Mathematical model of stress formation during vacuum resin infusion process

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1 Composites: Part B 30 (1999) Mathematical model of stress formation during vacuum resin infusion process I.B. Sevostianov, V.E. Verijenko*, C.J. von Klemperer, B. Chevallereau 1 Department of Mechanical Engineering, University of Natal, Durban 4041, South Africa Received 25 February 1998; accepted 29 May 1998 Abstract Composite material manufacturing technology based on vacuum infusion which is also known as resin film infusion technology, utilises a vacuum bag to debulk or compact parts of complete laminate. After debulking the resin is allowed to be infused by the vacuum to completely wet-out the reinforcements and eliminate air voids in the laminate structure. The resin infusion can also develop stresses in the fibres. Further, different types of heterogeneity can be formed in the laminae. The objective of this article is to develop a mathematical model of the stress and heterogeneity formation during the resin film infusion process. A heuristic model which considers the viscous flow through the porous reinforcement is developed and it allows an understanding of the influence of different process parameters on the pressure distribution in the infused resin. The reinforcement permeability tensor is defined by the Carman Kozeny equation and depends on average pore size and specific pore concentration. The use of a non-linear equation of filtration allows for a definition of the pressure distribution inside a viscous liquid resin dependant on the external flux. The fibres which form the preform are assumed as being the pure elastic bodies and the resin as a non-newtonian viscous liquid. The results obtained allow the simulation of complex manufacturing process to be carried out Elsevier Science Ltd. All rights reserved. Keywords: Resin film infusion process; A. Fabrics/textiles 1. Introduction The development of modern methods of composite manufacturing is governed mainly by cost, quality, health and safety considerations, as well as suitability. For some time now, the manufacturing process for medium to large structures requiring a high fibre volume content (more than 45%) has focused on development of methods such as resin transfer moulding, compression moulding and the use of autoclaves and vacuum bags. These methods work on the principle of impregnation of a fibre-made skeleton by a liquid polymer mass with subsequent polymerisation. High quality composite components can be manufactured by employing these methods with a wide range of fibre and resin combinations. However, for large size structures the cost of the tooling is relatively high in the case of resin transfer moulding, as the mould structure should withstand high moulding pressures. Tooling for vacuum infusion is of much lower cost owing to the fact that only one mould face is required. In this case a high structural stiffness is not * Corresponding author. 1 On leave from École Supérieure de L Énergie et des Matériaux, Univertsité d Orléans, Cedex 2, France. required as the tooling is subjected mainly to hydrostatic pressure [1]. As the tooling costs can be kept low, vacuum resin infusion techniques can theoretically produce composite materials at a lower cost without a loss of quality. Resin infusion utilises a vacuum bag to debulk or compact parts of a complete structure with the reinforcement material laid in a mould. The preform is first placed in an open mould that includes engraved micro-channels, connected perpendicularly to a wider main channel which serves as a resin gate, or alternatively, the network of micro-channels can be replaced by a layer of highly porous material placed on the top of the preform. A flexible plastic film is placed on the top of the preform to close the mould. Air is drawn from the preform using a vacuum pump; this compresses the preform and draws the resin through it. One of the main problems of the vacuum infusion technology is the control of the pressure distribution during the manufacturing process and the choice of corresponding process parameters. The high rate of resin flux can lead to high hydrostatic pressure in the resin which in turn can lead to the damage being generated in the woven reinforcement and the creation of voids. This can result in a loss of strength and even fracture of a pattern [2]. The vacuum infusion process is a relatively new technology and first publications /99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S (99)

