Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion

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1 Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion A.L. Jeswani * and J.A. Roux The University of Mississippi University, MS 38677, USA Received: 4 November 2005 Accepted: 2 March 2006 SUMMARY Resin Injection Pultrusion (RIP) is an automated, continuous process and is one of the most cost-effective methods for manufacturing composite materials with constant cross sections (such as rod stock, beams, channels and tubing). In the present work, a 3-D finite volume technique was developed to advance the liquid resin flow front through the fibre reinforcement in the injection pultrusion process. The objective of this study was to improve fibre reinforcement wet-out and thus the quality of the pultruded part in an injection pultrusion process. The complete wet-out of the dry reinforcement by the liquid resin depends on various design and process parameters. The design parameters explored in this study were the aspect ratio of the final composite, injection slot width, injection slot location from inlet of injection chamber, and location of the multiple injection ports. The numerical model simulates the flow of polyester resin through glass rovings and predicts the impact of the design (geometric) parameters on wet-out, resin pressure field, and resin velocity field. The location of the liquid resin flow front has been predicted for an injection slot, as well as for five discrete injection ports. INTRODUCTION Unlike other composite manufacturing methods, pultrusion offers some unique characteristics. Simple or complex geometric profiles of constant cross-sections can be cost- effectively fabricated using the pultrusion process. As the process is continuous, the production rate is high and hence more economical. A pultruded composite consists of (i) resin that binds the composite together with (ii) the reinforcing materials and yields a composite which has good chemical resistance and weather resistance; and (iii) a variety of ancillary materials such as pigments to impart colour, accelerators to cure the resin, internal release agents, etc. The resin may be an unsaturated polyester resin, a vinyl ester resin, or an epoxy resin. Continuous strand mats and/or continuous rovings are used as the reinforcing materials. A pultrusion machine consists of the following components: creel, resin wet-out chamber, forming dies, heated metal die, puller or driving mechanism, and cut-off saw. A schematic of resin injection pultrusion, often referred to as the closed bath technique, is given in Figure 1. In resin injection pultrusion the fibre reinforcement is pulled through the injection chamber and the resin is injected under pressure. As the resin is injected under pressure, good wet-out of the fibre reinforcement must be achieved. Then the fibre/resin system is passed through the heated die, where curing of the composite takes place. The injection pultrusion manufacturing process produces significantly less volatile emissions than open bath wet-out methods. In addition, resins with low pot-life can be used with the injection pultrusion process. The throughput of a resin injection system is higher than that of the open bath wet-out method. * Graduate Student; Faculty Rapra Technology, 2006 In the injection pultrusion process considerable experimental work has been conducted by researchers 1-3 to investigate the effect of various design and processing parameters. Recently, efforts Polymers & Polymer Composites, Vol. 14, No. 7,

2 A.L. Jeswani and J.A. Roux Figure 1. Schematic of resin injection pultrusion process Filter creel Preform plate Resin injection chamber Heated die Pullers Saw Final product have been devoted to the development of numerical models for computational modelling of the injection pultrusion manufacturing process. The numerical models for the injection pultrusion process are generally built on the similar numerical schemes that have been developed for the flow simulation of resin transfer moulding (RTM) process 4-7. Rahatekar and Roux 8 developed a 2-D finite volume method to predict the resin pressure field, resin velocity field, and resin moving flow front location. The injection pressure necessary to achieve complete wet-out were predicted for different processing parameters. Multiple injection slots were modelled, but discrete port injection cannot be modelled using this 2-D model. The impact of the location of the slot and effect of placement of multiple ports were not presented. Liu 9 developed a 2-D and 3-D finite element/nodal volume technique to simulate the resin flow through the reinforcement during the injection pultrusion process. One, two and three-dimensional problems were simulated to investigate the effect of various model and process parameters on the predicted resin flow during the process. Liu suggested using either a variable flow rate injection or constant pressure injection to achieve a good flow pattern in the injection pultrusion process. A three-dimensional model was recommended to simulate the resin flow for thick parts. Liu 10 also developed transient and iterative finite element/nodal volume models to predict the steady-state flow fronts during injection pultrusion. Numerical performance of transient and iterative models was investigated for various pultrusion process and material parameters such as pull speed, injection pressure and variation of permeability in the pulling and transverse directions. This model employs large amounts of CPU time. Only one injection slot, located on top of the injection chamber, was used for injecting resin through the fibre reinforcement. This model was used to simulate the liquid resin flow at low pull speeds. A numerical model for flow simulation and the curing of resin has been developed by Kommu, Khommami and Kardos 11 using the finite element/control volume (FE/CV) and finite difference techniques. The continuity equation and conservation of momentum equations are solved in 2-D using a Galerkin FE/CV technique. The energy and chemical species balance equations are solved in 3-D, where streamline upwind Petrov-Gelerkin (SUPG) or streamline upwind (SU) FE/CV are used to discretize the equations in two dimensions, while the finite differences have been used in the third dimension. The effect of fibre pull speed and reinforcement anisotropy on product quality was demonstrated. The simulation results were presented at very low pull speeds and the effect of discrete ports was not shown. Also the effect of varying other design parameters (such as the aspect ratio of the composite, and changing the location of the injection slot) was not presented in their work. 652 Polymers & Polymer Composites, Vol. 14, No. 7, 2006

