image planes are all in parallel. ii) Both cameras are enabled to view the same area of the object only by a movement of the camera lenses sideways and perpendicular to its optical axis. On a theoretical point of view we may consider the optical system shown in Fig. 1 and notice that the index i = 1, 2 denote respectively camera system. The orientations of the lens coordinate systems L(i), and of the detector coordinate systems D(i), are related to the orientation of the world coordinate system W, by the rotation matrices RL(i) and RD(i), respectively:. R L(i ).  −1  = 0 α (2i ) . 0 −1 −α. (i ) 1. α (2i )   − α 1(i )  1 . and R D(i ).  1  =  β 3(i ) − β (2i ) . − β (3i ) 1 β. (i ) 1. β (2i )   − β1(i )  1 . (3). where coordinate systems L(i), i=1,2 has been rotated by (α1(ι), α2(ι), π) around the (x, y, z) axes of W. The angles (β1(ι), β2(ι), β3(ι)) are the rotation angles of coordinate system D(i) around L(i). Now let the origin of L(i) be expressed in the world coordinate system, W, by the vector o(i)=(ox(i), oy(i), oz(i)), and let the origin of D(i) be expressed in the lens coordinate system, L(i), by the vector c(i)=(c1(i), c2(i), c3(i)). Then it can be shown that the relationship between the detector coordinates (X(i), Y(i)), and the corresponding point P(x, y, z) on the object expressed in terms of world coordinates is given by the following equations where we have dropped the camera index. (i). simplicity: ~ x (β1c2 − β 2 c1 − c3 ) − ~ y β 3c3 + c3 α 2 z c3 ~ x − ~2 Φ , ~ z z ~y (β c − β c − c ) + ~ x β 3 c 3 − c 3 α 1 z c 3 ~y 1 2 2 1 3 Y = − c 2 + β 3 c1 + − ~2 Φ . ~ z z X = −c1 − β3 c2 +. where ~ x = ( x + ox ) , ~ y = ( y + oy ). and ~z = ( z + o z ) .. B-3. (4a) (4b). for.

(35) and where. Φ. is defined, using the focal length f and the distortion factor. Ψ. of the. camera lenses, as. x − β1 ~ y − α 2 x + α1 y + Φ = β2 ~. (. Ψ ~2 ~2 x +y f +~ z. ),. (5). Let the object be subjected to a deformation. Then the motion of the object point P(x, y, z) will be described by the deformation vector (u, v, w). The cameras will register the apparent 2-D deformation described by (U(i), V(i)) i=1,2, which can be related to the true deformation vector by.  β1c2 − β 2c1 − c3 c3   3~ x2 + ~ y 2   ~ ~ ~ U = u − ~ 2 2 β 2 x − β1 y + α1 y − α 2 ( x + x ) + Ψ ~ ~   + z +w z    f + z   βc c  2~ x~ y  + v  ~ 3 3 − ~32 − β1~ (6a) x + α1 ~ x +Ψ + f +~ z   z + w z  ~  α c x (β1c2 − β 2c1 − c3 ) − ~ y β 3c3 + zα 2c3 c3  ~ x3 + ~ x~ y 2    + w ~ 2 3 − + Ψ 2  ~ ~ z (~ z + w) z 2  ( f + ~ z )   z + w. βc c  2~ x~ y  V = u  ~ 3 3 − ~32 − β 2 ~ x +α2~ x +Ψ + f +~ z   z + w z   β1c2 − β 2c1 − c3 c3   3~ x2 + ~ y 2   ~ ~ ~    + (6b) − ~ 2 2β 2 x − β1 y + α1 y − α 2 (x + x ) + Ψ + v ~ ~ + z +w z  f z     ~ x (β1c2 − β 2c1 − c3 ) − ~ y β 3c3 + zα 2c3 c3  ~ x3 + ~ x~ y 2   α c   + w ~ 2 3 − + Ψ 2  ~ ~ z (~ z + w) z 2  ( f + ~ z )   z + w where the camera index. (i). still is omitted for simplicity. A measurement with the. stereocamera system gives rise to a set of eight equations, similar to Eq. (4a) through Eq. (6b), and only the six unknowns, (x, y, z) and (u, v, w), are searched for. Hence, if the geometry of the triangulation system, focal length of the lenses and the distortion coefficient of the lenses are known from calibration, both the shape and the 3-D deformation can be calculated from these equations through an iterative non-linear optimisation process (4).. B-4.

