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

The 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.     

Investigation of unsaturated flow in woven,braided and stitched fiber mats during mold‐filling in resin transfer molding

In Resin Transfer Molding (RPM), which is a process to manufacture polymer composites, the impregnation of fibrous reinforcement In the form of mats by a thermosetting resin is modeled as the flow of a Newtonian liquid through a single length‐scale porous medium. While this approach is sufficiently accurate for random fiber‐mats, it can lead to appreciable errors when applied to woven, braided, or stitched fiber‐mats that contain two length scales. This work investigates the primary factors governing the isothermal unsaturated flow through such dual‐scale porous media. Two studies were conducted to better understand this phenomenon: the first experimenatally investigated the flow, while the second theoretically modeled the flow and identified important parameters affecting such a flow with the help of dimensionless analysis. In the first study, one‐dimensional constant injection rate experiments were performed using various fiber mats. The unsaturated flow behavior of various mats was characterized using a constant “sink” term in the continuity equation. Results indicated that for a given fiber‐mat, the magnitude of the sink effect was a function of the capillary number. In the second study, a numerical model was developed to describe flow through dual‐scale preforms in which the two flow domains, the inter‐ and intra‐tow regions, were coupled. We identified a dimensionless number called the sink effect index ψ that characterizes the magnitude of liquid absorption by the tows and is a function of the relative resistance to flow in the tow and inter‐tow regions, and the packing density of the tows. The parametric study of this index with the help of numerical simulations reveals its influence on the flow and identifies the distinct transient and steady‐state flow regimes.     

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.     

Analysis of two-regional flow in liquid composite molding

This study investigates the two-regional flow in Liquid Composite Molding (LCM) with emphasis on the race tracking phenomenon. An equivalent permeability is introduced to describe the flow capacity in the fiber free region. A lumped permeability is also used to further simplify the flow modeling by averaging the flow across the flow direction. Both the equivalent permeability approach and the lumped permeability approach were verified with experiments. It is found that they are capable of modeling the race tracking effects in LCM.     

Experimental analysis and simulation of flow through multi-layer fiber reinforcements in liquid composite molding

Liquid composite molding (LCM) is a process in which a reactive fluid is injected into a closed mold cavity with preplaced reinforcement. Combined layers of different permeabilities are often used in LCM, which creates through thickness and inplane porosity and permeability variations. These inhomogeneities may influence the flow front profile in the thickness direction. To investigate the effect of the through thickness inhomogeneities, mold filling experiments were performed using preforms containing layers of two different fiber architectures. Aqueous corn syrup solutions were injected into a tempered glass mold containing the reinforcement stack. The progress of the flow front at various locations within the reinforcement was measured by an electrical conductivity technique based on the insertion of small wires between the reinforcement layers. Experimental data reveal the details of the flow front shape as the fluid penetrates the preform. Using these data, a model is proposed to calculate the overall in-plane permeability of the preform. Numerical simulations of the flow front progression performed with the computer software RTMFLOT developed in our laboratory are compared to the experimental flow front for various stacking arrangements. Results show good agreement between simulations and experiments and demonstrate the capability of the software to simulate multi-layer flow process.     

Effect of fiber architecture on permeability in liquid composite molding

This study investigates the effect of fiber architecture on the permeability in liquid composite molding. The in-plane permeabilities of several glass fiber mats with different architectures were measured. A conceptual model based on the observed micro-scale flow pattern is proposed to explain the measured permeability results. It is found that the size of the pores outside the fiber tows and how these pores are connected determine the permeability of a fiber reinforcement.     

Sensor placement study for online flow monitoring in liquid composite molding

On‐line sensing can play an important part in controlling the quality of the final product in any manufacturing environment, including liquid composite molding (LCM). Having a sensor embedded within the part itself is often the most effective means of monitoring its condition at various stages of manufacturing and even throughout its useful life. However, given their intrusive nature, there are practical limitations imposed upon their size, quantity and trajectory within the part. This study explores the possibility of using a single lineal sensor to monitor the resin flow front during the mold filling stage of LCM, and to detect the onset of void formation and the presence of dry spots within the mold. Experiments were conducted to characterize the response of a fiber optic system previously developed for cure monitoring. Simulations were then performed to determine the optimal placement of just one such sensor in a mold to demonstrate that sufficient information on the mold filling process could be obtained. The purpose of the simulation work was to learn how to interpret the sensor response and, subsequently, use it to control the LCM process.     

