Effect of fiber‐mat anisotropy on 1D mold filling in LCM: A numerical investigation

The 1D flow experiment is one of the most common methods to measure the saturated and unsaturated permeabilities as well as to study the unsaturated flow in liquid composite molding (LCM) processes used for manufacturing polymer composites. The effective permeability along a flow direction in an anisotropic fiber mat, which is a function of the principal components of the permeability tensor and the angle between the principal and flow directions, is based on the assumption of uniform 1D flow in the mat. In the present paper, the validity of such unidirectional flow assumption is shown to depend on three factors, i.e., the fiber‐mat aspect ratio, the anisotropy ratio (the ratio of the major and minor principal in‐plane permeabilities), and the angle of the principal permeability direction. A mold‐filling simulation for hard‐mold LCM processes based on the control volume/finite element formulation is used to investigate how these three factors affect the 1D flow. A new algorithm for applying the uniform inlet‐pressure condition prevalent in the 1D flow mold under the constant‐flow‐rate injection is developed to match the actual conditions in the mold. Our numerical results show that the three aforementioned factors have significant influence on the inlet‐pressure history as well as on the mold‐filling pattern. Maximum deviations from the unidirectional flow predictions in the inlet‐pressure history as well as the flow‐front progress is seen when the principal permeability direction is at an angle of 45° with respect to the flow direction; these deviations worsen with a decrease in the mat aspect ratio and with an increase in the anisotropy ratio. However, the inlet‐pressure history remains linear and the progress of the average flow‐front remains predictable by the 1D flow theory. POLYM. COMPOS., 2008. © 2008 Society of Plastics Engineers     

In‐plane anisotropic permeability characterization of deformed woven fabrics by unidirectional injection. Part I: Experimental results

Because of the increasing use of polymer composites in a wide variety of industrial applications, the manufacturing of complex composite parts has become an important research topic. When a part is manufactured by liquid composite molding (LCM), the reinforcement undergoes a certain amount of deformation after closure and sealing of the mold. In the case of bidirectional woven fabrics, this deformation may significantly affect the resin flow and mold filling because of changes in the values of permeability. Among other considerations that govern the accuracy of numerical simulations of mold filling, it is important to predict the changes of permeability as a function of the local shearing angle of the preform. The resin flow through a fibrous reinforcement is governed by Darcy's law, which states that the fluid flow rate is proportional to the pressure gradient. The shape of the flow front in a point‐wise injection through an anisotropic preform is an ellipse. Part I of this article describes a new methodology based on the ellipse equation to derive the in‐plane permeability tensor from unidirectional injection experiments in deformed woven fabrics. Part II presents a mathematical model that predicts the principal permeabilities and their orientation for sheared fabrics from the permeability characterization of unsheared fabrics. Unidirectional flow experiments were conducted for a nonstitched, balanced, woven fabric for different shearing angles and fiber volume fractions. This article presents experimental results for deformed and undeformed fabrics obtained by unidirectional flow measurements. A comparison of the proposed characterization methodology with radial flow experiments is also included. POLYM. COMPOS. 28:797–811, 2007. © 2007 Society of Plastics Engineers.     

Flow front advancement during composite processing: predictions from numerical filling simulation tools in comparison with real‐world experiments

Liquid composite molding (LCM) techniques are innovative manufacturing processes for processing fiber reinforced polymer parts used e.g. for aerospace structures. Thereby the reinforcing material is placed in a mold and infiltrated with a low viscosity polymer matrix. Increasing production rates as well as part complexity lead to high production risks such as air inclusions or incomplete mold filling. Numerical mold filling simulations are promising tools enabling the composite manufacturing engineer to detect dry spots in the mold and find the optimal positions of the resin entry and ventilation system at an early process development stage. Today, different numerical models and software packages are available for modeling the flow through the reinforcing structure for visualization of the flow behavior. The goal of this study is the systematic comparison of two different software packages, namely PAM‐RTM^® and OpenFOAM. Both software tools are operated as they are commonly foreseen. Real world experiments under real process conditions are the basis for the assessment of the numerical predictions. The resin transfer molding (RTM) experiments are executed in a tool with a transparent upper mold half in order to see the flow front advancement. POLYM. COMPOS., 37:2782–2793, 2016. © 2015 Society of Plastics Engineers     

