Tow Saturation Research Articles

Efficient dual-scale flow and thermo-chemo-rheological coupling simulation during on-line mixing resin transfer molding process

Simulation tools are required to ease the determination of the optimal process parameters and injection strategy of short cycle resin transfer molding (RTM). The developed finite element method/volume of fluid numerical tool aims to simulate accurately and efficiently the flow of a reactive resin mixed on-line in a dual-scale porous reinforcement during the resin transfer molding process. A macroscopic mesh deals with the flow inside of the channels of the reinforcement while a representative microstructure associated to each element allows reproducing both the unsaturated area and the intra-tow resin storage. Degree of cure, temperature, and viscosity are updated and transported at each time step, both in the channels and in the tows of the fabric using advection equations and sink and source terms for inter-scale exchanges. A new flexible approach based on the textile’s geometry defines automatically the representative microstructure associated to each macroscopic element depending on its size and shape. Additionally, tow saturation is simplified under the assumption of high-speed injection to a sum of one-dimensional transverse tow saturation problems, which reduces the computational cost of the simulation. Convergence tests have highlighted the ability for the simulation tool to treat with an equivalent degree of accuracy a saturation problem with elements exhibiting element sizes three times smaller to three times bigger than the length of the unsaturated area. Significant computation time reductions have also been noticed when large elements were used. Finally thermo-chemo-rheological coupled simulations have been conducted, highlighting the importance of taking the dual-scale effect into account when simulating reactive injections with on-line mixing.

The Sink Term to Different Kinds of Fibrous Mat During the Unsaturated Filling Process

The fibrous pre-form of resin transfer molding is a dual-scale porous medium with two distinct scales of pores, i.e., pores in intra- and inter-tow, which produce an unsaturated infiltration phenomenon during filling. A sink term representing the delayed flow rate from the inter-tow gap into the intra-tow one is introduced to establish governing equations. This study mainly analyzes the sink term by tow saturation during the microscopic flow. First, fiber-tow permeability is calculated by FLOTRAN of ANSYS, Second, periodic unit cells are built according to different structures, and the concrete expression of the sink term is indirectly obtained through the numerical simulation and date fitting of tow saturation under different pressure and viscosity conditions. Results indicate that: the FLOTRAN module can be used to calculate the permeability of fiber tow in two directions; Moreover, the filling time and infiltration process for diverse unit cells with the same volume fraction are different; under the same injection condition, different unit cells have different parameters for the sink term.

The effect of fabric and fiber tow shear on dual scale flow and fiber bundle saturation during liquid molding of textile composites

In Liquid Composite Molding (LCM) processes, a fibrous reinforcement preform is placed or draped over a mold surface, the mold is closed and a resin is either injected under pressure or infused under vacuum to cover all the spaces in between the fibers of the preform to create a composite part. LCM is used in a variety of manufacturing applications, from the aerospace to the medical industries. In this manufacturing process, the properties of the fibrous reinforcement inside the closed mold is of great concern. Preform structure, volume fraction, and permeability all influence the processing characteristics and final part integrity. When preform fabrics are draped over a mold surface, the geometry and characteristics of both the bulk fabric and fiber tow bundles change as the fabric shears to conform to the mold curvature. Numerical simulations can predict resin flow in dual scale fabrics in which one can separately track the filling of the fiber tows in addition to flow of resin within the bulk fabric. The effect of the deformation of the bulk fabric due to draping over the tool surface has been previously addressed by accounting for the change in fiber volume fraction and permeability during the filling of a mold. In this work, we investigate the effect of shearing of the fiber tows in addition to bulk deformation during the dual scale filling. We model the influence of change in fiber tow characteristics due to draping and deformation on mold filling and compare it with the results when the fiber tow deformation effect is ignored. Model experiments are designed and conducted with a dual scale fabric to characterize the change in permeability of fiber tow with deformation angle. Simulations which account for dual scale shear demonstrate that the tow saturation rate is affected, requiring longer fill times, or higher pressures to completely saturate fiber tows in areas of a mold with high local shear. This should prove useful in design of components for applications in which it is imperative to ensure that there are no unfilled fiber tows in the final fabricated component.

