FILM STACKING IMPREGNATION MODEL FOR THERMOPLASTIC COMPOSITES APPLIED TO A NOVEL NET-SHAPE PREFORMING PROCESS

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1 The 8 th International Conerence on Flow Processes in Composite Materials (FPCM8) FILM STACKING IMPREGNATION MODEL FOR THERMOPLASTIC COMPOSITES APPLIED TO A NOVEL NET-SHAPE PREFORMING PROCESS S.T.Jespersen 1, M.D.Wakeman 1, D.Cramer 2, V.Michaud 1, and J-A.E.Månson 1 1 Ecole Polytechnique Fédérale de Lausanne (EPFL) Laboratoire de Technologie des Composites et Polymères (LTC), CH-1015 Lausanne, Switzerland: jan-anders.manson@epl.ch 2 Fiberorge, 3768 Highway 82, suite 204, Glenwood Springs, CO 81621, USA. ABSTRACT: In order to assess candidate impregnation methods or a novel netshape preorming method that uses low cost eedstock materials and automation, the impregnation phenomena must be understood. The preorming method comprises automated deposition o UD carbon ibre yarns together with a thermoplastic matrix along a preprogrammed path creating preorms o stacked material which are preconsolidated beore conventional stamporming. In order to evaluate dierent materials, improve stacking scenarios, and assess alternate preconsolidation routes, the iniltration kinetics must be considered in detail. The transverse iniltration o liquid thermoplastic polymer into a compressible unidirectional ibre bed has thereore been examined under isothermal conditions. An iniltration model, based on local luid low in compressible porous media has been extended to simulate iniltration o alternating matrix ilm and ibre layers, relating pressure, time, and temperature with the local ibre volume raction, pressure and liquid and solid velocities in the stacked material. The model has been validated by comparison with experimental results. The ibre volume raction distribution gives the optimum layer thickness values or a given set o conditions. In addition the results show that increased pressure leads to increased ibre bed compaction and hence decreases permeability and limits iniltration. KEYWORDS: Thermoplastic composites, Impregnation, Net-shape preorming INTRODUCTION The high viscosity o most thermoplastics has been one o the main hindrances or introducing high ibre content composites in high volume applications [1]. In order to apply the most appropriate materials or a given process, the iniltration phenomena must be analysed. Methods to decrease impregnation time, such as commingling and powder impregnation, have been reported in the literature and are used in commercial products. In the net shape tailored preorming process examined here, where UD carbon ibres together with a Polyamide matrix are automatically laid along a preprogrammed path, [2,3], ilm stacking is a candidate route to reduce the iniltration length and lower impregnation time. 165

2 The 8 th International Conerence on Flow Processes in Composite Materials (FPCM8) Impregnation o dry compressible preorms under constant pressure has been examined by Michaud et al. [4] or glass mat thermoplastics (GMT), extending an impregnation model by Sommer et al. [6,7], or the iniltration part o the process, previously used or soil theory and metal matrix composites. The preorm relaxation and equilibration ater iniltration was shown to dominate process time or pressures above 0.05MPa. This was also experimentally veriied. Control o these steps is thus important in order to prevent or tailor an inhomogeneous reinorcement distribution [4,5]. To apply and experimentally veriy the impregnation model or aligned ibre composites, a ibre bed consisting o aligned UD carbon ibres has been transversally iniltrated with a Polyamide (PA) resin. The impregnation ront is anticipated to be well deined, and a sluglow assumption can be applied [7]. The impregnation time is hence dominated by micro low behaviour since no macro low occurs. In addition, with consideration o the conlicting demands o maximizing inal part properties and minimizing production time and hence cost, the optimum stacking scenario must be deined. The uniormity o the inal ibre distribution, the eect o resin rich core layers or improved processing [9], and the average ibre content are important parameters to study. To examine these parameters, the eect o processing variables on an industrial ilm stacking scenario must be understood in order to optimise the entire process. Since no current model was able to examine the ilm stacking scenario in its complete state, a new model was built to adapt the single interace iniltration model to the problem. TRANSVERSE INFILTRATION To mathematically describe the constant pressure driven isothermal saturated iniltration o a compressible porous medium by a Newtonian liquid, a one dimensional iniltration model has been written based on the work o Michaud et al. [4,5,8,10] and Sommer et al. [6,7]. The model is used as a base or a ilm stacking impregnation model, where the time and distance space is discretized to examine complex stacking sequences through time. Fig. 1 Stages in the one dimensional iniltration model, ater Michaud [4] The initial condition beore iniltration is a relaxed ibre bed adjacent to liquid polymer (Fig. 1a.). Pressure is then applied on the material, instantaneously compacting the ibre bed to the initial ibre volume raction V i deined by the ibre network compliance, which has been measured or the UD ibre bed used (Fig. 1b). The impregnation ront then progresses into the ibre bed with the velocity u l (Fig. 1c.). At the same time, the ibre bed behind the impregnation ront relaxes back into the matrix with the velocity u s. At this main impregnation stage, momentum balance prescribes that the applied pressure P app will be 166