3 Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion Voorrakranam, Joseph, and Kardos 12 developed a 2-D mathematical model to simulate resin flow, cure, and heat transfer. Sensitivity of quality variables to important processing variables and parameters was predicted. The injection pultrusion process was studied from the point of view of product quality control to improve production rates. They concluded that in an injection pultrusion process an appropriate choice of injection pressure and temperature profile produces void-free parts of good quality that have small thermal and degree-of-cure gradients throughout the thickness. Discrete port injection cannot be modelled because it is a 2-D model. If more injection ports are used, then the wet-out rate (speed with which the reinforcing material is saturated with resin) increases and wet-out would probably be achieved at lower injection pressures. Higher injection pressure can result in good wetout, faster wet-out rates, and high production rates. In addition, the location and spacing of injection ports (in the case of multiple ports) will influence the wet-out; if a port is located near the inlet of the injection chamber, then the resin may spill out from the front of the chamber. It has been observed that some of the above mentioned parameters are interdependent, so it is important to understand the individual and related effects of these parameters on the wet-out process. This can readily be investigated with the present numerical model, and the model can help in guiding improvements so as to achieving complete wet-out in the resin injection chamber design of pultrusion manufacturing. Ding et al. 13 have developed a 2-D control volume/ finite element (CV/FE) model for flow simulation of the injection pultrusion process. His work was used to model the injection pultrusion of fibreglass-vinyl ester composite slats, and the material parameters were obtained by conducting experiments. The model was also used to generate a process window for the injection pultrusion of fibreglass-vinyl ester composites 14. This model assumes that no resin flow occurs in the width direction because this is a two-dimensional model. This model cannot be used if discrete port injection is used and/or the part geometry is three-dimensional. This present work is different from previous works 8-14 in that the model incorporates injection slot as well as discrete injection ports. This work corresponds to the pultrusion manufacturing of a polyester resin/ glass roving composite that requires significantly higher pull speeds than those investigated in Refs to achieve high product yields. In addition, a variety of geometrical design parameters is explored which have not been reported previously STATEMENT OF THE PROBLEM Wet-out is a very important process factor in the manufacture of pultruded composites. This work focuses on the wet-out process in the resin injection chamber of the overall pultrusion manufacturing process. Complete wet-out of the fibre reinforcement helps to manufacture a good quality product with good mechanical properties (such as strength). Description of the Injection Chamber The schematic of the computational domain for the numerical model of the injection chamber is illustrated in Figure 2 for discrete port injection and in Figure 3 for slot injection. The computational domain is divided into two regions, Region I and Region II, both of constant cross-sections. Region I is the region where the discrete injection ports or slots are located, and Region II is the latter part of the injection chamber, which is also the initial part (entrance) of the pultrusion die. An injection slot is placed in the top and bottom (dual injection) walls of Region I. A pump is used to inject the resin under pressure through the injection slot. Dry fibre reinforcement enters the injection chamber, and as it passes through Region I, the liquid resin impregnates the fibres. The total length of the computational domain is referred to as L T ( = 0.30 m). L IC and L D represent the lengths of Region I (injection chamber) and Region II (die entrance) and are taken to be 0.25 m and 0.05 m, respectively. H D and W D correspond to the height and width of the exit of Region II (the thickness and width of the final composite part). At the exit of the computational domain it is assumed that the fibre reinforcement and the resin are moving at the same velocity 15. Capabilities of Numerical Model In this study, Darcy s law 16 of flow through porous media was employed to simulate the flow of liquid resin through the fibre reinforcement. The current numerical model employed the finite volume method 17 to compute the pressure field and the flow field and thus predict the liquid resin flow front location. The program was executed on a personal computer (3.8 GHz, 2GB RAM). The solver used in this technique is very efficient as it utilises little computer storage and solves the system of equations Polymers & Polymer Composites, Vol. 14, No. 7,

4 A.L. Jeswani and J.A. Roux Figure 2. Schematic of the computational domain for discrete port injection chamber (not to scale) a) xy plane b) xz plane much faster than direct (matrix) methods. The program allows the user to input different process parameters and to study their effect on the resin flow front. The solution of the program yields the location of the liquid resin flow front at different time instances until steady state is reached. The program also determines the total simulated time for the flow front to reach steady state. Different permeability models can be selected to accurately model the flow of resin through the fibre matrix. Finite volume methods can deal directly with a non-uniform mesh in the physical domain. In this study, only a quarter of the domain was modelled because of the geometrical symmetry of the computational domain, so the grid points were reduced by 75%, thus saving computational space and time. 654 Polymers & Polymer Composites, Vol. 14, No. 7, 2006

5 Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion Figure 3. Schematic of the computational domain for slot injection chamber (not to scale) a) xy plane b) xz plane ANALYSIS In this section, we discuss the assumptions, the governing partial differential equation, the relation between fibre volume fraction and porosity, permeability models, boundary conditions, solution methods, and the algorithm. Assumptions The following assumptions were imposed to mathematically model the resin injection pultrusion process: The resin was an incompressible fluid. Darcy s law of flow through porous media (this Polymers & Polymer Composites, Vol. 14, No. 7,

