Continuous measurement of fiber reinforcement permeability in the thickness direction: Experimental technique and validation

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1 Continuous measurement o iber reinorcement permeability in the thickness direction: Experimental technique and validation P. Ouagne, Tariq Ouahbi, Chung Hae Park, Joël Bréard, Abdelghani Saouab To cite this version: P. Ouagne, Tariq Ouahbi, Chung Hae Park, Joël Bréard, Abdelghani Saouab. Continuous measurement o iber reinorcement permeability in the thickness direction: Experimental technique and validation. Composites Part B: Engineering, Elsevier, 2013, 45 (1), pp <hal > HAL Id: hal Submitted on 8 Mar 2013 HAL is a multi-disciplinary open access archive or the deposit and dissemination o scientiic research documents, whether they are published or not. The documents may come rom teaching and research institutions in France or abroad, or rom public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diusion de documents scientiiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche rançais ou étrangers, des laboratoires publics ou privés.

2 Continuous measurement o iber reinorcement permeability in the thickness direction: Experimental technique and validation Pierre Ouagne 1, Tariq Ouahbi 2, Chung Hae Park 2*, Joël Bréard 2, Abdelghani Saouab 2 1. Laboratoire PRISME, University o Orléans, 8 rue Leonard de Vinci, Orléans, France 2. Laboratoire d Ondes et Milieux Complexes, UMR 6294 CNRS, University o Le Havre, 53 rue de Prony, BP 540, Le Havre, France *To whom correspondence should be addressed: chung-hae.park@univ-lehavre.r Tel: , Fax: Abstract It is an important topic to measure the through-thickness permeability o iber reinorcements as the resin low in the thickness direction is widely employed in many composites manuacturing techniques. Continuous techniques or the permeability measurement by simultaneous abric compaction and liquid low have been recently proposed as an alternative way to the tedious and laborious conventional permeability measurement techniques. In spite o their eiciencies, these continuous techniques have some limits i the abric compaction speed or low rate is relatively great. To address this issue, a new equation or the permeability estimation is proposed. Parametric studies are perormed to investigate the inluences o the experimental conditions on the validity o the continuous technique. A dimensionless number is proposed as a measure o the relative error o the continuous technique. Key words: A. Fabrics/textiles; A. Polymer-matrix composites (PMCs); E. Resin transer molding (RTM); E. Resin low; Permeability

3 1. Introduction Liquid composite molding (LCM) processes such as the resin transer molding (RTM) process and the structural reaction injection molding (SRIM) process are widely adopted to manuacture complex structural parts at a relatively low cost in the aeronautic and automotive industries. The basic principle o these processes is the resin impregnation into dry iber reinorcement and this phenomenon is generally modeled by Darcy s law [1]. The resin impregnation becomes more diicult in the case o large part manuacturing, because the resin low path becomes long and the resin low velocity drops to a small value. Hence, in some LCM processes such as the vacuum assisted resin transer molding (VARTM) process and the Seeman composite resin inusion molding process (SCRIMP), high permeability layers (HPL) or distribution media (DM) may be integrated into the preorm stack to deal with this problem [2-4]. The resin is quickly impregnated through the HPL or DM and then the resin lows into the iber reinorcement in the through-thickness direction. Because most composite structures have smaller dimensions in the thickness direction than in the longitudinal directions, the low path can be greatly reduced and the resin impregnation can be acilitated. This principle is also adopted in the resin ilm inusion (RFI) process. In this context, the permeability o reinorcement is a key parameter to inluence the resin low as is deined by Darcy s law. u D Q A K P where u D is the volume averaged velocity, Q is the low rate, A is the cross section, K is the permeability, μ is the resin viscosity and P is the resin pressure. Permeability is represented by a three-dimensional tensor as it depends on the direction [5-6]. (1)

