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A reference specimen for permeability measurements of fibrous reinforcements for RTM
Composites: Part A 40 (2009) 244–250
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Composites: Part A journal homepage: www.elsevier.com/locate/compositesa
A reference specimen for permeability measurements of fibrous reinforcements for RTM Gerd Morren a,*, Massimo Bottiglieri a, Sven Bossuyt a, Hugo Sol a, David Lecompte b, Bart Verleye c, Stepan V. Lomov d a
Vrije Universiteit Brussel (VUB), Dept. Mechanics of Materials and Constructions, Pleinlaan 2, B-1050 Brussels, Belgium Royal Military Academy (RMA), Dept. Materials and Construction Engineering, Renaissancelaan 30, B-1000 Brussels, Belgium c Katholieke Universiteit Leuven (K.U.Leuven), Dept. Computer Science, Celestijnenlaan 200A, B-3001 Heverlee, Belgium d Katholieke Universiteit Leuven (K.U.Leuven), Dept. Metallurgy and Materials Engineering, Kasteelpark Arenberg 44, B-3001 Heverlee, Belgium b
a r t i c l e
i n f o
Article history: Received 28 August 2008 Received in revised form 21 November 2008 Accepted 26 November 2008
Keywords: A. Fabrics/textiles E. Resin Transfer Moulding (RTM) Permeability
a b s t r a c t The capability to simulate the flow of resin through a porous reinforcement by FE modelling has become very important for designing RTM production processes for high-performance composite parts. The key parameter in RTM flow simulations is the fibre reinforcement permeability. The measurement of this material parameter is still not standardized and many different set-ups have been proposed. Recently, a stereolithography technique was used to produce a textile-like solid specimen with anisotropic permeability, designed as a reference for calibration and comparison of permeability measurement set-ups and for validation of numerical permeability computation software. Unlike real textiles, the permeability properties of such reference specimens do not vary from test to test. Excellent repeatability of the experiments is achieved. When used for benchmarking, any discrepancy between different measurements on this specimen must be attributed to the set-up and data processing. This paper presents the first experimental measurements of the permeability of such reference specimens, obtained with a 2D central injection rig. The measured values, with principal components of the 2D permeability tensor of 2.47 ± 0.09 109 m2 and 5.44 ± 0.22 109 m2, are in good agreement with the values predicted using numerical permeability computation software. Statistics from a series of measurements using the same set-up show that the precision of the permeability identification depends on the data processing procedure. An approach which incorporates a numerical model that is also valid after the fluid reached an edge of the reinforcement performs significantly better than the approach, based on an analytical approximation, which was used before. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Liquid Composite Moulding (LCM), particularly its sub-class, Resin Transfer Moulding (RTM), is the state-of-the-art technology for producing textile reinforced composite parts. In LCM, liquid resin is injected into a mould holding a fibrous preform. Once the preform is impregnated, the resin cures and the finished component is de-moulded. It is imperative that the preform is sufficiently saturated with resin during the impregnation. Otherwise, the resulting part will contain unallowable void content. Consequently, one of the key issues in LCM process design is developing the injection strategy: placement of resin inlets and air vents, pressure variation, application of vacuum, etc. Although it is often feasible to find a reasonable injection strategy by trial and error, this method is risky and costly, especially if expensive moulds need to * Corresponding author. Tel.: +32 2 629 29 27; fax: +32 2 629 29 28. E-mail address: [email protected] (G. Morren). 1359-835X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2008.11.011
be manufactured, or when the material costs are very high. Therefore, virtual prototyping software has been developed to assist the engineer in correctly designing the mould [1,2]. Through injection simulations, the problem areas in a mould can be identified and the mould layout, i.e., the positions of resin injection points and air vents, as well as the injection strategy, can be adapted accordingly [2,3]. Moreover, the software can assist the designer in optimizing the injection process in order to obtain a robust production process with the shortest possible cycle time [4]. The injection process is modelled as the flow of a fluid (the resin) through a porous medium (the reinforcement). It is governed by Darcy’s law, i.e., the fluid velocity vector u is proportional to the pressure gradient
u¼
1
l
Krp
ð1Þ
where K is the permeability tensor, p the resin pressure, and l the fluid viscosity which is assumed constant for a Newtonian resin. For
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accurate simulations it is absolutely necessary to have reliable input data specifying mould geometry, fluid viscosity, reinforcement porosity and reinforcement permeability. Measurement of the permeability is not yet standardized nor normalised, and many different set-ups have been proposed. The measurements are very sensitive to various factors and large scatter in the identified permeability values is usually observed [5–10]. Such scatter is not surprising, since the permeability is affected by details of the geometry of the porous medium, which are highly variable for typical reinforcements. As the test specimen usually consists of a stack of layers, and each individual layer and the interface between layers allow a mixture of micro (filament level) and macro (fibre bundle level) flows, the variability is possibly created by [11]: nesting of the layers; mixture of micro and macro flows [12–20]; (non-uniform) shearing, stretching and compression of the textile layers; production variability and sampling procedure in the textile production; saturated and non-saturated fluid flow. Testing of a series of textile specimens therefore yields a statistical distribution of permeability values instead of deterministic values. The test rig itself also contributes to a broader distribution of identified permeability values due to errors on the pressure measurement, fluid viscosity values, limited mould cavity stiffness, boundary race effects and fluid velocity measurement. In practice, these sources of scatter will act simultaneously, making it difficult to distinguish the possible contributions. The maximum permeability value can easily be fourfold the minimum value, and relative standard deviations of 30% are common. Measured values obtained in different labs can differ even more (by a factor of 10). These issues are a problem for the calibration of test rigs and for comparison of results from different test rigs. Moreover, it presents a difficulty when numerical flow simulation software, for the numerical prediction of the permeability, is to be experimentally validated. Therefore, we developed a solid epoxy test specimen that can be used as a reference sample [21,22]. This object was produced with a stereolithography (SL) technique. The porous structure of the sample has the same main features as textile fabrics: the same order of magnitude of the pore sizes as well as a similar interconnectivity and tortuosity of the pores. However, the specimen was designed to avoid all of the sources of variability, inherent to real textiles, mentioned above. Since the permeability properties of the specimen do not vary from test to test, an excellent repeatability of the experiments is expected; any discrepancy between different measurements will be attributed to the set-up and data processing. As a result, this SL specimen can be used as a reference sample for calibration of test rigs and for comparison of results from different test rigs. Additionally, the SL sample has a simple unit cell, with accurately known geometry, which allows a correct and complete specification of the geometry in numerical permeability prediction software, allowing greater confidence in the experimental validation of such simulation programs than could be obtained with the various textiles used in previous validation efforts [22–24]. This paper presents a systematic study of the first experimental results obtained with this specimen: the permeability values, the scatter levels reached, the methodology of calibration, and practical solutions for some issues that arose with repeated experiments. The experiments were performed by means of a highly automated central injection rig, called ‘‘PIERS set-up”. This PIERS (Permeability Identification using Electrical Resistance Sensors) set-up enables a