6 A.L. Jeswani and J.A. Roux was used to simulate the flow of liquid resin through the fibre reinforcement). The resin viscosity was constant as the flow of liquid resin was essentially isothermal in the injection chamber. The numerical model was based on the 3-D Cartesian co-ordinate system. Kozeny-Carman and Gutowski permeability models were used to compute the components of the permeability tensor in the longitudinal and transverse directions. The pressure at the inlet to the injection chamber was assumed to be one atmosphere ( kpa). Mathematical Model Darcy s law 16 of flow through porous media is the most commonly used model for the flow of liquid resin through the fibre reinforcement during the processing of composites since the flow of liquid resin through a fibre matrix is analogous to the flow through a porous medium. In the injection pultrusion process, the total velocity of resin movement, u, referenced to a stationary co-ordinate system, is defined by u = {u v w} (1) where u, v, and w are the components of the resin velocity in three co-ordinate directions, defined by the following equations:- u U K P 11 K22 K33 = ; v = ; w = µφ x µφ y µφ z (2) In Equation (2) φ is the porosity, U is the velocity of the fibre reinforcement (pull speed) in the longitudinal (x) direction, P is resin pressure, and - K P x - K P y - K P ,, µφ µφ µφ z, are the velocity components of the liquid resin relative to the reinforcement. K 11, K 22, K 33 are the components of permeability in the x, y, and z directions, respectively, and µ is the viscosity of the liquid resin. The three expressions in Equation (2) are also called the Darcy momentum equations in the x, y and z directions, respectively. Substituting Equation (2) in Equation (1), the total resin velocity can be expressed as u U K P K K = µφ x µφ y µφ z (3) The continuity equation for flow of resin through the reinforcement is given by the following equation ( uφ) + ( vφ) + ( wφ) x y z = 0 (4) The governing pressure equation is obtained by substituting the momentum equations, Equation (3) into the continuity equation, Equation (4), which yields K + K K33 = ( x µ x y µ y z µ z x Uφ)= 0 (5) Since U and φ are constant in Region I and Region II, the term ( ) x Uφ vanishes. Thus, Equation (5) is the governing pressure equation for Region I and Region II. Fibre Volume Fraction and Porosity The fibre volume fraction (V fo ) of the composite material is defined as the volume fraction of fibre in the final composite; whereas, V f corresponds to the local fibre volume, (V f = V f (x)). The fraction of nonsolid volume is termed the porosity, φ. The porosity, φ, and the fibre volume fraction, V f, can be functions of the distance (x) in the longitudinal direction. In Region I and Region II of the computational domain, the fibre volume fraction and the porosity do not vary with distance in the x direction because the cross sectional area remains constant; hence V f (x) and φ(x) are constants (here V f (x) = V fo ) for this work. The relationship between local porosity φ(x) and local fibre volume fraction V f (x) is given in Equation (6). φ(x) = 1 V f (x) (6) Permeability Models For composite materials, permeability is partially a measure of the ease with which the liquid resin can flow through the fibre matrix; the higher the permeability, the lower the resistance to the flow of resin, and vice versa. Generally, composite materials are anisotropic, so the permeability is higher in the longitudinal direction than the transverse directions. The Kozeny-Carman model 18 predicts the permeability in the longitudinal direction. The equation used by Sharma 19, Raper 15, and Rahatekar 8 to calculate K 11 is 656 Polymers & Polymer Composites, Vol. 14, No. 7, 2006

7 Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion K 11 2 Rf = 4k ( ) 1 Vf 2 V f 3 (7) where k is the Kozeny constant, R f is the effective fibre radius (here, for glass rovings R f = 15 µm), and V f is the local fibre volume fraction. Sharma 19 used a value of 1.4 for k, as recommended by Batch 20. Gutowski s equations (Equation (8)) were used to predict the transverse permeability (K 22 = K 33 ) of the fibre reinforcement. The permeability in the transverse directions are expressed by the following equations K Va 1 2 R V f f = K = 4k Va + 1 V f (8) In this study the hexagonal fibre arrangement, the effective fibre diameter of 30 microns, and the empirical values (V a = and k = 0.2) from Gutowski s 21 work were employed. Boundary Conditions The computational domain is symmetric about the xy and xz-planes. Taking advantage of this symmetry, only a quarter of the computational domain is modelled. In addition, the boundary conditions have to be suitably modified to simulate the resin flow in a quarter of the computational domain. The modified pressure boundary conditions corresponding to Equation (5) are given below (Equations (9)-(19)). At the injection port/slot, the pressure is at injection pressure (input to the program). In Region I and Region II, since a slip boundary condition is used along the wall, Equation (9) to Equation (19) are the pressure boundary conditions. These are obtained by setting the component of the resin velocity normal to the wall equal to zero, i.e., no penetration of resin into the wall of the injection chamber. It is assumed 15 that at the outlet of the injection chamber, the velocity of the resin in the x-direction is equal to the fibre velocity in the x-direction (u = U). At the inlet of the computational domain (at x = 0), the fluid pressure has been assumed to be one atmosphere (101.3 kpa) as dry fibre reinforcement enters the injection chamber. P = P Inj at injection port/slot (9) P = P atm at x = 0 (10) x = 0 at x = length of injection chamber (11) y = 0 at y = 0 ( Region I ) (12) y = 0 at y = h(x) ( Region I ) (13) z = 0 at z = 0 ( Region I ) (14) z = 0 at z = l (x) ( Region I ) (15) y = 0 at y = 0 ( Region II ) (16) y = 0 at y = h(x) ( Region II ) (17) z = 0 at z = 0 ( Region II ) (18) z = 0 at z = l (x) ( Region II ) (19) Algorithm for Time Marching Scheme To solve the governing pressure partial differential equation, (Equation (5)), all the boundary conditions, initially based on velocity, were converted to pressure boundary conditions (Equations (9) - (19)). Then, the line-by-line TDMA (Tri-Diagonal Matrix Algorithm) technique 17 was employed to solve the pressure field for the entire computational domain at each time step. The overall solution marches forward by a time marching procedure. Having solved the pressure field at each time step, the velocity field is obtained by finite differencing of Darcy s equations (Equation (3)). The net liquid resin mass flow rate is calculated for all the control volumes in the domain. Each control volume in the domain is assigned a resin fill factor. The fill factor, F i,j,k, is defined as the fraction of the control volume occupied by liquid resin at a given time instant, relative to the maximum liquid resin the control volume can hold. In the numerical scheme, F i,j,k is related to the amount of resin in a given control volume. For a completely liquid filled control volume, the value of F i,j,k is unity (saturated reinforcement) and is zero (dry reinforcement) if the control volume is empty of liquid. Pressure is computed at a control volume if it is fully saturated with liquid resin; otherwise, atmospheric pressure is assigned to it. Then the time needed to fill the yet unfilled control volumes was determined. The minimum value of the time step is the amount of time required to fill the next quickest to fill control volume, which may Polymers & Polymer Composites, Vol. 14, No. 7,

