pull speed influence on fiber compaction and wetout in ... · n.b. masuram, j.a. rou, and a.l....

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1. INTRODUCTION

Resin injection pultrusion (RIP) is the most economical composite manufacturing process for uniform cross-section composites. In the resin injection pultrusion process, liquid resin is injected through the injection slots located on either side (top and bottom) of the tapered injection chamber walls. The main goal is to completely penetrate the resin through the fiber reinforcements and reach the center of the fiber bed to obtain thoroughly wetted fibers before reaching the exit of the injection chamber. A minimum injection pressure is required for the resin to penetrate through the fibers; this resin pressure also pushes the fibers away from the chamber walls, causing fiber compaction. Compacted fibers are difficult to penetrate and thus affect complete wetout achievement. Researchers in the past have modeled

the resin injection pultrusion process. Jeswani and Roux1 developed a 3D finite volume model to simulate resin flow through the fiber reinforcement in the RIP. Ranga et al.2 further investigated the effect of varying the injection chamber length and pull speed on the resin flow in tapered resin injection pultrusion. Other researchers3,4,5 studied the influence of varying fiber volume fractions for both injection chamber attached and detached die configurations, and the impact of geometric parameters on complete wetout achievement. None of these works1-5 has considered the fiber compaction due to resin injection pressure.

Shakya et al.6 investigated the effect of resin viscosity on fiber compaction in resin inject ion pul trusion manufacturing; this study employed

a 3-D Finite Volume Method (FVM) and Tri-Diagonal Matrix Algorithm (TDMA) to solve the governing equations for a non-tapered injection chamber. Gutowski et al.7,8,9 developed a mathematical model which allowed 3-D flow and 1-D consolidation of the composites. Experiments were conducted on prepregs of aligned graphite fibers with constant viscosity oil to study the deformation of the fibers in a “drained” state (oil impregnated, but zero pressure in the oil). The results revealed that the fibers can be treated as a deformable, non-elastic network, and can be modeled based on the bending beam behavior. They also concluded that the axial permeability of the fibers can be modeled by Carman-Kozeny theory and that their resin flow/deformation theory can be used to model the resin pressure history. Batch et al.10 presented data for fiber reinforcement compaction in resin transfer molding; experimental data for fiber compaction behavior were presented in the form of “compaction pressure” versus “fiber volume fraction”.

Pull Speed Influence on Fiber Compaction and Wetout in Tapered Resin Injection Pultrusion Manufacturing

N.B. Masuram1, J.A. Roux2, and A.L. Jeswani3

University of Mississippi, University, MS 38677 USA

Received: 29 June 2016, Accepted: 27 October 2016

SUMMARYIn the resin injection pultrusion process (RIP), liquid resin is injected into the tapered injection chamber through the injection slots to completely wetout continuously pulled fibers. As the resin penetrates through the fibers, the resin also pushes the fibers away from the wall towards the centerline, causing compaction of the fiber reinforcements. The fibers are squeezed together due to compaction, making resin penetration more difficult; thus at low resin injection pressures, the resin cannot effectively penetrate through the fibers to achieve complete wetout. However, if the resin injection pressure is too high, the fibers are squeezed together to such an extent that even greater injection pressure is necessary to wetout the compacted fibers. The design of the injection chamber significantly affects the minimum injection pressure required to wetout the fiber reinforcements. A tapered injection chamber is considered such that wetout occurs at lower injection pressures due to the taper angle of the injection chamber. In this study, the effect of fiber pull speed on the fiber reinforcement compaction and complete fiber wetout for a tapered injection chamber is investigated.

1Graduate Student2Faculty 3Principal Engineer, Osram Sylvania

419Polymers & Polymer Composites, Vol. 25, No. 6, 2017


Numerical simulation modeling and experimental study of the resin flow and heat transfer in the resin injection pultrusion process were presented by Ding et al.11. A control volume/finite element method (CV/FEM) was developed to solve the resin flow governing equations, together with the heat transfer and chemical reaction models. Kim et al.12,13 presented an experimental and analytical investigation of various dry reinforcement materials subjected to the compressive forces applied normal to their principle plane. Based on the data, they proposed a model to predict the permeability of resin through the fiber reinforcement as it moves through the tapered portion of the injection die, but this model did not investigate the various processing parameters that determine the flow front of the resin.

1.1 Present WorkThe objective of the current work is to employ a 3-D finite volume technique to simulate the resin flow through the fiber reinforcement with fiber compaction, and predict the liquid resin flow front location for various processing parameters in a tapered injection pultrusion process. As the resin penetrates through the fibers, the resin also pushes the fibers away from the wall towards the centerline, causing compaction of the fiber reinforcements. The fibers are squeezed together due to compaction, making resin penetration more difficult; thus at low resin injection pressures, the resin cannot effectively penetrate through the fibers to achieve complete wetout. Due to the compaction of fibers away from the wall, the permeability of the fiber matrix decreases; thus the minimum injection pressure required to achieve complete wetout increases. Due to the taper angle of the injection chamber, the interior resin pressure in the chamber increases as the fibers propagate along the chamber. Compaction is a practical phenomenon affecting the pultrusion process, and the tapered injection chamber effects the minimum

injection pressure required; this model yields more realistic results and will be beneficial in bringing forward more effective and efficient tapered injection chamber designs in pultrusion manufacturing.