3 The 8 th International Conerence on Flow Processes in Composite Materials (FPCM8) balanced between the eective load on the ibre network σ and the liquid matrix pressure P l. The iniltration model describes the volume raction evolution between x r and x over time. I the matrix layer has an adequate thickness, the impregnation ront may advance to ully impregnate the ibre preorm i the right processing parameters are used (Fig. 1 d1.). On the other hand, dry ibres will remain i the matrix layer is too thin (Fig. 1 d2.). It is assumed that the gas in the dry ibre preorm is at constant pressure and is driven out o the preorm or absorbed in the matrix with negligible resistance. The liquid and solid phases are taken as incompressible and homogeneous versus time. Euler coordinates are used throughout with x=0 at the interace between liquid and solid ater initial compression. Isothermal steady impregnation o a porous medium with a Newtonian luid is described by Darcy s law [8]. It is hence required that the low is governed by viscous orces and has a Reynolds number, R e 1, which is the case here due to the high viscosity and small low rates. Darcy s law, here without gravity eects states; K dp ul us = (1) ν 1 V dx dp/dx is the pressure gradient, K(V ) the permeability o the ibre bed calculated using the model rom Gebart [11] using the measured ibre radius o 4µm and V the volume raction ibre. The Newtonian matrix viscosity, v, was measured and modelled with an Arrhenius relationship with v=400pa s or 235 C and an activation energy o 70KJ/Mol. Neglecting internal and body orces such as gravitational orces in the solid ibre bed and the liquid matrix, stress equilibrium in one dimension yields; dp l dσ + = 0 (2) dx dx Further relationships are ound by applying mass conservation or liquid and solid phases respectively; dv d ( V us ) dv d ( 1 V ) ul ) + = + = 0 (3) dt dx dt dx A similarity solution is used to simpliy the problem as described by various authors [6,7]. This implies a Boltzmann transormation in Eulerian coordinates to ind a reduced parameter X, which combines distance and time. The similarity solution will, ollowing Mortensen et al [7], be valid or the case o constant applied pressure and a time independent viscosity. x xr x xr X = = (4) ψ t x x where ψ is a time independent measure o the iniltration speed. Factors or the velocities are then introduced. The iniltration ront velocity u l is governed by the actor l(x). ψl( X ) u l = (5) 2 t r The relaxation ront velocity u s is governed by the actor s(x). ψs( X ) u s = (6) 2 t 167

4 The 8 th International Conerence on Flow Processes in Composite Materials (FPCM8) Boundary conditions At the iniltration ront: x = x l (t), u s = 0, l=1+s(0), V = V c and P l = P g, which remains constant as long as the gas is expelled or is absorbed in the matrix, and neglecting the capillary pressure drop at the iniltration ront. At the preorm relaxation ront the conditions are as ollows; x = x s (t), P l = P app + P g and V = V r. Combining Eqn. 1 to 6 gives three non-linear irst-order dierential equations; 2 dv ( l s)( 1 V ) νψ = (7) dx 2KV dσ dv ds dx dl dx [ () ' V i = s X s 0 V (8) [ () ' V i = l X s 0 1 V (9) From the development o Eqn. 8, ollows that d((1-v )l+v s)/dx=0, showing the link between s and l, which simpliies the problem substantially since l(x) can be ound explicitly when V (X) and s(x) are known. Eqn. 7 and Eqn. 8 were solved or the two unctions V (X) and s(x), as well as or the parameter ψ, in a commercial code Matlab. A well converging optimum solution was ound using sequential quadratic programming with initial values or ψ 2 and s(x=0) compared with known solutions or V c and s(1). The impregnation and relaxation length evolution with time is calculated by integrating the impregnation velocities over time. The corresponding real positions x to the values o X are then ound to relate resin and ibre velocities, ibre volume ractions and pressures with x in the material as shown in Fig. 2a) and b). Fig. 2 The results or V together with a) polymer pressure and, b) low velocities or 20bar applied pressure, 250 C and 75s impregnation time FILM STACKING The isothermal iniltration model described in the previous section has been extended in order to be able to model a ilm stacking scenario by discretizing time and position. The model is able to consider any number o layers and layer thicknesses giving reedom to examine, or example, the use o a polymer rich low core. All data can be input via a graphical user interace (GUI) or be directly written into Excel. 168