very fast and automated measurement of the flow front evolution versus time [5,25]. To demonstrate, how the SL specimen can be used for assessment of data processing procedures, two different data processing schemes were used: the commonly used analytic approach was used and an inverse method [26]. Moreover, the experimental results are compared with the results from the flow simulation software FlowTex [22], for validation. 2. Materials and methods 2.1. Stereolithographic production of reference specimens Stereolithography is an additive fabrication process used to create three-dimensional objects from liquid photosensitive polymers that solidify when exposed to ultraviolet light. The object is built upon a platform situated just below the surface in a vat of liquid resin. A UV laser traces out the first layer, solidifying the model’s cross section while leaving excess areas liquid. Next, an elevator incrementally lowers the platform into the liquid polymer. A sweeper re-coats the solidified layer with liquid, and the laser traces the second layer atop the first. This process is repeated layer by layer, until the whole model is complete. The additive nature of the SL process allows the production of a structure with specific and complex internal features so that a kind of ‘‘artificial” reinforcement can be created in which the fluid flow path is curved much as it would be in conventional textiles. Moreover, this production technique enabled a design which, while it resembles typical reinforcements in important respects, avoids the aforementioned sources of scatter in the experiments and various modelling issues of the flow simulation software (Table 1). Note that, in particular, the complications and variability associated with the effects of dual-scale porosity on permeability are not encountered in the reference specimen, because its design focuses on the inter-yarn porosity which is the main factor defining permeability of woven, braided and knitted textile reinforcements. The tortuosity of the pores in the reference specimen is of the same order of magnitude as for typical textile reinforcements: the curvature of the channels is given by a characteristic length of 5 mm, a wave width of 1 mm and wave height of 0.5 mm. The SL specimen, which is designed for the PIERS 2D central injection rig, consists of about 3500 adjacent unit cells (Fig. 1). Such specimen could be used for 1D experiments as well and the structure can be easily adapted for through the thickness experiments and possible extra requirements of other test rigs to be used. 2.2. Permeability identification using electrical resistance sensors The experimental permeability identification is performed with the PIERS set-up. This set-up is described in detail elsewhere Table 1 Issues, eliminated in the SL specimen, that cause the permeability of textile performs to exhibit significant variations. Issue
SL specimen
Nesting Existence of micro-flows; (non-uniform) shearing, stretching and compression of the textile layers Tests are performed on different textile specimens
. . .consists of one layer . . .is a solid, rigid structure with a good surface quality . . .has good wear resistance and can be cleaned and reused . . .is periodic in the XY directions
The macro permeability is not equal to the meso-scale permeability as no perfect periodicity exists in the mould Textile geometry data are often missing or incomplete
. . .produced using precise CAD file
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Fig. 1. A unit cell of the SL specimen consisting of five layers (6 3 3 mm).
Fig. 2. CAD model of the PIERS set-up with a fibre reinforcement; the 60 sensors of the lower mould half are marked and two hypothetical flow front shapes are shown.
[5,25]. The heart of the set-up is a solidly supported steel mould that holds 120 DC-resistance based sensors (Fig. 2). The actual experiment involves injecting a Newtonian fluid (corn syrup [5,27]), centrally in the pre-placed reinforcement, and, as such, the propagating flow front will trigger the sensors on arrival. Using the flow front arrival times of the PIERS experiment, two different data processing schemes are employed to calculate the permeability, so that their respective effectiveness can be evaluated. The first approach is based on a least squares fit to a commonly used analytical approximation of the injection into a nearly-isotropic orthotropic medium, as was proposed by Adams and Rebenfeld [28–30]. This approach was implemented in the software program, called ‘‘PMPI” (Porous Media Permeability Identification) [5,25], that was initially used for permeability identification with the PIERS set-up. The second approach uses a numerical simulation (solution of Darcy equation) of the measurement, with an inverse method for identifying the permeability parameters. The inverse method incorporates a FE model that simulates the PIERS experiment and provides numerical flow front arrival times at the sensor locations. In this model the components of the inplane permeability tensor appear as parameters and the results, i.e., the flow front arrival times, are compared with those of the PIERS experiment. In general there will be a discrepancy between the two results. The parameters of the numerical model are then updated and the simulation is run again. The results are compared with the measurements, and if the agreement is not yet sufficient,
the model parameters are updated again and the simulation is repeated. This iterative solving process is continued until satisfactory agreement between experiment and simulation is reached. The parameter values that were used in the last simulation are taken as the permeability values of the object under study [26]. The three specimens were each tested once per session, in 10 sessions, always in the same order. Typically, only one session could be completed per day, to allow time for cleaning and drying the specimens completely after each test. During preliminary experiments, a problem was encountered. The SL specimens were severely bent after a number of measurements. This was found to be a consequence of corn syrup residues from the PIERS experiments. Apparently, the specimens were not sufficiently cleaned after every experiment and, when drying, uneven shrinkage in the sugar deposits caused the whole structure to bend. Moreover, a gradual decrease of the permeability values was observed. Consequently, a simple machine was developed to thoroughly clean the SL specimens. This machine has the same working principle as the PIERS set-up, but water is injected through the specimens instead of corn syrup. When the specimen was placed in the machine for 20–30 min after every experiment, no bending was observed any more. Nonetheless, new SL specimens were produced for final testing. A second problem was the accurate placement of the SL specimen inside the mould cavity. Some systematic asymmetry of the arrival times in preliminary experiments was found to be an artefact of misalignment of the circular hole in the centre of the SL specimen with the slightly smaller injection gate in the lower sensor plate. This problem was resolved by using a coaxial cylindrical shim to ensure precise alignment. 2.3. Numerical calculation of permeability: Stokes solution The permeability of a porous medium can be computed by solving the dimensionless Stokes equations