Darcy’s law14 of flow through porous media is used to stimulate resin flow through a fiber matrix. Gutowski’s compaction model7 has been utilized to compute the transverse permeability15 of the fiber matrix. The governing pressure equation is obtained by substituting the momentum equations from Darcy’s law14 into the continuity equation. The governing pressure equation is then discretized using the finite volume technique, and the pressure field is determined by solving the discretized equations using the line-by-line TDMA (Tri Diagonal Matrix

Algorithm) solution technique16. The fiber compaction behavior is modeled using a curve fit expression to the experimental data10 for rovings.

2. STATEMENT OF PROBLEM

The geometry of a tapered resin injection chamber is illustrated in Figure 1a and b; Region I is tapered and the Region II is not tapered. When the fibers pass through the tapered injection chamber for a non-compaction case, the fiber/resin system is uniformly compressed towards the chamber center increasing the fiber volume fraction and decreasing the fiber matrix permeability along the axial direction as shown in Figure 2. However, for the compaction case (Figure 3), when the liquid resin is injected into the fiber reinforcement the injection pressure

Figure 1. Tapered resin injection chamber showing the injection slot locations in (a) side view and (b) top view

420 Polymers & Polymer Composites, Vol. 25, No. 6, 2017

N.B. Masuram, J.A. Roux, and A.L. Jeswani

squeezes the fibers towards the center of the injection chamber and away from the chamber wall. This creates a lean fiber zone in the region near the wall and a dense fiber zone in the transverse direction somewhere away from the chamber wall. Figure 3 illustrates how fiber compaction is localized in the vicinity of the resin injection slot. At high resin injection pressures the fibers can be squeezed to such an extent that the permeability of the fibers becomes very low in the transverse direction and resin penetration becomes difficult. This increases the probability of resin backward flow along the chamber wall.

The effect of a geometric design parameter on the resin injection pultrusion process is explored by varying the chamber tapered angle (α). A slight change in the injection chamber taper angle may result in a significant impact on the minimum resin injection pressure required to achieve complete wetout. Compression ratio, CR, is defined as the ratio of the height of the injection chamber at the inflow boundary of Region I (HIC) (Figure 1) to the height of the injection chamber at the outflow boundary of Region II (HD); CR can be expressed as:

(1)

For the tapered injection chamber, HIC is greater than HD, and hence the value of CR is greater than 1; the taper angle (α) is given by:

(2)

In this work HD = 0.00318 m and LIC = 0.25 m with values of CR = 2, 3, and 4 were employed; these values yield from Eq. (2) the taper angles of α = 0.361°, 0.728°, and 1.09° respectively. For these very small taper angles the off-diagonal terms of the permeability were considered to be small such that only K11, K22 and K33 were employed in the modeling as seen in Eqs. (10a) and (11). The total length of the injection chamber (LT) is considered as 0.30 m.

The values for CR were chosen to be 2.0, 3.0 and 4.0; whereas the value for the tapered length (LIC) of the injection chamber for Region I is 0.25 m and the length of Region II (LD) of 0.05 m are fixed. The thickness of the pultruded composite material is 0.00318 m. This work addresses complete wetout for pull speeds (U) of 0.01524 m/s, 0.02032 m/s and 0.0254 m/s.

3. ANALYSIS

3.1 AssumptionsThe assumptions made in this study for modeling of a tapered injection pultrusion process are as follows: 1) The resin is an incompressible fluid. 2) The numerical model is developed in a

3-D Cartesian co-ordinate system. 3) Darcy’s law14 for liquid flow through a porous medium is employed to simulate the flow of resin through the fiber reinforcement. 4) The resin flow is basically isothermal; therefore the resin viscosity remains constant. 5) The Gutowski9 permeability model is employed to compute the permeability components in the longitudinal and transverse directions for fiber rovings. 6) The pressure at the inlet of the injection chamber is assumed to be atmospheric pressure (101.325 kPa).