5 The 8 th International Conerence on Flow Processes in Composite Materials (FPCM8) To ind the order o impregnation events all stacked layers are examined or each time step (typically 0.5s) rom zero to a user speciied impregnation time. When a ibre layer has been ully iniltrated or a matrix layer has been used up, the exact time or the event is recorded and excessive time is monitored. This ensures that intermediate ibre layers are impregnated rom both sides and that impregnation can continue rom one side i the other has run dry rom polymer. The result is a vector called Interace containing the apparent iniltration time at all interaces. Using the Interace values the amount o relaxation into the matrix or upper- xr up (n) and under-side xr down (n) or the dry ibre bed can be calculated, where n denotes the ibre layer. The iniltrated lengths x up (n) and x down (n) are determined correspondingly. For each individual ibre/matrix interace, the ibre volume raction is then ound in discrete steps o a user deined step length o typically 1500 per mm. The step lengths are adapted to each individual layer thickness or improved accuracy. The pure matrix and ibre parts are subdivided in the same way. For each o the incremental steps, the ibre volume raction is ound using the previously predicted ibre volume raction versus depth relation in the composite (x r and x ). An example o an arbitrary partially and ully impregnated composite can be seen in Fig. 3a) and b) respectively, rom which an important variation in V is seen. The obtained simulation results can be used to improve the layer stacking sequence and, or example, the resin layer thickness and appropriate surace matrix layers i, or example, a matrix rich surace is desired. Fig. 3 The results with 4 ibre layers processed at 250 C and 10bar or: a) a partially iniltrated material ater 30s and, b) a ully iniltrated material ater 100s The total time to complete impregnation o the composite is obtained by examining all individual layers and noting which has the longest iniltration time. I enough polymer thickness is speciied, the optimum i th layer thickness T ilm (i) can be ound that results in zero excess polymer. For the outer matrix layers the calculation is simpler, but or the i th layer it takes the general orm: T i = x i 1 xr i 1 x i 1 V + x i xr i x i V (10) ilm () down down down c up up up c The knowledge o the complete composite ibre volume raction distribution gives the thickness at any time, the average ibre volume raction, and the remaining porosity in the composite. 169

6 The 8 th International Conerence on Flow Processes in Composite Materials (FPCM8) EXPERIMENTAL VERIFICATION An experimental evaluation o the simulated results was perormed by impregnating aligned unidirectional carbon ibres with a Polyamide 6/12 copolymer or varying pressure and time. The impregnation depth was evaluated by analyzing optical micrographs as seen in Fig. 4 illustrating the dierence or a 15s and a 60s impregnation time at 250 o C and nominally 6 bar. Due to scattering in the measured values, several measurements were taken and average values used or the impregnation length. Fig. 4 Impregnation ater: a) 15s, and b) 60s by nominally 6bar at 250 C The irst set o veriication trials examined the eect o time on impregnation length, as shown in Fig. 5a using 6bar pressure and 250 C. The error bars or the simulation results correspond to the uncertainty in the pressure value or various experiments. The experimental results compare well with the simulation. It should be noted, that due to the machine response time, a non-negligible impregnation has already occurred at zero impregnation time, which is measured as the impregnation occurring when the applied pressure has just been reached and then removed. This will eectively move the experimentally based results towards a larger impregnation distance compared with the simulation results, especially or small impregnation times, which correlated well with the observed results. The second set o veriication trials examined the eect o pressure on impregnation length or a ixed impregnation time o 60s. The pressure dependence o impregnation or a constant temperature o 250 C was measured and showed close correlation with simulation results, as seen in Fig. 5b. Fig. 5 Simulation results and standard deviation bars or experimental data SIMULATION RESULTS AND DISCUSSION Having veriied the model against experimental impregnation values or changing time and pressure, the simulation model has been used to predict the eect o dierent stacking scenarios and processing parameters. Fibre layer thicknesses were measured in the relaxed state. The eect o temperature is shown in Fig. 6a.) or a stacking scenario with constant inal thickness. Small variations (0.002mm) are due to discretization step size. When simulating the impregnation behaviour the necessary amount o matrix depends on the applied pressure as shown in Fig. 6b.) and hence ibre bed compression. The optimum 170