Du Rerp ¼ f ru¼0
ð2Þ
on a (unit cell of the) digital model of the porous medium. Here, the applied body force f or an applied pressure gradient rp are input for the simulations, the velocity u(x, y,z) is the output. Re is the Reynolds number. The Stokes equations are a simplification of the general Navier–Stokes equations, and are valid for steady, isothermal, laminar flow of incompressible, Newtonian fluids. Once the velocity is computed, the permeability K is calculated via the dimensionless law of Darcy,
hui ¼
Re f K hrpi : L Fr
ð3Þ
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The symbol h i denotes volume averaging or homogenization, Fr is the Froude number of the flow and L is characteristic length of the geometry, for example the size of the computational unit cell. We developed a solver for the computation of the permeability of textiles [23]. The solver FlowTex applies a finite difference discretisation of the Stokes equations on a regular grid. This regular grid is very useful for the application with textiles, as this avoids difficult meshing of the fluid region of the digital model of the textiles. It was shown that this solver yields quite accurate results for real textiles if the unit cell geometry is represented correctly. However, the uncertainty of the geometry of real textiles and the variability of the measurement results allowed noticeable differences between the experimental and numerical results. To prove the validity of the numerical solution on a test case where the geometry of unit cell is defined with much higher precision than is achievable for textile structures, we compare numerical and experimental permeability values for the SL specimen. As the scatter of the experimental results is almost non-existent, and as a very accurate computer model of the specimen exists, the specimen allows for a more precise comparison between numerics and experiments. 3. Results and discussion
Table 2 Evaluation of the four dimensions. Dimensions
Llong
Ltrans
dtrans
dlong
Designed (mm) Average (mm) Std. Dev. (mm)
3 2.95 0.032
1.5 1.49 0.009
0.5 0.51 0.012
0.5 0.51 0.038
orientation reduces both the absolute error in the as-produced specimen geometry, because the overhang is smaller, and the relative error in the cavity dimensions, because the largest error is in the largest dimension. It also results in the smoothest surface in contact with the mould, which helps to avoid race-tracking or damage infliction by the mould. Characteristic dimensions of the as-produced specimen geometry (Fig. 3) were measured on photomicrographs taken with a Leica MZ12.5 optical microscope. Table 2 summarizes measurements of 108 micrographs taken from different regions of three different specimens. A tolerance on the order of 0.04 mm in the longitudinal direction and 0.01 mm in the transverse directions is achieved with the stereolithography process. The same tolerances were found on subsequently produced specimens, confirming that the stereolithography manufacturing process offers the repeatability and precise control of geometry required for a standard reference specimen.
3.1. Measurement of the reference specimens’ geometry 3.2. Permeability identification In the vertical direction of the SL machine, referred to as the Z-direction, the production technique is not as accurate as in the horizontal directions. This is due to various factors, e.g., the influence of gravity and the sweeper of the machine that systematically moves over every printed layer. These issues are especially noticeable when overhangs are printed, but were minimized by using a newly designed resin, as described in [21]. Because the horizontal directions are more accurate, the specimen was produced with the long direction of the unit cell along the vertical axis. This
Fig. 3. Photomicrograph indicating four characteristic dimensions of the asproduced SL specimen geometry.
The data were processed both using the ‘‘PMPI” software and using a new inverse method, so that their respective effectiveness can be evaluated. A summary of the results is given in Table 3, where each specimen is numbered according to the order in which they were tested during a session. The average values of permeability, identified with the two methods, do not have a statistically significant difference. However, the relative standard deviation (Rel. SD) is generally significantly lower when the inverse method is used. This is related to the inability of the analytical approach to use all of the available sensor data. A fundamental limitation of the analytical approach is that it assumes the preform to be infinite. When the fluid front reaches an edge of the reinforcement, that moment is considered as the end of the experiment (Fig. 2). Data from sensors which the flow front reached after the flow profile began to be affected by the edge of the reinforcement cannot be used, because the analytical approximation for the arrival times does not take the edges into account. The inverse method uses a numerical simulation of the injection, which changes the boundary conditions appropriately when the fluid front reaches an edge of the reinforcement. When using the inverse method with the finite element model to simulate the PIERS experiment, the experiment can usefully continue until all sensors are reached, allowing for a more accurate determination of the entire permeability tensor. As a direct result of using a greater number of sensors, the data-reduction scheme is more robust: if one sensor registers a deviant measurement, this will have a smaller influence on the final outcome of the calculation. In this context, it is worth noting that not all sensors contribute equally to the determination of the permeability tensor: data are weighted by reliability, and sensors in the direction of a principal component of the tensor contribute mostly to that component. In the experiments, it is observed that arrival times at sensors near the inlet are less reliable. Sensors further from the inlet already measure an average over a greater amount of time and material, so that the variability of those results is inherently lower. Thus, the ability of the inverse method to use all of the available sensor data is especially significant in the direction of the smaller permeability, where fewer sensors are reached in time to be used in the analytical approach.
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Table 3 The results of 30 (of which 2 are rejected) experiments. Processing scheme
Analytic approach (PMPI)
Inverse method
Average
SD
Rel. SD (%)
Average
SD
Rel. SD (%)
Specimen 1 K1 [E-9 m2] K2 [E-9 m2] Anisotropy (K2/K1) []
2.37 5.46 2.30
0.05 0.38 0.14
2.1 6.9 6.0
2.49 5.54 2.22
0.07 0.22 0.07
2.6 3.9 3.0
Specimen 2 K1 [E-9 m2] K2 [E-9 m2] Anisotropy (K2/K1) []
2.35 5.34 2.28
0.16 0.33 0.03
6.7 6.2 1.2
2.48 5.43 2.19
0.13 0.28 0.01
5.4 5.1 0.6
Specimen 3 K1 [E-9 m2] K2 [E-9 m2] Anisotropy (K2/K1) []
2.32 5.29 2.28
0.12 0.22 0.02
5.0 4.2 1.0
2.46 5.39 2.19
0.07 0.15 0.01
2.7 2.8 0.4
Specimens 1–2–3 K1 [E-9 m2] K2 [E-9 m2] Anisotropy (K2/K1) []
2.34 5.36 2.29
0.12 0.31 0.07
5.0 5.8 3.2
2.47 5.44 2.20
0.09 0.22 0.04
3.8 4.1 1.7
Parnas et al. [31] reported tests on a certain standard reference fabric (three-dimensional woven material) which requires a carefully designed experimental protocol to achieve consistently reproducible results. However, their results still showed a coefficient of variation of 15%. This is significantly higher than the reported scatter of Hoes et al. [5,11] obtained on a woven specimen with welldefined geometry, which consists of fused PVC-coated material. Hoes used the PIERS set-up with the PMPI software, and obtained coefficient of variation which varied between 5% and 10%. It was also concluded that the manufacturing process was not sufficiently repeatable which is important for a reference specimen. The scatter levels presented in this paper, especially those of the inverse method, are even lower than the ones obtained by Hoes. The results of the inverse method are illustrated in Fig. 4. These data were examined to identify extreme outliers. These are points of which there is a strong indication that they are outside the range of observations that can be reasonably expected. For finding outliers a box-and-whiskers plot was used. The seventh and tenth measurement, performed on specimen one, have both an extreme outlier in the K1 dataset and in the anisotropy dataset. This confirms our observations while performing these experiments. At that stage, we were already sceptical about the results because of the peculiar flow propagation and unexplainably large number of