3.2 Fiber Volume Fraction and PorosityFiber volume fraction (Vf (x,y)) of a composite material is the volumetric

Figure 2. Fiber distribution in a tapered resin injection chamber

Figure 3. Effect of compaction on fiber distribution in a tapered resin injection chamber



fraction of the fiber in the final composite. The porosity ϕ is defined as the non-solid volume in the composite. The sum of the fiber volume fraction and the porosity is always equal to unity, thus:

(3)

Both of these parameters depend upon the compression ratio (CR) or taper angle (α) as defined in Eqs. (1) and (2). Therefore, for a tapered injection chamber, the non-compaction axial fiber volume fraction (Vfo(x)) increases in the positive axial x-direction due to tapering. The non-compaction axial fiber volume fraction is minimum at the chamber inlet and increases with increasing longitudinal (x) coordinate in Region I, attains its maximum value at the end of the Region I and then remains essentially constant due to no tapering throughout Region II. For Region I, the non-compaction fiber volume fraction Vfo (x) is mathematically given as:

(4)

The x-dependence of Vfo (x) on the left side of Eq. (4) is due to the tapered wall of the injection chamber; whereas, the y-dependence of Vf (x,y) in Eq. (3) comes from the compaction model presented later in this work; Vfo on the right side of the Eq. (4) is the fiber volume fraction of the final pultruded product at the exit of the injection chamber; also h(x) is defined below in Eq. (10b).

3.3 Permeability ModelPermeability of a composite material is defined as the measure of the ease of liquid resin flow through the fiber matrix. Higher the permeability, lower will be the resistance to the flow of the resin and vice versa. The numerical model in this study utilizes the Kozeny-Carman model15 to predict the permeability of the fibers in the longitudinal x-direction and the

Gutowski’s model9 to predict the permeability of the fibers in the transverse (y and z) directions. The permeability of the fibers in longitudinal direction is given15 by:

(5)

where k is the Kozeny constant (here k = 0.093), Rf is the fiber radius (here, Rf = 15µm), and Vf is the local (Eq. (3)) fiber volume fraction. The permeability in the transverse directions is given as:

(6)

where V′a = Vfmax = 0.907 and k′ = 0.2 are parameters determined by the fiber hexagonal packing arrangement of the fiber rovings.

3.4 Governing Equations for Region I and Region IIThe governing pressure equation for Region I (Eq. (10a)) is derived by substituting the Darcy 3-D momentum equations14 (Eq. (7)) into the continuity equation (Eq. (8)):

(7)

(8)

this is further simplified by substituting the transverse fiber velocity in terms of taper angle and axial fiber velocity (Eq.(9)):

(9)

Combining Eqs. (7, 8 and 9) yields:

(10a)

where U is the pull speed and the vertical distance y varies according to the relation –h(x)≤y≤h(x) where:

(10b)

Similarly, the governing pressure equation for Region II (non-tapered section) is given as:



(11)

3.5 Boundary ConditionsThe governing pressure equations, Eq. (10a) and Eq. (11), are second order partial differential equations. Thus six spatial boundary conditions, two in each coordinate direction are required for solving the pressure field. Since the computational domain is symmetric about xz- and xy-planes, only one quarter of the computational domain needs to be modeled. The total number of finite volume nodes in the quarter domain was 10602. For this, the boundary conditions for the simulation of resin flow in the quarter computational domain are as follows:

P = Patm at x = 0 (12a)

P = Pinj at injection slot (xIC) (12b)

(Region I) (12c)

at y = 0 (Region I) (12d)

at z = WD/2 (Region I and II) (12e)

at z = 0 (Region I and II) (12f)

at y = HD/2 (Region II) (12g)

at y = 0 (Region II) (12h)

at x = LT (12i)

3.6 Compaction PhenomenonDue to the compaction of fibers and the tapering of the injection chamber in Region I, the fiber volume fraction can be a function of both the coordinates x and y. A new pressure field is computed at each time step and ∆P(y) (= PN - PP) is calculated for all the control volumes. Here, PP is the resin pressure at a particular node, and PN is the resin pressure at the northern neighbor node. The local fiber volume fraction Vf (x,y) at each control volume node is computed using ∆P(y) from the function given in Eq. (13).

(13a)

(13b)

here,

Vf(x,y) is the new local fiber volume fraction

Vfo(x) is the initial (t = 0) local fiber volume fraction at a given x- location

Vfmax is the maximum fiber volume fraction defined by the permeability model

Pref is a reference pressure (here Pref = 1000 Pa)

∆P (y) = PN - PP

∆Pmax is the ∆P(y) value at which Vf(x,y) = Vfmax

Equation (13) is a simple yet accurate curve fit to the compaction experimental pressure data10. To verify this simplified model, Eq. (13) is plotted with the actual data10 and compared with the Gutowski’s model9, see Figure 4; clearly Eq. (13) is a very close fit to the experimental data10.

The value of ∆Pmax used in this study was the value that yields the best overall match of Eq. (13a) to the experimental data10 and was determined by minimizing the difference between Eq. (13a) and the experimental data10. The sum of absolute differences along the curve of Eq. (13a) and the experimental data10 in Figure 4 was observed to be a minimum at the ∆Pmax value of 3.45 MPa. The variation of the sum of absolute differences at different ∆Pmax values are illustrated in Figure 5. Therefore, ∆Pmax = 3.45 MPa is used in all further investigation of this study.

