Effect of Fiber Volume Fraction in Fiber Reinforcement … · Polymers Polymer omposites, ol. 24, No. 1, 2016 9 Effect of Fiber olume Fraction in Fiber Reinforcement ompaction in

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7Polymers & Polymer Composites, Vol. 24, No. 1, 2016

Effect of Fiber Volume Fraction in Fiber Reinforcement Compaction in Resin Injection Pultrusion Process

1. INTRODUCTION

Resin injection pultrusion (RIP) is a manufacturing process to economically produce composite materials with uniform cross-section. In RIP, liquid resin is injected through the injection slots located on the injection chamber walls; the main goal is to effectively make the resin penetrate through the continuously pulled fibers and reach the center core of the fiber reinforcement to obtain completely wetted fibers at the exit of the injection chamber. This is called the complete wetout condition. High resin injection pressure is required to effectively penetrate through the fibers; this also pushes the fibers away from the walls causing fiber compaction. Compacted fibers are difficult to penetrate, and thus affect the complete wetout achievement. Research has been done in the past to model and study resin injection pultrusion process. Jeswani and Roux1 developed a 3D numerical model to

simulate the resin flow through the fiber reinforcement in the RIP. Later Palikhel et al.2 investigated the effects of varying fiber volume fraction on the resin flow front location for different lengths of injection chamber in both attached and detached-die configurations. Also, researchers3,4,5 have studied the impact of geometric parameters with variation in fiber volume fraction on the complete wetout achievement and have suggested criteria to achieve efficient results. However, none1-5 have considered fiber compaction due to the resin injection pressure. Some researchers have investigated the static fiber compaction behavior due to compressive forces which aided as a basis for the present study.

Gutowski et al.6,7,8 experimented on special 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 and thus a mathematical model allowing 3-D flow and 1-D consolidation of the composites was developed. Darcy’s law for fluid flow through an anisotropic porous medium was used to model the resin flow. Batch et al.9 presented data for fiber reinforcement compaction in resin transfer molding. The fibers under consideration were woven roving mats, random fiber mats, loose fiber rovings and uniaxial/biaxial roving mats. The experimental data for fiber compaction behavior were presented in the form of “compaction pressure” versus “fiber volume fraction” presentations. Further, the experimental data were fitted with a mathematical model which showed close agreement with one another.

Ding et al.10 presented the results of modeling, numerical simulation and experimental study of resin flow and heat transfer in the RIP. A control volume/finite element method (CV/FEM) was employed to solve the flow governing equations together with heat transfer and chemical reaction models.


N.S. Shakya*, J.A. Roux§, and A.L. Jeswani✝University of Mississippi, Department of Mechanical Engineering, University, MS 38677 USA

Received: 15 December 2014, Accepted: 13 April 2015

SUMMARYIn the resin injection pultrusion process (RIP), the liquid resin is injected into the continuously pulled fibers through the injection slots to cause complete wetout of the fibers. As the resin penetrates through the fibers, the resin also pushes the fibers away from the wall causing compaction of the fiber reinforcements. When the fibers are squeezed together due to compaction, the resin penetration becomes more difficult; thus a resin injection pressure below a certain pressure cannot effectively penetrate through the fibers and achieve complete wetout. However, if the resin injection pressure is too high, the fibers are squeezed together to such an extent that the fiber becomes essentially impenetrable by the liquid resin. The harder it is to penetrate through the fibers, greater is the tendency of the fibers to be pushed away from the wall and cause compaction and affect wetout. In this study, the effect of fiber volume fraction on the fiber reinforcement compaction and the complete wetout is presented.

*Graduate Student§Faculty✝Principal Engineer, Osram Sylvania

8 Polymers & Polymer Composites, Vol. 24, No. 1, 2016

N.S. Shakya, J.A. Roux, and A.L. Jeswani

Resin viscosity, degree of cure and fiber stack compressibility, and permeability were measured to investigate their influences on the RIP. Also, they developed an analytical model based on 1-D flow approximation for the resin flow in the injection die. A high pressure small tapered injection die was tested at different line speeds for experimental data which was used to verify the analytical solution.

Kim et al.11,12 investigated the compaction behavior of dry fiber reinforcement when subjected to normal static compressive forces at the principle plane. They obtained experimental data which were used to develop a mathematical model to predict the compaction behavior of the fiber reinforcement as it moved through the tapered portion of the injection chamber.

