Preform Porosity and Final Thickness Variability Prediction after Controlled Post-Infusion External Pressure Application with the FEA Model

Abstract

One of the reasons for the insufficiently wide use of the low-cost and low-labor vacuum infusion process in the production of polymer composite structures is the uneven distribution of pore pressure, porosity, and preform thickness at the final stage of filling the preform with liquid resin. This article presents the results of a theoretical study of the factors that govern the effectiveness of the known method of external controlled pressure on the preform in order to eliminate or significantly reduce the listed disadvantages. The study includes an analysis of scenarios for the implementation of this method, which differ in the state of the resin gate when external pressure is applied to the preform (open or closed), as well as the pressure in the vacuum vent (maintained unchanged or gradually increased to atmospheric pressure). The research tool was a finite element (FE) model that simulates resin flow according to Darcy’s law and controlled boundary conditions for a thin-walled rectangular preform. The results of the study confirmed the effectiveness of the process in achieving a more uniform distribution of porosity and preform thickness and are good qualitative agreement with the results of borrowed experiments, revealing the conditions for the occurrence of critical situations associated with the possible penetration of air into the preforms through the vacuum port and the reverse flow into the preform of the resin previously forced out through the resin gate.

1. Introduction

In the last two decades, vacuum-assisted technologies for the manufacturing of polymeric composite structures have become increasingly in demand in aerospace engineering, the production of wind turbines, shipbuilding, and civil engineering [1,2,3]. A common component of the kind of such technologies (VARTM, SCRIMP, RFI et al.) is the injection of liquid resin into a dry porous preform and its propagation therein under the action of a pressure gradient [4]. Such technologies usually include three successive stages: preparation and laying-up of preform layers, covered with a flexible vacuum bag and carefully isolated from atmospheric air; filling the preform with liquid resin injected from the resin gate and moving towards the vacuum vent; and the final stage, which may include additional exposure of the filled preform to increased temperature and pressure [2]. The fulfillment of the most important requirements for mechanical and strength properties, geometric accuracy, and climatic resistance of the molded part are determined by the values of the fiber volume fraction and the uniformity of its distribution in the preform, the void volume, provided at each of the three stages of the manufacturing process [5,6,7,8]. The research results presented in these papers show that the properties of parts manufactured using the infusion technology, usually are inferior to those manufactured using the hot-pressing technology of pre-impregnated prepregs, especially in terms of ensuring the permissible voids volume, as well as the required values of the fiber volume fraction and the uniformity of its spatial distribution across the preform. The preform is a compressible poroelastic frame, the sections of which are completely or partially filled with resin with varying pressure. Its increase leads to the expansion of pores, a decrease in the relative volume of reinforcement, and an increase in the thickness of the preform [9,10,11,12,13,14,15,16,17,18,19]. Thus, a gain in the pore pressure gradient leads to an increase in the resin velocity and, consequently, the performance of the vacuum infusion process, which contradicts the requirement to ensure uniform distribution of the fiber volume fraction and preform thickness. In addition, the poor repeatability of the process, due to its high sensitivity to the layout and regimes, has become an obstacle to its widespread use in high-tech industries.

Numerous studies have been aimed at finding reliable methods for monitoring the state of the preform during its filling with liquid resin. Among them are such sophisticated ones as a monitoring the 3D resin flow using hybrid piezoelectric-fiber sensor network or optical frequency domain reflectometry and long-gauge FBG sensors [20,21]. As technological improvements to overcome the noted difficulties, the post-infusion exposure during vacuum infusion of thermosetting composites reinforced with thermoplastic interlayer veils [22] and fiber prestressing to prevent their fraying and weakening during infusion [23,24] have been proposed. In addition, an effective and apparently very general solution could be the technology of controlled post-infusion external pressure, the various strategies of which have received a reliable experimental justification in [25,26]. The proposed method requires some complication of technological equipment but can be implemented without significant costs in the practice of manufacturing a wide range of polymer-composite structures. In the cited works, studies were carried out with samples of preforms of the simplest shape and relatively small sizes. Obviously, in order to obtain the necessary information about the phenomena that occur during the implementation of the process on larger more complex parts, it is necessary to understand how the size, shape of the parts, properties of resins and porous preforms will affect its results. In the presented article, this problem is investigated theoretically using a specially developed simulation tool. In one of the first works considering the post-infusion stage of the process [27], a one-dimensional model based on a compressed sponge is presented, which allows to predict the compaction of a thick-walled laminate. In most models [12,18,28,29], considerable attention is paid to the correct description of the compressive properties of porous preforms in both dry and wet states, providing the condition of conservation the resin mass flow.