2 514 I.B. Sevostianov et al. / Composites: Part B 30 (1999) on this subject appeared about 20 years ago. In 1978 Gotch proposed a vacuum impregnation with one solid tool face [3]. Liquid resin was poured onto dry fibres before being enclosed by a bag. Vacuum pressure only was used to draw the resin into the mould. Four years later the use of vacuum infusion was considered for manufacturing of composites with high fibre content [4]. It was demonstrated that using infusion, a high fibre volume fraction (between 43 and 60%) can be achieved at vacuum pressure of the order of 1 bar. During the 1980s more articles appeared reporting on the use of vacuum injection process in the manufacturing of high strength fibre reinforced composites for various applications [1,5,6]. Investigation of the process parameters only began in 1990s. The main subject of this research involves the conditions under which the formation and growth of voids occur during resin infusion. In 1990 Hayward and Harris [7] studied the influence of a vacuum in addition to the resin pressure during the resin transfer moulding process. They demonstrated that a reduction of voids occurs as a result of employing a vacuum. Lundström et al [8,9] studied the influence of pressure on void growth in the resin and it was shown that the boiling off of styrene under the vacuum is unlikely. A relation between the hydrostatic pressures in the resin and a change in void volume was proposed. Boey [10] studied how laminate void content may be reduced by using a vacuum bag infusion technique. Sefris et al [11 13] conducted an experimental study of crack formation during resin film infusion processes. Williams et al [1] noted that for the technology to progress, parameters such as maximum achievable fibre content and flow rates (linked to fabric permeability and resin viscosity) should be understood and their relationship with the level of vacuum, reinforcement/resin combinations and laminate qualities defined. Some publications on the related topics have recently appeared [14 17], however many aspects of the resin film infusion process are still under investigation. In this article we consider a simplified mathematical model which allows for understanding of the role of different process parameters in the vacuum resin infusion process. The simple physical methods of how the stress field develops during the resin film infusion process are discussed. The two extreme cases i.e. very high and very low flux rates are considered in order to understand the characteristic features of the transient stress field. A more detailed stress analysis is presented in Section Physical model of stress formation in woven fabric during the resin film infusion process A saturated preform is considered in the present study as a two phase material consisting of a solid network with a concentration of C s and a liquid resin with a concentration of C r. For a completely saturated volume the following equation is satisfied: C s C r ˆ 1: The driving force for an increase in stresses and strains in the preform during the manufacturing process is the internal pressure created by a hydrostatic compressive force P which results from the flux of resin infused by a vacuum pump operating externally. As the forces in the liquid and solid phases are in equilibrium the compressive stress in the resin is balanced by a tensile stress field acting on the fibre reinforcement. At the initial packing density the preform is an elastic porous media. However, when the resin flux begins to penetrate into the network the effective properties of this saturated media gradually become visco-elastic. A stress field comes into existence as a result of an irreversible change in the reinforcement s packing density. These stresses remain in the material after polymerisation, provided that the polymerisation occurs rapidly. A slow polymerisation process may allow these stresses to be relieved. The resin meniscus propagation into the depth of the body begins when the critical fibre packing density is reached, i.e. the preform is completely saturated. The extent of this propagation depends on the pressure in the resin liquid as well as on fibre fibre and fibre resin interaction potential. The saturation rate of the preform is governed by two processes, namely the flux rates; j ext through the resin gate, and j r from the surface to the interior. The flux rate near the resin gate is controlled externally and depends on the difference between the external pressure P E created by the vacuum pump and the hydrostatic pressure P in the resin: j ext ˆ B P E P : 2 The resin flow rate j r depends