8 A.L. Jeswani and J.A. Roux have resin in it but is not yet completely filled, and yet not overfilling any other control volume. As the flow front is advanced through time using this minimum time step, it is ensured that, at most, only one control volume is filled in one time step, and no control volume is overfilled as time advances forward. The fill factors of all unfilled or incompletely filled control volumes (where 0 F i,j,k <1) are updated at the end of each time step by using the minimum time step and the net mass flow rate for each control volume. To maintain the numerical stability of the algorithm, the pultruded part is not allowed to travel by more than the length of the nodal control volume in the pull direction during a given time step, i.e. L 0< tmin < U min (20) where L min is the minimum length of the control volume in the pull speed direction, and U is the fibre pull speed in longitudinal direction. This is a default time step size, and time is not allowed to advance by an amount greater than given in Equation (18). Hence, it is possible that no new control volumes are filled during a time step. This condition is checked at every time step, and no more than one control volume is allowed to be newly filled (F i,j,k = 1) at that time step. When steady state is reached no new control volumes are filled. RESULTS AND DISCUSSION In this 3-D study the effect of the following design (geometric) parameters on the injection pressure required to achieve complete resin wet-out were studied: location of the single (dual) injection slot, width of the (dual) injection slot, multiple (dual) injection slots and their location, and the aspect ratio of the final composite. In the first part of this study, an injection slot of 0.01 m wide located at 0.1 m from the inflow boundary (see Figure 3) was employed. In the second section five discrete ports, each 0.01 m x 0.01 m size with a gap of 5 mm between adjacent ports, and a gap of 2.5 mm between the port and the die side walls were used to study the impact of the design parameters on the injection pressure required to attain complete wet-out for discrete port injection. Each design parameter was varied with the other design parameters held at their nominal values. The nominal design parameter values selected for this study were the location of the single injection slot = 0.1 m, the width of the injection slot = 0.01 m. The aspect ratio of the final composite was m wide by m thick (2.5 in x in). The processing parameters selected were as follows: pull speed, U = m/s (60 in/min) or m/s (120 in/min), fibre volume fraction, V fo = 0.68, and resin viscosity, µ = 0.75 Pa. s. In the results section of this study the liquid resin pressures are everywhere expressed in gauge pressure. SLOT INJECTION Effect of Location of the Injection Slot The location of the injection slot is an important design parameter. If the injection slot were to be located near the inlet of injection chamber, then the resin might spill out from the front of the injection chamber, and if the injection slot were to be located near the exit of the injection chamber then the exit resin pressure could be high. In this study the single injection slot, 0.01 m wide, was placed at 0.05 m, 0.1 m, 0.15 m and 0.2 m from the inlet of the injection chamber and its effect on wet-out was studied. Cases 1, 2, 3 and 4 in Table 1 demonstrate the effect of the location of the single injection slot relative to the inlet of the injection chamber. It was observed that an injection pressure of 1.14 MPa was necessary for complete wet-out; any pressure below this value (1.14 MPa) would result in incomplete wet-out. Also the minimum injection pressure required to achieve complete wet-out remained the same (1.14 MPa) at all the different axial locations of the injection slot. A comparison of the centreline and die wall pressure profiles at steady state conditions for an injection slot placed at different axial locations is shown in Figure 4. It was observed that the die wall pressure initially rose to the injection pressure and then after the injection slot the die wall pressure dropped rapidly to a low pressure, after which the die wall pressure decreased slightly as it reached the end of the injection chamber. Behind the liquid resin flow front the centreline and die wall pressures became equal and the resin pressure is essentially uniform across the part thickness. Also as the injection slot is located farther downstream from the inlet of the injection chamber the resin pressure at the exit of the injection chamber increased. Effect of Width of the Injection Slot The width of the injection slot was another design parameter explored in this study. Wider injection slots require lower injection pressure to achieve complete wet-out, and the wet-out rate is higher 658 Polymers & Polymer Composites, Vol. 14, No. 7, 2006