1.1 Present StudyThis study presents the effect of fiber volume fraction on the resin flow front location and wetout in the resin injection pultrusion process when fiber compaction is taken into account. When the liquid resin at high pressure is injected into the injection chamber, the fiber becomes compacted and hence the transverse permeability of the fiber reinforcement decreases making the liquid resin penetration more difficult. Fiber compaction depends on various geometric and processing parameters; this study presents simulated results on how fiber volume fraction affects the fiber compaction behavior and ultimately the complete wetout. The results are analyzed with reference to the operational envelope, fiber reinforcement distribution, flow front location and chamber interior pressure. A 3-D numerical model has been employed to simulate the resin flow through the fiber reinforcement in RIP. Gutowski’s compaction model6 has been utilized to compute the transverse permeability of rovings fibers and Darcy’s law of resin flow through porous media has been utilized

to predict the flow front location during the process. A finite volume technique14 has been utilized to obtain discretization pressure equations; the line-by-line tridiagonal matrix algorithm (TDMA) technique14 has been utilized to solve these equations throughout the computational domain. The velocity fields are solved by finite differentiation of Darcy’s equation. The fiber compaction behavior is modeled using a curve fit expression to the experimental data9 for 748NT rovings. Since compaction practically occurs in RIP and fiber volume fraction is an important processing parameter in fiber reinforcement selection, the results presented in this study can be useful for guidance towards a more efficient pultrusion process.

2. STATEMENT OF PROBLEM

In RIP, the fibers are pulled through the resin injection chamber at a constant pull speed. The injection chamber in this study is a non-tapered configuration. Thus, if there is no compaction, the transverse permeability remains constant throughout the length of the injection chamber as shown in Figure 1 (the permeability does not change due to geometry of the injection chamber geometry). However, for the compaction case, when the liquid resin is injected into the fiber reinforcement, the high pressure squeezes the fibers

towards the centerplane and away from the wall; this creates a lean fiber zone in the region near the wall and a dense fiber zone in the transverse direction somewhere between the centerplane and the chamber wall. This condition is depicted in Figure 2. If the injection pressure is very high, the intensity of the compaction is so high that the fibers become essentially impenetrable and a fiber lean region might occur near the injection chamber wall. Therefore, it is easier for the liquid resin to flow backwards (upstream) than penetrate through the fibers and thus resin backflow occurs, which is not desirable. The fiber compaction behavior depends on the stiffness, orientation and fiber volume fraction of the fibers. If a fiber bed with constant stiffness and essentially uniform orientation is considered, the lower the fiber volume fraction is, the easier it is to compact the fibers and vice versa. This is obvious, because, the loosely packed fibers have more space to squeeze together and allow more compaction.

The schematic diagram of the computational domain of the injection chamber used in the numerical modeling is presented in Figure 3. The total length of the chamber is denoted as LT and taken as 0.30 m. The height and the width of the injection chamber are represented as HD and WD which also corresponds to the size of

Figure 1. Fibers distribution in non-tapered injection chamber with no compaction



the final pultruded product (here HD = 0.003175 m and WD = 0.0635 m). The injection slot starts at 0.10 m downstream from the chamber entrance and the injection slot width is taken to be 0.01 m (1 cm).

3. ANALYSIS

3.1 Fiber Volume Fraction and PorosityThe fiber volume fraction (Vf) is defined as the volumetric proportion

of the fibers in the composite material. Since there is no taper on the injection chamber, the fiber volume fraction will not vary along with the axial location due to chamber geometry. Porosity (φ) is defined as the volumetric proportion of non-solid matter in the composite material. Thus, the local porosity φ can be expressed as:

(1)

3.2 Permeability Model Permeability is the measure of the ease of resin flow through the fiber reinforcement. Therefore, the higher the permeability the easier it is for the resin to penetrate through it and vice versa. In this study, the Kozeny-Carman model13 is utilized to predict the permeability of the fibers in the longitudinal direction. The longitudinal permeability is calculated as:

(2)

where k is the Kozeny constant (here k = 0.093), Rf is fiber radius (here, Rf = 15 µm), and Vf is the local fiber volume fraction. The permeability in the transverse directions is calculated by utilizing Gutowski’s model7 which is given as:

(3)

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

3.3 Governing Equations and Boundary ConditionsThe governing pressure equation (Eq. 4) is derived by substituting the Darcy 3-D momentum equations into the continuity equation yielding:

Figure 2. Compaction of fibers due to resin injection pressure in non-tapered injection chamber

Figure 3. Schematic of the computational domain for slot injection non-tapered chamber (not to scale). (a) In xy-plane (side view), (b) In xz-plane (top view)



(4)

where P is resin pressure, K11, K22, K33 are the components of permeability in the x, y, and z directions, respectively, and µ is the viscosity of the liquid resin.

