Numerical simulation of prepreg resin impregnation effect in vacuum-assisted resin infusion/prepreg co-curing process

Abstract

A new finite element formulation was developed to simulate the prepreg resin impregnation effect in vacuum-assisted resin infusion/prepreg co-curing process. The numerical model combined the fiber compaction and resin flow model in prepreg part with resin impregnation front tracking model in dry fiber fabric. The influences of processing parameters, including various temperature and time, on the impregnation height in dry fiber fabric and change of fiber volume fraction in prepreg stack were analyzed by numerical model and micrographs in experiment. The accuracy of numerical model was validated by the good agreement between simulation and experimental results. These results are greatly helpful to optimize processing parameters and improve the manufacturing efficiency in co-cured vacuum-assisted resin infusion process.

Keywords

Polymer-matrix composites numerical simulation vacuum-assisted resin infusion resin flow co-curing

Introduction

Advanced polymer matrix composites have been widely applied as an alternative of traditional metal materials due to the low density and high specific strength and stiffness. Nowadays, affordability is the major challenge for composite application and reducing manufacturing cost is an effective way to solve this problem. Integral molding processes, such as co-curing, co-bonding and secondary bonding, are used to fabricate stiffened skin structures. In co-curing process, stiffeners are integrally cured with skin in one cure cycle. Fewer joints lighten the weight and reduce the assembly cost. Traditionally, stiffened skin structures are manufactured by prepreg autoclave process to obtain good processing quality and excellent mechanical performances. However, the laborious and time-consuming lay-up procedures increase fabrication cost and reduce product efficiency for complex shape stiffeners, e. g. “T”, “I” and “L” shape. On the other hand, fiber preform prepared in liquid composite molding process (LCM) provides flexible design and quick manufacture of complex stiffeners. Therefore, combination of the advantages of already established prepreg process and liquid composite molding process is a practical way to not only achieve excellent mechanical performances for skin but also save time and labor for stiffeners.

Recently, a new co-curing process, named co-cured liquid composite molding process (co-LCM), has been investigated and categorized into different processes, including co-cured resin transfer molding process (co-RTM), co-cured vacuum-assisted resin infusion process (co-VARI) and co-cured resin film infusion process (co-RFI). In co-LCM process, fiber fabric stiffeners infused by LCM resin and skin prepared by prepreg layers simultaneously cure together in one processing cycle. Many successful demonstrators, such as stiffener stiffened panel, spars and stringer reinforced fuselage, have been manufactured by co-LCM processes.^1–10 Co-RTM process was firstly proposed by Northrop Grumman Company to fabricate large and integral structures.^1,2 A 17% overall cost reduction of F-15 tail by co-RTM process compared with the typical fabrication process indicated that co-RTM was an affordable and practical technique.³ Co-RFI process was investigated by our previous research,^4–6 the compatibility of prepreg resin with RFI resin and the influences of various processing conditions, including stack position, temperature cycle and usage of tackifier, on the final processing quality were discussed. The results showed that good material compatibility and processing properties can be achieved under suitable processing condition control. In addition, co-VARI process, which applied out-of-autoclave (OOA) prepreg and fiber preform, was focused by more and more researchers due to the low requirement of equipment and mould investment compared with other co-LCM technologies.^7–10 Kaps et al.⁷ proved that no weakening effect was observed for contact zone generating between prepreg part and VARI part with a suitable selection of materials’ pairs. Fratta et al.⁸ noticed that prepreg resin impregnated dry fiber fabric under elevated temperature and vacuum pressure before resin infusion stage. This phenomenon played significant influences on the processing quality and performances of co-VARI structures. So it is worthy of investigating and evaluating the prepreg resin impregnation effect in co-VARI process.

Processing simulation is a cost-effective way to choose suitable processing parameter for composite manufacture which can avoid the trial and error experiment based on experiences. Traditionally, two kinds of process models are established: (1) Models involve the resin flow and fiber compaction of prepreg stack for autoclave process or hot pressing process.^11–14 In these models, prepreg stack is considered as saturated porous media, which satisfies the Boit’s saturated consolidation principle, fluid continuity equation and Darcy’s law. (2) Models emphasize the analysis of resin flow in unsaturated fiber preform for LCM process.^15–22 However, the “saturated” prepreg part and “unsaturated” fiber preform part require the combination of two kinds of simulation models to solve the resin impregnation effect in co-VARI process. Little simulation work has been done on this issue. Therefore, it is necessary to establish the suitable simulation model for co-VARI process.