4 Two permeability values are used to characterize iber reinorcements [7]. The irst one is called unsaturated permeability. It is measured by monitoring the low ront advancement as a unction o time under a given pressure gradient in the transient resin low [5-7]. The other one is reerred as saturated permeability. It is obtained by measuring the pressure gradient under a given low rate during the steady state low in the ully impregnated reinorcement [7]. As permeability is a reinorcement property which is independent o resin properties and processing conditions, the unsaturated permeability and the saturated permeability or a speciic reinorcement should be identical. In the literature, however, the ratio o unsaturated permeability to saturated permeability has been reported to be ¼ to 4 by experimental measurements [8-9]. The main reasons or the dierence between the unsaturated permeability and the saturated permeability have been assumed to be the void generation and the low induced deormation o iber reinorcements. In this work, this issue is not addressed and only the saturated permeability is discussed. In general, the permeability is expressed in terms o iber volume raction such as in the Kozeny-Carman equation. To obtain a relationship between iber volume raction and permeability, it is a usual way to obtain a single set o iber volume raction and permeability, by ixing iber volume raction and measuring low rate and pressure drop to evaluate a permeability value. Then, this procedure is repeated or dierent values o iber volume raction to obtain a number o data points which will be used to it a preassumed mathematical equation. In this paper, we call this method discrete method because we obtain a series o discrete values o iber volume raction and permeability (Figure 1(a)). Hence, a number o measurements are needed and the accuracy o measurement is improved as the number o data points is increased. This method,

5 however, is tedious and needs a long time. As an alternative way, some researchers proposed to measure the permeability while iber reinorcement is continuously compacted [10-14]. A stack o iber reinorcement layers is placed between two rigid tools and is compressed by a motion o one o the rigid tools (Figure 1(b)). The change o the gap between the upper tool and the lower tool induces a change o iber volume raction. At the same time, the pressure dierential or low rate is measured as a unction o time while the abric is compressed. The gap height can be converted into the iber volume raction and the pressure dierence or low rate is used to obtain the permeability by using Darcy s law, at each instant, during the reinorcement compression. In the current paper, this method is called continuous method because the reinorcement is continuously compressed. In this way, it can also be assumed that the data appears to be continuous i the resolution o data acquisition is suiciently ine. The advantage o the continuous methods over the discrete methods is the reduction o the number o measurements and o the time to work. A relationship between iber volume raction and permeability can be obtained by a single measurement in the continuous methods, whereas many measurements are needed in the discrete methods. Two kinds o continuous methods are ound in the literature. In the irst method, a saturated abric stack is squeezed by rigid platens without any external liquid low. In this case, the liquid low is induced only by the platen velocity. In the second method, a abric stack is compacted while it is submitted to an external liquid low. In this case, the liquid low is induced both by the platen motion and by the external liquid low applied to the abric stack. The continuous methods have been used to identiy the in-plane permeabilities [10-11]. The resin low takes place in the longitudinal direction while the abric is compressed in

6 the thickness direction. Not only the permeabilities o isotropic preorms but also the permeabilities o anisotropic preorms can be obtained once the ratio o two principal in-plane permeabilities is known [11]. Because the anisotropic ratio may depend on iber volume raction, however, a signiicant number o extra measurements may be required. Scholz et al. proposed a continuous method to measure through-thickness permeability by applying a low o liquid or gas in the thickness direction [12]. They ound that the permeability values obtained by injecting a gas or liquid showed close agreements with each other. However, the permeability values obtained by the continuous method were not compared with those obtained by the discrete method. Hence, the reliability o the continuous method was still questionable. Ouagne and Bréard used a similar experimental technique and showed that the permeability values obtained by the continuous method were close to those obtained by the discrete method, i the compression speed was suiciently low [13]. Using the same experimental device, they ound that the dierence between the permeability values obtained by the continuous method and by the discrete method could be signiicant depending on the experimental condition such as the abric compaction speed and the low rate [14]. In this work, the reasons or the discrepancy between the continuous method and the discrete method are analyzed, and a new equation or the permeability evaluation by the continuous method is suggested to address this problem. Then, some experimental results o permeability measurements by the discrete method and by the continuous method are presented or dierent experimental conditions and or dierent reinorcements. Finally, the validity o the continuous method is examined by parametric studies or dierent values o abric compaction speed and low rate,