(36) The system described is the core of the method to measure the deformation during vacuum infusion. However, to make the system work properly in this context certain actions had to be realized. Several methods to produce and apply dots of the right size (approximately 1 mm2) on the bag were evaluated. An acceptable pattern was achieved by manually drawing dots using a black marker pencil or a ball shaped dot brush on a white background (ordinary spray paint). However, this method is far to time consuming and operator dependent to be satisfactory. Sifting confetti-like flakes over fresh paint is a fast method to produce excellent patterns but it failed for this application since the surface of the flakes were too glossy. With the requirements of optical properties and a fast and operator independent application, the final solution was a matt foundation layer of black spray paint (Alcro Servalac Spray 552) to eliminate reflections and white granite imitation spray paint (Alcro Servalac Spray Granite 581) to generate the speckle pattern.. Two CCD-cameras, each equipped with a 25-mm lens, horizontally separated by 430 mm were mounted 1660 mm vertically above the moulding tool on an aluminium profile purpose-built holding frame. With this set-up, a square area of 250 mm side length was monitored for out-of-plane displacements up to 100 mm with a noise level from the stereo-DSP system itself of less than 10 microns. The system was calibrated before each new run.. Impregnation: Materials, Lay-up and Injection strategy. A non-crimp fabric (ncf), Devold DBT-800-E06, was chosen as base in the lay-up. On top of the ncf, a continuous strand mat (csm), Vetrotex Unifilo U813 300, was used to enhance the flow. The horizontal extent of the stack was 800 by 800 mm2. The chosen resin was the polyester Synolite 6811-N-1 from DSM Resins.. For the stacking of the ncf, two sequences were investigated, one with isotropic inplane permeability and one with anisotropic in-plane permeability. The isotropic inplane permeability was achieved by shifting each layer of reinforcement 90° with respect to the previous one. For the anisotropic in-plane permeability, all layers were aligned with respect to the roll direction. In both cases 8 layers of ncf was used and different numbers of flow enhancing layers were applied on top in different runs, namely 0, 1, 2 and 3 for the isotropic case and 1 and 2 for the anisotropic case. In all B-5.

(37) this gave six different combinations to be evaluated. Pre-compaction and other possible effects of storage were minimized by taking all pieces randomly from the fabric-roll.. After reducing the pressure along the perimeter of the stack, resin was injected through a vertical hole in the tool at the centre of the stack, i.e. point injection with radial flow. In order to obtain well defined in flow conditions, a corresponding circular hole of 12 mm in diameter had been punched in the centre of each layer, including flow enhancing layers. The injections were carried out until complete saturation of the stack. Then the resin supply was cut off, keeping the vacuum level on the outlets throughout curing of the resin.. RESULTS AND DISCUSSION For all measurements it was possible to obtain a full out-of-plane displacement field of the area of observation (the 250 by 250 mm2 area). This is exemplified in Fig. 2 being the result of an instant measurement 5 minutes after the injection started for an anisotropic ncf lay-up with two layers of csm on top. The inlet is in the origin to the left in the figure, and the resin is flowing out towards the perimeter. Starting from the origin and moving outward there is a reduction in thickness in all directions but as we approach the resin flow front the thickness of the stack instead increases and a ditch is formed, similar to observations in (2).. To take the discussion further the position of the bag is now averaged over the angular direction and it is presented at several points of time during impregnation; cf. Fig. 3. The results still originate from the injection with the anisotropic stack with two flow layers and the lowest height has been set as the zero reference. Firstly, all results are secured at about an order of magnitude above noise level of the DSP system; cf. the previous section. Secondly, the absolute height of the ditch varies with time but is about 50 µm. When comparing this result to the other experiments it can be concluded that the ditch becomes more pronounced the greater the number of flow layers added to the stack, while not at all present in their absence. Consequently, nearly all of the B-6.