A gas flow method for determination of in‐plane permeability of fiber preforms

Resin flow plays a crucial role in many composite manufacturing processes. The most important parameters used in modeling and designing mold filling are the permeability of the fibrous preform, which is a kind of flow conductance and a property of the reinforcement, and the viscosity of the resin. The extent reaction, or degree of cure, is also important and causes change of chemical during mold filling. To determine the permeability of fiber preform searchers have been using liquid flow analysis. In this study, a new scheme for determining permeability using gas flow is proposed. In conventional liquid flow methods, radial propagation of the polymer into a porous medium is measured and used to determine permeability, whereas in the gas flow method, the several different preform geometries is measured and used. The effectiveness of the gas flow method was verified by comparing it with conventional methods.     

Modeling and simulation of fiber‐reinforced polymer mold‐filling with phase change

A gas‐solid‐liquid three‐phase model for the simulation of fiber‐reinforced composites mold‐filling with phase change is established. The influence of fluid flow on the fibers is described by Newton's law of motion, and the influence of fibers on fluid flow is described by the momentum exchange source term in the model. A revised enthalpy method that can be used for both the melt and air in the mold cavity is proposed to describe the phase change during the mold‐filling. The finite‐volume method on a non‐staggered grid coupled with a level set method for viscoelastic‐Newtonian fluid flow is used to solve the model. The “frozen skin” layers are simulated successfully. Information regarding the fiber transformation and orientation is obtained in the mold‐filling process. The results show that fibers in the cavity are divided into five layers during the mold‐filling process, which is in accordance with experimental studies. Fibers have disturbance on these physical quantities, and the disturbance increases as the slenderness ratio increases. During mold‐filling process with two injection inlets, fiber orientation around the weld line area is in accordance with the experimental results. At the same time, single fiber's trajectory in the cavity, and physical quantities such as velocity, pressure, temperature, and stresses distributions in the cavity at end of mold‐filling process are also obtained. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 42881.     

Prediction of flow–induced process variables based on similarity analysis in the liquid molding process

In general, a numerical scheme is a widely accepted technique for estimating resin flow in the liquid molding process. A numerical mold filling analysis is essential to optimize the manufacturing process of a composite. However, finding an optimal condition from the numerical analysis requires many numerical calculations. The efforts can be greatly reduced if a similarity solution replaces the repeated numerical calculations. In this study, similarity relations are proposed to predict the flow‐induced process variables. such as resin pressure, resin velocity, and flow front evolution time, during mold filling. Numerical simulations are performed for two cases where a material property, an injection condition or a part shape is different. The model is verified by applying the similarity relation for two numerical results obtained from the thin shell structure.     

Experimental analysis and numerical modeling of flow channel effects in resin transfer molding

Composite manufacturing by Liquid Composite Molding (LCM) processes such as Resin Transfer Molding involve the impregnation of a net‐shape fiber reinforcing perform a mold cavity by a polymeric resin. The success of the process and part manufacture depends on the complete impregnation of the dry fiber preform. Race tracking refers to the common phenomenon occurring near corners, bends, airgaps and other geometrical complexities involving sharp curvatures within a mold cavity creating fiber free and highly porous regions. These regions provide paths of low flow resistance to the resin filling the mold, and may drastically affect flow front advancement, injection and mold pressures. While racetracking has traditionally been viewed as an unwanted effect, pre‐determined racetracking due to flow channels can be used to enhance the mold filling process. Advantages obtained through controlled use of racetracking include, reduction of injection and mold pressures required to fill a mold, for constant flow rate injection, or shorter mold filling times for constant pressure injection. Flow channels may also allow for the resin to be channeled to areas of the mold that need to be filled early in the process. Modeling and integration of the flow channel effects in the available LCM flow simulations based on Darcian flow equations require the determination of equivalent permeabilities to define the resistance to flow through well‐defined flow channels. These permeabilities can then be applied directly within existing LCM flow simulations. The present work experimentally investigates mold filling during resin transfer molding in the presence of flow channels within a simple mold configuration. Experimental flow frot and pressure data measurements are employed to experimentally validate and demonstrate the positive effect of flow channels. Transient flow progression and pressure data obtained during the experiments are employed to investigate and validate the analytical predictions of equivalent permeability for a rectangular flow channel. Both experimental data and numerical simulations are presented to validate and characterize the equivalent permeability model and approach, while demonstrating the role of flow channels in reducing the injection and mold pressures and redistributing the flow.     