7 through numerical simulations. A dimensionless number is proposed as a measure o the error in the use o the continuous method. 2. Experimental method 2.1 Experimental device The device developed in the previous work was used again in the current work [13]. The schematic diagram and the photo view o this device are shown in Figure 2. A brie description o the device is presented in this section and the details can be ound in the reerence [13]. This device consists o a stainless steel cylindrical pot within which the vertical motion o a piston induces the compaction o the iber reinorcement which is placed between the lower ixed bronze grid and the upper mobile bronze grid. The motion o the piston controlled by a universal testing machine (Instron 8802) leads to a vertical motion to the upper bronze grid at a pre-assigned constant displacement rate. The lower and upper perorated bronze grids are used to obtain a uniorm liquid lux through the iber reinorcement to be tested. A silicon joint is applied at the perimeter o the test reinorcement to avoid race tracking eects. The actual diameter o the circular test reinorcement submitted to the liquid low is 100 mm. The test liquid which enters the lower chamber in the cylindrical pot passes through the test reinorcement and leaves the upper chamber through the low outlet. The liquid low entering the lower chamber is provided rom a six liter syringe which is placed on another universal test machine (Instron 5867) and the low rate is controlled by the crosshead speed o the universal test machine. A pressure transducer (Entran EPXO-X7) is placed below the lower ixed bronze grid to measure the pressure o the liquid entering the test reinorcement. It is assumed that the pressure loss by the upper and lower perorated

8 bronze grids is negligible by dint o their highly porous microstructure. It is also assumed that the pressure o the liquid leaving the test reinorcement is close to zero because the low resistance in the upper chamber is negligible. 2.2 Test materials and experimental conditions Silicon oil (viscosity: 0.1 Pas) was used as a test liquid. As test reinorcements, we used three iber reinorcements. A. E glass 5 harness satin weave (areal weight: 620 g/m 2, density: 2.56 g/cm 3 ) B. Carbon interlock weave (areal weight: 625 g/m 2, density: 1.74 g/cm 3 ) C. Flax random mat (areal weight: 520 g/m 2, density: 1.56 g/cm 3 ) The permeabilities o the three reinorcements were measured by the continuous method as well as by the discrete method. In the permeability measurement by the discrete method (see Figure 1 (a)), a abric stack composed o twenty layers at the same layer angle was placed between the upper and lower bronze grids which were stationary during the liquid low. Fiber volume raction was computed as ollows. M s N V H where V is the iber volume raction, M s is the areal weight o reinorcement, N is the number o abric layers, H is the distance between the bronze grids or the thickness o abric stack, and is the iber density. While the gap between the bronze grids was ixed, the test liquid lowed through the reinorcement at a pre-assigned constant low (2) rate ( m 3 /s or all the cases) and the pressure at the lower chamber was measured. This procedure was repeated with the same stack o the reinorcement layers or dierent gap heights between the bronze grids. The measurement o pressure was repeated or various gap heights rom a large gap height to a small gap height. Hence,

9 the permeability values were identiied rom a low iber volume raction to a high iber volume raction. Given the type o reinorcement, tests were perormed three times and the average value was taken. Hence, three stacks o abrics were used or each type o reinorcement. In the continuous measurement o permeability (see Figure 1 (b)), a stack o abrics was prepared in the same way as was in the discrete method. In this case, however, the upper grid moved downward to compact the abric stack at a pre-assigned constant speed while the test liquid was passing through the abric stack at a pre-assigned constant low rate. The gap height was computed at each instant rom the initial gap height and the speed o the upper bronze grid. Once the gap height is known, the iber volume raction can be calculated at each instant by Equation (2). The pressure at the lower chamber was measured as a unction o time. Consequently, the gap height and the pressure at the lower chamber were obtained as a unction o time in the continuous method. For each type o reinorcement, tests were perormed three times and a new stack o abrics was used or a new test. Hence, three stacks o abrics were prepared or each type o reinorcement. 2.3 Permeability calculation by the discrete method I it is assumed that the pressure distribution is linear and the pressure gradient is uniorm in the reinorcement, the negative pressure gradient can be expressed by the ratio o the pressure drop to the total thickness o the abric stack (Figure 3 (a)). dp dz P H P in H P out (3) where P in is the liquid pressure at the entrance o the abric stack in the lower chamber and P out is the liquid pressure at the exit o the abric stack in the upper chamber. The