9 Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion Table 1. Injection pressure required for complete wet-out for a single slot placed at different axial locations and for different slot widths and part thicknesses Case # U m/s (in/min) V fo µ Pa. s Injection Pressure (Gauge) MPa (Psi) Slot Width m Location of Injection Slot m Part Width, m (in) Part Thickness m (in) (60) (165) (2.5) (0.125) (60) (165) (2.5) (0.125) (60) (165) (2.5) (0.125) (60) (165) (2.5) (0.125) (60) (615) (2.5) (0.125) (60) (435) (2.5) (0.125) (60) (265) (2.5) (0.125) (60) (225) (2.5) (0.125) (60) (590) (2.5) (0.25) (60) (2180) (2.5) (0. 5) Figure 4. Centreline (CL) and die wall (DW) pressure (gauge) profiles for an injection slot located at 0.05 m, 0.1 m, 0.15 m, and 0.2 m, U = m/s, V fo = 0.68, µ = 0.75 Pa.s, H D = m, W D = m because wider slots allow larger amounts of resin through them than narrower slots. Slot widths of m, m, m, m and 0.01 m were investigated in this study, with the 0.01 m wide slot being the nominal value. Cases 2, 5, 6, 7, and 8 in Table 1 show the injection pressures required to achieve complete wet-out. As the slot width was reduced the injection pressure necessary for complete wet-out increased. Figure 5 illustrates the non-linear relation between the slot Polymers & Polymer Composites, Vol. 14, No. 7,

10 A.L. Jeswani and J.A. Roux injection pressures necessary for complete wetout and the injection slot widths. As the injection slot width increased from m, the injection pressure necessary for complete wet-out dropped rapidly till the slot width became m. Then the required injection pressure for complete wetout decreased slowly with further increases in the injection slot width. The centreline and die wall pressure profiles for different injection slot widths are illustrated in Figure 6; as expected, a narrow slot width required higher injection pressures to move the liquid resin through the fibre reinforcement and achieve complete wet-out. The die wall pressure initially rose to the injection pressure and Figure 5. Injection pressure necessary for wet-out for different injection slot widths Figure 6. Centreline (CL) and die wall (DW) pressure (gauge) profiles for different injection slot widths 660 Polymers & Polymer Composites, Vol. 14, No. 7, 2006

11 Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion then after the injection slot the die wall pressure dropped rapidly to a lower pressure. The die wall pressure decreased slightly as it reached the end of the injection chamber. The centreline and die wall pressures behind the liquid resin flow front became equal and the resin pressure was essentially uniform across the part thickness. As the injection slot width increased, the resin pressure at the exit of the injection chamber also decreased. Effect of the Aspect Ratio (Part Thickness) of the Final Composite Polyester/glass composites with different aspect ratios were modelled in this study. The width of the part was kept constant ( m, 2.5 in) and the effect of different part thicknesses on injection pressures required to achieve complete wet-out was studied. The predicted injection pressure necessary for complete wet-out for a polyester/glass composite of m (0.125 in), m (0.25 in), and m (0.5 in) part thicknesses are summarised in Table 1 (Cases 2, 9, and 10). As the part thickness increased, the injection pressure required for complete wet-out also increased; higher injection pressures were necessary for complete wet-out because it became difficult for the resin to impregnate the fibre reinforcement completely as the part became thicker. The injection pressure for complete wet-out is also shown as a function of the part thickness in Figure 7. There was a non-linear relationship between the injection pressure needed for wet-out and the part thickness. Figure 7 shows that the injection pressure required for complete wet-out increased rapidly as the part thickness increased. Figure 8 illustrates the centreline and die wall pressure profiles for different part thickness for a single injection slot located at 0.1 m from the inlet of the injection chamber. As the part became thicker it was observed that the liquid resin flow front moved further towards the inlet of the injection chamber, i.e., there was more back flow of resin as the part thickness increased; this was due to the higher injection pressure which pushed some resin upstream. Figure 9 shows the gauge isopressure contours and liquid resin flow front for different part thicknesses (H D ). The thick, dark contour corresponds to the liquid resin flow front; the thin lines correspond to isopressure contours within the liquid resin region. It should be noted that these figures are not to scale ; this was done in order to make the results more viewable and understandable. The actual composite in Figure 9 corresponds to a very Figure 7. Injection pressure (gauge) versus part thickness (aspect ratio) for an injection slot (0.01 m wide) and discrete port injection (0.01 m by 0.01 m) Polymers & Polymer Composites, Vol. 14, No. 7,

12 A.L. Jeswani and J.A. Roux Figure 8. Centerline and die wall pressure profiles for different part thickness for an injection slot Figure 9. Steady-state flow front profile and gauge isopressure (kpa) contours for polyester resin/glass roving and slot injection configuration, U= m/s, V fo = 0.68, µ = 0.75 Pa.s, Slot Location = 0.01 m (not to scale). (a) H D = m (0.125 in) (Case 2), (b) H D = m (0.5 in) (Case 10) (a) (b) 662 Polymers & Polymer Composites, Vol. 14, No. 7, 2006

