18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS NON-UNIFORMITY OF THE FILAMENT DISTRIBUTION IN FIBRE BUNDLES AND ITS EFFECT ON DEFECT FORMATION IN LIQUID COMPOSITE MOULDING F. Gommer*, A. Endruweit, A.C. Long Faculty of Engineering – Division of Materials, Mechanics & Structures, University of Nottingham, University Park, Nottingham NG7 2RD, UK * Corresponding author (emxfg@nottingham.ac.uk) Keywords : Liquid Composite Moulding, permeability, dry spot formation, filament distribution 1 Motivation with increasing cavity height, i.e. decreasing level of fabric compression (illustrated qualitatively in Fig. Minimisation of the void content created during 1). impregnation of reinforcement fabrics with liquid With increasing level of compression, the filament resin systems, is critical for the quality of finished distribution within the fibre bundles tends to become polymer composite components, in particular if more uniform, which is related to the reduction in Liquid Composite Moulding (LCM) processes are inter-filament spacing and increasing packing employed for manufacture. Different flow velocity density. This is illustrated in Fig. 2, where the of the injected resin in different zones of the filament distribution is characterised by the average reinforcement may result in an uneven flow front distances between a filament and its neighbours, and formation of resin-free dry spots. These may which decrease with increasing level of compression. result in a reduction in the matrix-dominated Increasing packing density is equivalent to a more mechanical properties, in particular strength in shear, uniform permeability distribution (at the micro- bending and compression, of the finished composite. scale) and even flow front propagation, eventually The main focus of this study is the characterisation resulting in a low content of entrapped gas bubbles, of the local distribution of filaments within fibre even if the total bundle permeability is reduced. bundles and the influence of the degree of The local distribution of V f , which is correlated to uniformity on formation of micro-scale voids. the filament distribution, can be determined by analysis of micrographs (e.g. employing the moving 2 Material characterisation window technique). An example for the distribution is given in Fig. 3. Composite plaques with dimensions 125 mm × 60 mm were made from uni-directional carbon fibre fabric (filament count in fibre bundles c f = 12K) and 3 Permeability field an epoxy resin system. The plaques were moulded For characterisation of flow within fibre bundles, by injecting the liquid resin into a stiff metallic tool local permeability values can be calculated by containing the fabric. The resin viscosity during homogenisation of filaments and inter-filament injection ( = 0.025 Pa×s) was controlled via its spaces. From the local fibre volume fraction V f ( x , y ), temperature. Specimens were moulded at different the local permeability of the fibre bundle parallel cavity height, i.e. level of fabric compression, and ( K 1 ) and perpendicular ( K 2 ) to its axis can be injection pressure. determined based on the equations derived by Micrographic analysis of the moulded and cured Gebart [1], specimens allowed the filament distribution within fibre bundles, which is typically non-uniform, to be 5 / 2 3 2 ( 1 V ) V R f , f max 2 , (1) identified and micro-scale dry spots to be detected. K K c 1 R 1 2 2 2 4 c V V The results indicate that at given injection pressure, 1 f f number and size of intra-bundle dry spots increase
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS where c 1 , c 2 and V fmax are geometrical constants. The for each type of arrangement, K 2 decreases values of the constants in Eq. (1) depend on the continuously with increasing V f . The most filament packing arrangement, which can be significant discontinuity occurs at the transition from characterised by the number of nearest neighbours of triangular to square filament arrangement. This a filament, N nn , i.e. the number of neighbours with reflects the dimensions of gaps between filaments, (approximately) identical minimum distance. For which are small for N nn = 3, even if V f is relatively periodic filament arrangements, c 1 and c 2 can be low, and larger for N nn = 4 at slightly increased V f . determined in analogy to the analytical derivation However, the dependencies of K 1 and K 2 on V f described by Gebart for square ( N nn = 4) and plotted in Fig. 5 apply locally and do not necessarily hexagonal ( N nn = 6) packing. For triangular ( N nn = 3) imply that a whole bundle, in which local effects are packing, c 1 may be approximated by the value for a averaged over the bundle dimensions, behaves in the circular arrangement, which is 2 based on the values same way. given by Gebart. Considering flow through a unit Based on typical measured dimensions of fibre cell, the value of c 2 can be approximated as 0.69. For bundle cross-sections, randomised local values of V f a pentagonal ( N nn = 5) filament arrangement, c 1 and can be generated, which follow the corresponding c 2 can be determined from interpolation based on the experimentally observed distributions (as in Fig. 3) power law approximations and thus reproduce the non-uniform filament distributions in the actual bundles. For each local 0 . 26 1 . 57 c 2 . 63 N and , (2) c 3 . 75 N value of V f , K 1 and K 2 can be determined from Fig. 1 nn 2 nn 5. Since the difference in inter-filament void sizes which were derived by curve fitting to the constants ( V f ) determines the difference in local flow front for three, four and six nearest neighbours. Values for propagation in the voids ( K 1 ) and the fluid exchange V fmax can be determined analytically based on between voids ( K 2 ) [2], statistical evaluation of the geometrical considerations. For a number of generated local distributions (Fig. 6) and their filament arrangements characterised by N nn , gradients may give some indication on the estimated values of c 1 , c 2 and V fmax are listed in Table probability for dry spot formation or the void 1. content to be expected. The number of nearest neighbours tends to increase with increasing fibre volume fraction, i.e. increasing packing density. A correlation between N nn and V f 4 Micro-scale flow simulation can be established based on the probability Complementing the approach of local distributions of V f at different values of N nn (which homogenisation and permeability calculation were generated assuming V f to be normally described in the previous section, non-uniform distributed), as shown in Fig. 4. These were filament distributions were modelled in detail to determined by identifying zones with defined allow 2D flow to be simulated on fibre bundle cross- filament arrangement (characterised by N nn ) on sections (using the CFD code FLUENT). While the micrographs of fibre bundle cross-sections and the feasibility of this approach has been demonstrated local V f in these zones. From Fig. 4, the value of N nn before, e.g. by Cai and Berdichevsky [3], modelling most probable to be found at a given V f was flow through arrays of individual filaments is not determined. The results listed in Table 2 allow N nn to practical at the fibre bundle scale with typically be estimated as a function of V f . several thousand filaments. The filament For a fibre bundle with randomly distributed arrangement in the models was correlated to actual filaments, Eq. (1) allows the permeability to be distributions via the measured distances between approximated locally based on V f ( x , y ) and the local neighbouring filaments (Fig. 2). The micro-structure values of c 1 , c 2 and V fmax , which are estimated from was generated following an adjusted version of the N nn ( x , y ). The results plotted in Fig. 5 show that K 1 procedure described by Vaughan and McCarthy [4]. decreases continuously with increasing V f . On the Here, a pre-determined number of filaments are other hand, K 2 is a discontinuous function of V f . The placed at given distances, which are picked discontinuities are related to changes in filament randomly from the measured distributions, and in arrangement with increasing packing density, where random directions relative to a randomly placed
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