Abstract. 1 Introduction

Transcription

1 Identification of the permeability properties of afiberreinforcement in the RTM process by a mixed numerical/experimental method D. Athanasiadis & H. Sol Dept Mechanics ofmaterials and Constructions, Free University ofbrussels (VUB), Pleinlaan 2,B-1050 Brussels, Belgium dathana@vub.ac.be & hugos@vub.ac.be Abstract This article describes a new method for the evaluation of the permeabilities of fiber reinforcements, which are required for the simulation of the Resin Transfer Moulding process for composite materials. It is indeed found that the existing methods for permeability measurements have a lot of drawbacks. The proposed method is a so-called mixed numerical/experimental method for material property identification. The principle of a mixed numerical /experimental method is to compare an experimental observation on a test set-up with a computed observation using a numerical simulation of the same set-up. The permeability parameters in the numerical model are the unknown material properties that the method aims to identify. These parameters in the numerical model will be tuned in such a way that the computed observation matches the experiments. 1 Introduction Composites have generated a tremendous amount of interest in recent years for substitution over steel parts in structural applications for their well-known properties. Of the various basic processes commonly used in the worldwide composites industry, RTM is enjoying one of the fastest growth rates of them all. Indeed, the RTM-technique allows to produce

2 170 Computer Methods in Composite Materials complex, large-sized structural components on a automated way, achieving small to medium quantity of production. Also the developments in machinery, materials and mould making contribute to this advancement. Another reason arises from growing legislation around the world, which is restricting solvent emissions from workshops. The RTM-technique reduces such emission to virtually zero. Also, existing finite element simulation softwares of the resin injection can be a powerful tool for optimization strategies and process developments. Though, they require a good knowledge of the reinforcement permeability for various fiber volume fractions. There is no standard technique for measuring the complete permeability tensor of the fibrous materials. Therefore, this article aims to propose the possibility of determining the complete, three dimensional permeability tensor using only one, automated experiment. 2 The RTM process The Resin Transfer Moulding process consists of injecting a precatalysed, reactive thermoset resin into a dry fibre preform, preplaced in a closed mould cavity (Figure 1). The mould and /or resin can be heated in order to decrease the resin's viscosity. Once the mould isfilled,the resin is cured and the part ejected. No polymerisation reaction (and thus no exothermically behaviour) is assumed during the part filling. FLUID HCATING SYSTEM BOUND. CONO. MOLD WAIL BOUND. COND. II Figure 1. The RTM process. The resin impregnation of a fibrous preform may be predicted as a flow of Newtonianfluidthrough a porous medium by the law of Darcy,

3 Computer Methods in Composite Materials In this equation, {V} is the resin velocity vector [m/s], { Vp] is the pressure gradient vector [Pa/m], ju is the dynamic viscosity of the resin [Pa.s] and [k] is the second order permeability tensor [m% Thus, the permeability characterises the porous material in terms of conductivity to the fluid flow for a given injection pressure. The resin velocity vector must satisfy the continuity equation for an incompressible fluid, Combining (1) with (2) gives, V.F = 0. (2) (3) The pressure p and/or the pressure gradient Vp must be specified at each time step at the boundaries of the evolving domain. At the resin front, the pressure is zero. At the injection port, the pressure value as a function of time is specified. Along the impermeable mould walls, the normal derivative of the pressure vanishes, since there is no resin flow through the mould wall. These equations can be solved with finite element methods. 3 Numerical simulation of the RTM process In a numerical simulation, at each time step, Darcy's equation is solved inside the saturated part of the mould. In fact, the transient impregnation process is approximated by a succession of steady states. This approximation is valid for relatively small time steps. A commercial available software, called 'LCMFLOT', uses non-conforming finite elements with a fixed triangular mesh to model the mould with its preform contents (after Gauvin R., Trochu F, a.o., [l]-[4]). The nonconforming elements result in discontinuities of the pressure field between the element borders, but have the advantage of automatically satisfying the local mass conservation. The non-conforming element formulation avoids the definition of a so-called 'control volume' associated to the nodes of the mesh (as in traditional numerical

4 172 Computer Methods in Composite Materials formulations of a flow front). This non-conforming element formulation allows the modelling of drastically permeability changes from one area in the mould to another (e.g. to model edge effects). Figure 2 shows a comparison between a numerically computed flow front, obtained with LCMFLOT, and the actual experiment. Numerical models require precise information on the physical and geometrical parameters involved during the flow of the resin through the preform. The permeability tensor is the most important physical parameter that must be measured for successful simulation. Figure 2. Comparison between an experimentally measured (a) and a computed (b) flow front. 4 Traditional methods for permeability measurement 4.1 Uni-directional flow measurement Figure 3 shows a typical experimental set-up for uni-directional flow measurement (e.g. Trochu, Gauvin, a.o.[5]-[7]). The cavity is transparent and photocells are used to record the flow front positions. Either constant flow or constant pressure experiments can be run. The uni-directional permeability component is obtained by using eqn (1) for uni-directional flow.