3.7 Algorithm for Redistribution of Fiber ReinforcementWhen there is no compaction, the local fiber volume fraction at any x-location is equal to the initial fiber volume fraction (Vfo(x)) from Eq. (4). When compaction takes place, the algorithm calculates the



local fiber volume fraction at all the control volumes in the y-direction at a particular axial x-location and makes sure that the total amount (cross-sectional area) of fibers is conserved at that axial cross-section. The algorithm for the redistribution of the fibers is described below.

1. Initially, there is no compaction. Therefore, the local fiber volume fraction is equal to the initial fiber volume fraction (same as dry fibers) i.e., Vf(x,y) = Vfo(x) from Eq.(4).

2. Advance the time until a control volume is filled with resin and calculate the pressure field.

3. Based on this calculated pressure field, compute the pressure difference domain vertically in the y-direction starting from the centerline and progressing towards the top chamber boundary. Using the forward differencing technique calculate ∆P=PN - PP for each control volume and assign this ∆P value as the center node ∆P.

4. Using Eq. (13) calculate the local fiber volume (area) fraction Vf (x,y) for the control volume corresponding to the ∆P assigned to that control volume.

5. Using the ∆P at the control volume next to the centerline, compute

Vf (x,y) from Eq. (13) such that Vf (x,y) < Vfmax. The total fiber area across the entire composite must remain constant; expressed mathematically this relation is given by:

(14)

where, ∆yi is the height of a specific control volume.

Note: • A control volume with zero

thickness is a control volume at the chamber centerline at a particular x-location.

• The number of non-zero thickness control volumes is equal to the number of y-nodes minus one, i.e. Ncv = Ny -1, where Ny is the number of pressure nodes in the y-direction.

• If there is no compaction, Vf(x) = Vfi(x) = Vfo(x) and thus Eq. (14) yields Vfo(x) = Vfo(x) as it should to conserve the total fiber area across any cross-section.

6. For the control volume next to the centerline, the ∆P and Vf(x,y) relation can summarized as:

(a) For ∆P ≥ PRef, Vfo(x) ≤ Vf(x,y) ≤ Vfmax

(b) For ∆P = 0 or ∆P ≤ PRef, Vf(x,y) = Vfo(x)

When ∆P ≥ PRef, the value of Vf(x,y) for a particular control volume increases from Vfo(x) to a higher value. Hence, to conserve the total amount (area) of fibers at any injection chamber cross-section, the “total” fiber volume (area) fraction of the remaining control volumes in the transverse direction must decrease accordingly. When there is an increase in the fiber volume fraction in a control volume (say control volume # 1, which is the control volume next to the centerline), then the

Figure 4. Relation between local fiber volume fraction Vf (x,y) and ∆P (y)/Pref (∆Pmax=3.45MPa, Pref = 1000 Pa, Vfmax = 0.73, Vfo = 0.49)

Figure 5. Variation of sum of absolute differences with ∆Pmax



increase in fiber area in that control volume will correspond to ∆y1WD[Vf(x,y)-Vfo(x)]; the fiber area increase in this control volume must result in a decrease in the total fiber area among the remaining control volumes along the y-direction. For the ith control volume, vertical height of that control volume is referred as ∆yi in finite difference form, whereas its vertical distance from the centerline is denoted as yi (Figure 6).

As a first “step”, it is assumed that, this decrease in fiber area is shared equally among the remaining control volumes in the y-direction. Mathematically,

(15)

where, 2V̂ is the average fiber area fraction of the remaining (Ncv – 1) control volumes in the y-direction after the increase in the fiber area of the particular control volume under compaction. This is done to maintain the balance of the overall fiber area at any x-location. Now solving for 2V̂ yields:

(16)

Now, as a next “step”, compute the fiber volume (area) fraction for control volume # 2 using its corresponding ∆P and Eq. (16). Thus, now the average area fraction 3V̂ , for the remaining (Ncv – 2) control volumes becomes:

(17)

This sequential stepping process continues up to, but not including, the last control volume next to the top boundary wall of the injection chamber. This stepping sequence of the above process can be generalized from the above equations for the jth control volume as:

(18)

To facilitate the computation for the finite volume analysis, the integral form of Eq. (18) is represented in finite difference form as:

(19)

Here, Ncv is the number of non-zero thickness control volumes in the y-direction which can be calculated as Ncv = Ny - 1, where Ny is the number of pressure nodes in the y-direction. To find the fiber volume (area) fraction for the non-zero thickness control volume next to the top chamber boundary (j = Ncv), Eq. (19) can be written as:

(20)



Also, VfNCV= NCV for only the one

control volume next to the top boundary, the average ( NCV

) fiber volume fraction is the same as the local (VfNCV

) fiber volume fraction for the control volume next to the top chamber wall.