on the gradient of the hydrostatic pressure in the resin and it can be written according to Darcy s law as: j r ˆ D h 7P; 3 where D is the permeability of the preform and h is the viscosity of the resin. The permeability of the matrix material can generally change during the infusion process. Dave [18] proposed that permeability is not constant but can be defined as a product D ˆ D i D r, where D i is the intrinsic permeability and D r the relative permeability which varies from 0 to 1 depending on preform s saturation. The intrinsic permeability depends on the porosity of preform. This dependence can be approximated by the Carman Kozeny equation D i ˆ 1 C s 3 5 C s Sr f C s r 2 p: 4 Here r f is the density of the fibres which form the woven material; S is the specific surface area of the woven material and r p is the corresponding effective pore size of the network. For simplicity we will assume that D r ˆ 1 during

3 I.B. Sevostianov et al. / Composites: Part B 30 (1999) the process. At the external surface of the preform the resin flow density j r equals the flux rate through the resin gate j ext. Therefore, the stress gradient in the resin is governed by the external flux. This special condition allows us to estimate the average size of the viscous fingering (partially saturated zone) before a completely saturated layer is formed at the surface. The moment the resin meniscus begins to move into the interior, the capillary pressure in the resin reaches its critical value P c which is proportional to the ratio of the resin-vapour interface energy g rv. This ratio is defined as the surface tension of the liquid divided by the average pore radius in the woven r p, viz. P c ˆ 2g rvcos u ; 5 r p where u is the contact angle (see Fig. 1). Taking into account that 7P P c =l c we obtain from Eq. (3) the following estimate for the decay length of concentration profile l c : l c ˆ D h r P c j ext : Fig. 1. Wetability angle. We now relate the decay length to the resin fingers contained in the partially saturated layer of the body. In Fig. 2, l c corresponds to the differential thickness; b a l c. The resin propagation into the woven fabric is characterised by two stages. In stage 1 the preform material is not quite saturated but already fingered. Stage 1 ends when the meniscus of resin begins to move into the preform 6 to create a completely saturated layer. This is also the beginning of stage 2. The various zones for saturated and unsaturated woven through the thickness are shown in Fig. 2. Following Biot [19] we define the strain in a composite as a local quantity over a small but finite area. The area over which the strain is measured is large enough to provide an average of a sufficient number of fibres and pores. By using this assumption there is no need to consider the local deviation of strain from the local average. Similarly, we define the stress s (acting on the woven material) as it is measured in the experimental studies namely, as the ratio of force F divided by a small (but finite) area V on which the force is applied. Thus s ˆ F=V. Following Biot [19] and Terzaghi [20] the strains can be expressed as linear combinations of the stresses within the elastic range of deformation of the porous solid. As long as the pore pressure is not considered the deformation of the porous medium can be treated in the same way as the deformation of a non-porous elastic solid. Further, we assume that the material is statistically homogenous and an isotropic solid. In order to incorporate the effect of pore pressure P on the strains we make an important assumption that the strains are linearly related to the pore pressure, viz. 1 ij ˆ 1 2m w s ij 1 3 s kk d ij 1 9K w s kk d ij 1 3H Pd ij: In Eq. (7) the last term represents strain owing to the pore pressure and depends on a modulus H introduced by Biot [19]. Without pore pressure, the moduli K w, and m w of the woven material can be defined experimentally, as can H. It can be easily shown by substitution that if we define an effective stress s eff ij ˆ s ij gpd ij, where g ˆ K w =H, then Eq. (7) can be reduced to the following form: 1 ij ˆ 1 2m w h s eff ij 1 3 seff kk d ij i 1 9K w s eff kk d ij which shows that the static problem for any deformation in porous media with pore pressure can be reduced to an elastic problem of non-porous media. The exact value of the parameter g is controversial. 7 8 Fig. 2. Schematic of various zones of a preform subjected to an infusion process, together with typical changes in the capillary pressure in the resin, and the concentration of the fibres.