Due to the fact that the state of a compressible preform filled with liquid resin can be estimated in the experiment only by normal displacements of points on its open surface, relations were developed in [10,30] that couple the magnitude of these displacements with local changes in strains, porosity and fiber volume fraction. The experimental methods used for this purpose and confirmation of their reliability are described in detail in [25,26,31,32]. The presented study is focused on the development of software tools designed to simulate the post-infusion impact on the preform by controlled external pressure according to the methodology described in [13,15,25,26], where it is always assumed that the preform is initially completely filled with liquid resin. In practice, this requirement is not always met due to incomplete impregnation of the entire volume with resin and the formation of dry spots in different parts of the infused preform. That is why the software module described below was developed as a compatible addition to the software tool described in [33,34] and capable of simulating the actual infusion stage. The modeling method used in the described module is based on poroelasticity relations; and its operation as a stand-alone for clarity and better understanding is illustrated by a simplified example of a rectangular preform. It is assumed that in the initial state, the preform is completely filled with liquid resin, the pressure and viscosity of which are subject to certain distributions, adopted according to some reasonable assumptions. Thermal and thermo-kinetic effects are excluded from consideration.

The text of the article is structured as follows. Initially, the relations of classical poroelasticity and the flow of a viscous fluid in a porous medium are considered with their adaptation to the case of a thin-walled preform with a fixed lower surface. It is assumed that the preform has a transversal isotropy of elastic properties and permeability. The resulting model description of preform deformations, associated changes in porosity and permeability, which affect the flow of viscous resin, obtained as a result of these assumptions, is used in the finite element formulation of the problem. Next, two scenarios for the implementation of the post-infusion stage of the process are considered, which begin after the stabilization of the resin flow, when the inlet (through the resin gate) and outlet (through the vacuum valve) flows are equalized. At this moment, a gradual increase in pressure begins, which acts on the open outer surface of the preform, which can be accompanied by a controlled rise of the outlet pressure to atmospheric pressure with a varying delay. In the first scenario, both the inlet and outlet are open throughout the entire process, while in the second, the resin gate is closed from the start of the applied external pressure. The following analysis of the simulation results allows to identify the composition and influence of the controlled factors of the process on its final results, as well as to find situations that can lead to the irreparable defects in the molded composite part.

2. Modeling Problem Statement

An analysis of the scenarios for application of controlled external pressure on a composite preform, studied experimentally in [25,26], demonstrates their similarity to the situation considered in the classical Mandel’s problem [35], when a compressive external force acts on a certain porous volume filled with liquid. This volume has part of the open boundaries and part of the closed, preventing the outflow of fluid outward. The full set of the constitutive equations consists of the displacements u in poroelastic body, the equation for the internal pressure, the equilibrium equation, the Darcy’s law and the continuity equation for the fluid content. These equations can be transformed to the system of Navier–Cauchy, which in the case of a transversely isotropic (xy plane of transversal isotropy) porous material has the form (1), and diffusion Equation (2) for the pore pressure p_m [31].

$$\begin{gathered} M_{xx}\frac{{\partial }^2{u}_x}{\partial x^2}+G\frac{{\partial }^2{u}_x}{\partial y^2}+G^{\prime }\frac{{\partial }^2{u}_x}{\partial z^2}+\left(M_{xy}+G\right)\frac{{\partial }^2{u}_y}{\partial x\partial y}+\left(M_{xz}+G^{\prime }\right)\frac{{\partial }^2{u}_z}{\partial x\partial z}-{\alpha }_x\frac{\partial p_m}{\partial x}=0 \\ G\frac{{\partial }^2{u}_y}{\partial x^2}+M_{xx}\frac{{\partial }^2{u}_y}{\partial y^2}+G^{\prime }\frac{{\partial }^2{u}_y}{\partial z^2}+\left(M_{xy}+G\right)\frac{{\partial }^2{u}_x}{\partial x\partial y}+\left(M_{xz}+G^{\prime }\right)\frac{{\partial }^2{u}_z}{\partial y\partial z}-{\alpha }_x\frac{\partial p_m}{\partial y}=0 \\ {G}^{\prime }\frac{{\partial }^2{u}_z}{\partial x^2}+G^{\prime }\frac{{\partial }^2{u}_z}{\partial y^2}+M_{zz}\frac{{\partial }^2{u}_z}{\partial z^2}+\left(M_{xz}+G^{\prime }\right)\frac{{\partial }^2{u}_x}{\partial x\partial z}+\left(M_{xz}+G^{\prime }\right)\frac{{\partial }^2{u}_y}{\partial y\partial z}-{\alpha }_z\frac{\partial p_m}{\partial z}=0 \end{gathered}$$