7. Calculate VfNCV= NCV

from Eq. (20); note if NCV

>0, then this sequential process yields the fiber area fraction distribution across the composite in the y-direction; however it is possible that NCV

≤ 0 might occur.

(a) If (VfNCV= NCV) ≤ 0,

• Then assign R1 = VfNCV

• Now assign NCV = 0.01 and VfNCV

= NCV

this is done to keep the permeabilities in Eq. (5) and Eq. (6) from becoming undefined. However the permeabilities will become large as it is high for a very low local fiber volume fraction.

• Next subtract the absolute value | R1| of the calculated negative fiber volume fraction and the additional 0.01 from the local fiber volume fraction of the control volume number Ncv – 1 to conserve the total overall fiber volume fraction at the particular cross-section.

Mathematically, this can be stated as:

(21)

Here, we have Vf(NCV-1) on either side of the Eq. (21) where, the term on the right side of the equation is calculated using the Eq. (16) and the other is calculated by conserving the total fiber volume fraction at this particular cross-section; Eq. (21) is to be interpreted as written in computer logic.

8. If Vf(NcvV-1) ≤ 0,

• Assign 2RV̂ = 1)f(NcvV �

• Assign 1)Ncv( �fV = 0.01

• Again to maintain the total overall fiber volume fraction.

9. Repeat the process until Vf(Ncv-j)>0 is satisfied to ensure that there are no control volumes with negative fiber volume (area) fractions and overall fiber cross-sectional area is conserved.

10. Now advance another time step and repeat step 2 through 9 until steady-state is reached.

This algorithm will ensure that the overall fiber volume (area) fraction across any cross-section remains constant even though there is a fiber volume (area) fraction distribution along the y-direction due to compaction. In summary, Eq. (16) is utilized to compute the compacted fiber volume fraction for all the control volumes in the transverse y-direction except the control volumes next to the injection chamber wall (i.e. control volume Ncv). For this control volume Eq. (20) is utilized and steps 7 - 9 above are employed. This procedure allows the fibers to be displaced away from the injection chamber wall due to pressure gradients (∆P(y)) across

specific control volumes. With the fibers pushed towards the chamber center, there are only a reduced number of fibers left in the control volumes near the chamber wall. In such cases, the algorithm mentioned in steps 6 - 9 ensures that the overall amount of fiber volume (area) fraction at any given cross-section is conserved.

4. RESULTS

This study explores the impact of pull speed (U) on the fiber reinforcement wetout when fiber compaction is taken into account in a tapered resin injection pultrusion chamber. The results have been simulated for three different pull speeds: U = 0.01524 m/s (36 inch/min), U = 0.02032 m/s (48 inch/min) and U = 0.0254 m/s

Figure 6. Schematic of computational domain with the grid



(60 inch/min) at three different compression ratios for the tapered chamber: CR = 2.0, CR = 3.0 and CR = 4.0 with chamber length LT = 0.30 m and width WD = 0.00635 m, height HD = 0.00318 m; the injection slot is located (Figure 1) at xIC = 0.10 m from the inlet boundary with an injection slot width of ∆x = 0.01 m, and at a nominal finished product fiber volume fraction of Vfo = 0.68 and a nominal liquid resin viscosity of μ = 0.75 Pa.s; this would correspond to a polyester resin/fiber glass rovings composite. Pressures in the results are gauge pressures, accept for the absolute resin injection pressure in Table 1, all of which are normalized by one atmosphere of pressure, Patm, and the chamber length is normalized by LT. The results of these simulations are compared to the non-compaction resin injection pultrusion case. The details of how the compaction process interacts with the respective fiber pull speeds, and eventually impacting the wetout process, will be explained.

4.1 Injection Pressure Variation and Compaction InteractionA minimum injection pressure is required to achieve complete fiber reinforcement wetout for a given set of processing parameters and taper angle of the injection chamber. The compaction case is compared to the non-compaction case of a tapered resign injection pultrusion process. Exploring the differences between

the two cases, one can see that the compaction of fiber reinforcements makes it more difficult for the liquid resin to reach the chamber centerline and hence to achieve complete fiber wetout. In the tapered case, there is no upper level injection pressure limit to achieve wetout, this is due to fibers not being highly bunched together in the tapered region of the injection chamber. Wetout occurs more readily in a non-compaction case compared to a compaction case due to less resistance to resin flow.

When the resin injection pressure is above the minimum injection pressure limit, complete wetout of the fiber reinforcement will be achieved. However, when the resin injection pressure is below the minimum pressure limit, the resin cannot effectively penetrate through the fiber reinforcement; instead resin is readily swept downstream by the fiber velocity before it can penetrate through to the centerline (complete wetout). One can see from Figure 7 that wetout has “not” been achieved (dry core along chamber centerline) and that there is no significant resin back-flow from the injection slot which is located at x/LT = 0.333. The injection pressure (Pinj = 0.106 MPa) is too low to cause significantly high fiber compaction; also, this injection pressure is not high enough for resin to penetrate through the fiber reinforcement to

reach the centerline. In this case, the resin is swept downstream with the fiber velocity before it can reach the centerline and yields incomplete fiber wetout; this would produce a poorly manufactured product.