Modeling void formation and unsaturated flow in liquid composite molding processes: a survey and review

In this study, we present a review of the modeling of void formation and unsaturated flow in liquid composite molding processes. We examine modeling efforts considering all the mechanisms involved such as void formation and transport, bubble compression, and gas dissolution. In particular, the capillary number is identified as a key parameter for void formation and transport. Numerical simulation studies are reviewed, and a state-of-the-art is presented. The influence of microvoids on the global resin flow is also investigated. To model the unsaturated flow more accurately, we suggest considering the surface tension or capillary pressure, variation in permeability in terms of saturation and fiber displacement, as well as tow saturation. From this investigation, the apparent permeability and pressure profile in saturated and unsaturated flows are compared.

Modeling and simulation of voids and saturation in liquid composite molding processes

We propose modeling and simulation of the void formation and the tow saturation in liquid composite molding processes. The present model addresses the void formations in the macropore between fiber tows as well as in the micropore inside fiber tows. We also consider the bubble compression and tow saturation after voids are formed at the flow front. Finally, a void migration model is considered. The present models are validated by a comparison between simulation results and experimental data. The simulation results successfully represent important features of the void physics: the correlation of void formation at the flow front with capillary number, the advantage of vacuum application at air vents to reduce the void content inside tows, and the existence of partially saturated zone behind the global flow front. The representation of mold filling patterns by a degree of saturation shows the presence of a bubbly zone behind the flow front.

Fast liquid composite molding simulation of unsaturated flow in dual‐scale fiber mats using the imbibition characteristics of a fabric‐based unit cell

AbstractThe use of the dual‐scale fiber mats in liquid composite molding (LCM) process for making composites parts gives rise to the unsaturated flow during the mold‐filling process. The usual approaches for modeling such flows involve using a sink term in the mass balance equation along with the Darcy's law. Sink functions involving complex microflows inside tows with realistic tow geometries have not been attempted in the past because of the problem of high computational costs arising from the coupling of the macroscopic gap flows with the microscopic tow flows. In this study, a new “lumped” sink function is proposed for the isothermal flow simulation, which is a function of the gap pressure, capillary pressure, and tow saturation, and which is estimated without solving for the microscopic tow simulations at each node of the FE mesh in the finite element/control volume algorithm. The sink function is calibrated with the help of the tow microflow simulation in a stand‐alone unit cell of the dual‐scale fiber mat. This new approach, which does not use any fitting parameters, achieved a good validation against a previous published result on the 1D unsaturated flow in a biaxial stitched mat—satisfactory comparisons of the inlet‐pressure history as well as the saturation distributions were achieved. Finally, the unsaturated flow is studied in a car hood‐type LCM mold geometry using the code PORE‐FLOW© based on the proposed algorithm. POLYM. COMPOS., 31:1790–1807, 2010. © 2010 Society of Plastics Engineers.

A phenomenological model for fiber tow saturation of dual scale fabrics in liquid composite molding

Advanced composites are manufactured by liquid composite molding by impregnating a thermoset resin into a stationary woven or stitched preform. For a successful injection, the manufactured part should fill all the empty spaces between the fiber tows and inside the fiber tows with the resin. The fiber tows in such preforms have orders of magnitude lower permeability than the regions between the fiber tows, which makes them difficult to fill and hence susceptible to formation of microvoids. Numerical simulations can address the filling of fiber tows but it is difficult to capture the essential physics of their filling in a model created entirely from first principles due to the complexity of the flow which involves anisotropic permeability of flow along and across a fiber tow, uneven packing, fiber sizing, capillarity and the treatment of entrapped air. Hence, in this article we adopt a phenomenological approach in which we compare some of the possible models with an experimental procedure. The experimental procedure provides a quantitative measure of the filling of fiber tows during the impregnation process. A numerical simulation based on the dual scale flow was developed with different constitutive models that described the filling of the fiber tows. The predictions of the different models are compared with the experimental results under different processing conditions to select the model that most accurately describes the tow filling behavior. POLYM. COMPOS., 31:1881–1889, 2010. © 2010 Society of Plastics Engineers.