Curing kinetics of medium reactive unsaturated polyester resin used for liquid composite molding process

The cure kinetics of medium reactivity unsaturated polyester resin formulated for Liquid Composite Molding process simulation was studied by Differential Scanning Calorimetry (DSC) under isothermal conditions over a specific range of temperature. For isothermal curing reactions performed at 100, 110, and 120°C, several influencing factors were evaluated using the heat evolution behavior of curing process. We propose two‐ and three‐parameter kinetic models to describe the cure kinetics of thermoset resins. Comparisons of the model solutions with our experimental data showed that the three‐parameter model was the lowest parameter model capable of capturing both the degree of cure and the curing rate qualitatively and quantitatively. The model parameters were evaluated by a non‐linear multiple regression method and the temperature dependence of the kinetic rate constants thus obtained has been determined by fitting to the Arrhenius equation. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Viscosity modeling of a medium reactive unsaturated polyester resin used for liquid composite molding process

The development of new composite product for an application through liquid composite molding (LCM) process simulation requires submodels describing the raw material characteristics. The viscosity during resin cure is the major submodel required for the effective simulation of mold-filling phase of LCM process. The viscosity of the resin system during mold filling changes as the cure reaction progresses. Applied process temperature also affects the viscosity of the resin system. Hence, a submodel describing the resin viscosity as a function of extent of cure and process temperature is required for the LCM process simulation. In this study, a correlation for viscosity during curing of medium reactive unsaturated polyester resin, which is mostly used for the LCM process, has been proposed as a function of temperature and degree of cure. The viscosity and the degree of cure of reacting resin system at different temperatures were measured by performing isothermal rheological and isothermal differential scanning calorimetry experiments, respectively. A nonlinear-regression analysis of viscosity and degree of cure data were performed to quantify the dependence of viscosity on temperature and extent of cure reaction. Comparisons of model solutions with our experimental data showed that the proposed empirical model is capable of capturing resin viscosity as a function of extent of cure and temperature qualitatively as well as quantitatively. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

An interface‐update‐based implicit algorithm for mold filling simulation of liquid composite molding

In this article, a new implicit numerical algorithm has been presented for mold filling simulation in liquid composite molding process. The new implicit numerical algorithm is based on the update of flow interface to track flow front for each time step. Nodes of mesh are divided into three groups, i.e. filled nodes, interface nodes (or partially filled nodes), and empty nodes. Governing equations of filled nodes are solved to obtain pressure distribution; filling fractions of interface nodes are checked to determine if any node is needed to be added to filled nodes or be removed from filled nodes. The local LU factorization solver and preconditioned conjugated gradient iterative solver were employed to investigate the new implicit algorithm. Case studies demonstrated the performance of the proposed implicit algorithm. The new implicit algorithm reduced the computational complexity to below 2.0 power order of problem sizes. POLYM. COMPOS., 27:271–281, 2006. © 2006 Society of Plastics Engineers.     

Numerical simulation of unsaturated flow in woven fiber preforms during the resin transfer molding process

In this paper, the unsaturated flow encountered in the woven or stitched fiber mats used in RTM is simulated using an adaptation of the Finite Element Method/Control Volume (FEM/CV) technique. The movement of resin through such fiber mats is modeled as flow through dual scale porous media and the mass balance in such media creates a sink term in the equation of continuity of the macroscopic flows. Combining this equation with Darcy's law leads to a non-homogeneous non-linear elliptic partial differential equation for pressure that is solved iteratively. First the simulation is used to study simple flows encountered during the characterization of preforms, such as the constant injection pressure 1-D flow and the constant flow rate radial injection flow. Previously observed experimental results of relatively flatter pressure histories for the latter type of flows in wove fiber mats are replicated, both numerically and analytically, by the pressure equation with the sink term. A quantity called pore volume ratio is shown to play an important role in such flows. Finally, the unsaturated flow in a typical RTM mold, packed with woven fiber mats, is simulated numerically, and inlet pressures, fill times, and mat saturation are studied.     