(1)

$$\frac{\partial p_m}{\partial t}-{\kappa }_{x}M\frac{{\partial }^2{p}_m}{\partial x^2}-{\kappa }_{x}M\frac{{\partial }^2{p}_m}{\partial y^2}-{\kappa }_{z}M\frac{{\partial }^2{p}_m}{\partial z^2}=-{\alpha }_{x}M\left(\frac{\partial e_{xx}}{\partial t}+\frac{\partial e_{yy}}{\partial t}\right)-{\alpha }_{z}M\frac{\partial e_{zz}}{\partial t}$$

(2)

In these equations $M_{xx},M_{xy},M_{xz},M_{zz}$ are the components of the stiffness matrix, expressed in terms of Young’s moduli and Poisson’s ratios of the material, $G$ and $G^{\prime }$ are the shear moduli in the xy and xz (yz) planes, respectively [35]. The source term in Equation (2) contains the time derivatives of the strain e_ij in a porous medium, which can be expressed through the solution of Equation (1).

All relations given below were obtained under the following assumptions. The preform of a molded composite structure is a thin-walled body, which lower surface is fixed. The external pressure p_appl applied to the upper preform surface and the pore pressure p_m cause only changes in the thickness of the preform, whose compressibility dependence on the strain is the same at every point in the preform. The material of the porous frame is considered homogeneous, the microstructure of which is neglected. So, taking into account these assumptions, the Biot modulus M can be expressed as [35]

$$M={\left[\varphi /K_f+\left(1-\varphi \right)/K_S\right]}^{-1},$$

(3)

where ϕ is a porosity, K_f is the bulk modulus of the fluid, K_s >> K_f is the effective bulk modulus of the solid (reinforcement) phase, and K is the drained bulk modulus of the frame determined by the relationship [35]

$$1/K=1/K_S+\varphi /K_{\varphi }.$$

(4)

In Equation (4) K_ϕ << K_f is the pore volume bulk modulus. The components of the Biot effective stress tensor $\alpha ={[\begin{array}{cccccc}{\alpha }_x& {\alpha }_x& {\alpha }_z& 0& 0& 0\end{array}]}^T$ in a case of transversely isotropic material are defined as [35]

$${\alpha }_x=1-\left(M_{xx}+M_{xy}+M_{xz}\right)/3K_s; {\alpha }_z=1- \left(2M_{xz}+M_{zz}\right)/3K_s.$$

(5)

The mobility tensor κ in Equation (2) is the ratio of the permeability tensor Ξ of a porous medium to the dynamic viscosity of the fluid μ_f:

κ = Ξ/μ_f,

(6)

and the permeability tensor Ξ is related to the porosity by the Kozeny–Karman relation

Ξ = Ξ₀ · ϕ³/(1 − ϕ²),

(7)

where the symmetric tensor Ξ₀ is expressed in the form of a diagonal matrix (Ξ_x0 Ξ_x0 = Ξ_y0 Ξ_z0) containing the components, which values usually obtained experimentally.

The significant computational complexity of solving the problem (1), (2), revealed in preliminary numerical experiments, made it important to simplify the mechanical part of the problem, i.e., refusal to use the system (1). This became possible due to the introduced assumptions described above. They allowed to introduce the effective compressive stress p_c, which depends on the applied external stress p_appl and pore pressure p_m according to

$$p_c=p_{appl}-{\alpha }_z·p_m,$$

(8)

and to express the dependence of the fiber volume fraction V_f = 1 − ϕ on the compressive pressure, using the experimental data on the compressibility of the wet preform, borrowed in [36]. Approximations by 3rd order splines of this dependence and the corresponding dependence of Young’s modulus in the normal direction to the compressible surface on the fiber volume fraction are shown in Figure 1a,b.