At the minimum injection pressure limit (Pinj = 0.116 MPa), complete wetout will occur for U = 0.02032 m/s (48 in/min). Figure 8 shows the spatial resin distribution illustrating the steady-state resin flow condition inside the tapered injection chamber. It can be observed that at the minimum injection pressure limit, complete wetout has been achieved near the exit of Region I (tapered portion) in the injection chamber. The injection pressure is high enough to penetrate through the somewhat compacted fiber matrix to achieve complete wetout just before the fiber/resin system exits Region I of the injection chamber.

Increasing the injection pressure (Pinj = 0.132 MPa) higher than the minimum injection pressure now results in even more compaction and more backflow and also more resin penetration at the same time as seen in Figure 9. It is noted that complete wetout (resin reaches centerline) occurs further upstream than at the minimum injection pressure limit (Figure 8). Figures 7, 8 and 9 demonstrate how the liquid resin flow font changes shape and location as the resin injection pressure is increased.

Table 1. Pull speed impact on minimum injection pressure for complete wetout for LT = 0.30 m, HD = 0.00318 m, WD = 0.00635 mCase CR Viscosity

μ (Pa.s)

Fiber Volume Fraction

Vfo

Pull SpeedU (m/s)

Min Inj PressureMPa(psia)

Peak Interior PressureMPa (psig)

With Compaction Without Compaction1 2 0.75 0.68 0.01524 0.199 (29.0) 0.025 (3.6) 1.409 (204.4)2 2 0.75 0.68 0.02032 0.285 (41.4) 0.405 (58.7) 2.028 (294.1)3 2 0.75 0.68 0.0254 0.334 (48.4) 0.590 (85.6) 2.539 (368.3)4 3 0.75 0.68 0.01524 0.106 (15.4) 0.124 (18.0) 1.052 (152.6)5 3 0.75 0.68 0.02032 0.117 (16.9) 0.224 (32.5) 1.412 (204.8)6 3 0.75 0.68 0.0254 0.132 (19.2) 0.582 (84.4) 1.769 (256.6)7 4 0.75 0.68 0.01524 0.101 (15.0) 0.336 (48.7) 0.793 (115.0)8 4 0.75 0.68 0.02032 0.101 (15.0) 0.483 (70.0) 1.074 (155.8)9 4 0.75 0.68 0.0254 0.101 (15.0) 0.548 (79.5) 1.356 (196.7)



4.2 Comparison of Compaction versus Non-CompactionTo appreciate the contrast between the compaction and non-compaction cases, a non-compaction model was also employed; the minimum injection pressure to achieve complete wetout in a non-compaction case was found to be lower as there is less resistance to the flow of resin since the fibers are not squeezed together by resin pressure gradients near the injection slot. The fibers in the non-compaction case are pushed closer together due to the injection chamber taper, but not due to the resin pressure gradient near the injection slot. For the non-compaction case, the fiber volume fraction distribution is uniform (Figure 2) at any given axial x-location cross section. Figure 10 shows the centerline and chamber wall pressure profiles along the axial length of the injection chamber and compares both the compaction and non-compaction cases for the three different pull speeds under study: U = 0.01524 m/s (36 inch/min), U = 0.02032 m/s (48 inch/min) and U = 0.0254 m/s (60 inch/min) at a compression ratio of CR = 2.0, for a nominal fiber volume fraction of Vfo = 0.68 and for a nominal resin viscosity of µ = 0.75 Pa.s.

Though the minimum injection pressure required to achieve complete wetout in a compaction case is higher as compared to that of a non-compaction case, the peak internal pressure is lower for the compaction case because the resin does not penetrate to the centerline until much further downstream. The distance between where resin reaches the centerline to the start of Region II of the chamber is the length over which resin compression occurs. This length of resin compression distance strongly influences the peak internal pressure; in general, the shorter the length of this compression distance the lower will be the peak internal pressure. Figures 11 and 12 also show a similar comparison for compression ratios: CR = 3.0 and CR = 4.0 respectively. From

Figure 7. Resin flow front profile and gauge isopressure (P/Patm) contours for polyester resin/glass: (LT = 0.30 m, HD = 0.00318 m, WD = 0.00635 m, CR = 3.0, Vfo = 0.68, µ = 0.75 Pa.s, U = 0.02032 m/s (48 in/min), ∆Pmax = 3.45 MPa, Pinj = 0.106 MPa)





Figures 10, 11 and 12, it is seen that the peak internal resin pressure in the tapered injection chamber increases as the pull speed increases, where Patm is one atmosphere of pressure.