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.     

Resin transfer molding process optimization using numerical simulation and design of experiments approach

The art of resin transfer molding (RTM) process optimization requires a clear understanding of how the process performance is affected by variations in some important process parameters. In this paper, maximum pressure and mold filling time of the RTM process are considered as characteristics of the process performance to evaluate the process design. The five process parameters taken into consideration are flow rate, fiber volume fraction, number of gates, gate location, and number of vents. An integrated methodology was proposed to investigate the effects of process prameters on maximum pressure and mold filling time and to find the optimum processing conditions. The method combines numerical simulation and design of experiments (DOE) approach and is applied to process design for a cylindrical composite part. Using RTM simulation, a series of numerical experiments were conducted to predict maximum pressure and mold filling time of the RTM process. A half‐fractional factorial design was conducted to identify the significant factors in the RTM process. Furthermore, the empirical models and sensitivity coefficients for maximum pressure and mold filling time were developed. Comparatively close agreements were found among the empirical approximations, numerical simulations, and actual experiments. These results were further utilized to find the optimal processing conditions for the example part.     

Calibration of one‐dimensional flow setup used for estimating fabric permeability using three different reference media

Experimental estimation of the permeability of reinforcement fabrics is very important in conducting accurate mold‐filling simulations for liquid composite molding (LCM) processes employed to manufacture polymer matrix composites. In this study, the one‐dimensional (1D) flow based permeability measuring setup was calibrated for the first time using three different reference media: an aluminum block with drilled parallel holes, a lattice of 3D unit cells created using rapid prototyping, and carbon fabric used in the recently concluded permeability bench‐mark study [Vernet N, et al. Compos Part A, 61, 172 (2014)]. The steady‐state permeability was estimated for all the three cases while the transient permeability was estimated only for the lattice‐type and carbon fabric media. The carbon‐fabric results were presented as the transient and steady‐state permeabilities for three different directions of 0°, 45°, and 90°, and the in‐plane principal permeability components were calculated using the correlations for anisotropic fabrics. The results for the aluminum‐plate and lattice‐like media were compared with the previous numerical and experimental studies and good agreement was observed. To validating the carbon‐fabric results, the experimental permeability was compared with two different analytical permeabilities for dual‐scale porous media [Papathanasiou, Int. J. Multiphase Flow, 27 ( 8 ), 1451 (2001) and K.M. Pillai and S.G. Advani, Transport Porous Med., 21 ( 1 ), 1 (1995)], and a good agreement with experimental results established the accuracy of our 1D flow setup. The study raises some important questions on the permeability benchmark study conducted recently [Vernet N, et al. Compos Part A, 61, 172 (2014)]. POLYM. COMPOS., 37:925–935, 2016. © 2014 Society of Plastics Engineers     

A temperature‐dependent adaptive controller. Part II: Design and implementation

A generic online temperature‐dependent adaptive control procedure to redefine the controller parameters was developed from dynamic models to achieve good tracking of injection‐velocity setpoint profiles during filling of a mold cavity. This adaptive control procedure (ACP) incorporates algorithms for process open‐loop testing and modeling, control simulations, and online controller updating. These functionalities are embedded into a main program that provides overall control of mold‐filling velocity. The controller's dynamic matrix is updated as changes in the setpoint melt temperature occur. It was shown that the ACP can provide an effective and systematic approach for controlling injection mold‐filling velocity for any plastic material over its operating melt temperature range. Polym. Eng. Sci. 44:1934–1940, 2004. © 2004 Society of Plastics Engineers.     