(38) local deformation forming the ditch takes place in the flow layer. By definition this is the layer where most of the resin flows and the formed ditch therefore hinders the impregnation. In the current case the reduction in height is about 4%, which almost certainly gives a much larger decrease in the permeability of the flow layer. Hence this phenomenon should either be minimized or it must be considered when doing models or simulations of the vacuum infusion process. Thirdly, the ditch moves towards the perimeter during the injection. This movement follows neatly the flow front of the resin, se Fig. 3 where the through thickness flow front lead-lag (10) 45degress to the principal directions is indicated as horizontal lines at the bottom of the figure (11). The close relationship between the ditch and the flow front indicates that the elasticity of the stack, or actually the elasticity of the flow layers, decreases when the resin wets the fibres.. The detailed study presented above showed that a ditch is formed and that it moves with the resin flow front. However it is also of interest to measure the overall alteration in thickness of the fibre stack. In the case presented in Figure 2 and 3 the resin supply was cut 15 minutes after the injection started, but the vacuum level at the outlet was retained until the processing was complete. This resulted in a seemingly perpetual reduction in thickness of the fibre stack, cf. Figure 4. The curves in Figure 4 are obtained with the same angular averaging method as before but now with the thickness before impregnation as zero-height reference. The reduction in thickness can probably not be attributed to shrinkage of the resin. A parallel measurement on the actual resin with curing agent showed an almost constant viscosity throughout the 50 minutes. The plausible reason for the reduction in height with time is instead that the elasticity of the fibre preform is further reduced and the resin is redistributed and flows out through the outlets. The overall decrease in thickness is rather large, about 10% of the total final thickness as shown in Fig. 4. Similar results hold for all investigated cases, except again for when no flow layers were used. It is thus clear that the flow layers are responsible for the post packing, and consequently an increased strength to weight ratio of the final laminate. Naturally any thickness reduction will stop during the curing of the resin and a final thickness will be achieved.. B-7.

(39) CONCLUSIONS In conclusion we have presented a new method, based on a DSP-system, to measure thickness variations in the vacuum infusion process. With the method it is possible to in-situ measure the whole displacement field of the flexible bag. This feature enables a use of this method in production control and optimisation. The actual measurements have furthermore highlighted several characteristics of the vacuum infusion process. The existence of a ditch trailing the flow front indicates that lubrication from wetting of the fibres has a significant importance that must be considered in modelling of the process. The continuous reduction in height with time identifies a time dependent elasticity of the fibre preform and a redistribution of resin after closure of the resin supply. It is also elucidated that the ditch and the post packing are effects of the flow enhancing layers. From a flow enhancing point of view any decrease in thickness of the flow enhancing layers clearly defeats the purpose of flow enhancing layers, while from a material characteristic point of view, this obviously increases the strength to weight ratio of the final laminate. Hence the evident solution is a flow enhancing layer that collapses at the end of the filling of the mould.. ACKNOWLEDGEMENTS The authors would like to thank the staff at the Swedish Institute of Composites where the experiments were done. Our special thanks to Allan Holmgren at Luleå University of Technology for technical support. This work was supported by the Swedish Research Council for Engineering Sciences (TFR).. B-8.

(40) REFERENCES 1.. A. Hammami and B. R. Gebart, “Analysis of the Vacuum Infusion Molding Process”, Polymer Composites, 21, 28-40, (2000).. 2.. C. D. Williams, S. M Grove and J. Summerscales, “The compression response of fibre-reinforced plastics during manufacture by the resin infusion under flexible tooling method”, Composites Part A, 29A, 111-114, (1998).. 3.. O. Løkberg, “Electronic speckle pattern interferometry”, Physics in Technology 11,16-22, (1980).. 4.. P. Synnergren and M. Sjödahl, “A stereoscopic digital speckle photography system for 3-D displacement field measurements”, Opt. Lasers Eng., 31, 425433, (1999).. 5.. M. Sjödahl, “Accuracy in digital speckle photography”, Appl. Opt., 36, 28752885, (1997).. 6.. T. C. Chu, W. F. Ranson, M. A. Sutton and W. H. Peters, “Applications of digital image correlation techniques to experimental mechanics”, Expr. Mech. 25, 232-244, (1985).. 7.. S. R. McNeill, W. H. Peters and M. A. Sutton, “Estimation of stress intensity factor by digital image correlation”, Eng. Fracture Mech. 28, 101-112, (1987).. 8.. P. Johnsson, “Strain field measurements with dual-beam digital speckle photography”, Opt. Lasers Eng. 30, 315-326, (1998).. 9.. J. D. Helm, S. R. McNeill and M. A. Sutton “Improved three-dimensional image correlation for surface displacement measurements”, Opt. Eng. 35, 1911-1920, (1996).. 10.. X. Sun, S. Li and L. J. Lee, “Mold Filling Analysis in Vacuum-Assisted Resin Transfer Molding. Part 1: SCRIMP Based on a High-Permeable Medium” Polymer Composites, 19, 807-817, (1998).. 11.. H. M. Andersson, T. S. Lundström, B. R. Gebart and R. Långström, Submitted for publication.. B-9.

(41) FIGURES. Figure 1. Schematic diagram over the stereoscopic camera set-up used in the study.. B - 10.