malfunctioning sensors. Note that the anisotropy is very useful to indentify outliers. Because the viscosity is the same for both principal directions, when the ratio of the two permeabilities is calculated, the effects of changes in viscosity will cancel. As presented in Table 3, the relative standard deviation of the anisotropy ratio is significantly smaller than the relative standard deviation of the respective permeabilities. Therefore, we believe there is room for improvement of precision of the permeability identification by automating the viscosity measurements. Currently, the viscosity is measured before and after the injections in each of three specimens, to compensate for possible variations, using a Brookfield RVDVII+ viscometer [32]. This renders a higher uncertainty on the viscosity that has to be considered for the middle experiment which may explain why, especially for specimen two, the relative standard deviation of the permeability is significantly higher than the relative standard deviation of the anisotropy. More accurately accounting for viscosity is an interesting open question which could perhaps be addressed by performing an in-line viscosity measurement. This would allow considering a viscosity value at each time step of the FE simulation of the PIERS experiment. The deviation of the anisotropy of specimen one is significantly higher than the deviation of the anisotropy’s of the other two specimens. This indicates that each first experiment, out of the three performed per day, was less successful than the subsequent two. It seems more likely that this is due to irregularities when starting up the machine than to a problem with that particular specimen, but neither hypothesis can be completely ruled out without extensive further investigation. On a final note, prior to the presented measurements, three experiments were performed with an injection pressure that was higher by a factor of about 1.5, but no conclusive difference can be observed with respect to the presented permeability results. The three experiments, with higher injection pressure, yield principal components of the 2D permeability tensor of: 2.48 ± 0.05 109 m2 and 5.52 ± 0.15 109 m2. 3.3. Computed permeability
Fig. 4. Permeability values identified using the inverse method.
Figs. 5 and 6 show the result of a numerical fluid simulation on the unit cell of the specimen. Fig. 5 shows streamlines of the fluid flow, and half of the computational geometry. Fig. 6 is a 2D cut of the geometry, showing the computed pressure distribution at the centre of the specimen. For the simulation, no-slip boundary conditions were used at the boundary between the fluid–solid domains. In the in-plane direction, periodic boundary conditions
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Fig. 5. Half of the computational specimen model, with streamlines of the computed fluid flow.
were set at the specimen boundary. On the top and the bottom, ‘wall’ conditions were set, corresponding to the mould plates which do not allow fluid to flow in that direction. Fig. 7 presents the experimental permeability values, and the computed values, for both in-plane directions. On the figure, also a comparison between experimental and numerical values for a Plain Woven Fabric (PWF) is shown. More details about the PWF
can be found in Verleye et al. [24]. Here, we present the results again, to give an indication of the accuracy of permeability computations on textiles and on the SL specimen. We can conclude that the numerical solution of Stokes equation computes the permeability of the specimen accurately. Thus, the methodology and implementation are correct. When recalcitrant difficulties in
Fig. 6. 2D cut of the geometry, showing the computed pressure distribution at the centre of the specimen.
Fig. 7. Computational and experimental permeability values for the SL structure and a Plain Woven Fabric (PWF).
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textile modelling, such as accurately predicting nesting and compression, especially at high volume fractions, are avoided, then the agreement between measurements and simulations is excellent. The numerical results, with principal components of the 2D permeability tensor of 2.2 109 m2 and 6.3 109 m2, correspond very well with the experimental results. Note that the agreement between the greater permeability values is slightly less than between the smaller permeability values. This is probably due to the fact that the greater principal permeability coincides with the slightly less accurate (vertical) direction of the production machine. Videlicet, along the latter direction a higher deviation is found on the specimens’ dimensions (Table 2). Consequently, it is to be expected that the three SL specimens differ more along that direction than along the direction of the smaller permeability. These issues may explain the findings in Table 3 where it is shown that the specimens’ average K2 values differ more amongst each other than the specimens’ average K1 values and that the relative standard deviation of the overall K2 value is higher than the one of the overall K1 value. 4. Conclusions The textile-like solid SL specimen, described in this paper, is proven to be suitable as a reference medium for measurement of permeability: 1. In the experiments performed by means of a 2D central injection rig, the relative standard deviation of permeability was less than 5%, which proves the sources of variability inherent to real textiles are eliminated. 2. Hitherto unproven differences in the effectiveness of two different methods for processing the measurement data were demonstrated. The variability of results from an inverse method, using a finite element model, is lower than with the standard approach, based on an analytical approximation of the flow front positions. 3. For the experimental validation of numerical unit cell-scale permeability prediction software, the SL sample has the advantage that its geometry can be correctly specified as a periodic structure with a unit cell of accurately known dimensions. Compared with the various textiles used in previous validation efforts, it enables greater confidence that the experimental data correspond exactly to the simulation, and therefore a more convincing validation. Previously proposed numerical methods based on solution of Stokes equation, have been validated by comparison of the predicted and experimentally measured permeability values for the SL reference specimen. Prospectively, the reference specimen will be implemented in the International Permeability Benchmarking Exercise (IPBE). This is a broad international activity aiming towards detecting deficiencies in the currently available methods and apparatus for identification of permeability of fibrous reinforcements. As opposed to benchmarking with real textiles, this specimen will isolate the variability arising from the different set-ups from the inherent variability of textiles. As a result, this benchmark can be used as a rallying point for the characterization of the variability of real textiles, and contribute to an understanding of effects due to dualscale porosity, capillary forces, etc. Acknowledgements The authors recognize the financial support of the IWT, the Flemish governmental organization for scientific and industrial research support.