Cure monitoring of the liquid composite molding process using fiber optic sensors

Fluorescence has been demonstrated to be an accurate tool for monitoring resin cure. It is measured using an evanescent wave fiber-optic sensor. An economical optical fiber sensor has been developed with a refractive index greater than 1.6, permitting evanescent wave monitoring of epoxy resins. The fluorescence wave-length-shift, which has been correlated with monomer conversion, is monitored during the liquid molding process. Unidirectional glass fabrics with volume fractions from 40% to 60% were injected with epoxy resin at a variety of driving pressures and cured at several temperatures. Several composite parts were fabricated to test the effects of vacuum pressure, injection rate, cure temperature, and fiber fraction on the performance of the sensor. The sensitivity of the evanescent wave fluorescence sensor to the condition of the resin system was also examined. The sets of resin/hardener samples were subjected to rigorous chemical analysis to determine the extent of their differences.     

Preparation and delayed release of poly(lactide‐ co‐glycolide)/ketoconazole composite fiber mats

In this study, slow release materials–poly(lactide‐co‐glycolide) (PLGA) ultrafine fiber mats containing different ketoconazole (KCZ) contents were prepared and their release behaviors were investigated in vitro. PLGA/KCZ ultrafine fiber mats were prepared via electrospinning and characterized by means of scanning electron microscope, Fourier transform infrared, X‐ray diffraction (XRD), and thermal gravimetric analysis. The slow release properties of PLGA/KCZ fiber mats in vitro were studied by measuring the concentrations of KCZ dissolved in the phosphate buffered solution (pH = 4.5) at a programmed time. Results indicated that KCZ could be dispersed in PLGA very well in a wide range of KCZ content from 10 to 100% with respect to PLGA. Most KCZ in PLGA fibers were physically dispersed. The thermal decomposition temperature of PLGA was lowered due to the incorporation of KCZ. With increased drug concentration, the release amount would increase in unit time. The two‐stage releases would be sustained to achieve the effective utilization of KCZ. POLYM. COMPOS., 2013. © 2013 Society of Plastics Engineers     

Effects of fiber mat architecture on void formation and removal in liquid composite molding

Liquid composite molding (LCM) processes such as resin transfer molding and structural reaction injection molding are considered to be high potential processes for the mass production of composite parts. The resin injection step in LCM consists of two simultaneous flows: bulk mold filling and tow wetting. This complexity often results in the entrapment of air in the composite part, which is known to result in degradation of part performance, In this work, systematic investigation of the resin flow behavior through various types of glass fiber reinforcements is carried out by flow visualization. The objective is to relate the fiber mat architecture to the micro scale flow pattern and void formation, movement, and removal. An optical image analysis and processing technique is developed to help quantify void formation. Void formation is related to liquid properties and fiber-liquid contact angle. Although the focus of the study is LCM, the results can be directly applied to other composite manufacturing processes that involve advancement of resin in a dry fiber reinforcement.     

Direct meso‐scale simulations of fibres in turbulent liquid flow

A procedure for direct, meso‐scale simulations of flexible fibres immersed in liquid flow is introduced. The fibres are composed of chains of spherical particles connected through ball joints with the bending stiffness of the joints as a variable. The motion of the fibres and the liquid is two‐way coupled with full resolution of the solid–liquid interface. First the simulation procedure is validated by means of an analytical solution for sphere doublets in zero‐Reynolds simple shear flow. Subsequently we use the numerical method to study inertial flows with fibres, more specifically the interaction of a fibre with isotropic turbulence.     

Liquid flow in molds with prelocated fiber mats

The mechanism associated with mold filling in the manufacture of structural RIM (SRIM) and resin transfer molding (RTM) composites is studied by means of flow visualization and pressure drop measurements. To facilitate this study, an acrylic mold with a variable cavity was constructed and the flow patterns of nonreactive fluid flowing through various layers, types, and combinations of preplaced glass fiber reinforcement mats were photographed for both evacuated and nonevacuated molds. The pressure drops in the flow through a single type of reinforcement (e.g., a continuous strand random fiber mat) and also a combination of reinforcement types (e.g., a stitched bidirectional mat in combination with a random fiber mat) were recorded at various flow rates to simulate high-speed feeding processes (e.g., SRIM) and low-speed feeding processes (e.g., RTM). By changing the amount of reinforcement placed into the mold, the permeabilities of the different types and combinations of glass fiber mats were obtained as a function of porosity. It is shown that partially evacuating the mold cavity decreases the size of bubbles or voids in the liquid, but ultimately increases the maximum pressure during filling. The results also show that glass fiber mats exhibit anisotropic permeabilities with the thickness permeability, K_z, being extremely important and often the determining factor in the pressure generated in the mold during filling.     