Physical and numerical modeling of mold filling in resin transfer molding

Finite element modeling and experimental investigation of mold filling in resin transfer molding (RTM) have been performed. Flow experiments in the molds were performed to investigate resin flow behavior into molds of rectangular and irregular shapes. Silicone fluids with viscosity of 50 and 100 centistoke as well as EPON 826 epoxy resin were used in the mold filling experiments. The reinforcements consisted of several layers of woven fiberglass and carbon fiber mats. The effects of injection pressure, fluid viscosity, type of reinforcement, and mold geometry on mold filling times were investigated. Fiber mat permeability was determined experimentally for the five-harness and eight-harness woven mats. Resin flow through fiber mats was modeled as flow through porous media. Pressure distributions inside both types of molds were also determined numerically. In the case of resin flow into rectangular molds, numerical results agreed well with experimental measurements. Comparison between the experimental and numerical results of the resin front position indicated the importance of edge effects in resin flow behavior in small cavities with larger boundary areas. Reducing the resistance to resin flow at the edge region in the numerical model allowed for good agreement between the numerical simulation and the physical observations of the resin front position and mold filling time.     

Effect of texture on color variation in inkjet‐printed woven textiles

Inkjet‐printed textiles are influenced by a wide range of parameters due to highly diverse textile structures and the resulting textures. The goal of this study is to understand the effect of texture on color appearance in inkjet‐printed woven textiles. Cotton‐woven samples were constructed with nine different weave structures. Each sample was digitally printed with identical squares of primary colors cyan, magenta, and yellow and secondary colors red, green, and blue. The amount of ink applied was controlled consistently with an image editing software. CIE L* values were calculated from the measured reflectance. 25 observers ranked the perceived texture and color lightness of each sample. Perceived visual texture and perceived color lightness scales were estimated from the rankings using the rank order method. The measured CIE L* values and the scale of perceived lightness were positively related for the primary and secondary colors. Instrumental measurements of the textile surface characteristics were positively related to the visual scale. Texture was demonstrated to cause a measurable effect on color results in inkjet printing, both using instrumental and perceptual measures. To investigate if the color differences were substantial enough to cause “out of tolerance” ratings in textiles based on common textile industry color acceptance procedures, color differences among the samples were calculated and compared to a reference sample. Results demonstrated that color variation due to texture was sufficient to lead to rejection of a printed color in comparison to a color specification. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 297–303, 2015     

Simulations and measurements of in‐mold melt flow during the injection molding of polystyrene

Simulations are often used to model polymer flow during injection molding to design molds and select processing parameters. It is difficult to determine the accuracy of these simulations due to a lack of experimentally measured in‐mold velocimetry and melt‐front progression data. This article compares the results from commercial mold‐filling simulation software to experimental data obtained via particle image velocimetry (PIV) in a special optical‐access mold with a rectangular cavity. Moldflow was used to simulate the mold filling by a polystyrene melt in the experimental configuration, and these simulated results are compared to the appropriately averaged time‐varying velocity field measurements. Simulated results for melt‐front progression are also compared with experimentally observed flow fronts. The ratio of the experimentally measured average velocity magnitudes to the simulation magnitudes was found on average to be 0.99 with a standard deviation of 0.25, and the difference in velocity orientations was found to be 0.9° with a standard deviation of 3.2°. The corner area opposite the gate was most problematic for the simulation. The region behind the front also had a relatively high simulation error, though not as severe as that in the corner. POLYM. ENG. SCI. 2013. © 2012 Society of Plastics Engineers     

FEM calculations of capillary rheometer flow for carbon‐filled liquid crystal polymer composites