In-plane Young’s modulus Y_x is taken to be n times (n = 4) greater than the modulus Y_z(V_f). Taking into account the assumptions made, the bulk modulus of the compressible preform’s elastic frame can be expressed through Y_z modulus and ν_zx Poisson’s ratio

$$K_{\varphi }=Y_z/\left(1-2{\nu }_{zx}\right).$$

(9)

Relation (8), together with the semi-empirical dependence Y_z(V_f), makes it possible, by virtue of the assumptions made, to express the out-of-plane e_z and in-plane e_x strains of the preform in the form

$$\begin{array}{cc}{e}_z=\left(\varphi -{\varphi }_{\max }^0\right)/\left(1-\varphi \right),& e_x=-{\nu }_{xz}·e_z,\end{array}$$

(10)

where ${\varphi }_{\max }^0$ is the initial local porosity before resin infusion.

The set of relations (2)–(10), from which system (1) is excluded, completes the formulation of the problem. The properties of the materials used in the model are presented in

Table 1. Properties of the modeled system components.

Designation	Value	Meaning
νxz/νzx/νxy	0.15/0.0375/0.3	Poisson’s ratios
Ξ0	(2 2 0.5)·10−11 m2	Minimum preform permeability components
Ys	5·1010 Pa	Young’s modulus of reinforcing fibers
νs	0.3	Poisson’s ratio of reinforcing fibers
Ks	4.17·1010 Pa	Bulk modulus of reinforcing fibers
Kf	2·109 Pa	Bulk modulus of liquid resin
ρf	1200 kg/m3	Mass density of liquid resin

.

3. Finite-Element Implementation of the Problem of Post-Infusion Pressure Application to Preform. Stand-Alone Version

3.1. Geometry and Finite-Element Meshing

To facilitate understanding of the ongoing processes, the geometry of the model is significantly simplified compared to real composite structures made using vacuum infusion technology, but the dimensions, although larger than those in experimental works [13,15,25,26], are commensurate with the composite structures of interest. The sizing decision was a compromise based on the viscosity of the resin to be used and the process duration. The appearance and dimensions of the preform are shown in Figure 2. The locations of the vacuum vent and resin are similar to those given in our works [33,34]. The distances d_inl and d_out from an arbitrary point in the preform to the resin gate and vacuum vent, respectively, which used when forming the initial conditions of the problem, are calculated by the formulas

$$d_{inl}=\sqrt{{\left(x-x_{inl}\right)}^2+{\left(y-y_{inl}\right)}^2}, d_{out}=\sqrt{{\left(x-x_{out}\right)}^2+y^2},$$

(11)

where $x_{inl},y_{inl},x_{out}$ are the coordinates of the centers of the named ports.

The size of the finite elements corresponded to the propagation velocity of the liquid resin. Preliminary numerical experiments with various FE mesh partitions determined the maximum value of the superficial fluid velocity, which reached 0.1 mm/s at the increasing external compressive pressure. Based on this result, the following final parameters of the FE meshing were adopted. A 2D mesh of triangular elements with sides 2 to 2.5 mm long with equal scale along the x and y axes, built on the upper surface of the preform and containing 38,016 elements, was extruded in three layers 1.66-mm thick in the direction of the lower surface. The resulting mesh, consisting of 76,464 triangular and rectangular boundary elements and 114,048 3D hexahedral elements, is shown in Figure 3. Modeling of all considered cases showed stable convergence of the computation.

3.2. Initial Conditions

Due to the fact that the start of the post-infusion simulation should occur after the completion of filling the preform with resin, the initial conditions for the pore pressure p_m, porosity ϕ, and viscosity μ of the resin should correspond to this time instant. However, the work of the described modeling tool is presented here in stand-alone mode. Therefore, before the start of the process, a preliminary stage is carried out, during which an arbitrarily given initial distribution of pore pressure $p_m^{init}$

$$p_m^{init}\left(x,y\right)=p_m^0\left(d_{inl}\left(x,y\right)/d_{\max }\right)$$

(12)

is settled by solving the Darcy’s flow equation. The plot of the tabulated function $p_m^0$ is shown in Figure 4a, and the maximum distance to the inlet d_max for the considered geometry is taken to be 0.64 m. The simulation of the post-infusion stage began after the stabilization of the flow, when the mass flows of the liquid passing through the inlet and outlet, which initially had significantly different values, became almost equal, asymptotically approaching each other (see Figure 4b).