13 Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion long and very thin domain, which makes it useful to display the results geometrically but not to scale. It was observed that as the pultruded part became thicker the liquid resin flow front moved upstream. In addition, the liquid resin flow front reached the centreline further downstream as the part became thicker. Effect of the Multiple Injection Slots In this work multiple (dual) injection slots (two, three and four slots) each 0.01 m wide were modelled and the injection pressure required to achieve complete wet-out was predicted. Tables 2, 3 and 4 summarise the injection pressures necessary to attain complete wet-out for two, three, and four (dual) injection slots respectively. For multiple slot injection (Tables 2, 3 and 4), the simulations were conducted at two pull speeds ( m/s and m/s) and for two part thicknesses ( m and m). If two injection slots, each of 0.01 m wide, were placed adjacent to each other without any gap between them (Case 11 in Table 2) then they acted as a single slot of 0.02 m wide and an injection pressure of 0.69 MPa was necessary to achieve complete wet-out. By using two injection slots, the injection pressure necessary for complete wet-out was reduced from 1.14 MPa (single slot Case 2, Table 1) to 0.69 MPa. In addition, if the injection slots were separated by 0.01 m (Case 12) then the injection pressure required for complete wet-out dropped further to 0.66 MPa. It was found that by separating the injection slots by more than 0.01 m the injection pressure required for complete part wet-out remained the same (0.66 MPa) as for 0.01 m injection slot separation. Hence separation distances greater than 0.01 m did not result in a lower injection pressure being needed to achieve complete wet-out. For a pull speed of m/s the predicted injection pressures for a no slot separation and a slot separation of 0.01 m were 1.34 MPa and 1.31 MPa respectively (Cases 13 and 14 in Table 2). Doubling the pull speed essentially requires doubling of the slot injection pressure required to achieve complete wet-out. Cases 15, 16, 17 and 18 in Table 2 summarise the injection pressures necessary for complete wetout, but for a part thickness of m (0.25 in). The trends discussed above for a part thickness of m (0.125 in) are the same as that for a part m (0.25 in) thick. Table 3 summarises the predicted injection pressure required to attain complete wet-out for a three slot injection configuration at two pull speeds (U = Table 2. Effect of multiple injection slots (two) and their location Case # U m/s (in/min) V fo µ Pa. s Injection Pressure (Gauge) MPa (Psi) Slot Width m Location of Injection Slots m I II Part Width m (in) Part Thickness m (in) (60) (100) (2.5) (0.125) (60) (95) (2.5) (0.125) (120) (195) (2.5) (0.125) (120) (190) (2.5) (0.125) (60) (370) (2.5) (0.25) (60) (320) (2.5) (0.25) (120) (740) (2.5) (0.25) (120) (635) (2.5) (0.25) Polymers & Polymer Composites, Vol. 14, No. 7,

14 A.L. Jeswani and J.A. Roux Table 3. Effect of multiple injection slots (three) and their location Case # U m/s (in/min) V fo µ Pa. s Injection Pressure (Gauge) MPa (Psi) Slot Width m Location of Injection Slots m I II III Part Width m (in) Part Thickness m (in) (60) (70) (2.5) (0.125) (60) (70) (2.5) (0.125) (120) (140) (2.5) (0.125) (120) (135) (2.5) (0.125) (60) (280) (2.5) (0.25) (60) (230) (2.5) (0.25) (60) (225) (2.5) (0.25) (120) (555) (2.5) (0.25) (120) (455) (2.5) (0.25) (120) (445) (2.5) (0.25) m/s and m/s) and part thicknesses (H D = m and m). When the three slots each of 0.01 width were placed adjacent to each other without any gap, they acted as a single slot 0.03 m wide (Case 19, Table 3) and an injection pressure of 0.48 MPa was needed to achieve complete wet-out. When the injection slots were separated by a gap of more than 0.01 m (Case 20) then the injection pressure required to achieve complete wet-out remained at 0.48 MPa. If the pull speed was doubled (U=0.051 m/s) then the injection pressure was also almost doubled for a single slot of 0.03 m width (Case 21) and if a gap of 0.01 m was introduced between the slots then the injection pressure dropped down to 0.93 MPa (Case 22, Table 3). Cases in Table 3 summarise the injection pressures necessary to achieve complete wet-out for a part m thick. From Cases it was observed that for the three slot injection case the minimum injection pressure necessary for complete wet-out was obtained when the slots were separated by a gap of 0.02 m and any separation above 0.02 m did not yield any improvement in (lowering of) the injection pressure required to achieve wet-out. The predicted injection pressures required to attain complete wet-out for a four slot injection case at different pull speeds and different part thickness are summarised in Table 4. When the four slots each of 0.01 width were placed adjacent to each other without any gap, they acted as a single slot 0.04 m wide (Case 29, Table 4) and an injection pressure of 0.38 MPa was needed to achieve complete wet-out. A minimum injection pressure of 0.34 MPa (Case 30) was necessary to attain complete wet-out when the four injection slots were separated by a gap of 0.01 m or more. The injection pressure required to achieve complete wet-out was almost doubled if the pull speed was doubled (U=0.051 m/s) (Cases 29, 31, and 30, 32). Cases 33, 34, 35 and 36 in Table 4 summarise the injection pressure necessary to achieve complete wet-out for a part m thick. From these cases it was observed that for a four slot injection configuration the minimum injection pressure necessary for complete wet-out was obtained when the slots were separated by a gap of 0.01 m, and any separation greater than 0.01 m still required the same injection pressure. Figures 10 and Figure 9(a) show the gauge isopressure contours and the liquid resin flow front 664 Polymers & Polymer Composites, Vol. 14, No. 7, 2006