10 permeability can be obtained rom Darcy s law in terms o the low rate and the inlet pressure, assuming that the outlet pressure is zero. HQ K d P A in where K d represents the permeability value obtained by the discrete method. (4) 2.4 Permeability calculation by the continuous method In the previously mentioned reerences [12-14], the same equation as was used in the discrete method (Equation (4)) has been applied to evaluate the permeability by the continuous method. It was ound, however, that the permeability evaluation by the continuous method was dependent on the abric compaction speed which was not considered in Equation (4) [14]. To address this issue, two phenomena induced by the abric compaction are considered: the iber motion and the non-linear pressure gradient. In act, the permeability evaluation by Darcy s law is based on the assumption that the iber bed is stationary during the liquid low. I there is a motion o iber, Darcy s law should be modiied considering the iber velocity. In this case, the relative velocity which is the dierence between the liquid velocity and the iber velocity should be associated with the negative pressure gradient. K u D u P (5) where u is the iber velocity. In the continuous method where the abric stack is compressed by the downward motion o the upper grid, the iber velocity cannot be ignored. Moreover, the iber velocity depends on the position o the iber. For example, the iber velocity just beneath the upper mobile grid equals to the negative value o the abric compaction speed whereas the iber velocity just above the lower ixed grid is

11 zero (Figure 3 (b)). Hence, we propose to use the hal o the negative abric compaction speed as the mean value o the iber velocity to evaluate the permeability by the continuous method. K c H Q U P A 2 in c (6) where U c is the abric compaction speed or the upper mobile grid displacement rate. K c denotes the permeability obtained by the continuous method. In Equation (6), the thickness o the abric stack (H) and the inlet pressure (P in ) are obtained as a unction o time. Consequently, the iber volume raction can be calculated rom the thickness o the abric stack by Equation (2) and the permeability (K c ) can be obtained by Equation (6), as a unction o time (Figure 1 (b)). The second problem is the non-linear pressure gradient in the abric stack under applied abric compaction and liquid low (Figure 3 (b)). One o the important assumptions in Equation (3) is that the pressure gradient is uniorm and the pressure proile is linear in the reinorcement at each instant. I there is a time dependent change o iber volume raction, such as in the vacuum inusion process and the resin ilm inusion process, the rate o iber volume raction should be taken into account in the mass conservation equation. Moreover, the iber velocity should be considered in Darcy s law as was described in Equation (5). Subsequently, the iber volume raction becomes nonuniorm in the abric stack by the iber motion during the liquid low and the abric compaction, and the mass conservation equation in the thickness direction should be modiied including the terms representing the volumetric change rate and the iber velocity [15]. z K P 1 z V V t u V z (7)

12 I there is no iber motion and the iber volume raction is uniorm, both the terms on the right hand side disappear and the pressure distribution becomes linear. I the iber velocity is no more negligible or the iber volume raction is non-uniorm, however, the terms on the right hand side should be considered and the pressure distribution becomes non-linear [15]. In general, the ibers are compacted along the liquid low and the iber volume raction is higher in the downstream (Figure 3 (b)). Thereore, the local permeability becomes lower in the downstream and the global liquid low is decided by the lowest local permeability in the downstream. Consequently, the permeability values measured in the abrics with non-uniorm iber volume raction (e.g. under compaction) appears to be lower than those measured in the abrics with uniorm iber volume raction. In the previous section (1. Introduction), two continuous methods were presented, viz., the squeezing o a saturated abric stack without external liquid low and the compaction o a abric stack under an applied liquid low. In the irst case, the relative velocity due to the iber motion is an important issue whereas the iber volume raction is relatively uniorm. In the second case, however, both the relative velocity due to the iber motion and the non-uniormity o iber volume raction should be taken into account to evaluate the permeability. 2.5 Results and discussion In Figure 4, the permeability values o three dierent reinorcements measured by the continuous method as well as by the discrete method are presented. In general, permeabilities are plotted in the logarithmic scale against iber volume raction. In this way, a great error at high permeability zone (e.g m 2 ) appears to be the same as a