The composition of Eq. (4) requires six spatial pressure boundary conditions for the solution of the pressure field. The boundary conditions, which were initially based on the velocity, were redefined into pressure boundary conditions using Darcy’s momentum equations. Since the injection chamber is symmetric in xy and xz-planes, only a quarter domain was modeled to solve the fields. The pressure boundary conditions are as follows:

(5a)

(5b)

(5c)

(5d)

(5e)

(5f)

(5g)

The inlet pressure is taken as one atmosphere (101.3 kPa) (Eq. (5a)). The pressure at the injection slot is equal to the resin injection pressure (Eq. (5b)). For the boundary conditions at the walls, it is assumed that resin cannot penetrate through the walls; thus the resultant of the resin velocity normal to the wall is set equal to zero (Eqs. (5c) through (5f)). Finally, the resin velocity at the exit of the injection chamber is equal to the fiber pull speed which yields Eq. (5g).

3.4 Solution TechniqueAll the governing equations are solved using the line-by-line Tri-Diagonal Matrix Algorithm (TDMA) technique14. A time marching procedure is employed to reach the steady state solution. The velocity fields are calculated at each time step by finite differencing the Darcy’s momentum equations. The quarter computational domain is populated with 7260 computational nodes to obtain the pressure field throughout the injection chamber. Each node is associated with a control volume which is assigned a resin fill factor to keep track of the location of the resin flow front. Resin fill factor, Fi,j,k is defined as the fraction of the control volume filled by resin at a particular time instant with respect to the maximum resin the control volume can hold. Thus a fill factor of 1 implies that the control volume has been completely filled with the liquid resin whereas a fill factor of 0 implies completely dry fibers. The pressure is computed for a node only if the control volume associated with it has a fill factor “1” (it is completely filled with resin); else, atmospheric pressure is assigned to it. Next, the time required to fill the next quickest to fill control volume is calculated. It is always ensured that as the resin advances through the fibers in the computational domain, only one control volume and no more is filled at one time step. The fill factors for empty and incompletely filled control volumes (where 0 ≤ Fi,j,k <1) are updated at the end of each time step. It is also ensured that the pultruded fibers travel no more than a nodal distance in the pull direction in one time step.

(6)

where Lmin is the minimum length of the control volume in the pull speed direction and U is the fiber pull speed in the axial direction (x). Equation (6) governs the default time step size, and thus ensures that, at every time step no more than one control volume

is allowed to be newly filled. When steady-state solution is achieved, the number of filled and unfilled control volume in the computational domain remains unchanged and the algorithm terminates.

3.5 Compaction ModelingIn this study, the fiber reinforcement compaction in RIP has been modeled utilizing the experimental data provided by Batch et al.9. The experimental data9 were curve fitted to obtain a simplified expression (Eq. (7)) for fiber volume fraction as a function of transverse pressure difference (P(y) = PN - Pp). Here, Pp is the resin pressure at a particular node, and PN is the resin pressure at the northern neighbour node. The pressure difference (∆P(y)) is calculated for each control volume at each time step which is then utilized to calculate the local fiber volume fraction (Vf) using the curve fit expression (Eq.(7)). The curve fit expression was compared with the experimental data9 and the Gutowski’s model7 as shown in Figure 4; it was found that the expression was in good agreement with both the experimental data as well as the Gutowski’s compaction model:

(7a)

(7b)

here, Vf(y) is the new local fiber volume fraction due to the compaction pressure ∆P(y), Vfo is the initial (t = 0) and average fiber volume fraction at a given location, Vfmax is the maximum fiber volume fraction possible defined by the Gutowski permeability model7, Pref is a reference pressure (here Pref = 1000 Pa), ∆P (y) = PN - PP and ∆Pmax is the ∆P(y) value at which Vf (y) = Vfmax.



3.5.1 Algorithm for Redistribution of Fiber ReinforcementInitially, the local fiber fraction of all the control volumes remain constant as there is no fiber compaction, i.e. Vf (y) = Vfo. When liquid resin is injected into the fibers, the resin injection pressure causes compaction of the fibers, and thus the fiber volume fraction across the transverse direction gets affected. To maintain the integrity of the system, the fibers should be redistributed throughout the control volumes in the transverse direction in such a way that the total amount (area) of the fibers remains conserved at each axial location cross-section. The algorithm for the fiber redistribution process is described below.