In this article, a simulation model, combining the “saturated” prepreg part and “unsaturated” fiber fabric part, was presented to study prepreg resin impregnation effect in co-VARI process. The impregnation height in dry fiber fabric and change of fiber volume fraction in prepreg stack were investigated under various temperature and time by simulation model and experiment. The accuracy of this simulation model was validated through the comparison between experimental and numerical results. It is helpful to optimize the processing procedures for co-VARI process.

Simulation model

Assumption

The basic assumptions of simulation model are illustrated as follows: (1) the prepreg part is idealized as a void-free fiber bed completely saturated with resin and the dry fiber fabric is fully unsaturated at the beginning of co-VARI process; (2) the resin in prepreg part is assumed to behave as incompressible Newtonian fluid; (3) the fiber bed in both prepreg part and VARI part is regarded as porous media and resin flow in porous fiber bed obeys Darcy’s law; (4) the individual fibers are incompressible and (5) body forces such as gravity are negligible.

Compaction and flow model in prepreg part

In unsaturated fiber preform, dry fabric is assumed to be completely elastic and the external load is fully transferred to the saturated prepreg part. The effective stress theory proposed by Boit²³ is applied to develop the compaction and flow model in prepreg part of co-VARI process. Based on the effective stress theory, the resin flow velocity in prepreg part is very low. Quasi-static procedure is considered during the consolidation process. Thus, viscous shear stress can be negligible. The external load is shared by resin and fiber bed. The force equilibrium equation for differential element of the prepreg part is as follows

\frac{\partial σ_{ij}}{\partial x_{j}} + \frac{\partial P}{\partial x_{i}} = 0

(1)

Where

σ_{ij}

and P are the fiber-effective stress and resin pressure, respectively. Subscript i and j represent x (width direction) or z (thickness direction) Cartesian coordinates of laminates.

The simplified constitutive equation²⁴ is

{σ_{xx} σ_{zz} τ_{xz}} = [E_{xx} 000 E_{zz} 000 G_{xz}] {ɛ_{xx} ɛ_{zz} γ_{xz}}

(2)

{σ_{xx} = E_{xx} ɛ_{xx} σ_{zz} = A_{s} (\sqrt{V_{f} / V_{0}} - 1) / (\sqrt{V_{a} / V_{f}} - 1)^{4} τ_{xz} = G_{xz} γ_{xz}

(3)

where

E_{xx}

E_{zz}

and

G_{xz}

are the fiber bundle elastic constants;

ɛ_{xx}

ɛ_{zz}

and

γ_{xz}

are the strains; V_f is the fiber volume fraction; V_a is the maximum available fiber volume fraction; V₀ is the initial fiber volume fraction and A_s is a spring constant.

The conservation of mass in the representative element can be given as follows

\frac{\partial (φ ρ d x d y d z)}{\partial t} = [\frac{\partial (ρ v_{x})}{\partial x} + \frac{\partial (ρ v_{y})}{\partial y} + \frac{\partial (ρ v_{z})}{\partial z}] d x d y d z

(4)

where the left item of the equation is the change rate of fluid mass and the right item is the total flow in the unit element. v_x,v_y and v_z are the seepage velocities of resin within the composite in x, y and z directions; φ and ρ are the porosity and resin density.

Resin flow through the porous fiber bed obeys Darcy’s law and resin is assumed to be incompressible. The bulk strain is equal to the change rate of porosity and the flow continuity equation can be expressed as

\frac{\partial ɛ_{v}}{\partial t} = - [\frac{\partial}{\partial x} (\frac{K_{xx}}{μ} \frac{\partial P}{\partial x}) + \frac{\partial}{\partial y} (\frac{K_{yy}}{μ} \frac{\partial P}{\partial y}) + \frac{\partial}{\partial z} (\frac{K_{zz}}{μ} \frac{\partial P}{\partial z})]

(5)

where

K_{xx}

K_{yy}

and

K_{zz}

are the fiber bed permeability which are the function of fiber volume fraction; μ is resin viscosity and

ɛ_{v}

is the bulk strain.