4 516 I.B. Sevostianov et al. / Composites: Part B 30 (1999) Fig. 3. Schematic plot of various parts of the longitudinal stress field in a saturating plate for (a) low flux rate, (b) medium rate, and (c) very high external flux rate. The stress field was separated into four parts connected with vacuum pressure s v, hydrostatic stress s c due to the capillary pressure in the resin, the stress s s due to differential expansion of the partially saturated (or fingered) zone (between r ˆ a and r ˆ b) with respect to the initial condition, and the stress s D due to the differential expansion of the unsaturated part. Based on theoretical grounds Terzaghi [20] suggested that g should be equal to the porosity but found experimentally that g 1. Nur and Byrelee [21] add that they have derived an exact expression for the coefficient g which is valid for porous solids showing an isotropic behaviour. This expression is g ˆ 1 K w =K s, where K s is the intrinsic bulk modulus of the solid. Their derivation, as they indicated, could be extended to include anisotropy. It is important to note that if we consider linear visco-elastic materials, then the elastic constants in Eqs. (7) and (8) should be replaced by corresponding time operators. To understand how the stress field arises during the infusion process it is essential to discuss two limit cases, i.e. case (i) when the flux rate through infusion gate approaches infinity, and case (ii) when this flux rate approaches zero, as well as an intermediate case (iii) which is of practical importance. Case (i): When the flux rate tends to infinity, stage 1 does not exist at all, i.e. P E =P c!. For this case, the resin meniscus immediately moves into the preform. A maximum gradient of stress-free strain owing to a differential change in the fibre packing density is formed and viscous fingering does not take place. In this case there are two sources of internal stress: the capillary pressure and the differential volume change between the saturated outer layer and the interior part of the preform. The volume expansion of the saturated, outer part of the woven material occurs as a result of excess resin. Stress relaxation of the fingered network in an unsaturated region is prevented by the inability of fibres to rearrange owing to elastic behaviour of these regions. The expansion of the resin-filled region of the preform is constrained by the inner unsaturated region and thus longitudinal tensile stresses in the unsaturated region are balanced by compressive stresses in the preform (see Fig. 3(c)). As the tensile forces in the unfilled region have to balance the compressive forces in the saturated part of the pattern, the stresses in both regions are changing as the resin meniscus moves towards the interior. Case (ii): When the external flux rate tends to zero the stress gradient in the packed fibres also tends to zero. Thus, the stresses acting on the woven material are mostly uniform throughout the pattern. In addition, once the resin meniscus moves from the surface to the interior, no differential strain will arise, i.e. tensile stresses do not arise within the unsaturated region as shown in Fig. 3(a). Case (iii): This is the most practical case as the external flux rate is finite and a smooth density gradient develops from the surface to the interior of the woven material. In this case, as the resin fingering front begins to move into the interior to form a resin infused layer, the peak stress in the unsaturated part of the woven will be proportional to the difference between the deformation of the two parts of material being saturated., i.e. the difference between the minimum packing density reached in the resin-filled part of the body and the average packing density in the unsaturated region. The various stress components are schematically shown in Fig. 3(b). The average packing density is proportional to the inverse rate of the external flux, i.e. the tensile longitudinal stress in the unsaturated part will increase as this rate increases. In summarising all the three cases it is obvious that the maximum tensile stress in the unsaturated part of the woven material is proportional to the difference between the average packing densities in the two regions separated by the meniscus of the resin. Thus, a condition for the crack growth can be obtained from an estimation of the energy release rate for cracking of a thin layer fixed on a substrate. This energy release rate G is proportional to the product of the