1. Initially, the local fiber volume fraction is equal to the original (overall) fiber volume fraction; i.e. Vf (y) = Vfo.

2. Advance time step until another control volume (the one that is quickest to fill) is filled with liquid resin and calculate the pressure field.

3. Scan the domain line-by-line in the y-direction starting from the centerplane and progressing towards the top chamber wall

boundary. Calculate ∆P = ∆P(y) = PN - PP for each control volume and assign this ∆P value at the center node.

4. Calculate the local fiber volume (area) fraction Vf(y) for each control volume using Eq. (7) based on the corresponding ∆P(y) value assigned to each control volume. The calculated local fiber volume fraction should never exceed the maximum fiber volume fraction, i.e. Vf(y) < Vfmax, and the total fiber volume across the entire composite cross-section must remain constant. Mathematically it can be written as:

or,

(8)

where, ∆yi is the height of a given control volume. Ncv is the number of non-zero thickness control volumes in the y-direction. When, there is no compaction, Eq. (8) yields Vf(y) = Vfi(y) = Vfo, which is also theoretically correct as the fiber volume (area) fraction should be conserved at any axial cross-section.

5. When the value of ∆P for a particular control volume increases above the reference pressure due to the resin injection pressure, the control volume may experience fiber compaction and thus the value of Vf(y) for that particular control volume increases from Vfo to a higher value. If the value of ∆P is less than the reference pressure (Pref) value then the local fiber volume fraction remains unchanged, i.e. equal to the original fiber volume fraction (Vfo). This relation between ∆P and Vf(y) can be summarized as:

a) For ∆P ≥ Pref, Vfo ≤ Vf(y) ≤ Vfmax

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

Now, if fiber compaction occurs, and the fiber volume fraction of a control volume increases, this increase in fiber volume fraction must be accommodated by a decrease in fiber volume fraction in other control volume(s) at that particular axial location cross-section so that the “total” fiber volume (area) remains conserved. Also it should be noted that the local fiber volume fraction can never exceed Vfmax.

When compaction occurs and there is an increase in fiber volume fraction in a control volume (say control volume #1, next to the centerplane), then the increase in fiber volume (area) can be mathematically represented as ∆y1WD[Vf(y)-Vfo]. Since the total fiber volume (area) fraction must be conserved at all axial cross-section locations, the remaining control volumes at that particular axial location must somehow compensate for this increase in fiber volume fraction. To do so, initially, it is assumed that the remaining fiber volume fraction is distributed evenly amongst all the remaining control volumes. Hence the new average fiber volume fraction for the remaining control volumes is calculated. In the next step, the fiber volume fraction for the next control volume (control volume #2) is calculated using the corresponding ∆P in Eq. (7). Again a new average fiber

Figure 4. Relation between local fiber volume fraction Vf (y) and ∆P (y)/Pref (∆Pmax= 3.75 MPa, Pref = 1000 Pa, Vfmax = 0.73, Vfo = 0.49)



volume fraction for the now remaining control volumes is calculated and the process continues till the control volume next to the chamber wall is reached. This stepping sequence can be generalized as:

(9)

To facilitate the computation for the finite volume approach, the integral form of Eq. (9) can be represented in finite difference form as:

(9a)

For the ith control volume, the vertical height of that control volume is referred as ∆yi, whereas its vertical distance from the centerplane is referred as yi as shown in Figure 5.

When j = Ncv-1, Eq. 9a yields the expression for the average fiber volume fraction for the control volume next to the top boundary which is given as:

(10)

For the last control volume (next to the top boundary wall), the local fiber volume fraction and the average fiber volume fraction is the same, i.e.VfNCV= V̂NCV

6. Using Eq. (10),VfNCV= V̂NCV = is calculated. If V̂NCV

> 0, the sequential process yields the correct fiber volume (area) fraction across the composite at the particular

axial distance under consideration. However, if V̂NCV

> 0, then the algorithm proceeds as follows:

a) If (VfNCV= V̂NCV) ≤ 0,

• Assign V̂ R1 = VfNCV

.

• Now assign V fNCV= V̂NCV =

0.01. This is done to keep the permeabilities in Eqs. (3) and (4) from becoming undefined. However, the permeabilities will become large for V̂NCV

= 0.01 as a low fiber volume fraction means easy resin penetration.

• Now to conserve the total overall fiber volume (area) fraction at the particular cross-section, subtract the absolute value | V̂ 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. Mathematically,

or, simplifying yields

b) Repeat the same process by checking if Vf(Ncv-1) ≤ 0. If no, then the appropriate redistribution of the fibers has been achieved for that particular cross-section otherwise the algorithm process as explained previously.