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Computation of permeability of textile with experimental validation for monofilament and non crimp fabrics. Berlin: Springer; 2007. p. 93–109. [25] Hoes K, Dinescu D, Sol H, Vanheule M, Parnas RS, Luo Y, et al. New set-up for measurement of permeability properties of fibrous reinforcements for RTM. Compos Part A 2002;33(7):959–69. [26] Morren G, Bossuyt S, Sol H. 2D permeability tensor identification of fibrous reinforcements for RTM using an inverse method. Compos Part A 2008;39A(9):1530–6. [27] Steenkamer DA, McKnight SH, Wilkins DJ, Karbhari VM. Experimental characterization of permeability and fiber wetting for liquid moulding. J Mater Sci 1995;30(12):3207–15. [28] Adams KL, Miller B, Rebenfeld L. Forced in-plane flow of an epoxy resin in fibrous networks. Polym Eng Sci 1986;26:1434. [29] Adams KL, Rebenfeld L. In-plane flow of fluids in fabrics: structure/flow characterization. Text Res J 1987;57:647. [30] Adams KL, Russel WB, Rebenfeld L. Radial penetration of a viscous liquid into a planar anisotropic porous medium. Int J Multiphase Flow 1988;14(2): 203–15. [31] Parnas RS et al. Permeability characterization. Part 1: a proposed standard reference fabric for permeability. Polym Compos 1995;16(6):429–45. [32] Brookfield Laboratories. Brookfield DV-II+ programmable viscometer. Middleboro, MA, USA: Brookfield Engineering.
Contents lists available at ScienceDirect
Composites: Part A journal homepage: www.elsevier.com/locate/compositesa
A reference specimen for permeability measurements of fibrous reinforcements for RTM Gerd Morren a,*, Massimo Bottiglieri a, Sven Bossuyt a, Hugo Sol a, David Lecompte b, Bart Verleye c, Stepan V. Lomov d a
Vrije Universiteit Brussel (VUB), Dept. Mechanics of Materials and Constructions, Pleinlaan 2, B-1050 Brussels, Belgium Royal Military Academy (RMA), Dept. Materials and Construction Engineering, Renaissancelaan 30, B-1000 Brussels, Belgium c Katholieke Universiteit Leuven (K.U.Leuven), Dept. Computer Science, Celestijnenlaan 200A, B-3001 Heverlee, Belgium d Katholieke Universiteit Leuven (K.U.Leuven), Dept. Metallurgy and Materials Engineering, Kasteelpark Arenberg 44, B-3001 Heverlee, Belgium b
a r t i c l e
i n f o
Article history: Received 28 August 2008 Received in revised form 21 November 2008 Accepted 26 November 2008
Keywords: A. Fabrics/textiles E. Resin Transfer Moulding (RTM) Permeability
a b s t r a c t The capability to simulate the flow of resin through a porous reinforcement by FE modelling has become very important for designing RTM production processes for high-performance composite parts. The key parameter in RTM flow simulations is the fibre reinforcement permeability. The measurement of this material parameter is still not standardized and many different set-ups have been proposed. Recently, a stereolithography technique was used to produce a textile-like solid specimen with anisotropic permeability, designed as a reference for calibration and comparison of permeability measurement set-ups and for validation of numerical permeability computation software. Unlike real textiles, the permeability properties of such reference specimens do not vary from test to test. Excellent repeatability of the experiments is achieved. When used for benchmarking, any discrepancy between different measurements on this specimen must be attributed to the set-up and data processing. This paper presents the first experimental measurements of the permeability of such reference specimens, obtained with a 2D central injection rig. The measured values, with principal components of the 2D permeability tensor of 2.47 ± 0.09 109 m2 and 5.44 ± 0.22 109 m2, are in good agreement with the values predicted using numerical permeability computation software. Statistics from a series of measurements using the same set-up show that the precision of the permeability identification depends on the data processing procedure. An approach which incorporates a numerical model that is also valid after the fluid reached an edge of the reinforcement performs significantly better than the approach, based on an analytical approximation, which was used before. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Liquid Composite Moulding (LCM), particularly its sub-class, Resin Transfer Moulding (RTM), is the state-of-the-art technology for producing textile reinforced composite parts. In LCM, liquid resin is injected into a mould holding a fibrous preform. Once the preform is impregnated, the resin cures and the finished component is de-moulded. It is imperative that the preform is sufficiently saturated with resin during the impregnation. Otherwise, the resulting part will contain unallowable void content. Consequently, one of the key issues in LCM process design is developing the injection strategy: placement of resin inlets and air vents, pressure variation, application of vacuum, etc. Although it is often feasible to find a reasonable injection strategy by trial and error, this method is risky and costly, especially if expensive moulds need to * Corresponding author. Tel.: +32 2 629 29 27; fax: +32 2 629 29 28. E-mail address: [email protected] (G. Morren). 1359-835X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2008.11.011
be manufactured, or when the material costs are very high. Therefore, virtual prototyping software has been developed to assist the engineer in correctly designing the mould [1,2]. Through injection simulations, the problem areas in a mould can be identified and the mould layout, i.e., the positions of resin injection points and air vents, as well as the injection strategy, can be adapted accordingly [2,3]. Moreover, the software can assist the designer in optimizing the injection process in order to obtain a robust production process with the shortest possible cycle time [4]. The injection process is modelled as the flow of a fluid (the resin) through a porous medium (the reinforcement). It is governed by Darcy’s law, i.e., the fluid velocity vector u is proportional to the pressure gradient
u¼
1
l
Krp
ð1Þ
where K is the permeability tensor, p the resin pressure, and l the fluid viscosity which is assumed constant for a Newtonian resin. For
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accurate simulations it is absolutely necessary to have reliable input data specifying mould geometry, fluid viscosity, reinforcement porosity and reinforcement permeability. Measurement of the permeability is not yet standardized nor normalised, and many different set-ups have been proposed. The measurements are very sensitive to various factors and large scatter in the identified permeability values is usually observed [5–10]. Such scatter is not surprising, since the permeability is affected by details of the geometry of the porous medium, which are highly variable for typical reinforcements. As the test specimen usually consists of a stack of layers, and each individual layer and the interface between layers allow a mixture of micro (filament level) and macro (fibre bundle level) flows, the variability is possibly created by [11]: nesting of the layers; mixture of micro and macro flows [12–20]; (non-uniform) shearing, stretching and compression of the textile layers; production variability and sampling procedure in the textile production; saturated and non-saturated fluid flow. Testing of a series of textile specimens therefore yields a statistical distribution of permeability values instead of deterministic values. The test rig itself also contributes to a broader distribution of identified permeability values due to errors on the pressure measurement, fluid viscosity values, limited mould cavity stiffness, boundary race effects and fluid velocity measurement. In practice, these sources of scatter will act simultaneously, making it difficult to distinguish the possible contributions. The maximum permeability value can easily be fourfold the minimum