Modeling the impact of capillary pressure and air entrapment on fiber tow saturation during resin infusion in LCM

Traditionally, capillary effects have been neglected when modeling the filling stage of Liquid Composite Molding processes. This simplification is justified because the inlet resin pressures are much higher than the capillary pressure. This simplification is also acceptable when impregnating fabrics in which their fiber tows saturate at the same rate as the bulk preform. However, this assumption is questionable for fabrics that exhibit dual scale in which the fiber tows saturate at a much slower rate than the bulk preform. In such cases, the capillary pressure can influence the time to saturate a fiber tow significantly and impact the overall impregnation dynamics. Since the flow front velocity inside the fiber tows is significantly smaller than the flow around them, it is important to include the capillary pressure that may aid the saturation of the tow. In this paper, we modify our existing simulation that can predict the filling of the bulk preform and the saturation of the fiber tows to include the capillary forces at the fiber tow level. Important parameters are identified and grouped in non-dimensional form. A parametric study is conducted to examine the role of these dimensionless parameters on the overall tow saturation levels. The modeling is extended to include the effect of entrapped air inside the tows on the overall saturation of the preform. An experimental technique using the optical properties of vinyl ester and glass fiber was used to qualitatively validate the proposed model.

Modelling microscopic flow in woven fabric reinforcements and its application in dual-scale resin infusion modelling

Abstract A physical unit cell impregnation model is proposed for the micro-scale flow in plain woven reinforcements. The modelling results show a characteristic relationship between tow impregnation speed, the surrounding local macro-scale resin pressure and the tow saturation within the unit cell. This relationship has been formulated into a mathematical algorithm which can be directly incorporated into a continuum dual-scale model to predict the ‘sink’ term. The results using the dual-scale model show a sharp resin front in inter-tow-pore spaces and a partially saturated front region in intra-tow-pore spaces. This demonstrates that the impregnation of fibre tows lags behind the resin front in the macro pore spaces. The modelling results are in agreement with two reported experimental observations. It has been shown that the unsaturated region at the flow front could increase or have a fixed length under different circumstances. These differences are due to the variation in tow impregnation speed (or the time required for the tow to become fully impregnated), the weave architecture and the nesting and packing of plies. The modelling results have also demonstrated the drooping of the inlet pressure when flow is carried out under constant injection rates. The implementation of the algorithm into a dual-scale model shows coherence with a single-scale unsaturated model, but demonstrates an advantage in flexibility, precision and convenience in application.

Modeling resin flow and fiber tow saturation induced by distribution media collapse in VARTM

Vacuum assisted resin transfer molding (VARTM) is a liquid composite molding (LCM) technique to manufacture large scale composite structures. Fiber preforms are placed on a tool surface and covered by highly permeable layer known as the distribution media to enhance the flow in the in-plane direction. The assembly is enveloped in a plastic bag and a vacuum draws the resin into the preform through the distribution media. Woven and stitched preform architecture contain tightly packed fiber tows which have much lower permeability as compared to the bulk permeability of the fabric. Thus, the tows saturate with resin much later than the pores between the fiber tows and are more prone to microvoid creation, which are detrimental to part performance. Numerical modeling can predict the fiber tow saturation, but it tends to significantly under-predict saturation in VARTM process as compared to experimental results. To improve the predictions one needs to model the post-filling stage in VARTM. After the injection is discontinued, the resin pressure will drop and increase the compaction pressure on the fabric and the distribution media. This will compress the distribution media forcing the resin into the fiber tows and towards the resin trap at the vent location. This post-filling flow has not been addressed in traditional filling simulations. The current work analyzes the resin flow from the collapsing distribution media into unsaturated fiber tows. First, the governing formulation is derived and conditions under which the mathematical model can be simplified are stated. Next, a simplified analytic solution is provided to determine the significant non-dimensional parameters that influence the post-filling process. Finally, the post-filling stage is added to a mold filling simulation package and the predictions of unsaturated fiber tows are found to be more in line with experimental observations.