• Assign V̂ R2 = Vf(Ncv-1) and let

Vf(Ncv-1) = 0.01

• Again to maintain the total overall fiber volume fraction, fiber re-distribution is done as:

or,

7. The process continues until Vf(Ncv-j)

>0 is satisfied to ensure

Figure 5. Schematic of the computational domain with the grid



that there are no control volumes with negative fiber volume (area) fractions and yet the overall fiber cross-sectional area is preserved.

8. Advance to next time step and repeat steps from 2 through 8 iteratively until the steady-state condition is reached.

Hence the above algorithm ensures that the fibers are distributed appropriately (0 > Vf(y) ≥ Vfmax) along the transverse direction at any axial location when compaction occurs due to the resin injection pressure.

4. RESULTS

The effect of fiber volume fraction on the fiber reinforcement wetout with fiber compaction is presented in this study. The results have been simulated for three different cases of original fiber volume fractions: Vfo= 0.64, Vfo = 0.68, and Vfo = 0.72 at U = 0.01524 m/s (36 in/min).

4.1 Operational EnvelopeFigure 6 depicts the comparison between the operational envelopes for the three different original fiber volume fractions under study, namely: Vfo = 0.64, Vfo = 0.68, and Vfo = 0.72 for a resin viscosity of µ = 0.75 Pa.s at U = 0.01524 m/s (36 in/min). The complete wetout of the fiber reinforcement can be achieved when the injection pressure is between the upper and the lower branch of the operational envelope. When the injection pressure is below the lower branch of the operational envelope the resin cannot penetrate effectively in the transverse direction; instead it is swept downstream with the fiber velocity before it can reach the centerline to cause complete wetout. When the injection pressure is above the upper branch of the operational envelope, the injection pressure gradient is so high that it compacts the fibers to such an extent that the fiber reinforcement becomes essentially impenetrable; hence complete wetout is not achieved. Furthermore, it can be

deduced from Figure 6 that the lower the original fiber volume fraction, the easier it is to achieve complete wetout and vice versa. This is also characterized in Figure 6 by the lower ∆Pmax value and comparatively lower injection pressure required for wetout at the lower fiber volume fraction system. A lower ∆Pmax value also implies that the fibers are more easily compacted. It can be seen that, for a fiber volume fraction of Vfo = 0.64, wetout can be achieved even for a low ∆Pmax ≈ 2.00 MPa. This means, the low original fiber volume fraction allows easier resin penetration and hence no excessive compaction of the fiber reinforcement occurs. On the contrary, the higher original fiber volume fraction such as Vfo = 0.68 and Vfo = 0.72 cannot achieve wetout at any injection pressure for ∆Pmax ≤ 3.55 MPa. This is because the denser fiber volume offers more resistance to resin penetration for achieving complete wetout, thus in this case a higher injection pressure becomes necessary. However, a lower ∆Pmax may allow easier compaction, and a high injection pressure can create a

compacted region in the transverse direction where the fibers become essentially impenetrable. To better understand the phenomenon, “three” different points (injection pressures) namely A, B, C in Figure 6 at ∆Pmax = 3.75 MPa are chosen for investigation. The value of ∆Pmax = 3.75 MPa is based on the experimental data9 employed to derive the compaction model (Eq. (7)) as shown in Figure 4. The points in Figure 6 (points A and B) near the lower limit curves are compared with the non-compaction case to illustrate how compaction affects the wetout process. The point C in Figure 6 near the upper limit curve is compared for different fiber volume fractions to present an idea about the effect of original fiber volume fraction in compaction influences complete wetout achievement. Note that wetout for ∆Pmax = 3.75 MPa is possible for a range of injection pressures for Vfo = 0.64 (0.25 MPa to 1.86 MPa) and Vfo = 0.68 (0.86 MPa to 1.86 MPa), but wetout is not possible for Vfo = 0.72Pa.s at any injection pressure. Now the phenomenon occurring at points A, B and C will be discussed in detail.