5 I.B. Sevostianov et al. / Composites: Part B 30 (1999) Fig. 4. Schematic of the problem considered for mathematical modelling. energy density and the thickness of the infused layer, viz. h b G ˆ z s w k E 2 ; 9 w Where h is the thickness of the preform layer, b is the thickness of the un-infused section of the preform layer, E w is the Young s Modulus of the saturated zone, s k is the component of the stress tensor perpendicular to the flow direction, and z is an experimental constant. Catastrophic crack growth occurs when the energy release rate in the unsaturated region exceeds its fracture toughness, i.e. G G c. Stable crack growth will be observed for G ˆ G c. This simplified heuristic model elucidates the main features of the resin infusion process: damage can only occur when the resin meniscus begins to penetrate into the matrix material; damage is more probable with increased external resin flux; with an increase of the body size the fracture probability increases, as the energy release rate is proportional to the thickness of the infused layer. The present mathematical formulation of the proposed physical model does not allow further insight into the interplay of various interactions which occur during the vacuum resin infusion process. In Section 3 a more rigorous formulation is presented in which the aforementioned model will be used as a guideline. 3. Analysis of stresses For a more rigorous calculation of the stress field in the solid preform material the coupled field problem for the two phase system consisting of the solid network and the fluid resin has to be studied. The stress in the resin can be described by a hydrostatic field, as: s ik ˆ P z; t d ik : 10 The negative sign is used here to indicate compressive stresses in the resin which are accepted as a negative, while compression in the fluid usually corresponds to the positive pressure. In the solid preform material we will distinguish two different zones: the saturated and unsaturated which are shown schematically in the Fig. 4. The interface between these two zones corresponds to the location of the penetrating resin front h(t). Denoting the deviatoric stresses as s ik and the hydrostatic stress as s ˆ tr s=3 ˆ s ii =3, the constitutive law for the woven composite can be expressed as: s ˆ s ik ˆ E w 1 2n w e e f 11 Ew 1 n w e ij h w e ij H x h : 12 Here H x h is the Heaviside function which is equal to 1 in the saturated zone, i.e. when x h t, and zero otherwise; e ik are the shear strains; e ˆ e ii =3 is the volumetric strain; and e f is the stress-free strain corresponding to the volume change caused by the resin infusion and is given by: e f ˆ ln C s C C s : 13 C 0 In Eq. (13) C 0 is the concentration of the solid fibres in the initial stage. The stress-free strain can be related to the hydrostatic pressure P in the resin via the change of the solid phase concentration C s as: C s t ˆ C s 0 K w P t C s 0 : 14 Mathematically the aforementioned problem is a variation of the well known Stephan s problem. Thus, an additional equation to describe the resin film penetration into the woven material is required. Denoting the co-ordinate of the interface as h(t) the following equation can be used [22]: 7P ˆ h 1 C s 0 P c =K w C s 0 D ds t ; 15 dt where S(t) is the position of the interface between saturated and unsaturated regions of the woven material i.e. the location of the resin front. The stress field in the woven material can be calculated

6 518 I.B. Sevostianov et al. / Composites: Part B 30 (1999) Fig. 5. Typical autoclave cycle for a resin infusion process using an epoxy resin. from the local mechanical equilibrium conditions 2s ik 2x i ˆ 2P 2x k ; x 3 h t ; 16 2s ik ˆ 0; x 2x 3 h t : i For the film shown in Fig. 4 the boundary conditions are u z 0; t ˆ0; u x ˆ u y ˆ 0; s 33 x 3 ; t ˆ 1 C s x 3 ; t P x C s x 3 ; t 3 ; t ; 17 where u i are the components of the displacement vector, and s zz is the stress component normal to the film surface. It has to be noted that P h; t is equal to zero if the resin meniscus does not penetrate into the body. In order to solve the aforementioned set of equations we need to determine the stress field in the resin. It is