There is an emerging market for conductive resins for use in fuel cell bipolar plates. This research focuses on developing a finite element model of a capillary rheometer. Comsol Multiphysics 3.2b was used to model the flow of a remeltable thermoplastic matrix material, Vectra A950RX Liquid Crystal Polymer, with varying amounts of either a carbon black or synthetic graphite filler, to obtain the velocity profile and pressure drop of these composites within the capillary. Previous experimental results have shown that the molten composites obey a shear‐thinning power law behavior. When comparing the model predicted pressure drops from the model with the experimental data, very good agreement was obtained. This signifies that the rheological behavior of the composites can be described by a power law relationship, using parameters specific to each composite. When comparing the modeled velocity profile with the theoretical profile, it was found for all composite formulations that the velocity becomes fully developed within a length of 0.05 times the diameter of the tube, independent of the power law parameters n and m. This work is a necessary first step in developing 2D or 3D mold filling simulations for fuel cell bipolar plate applications. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Integrated simulations of structural performance,molding process,and warpage for gas‐assisted injection‐molded parts. III. Simulation of cyclic,transient variations in mold wall temperatures

Whether it is feasible to perform an integrated simulation for structural analysis, process simulation, as well as warpage calculation based on a unified CAE model for gas‐assisted injection molding (GAIM) is a great concern. In the present study, numerical algorithms based on the same CAE model used for process simulation regarding filling and packing stages were developed to simulate the cooling phase of GAIM considering the influence of the cooling system. The cycle‐averaged mold cavity surface temperature distribution within a steady cycle is first calculated based on a steady‐state approach to count for overall heat balance using three‐dimensional modified boundary element technique. The part temperature distribution and profiles, as well as the associated transient heat flux on plastic–mold interface, are then computed by a finite difference method in a decoupled manner. Finally, the difference between cycle‐averaged heat flux and transient heat flux is analyzed to obtain the cyclic, transient mold cavity surface temperatures. The analysis results for GAIM plates with semicircular gas channel design are illustrated and discussed. It was found that the difference in cycle‐averaged mold wall temperatures may be as high as 10°C and within a steady cycle, part temperatures may also vary ∼ 15°C. The conversion of gas channel into equivalent circular pipe and further simplified to two‐node elements using a line source approach not only affects the mold wall temperature calculation very slightly, but also reduces the computer time by 95%. This investigation indicates that it is feasible to achieve an integrated process simulation for GAIM under one CAE model, resulting in great computational efficiency for industrial application. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 339–351, 1999     

A simplified in‐plane permeability model for textile fabrics

In this paper, a simplified in‐plane permeability model for textile fabrics is developed. The model is based on a rectangular unit cell geometry, the one‐dimensional Stokes equation for flow in the channels or gaps between fiber tows, and the one‐dimensional Brinkman equation for flow in fiber tows. Three different textile fabrics are considered in the model: plain woven, 4‐harness, and bidirectional stitched fiberglass mats. The model incorporates the effect of porosity changes on permeability of fiber preforms under compression, which usually occurs in the molding process. To verify the validity of the model, the theoretical values are compared with a set of permeability measurements. Good agreement is found between the model prediction and the permeability measurements in the porosity ranges of ϕ ≤ 0.59 for plain woven fiber mats, ϕ ≤ 0.60 for 4‐harness fiber mats and ϕ ≤ 0.62 for bidirectional stitched fiber mats.     

Computational fluid dynamics applied to the vacuum infusion process

An all‐purpose computational fluid dynamics software is used for simulations of the vacuum infusion process. The study comprises simulations of a full three‐dimensional two‐phase flow through a porous medium. The medium that has an anisotropic, spatial‐ and time‐dependent permeability is located in a complex mold with moving boundaries. With this generalization, different material combinations, processing conditions, and even other manufacturing techniques can be evaluated. The strength of the presented approach is exemplified by simulations of mold filling of a real part, using a typical vacuum infusion set‐up. In addition to the overall development of the model, a number of specific aspects and phenomena are investigated and evaluated. Local lead of the flow front and a minor influence in overall flow front lead‐lag, with no influence on the fill time, is the result of simulations of edge effects due to poor preform fitting. POLYM. COMPOS., 26:231–239, 2005. © 2005 Society of Plastics Engineers