The minimum injection pressure necessary to achieve complete wetout and the corresponding peak internal pressure in the injection chamber for the three values of pull speed at three different compression ratios are summarized in Table 1. The minimum injection pressure required to achieve complete wetout in the compaction cases were used for the cases without compaction for comparison between the two cases. From Table 1 it can be deduced that the higher the compression ratio of the injection chamber the easier (lower injection pressure) it is to achieve complete wetout. At CR = 4.0 the minimum injection pressure required to achieve wetout is quite low (slightly above atmospheric pressure). The peak internal pressure also increases as the pull speed of the fibers increases.

In a tapered resin injection pultrusion chamber for the same injection pressure, wetout of fibers occurs (reaches the centerline) further upstream in the non-compaction case compared to the case with compaction. Due to compaction, fibers are pushed away from the wall causing a fiber lean region near the wall. Thus the fibers are compacted away from the wall causing a fiber dense region away from the wall and thus opposing the flow of resin towards the centerline. Compaction delays the axial location where the resin reaches the centerline. Thus a higher injection pressure is required in the compaction case as compared to the non-compaction case. Figures 13 and 14 show the isopressure contours for a given injection pressure for compaction and non-compaction cases respectively. It is evident that the resin reaches the centerline for the non-compaction case in Figure 14 further upstream as compared to the compaction case in Figure 13.

Figure 10. Centerline (CL) and chamber wall (CW) pressure axial profiles and comparison of compaction and non-compaction cases for different pull speeds: (LT = 0.30 m, HD = 0.00318 m, WD = 0.00635 m, CR = 2.0, Vfo = 0.68, µ = 0.75 Pa.s)





4.3 Effect of Pull Speed and Compaction of FibersThe minimum resin injection pressure required to achieve complete wetout at any given condition depends strongly on the pull speed. From Table 1 it is seen that the minimum injection pressure to achieve complete wetout increases with an increase in pull speed at any specific compression ratio, fiber volume fraction, and resin viscosity. The normalized isopressure contours for a pull speed U = 0.01524 m/s (36 in/min) and a compression ratio of CR = 2.0 and nominal fiber volume fraction and nominal resin viscosity and with compaction is presented in Figure 15a. The variation of the fiber volume fraction distribution in the transverse direction (y-direction) due to compaction is depicted in Figure 15b. Since the resin injection pressure into the chamber is at the minimum injection pressure, the resin penetrates through the compacted fiber reinforcement to the centerline (Figure 15a) while simultaneously resin is swept in the axial (x) direction due to the fiber velocity. In this case, the resin reaches the centerline to achieve wetout near the exit (x/LT = 0.80) of the Region I of the injection chamber (Figure 15a).

Near the injection slot, the resin pressure pushes fibers in the transverse direction. The fiber volume fraction is essentially uniform upstream of the injection port location (x/LT = 0.175), then the fiber volume fraction increases downstream as seen in Figure 15b due to tapering. At x/LT = 0.358, which is at the resin injection slot, the transverse fiber volume fraction has a very low fiber region near the injection slot wall due to the injection pressure pushing fibers away (at y/(HD/2) = ±0.75) from the wall; as a result of this the fiber volume fraction changes (increases) at y/(HD/2) = ±0.35 in the transverse direction to compensate for the low fiber region near the wall at y/(HD/2) = ±0.75.

Figure 13. Resin flow front profile and gauge isopressure (P/Patm) contours for polyester resin/glass roving with compaction: (LT = 0.30 m, HD = 0.00318 m, WD = 0.00635 m, CR = 3.0, Vfo = 0.68, µ = 0.75 Pa.s, U = 0.02032 m/s (48 in/min), ∆Pmax = 3.45 MPa, Pinj = 0.129 MPa)

Figure 14. Resin flow front profile and gauge isopressure (P/Patm) contours for polyester resin/glass roving with non-compaction: (LT = 0.30 m, HD = 0.00318 m, WD = 0.00635 m, CR = 3.0, Vfo = 0.68, µ = 0.75 Pa.s, U = 0.02032 m/s (48 in/min), ∆Pmax = 3.45 MPa, Pinj = 0.129 MPa)

Figure 15a. Resin flow front profile and gauge isopressure (P/Patm) contours for polyester resin/glass roving: (LT = 0.30 m, HD = 0.00318 m, WD = 0.00635 m, CR = 2.0, Vfo = 0.68, µ = 0.75 Pa.s, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.45 MPa, Pinj = 0.199 MPa)



At x/LT = 0.725 of the injection chamber, this is the axial location between the injection slot and Region II of the injection chamber, the transverse fiber volume fraction increases significantly due to both injection compaction and tapering of the injection chamber. Further downstream in the straight portion (i.e. at x/LT = 0.908) the local fiber volume fraction reaches the maximum fiber volume fraction (Vf(x,y) = Vfo = 0.68). The transverse fiber volume fraction profiles at different locations show the variation of fibers in the transverse direction due to the small fiber lean region just above the injection chamber wall in the vicinity of the injection port. This fiber lean region is formed due to the injection pressure at which the resin is injected into the chamber. The injection pressure pushes the fibers towards the center of the chamber; thus resulting in fiber lean regions and fiber concentrated regions.