(42) 0.2. w [mm]. 0.15 0.1 0.05 0 0 200. 100 100. 200 0 x [mm]. y [mm]. Figure 2. Out-of-plane displacement field obtained with stereoscopic DSP system.. B - 11.

(43) Figure 3. Bag positions during injection with corresponding through-thickness flow. fronts as horizontal lines.. B - 12.

(44) Figure 4. Thickness before, during, and after injection.. B - 13.

(45) Paper C.

(46) NUMERICAL MODEL FOR THE VACUUM INFUSION PROCESS. H.M. Andersson*, T.S. Lundström, and B.R. Gebart. Division of Fluid Mechanics, Luleå University of Technology SE-971 87 Luleå, Sweden. *) To whom correspondence should be addressed.

(47) ABSTRACT. The focus is set on the development and evaluation of a numerical model describing the impregnation stage of a method to manufacture fibre reinforced polymer composite, namely the vacuum infusion process. Examples of items made with this process are hulls to sailing yachts and containers for the transportation industry. The impregnation is characterized by a full three-dimensional flow in a porous medium having an anisotropic, spatial- and time-dependent permeability. The numerical model has been implemented in a general and commercial Computational Fluid Dynamic software through custom written subroutines that: i) couple the flow equations to the equations describing the elasticity of the fibre reinforcement, ii) modify the momentum equations to account for the porous medium flow and iii) remesh the computational domain in each time step to account for the deformation by pressure change. The verification of the code showed excellent agreement with analytical solutions and very good agreement with experiments. The numerical model can easily be extended to more complex geometry and to other constitutive equations for the permeability and the compressibility of the reinforcement..

(48) INTRODUCTION. There are numerous ways to manufacture fibre reinforced polymer composites ranging from hand lay-up in small series to fully automatic pressing of components to the automotive industry. A method that is being increasingly used for production in small series is the vacuum infusion process. The advantage with this method is that large and high strength items can be produced in relatively low cost tooling and with low emissions of harmful substances. Examples of products are hulls to sailing yachts and containers for the transportation industry. The vacuum infusion technique is well known and established since long. The first patents are registered already in 1950 [1]. Still, process development has until recent years mainly been based on trial and error and the behaviour of the process is therefore not fully understood and the modelling is so far not sufficient [2, 3]. The risk of severe economic losses in the case of an unsuccessful charge is augmented with an increased part size and the corresponding increase in material value. An essential requirement for an optimised and reliable processing is therefore the development of tools that can guide the processing engineers in the choice of reinforcements, flow enhancing technique, injection strategy, injection parameters, etc.. The fundamental principle of the vacuum infusion process is that dry reinforcement is placed on a stiff mould half and covered with a flexible and airtight bag. The bag is then sealed to the mould except at certain positions being open for resin supplies and outlets. By keeping the pressure atmospheric at the resin inlets and reducing the pressure at one or several positions in the formed cavity, liquid resin is forced to impregnate the stack. A further result of the difference between the ambient pressure and the pressure within the cavity is a compaction force and a corresponding compression of the elastic stack. Once the mould is sufficiently filled, the pressure in the cavity is evened out and the resin is cured. In order to shorten the cycle-time, flow enhancing methods are often used with the vacuum infusion process. This may result in an important out-of-plane flow at the flow-front that is often neglected in the modelling of the well-characterised process Resin Transfer Moulding (RTM). Another difference from RTM is the variation of height of the cavity as a function of the local pressure, implying that the flow and compaction equations become coupled. C-1.

(49) To increase the understanding of the vacuum infusion process we have performed a study of real mouldings in a simple geometry [4, 5]. In particular, a Digital Speckle Photography system has been used to measure the overall movement of the fibres and the through thickness flow front has been measured with flow visualisation, video recording and image analysis. The experimental study was confined to one geometry and one particular material combination. A generalisation of the results to form prevalent conclusions and rules-of-thumb is therefore inevitable. One step towards a generalisation was presented in [6] where a one-dimensional model was derived. In this paper we move further by performing simulations on the vacuum infusion process in a general 3D Computational Fluid Dynamics (CFD) code. The advantage of taking such an approach is that the calculations are based on equations tested in numerous applications, that we can do simulation in almost any geometry, and that we, quite easily, can extend our simulations to deal with, for instance, other constitutive equations and additional phenomena.. ANALYTICAL BACKGROUND. During all fabrication of fibre reinforced composites the resin is, in some way, forced into the fibre network. In order to predict the time for the resin to fill a certain volume of pore space between fibres and the corresponding filling pattern, analytical expressions and mould filling simulation codes have been developed [7-10]. These tools are mainly designed for the Resin Transfer Moulding process with stiff moulds and are based on conservation of mass and Darcy’s law which in two dimensions may be expressed as:. u i ,i = 0. ui (1 − f ) = −. K ij. µ. p, j. i,j = 1,2. (1a-b). where u is the volumetric flux density (also called superficial velocity) in the fibre preform, f the fibre volume fraction, K the permeability of the fibre preform, µ the viscosity of the resin and p the pressure. The combination of Eq. (1a-b) applies to. C-2.