Figure 6. Injection pressure to achieve complete wetout as a function of ∆pmax for a slot injection configuration with fiber compaction for polyester resin/ glass (U= 0.01524 m/s (36 in/min), Vfo = 0.64, Vfo = 0.68, Vfo = 0.72, µ = 0.75 Pa.s, HD = 0.00318 m, WD = 0.0635 m, Pref = 1000 Pa)



4.2 Point A: Near Lower Limit Curve for Vfo= 0.64, Inside Operational EnvelopePoint A (Pinj = 0.51 MPa) is within the operational envelope of Vfo = 0.64 but outside the operational envelope of Vfo = 0.68 Pa.s. Therefore, the injection pressure at Point A will result in complete wetout of the fiber reinforcement for Vfo = 0.64; whereas, for Vfo = 0.68, this injection pressure will not result in complete wetout. Since, the interest of this research work is the complete wetout situation, only the simulated results at point A for Vfo = 0.64 will be presented and compared with the simulated result from the no-compaction case for point A in Figure 6. Figure 7a depicts the steady-state flow front (thick line) and gauge isopressure contours (thin lines) for the no-compaction case for a polyester resin/glass roving composite along the center xy-plane of the resin injection chamber. When the fiber compaction is not considered the fiber volume fraction remains essentially constant everywhere allowing the resin to penetrate easily. Therefore, it can be observed from Figure 7a for the no-compaction situation that complete wetout has been achieve immediately near the injection slot region without any noticeable backflow. However, when compaction (Figure 7b) is also taken into account, the resin pressure pushes the fibers away from the wall creating a lean fiber zone near the wall and a dense fiber zone away from the wall in the transverse (y) direction. The resin penetration in this case is comparatively more difficult and more complex; thus there is a greater chance of backflow due to the less resistance imposed by the lean fiber zone near the wall. The resin also flows in the transverse (y) direction but comparatively slower than the non-compaction case. Finally, the injection pressure of 0.51 MPa is able to give complete wetout at about the same axial distance as in the non-compaction case but with the resin issuing out of the entrance region.

Figure 7a. Resin flow front profile and gauge isopressure (p/patm) contours for polyester resin/glass roving and slot injection configuration without compaction: Point A (Vfo = 0.64, µ = 0.75 Pa.s, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), Pinj = 0.51 MPa, Pref = 1000 Pa)

Figure 7b. Resin flow front profile and gauge isopressure (p/patm) contours for polyester resin/ glass roving and slot injection: Point A (Vfo = 0.64, µ = 0.75 Pa.s, LT = 0.3m, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 0.51 MPa, Pref = 1000 Pa)

Figure 7c. Variation of fiber volume fraction in y-direction corresponding to different x-locations of the injection chamber for polyester resin/ glass roving and slot injection: Point A (Vfo = 0.64, µ = 0.75 Pa.s, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 0.51, MPa, Pref = 1000 Pa)



The variation of the fiber volume fraction in the transverse direction due to compaction is depicted in Figure 7c. It can be clearly seen from Figure 7c that a lean fiber zone occurs near the wall and the denser fiber zone occurs at y ≈ ± 0.80. The variation of the resin pressure in the transverse direction is depicted in Figure 7d. The occurrence of a lean fiber zone and dense fiber zone can also be rationalized from this graph. The high pressure gradient corresponds to the fiber compaction zone (fiber dense region). As the injection pressure

dissipates in the transverse direction, the fiber volume fraction (Figure 7c) gradually levels up to the original fiber volume fraction (Vfo = 0.64) and remains essentially unchanged at x/LT ≥ 0.698.

Figure 7e shows the comparison between the axial pressure profiles along the centerline and the chamber wall regions for the compaction and no-compaction cases. In the no-compaction case, there is essentially no pressure rise inside the injection

chamber up to the injection slot region. At the injection slot, the pressure rises rapidly due to the resin injection pressure. The resin injection pressure remains constant across the injection slot. After the injection slot region the centerline pressure starts to build up rapidly as the resin penetrates through the fibers easily. Wetout is achieved immediately (point where centerline pressure rises) near the injection slot region. At this point, the chamber wall and the centerline pressure levels up to the same value and remains in concert throughout the downstream region. The pressure decreases slowly in x-direction as the resin-fiber system moves downstream. In the compaction case, the chamber wall and centerline pressures behave differently. It can be seen from Figure 7e that the chamber wall pressure exists even at the entrance region; this is because of the resin backflow. However, the centerline pressure does not rise until past the injection slot region. Downstream of the injection slot region the centerline pressure increases rapidly due to resin penetration (just like the no-compaction case) until complete wetout of the fibers is achieved. At this point the centerline pressure levels up with the chamber wall pressure; both pressures remain equal once wetout is achieved.