value, and relative standard deviations of 30% are common. Measured values obtained in different labs can differ even more (by a factor of 10). These issues are a problem for the calibration of test rigs and for comparison of results from different test rigs. Moreover, it presents a difficulty when numerical flow simulation software, for the numerical prediction of the permeability, is to be experimentally validated. Therefore, we developed a solid epoxy test specimen that can be used as a reference sample [21,22]. This object was produced with a stereolithography (SL) technique. The porous structure of the sample has the same main features as textile fabrics: the same order of magnitude of the pore sizes as well as a similar interconnectivity and tortuosity of the pores. However, the specimen was designed to avoid all of the sources of variability, inherent to real textiles, mentioned above. Since the permeability properties of the specimen do not vary from test to test, an excellent repeatability of the experiments is expected; any discrepancy between different measurements will be attributed to the set-up and data processing. As a result, this SL specimen can be used as a reference sample for calibration of test rigs and for comparison of results from different test rigs. Additionally, the SL sample has a simple unit cell, with accurately known geometry, which allows a correct and complete specification of the geometry in numerical permeability prediction software, allowing greater confidence in the experimental validation of such simulation programs than could be obtained with the various textiles used in previous validation efforts [22–24]. This paper presents a systematic study of the first experimental results obtained with this specimen: the permeability values, the scatter levels reached, the methodology of calibration, and practical solutions for some issues that arose with repeated experiments. The experiments were performed by means of a highly automated central injection rig, called ‘‘PIERS set-up”. This PIERS (Permeability Identification using Electrical Resistance Sensors) set-up enables a
very fast and automated measurement of the flow front evolution versus time [5,25]. To demonstrate, how the SL specimen can be used for assessment of data processing procedures, two different data processing schemes were used: the commonly used analytic approach was used and an inverse method [26]. Moreover, the experimental results are compared with the results from the flow simulation software FlowTex [22], for validation. 2. Materials and methods 2.1. Stereolithographic production of reference specimens Stereolithography is an additive fabrication process used to create three-dimensional objects from liquid photosensitive polymers that solidify when exposed to ultraviolet light. The object is built upon a platform situated just below the surface in a vat of liquid resin. A UV laser traces out the first layer, solidifying the model’s cross section while leaving excess areas liquid. Next, an elevator incrementally lowers the platform into the liquid polymer. A sweeper re-coats the solidified layer with liquid, and the laser traces the second layer atop the first. This process is repeated layer by layer, until the whole model is complete. The additive nature of the SL process allows the production of a structure with specific and complex internal features so that a kind of ‘‘artificial” reinforcement can be created in which the fluid flow path is curved much as it would be in conventional textiles. Moreover, this production technique enabled a design which, while it resembles typical reinforcements in important respects, avoids the aforementioned sources of scatter in the experiments and various modelling issues of the flow simulation software (Table 1). Note that, in particular, the complications and variability associated with the effects of dual-scale porosity on permeability are not encountered in the reference specimen, because its design focuses on the inter-yarn porosity which is the main factor defining permeability of woven, braided and knitted textile reinforcements. The tortuosity of the pores in the reference specimen is of the same order of magnitude as for typical textile reinforcements: the curvature of the channels is given by a characteristic length of 5 mm, a wave width of 1 mm and wave height of 0.5 mm. The SL specimen, which is designed for the PIERS 2D central injection rig, consists of about 3500 adjacent unit cells (Fig. 1). Such specimen could be used for 1D experiments as well and the structure can be easily adapted for through the thickness experiments and possible extra requirements of other test rigs to be used. 2.2. Permeability identification using electrical resistance sensors The experimental permeability identification is performed with the PIERS set-up. This set-up is described in detail elsewhere Table 1 Issues, eliminated in the SL specimen, that cause the permeability of textile performs to exhibit significant variations. Issue
SL specimen
Nesting Existence of micro-flows; (non-uniform) shearing, stretching and compression of the textile layers Tests are performed on different textile specimens
. . .consists of one layer . . .is a solid, rigid structure with a good surface quality . . .has good wear resistance and can be cleaned and reused . . .is periodic in the XY directions
The macro permeability is not equal to the meso-scale permeability as no perfect periodicity exists in the mould Textile geometry data are often missing or incomplete
. . .produced using precise CAD file
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Fig. 1. A unit cell of the SL specimen consisting of five layers (6 3 3 mm).
Fig. 2. CAD model of the PIERS set-up with a fibre reinforcement; the 60 sensors of the lower mould half are marked and two hypothetical flow front shapes are shown.
[5,25]. The heart of the set-up is a solidly supported steel mould that holds 120 DC-resistance based sensors (Fig. 2). The actual experiment involves injecting a Newtonian fluid (corn syrup [5,27]), centrally in the pre-placed reinforcement, and, as such, the propagating flow front will trigger the sensors on arrival. Using the flow front arrival times of the PIERS experiment, two different data processing schemes are employed to calculate the permeability, so that their respective effectiveness can be evaluated. The first approach is based on a least squares fit to a commonly used analytical approximation of the injection into a nearly-isotropic orthotropic medium, as was proposed by Adams and Rebenfeld [28–30]. This approach was implemented in the software program, called ‘‘PMPI” (Porous Media Permeability Identification) [5,25], that was initially used for permeability identification with the PIERS set-up. The second approach uses a numerical simulation (solution of Darcy equation) of the measurement, with an inverse method for identifying the permeability parameters. The inverse method incorporates a FE model that simulates the PIERS experiment and provides numerical flow front arrival times at the sensor locations. In this model the components of the inplane permeability tensor appear as parameters and the results, i.e., the flow front arrival times, are compared with those of the PIERS experiment. In general there will be a discrepancy between the two results. The parameters of the numerical model are then updated and the simulation is run again. The results are compared with the measurements, and if the agreement is not yet sufficient,