(50) flow in porous media as long as the Reynolds number is sufficiently low, the fibres are stationary and the fluid is incompressible and can be modelled as Newtonian. In the vacuum infusion process the fibres are allowed to move in the through thickness direction and the equations are modified accordingly [6]:. (uh )i ,i = − ∂h ,. p + pr = po , K ij = g1ij (h ) and h = g 2 ( pr ). ∂t. (2a-d). where h is the height of the stack, pr is the pressure on the reinforcement, po is the ambient pressure and g1,2 are constitutive functions. These functions can be derived experimentally from permeability and compaction measurements. Fortunately only a few measurements are required since a number of theoretical models have been proposed. Two models for the permeability were presented by Gebart [11] for flow along and perpendicular to a perfect arrangement of fibres. Both these models are expressed in terms of the fibre volume fraction, f and the fibre radius R according to:. 8 (1 − f ) 2 R , K // = c f2 3.  K ⊥ = C  .  f max − 1  f . 5/ 2. R2,. f =. nζ hρ. (3a-c). The maximum fibre volume fraction fmax and the two constants c and C are dependent on the actual fibre arrangements, e.g. quadratic or hexagonal packing, n is the number of layers of the fabric, ζ is the surface weight of each layer fabric and ρ the density of the fibres. The first of these equations is based on the hydraulic radius and can be recognized as the often-used Kozeny-Carman equation. The relation between the pressure on the reinforcement and the height of it is often written in the following form [12]:. (. pr = kE f m − f 0m. ). (4). where k and m are constants, E the stiffness of the fibres and f0 the fibre volume fraction of the reinforcement without any load. By a micromechanical analysis it has been shown that the constant m is equal to 3 for 3D wads and 5 for planar networks [12]. Many reinforcements used in vacuum infusion do, however, consist of. C-3.

(51) continuous fibre bundles. For such materials m has empirically been given values spanning from 7 to 15.5 [13]. It has further been shown that the elasticity is reduced by lubrication of the fibres when the reinforcement is impregnated with resin [4]. To be able to account for the new elastic response in the numerical model, Eq. (4) must be adjusted. A true modification can be derived from compaction measurements of wetted and dry reinforcements. We will however at this stage take a heuristic approach and use the following relationship:. (. pr = kE f m − ( f 0 + κ ). m. ). (5). where κ accounts for the softening of the reinforcement and is consequently zero for a dry fabric and larger than zero for a wetted fabric.. The equations required to model the impregnation taking place during vacuum infusion have now been outlined. These equations were previously solved in a quasistationary way with flow in one direction only [6]. However to get a complete solution another approach must be used. We will here present such an approach based on a general CFD-code.. NUMERICAL MODEL. A general application of a numerical solution method to a physical problem involves the choice of mathematical model, discretization method, coordinate system, numerical grid, iterative methods, etc. Here, the eligibility is defined to the components available in the commercial and general CFD software CFX-4 from AEA Technologies [14]. CFX-4 is a finite-volume based code using a structured multiblock grid. The code offers a number of choices regarding, for instance, the mathematical models and iterative methods and it handles moving boundaries by the Volume of Fluid algorithm [15]. The latter was naturally crucial in the choice of code while the former facilitate a development of the model to similar processes and other materials. The modelling of the vacuum infusion process in CFX implies several subtle challenges and we shall deal with these in due order.. C-4.