4.3 Point B: At Lower Limit Curve of Vfo = 0.68Point B (Pinj = 0.87 MPa) is at the lower curve limit for Vfo = 0.68 and within the operational envelope of Vfo = 0.64. Thus, this injection pressure will result in complete wetout for both Vfo = 0.64 and Vfo = 0.68. The simulated steady-state resin flow fronts for the no-compaction case for Point B is similar to that of Point A and immediate wetout is achieved close to the injection slot. The compaction case for Vfo = 0.68 is illustrated in Figure 8a. The explanation to the phenomenon occurring at point B for the compaction as well as the no-compaction cases for Vfo = 0.68 is similar to that of point A.

Figure 7d. Variation of injection chamber pressure in y-direction corresponding to different x-locations of the injection chamber for polyester resin/ glass roving and slot injection: Point A (Vfo = 0.64, µ = 0.75 Pa.s, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 0.51 MPa, Pref = 1000 Pa)

Figure 7e. Comparison of the centerline and the chamber wall axial pressure (gauge) profiles at different axial locations (x/LT): Point A (Vfo = 0.64, µ = 0.75 Pa.s, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 0.51 MPa, Pref = 1000 Pa)



Since this section focuses on the effects of the original fiber volume fraction in the resin injection pultrusion process, a comparison with the lower fiber volume fraction case (Vfo = 0.64) is presented for point B.

When the original fiber volume fraction is 0.68 (Figure 8a), then complete wetout is achieved considerably downstream, almost near the injection chamber exit. Also, it is to be noted that the injection pressure at point B (Pinj = 0.87 MPa) is the lower limit (Figure 6) of the injection pressure required to achieve complete wetout for Vfo = 0.68. Any injection pressure below this value will not result in complete wetout for Vfo = 0.68. It can be observed from Figure 8a that there is some backflow near the injection slot region. This backflow can also be explained from the fiber volume fraction variation shown in Figure 8b; the lower dips and upper peaks in the local fiber volume fraction curve correspond to the lean and dense fiber regions created near the wall respectively. Since the dense fiber region offers higher resistance to the resin flow in the transverse (y) direction, the resin starts flowing backwards (upstream) through this lean fiber region. However, the resin injection pressure is not so high enough as to cause the resin to flow out from the entrance region. For Vfo = 0.64, the injection pressure (Pinj = 0.87 MPa) is well inside the operational envelope (Figure 6). This is because of the fact that Vfo = 0.64 offers less resistance to resin flow; hence, the resin at a lower injection pressure can easily penetrate through the fibers and wetout is achieved considerably earlier (Figure 8c). Also due to the ease in resin penetration, fiber compaction of the low fiber volume fraction reinforcement is less prominent. The variation of local fiber volume fraction for Vfo = 0.64 is represented in Figure 8d. When a comparison is made between the local fiber volume fraction graphs, Figure 8d and Figure 8b, it can be observed that, for Vfo = 0.64, the fibers are not

Figure 8a. Resin flow front profile and gauge isopressure (p/patm) contours for polyester resin/ glass roving and slot injection: Point B (Vfo = 0.68, µ = 0.75 Pa.s, LT = 0.3 m, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 0.87 MPa, Pref = 1000 Pa)

Figure 8b. Variation of fiber volume fraction in y-direction corresponding to different x-locations of the injection chamber for polyester resin/ glass roving and slot injection: Point B ( Vfo = 0.68, µ = 0.75 Pa.s, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 0.87 MPa, Pref = 1000 Pa)

Figure 8c. Resin flow front profile and gauge isopressure (p/patm) contours for polyester resin/ glass roving and slot injection: Point B (Vfo = 0.64, µ = 0.75 Pa.s, LT = 0.3m, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 0.87 MPa, Pref = 1000 Pa)



as much pushed away from the wall as in the case of Vfo = 0.68. However, as Vfo = 0.64 is already fiber lean, even a comparatively lower compaction phenomenon or pushing away of fibers from the wall can result in excessive backflow through the entrance region.

Figure 8e depicts a comparison between the chamber wall and centerline pressure for Vfo = 0.68 and Vfo = 0.64. For Vfo = 0.68 at Pinj = 0.87, there is some resin backflow, but not enough to exude out from the entrance region. The chamber wall pressure curve clearly depicts greater backflow in Figure 8e for Vfo = 0.64. The drop in chamber wall pressure (Figure 8e) after the injection slot region signifies the resin penetration through the fibers. Once complete wetout is achieved, the centerline pressure rises rapidly. However, in Figure 8e the chamber wall and centerline pressure do not become equal before the exit.