On‐line mixing during injection and simultaneous curing in liquid composite molding processes

Liquid composite molding (LCM) processes such as resin transfer molding (RTM) and vacuum assisted RTM (VARTM) are used to manufacture high quality and net‐shape fiber reinforced composite parts. All LCM processes impregnate fiber preforms packed in a mold cavity with a thermoset resin. After the preform is fully saturated, the injection is discontinued but the resin continues to cure. Once the curing step is complete, the part is de‐molded. The resin has to be mixed with a curing agent to cure. Typically, the resin and the curing agent are mixed together in a pressure pot before the injection. This has several disadvantages, such as storage of large amounts of hazardous polymerizing resin, wastage, and cleaning of cured resin from the injection line. This paper proposes the implementation and calibration of an alternative to this technique. The approach is to mix the curing agent with the resin as the resin enters the mold through a separate system featuring two feed‐lines. Such a system will enable one to maintain a uniform gel time throughout the part by varying the mixing ratio of resin and the catalyst during the injection. An experimental study of such on‐line mixing to obtain simultaneous curing and to reduce the overall curing time is conducted and presented in this paper. Implementation of a control scheme that varies the curing agent during injection and its effect on cure time is benchmarked with the process in which the percentage of curing agent is held constant. The gel time for the fabricated parts was reduced by 20–25% by continuously varying the percentage of curing agent during injection. POLYM. COMPOS., 26:74–83, 2005. © 2004 Society of Plastics Engineers     

Spatially homogeneous gelation in liquid composite molding

On‐line mixing of the resin with its curing agents prior to injection into a mold is a common industrial technique for fabricating composite parts. For vinyl‐ester resins that cure via free radical polymerization, the concentrations of retarder, accelerator, and initiator are pre‐selected and cannot be changed during the injection. Hence, the resin that enters the mold the earliest has cured longer than the resin that enters the mold later, since the gel time for the resin is the same, owing to the fixed ratio of the curing agents. This approach leads to inhomogeneous cure of the resin and consequently to longer residence time of the resin in the mold. It requires an additional 50 to 75 percent of the filling time before a part can be de‐molded. In this study, it is shown that by adjusting the concentration of curing agents during the injection, a more homogeneous gel time throughout the mold can be achieved. The time to de‐mold is reduced to 18‐24 percent of the filling time. Sensors that measure the conductivity of the resin were used to detect the location and monitor the cure of vinyl‐ester. This approach could be extended to other resin systems to control the spatial curing of the resin in the mold.     

Numerical simulation of three‐dimensional fiber orientation in injection molding including fountain flow effect

It is essential to predict the nature of flow field inside mold and flow‐induced variation of fiber orientation for effective design of short fiber reinforced plastic parts. In this investigation, numerical simulations of flow field and three‐dimensional fiber orientation were carried out in special consideration of fountain flow effect. Fiber orientation distribution was described using the second‐order orientation tensor. Fiber interaction was modeled using the interaction coefficient C_I. Three closure approximations, hybrid, modified hybrid, and closure equation for C_I=0, were selected for determination of the fiber orientation. The fiber orientation routine was incorporated into a previously developed program of injection mold filling (CAMPmold), which was based on the fixed‐grid finite element/finite difference method assuming the Hele‐Shaw flow. For consideration of the fountain flow effect, simplified deformation behavior of fountain flow was employed to obtain the initial condition for fiber orientation in the flow front region. Comparisons with experimental results available in the literature were made for film‐gated strip and centergated disk cavities. It was found that the orientation components near the wall were were accurately predicted by considering the fountain flow effect. Test simulations were also carried out for the filling analysis of a practical part, and it was shown that the currently developed numerical algorithm can be effectively used for the prediction of fiber orientation distribution in complex parts.