13 small error at lower permeability zone (e.g m 2 ), because both o them are represented by a single scale with the same length in the vertical axis. Hence, permeabilites are plotted in the linear scale or the accurate comparison o discrepancy, in this work. It should be also kept in mind that there is a unique value o permeability or a given iber volume raction and the permeability values obtained by the discrete method are considered as the reerence values in this work even though the permeability values obtained by the continuous method are plotted together in the same graph. The objective o this section is to see the relative error o the continuous method compared with the discrete method. To evaluate the permeability values by the continuous method, two equations were used and the results were compared: Equation (4) without iber velocity and Equation (6) with iber velocity. Compared with the continuous permeability measurements without considering the iber velocity (Equation (4) and hollow dots in Figure 4), the continuous permeability measurements considering the iber velocity (Equation (6) and solid dots in Figure 4) are in closer agreements to the discrete permeability measurements. Even though the discrepancy becomes generally marginal with considering the abric compaction speed in Equation (6), there is still some dierence between the discrete and the continuous methods. From the experimental results, some general conclusions can be drawn. A. The permeability values obtained by the continuous method are generally lower than the permeability values by the discrete method. B. The dierence between the two methods becomes greater as the iber volume raction becomes lower. C. The dierence between the two methods increases as the abric compaction speed increases.

14 In the subsequent section, these issues are investigated by parametric studies using numerical simulations o liquid low and abric compaction. Then, a dimensionless number is proposed as a measure o error in the continuous method. 3. Validation o the continuous method 3.1 Numerical simulation In order to investigate the inluences o non-uniorm iber volume raction and iber velocity on the validity o the continuous method, it is indispensable to observe the distributions o iber volume raction and o liquid pressure in the thickness direction during the low and compression. This experimental observation is diicult to conduct, however, because the thickness o abric stack is very small. Hence, numerical simulations o abric deormation and resin low in mesoscopic or microscopic scale can be attractive approaches [16-18]. Simultaneous simulation o abric deormation and resin low is a diicult task, however, because there is a mutual inluence between the low-induced abric deormation and the permeability alteration by the change o abric microstructure. Instead, numerical simulations based on the mass conservation and the orce equilibrium at a mascroscopic scale may be a practical alternative way [19]. The computer code developed in the previous work has been improved, by considering the iber velocity, to simulate the liquid low in the thickness direction and the iber compaction in the abric stack as represented in Equation (7) [19]. We need another governing equation to describe the orce balance condition. P comp P (8) where P comp is the total compaction pressure applied to the abric stack (to be measured by Instron 8802 connected to the piston on the upper mobile grid) and is the elastic

15 stress by abric deormation. The permeability and the abric deormation stress can be represented as a unction o iber volume raction. K a V b d c V (9) (10) Equation (10) is known as "Toll and Manson" equation which is an empirical relation between abric compaction stress and iber volume raction [20, 21]. In a similar way, the in-plane or transverse permeability values have also been related to iber volume raction by using a similar empirical power law model [22]. As boundary conditions, a low rate and zero iber velocity are assigned at the lower ace o the abric stack. A iber velocity which is the negative value o the abric compaction speed and zero liquid pressure are assigned at the upper ace o the abric stack. The permeability measurement by the continuous technique was simulated by the computer code. The objective o the numerical simulations was to investigate i the continuous method successully reproduced the permeability values by the discrete method. Hence, the permeability values by the discrete method were used as input data or the numerical simulations and the permeability values by the continuous methods were the output results o the numerical simulations (Figure 5). Given the permeability values obtained by the discrete method which were considered as the true permeability values o the reinorcement and the iber stress values obtained by independent measurements, numerical simulations were perormed. The identiication procedure o iber stress model coeicients has been described in the authors previous work [21]. The model coeicients used in Equations (9) and (10) are listed in Table 1. At each numerical simulation, the inlet pressure was obtained as a

16 unction o time. The thickness o abric stack was computed rom the abric compaction speed and the initial thickness value. Then, the average iber volume raction (V,ave in Figure 5) was obtained as a unction o time by using Equation (2) because the iber volume raction was varied with the position. Subsequently, the permeability was computed as a unction o time by Equation (6) rom the inlet pressure obtained by the numerical simulation and the thickness o the abric stack. The permeability values or each average iber volume raction obtained in this way were considered as the permeability by the continuous method. 3.2 Parametric study Parametric studies were conducted or the three dierent reinorcements described in Section 2.2, to investigate the inluences o the low rate and the abric compaction speed upon the validity o the continuous method. In the case o the glass satin weave and the carbon interlock weave, the permeability values obtained by the continuous method (i.e. by numerical simulations) were compared with the permeability values obtained by the discrete method or three low rate values (510-7 m 3 /s, 10-6 m 3 /s and m 3 /s) and or three compaction speed values (0.2 mm/min, 1 mm/min and 5 mm/min). In the case o the lax random mat, higher low rates (210-6 m 3 /s, 10-5 m 3 /s and m 3 /s) were used because there was little discrepancy or lower low rates between the permeability values obtained by the continuous method and those obtained by the discrete method. 3.3 Results and discussion