4.17 Point C: On Upper Limit Curve of Vfo=0.68 Point C (Pinj = 1.86 MPa) in Figure 6 is on the upper limit curve of Vfo = 0.68 and just barely within the operational envelope of Vfo = 0.64. Therefore, complete wetout can be achieved for both Vfo = 0.64 and Vfo = 0.68 at this injection pressure. The injection pressure at point C is the highest amongst the three points under study in Figure 6; this high injection pressure causes more compaction of the fibers. Thus, more fibers are pushed away from the wall and the dense region in the transverse direction is even denser than for points A and B. There is obviously a greater chance of backflow since there is more resin flow resistance in the transverse direction and lower resin flow resistance near the wall region. In this case, the resin is excessively (Figure 9a) exuding out from the entrance region. However, the resin pressure is high enough to slowly penetrate through the dense fiber region, and gradually it reaches the centerline to result in complete

Figure 8d. Variation of fiber volume fraction in y-direction corresponding to different x-locations of the injection chamber for polyester resin/ glass roving and slot injection: Point B ( Vfo = 0.64, µ = 0.75 Pa.s, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 0.87 MPa, Pref = 1000 Pa)

Figure 8e. Comparison of the centerline and the chamber wall axial pressure (gauge) profiles at different axial locations (x/LT): Point B (Vfo = 0.64, Vfo = 0.68, µ = 0.75 Pa.s, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 0.87 MPa, Pref = 1000 Pa)

Figure 9a. Resin flow front profile and gauge isopressure (p/patm) contours for polyester resin/ glass: Point C (Vfo = 0.68, µ = 0.75 Pa.s, LT = 0.3m, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 1.86 MPa, Pref = 1000 Pa)



wetout just before the exit region. The compaction phenomenon and the fiber volume fraction distribution within the injection chamber is depicted in Figure 9b. Figure 9c shows the steady-state iso-pressure contours at point C for Vfo = 0.64. Unlike the Vfo = 0.68 case (Figure 9a), wetout is achieved well ahead of the exit region for Vfo = 0.64. This is because the resin penetration for the lower fiber fraction composite is easier. Since the sparser fibers offer less resistance to the resin penetration, the compaction is not as prominent as in the dense fiber situation. Note that the lower blips in Figure 9d (for Vfo = 0.64) are not as low as in Figure 9b (Vfo = 0.68). The compaction occurring in the wall region pushes the fiber away from the wall which additionally facilitates the resin backflow. Thus, for Vfo = 0.64 (Figure 9c) the backflow is excessive and the liquid resin is exuding out through the entrance region.

5. CONCLUSIONS

The results showed that the wetout achievement was more difficult at higher fiber volume fractions. This seemed quite obvious as it is evident that greater fiber volume will hinder easy resin penetration; thus high injection pressure and ∆Pmax becomes necessary. Also, more compaction is likely to occur at high fiber volume fractions since the resin will rather tend to push the dense fibers reinforcement away from the chamber wall than penetrate through it. It was also observed that for the lower fiber volume fraction system, complete wetout was achieved considerably earlier as the resin would easily penetrate through the fibers. However, excessive backflow would result with the low fiber volume fraction and it is worth noting that all of the simulated results for the lower fiber volume fraction (Vfo = 0.64) system resulted in resin backflow issuing out of the entrance region. Additionally, low fiber volume fractions might result in a mechanically weak pultruded composite. Therefore, a fiber volume fraction is desired such

Figure 9b. Variation of fiber volume fraction in y-direction corresponding to different x-locations of the injection chamber for polyester resin/ glass roving and slot injection: Point C (Vfo = 0.68, µ = 0.75 Pa.s, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 1.86 MPa, Pref = 1000 Pa).

Figure 9c. Resin flow front profile and gauge isopressure (p/patm) contours for polyester resin/ glass roving and slot injection: Point C (Vfo = 0.64, µ = 0.75 Pa.s, LT = 0.3m, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 1.86 MPa, Pref = 1000 Pa)

Figure 9d. Variation of fiber volume fraction in y-direction corresponding to different x-locations of the injection chamber for polyester resin/ glass roving and slot injection: Point C (Vfo = 0.64, µ = 0.75 Pa.s, HD = 0.00318 m, WD = 0.00635 m, U = 0.01524 m/s (36 in/min), ∆Pmax = 3.75 MPa, Pinj = 1.86 MPa, Pref = 1000 Pa)



that even after compaction there is enough space between the fibers for the resin to penetrate through, and thus cause complete wetout and yield a good quality pultruded product.

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