governed by the viscous flow of the resin through the elastic part of the woven material. In addition to the Darcy s law this flow problem can be described by the continuity equations for the liquid and the solid phases as 2C L 2t 7 j r ˆ Kw K L 2P 2t 7P j r ; 18 where K L is the bulk modulus of the liquid phase. For simplicity, we assume that K L does not depend on pressure. Table 1 Material properties used in numerical simulation Material properties of resin Material properties of fibre Viscosity h 0 ˆ Pa s Young s modulus ˆ 4.2 GPa P c ˆ 160 kpa Poisson s ratio ˆ 0.25 Compressibility modulus ˆ Permeability ˆ MPa Initial volume fraction ˆ 0.5 Using Eqs. (1), (3), (14) and (18) we can derive the following equation for the pressure field in the resin: 2P x 3 ; t 2t K L hk w 7 D7P x 3 ; t D h 7P 2 ˆ 0: 19 In deriving Eq. (19) it was taken into account that the permeability D of the woven material changes with the solid concentration and it was also assumed that the bulk modulus of the liquid is essentially less than that of the solid. The solution of Eq. (19) has to fulfil the following boundary condition: D h 7P 0; t ˆj ext 4. Results and discussion 20 The finite difference method (FDM) is in general considered to be the most suitable for the solution of moving boundary problems [22]. For the solution of the present problem both the implicit and explicit schemes [23] of FDM were used. However, the explicit expression of the time derivative on the moving boundary led to an unstable solution. Thus the finite element method (FEM) was also used in this study. The viscosity of the resin depends significantly on the temperature of the process. The corresponding dependence can be represented in the following form [24]: h T ˆh 0 exp 6 ka ; 21 T where m, 6 and k are constants which have to be obtained from the experiment, a denotes the degree of cure and T is a temperature in Celsius of the process. As an example, the data obtained by Kang et al. [25] were used in the present study: a ˆ 0.2, k ˆ 26.89, 6 ˆ Temperature changes with time in the vacuum resin

7 I.B. Sevostianov et al. / Composites: Part B 30 (1999) Fig. 6. Spatial distribution of the pressure at varying moments in time. (1) t/ t f ˆ 0.1; (2) t/t f ˆ 0.5; (3) t/t f ˆ 1. infusion process. The history of temperature change which was used in the calculations is shown in Fig. 5. For simplicity, external applied pressure was not considered in this example. However, it can be taken into account by using superposition methods. Mechanical parameters for the resin and solid woven materials are presented in Table 1. The pressure distribution through the plate thickness is presented in Fig. 6 at different moments in time. The difference between the analysis performed on the basis of FDM and FEM is in the order of 7%. The time-dependent behaviour of the pressure at two control points in the saturated zone is presented in Fig. 7 for different values of j ext /l where l is the thickness of the preform. Examples of the analysis of the stress field are presented in the Figs. (8) and (10). As Fig. 8. Spatial distribution of the longitudinal stress at varying moments of time. (1) t/t f ˆ 0.1; (2) t/t f ˆ 0.5; (3) t/t f ˆ 1. discussed earlier, the stress field depends strongly on the resin flux rate (more accurately, on the relation j ext /l). As P c was taken as a constant, an increase in the ratio between the vacuum created pressure and capillary pressure P E /P c serves as a measure of an increasing process rate. These figures show different stages of the manufacturing process. For instance, for a low external flux we observe a step like change in the longitudinal stress at the surface when a completely saturated layer starts to form. This is the time when the resin meniscus starts to penetrate into the interior of the material. The comparison with similar plots for a higher flux rate are given in the Fig. 9 which shows that an increase in the flux rate creates higher longitudinal peak stresses at the bottom of the layer. In order to have a full Fig. 7. Time dependence of the capillary pressure for varying resin flux rates. 1: 100 cc/min, 2: 50 cc/min, 3: 20 cc/min, 4: 10 cc/min. Fig. 9. Spatial distribution of the longitudinal stress at the bottom of the preform for varying flux rates. (1) 100 cc/min; (2) 50 cc/min, (3) 20 cc/min, 4: 10 cc/min.