The boundary conditions for inlet pressure p_inl = 100 kPa and outlet pressure p_out = 20 kPa, the values of which are accepted in most works studying the vacuum infusion of composites, are maintained unchanged throughout the duration of stabilization process. The results of pore pressure and fluid flow preliminary stabilization are shown in Figure 5.

In the presented version of the process, no temperature or thermal-kinetic effects are taken into account. Therefore, the distribution of resin viscosity in the preform body is taken unchanged, approximately corresponding to the real distribution after 1.5 h, during which the resin filled the preform:

$$\mu \left(x,y\right)=0.5·\left[0.1+{\tanh }^2\left(d_{inl}\left(x,y\right)/d_{\max }\right)\right] \mathrm{Pa}·\mathrm{s}.$$

(13)

This distribution is shown in Figure 6.

3.3. The Darcy’s Law Equation and Boundary Conditions

The assumptions introduced in Section 2 reduced the problem to a single PDE (2). The complete problem statement was implemented in the Comsol Multiphysics environment, in the Multiphysics mode, which contains two main nodes: Darcy’s Law and Poroelasticity. Darcy’s law in the transient mode includes a sub-nodes Porous medium, where the diffusion equation has the form (14):

$${\rho }_f{S}_p\frac{\partial p_m}{\partial t}+\nabla ·{\rho }_f\left[-\mathbf{\kappa }\left(\nabla p_m\right)\right]=Q_m,$$

(14)

where the Darcy’s flow is accepted as the Flow model, and Storage model in the linearized form is a weighted sum of two compressibilities, of fluid χ_f = 1/K_f and of porous frame χ_p = 1/K:

S_p = ϕ·χ_f + (1 − ϕ) χ_p.

(15)

Mass source Q_m in Equation (14) is defined as

$$Q_m=-{\rho }_f·\left({\alpha }_z·d{e}_z/dt+2·{\alpha }_x·d{e}_x/dt\right).$$

(16)

All boundaries except inlet and outlet are closed to fluid flow: n·u = 0.

On the upper surface, at the moment of resin flow stabilization completion (hereinafter taken as zero time count), the external pressure gradually increases and then stabilizes according to the law

$$p_{appl}\left(t,\Delta t,p_{add}\right)=p_{atm}+p_{add}·H_2\left(t,\Delta t\right),$$

(17)

where: H₂ is the Heaviside function with continuous second derivative, p_atm = 100 kPa—is the atmospheric pressure, p_add is an additional pressure, and Δt is duration of the pressure change (rise time). In all numerical experiments described below, Δt = 10 min is assumed, taking into account the inertance of the resin flow, depending on its viscosity and the permeability of the preform. Reducing this time was undesirable, since it could lead to a sharp change in flow velocities and numerical instability. This choice was also consistent with the specification of the Vacmobile 20/2 mobile vacuum system to be used.

This boundary condition is used unchanged in all simulated scenarios.

In the always open vacuum vent, the pressure p_vac = 20 kPa is initially maintained, which can remain unchanged during the entire post-infusion stage (no outlet control), or increase to atmospheric pressure p_atm with some delay t_lag after applying an external compressive pressure (outlet pressure control), as shown in Figure 7:

$$p_{out}\left(t,\Delta t,t_{lag},p_{add}\right)=p_{vac}+\left(p_{atm}-p_{vac}\right)·H_2\left(t-t_{lag},\Delta t\right).$$

(18)

The boundary condition for the resin gate is different for the two scenarios under study. In the first one, the inlet is open and the pressure in it is maintained equal to atmospheric p_inl = p_atm, due to which resin flushing occurs. In the second scenario, at the stage of resin flow stabilization, the inlet is open, but after stabilization is completed, the inlet closes immediately: n·u = 0. Therefore, Equation (14) is solved in two steps, each of which uses different boundary conditions for the resin gate.