5 Computer Methods in Composite Materials Liftfc irijector "* >/ 4 * Pressure transducer 5- Saturated febric I, ^- thytabrlc ',< \ 7-'" "-"- ' Figure 3. Uni-directional flow measurement. With this set-up, one should be careful to prevent any flow edge racing effects. Precautions should be taken to ensure a constant cavity thickness, because the pressure can deform the transparent plate. Also the lack of homogeneity in the case of strand mats can make it difficult to obtain a reliable permeability. 4.2 Bi-directional flow measurement For low permeability reinforcements such as some fabrics, it becomes extremely difficult to avoid edge effects in an uni-directional flow measurement. In such cases, it is better to measure the in-plane permeabilities using a bi-directional flow set-up. Figure 4 shows a typical experimental set-up for bi-directional flow (e.g. Trochu, a.o., [8]-[9]). Load Sensor Digital Camera Hydraulic Cylinder Pressure Transducer Reinforcement Figure 4. Bi-directional flow measurement.

6 174 Computer Methods in Composite Materials A digital camera can record the flow front shape in successive positions through a transparent cavity. Constant inlet flow or constant inlet pressure experiments can be run. The constant inlet pressure is usually performed because it corresponds to most industrial installations. Errors in the estimations of the permeability are influenced by the precision of the flow front recording system, the flexibility of the transparent plate and the mobility of the fibres at the inlet boundary (especially at higher front velocities). 4.3 Through thickness permeability measurement For the through thickness permeability measurement the law of Darcy is applied directly in the transverse direction. The resin flow is forced by a pressure gradient through a stack of circular reinforcements (see figure 5). The cutting of the circular samples must be performed carefully in order to avoid edge-racing effects. The measurements are performed in a completely saturated situation. The velocity and the pressure gradient are recorded at different time steps. _ Fiber Sample Pressure Transducer Inlet Pipe Figure 5. Measurement of through thickness permeability. 5 Mixed Numerical/experimental method The above described measurement procedures are time consuming. A lot of care is necessary during sample preparation and registration of the

7 Computer Methods in Composite Materials 175 flow front at different time steps. Several test set-ups are required for the identification of the permeability tensor in three dimensions. The mixed numerical/experimental method aspires to identify simultaneously and automatically all the permeability components in one experiment using one test specimen. The considered permeability components can be stored in a vector {k}. The principle of the method is to compare an experimentally observed flow front arrival time vector {t}exp with the same vector {t}num computed with a numerical model of the experiment (using as numerical core the program LCMFLOT). Starting from an initial guess, the permeability components {k} in the numerical model will be iteratively tuned in such a way that the computed arrival time vector matches the observed vector as close as possible (Figure 6). (P(t)}exp EXPERIMENT fexp. [CORRELATION! Figure 6. Principle of the mixed numerical/experimental method for permeability identification. A mixed numerical experimental method requires sufficient information contents in the measurement vector. In this particular case this means that the arrival times in the measurement points must be sensitive for variations of each of the permeability components. The experiment must be designed in such a way, that for each component of the permeability matrix, at least one component of the arrival time vector will be strongly influenced by variations of the magnitude of the component. A logical suitable experiment seems to be a combination of the traditional central injection ( for the identification of the in-plane permeabilities) combined with the through-thickness test (for the identification of the transverse

8 176 Computer Methods in Composite Materials permeabilities). Therefore, a central injection will be executed on a thick pile of fibre reinforcements (Figure 7). Due to the considerable reinforcement thickness, a delay in the arrival times of the fluid front at the sensor points of the upper plate will occur. This delay will be inversely proportional with the value of the transverse permeability. Flow front Thick pile Figure 7. Three dimensional evolution of the flow front. The arrival times in regularly distributed measurement points in the upper and lower plates of a mould cavity with a central injection point (Figure 8) will be recorded automatically with a data acquisition system. The arrival time of the flow front in a measurement point will be observed by a transducer, sensitive for an electrical resistance modification caused by the resin. At this moment, a cheap and robust sensor type is successfully developed for its purpose. The flow front detection transducers can easily be integrated in steel mould plates. XXX #X X X 48 measurement points and central injection gate (lower mould plate) 49 measurement points (upper mould plate) Figure 8. Regular grid of measurement points and inlet gate in the upper and lower plate of the mould.