8 520 I.B. Sevostianov et al. / Composites: Part B 30 (1999) Acknowledgements Partial financial assistance for this research was provided by Kentron, a division of Denel, through a project awarded to the Centre for Composite Materials and Structures at the University of Natal. References Fig. 10. Spatial distribution of the perpendicular stress at varying moments of time. (a) t/t f ˆ 0.1; (2) t/t f ˆ 0.5; (3) t/t f ˆ 1. picture of the stress field development in the pattern, the co-ordinate and time variations of the s zz are presented for j ext ˆ 20 cc/min in Fig. 10. During the main part of the process s zz is compressive. Only at the very end of the saturation process do we find the tensile stress at the top of the pattern (i.e. the surface from which the resin penetration has started). 5. Conclusions The resin film infusion process developed for autoclave processing of composite structures with a high fibre volume content was analytically modelled and examined in this article. One of the main problems in this process is microcracking in the interlaminar regions and void formation in the resin. These defects decrease the strength of the fibre composite manufactured by use of this process and can even lead to the fracture of the material. Pressure is related to the rate of infusion, preform permeability and resin viscosity and is governed by Darcy s law. In the present study it was assumed that the compressibility coefficient of fibres was essentially higher than that of the resin. However, fibrous preforms, which may be considered as a porous media, were assumed to be sufficiently compressible. The non-linear equation of filtration is derived in order to obtain the pressure field in the resin. Owing to the moving front of the resin the problem can be reduced to a particular case of Stephan s law. This problem is solved by FDM as well as by FEM. The analysis of the stress formation during the resin film infusion is also investigated. The solutions obtained on the basis of FEM and FDM differ by less than 7%. The results obtained provide guidelines for further study of the vacuum resin infusion process as well as for the fibre reinforced composite materials manufactured by this process. [1] Williams C, Summerscales J, Grove S. Resin infusion under flexible tooling (RIFT): A review. Composites 1996;27A: [2] Gudmundson P, Lundemo C, Gebart R. An evaluation of alternative injection strategies in RTM, SICOMP Technical reports, TR [3] Gotch TM, Improved production process for manufacture of GRP on British Rail. In: Proceedings of the Eleventh Reinforced Plastics Conference, BPF RPG, Brighton, p [4] Alten R, Best PF, Short D. Vacuum injection moulding of high volume fraction fibre composites. In: Proceedings of the thirteenth Reinforced Plastics Conference, BPF RPG, Brighton, p [5] Tengler H. Vakuum-Injektionsverfahren. Z. Kunststoffe 1985;75(2): [6] Thirion JM, Girardy H, Waldvogel U. New development for producing high-performance composite components by the RTM process. Composites (Paris) 1988;28(3): [7] Hayward JS, Harris B. The effect of vacuum assistance in resin transfer moulding. Composites Manufact. 1990;1: [8] Lundström TS, Gebart BR, Lundemo CY. Void formation in RTM. J Reinforced Plastics Composites 1993;12: [9] Lundström TS. Measurment of void collapse during resin transfer moulding. Composites 1997;28A: [10] Boey FYC. Reducing the void content and its variability in polymeric fibre reinforced composite test specimens using a vacuum injection moulding process. Polymer Test 1990;9: [11] Ahn KJ, Seferis JC, Letterman L. Autoclave resin infusion process, analysis and prediction of resin contents, SAMPE Quart, January 1990, p [12] Shim S-B, Ahn K, Seferis JC, Berg AJ, Hudson W. Flow and void characterization of stitched structural composites using resin film infusion process (RFIP). Polymer Composites 1994;15: [13] Shim S-B, Ahn K, Seferis JC, Berg AJ, Hudson W. Cracks and microcracks in stitched structural composites manufactured with resin film infusion process. J Adv Mater 1995;3: [14] Gutowski TG, Morigaki T, Zhong C. The consolidation of laminate composites. Composite Mater 1987;21: [15] Kim YR, McCarthy SP, Fanucci JP. Compressibility and relaxation of fibre reinforcments during composite processing. Polymer Composites 1991;12: [16] Griffin PR, Grove SM, Guild FG, Russel P, Short D, Summerscales D, Taylor E. The effect of reinforcement architecture on the long range flow in fibrous reinforcements. Composites Manufact 1995;6: [17] Loos AC, MacRae JD. A process simulation model for the manufacture of a blade-stiffened panel by the resin film infusion process. Composites Sci Tech 1996;56: [18] Dave RS, Houle S. The role of permeability during resin transfer molding. In: Proceedings Am Soc Composites. Fifth Tech Conference, East Lansing, June p [19] Biot MA. General theory of three-dimensional consolidation. J App Phys 1941;12: [20] Terzaghi K. Theoretical soil mechanics. New York: Wiley, 1943.

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