Resin impregnation front tracking model

The volume of fluid (VOF) method is employed to track the resin impregnation front in VARI part^16,25

\frac{\partial C}{\partial t} + \frac{v_{x}}{φ} \frac{\partial C}{\partial x} + \frac{v_{y}}{φ} \frac{\partial C}{\partial y} + \frac{v_{z}}{φ} \frac{\partial C}{\partial z} = 0

(6)

where C is the fractional volume function; v_x,v_y and v_z denote the seepage velocities in x, y and z direction, respectively; φ is the porosity of fiber preform.

Once the external pressure is applied, the compaction of prepreg stack occurs and the seepage velocities are calculated by compaction and flow model. Then the seepage velocity is used in equation (6) to track the resin impregnation front in dry fiber fabric. The resin viscosity and fiber bed permeability at saturated area, including prepreg part and impregnation region in VARI part, are updated at each time step in the solution.

Experimental and numerical data analysis

Experiment

Four-mm-thickness unidirectional laminates are manufactured by co-VARI process and the bagging arrangement is shown in Figure 1. Sixteen pieces of MTM44-1 prepreg (supplied by Advanced Composites Group Co., Ltd.) with 300 mm × 200 mm were firstly placed on a tool plate and fiber preform prepared by 10 layers of T700SC unidirectional fabric (supplied by Jiangsu Tianniao High Technology Co., Ltd.) was laid on the prepreg stack. The whole stacks were covered with peel ply, distribution medium and then sealed by vacuum bag. The infusion resin (self-preparation) was sucked into fiber fabric under –0.1 MPa vacuum pressure and laminates eventually cured in an oven with a dwell of 130℃ for 2 h and a post-cure at 180℃ for 2 h.

In order to enhance the resin mixture between prepreg resin and infusion resin and avoid the resin-rich region at prepreg-fabric interface, a unique processing procedure, named holding compaction stage, was added before resin infusion stage for co-VARI process as shown in Figure 2. In this stage, the whole assembly was heated to infusion temperature, holding for a period of time under vacuum of –0.1 MPa. As the prepreg resin softened, prepreg resin impregnated dry fiber fabric.

Based on the rheological property of prepreg resin in Figure 3, different holding temperatures with different resin initial viscosities, including 60℃ (650 Pa·s), 90℃ (55 Pa·s) and 120℃ (10 Pa·s) were selected for the holding compaction stage. Meanwhile, at each selected temperature, various holding times at the holding compaction stage, including 0 min, 20 min and 40 min, were chosen to change the resin impregnation effect.

To distinguish the influences of processing parameters on the prepreg resin impregnation effect in dry fiber preform, the cross-sections of co-cured laminates were observed using fluorescent microscope (IX71, Olympus Inc., Japan) because the cured prepreg resin exhibited blue fluorescence under ultraviolet light. The cured laminates were cut into small specimens and the cross-sections were wet-grounded with finer silicon carbide paper from 600 grits to 3000 grits to ensure the smooth surface of specimens. Meanwhile, the thickness of specimens should be thin enough (below 0.5 mm) to be penetrated by ultraviolet light which was favorable to excite sufficient fluorescence for observation.

A parameter, called impregnation height, was defined to characterize the different degrees of resin impregnation effect as shown in Figure 4. The parameter indicated the distance from the prepreg-fabric interface to the resin mixture interface in dry fiber fabric, which can be obtained by measuring the arithmetic mean value of at least five positions in fluorescent micrographs.

Figure 5 gives the method to calculate the experimental fiber volume fraction at 10 regions in the thickness direction. The fiber volume fraction for each single zone is obtained by the digital microscopy and image analysis software.