15 Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion Table 4. Effect of multiple injection slots (four) and their location Part Thickness m (in) Part Width m (in) Location of Injection Slots m Slot Width m Injection Pressure (Gauge) MPa (psi) V fo µ Pa. s Case # U m/s (in/min) I II III IV (60) (55) (2.5) (0.125) (60) (50) (2.5) (0.125) (120) (110) (2.5) (0.125) (120) (100) (2.5) (0.125) (60) (215) (2.5) (0.25) (60) (175) (2.5) (0.25) (120) (430) (2.5) (0.25) (120) (350) (2.5) (0.25) for the multiple injection slot configurations. It was observed from Figure 10 that the liquid resin flow front reached the centreline after the last injection slot, so as the number of injection slots increased the liquid resin flow front also shifted downstream in the axial direction. Figure 11 illustrates the centreline and die wall pressure profiles for single and multiple (two, three and four) injection slot configurations for a pull speed of m/s and part thickness of m. As the number of injection slots increased the injection pressure required to achieve complete wet-out decreased. For a four injection slot configuration an injection pressure of 0.34 MPa (Case 30, Table 4) was necessary to achieve complete wet-out compared to 1.14 MPa (Case 2, Table 1) for a single slot configuration. Decreasing the injection pressures is desirable both from safety and from equipment perspectives and hence the use of multiple injection slots would be advantageous. DISCRETE PORT INJECTION In this study five discrete injection ports each of size 0.1 m x 0.1 m were modelled (see Figure 2) to study the impact of the variation in design (geometric) parameters on the discrete port injection pressure necessary to attain complete wet-out. The gap between the die side wall and the port was 2.5 mm and the gap between adjacent ports was 5 mm. These five injections ports were placed at 0.1 m from the starting of the injection chamber (same as for slot injection) as shown in Figure 2. Table 5 summarises the injection pressures necessary for complete part wet-out at different part thicknesses (Cases 37, 38, and 39) and different axial location of the discrete port injection configuration (Case 40). Any injection pressure below these values would result in incomplete wet-out. As the part thickness increased it became difficult for the resin to impregnate the fibre completely and thus higher injection pressures were necessary for complete wetout of thicker parts. For the discrete injection port configuration the injection pressure necessary for complete wet-out increased non-linearly with part thickness (H D ), as seen in Figure 7. It was observed that by doubling the part thickness from m to m the injection pressure necessary to achieve wet-out increased by 33% and when the part thickness was doubled from m to m the injection pressure required for complete wet-out increased rapidly by 137%. For Polymers & Polymer Composites, Vol. 14, No. 7,

16 A.L. Jeswani and J.A. Roux Figure 10. Steady-state flow front profile and gauge isopressure (kpa) contours for polyester resin/glass roving and multiple slot injection configurations, U= m/s, V fo = 0.68, µ = 0.75 Pa.s, H D = m (0.125 in) (not to scale). (a) three injection slots (Case 20), (b) four injection slots (Case 30) (a) (b) Figure 11. Centreline and die wall pressure profiles for single slot and multi slot injection for U = m/s (60 in/ min), H D = m (0.125 in) 666 Polymers & Polymer Composites, Vol. 14, No. 7, 2006

17 Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion the discrete port configuration described here, it always required much higher injection pressures to achieve complete wet-out. Figure 12 illustrates the steady-state liquid resin flow front profile and the gauge isopressure contours for the five discrete port resin injection configuration (Case 37). Figure 12 shows the isopressure profiles for the top surface of the die (top xz plane in Figure 2). The dark line illustrates the liquid resin flow front and the thin lines are isopressure contours within the liquid region. An injection pressure of 5.83 MPa was required to achieve complete wet-out both through the part thickness and through the part width (Figure 12). If the injection pressure was less that 5.83 MPa then complete wet-out was not achieved. For the discrete port injection configuration it was found that if the injection pressure was greater than or equal to 1.14 MPa (Case 2, Table 1) and less than 5.83 MPa then the liquid resin reached the centreline through the thickness but could not penetrate through the width of the part. When a series of five discrete ports (two rows of 5 injection ports each or a total of 10 injection ports) were added inline at 0.12 m (Case 40) from the inlet of the injection chamber to the existing discrete port configuration (Figure 2) the injection pressure required to achieve complete wet-out was reduced by 50% from 5.83 MPa to 2.93 MPa. Figure 13 illustrates the steady-state liquid resin flow front profile and the gauge isopressure contours Table 5. Injection pressure required for complete wet-out for a discrete port injection configuration Case # U m/s (in/min) V fo µ Pa. s Injection Pressure (Gauge) MPa (Psi) Port Width m Location of Injection Ports m Part Width m (in) Part Thickness m (in) (60) (845) (2.953) (0.125) (60) (1125) (2.953) (0.25) (60) (2665) (2.953) (0.5) (60) (425) and (2.953) (0.125) Figure 12. Steady-state flow front profile and gauge isopressure (kpa) contours for polyester resin/glass roving and discrete port injection configuration, U = m/s, V fo = 0.68, µ = 0.75 Pa.s, discrete port location = 0.1 m (Case 37) (not to scale) Polymers & Polymer Composites, Vol. 14, No. 7,

18 A.L. Jeswani and J.A. Roux Figure 13. Steady-state flow front profile and gauge isopressure (kpa) contours for polyester resin/glass roving and discrete port injection configuration, U = m/s, V fo = 0.68, µ = 0.75 Pa.s, discrete port location = 0.1 m and 0.12 m (Case 40) (not to scale) for Case 40 in Table 5 for the discrete port resin injection configuration. Since multiple injection ports were used in the axial and width directions, the injection pressure necessary for complete wetout was considerably lower and the resin pressure at the exit of the injection chamber was less than for Case 37 (Figure 12). CONCLUSIONS The numerical model developed can be a useful guide to experimental work by identifying the sensitivity and range of the design parameters. It is a useful tool to predict the impact of various design (geometric) parameters related to pultrusion manufacturing of polymeric composites, and for understanding their effects on the wet-out, the injection pressure necessary to achieve complete wet-out, and the location of the liquid resin flow front. It has been shown that for the high pull speed resin injection pultrusion manufacturing of a polyester/glass roving composite the slot injection configuration is favourable to the discrete port configuration. Lower injection pressures are needed by the slot injection configuration than by the discrete port configuration to achieve complete wet-out. In addition, multiple slot injection and multiple discrete port injection configurations mean that much lower injection pressure are required for complete wet-out. Lower injection pressures are desirable both from a safety consideration and from cost of equipment consideration. The simulation results predicted a non-linear increase in the injection pressure necessary for complete wet-out as a function of the part thickness for an injection slot and for the discrete port injection configurations. Non-linear behaviour with regard to the injection pressure required for complete wet-out was also observed for different single injection slot widths. ACKNOWLEDGEMENTS The authors want to thank Dr. Ellen Lackey and Dr. James Vaughan for their valuable insight and recommendations during the course of this work. NOMENCLATURE x Axial co-ordinate, in the longitudinal direction of fibre, m y Vertical co-ordinate, in the transverse (height) direction of fibre, m z Co-ordinate along the width dimension, m IP Injection Pressure, Pa IS Injection Slot K 11 Permeability in x (axial) direction, m 2 K 22 Permeability in y (transverse) direction, m 2 K 33 Permeability in z (transverse) direction, m 2 P Pressure, Pa R f Effective fibre radius, m φ Porosity U Fibre velocity in x (axial) direction, m/s u Resin velocity in x (axial) direction, m/s 668 Polymers & Polymer Composites, Vol. 14, No. 7, 2006