Desirable features in mold filling simulations for Liquid Composite Molding processes

AbstractNumerical simulations of the mold filling process in various Liquid Composite Molding (LCM) techniques, in which the fiber reinforcements represent the porous media and the polymeric resin is the impregnating fluid, have been successfully utilized for over a decade now, but they continue to be under dynamic development. Some of the recent applications are the increased emphasis on design optimization, control of the impregnation process and the rapid introduction of new LCM techniques such as the Vacuum Assisted Resin Transfer Molding (VARTM). This paper describes the requirements that these new applications demand on the implementation of such numerical simulation for modeling mold filling in LCM processes, namely Resin Transfer molding (RTM) and VARTM. Liquid Injection Molding Simulation (LIMS) developed at the University of Delaware, which can simulate the flow in such processes, has been modified to encompass these features. It addresses practical issues concerning modeling the part geometry, such as the proper choice of one‐, two‐ and three‐dimensional elements and their effective combinations. It also describes the simulation of non‐trivial boundary conditions, placement of sensors and allowing for resin injection control using the functions built into the simulation program and the embedded scripting language. Several examples are presented to highlight the importance of its flexibility. The paper also addresses some VARTM specific issues, such as the modeling of distribution media, dimensional change during filling and fiber tow saturation. Polym. Compos. 25:355–367, 2004. © 2004 Society of Plastics Engineers.

The implications of fiber compaction and saturation on fully coupled VARTM simulation

Vacuum Assisted Resin Transfer Molding (VARTM) is a process by which resin is drawn through fiber preforms in a one-sided mold using an induced pressure gradient. Although the approach to model flow in VARTM is similar to the Resin Transfer Molding (RTM) process, modeling in VARTM can be significantly more complex if one accounts for fiber compaction and the dual scale nature of the fiber preform which is present in RTM but often neglected. This article investigates the influence of fiber compaction and fiber tow saturation during mold filling in the VARTM process. A non-rigid control volume is used to formulate a set of governing equations to describe the resin flow. Tow impregnation at the micro-scale is coupled with global resin flow at the macroscale by applying conservation of mass principles. Preform compaction is modeled as a non-linear spring bed where compaction pressure is dynamically distributed between the resin and the preform. The variation in preform permeability is modified due to the changes in the fiber volume fraction as a result of changing compaction. A simple one-dimensional mold filling case is solved to investigate the role of compaction and dual scale porous media in VARTM processes. A parametric study allows us to identify situations in which one can neglect compaction and saturation and conditions under which a fully coupled model should be applied for satisfactory results.

A numerical model to predict fiber tow saturation during liquid composite molding

A dual scale porous medium contains two distinct scales of pores. We will consider the case in which small scale pores are ordered within well-defined sub-regions. Typical examples of such media are textile preforms used in various composite-manufacturing processes. Rigorously, the phenomenon can be modeled by using Darcy's law to describe flow through porous medium and mass conservation for the flow within the larger pores. The smaller pores can be included within these equations as a sink term. This approach, though straightforward, poses implementation difficulties. In this paper, we suggest an alternative way to model this concept. We use the standard finite element/control volume approach and model the “internal” sink term by appending extra one-dimensional elements to control volumes associated with the control volumes of discretized part geometry. This approach offers two advantages over previously attempted schemes: (1) the problem to be solved remains linear and flow can be calculated explicitly within the time domain and (2) existing simulation packages for RTM filling simulation will be able to incorporate saturation effects to simulate the flow in dual scale media. To illustrate this point we present the implementation of the developed algorithm within the frameworks of an existing simulation package LIMS. The implementation is capable of providing saturation data during filling of arbitrarily shaped part and can capture the influence of saturation on filling pressure or flow-rate. This should prove useful in determining the time needed to completely saturate the fiber tows, which is crucial for part performance and also allow us to explain the variation in injection pressure and difficulties in “assigning” single scale permeability for such porous medium.