Simulation

The actual length and thickness of co-VARI laminate are 300 mm and 4 mm, respectively. However, prepreg resin impregnates fiber fabric through thickness direction (Z-axis). Thus, the established simulation model is simplified from three-dimensional model to one-dimensional model. The geometry dimension for simulation is shown in Figure 6. The thickness is still 4 mm (line A–D), but the length is only 0.5 mm (line A–B) to reduce the computational cost. Due to the nonlinearity between stress and strain through thickness direction in equation (3), 400 elements are uniformly assigned for 4 mm to ensure the convergence and stability of solution. Meanwhile, five elements are uniformly assigned for the 0.5-mm-length direction to improve the computational efficiency. It is initially assumed that displacement for the whole domain and resin pressure in prepreg part are zero before the external pressure is applied. The boundary conditions for geometry model after applying the external pressure are listed in Table 1.

Table 1.

Boundary conditions for simulation model.^a

	Displacement	External pressure	Flow
Line A-B	$u_{x} = 0, u_{z} = free$	$P_{atm}$	$P = 0$
Line C-D	$u_{x} = 0, u_{z} = 0$	—	$\partial P / \partial n = 0$
Line A-D and B-C	$u_{x} = 0, u_{z} = free$	—	$\partial P / \partial n = 0$

u_x and u_z are the displacements of x and z directions; line M-N is the interface of prepreg part and VARI part.

MTM44-1 prepreg is a kind of zero-bleeding unidirectional prepreg with the initial fiber volume fraction of 54%. Temperature rises from 25℃ to each selected holding temperature at 5℃/min and holds for 40 min. Zero min at holding compaction stage starts from the time when the temperature reaches each selected temperature. The corresponding viscosity-time curves for prepreg resin are presented in Figure 7. The material properties used in simulation model are summarized in Table 2.

Table 2.

Material properties used in simulation model.

(a) Carbon fiber transverse permeability model

K_{zz} = \frac{r_{f}^{2}}{4 k_{z}'} \frac{(\sqrt{V_{a} / V_{f}} - 1)^{3}}{(\sqrt{V_{a} / V_{f}} + 1)} (m^{2}), r_{f} = 3.5 μ m, V_{a} = 0.907

Prepreg stack:

k_{z}' = 0.24

Fiber fabric:

k_{z}' = 0.15

(b) Carbon fiber bed compaction model

σ_{zz} = \frac{3 π E}{β^{4}} \frac{\sqrt{1 + ɛ_{zz}} - 1}{\sqrt{1 + ɛ_{zz}} (\sqrt{V_{a} / V_{0} (ɛ_{zz} + 1)} - 1)^{4}}

Prepreg stack:

β = 390, E = 230 GPa, V_{a} = 0.907, V_{0} = 0.54

Fiber fabric:

β = 450, E = 230 GPa, V_{a} = 0.907, V_{0} = 0.50

Viscosity characteristic of prepreg resin under different processing conditions at holding compaction stage are shown in Figure 7

Analysis of experimental and simulation results

Figure 8 gives the impregnation heights under various processing conditions according to simulation model. It is found that impregnation heights increase slowly and exhibit linear change at the holding temperature of 60℃ and 90℃ as time extension. It is ascribed that the relatively high resin viscosity hinders the resin impregnation in dry fiber fabric. For the temperature at 120℃, the impregnation heights climb quickly at the beginning of stage due to the low resin viscosity, while a slower increase occurs at the following stage (after 1000 s) because the longer impregnation distance reduces the driving force and resin viscosity rises as time increases as shown in Figure 7. It is demonstrated that increasing holding temperature and prolonging holding time are favorable to enhance the prepreg resin impregnation effect in dry fiber fabric, especially for the high temperature of 120℃.