With an increase in the pull speed from U = 0.0154 m/s (36 in/min) (Figure 15a) to U = 0.02032 m/s (48 in/min) (Figure 16a) the axial location at which the resin reaches the centerline is moved further upstream due to the increased injection pressure (Pinj = 0.285 MPa) as in Figure 16a. The same phenomena is followed for the pull speed of U = 0.0254 m/s (60 in/min) (Figure 17a) (Pinj = 0.334 MPa) and the axial location of wetout is moved even further upstream due to the higher injection pressure compared to both of the two previous pull speeds with Figure 17a. The transverse fiber volume fraction profiles are similar to that in Figure 15b and are shown in Figure 16b and Figure 17b. From Figures 15a, 16a and 17a it is observed that the point of wetout achievement (resin reaches centerline) of the fiber reinforcements is moving upstream with an increase in injection pressure or an increase in pull speed. Thus the peak internal resin pressure increases due to the increasing length of the resin compression zone (length from where resin reaches centerline to the end of Region I).

Figure 15b. Variation of fiber volume fraction in y-direction corresponding to different x-locations of the injection chamber for polyester resin/glass roving: (LT = 0.30 m, HD = 0.00318 m, WD = 0.00635 m, CR = 2.0, Vfo = 0.68, µ = 0.75 Pa.s, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.45 MPa, Pinj = 0.199 MPa)

Figure 16a. Resin flow front profile and Gauge isopressure (P/Patm) contours for polyester resin/glass roving: (LT = 0.30 m, HD = 0.00318 m, WD = 0.00635 m, CR = 2.0, Vfo = 0.68, µ = 0.75 Pa.s, U = 0.02032 m/s (48 in/min), ∆Pmax = 3.45 MPa, Pinj = 0.285 MPa)




To verify that the overall fiber volume fraction is correctly conserved, the trapezoidal rule numerical integration was employed to calculate the average fiber volume fraction at various axial locations (x/LT) (Figures 15b, 16b and 17b). It was verified that all calculated average fiber volume fractions were essentially equal to the theoretical value given by Eq. (4) at every axial location (x/LT) thus confirming that the overall cross-sectional fiber volume fraction has been conserved and the fibers are reasonably distributed in the transverse y-direction.

The minimum injection pressure required to achieve complete wetout for CR = 4.0 (Table 1) is the same for the various pull speeds under study; this is because of the high compression ratio or taper angle. The peak internal pressure increases with pull speed, this is because the injected resin is being compressed slowly in case-7 of Table 1, quickly in case-8 of Table 1 and more quickly in case-9 of Table 1. Therefore, the time required to compress the resin decreases and thus the chamber internal pressure increases as the resin is being

compressed quickly. The quicker the resin is compressed the higher is the resin pressure and vice versa.

5. CONCLUSIONS

The model developed in this study is useful to predict the impact of fiber compaction on the wetout achievement for different taper angles of the injection chamber. As there is less opposition to resin flow in the non-compaction case, the minimum injection pressure required to achieve complete wetout is lower compared to a compaction case. It was shown that the complete wetout in the non-compaction case occurs further upstream as compared to the compaction case. Due to this, the resin compression region increases and a higher internal pressure occurs in the non-compaction case. Considering compaction of the reinforcements, the simulations are more realistic and provide better results.

The results for various fiber pull speeds and compression ratios show that the wetout achievement becomes more difficult as the pull speed increases and wetout becomes easier as the compression ratio increases. Thus, a lower fiber pull speed requires a lower injection pressure to achieve complete wetout. At higher pull speed, the fibers are drawn through the exit at a higher velocity and the resin is swept downstream without achieving complete wetout at low injection pressures. Therefore, a higher injection pressure is required to achieve complete wetout before the resin exits the Region I of the injection chamber. As the pull speed increases the peak internal pressure also increases as well as an increase in the minimum injection pressure. However, at higher compression ratios such as CR = 4.0, the minimum pressure required to achieve wetout is slightly above atmospheric pressure; however, the peak internal resin pressure increases with an increase in pull speed. Thus, moderate pull speed and compression ratio are desirable, in order to obtain a good quality pultruded composite.

Figure 17a. Resin flow front profile and gauge isopressure (P/Patm) contours for polyester resin/glass roving: (LT = 0.30 m, HD = 0.00318 m, WD = 0.00635 m, CR = 2.0, Vfo = 0.68, µ = 0.75 Pa.s, U = 0.0254 m/s (60 in/min), ∆Pmax = 3.45 MPa, Pinj = 0.334 MPa)




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