the model parameters are updated again and the simulation is repeated. This iterative solving process is continued until satisfactory agreement between experiment and simulation is reached. The parameter values that were used in the last simulation are taken as the permeability values of the object under study [26]. The three specimens were each tested once per session, in 10 sessions, always in the same order. Typically, only one session could be completed per day, to allow time for cleaning and drying the specimens completely after each test. During preliminary experiments, a problem was encountered. The SL specimens were severely bent after a number of measurements. This was found to be a consequence of corn syrup residues from the PIERS experiments. Apparently, the specimens were not sufficiently cleaned after every experiment and, when drying, uneven shrinkage in the sugar deposits caused the whole structure to bend. Moreover, a gradual decrease of the permeability values was observed. Consequently, a simple machine was developed to thoroughly clean the SL specimens. This machine has the same working principle as the PIERS set-up, but water is injected through the specimens instead of corn syrup. When the specimen was placed in the machine for 20–30 min after every experiment, no bending was observed any more. Nonetheless, new SL specimens were produced for final testing. A second problem was the accurate placement of the SL specimen inside the mould cavity. Some systematic asymmetry of the arrival times in preliminary experiments was found to be an artefact of misalignment of the circular hole in the centre of the SL specimen with the slightly smaller injection gate in the lower sensor plate. This problem was resolved by using a coaxial cylindrical shim to ensure precise alignment. 2.3. Numerical calculation of permeability: Stokes solution The permeability of a porous medium can be computed by solving the dimensionless Stokes equations
Du Rerp ¼ f ru¼0
ð2Þ
on a (unit cell of the) digital model of the porous medium. Here, the applied body force f or an applied pressure gradient rp are input for the simulations, the velocity u(x, y,z) is the output. Re is the Reynolds number. The Stokes equations are a simplification of the general Navier–Stokes equations, and are valid for steady, isothermal, laminar flow of incompressible, Newtonian fluids. Once the velocity is computed, the permeability K is calculated via the dimensionless law of Darcy,
hui ¼
Re f K hrpi : L Fr
ð3Þ
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The symbol h i denotes volume averaging or homogenization, Fr is the Froude number of the flow and L is characteristic length of the geometry, for example the size of the computational unit cell. We developed a solver for the computation of the permeability of textiles [23]. The solver FlowTex applies a finite difference discretisation of the Stokes equations on a regular grid. This regular grid is very useful for the application with textiles, as this avoids difficult meshing of the fluid region of the digital model of the textiles. It was shown that this solver yields quite accurate results for real textiles if the unit cell geometry is represented correctly. However, the uncertainty of the geometry of real textiles and the variability of the measurement results allowed noticeable differences between the experimental and numerical results. To prove the validity of the numerical solution on a test case where the geometry of unit cell is defined with much higher precision than is achievable for textile structures, we compare numerical and experimental permeability values for the SL specimen. As the scatter of the experimental results is almost non-existent, and as a very accurate computer model of the specimen exists, the specimen allows for a more precise comparison between numerics and experiments. 3. Results and discussion
Table 2 Evaluation of the four dimensions. Dimensions
Llong
Ltrans
dtrans
dlong
Designed (mm) Average (mm) Std. Dev. (mm)
3 2.95 0.032
1.5 1.49 0.009
0.5 0.51 0.012
0.5 0.51 0.038
orientation reduces both the absolute error in the as-produced specimen geometry, because the overhang is smaller, and the relative error in the cavity dimensions, because the largest error is in the largest dimension. It also results in the smoothest surface in contact with the mould, which helps to avoid race-tracking or damage infliction by the mould. Characteristic dimensions of the as-produced specimen geometry (Fig. 3) were measured on photomicrographs taken with a Leica MZ12.5 optical microscope. Table 2 summarizes measurements of 108 micrographs taken from different regions of three different specimens. A tolerance on the order of 0.04 mm in the longitudinal direction and 0.01 mm in the transverse directions is achieved with the stereolithography process. The same tolerances were found on subsequently produced specimens, confirming that the stereolithography manufacturing process offers the repeatability and precise control of geometry required for a standard reference specimen.
3.1. Measurement of the reference specimens’ geometry 3.2. Permeability identification In the vertical direction of the SL machine, referred to as the Z-direction, the production technique is not as accurate as in the horizontal directions. This is due to various factors, e.g., the influence of gravity and the sweeper of the machine that systematically moves over every printed layer. These issues are especially noticeable when overhangs are printed, but were minimized by using a newly designed resin, as described in [21]. Because the horizontal directions are more accurate, the specimen was produced with the long direction of the unit cell along the vertical axis. This
Fig. 3. Photomicrograph indicating four characteristic dimensions of the asproduced SL specimen geometry.
The data were processed both using the ‘‘PMPI” software and using a new inverse method, so that their respective effectiveness can be evaluated. A summary of the results is given in Table 3, where each specimen is numbered according to the order in which they were tested during a session. The average values of permeability, identified with the two methods, do not have a statistically significant difference. However, the relative standard deviation (Rel. SD) is generally significantly lower when the inverse method is used. This is related to the inability of the analytical approach to use all of the available sensor data. A fundamental limitation of the analytical approach is that it assumes the preform to be infinite. When the fluid front reaches an edge of the reinforcement, that moment is considered as the end of the experiment (Fig. 2). Data from sensors which the flow front reached after the flow profile began to be affected by the edge of the reinforcement cannot be used, because the analytical approximation for the arrival times does not take the edges into account. The inverse method uses a numerical simulation of the injection, which changes the boundary conditions appropriately when the fluid front reaches an edge of the reinforcement. When using the inverse method with the finite element model to simulate the PIERS experiment, the experiment can usefully continue until all sensors are reached, allowing for a more accurate determination of the entire permeability tensor. As a direct result of using a greater number of sensors, the data-reduction scheme is more robust: if one sensor registers a deviant measurement, this will have a smaller influence on the final outcome of the calculation. In this context, it is worth noting that not all sensors contribute equally to the determination of the permeability tensor: data are weighted by reliability, and sensors in the direction of a principal component of the tensor contribute mostly to that component. In the experiments, it is observed that arrival times at sensors near the inlet are less reliable. Sensors further from the inlet already measure an average over a greater amount of time and material, so that the variability of those results is inherently lower. Thus, the ability of the inverse method to use all of the available sensor data is especially significant in the direction of the smaller permeability, where fewer sensors are reached in time to be used in the analytical approach.