9 Computer Methods in Composite Materials 177 Hence, the flow front progression on the mould surfaces can be monitored on a PC Also, the steel mould plates reduce considerably the deformation problem of the mould plates under the applied injection pressures. The inlet pressure can be recorded as a function of time with a pressure transducer. 6 Conclusion It is clear that the existing methods for the identification of permeabilities (uni-axial testing, central injection and through the thickness injection) are cumbersome and time consuming from an experimental point of view. The accuracy of the results also strongly depends from the accuracy of the assumed analytical solution of the Darcy equations. The uni-axial test and the through-thickness test have both the difficulty of 'high ways' (zones of high permeability due to the non-presence of reinforcement) for the resin at the borders of the fibre reinforcement. Prevention or even reduction of the effect of these high ways requires very skilful experimentators and very time consuming preparation of the test specimens and experimental set-up. The central injection test suffers from the fact that for anisotropic reinforcements, no correct analytical solution of the Darcy equations is present. It also has the considerable practical difficulty of requiring a circular hole in the reinforcements at the injection place (the resin must indeed enter the reinforcement as a planar flow). The excisting uni-axial and central injection tests require the observation of the evolution of the flow front through a transparent upper mould plate. This plate is thus not rigid (thin glass or plexi) and deforms due to the internal resin pressure. The deformations cause a different volume fraction of the reinforcement and thus destroy the assumption of homogeneous permeability distribution. The observation by cameras or manual observation with stopwatches and geometrical marks put on the transparent mould also introduces considerable experimental errors. All these assume constant pressure or constant flow rate is applied, which is in reality never exactly the case. The proposed method shows non-of these disadvantages. The numerical model represents Darcy's law in 3 dimensions with an adjustable accuracy (the density of the finite element grid). There are no 'high ways' and no difficult specimen preparation is required. Due to the relative big mould cavity thickness, small heterogeneities of the fibre reinforcement are out averaged. The method requires no cameras or visual inspection, hence very rigid mould parts can be used in the experimental set up. The

10 178 Computer Methods in Composite Materials method allows to give different confidence weights to each measurement point (e.g. a smaller weight for measurement points close to the injection point). Hence the method can be 'tuned' by experience. The injection pressure is registrated and may be variable in time. The method will give error bounds for the obtained results. These error bounds take the experimental error and the accuracy of the numerical model into account. The measurement procedure and identification can be automated, using one experiment for the complete permeability characterisation. On a fundamental research level, the authors aim to obtain satisfactory results with the mixed method, for the permeability identification of fibrous reinforcements. References [1] Gauvin, R. & Francois, T., Key issues in numerical simulation for liquid composites molding processes, Composites '96 & Oriented Polymers Symposium, 9-11 October, [2] Trochu, F, Ferland, P. & Gauvin R, Numerical simulation of the RTM / SR1M process, 4* Japan International Sampe Symposium & Exhibition (Jisse-4), Tokyo, September, [3] Trochu, F., Gauvin, R & Gao, D-M, Numerical Analysis of the Resin Tranfser Moulding Process by the Finite Element Method, Advances in Polymer Technology, Vol. 12, No. 4, [4] Trochu, F, Gauvin, R, Gao D-M & Boudreault, J.-F., RTMFLOT. An integrated software enviroment for the computer simulation of the Resin Transfer Moulding process, 48th Annual Conference, Composites Institute, The Society of the Plastics Industry, 8-11 February, [5] Diallo, ML, Gauvin, R. & Trochu F, Experimental analysis and simulation of flow through multilayer fiber reinforcements in Liquid Composites Moulding, Polymer Composites, December [6] Diallo, ML, Gauvin, R & Trochu, F., Key factors affecting the permeability measurement in continuous fiber reinforcements, 11^ International Conference on Composite Materials, Gold Coast, Australia, Julyl997.

11 Computer Methods in Composite Materials 179 [7] Ferland, P., Trochu, F. & Guittard D, Concurrent methods for permeability measurement in Resin transfer Moulding, Polymer Composites, Vol. 17, No. 1, February, [8] Gauvin, R, Trochu, F, Lemenn, Y & Diallo, L., Permeability measurement and flow simulation through fiber reinforcement, polymer Composites, Vol. 17, No. 1, February, [9] Hammami, A., Trochu, F, Gauvin, R & Wirth, S., Directional permeability measurement of deformed reinforcement, Journal of Reinforced Plastics and Composites, Vol. 15, June, 1996.