7 The 8 th International Conerence on Flow Processes in Composite Materials (FPCM8) thickness, which is twice the size or the inner layers having two ibre interaces, has been used in all ollowing simulation runs to give the minimum inal part thickness. Fig. 6 a) Composite thickness evolution or our 0.2mm ibre layers and constant excess matrix, b) Necessary matrix thickness or outer and inner matrix layers depending on pressure or 0.2mm ibre layer thickness One o the undamental results rom the simulation is the change in impregnation time with resin viscosity or dierent ibre layer thicknesses, here seen in Fig. 7 or constant ibre layer thickness scenarios. This can directly be used to ind the impregnation cycle time or the given process and material combination. Fig. 7 Time to ull impregnation as unction o resin viscosity and ibre layer thickness A pressure increase will increase the impregnation velocity up to a certain threshold value (here 20bar) even though the permeability decreases due to ibre bed compaction, as seen rom Fig. 8a. By using this pressure, the impregnation time is optimized, but still depends on temperature, as shown in Fig. 8b, where the porosity content is monitored over time. Fig. 8 For 0.2mm ibre layer thickness; a) Time or complete impregnation and b) The porosity content in the composite through process time at 20bar 171

8 The 8 th International Conerence on Flow Processes in Composite Materials (FPCM8) CONCLUSIONS An iniltration model has been developed and validated using the current process o ilm stacking o UD ibres and thermoplastic matrix layers. Experimental measurements show good agreement with simulation results without the need or itting parameters. Using the model, it has been possible to ind optimum layer thickness values or given processing conditions. Furthermore, an optimum pressure with respect to impregnation eiciency was ound, which is smaller than the maximum applied pressure. This is explained by the act that increased pressure compacts the ibre bed and hence decreases permeability and limits iniltration. The model can be used to optimize a given production scenario and the materials used, and thus help reduce the development cost or new ibre impregnation technologies. Acknowledgements This work was supported by Fiberorge. The authors wish to acknowledge rom EPFL: G. Tornare and rom Fiberorge: A. Burkhart and J. Fox-Rubin. REFERENCES 1. J.-A. E. Månson, M. D. Wakeman, P. E. Bourban, and P. W. Sunderland, "Driving orces or cost-eective composites: new demands on materials and processes", Proc. ICCM 12, M. D. Wakeman, D. Cramer and J.-A. E. Månson, "Technical cost modelling o an automated netshape preorming process or thermoplastic composites: a case study", Proc. Sampe Paris A. Ross, "Tailored carbon iber blanks set to move into steel stamping area", Highperormance Composites, January, 2006, pp V. Michaud, and J.-A. E. Månson, "Impregnation o compressible iber mats with a thermoplastic resin. Part I: Theory", Journal o composite materials, Vol. 35, no.13, 2001, pp V. Michaud, R.Törnqvist and J.-A. E. Månson, "Impregnation o compressible iber mats with a thermoplastic resin. Part II: Experiments", Journal o composite materials, Vol. 35, no.13, 2001, pp J. L. Sommer, and A. Mortensen, "Forced unidirectional iniltration o deormable porous media", Journal o luid mechanics, Vol. 311, 1996, pp A. Mortensen, C. San Marchi, and V. Michaud, "Capillarity in iniltration processing: A review o principles and their extension to reactive iniltration". Proc. Int. Con. High temperature capillarity, 1997, pp V. Michaud, and A. Mortensen, "Iniltration processing o ibre reinorced composites: governing phenomena", Composites part A-applied science and manuacturing, Vol. 32, 2001, pp M. D. Wakeman, P. Blanchard and J.-A. E. Månson, "Void evolution during stamporming o thermoplastic composites". Proc. ICCM 15, V. J. Michaud, J. L. Sommer, and A. Mortensen, "Iniltration o ibrous preorms by a pure metal: Part V. Inluence o preorm compressability", Metallurgical and materials transactions A, Vol. 30, 1999 pp B. R. Gebart, "Permeability o unidirectional reinorcements or RTM", Journal o Composite Materials, Vol. 26 no. 8,