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Table 3 The results of 30 (of which 2 are rejected) experiments. Processing scheme
Analytic approach (PMPI)
Inverse method
Average
SD
Rel. SD (%)
Average
SD
Rel. SD (%)
Specimen 1 K1 [E-9 m2] K2 [E-9 m2] Anisotropy (K2/K1) []
2.37 5.46 2.30
0.05 0.38 0.14
2.1 6.9 6.0
2.49 5.54 2.22
0.07 0.22 0.07
2.6 3.9 3.0
Specimen 2 K1 [E-9 m2] K2 [E-9 m2] Anisotropy (K2/K1) []
2.35 5.34 2.28
0.16 0.33 0.03
6.7 6.2 1.2
2.48 5.43 2.19
0.13 0.28 0.01
5.4 5.1 0.6
Specimen 3 K1 [E-9 m2] K2 [E-9 m2] Anisotropy (K2/K1) []
2.32 5.29 2.28
0.12 0.22 0.02
5.0 4.2 1.0
2.46 5.39 2.19
0.07 0.15 0.01
2.7 2.8 0.4
Specimens 1–2–3 K1 [E-9 m2] K2 [E-9 m2] Anisotropy (K2/K1) []
2.34 5.36 2.29
0.12 0.31 0.07
5.0 5.8 3.2
2.47 5.44 2.20
0.09 0.22 0.04
3.8 4.1 1.7
Parnas et al. [31] reported tests on a certain standard reference fabric (three-dimensional woven material) which requires a carefully designed experimental protocol to achieve consistently reproducible results. However, their results still showed a coefficient of variation of 15%. This is significantly higher than the reported scatter of Hoes et al. [5,11] obtained on a woven specimen with welldefined geometry, which consists of fused PVC-coated material. Hoes used the PIERS set-up with the PMPI software, and obtained coefficient of variation which varied between 5% and 10%. It was also concluded that the manufacturing process was not sufficiently repeatable which is important for a reference specimen. The scatter levels presented in this paper, especially those of the inverse method, are even lower than the ones obtained by Hoes. The results of the inverse method are illustrated in Fig. 4. These data were examined to identify extreme outliers. These are points of which there is a strong indication that they are outside the range of observations that can be reasonably expected. For finding outliers a box-and-whiskers plot was used. The seventh and tenth measurement, performed on specimen one, have both an extreme outlier in the K1 dataset and in the anisotropy dataset. This confirms our observations while performing these experiments. At that stage, we were already sceptical about the results because of the peculiar flow propagation and unexplainably large number of
malfunctioning sensors. Note that the anisotropy is very useful to indentify outliers. Because the viscosity is the same for both principal directions, when the ratio of the two permeabilities is calculated, the effects of changes in viscosity will cancel. As presented in Table 3, the relative standard deviation of the anisotropy ratio is significantly smaller than the relative standard deviation of the respective permeabilities. Therefore, we believe there is room for improvement of precision of the permeability identification by automating the viscosity measurements. Currently, the viscosity is measured before and after the injections in each of three specimens, to compensate for possible variations, using a Brookfield RVDVII+ viscometer [32]. This renders a higher uncertainty on the viscosity that has to be considered for the middle experiment which may explain why, especially for specimen two, the relative standard deviation of the permeability is significantly higher than the relative standard deviation of the anisotropy. More accurately accounting for viscosity is an interesting open question which could perhaps be addressed by performing an in-line viscosity measurement. This would allow considering a viscosity value at each time step of the FE simulation of the PIERS experiment. The deviation of the anisotropy of specimen one is significantly higher than the deviation of the anisotropy’s of the other two specimens. This indicates that each first experiment, out of the three performed per day, was less successful than the subsequent two. It seems more likely that this is due to irregularities when starting up the machine than to a problem with that particular specimen, but neither hypothesis can be completely ruled out without extensive further investigation. On a final note, prior to the presented measurements, three experiments were performed with an injection pressure that was higher by a factor of about 1.5, but no conclusive difference can be observed with respect to the presented permeability results. The three experiments, with higher injection pressure, yield principal components of the 2D permeability tensor of: 2.48 ± 0.05 109 m2 and 5.52 ± 0.15 109 m2. 3.3. Computed permeability
Fig. 4. Permeability values identified using the inverse method.
Figs. 5 and 6 show the result of a numerical fluid simulation on the unit cell of the specimen. Fig. 5 shows streamlines of the fluid flow, and half of the computational geometry. Fig. 6 is a 2D cut of the geometry, showing the computed pressure distribution at the centre of the specimen. For the simulation, no-slip boundary conditions were used at the boundary between the fluid–solid domains. In the in-plane direction, periodic boundary conditions
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Fig. 5. Half of the computational specimen model, with streamlines of the computed fluid flow.
were set at the specimen boundary. On the top and the bottom, ‘wall’ conditions were set, corresponding to the mould plates which do not allow fluid to flow in that direction. Fig. 7 presents the experimental permeability values, and the computed values, for both in-plane directions. On the figure, also a comparison between experimental and numerical values for a Plain Woven Fabric (PWF) is shown. More details about the PWF
can be found in Verleye et al. [24]. Here, we present the results again, to give an indication of the accuracy of permeability computations on textiles and on the SL specimen. We can conclude that the numerical solution of Stokes equation computes the permeability of the specimen accurately. Thus, the methodology and implementation are correct. When recalcitrant difficulties in
Fig. 6. 2D cut of the geometry, showing the computed pressure distribution at the centre of the specimen.
Fig. 7. Computational and experimental permeability values for the SL structure and a Plain Woven Fabric (PWF).
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textile modelling, such as accurately predicting nesting and compression, especially at high volume fractions, are avoided, then the agreement between measurements and simulations is excellent. The numerical results, with principal components of the 2D permeability tensor of 2.2 109 m2 and 6.3 109 m2, correspond very well with the experimental results. Note that the agreement between the greater permeability values is slightly less than between the smaller permeability values. This is probably due to the fact that the greater principal permeability coincides with the slightly less accurate (vertical) direction of the production machine. Videlicet, along the latter direction a higher deviation is found on the specimens’ dimensions (Table 2). Consequently, it is to be expected that the three SL specimens differ more along that direction than along the direction of the smaller permeability. These issues may explain the findings in Table 3 where it is shown that the specimens’ average K2 values differ more amongst each other than the specimens’ average K1 values and that the relative standard deviation of the overall K2 value is higher than the one of the overall K1 value. 4. Conclusions The textile-like solid SL specimen, described in this paper, is proven to be suitable as a reference medium for measurement of permeability: 1. In the experiments performed by means of a 2D central injection rig, the relative standard deviation of permeability was less than 5%, which proves the sources of variability inherent to real textiles are eliminated. 2. Hitherto unproven differences in the effectiveness of two different methods for processing the measurement data were demonstrated. The variability of results from an inverse method, using a finite element model, is lower than with the standard approach, based on an analytical approximation of the flow front positions. 3. For the experimental validation of numerical unit cell-scale permeability prediction software, the SL sample has the advantage that its geometry can be correctly specified as a periodic structure with a unit cell of accurately known dimensions. Compared with the various textiles used in previous validation efforts, it enables greater confidence that the experimental data correspond exactly to the simulation, and therefore a more convincing validation. Previously proposed numerical methods based on solution of Stokes equation, have been validated by comparison of the predicted and experimentally measured permeability values for the SL reference specimen. Prospectively, the reference specimen will be implemented in the International Permeability Benchmarking Exercise (IPBE). This is a broad international activity aiming towards detecting deficiencies in the currently available methods and apparatus for identification of permeability of fibrous reinforcements. As opposed to benchmarking with real textiles, this specimen will isolate the variability arising from the different set-ups from the inherent variability of textiles. As a result, this benchmark can be used as a rallying point for the characterization of the variability of real textiles, and contribute to an understanding of effects due to dualscale porosity, capillary forces, etc. Acknowledgements The authors recognize the financial support of the IWT, the Flemish governmental organization for scientific and industrial research support.
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