(52) Governing Equations and the Finite Volume Method. The equations to be solved are the general conservation laws. In Cartesian coordinates using tensor notation, the differential form of the full 3D generic conservation equation is [15]: ∂ ( ρφ ) ∂ (ρu jφ ) ∂  ∂φ  + qφ + = Γ ∂t ∂x j ∂x j  ∂x j . (6). where Γ is the diffusivity of the considered quantity φ. For conservation of mass, where φ = 1, Eq. (6) simply reduces to the continuity equation and for conservation of momentum, where φ = ui, it reduces to the Navier-Stokes equations for a Newtonian fluid. By changing the coefficients and adding source terms (qφ), Eq. (6) can be modified to correspond to the applied conditions. Most commercial CFD codes allow such modifications. The finite volume method solves the integral form of the generic conservation equation, Eq. (6): ∂ ∂φ ρφ dΩ + ∫ ρφv j n j dS = ∫ Γ n j dS + ∫ qφ dΩ ∫ ∂t Ω ∂x j S S Ω. (7). In fluid flow it is more convenient to deal with the flow within a certain spatial region rather than with a given quantity of matter. The solution domain is therefore divided into a finite number of control volumes (CV), where Ω and S denote the volume and the surface of the CV. Eq. (7) is applied to each CV, ensuring conservation both for the single CV and for the whole solution domain, i.e. the method is conservative by construction. Approximating surface and volume integrals by appropriate quadrature formulae then results in an algebraic equation for each CV [15].. Flow Through Porous Media. The geometry of the individual fibres in the reinforcement is in this case clearly too complex to be resolved with a grid. Instead the Navier-Stokes equations are modified to account for the extra pressure drop in the flow generated by the flow through the porous medium. This is implemented while retaining both advection and diffusion terms [14]. The mathematical representations of the alteration are transfer terms for. C-5.

(53) the interaction between fluid and solid, in addition to the usual pressure gradient and diffusion terms in the momentum equation. With γ as the volume porosity scalar and. Aij as the area porosity tensor for a porous medium, the general scalar equation (Eq. (6)) for conservation of momentum for an incompressible fluid is: ∂ (γρU i ) + (ρA jkU kU i ), j − µ (Ajk (U k ,i + U i ,k )), j = −γR jiU i − γp, j ∂t. (8). where Rij represents a resistance to the flow in the porous medium, proportional to the inverse of the permeability, K ij−1 . If the permeability is low, the first term on the right hand side of Eq. (8) becomes very large and is balanced by the pressure gradient term, while the convective and diffusive terms on the left hand side are negligible in comparison. Thus, in the limit of a large resistance and stationary flow, Eq. (8) reduces to 0 = R jiU i + p, j. (9). Eq. (8) corresponds to Brinkman’s equation [16]. In the limit of low permeability, where the superficial velocity viscous term becomes negligible, Eq. (8) becomes identical to Darcy’s law, Eq. (9). Thus, the final outcome of importance is that in CFX-4, where Eq. (8) is solved, the results will be the same as if Darcy’s equation, Eq. (9), was solved.. Moving boundaries. We will encounter two types of moving boundaries. First, the impregnation process is modelled as homogenous two-phase flow with a free surface. Mathematically this implies that the momentum equations yield identical velocity fields for both phases, except for the volume fractions, which are obtained by solving separate continuity equations. This approximation is valid since the volume fractions are close to either zero or unity in the majority of the control volumes. An appropriate initial specification of the volume fractions of the two phases is a sharp change across the interface separating them. Due to numerical diffusion, the interface will become geometrically smeared out with time. In order to conserve the initial sharpness of the. C-6.

(54) interface, CFX-4 provides a special surface sharpening algorithm for two-phase flows [14]. Provided the mesh is fine enough to resolve the free surface, the algorithm identifies fluid on the wrong side of the interface and moves it to the correct side, with the condition that volume is at all times conserved. Also, each time step should allow the flow front to advance not more than one computing cell at a time.. Second, the deformation of the reinforcement due to the combination of external pressure and local reinforcement and resin pressure inside the bag defines the other type of moving boundary. The thickness of the stack is calculated based on a force balance according to Eq. (5), where the difference between wet and dry reinforcement has been included. The permeability is then updated according to Eq. (3a). This is followed by iterations of the solution for a new pressure distribution. When convergence is achieved, a new time step is applied and the whole procedure is repeated from the beginning. At all times, the numeric grid has to be updated to the changes in geometry.. VERIFICATION AND VALIDATION OF MODEL WITH STIFF MOULD. Verification is defined by Roache [17] as a demonstration that the numerical solution of a set of partial differential equations is correct, while validation is defined as a demonstration that the chosen set of equations is the best possible representation of the real physical situation. We shall start the verification process by solving Darcy’s law for a transient flow through a porous medium between parallel solid boundaries. The analytical solution for an isotropic permeability is [11]:. x 2f =. 2 K∆p t µ (1 − f ). (10). where xf is the flow front position measured from the inlet. In order to compare the results from the numerical solution to the analytical solution, i.e. verify the numerical model, both solutions are carried out for a real case [4, 5]. The permeability of the reinforcement is set to 9.2·10-11 m2, the driving pressure to 0.1 MPa, the resin viscosity to 0.180 Pas and the fibre volume fraction to 52.5%. The solid dots in Fig. 1 C-7.