19 Numerical Modelling of Design Parameters for Manufacturing Polyester/Glass Composites by Resin Injection Pultrusion v Resin velocity in y (transverse) direction, m/s w Resin velocity in z (transverse) direction, m/s µ Viscosity of liquid resin, Pa. s V fo Fibre volume fraction of the finished product V f Local fibre volume fraction, V f (x) V a Empirical constant in Gutowski s equation k Empirical constant in Gutowski s equation k Kozeny constant ρ Density of the liquid resin, kg/m 3 F i,j,k Fill factor for a specific control volume REFERENCES 1. Lackey, E., Vaughan, J.G. and Roux, J.A., Experimental Development and Evaluation of a Resin Injection System for Pultrusion, Journal of Advanced Materials, 29, (1997), Dube, M.G., Batch, G.L., Vogel, H.H. and Mcosko, C.W., Reaction Injection Pultrusion of Thermoplastic and Thermoset Composites, Polymer Composites, 16, (1995), Kim, Y.R., Behavior of Fibre Reinforcement and Resin Flow During the Injection Pultrusion Process, PhD Thesis, University of Lowell, (1990). 4. Lee, I.J., Young, W.B. and Lin, R.J., Mould Filling and Cure Modelling of RTM and SRIM Processes, Composite Structures, 27, (1993), Bruschke, M.V. and Advani, S.G., A Finite Element/Control Volume Approach to Mould Filling in Anisotropic Porous Media, Polymer Composites, 11, (1990), Varma, R.R. and Advani, S.G., Three- Dimensional Simulations of Filing in Resin Transfer Moulding, Advances in Finite Element Analysis in Fluid Dynamics, ASME FED, Vol. 200, (1994). 7. Trochu, F., Boudreault, J.F., Gao, D.M. and Gauvin, R., Three Dimensional Flow Simulation for the Resin Transfer Moulding Process, Material Manufacturing Process, 10, (1995), Rahatekar, S.S. and Roux, J.A., Numerical Simulation of Pressure Variation and Resin Flow in Injection Pultrusion, Journal of Composite Materials, Vol. 37, (2003), Liu, X.L., A Finite Element/Nodal Volume Technique for Flow Simulation of Injection Pultrusion, Composites: Part A, 34, (2003), Liu, X.L., Iterative and Transient Numerical Models for Flow Simulation of Injection Pultrusion, Composite Structures: 66, (2004), Kommu, S., Khomami, B. and Kardos, J.L., Modelling of Injection Pultrusion Processes: A Numerical Approach, Polymer Composites, 19, (1998), Voorakaranam, S., Joseph, B. and Kardos, J.L., Modelling and Control of an Injection Pultrusion Process, Journal of Composite Materials, 33, (1999), Ding, Z., Li, S., Yang, H. and Lee, L.J., Numerical and Experimental Analysis of Resin Flow and Cure in Resin Injection Pultrusion (RIP), Polymer Composites, 21, (2000), Ding, Z., Li, S. and Lee, L.J., Influence of Heat Transfer and Curing on the Quality of Pultruded Composites II: Modelling and Simulation, Polymer Composites, 23, (2002), Raper, K.S., Roux, J.A., McCarty, T.A. and Vaughan, J.G., Die Inlet Contour Impact on the Pressure Rise in a Pultrusion Die, Journal of Composite Materials, Vol. 34, February 2000, Darcy, H., Les fontaines publique de la ville de Dijon. Paris: Dalmont, Patankar, S., Numerical Heat and Fluid Flow, Hemisphere Publishing Corporation, New York, Carman, P.C., Fluid Flow Through Granular Beds, Trans. Int. Chem. Eng., 15, (1937), Sharma, D., McCarty, T.A., Roux, J.A. and Vaughan, J.G., Investigation of Dynamic Pressure Behavior in a Pultrusion Die, Journal of Composite Materials, Vol. 32, July 1998, Batch, G.L. and Macosko, C.W., Analysis of Pressure, Pulling Force, and Sloughing in Pultrusion, Polymer Process Engineering, Vol. 3, (1985), Gutowski, T.G., Cai, A., Bauer, S., Boucher, D., Kingery, J. and Wineman, S., Consolidation Experiments for Laminate Composites, Journal of Composite Materials, Vol. 21, July 1987, Polymers & Polymer Composites, Vol. 14, No. 7,