The comparison of impregnation heights from the fluorescent micrographs and simulation model under various processing conditions is presented in Figure 9. The impregnation heights between experimental and simulation results are similar for all cases. However, the experimental results are slightly larger than the simulation results at the holding temperature of 60℃ and 120℃. For the cases at 60℃, little prepreg resin is taken up by dry fiber fabric due to high resin viscosity at holding compaction stage. Only the bottom of fiber fabric at the prepreg-fabric interface (less than 0.1 mm) is impregnated by prepreg resin. The adhesive force between prepreg stack and fiber fabric is weak. The infusion resin fills in the prepreg-fabric interface and results in resin-rich region, which influences the accuracy of statistical values for impregnation height (Figure 10a). When the temperature rises to 90℃, lower resin viscosity increases the impregnation height in dry fiber fabric from less than 0.1 mm to about 0.2 mm as time extends from 0 to 40 min. Moreover, prepreg resin sticks fiber tows with prepreg stack. No resin-rich region is observed at prepreg-fabric interface (Figure 10b). At the holding temperature of 120℃, prepreg resin with relatively low viscosity enlarges the impregnation height from 0.2 to 0.6 mm, which is larger than the thickness of single-fiber fabric. The uniform porous medium assumption for dry fiber fabric in simulation model is not suitable because the inter-tow gap between layers forms a quick “flow channel” for prepreg resin impregnation. Moreover, dry spot (see the ellipse circle in Figure 10c) occurs in the fiber tows due to the smaller permeability of inner fiber tows compared with that of inter-tow gap in experiment. But in the assumption of simulation model, the fiber fabric is uniformly and fully impregnated by prepreg resin without insufficient region once the resin impregnation front passes. So larger impregnation heights can be obtained in experiment in the same bleeding prepreg resin at 120℃. Therefore, suitable prepreg impregnation effect improves the adhesion between dry fiber fabric and prepreg stack, which is favorable to reduce the resin-rich region at prepreg-fabric interface and enhance resin mixture of two resins in the following infusion stage.

Fiber volume fraction distribution is crucial for the final performances of composite structure. Resin impregnation effect at holding compaction stage takes some prepreg resin into dry fiber fabric, which is similar with the bleeding effect in resin bleeding process. This phenomenon may change the fiber volume fraction distribution in prepreg stack. Figure 11 gives the fiber volume fraction distribution in prepreg stack under different processing conditions from the prepreg-fabric interface to the bottom of laminates. Fiber volume fraction sharply increased from 54% to 68% at the top 0.15 mm of prepreg stack and maintains the initial value of 54% for the other region through thickness direction. There is negligible difference between cases with different holding times at 60℃, which is attributed to the weak flowability of high prepreg resin viscosity at 60℃. As the temperature increases to 90℃, lower resin viscosity enhances the prepreg resin flow into dry fiber fabric. So fiber compaction area enlarges compared with cases at 60℃. But most layers of prepreg stack are still less compacted or even un-compacted. When the temperature rises to 120℃, prolonging the holding time accelerates the resin loss in prepreg stack. Fiber volume fraction presents an obviously gradual change from the prepreg-fabric interface. Thus, low prepreg resin viscosity at high holding temperature with longer holding time (e.g. 120℃, 40 min) results in a smooth transition through the thickness direction, which is beneficial to the performances of co-VARI laminates.

The fiber volume fraction of prepreg part in thickness direction from experiment is shown in Figure 12. The change tendency is well coincident with that obtained from simulation model. However, the fiber volume fractions from experiment are smaller compared with the simulation results. It is ascribed that fiber bridge effect exists during holding compaction stage which limits further increase of fiber volume fraction. But the fiber arrangement is considered as ideal state without fiber contact between each other in the simulation model before achieving the maximum available fiber volume fraction.

In summary, based on the comparison of impregnation height and fiber volume fraction between simulation and experimental results, the established simulation model is validated to accurately predict the prepreg resin impregnation effect at holding compaction stage.

Conclusion

A numerical model was established to simulate prepreg resin impregnation effect in co-VARI process. This model coupled the fiber compaction and resin flow model based on the Boit’s saturated consolidation principle, the fluid continuity equation and Darcy’s law and unsaturated resin impregnation front tracking model based on VOF method. The influences of processing parameters, such as different holding temperature and time, on impregnation height and fiber volume fraction distribution in prepreg stack were investigated by numerical simulation and micrographs in experiment.

The results show that higher holding temperature and longer holding time promote the impregnation height in co-VARI process. Dry fiber fabric can take some prepreg resin from the upper layers of prepreg stack at holding temperature of 90℃ and 120℃, which improves the fiber volume fraction at prepreg-fabric interface. Moreover, gradual transition of fiber volume fraction can be obtained with higher holding temperature and longer holding time (e. g. 120℃, 40 min), resulting from lower prepreg resin viscosity. In addition, the good coincidence between simulation and experimental results presents the accuracy of numerical model. Therefore, the developed model is favorable to optimize the processing parameters and improve the manufacture efficiency in co-VARI process.

Footnotes

Conflict of interest

None declared.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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