(55) represent the numerical solution, for which the smallest time steps are of order 10-2 s, whereas the straight line is predicted by Eq. (10). A straight line fitted to the numerical solution reveals a difference from the analytical solution of less than 1%. Even though the error from truncation errors, etc, could probably be decreased further by grid refinement and tighter iterative convergence criterion, this error level was considered acceptable. Now, bringing the verification process one step further, we study the more general case of two materials of equal thickness (10 mm), one on top of the other, each with a different and non-isotropic permeability. The curves in Fig. 2 show the resulting flow front at different times steps (1, 5 and 13 seconds respectively) as calculated by the CFD code whereas the solid dots are predicted by a traditional RTM simulation program solving Darcy’s law [10]. As an indirect verification, Fig. 2 shows an excellent agreement. For reference, the ratio of the inplane permeability and the through thickness permeability is 10 for both materials, which is also the ratio of the in-plane permeability for the two materials as compared to each other. For the validation process we turn to experimental result presented by Gebart et al [18]. Again we study the general case of two materials of equal thickness,. s, one on top of the other. Now we let both materials have different but isotropic permeability, K1 and K2, meaning that the permeability in the through thickness direction and in the in-plane direction is equal within each material. Also, the fibre volume fraction is assumed to be the same for both materials. Under these conditions, it has been shown both analytically and experimentally [7, 18] that the ratio of the flow front lead-lag l [19] and the layer thickness s is a linear function of. K1 K 2. with an experimentally obtained constant of proportionality of 0,38. The solid straight line in Fig. 3 with a slope of 0,37 is a best fit to numerical solutions (solid dots) obtained with the CFD code for the shown permeability ratios and a fibre volume fraction of 50%. Thus the overall conclusion is that the new CFD-based model is an acceptable approximation of the mathematical model for vacuum infusion.. C-8.

(56) EXAMPLES OF SIMULATIONS WITH THE FULL MODEL. We will here exemplify the strength of the developed method by results from three simulations in a simple geometry. The results are illustrated by the liquid volume fraction in the pores during the injection followed by the corresponding pressure distribution in the resin. First, consider a low Reynolds number and parallel flow of a Newtonian liquid into a porous medium having a constant permeability. With the medium confined in a mould consisting of two parallel and stiff plates, the pressure gradient is constant in the flow direction as shown in Fig. 4a-b. However, the pressure distribution changes in accordance with the shape of the flow front when two layers of fibre reinforcement with different permeability are used, cf. Fig. 5a-b. Here the ratio of the in-plane permeability of the upper layer, K1, and the in-plane permeability of the lower layer, K2, is 10. The permeability in the transverse direction is held constant and equal to K2 in both layers. In the last example, show in Fig. 6a-b, the upper stiff mould is replaced by a flexible bag, cf. Eq. (5). Now the thickness of the stack is largest at the inlet where the pressure in the resin approaches the ambient pressure. Moving towards the outlet where the vacuum level is highest, the thickness becomes smaller and smaller. Also, the decrease in elasticity as a result of lubrication of the fibres results in a thickness minimum at the flow front. Moreover, as can be seen from a qualitative comparison between Fig. 4b and 6b, the minimum is not a result of a different pressure field compared to the stiff mould case. It should however be noticed that the value of κ that is used (κ = 0.1) has only been guessed and is probably less than what can be expected in a real moulding. To what extent this will influence the pressure gradient is the subject of ongoing work in our group.. CONCLUSIONS AND FUTURE WORK. It has here been shown that the general and commercial CFD-code CFX-4 can be used for simulations of the vacuum infusion process. As compared to standard RTMsimulation programs it is possible to account for the effects of through thickness flow. In contrast to RTM-codes the new model also accounts for thickness variations during impregnation, which is crucial for a realistic model [4, 5]. The verification of the code. C-9.