17 The results o numerical simulations are shown in Figure 6. The relative errors o the permeability values by the continuous method to those obtained by the discrete method are deined by the ollowing relation. K Err d K K d c The same conclusions as were previously drawn in the section 2.5 can be made. Moreover, we can see that there is an inluence rom the low rate as well as rom the abric compaction speed. The dierence between the continuous method and the discrete method increases as the low rate increases. As the low rate or the abric compaction speed increases, the abric compaction becomes greater at the downstream. This leads to an increase o iber volume raction and the corresponding increase o the low resistance at the downstream. As a result, the global low resistance drops, and a lower permeability is obtained in the reinorcement with a non-uniorm distribution o iber volume raction than in the reinorcement with a uniorm distribution o iber volume raction. For the same low rate (210-6 m 3 /s) and the same compaction speed (5 mm/min), in particular, the dierence between the permeabilities obtained by the discrete method and by the continuous method was relatively small in the case o the lax random mat (see Figure 6 (g)), whereas they were relatively great in the case o the glass satin weave (see Figure 6 (c)) and the carbon interlock weave (see Figure 6 ()). In the case o the lax mat, the eect o abric compaction was relatively small and there was little inluence rom the low rate and the abric compaction speed. This implies that the validity o the continuous method depends on the abric type, especially the abric compaction behavior, as well as on the low rate and the abric compaction speed. Hence, a dimensionless number is proposed or the quantitative validation o the continuous method. The basic assumption adopted in the discrete method was the linear (11)

18 AH Q t t U V u u H z z V V V c ave ave *, *, *,,, * c d b V U A Q V acd bh z V u t V V z V V cd a V z d b 1 1 * *, * * *, * * 1 * * z V V U u t V A Q V acd bh z V V z ave c d b ave d b pressure proile. For this assumption to be valid, the two terms on the right hand side in Equation (7) should vanish. Equation (7) with two variables, viz. pressure and iber volume raction, can be converted into an equation with a single variable o iber volume raction, rom the orce balance condition represented in Equation (8) and the relations or the reinorcement permeability and iber deormation stress represented by Equations (9) and (10), respectively. (12) Then, the governing equation or iber volume raction is non-dimensionalized introducing a scaling parameter and dimensionless numbers. (13) Subsequently, we obtain a dimensionless orm o the governing equation. (14) Finally, we can deine a dimensionless number to represent a magnitude o the right hand side terms as shown below. (15) I one plots the numerical relative errors as deined in Equation (11), all the results in Figure 6 can be represented by a single master curve, regardless o reinorcement type, in terms o the dimensionless number deined in Equation (15) (see Figure 7). The numerical relative error increases as the dimensionless number increases. It should be noted that the relative error in the case o the lax random mat is smaller than those in the case o the glass satin weave and the carbon interlock weave or the same compaction speed and the same low rate because the dimensionless number or the lax mat is smaller than those or the other reinorcements (Figure 8). The increase o the compaction speed and the low rate results in the increase o the dimensionless number

19 and in the corresponding increase o the relative error as shown in Figure 7. As the iber volume raction decreases, the dimensionless number increases and the relative error increases. It should be noted that the thickness o the abric stack should be suiciently small, because the dimensionless number is proportional to the abric stack thickness. Besides, low viscosity liquid is avorable to reduce relative errors as the dimensionless number is proportional to the liquid viscosity. As a consequence, the experimental conditions in the continuous permeability measurement should be adjusted to minimize relative errors in terms o the dimensionless number considering not only the test conditions such as the low rate and the abric compaction speed but also the material properties such as the liquid viscosity and the abric compaction behavior (viz. elastic iber stress model). 4. Conclusions The limit o validity o the continuous permeability methods where the abric stack is continuously compressed during the liquid low was investigated in this work. Through the experimental measurements o the permeability in the thickness direction, the discrepancies between the discrete method and the continuous method were observed. To investigate the inluences o the experimental test conditions such as the low rate and the abric compaction speed, numerical simulations were perormed or various conditions. A dimensionless number to quantiy the relative error o the continuous method was proposed. It was ound that the relative errors can be plotted by a master curve in terms o the proposed dimensionless number regardless o abric type. From the investigation, it can be concluded that low low rate, low compression speed, small