The transient problem (14) with the initial and boundary conditions described above was solved using the BDF (backward differentiation formula) solver with automatic step determination, limited manually by values from 5 to 60 s at different stages of the process. The choice of these restrictions was performed at the preliminary setting of the computation parameters on the base of the actual process speed and the convergence plot analysis during simulation. To reliably ensure numerical stability, the value of restrictions per time step was assigned 3–5 times less than the steps offered by the BDF algorithm. At each time step, factorization and solving large systems of sparse equations were performed by the PARDISO direct solver, which is high performance, robust, memory efficient, and able to operate using both shared and distributed memory architectures.

3.4. Postprocessing of Calculation Results

The Comsol Multiphysics FE modeling tool allows you to reconstruct the spatial distribution in the simulated domain of any given variable and create a snapshot of that distribution at every time step. The probes of these variables defined in the software module (volume-averaged, maximum and minimum values) are used to plot their time dependences. Fluxes of velocity and transported fluid mass through the inlet/outlet surfaces are determined by calculating the corresponding surface integrals at each simulation step. Examples of simulation results presentation are given below.

4. Modeling Results

Figure 8, Figure 9 and Figure 10 give a general understanding of the nature of changes after the application of controlled compression pressure in the distributions of the pore pressure, porosity, and thickness of the infused preform.

Figure 8, Figure 9 and Figure 10 demonstrate significantly better post-processing results for the 1st scenario in terms of achieving a uniform distribution of pore pressure and preform wall thickness. In addition, outlet pressure equalization to atmospheric also improves the uniformity of the preform thickness distributions. Despite the fact that differences in the properties of the components used have a significant effect on the results of measurements in experiments, it should be noted that the results presented and the experimental data published in [25,26] are in good agreement. Thus, increasing the outlet pressure seems to be very appropriate. This is quite acceptable taking into account the fact that at the final stage of molding the structure, the viscosity of the resin increases significantly. However, such a solution requires the obligatory exclusion of the reverse flow from the vacuum line into the preform. This issue will be discussed below.

The influence of the layout and the mode of post-infusion pressures control on the dynamics of resin evacuation from the preform is demonstrated by the time dependences of the mass flow leaving through the inlet and outlet (see Figure 11).

Attention should be paid to two extremely undesirable situations presented in Figure 11b,c. Figure 11b shows the reversal of the flow direction in the outlet. Namely, at the time of ~46 min, this flux is directed inside the preform. However, this means that the air contained in the resin trap will enter the preform. For comparison, the orientation of the streamlines at times 13 and 46 min is shown in Figure 12a,b.

Figure 11c shows the situation when the excess resin that came out of the inlet returns inward to the preform. Such phenomena must also be excluded, especially when using highly active thermosetting resins. The distribution of streamlines at the times of 13 min and 105 min is shown in Figure 12c,d.

These considered critical situations demonstrate the importance of choosing the right delay time and outlet pressure growth rate when using the first scenario. Note that when modeling the second scenario, no such situations were found.

The groups of time dependences of the average pore pressure, its average gradient, and the accumulated volume of resin removed from the preform for various options for the post-infusion process implemented according to the first and second scenarios, presented in Figure 13, allow us to draw conclusions about the possibility of achieving the required quality indicators in the minimum time. Note that the diagrams in Figure 13a–d are built using the results of monitoring the corresponding probes throughout the entire duration of the process, while the diagrams in Figure 13e,f are obtained by integration of the time dependences of the mass fluxes of resin leaving the inlet and outlet of the type shown in Figure 11. It can be seen that the first scenario provides a much faster and better equalization of the pore pressure in the preform compared to the second scenario. The removal rate and total amount of excess resin removed is also significantly higher in the first case.

A comparison of the diagrams in Figure 13a,c,e shows that when implementing the first scenario, the use of a controlled increase in pressure at the outlet is preferable, since it provides a minimum pressure gradient in the preform and, consequently, more uniform porosity, although with a slightly smaller volume of removed excess resin than when maintaining vacuum pressure at the outlet. The dependence of the final indicators of the two considered process scenarios for various pressure control strategies is shown in Figure 14. Obviously, this information should be considered first when deciding on the choice of one or another method for improving the quality indicators of the composite structure obtained as a result of the vacuum infusion stage.