(57) showed an excellent agreement to analytical expressions and excellent conformity with simulations done with an RTM-code. Validation of the model against impregnation of a heterogeneous stack of reinforcements indicates that the chosen set of equations is a most adequate representation of reality.. Future work will involve further validation of the code against experimental results [4, 5] and simulation of vacuum infusion of real components. Furthermore the code will be used to form general guidelines for the vacuum infusion process. Finally we will investigate the possibility of process optimisation and studies of the effect of new types of materials and processing conditions.. ACKNOWLEDGEMENTS. This work was supported by the Swedish Research Council for Engineering Sciences (TFR). We are happy to acknowledge the contributions from Anna-Maria Gustafsson, Henrik Jacobsson and Olle Törnblom at Luleå University of Technology who performed the early work on the numerical model.. C - 10.

(58) REFERENCES. 1. Marco method, US Patent No 2495640, 1950. 2. C. Williams, J. Summerscales and S. Grove, ”Resin Infusion under Flexible Tooling (RIFT): a review”, Composites Part A, 27A, 1996, pp517. 3. F. C. Smith, “The Current Status of Resin Infusion as an Enabling Technology for Toughened Aerospace Structures”, Mat Tech, 14.2:71-80, 1999. 4. H. M. Andersson, T. S. Lundström, B. R. Gebart and P. Synnergren, Submitted for. publication in Polymer Composites. 5. H. M. Andersson, T. S. Lundström, B. R. Gebart and R. Långström, Submitted for. publication in Polymer Composites. 6. A. Hammami and B. R. Gebart, “Model for vacuum infusion moulding process”,. Plastics, Rubber and Composite Processing and Applications, 27(4), 1998, pp. 185. 7. C. A. Fracchia and C. L. Tucker III, “Simulation of Resin Transfer Mold Filling”,. 6th Annual Meeting of the Polymer Processing Society, Nice, France, 1990. 8. B. R. Gebart, C. Y. Lundemo and P. Gudmundson, “An evaluation of alternative injection strategies in RTM”, 47th Annual Conference of the Society of Plastics. Institutes, Cincinatti, USA, 1992. 9. M. L. Diallo, R. Gauvin and F. Trochu, “Experimental Analysis and Simulation of Flow Through Multi-layer Fiber Reinforcements in Liquid Composite Molding”,. Polymer Composites, Vol. 19, No. 3, 1998. 10. A. Koorevaar, “Simulation of the Resin Transfer Moulding (RTM) process”,. Techtextil-Symposium, 1995. 11. B. R. Gebart, “Permeability of Unidirectional Reinforcements for RTM”, Journal. of Composite Materials, Vol. 26, No. 8, 1992. 12. S. Toll, “Packing mechanisms of fiber reinforcements”, Polymer Engineering and. Science, 1998 (Aug). 13. T. S. Lundström and E. Sandlund, “Permeability and compression of RTM reinforcements”, Composites and Sandwich Structures, Eds. J. Bäcklund, D. Zenkert and B. T. Åström, EMAS Publishing, Stockholm, 1997, pp. 317. 14. AEA Technology plc, “CFX 4.3: Solver”, CFX-International, Oxfordshire, UK, 1999.. C - 11.

(59) 15. J. H. Ferziger and M. Peric, “Computational Methods for Fluid Dynamics”, Springer, Berlin, 1999. 16. M. Kaviany, “Principles of heat transfer in porous media”, Springer, New York, 1995. 17. P. J. Roache, “Verification of Codes and Calculations”, AIAA Journal, Vol. 36, No. 5, 1998. 18. B. R. Gebart, P. Gudmundson, L. A Strömbeck and C. Y. Lundemo, “Analysis of the permeability in RTM reinforcements”, 8th International Conference on. Composite Materials, Honolulu, USA, 1991. 19. X. Sun, S. Li and L. J. Lee, “Mold Filling Analysis in Vacuum-Assisted Resin Transfer Molding. Part 1: SCRIMP Based on a High-Permeable Medium”,. Polymer Composites, 19, 807-817, 1998.. C - 12.

(60) FIGURES. 5. 3. 2. 2. 3. xf (m *10 ). 4. 2. 1. Numerical solution Analytical solution. 0 0. 5. 10. 15. 20. Time (s) Figure 1. Numerical solution (dots) and analytical solution (straight line) for transient. flow through a porous medium of isotropic permeability between parallel solid boundaries.. C - 13.

(61) 20 CFX code RTM code. Height (mm). 15. 10. 5. 0 0. 10. 20. 30. 40. 50. Position (mm) Figure 2. Numerical solutions for transient flow through two non-isotropic materials. of equal height between solid parallel boundaries. With flow from left to right, the curves represent the flow front after 1, 5 and 13 seconds respectively. The solid dots are solutions obtained with an RTM-code [10].. C - 14.

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