20 thickness o abric stack and low viscosity liquid are advantageous to reduce relative errors. In this work, it has been assumed that the permeability values obtained by the discrete method are the reerential values. From the deinition o the dimensionless number in Equation (15), however, we can see that the error can be signiicant i the low rate is great, even though the abric compaction speed is zero. Thereore, a low low rate should be applied even in the discrete permeability method, in order to avoid a nonuniorm distribution o iber volume raction induced by the iber compaction along the liquid low. Acknowledgements This work has been perormed in the ramework o the research program LCM3M / ANR (the French National Research Agency). The authors would like to appreciate the inancial support to this research program rom the French ministry o the research and higher education. Reerences 1. Darcy H. Les ontaines Publiques de la ville de Dijon. Paris: Dalmont, Han K, Jiang S, Zhang C, Wang B. Flow modeling and simulation o SCRIMP or composites manuacturing; Composites Part A 2000; 31(1): Sun X, Li S, Lee LJ. Mold illing analysis in vacuum-assisted resin transer molding. Part I: SCRIMP based on a high-permeable medium. Polymer Composites 1998; 19(6):

21 4. Ni J, Li S, Sun X, Lee LJ. Mold illing analysis in vacuum-assisted resin transer molding. Part II: SCRIMP based on grooves. Polymer Composites 1998; 19(6): Ahn SH, Lee WI, Springer GS. Measurement o the three-dimensional permeability o iber preorms using embedded iber optic sensors. Journal o Composite Materials 1995; 29(6): Turner DZ, Hjelmstad KD. Determining the 3D permeability o ibrous media using the Newton method. Composites Part B 2005; 36(8): Parnas RS, Flynn KM, Dal-Favero ME. A permeability database or composite manuacturing. Polymer Composites 1997; 18(5): Dungan FD, Sastry AM. Saturated and unsaturated polymer lows: microphenomena and modeling. Journal o Composite Materials 2002; 36(13): Pillai KM, Modeling the unsaturated low in liquid composite molding processes: a review and some thoughts, Journal o Composite Materials 2004; 38(23): Buntain MJ, Bickerton S. Compression low permeability measurement: a continuous technique. Composite Part A 2003; 34(5): Comas-Cardona S, Binétruy C, Krawczak P. Unidirectional compression o ibre reinorcements. Part 2: A continuous permeability tensor measurement. Composites Science and Technology 2007; 67(3-4): Scholz S, Gillespie Jr JW, Heider D. Measurement o transverse permeability using gaseous and liquid low. Composites Part A 2007; 38(9): Ouagne P, Bréard J. Continuous transverse permeability o ibrous media. Composites Part A 2010; 41(1):

22 14. Ouagne P, Bréard J. Inluence o the compaction speed on the transverse continuous permeability, The 10 th International Conerence on Flow Processes in Composite Materials (FPCM10). Ascona, Swiss, July 11-15, Park CH, Saouab A. Analytical modeling o composite molding by resin inusion with lexible tooling: VARI RFI processes. Journal o Composite Materials 2009; 43(18): Charmetant A, Vidal-Sallé E, Boisse P. Hyperelastic modelling or mesoscopic analyses o composite reinorcements, Composites Science and Technology 2011; 71(14): De Luycker E, Morestin F, Boisse P, Marsal D. Simulation o 3D interlock composite preorming, Composite Structures 2009; 88(4): Silva L, Puaux G, Vincent M, Laure P. A monolithic inite element approach to compute permeability at microscopic scales in LCM processes, International Journal o Material Forming 2010; 3(s1): Ouahbi T, Saouab A, Bréard J, Ouagne P, Chatel P. Modeling o hydro-mechanical coupling in inusion processes. Composites Part A 2007; 38(7): Toll S, Manson JAE. An analysis o the compressibility o iber assemblies. Proceeding o the sixth International Conerence on Fiber-Reinorced Composites, Institute o Materials, Newcastle upon Tyne, UK, 1994: 25/1-25/ Ouagne P, Bréard J, Ouahbi T, Saouab A, Park CH. Hydro-Mechanical Loading and Compressibility o Fibrous Media or Resin Inusion Processes, International Journal o Materials Forming 2010; 3:

23 22. Gauvin R, Clerk P, Lemenn Y, Trochu F. Compaction and creep behavior o glass reinorcement or liquid composites molding, Proceeding o ASM/EDS Advanced Composites Conerence, Dearborn, Michigan, 1994: Figure captions Figure 1. Two permeability measurement methods (a) Discrete method or permeability measurement (b) Continuous method or permeability measurement Figure 2. Experimental device or permeability measurement (a) Schematic diagram (b) Photo view Figure 3. Distribution o iber volume raction and pressure proile (a) Discrete method (without abric compaction) (b) Continuous method (with abric compaction) Figure 4. Experimental results o permeability by the discrete method and by the continuous method (a) Glass satin weave (b) Carbon interlock weave (c) Flax random mat Figure 5. Numerical simulation procedure or permeability evaluation in the continuous method Figure 6. Results o numerical simulations or permeability evaluation by the continuous method (a) Glass satin weave (Q=510-7 m 3 /s)

24 (b) Glass satin weave (Q=10-6 m 3 /s) (c) Glass satin weave (Q=210-6 m 3 /s) (d) Carbon interlock weave (Q=510-7 m 3 /s) (e) Carbon interlock weave (Q=10-6 m 3 /s) () Carbon interlock weave (Q=210-6 m 3 /s) (g) Flax random mat (Q=210-6 m 3 /s) (h) Flax random mat (Q=10-5 m 3 /s) (i) Flax random mat (Q=510-5 m 3 /s) Figure 7. Relative error against dimensionless number Figure 8. Fiber volume raction against dimensionless number Table captions Table 1. Model coeicients or abric permeability and elastic deormation stress

25 Equation (9) Equation (10) a [m 2 ] b c [Pa] d Glass satin weave Carbon interlock weave Flax random mat Table 1.

26 Measurement 1 Measurement 2 Measurement 3 H 1 H 2 H 3 P 1 P 2 P 3 Flow rate: Q 1 Q 2 Q 3 Computation: H, N,, M s V (Eq. 2), Q, A, P, H, μ K (Eq. 4) K (V 1, K 1 ) (V 2, K 2 ) (V 3, K 3 ) V Figure 1.(a) t 1 t 2 t 3 U c H(t 1 ) U c H(t 2 ) U c H(t 1 ) Q P(t 1 ) Q P(t 2 ) Q P(t 1 ) Computation: U C H(t)=H(0)-U c t H(t), N,, M s V (t) (Eq. 2) K Single measurement (during a compression) Q, A, P(t), H(t), μ K(t)=K(V ) (Eq. 6) V Figure 1.(b)

27 Flow outlet Piston Upper chamber Mobile grid Silicon joint Fixed grid Flow inlet Silicon joint Fibrous reinorcements 100 mm diameter Pressure sensor Lower chamber Figure 2 (a) Figure 2 (b)

28 Fixed z Downstream ( dw ) grid H(t) Upstream ( up ) Q Fixed grid P in P(z,t) Fiber volume raction: V,up = V,dw Fiber velocity: u,up = 0, u,dw = 0 Figure 3 (a) U c Mobile z Downstream ( dw ) grid H(t) Upstream ( up ) Q Fixed grid P in P(z,t) Fiber volume raction: V,up < V,dw Fiber velocity: u,up = 0, u,dw = - U c Figure 3 (b)

29 Figure 4 (a) Figure 4 (b)

30 Figure 4 (c)

31 Input: U c, Q, K d, Simulation: H(t), P(z,t), V (z,t) U c P(z=H(t)) =0 z Mobile grid u (z=h(t)) = - U c H(t) Fixed grid Q u (z=0) = 0 Output data: P in (z=0,t) Permeability evaluation: V,ave (t) (Eq. 2) and K c (t)=k c (V,ave ) (Eq. 6) Figure 5

32 Figure 6 (a) Figue 6 (b)

33 Figure 6 (c) Figure 6 (d)

34 Figure 6 (e) Figure 6 ()

35 Figure 6 (g) Figure 6 (h)

36 Figure 6 (i)

37 Figure 7. Figure 8.