5. Discussion

Even a cursory review of the results presented above shows that for the most part they qualitatively coincide with the experimental data published in [13,14,15,25,26]. This applies to completely matching conclusions about the most important results of the process formulated in [26], such as a decrease in the variation of the laminate thickness, the time of equalization of the pore pressure in the preform, and an increase in the fiber volume fraction by removing the excess resin. A comparison of the conclusions about the difference in the features of processes with an open and closed resin gate also demonstrates their identity. A detailed quantitative correspondence between the results presented in the article and the experimental results in [25,26] is not entirely justified due to possible differences and the lack of necessary information about the properties of the used preforms and resins, as well as due to the difference in the sizes of the experimentally studied (20 cm·15 cm) and modeled (60 cm·40 cm) preforms. Nevertheless, the analysis of process indicators, such as a decrease in preform thickness (experiment 15–25%, FE model ~20%), an increase in values, and a decrease in the variation in the fiber volume fraction (experiment 0.59–0.61, FE model ~0.59), confirms a good quantitative agreement between the results of both studies.

However, the results of the work of our FE model significantly exceed in terms of achievable quality indicators what is presented in the referred experimental works. There is no contradiction in this, since in the experiment there is always a significant element of uncertainty associated with the variation in the properties of components, regimes, with the occurrence of extraneous processes that are not taken into account in numerical models. The theoretical results presented in the article are physically correct, which is additionally confirmed by the equality of resin flows through both open ports after the flow in the preform is settled. A comparison of the instantaneous spatial distributions of pore pressure, porosity, and preform thickness demonstrates their significant similarity, which confirms their interdependence dictated by the governing equations.

With a consistently low pressure in the vacuum vent or with an uneven distribution of pore pressure, it is very important to make the right decision about the moment to stop the post-infusion process. The correct answer to this question depends on the actual rheological properties of the resin. The consequence of shutting down processes at low resin viscosity can be, for example, the continued not controlled equalization of the pore pressure in the preform, which can lead to deviations from the predicted parameters and specifications. Therefore, the first scenario with outlet pressure control seems to be more efficient, since it ensures equalization of the pore pressure, bringing it to atmospheric pressure, preventing spontaneous deformations of the preform. In some cases, to prevent the formation of areas with a sharply increased or decreased pore pressure, it is advisable to use several resin injection points, possibly with different throughputs, or runners. Then, the proposed modeling tool can also assist in the correct choice of a rational process layout.

Due to the introduced assumptions, the description of the processes taking place in the preform is greatly simplified. When the proposed tool is combined with the previously developed simulation module [33,34], which takes into account the thermal physics and kinetics of phenomena in resins, the picture of the reconstructed processes will be more realistic and complex. However, this inevitable complication, which makes it difficult to widely use vacuum infusion technologies in industrial practice, will make it possible to predict the results of ongoing processes with greater accuracy and, therefore, efficiency. However, a necessary condition for the successful operation of simulation systems similar to the one presented is the possibility of experimental determination of all the required properties of the components used.

Concerning more applied issues, it should be recognized that one of the most difficult problems in the technological support of vacuum infusion processes is the use of the required pressure chambers. A possible solution is to upgrade the autoclaves to include thermally insulated vacuum and resin lines with independent pressure control. This is a particular technical challenge, but process modeling for a preform of arbitrary geometry, filled at controlled temperature and external pressure, can be easily implemented after combining the previously developed [33,34] and considered software tools. The development of such a simulation tool, which will also optimize the cycle times, is the goal of our future research.

6. Conclusions

The aim of the presented study was to develop a software tool implemented as a FE model designed to simulate and optimize the post-infusion effect of controlled pressure on a preform that has passed the resin filling stage in order to homogenize the pore pressure as well as reduce and equalize the distribution of porosity, providing improved geometry and mechanical properties of the produced polymer-composite structure. The method used is based on poroelasticity equations with introduced assumptions, justified by the specific shape and boundary conditions for the molded structure. In the article, in relation to the simplified geometry of the simulated system, two scenarios for the implementation of post-infusion processes, which differ in the layouts and the control strategy, are considered. The results of the study made it possible to identify the main factors influencing the course of the simulated processes, critical situations, the consequence of which may be the occurrence of irreparable defects. A comparison of the simulation results with borrowed reliable experimental data confirmed the adequacy of the results and the acceptable computational complexity of the developed software tool. In conclusion, the possibility of using it with the previously developed FE module for modeling the infusion stage of the process in the practice of manufacturing polymer-composite structures with strict technical requirements is discussed.