Nonisothermal transient filling simulation of fiber suspended viscoelastic liquid in a center‐gated disk

The present study numerically investigates a fiber orientation in injection‐molded short fiber reinforced thermoplastic composite by using a rheological model, which includes the nonlinear viscoelasticity of polymer and the anisotropic effect of fiber in the total stress. A nonisothermal transient‐filling process for a center‐gated disk geometry is analyzed by a finite element method using a discrete‐elastic‐viscous split stress formulation with a matrix logarithm for the viscoelastic fluid flow and a streamline upwind Petrov–Galerkin method for convection‐dominated problems. The numerical analysis result is compared to the experimental data available in the literature in terms of the fiber orientation in center‐gated disk. The effects of the fiber coupling and the slow‐orientation kinetics of the fiber are discussed. Also, the effect of the injection‐molding processing condition is discussed by varying the filling time and the mold temperature. POLYM. COMPOS., 2011. © 2010 Society of Plastics Engineers     

Investigation of fiber orientation states in injection‐compression molded short‐fiber‐reinforced thermoplastics

Injection‐compression molding (ICM) has received increased attention because of its advantages over conventional injection molding (CIM). This article aims to investigate the effects of five dominating ICM processing parameters on fiber orientation in short‐fiber‐reinforced polypropylene (SFR‐PP) parts. A five‐layer structure of fiber orientation is found across the thickness under most conditions in ICM parts. This is quite different from the fiber orientation patterns in CIM parts. The fibers orient orderly along the flow direction in the shell region, whereas most fibers arrange randomly in the skin and the core regions. Additionally, the fiber orientation changes in the width direction, with most fibers arranging orderly along the flow direction at positions near the mold cavity wall. The results also show that the compression force, compression distance, and compression speed play important roles in determining the fiber states. Thicker shell regions, in which most fibers orient remarkably along the flow direction, can be obtained under larger compression force or compression speed. Moreover, the delay time has an obvious effect on the fiber orientation at positions far from the gate. However, the effect of compression time is found to be negligible. POLYM. COMPOS., 31:1899–1908, 2010. © 2010 Society of Plastics Engineers.     

Improved through‐plane electrical conductivity in a carbon‐filled thermoplastic via foaming

Flow‐induced orientation of the conductive fillers in injection molding creates parts with anisotropic electrical conductivity where through‐plane conductivity is several orders of magnitude lower than in‐plane conductivity. This article provides insight into a novel processing method using a chemical blowing agent to manipulate carbon fiber (CF) orientation within a polymer matrix during injection molding. The study used a fractional factorial experimental design to identify the important processing factors for improving the through‐plane electrical conductivity of plates molded from a carbon‐filled cyclic olefin copolymer (COC) containing 10 vol% CF and 2 vol% carbon black. The molded COC plates were analyzed for fiber orientation, morphology, and electrical conductivity. With increasing porosity in the molded foam part, it was found that greater out‐of‐plane fiber orientation and higher electrical conductivity could be achieved. Maximum conductivity and fiber reorientation in the through‐plane direction occurred at lower injection flow rate and higher melt temperature. These process conditions correspond with foam flow during filling of the mold cavity, indicating the importance of shear stress on the effectiveness of a fiber being rotated out‐of‐plane during injection molding. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Coupled analysis of injection molding filling and fiber orientation,including in-plane velocity gradient effect

On injection molding of short fiber reinforced plastics, fiber orientation during mold filling is determined by the flow field and the interactions between the fibers. The flow field is, in turn, affected by the orientation of fibers. The Dinh and Armstrong rheological equation of state for semiconcentrated fiber suspensions was incorporated into the coupled analysis of mold filling flow and fiber orientation. The viscous shear stress and extra shear stress due to fibers dominate the momentum balance in the coupled Hele-Shaw flow approximation, but the extra in-plane stretching stress terms could be of the same order as those shear stress terms, for large in-plane stretching of suspensions of large particle number. Therefore, a new pressure equation, governing the mold filling process, was derived, including the stresses due to the in-plane velocity gradients. The mold filling simulation was then performed by solving the new pressure equation and the energy equation via a finite element/finite difference method, as well as evolution equations for the second-order orientation tensor via the fourth-order Runge-Kutta method. The effects of stresses due to the in-plane velocity gradient on pressure, velocity, and fiber orientation fields were investigated in the center-gated radial diverging flow in the cases of both an isothermal Newtonian fluid matrix and a nonisothermal polymeric matrix. In particular, the in-plane velocity gradient effect on the fiber orientation was found to be significant near the gate, and more notably for the case of a nonisothermal polymer matrix.     

Numerical simulation of fiber orientation in injection molding of short-fiber-reinforced thermoplastics

The present study develops a numerical simulation program to predict the transient behavior of fiber orientations together with a mold filling simulation for short-fiber-reinforced thermoplastics in arbitrary three-dimensional injection mold cavities. The Dinh-Armstrong model including an additional stress due to the existence of fibers is incorporated into the Hele-Shaw equation to result in a new pressure equation governing the filling process. The mold filling simulation is performed by solving the new pressure equation and energy equation via a finite element/finite difference method as well as evolution equations for the second-order orientation tensor via the fourth-order Runge-Kutta method. The fiber orientation tensor is determined at every layer of each element across the thickness of molded parts with appropriate tensor transformations for arbitrary three-dimensional cavity space.     

Prediction of fiber orientation in injection molded parts of short-fiber-reinforced thermoplastics

Fiber orientation induced by injection mold filling of short-fiber-reinforced thermoplastics (FRTP) causes anisotropy in material properties and warps molded parts. Predicting fiber orientation is important for part and mold design to produce sound molded parts. A numerical scheme is presented to predict fiber orientation in three-dimensional thin-walled molded parts of FRTP. Folgar and Tucker's orientation equation is used to represent planar orientation behavior of rigid cylindrical fibers in concentrated suspensions. The equation is solved about a distribution function of fiber orientation by using a finite difference method with input of velocity data from a mold filling analysis. The mold filling is assumed to be nonisothermal Hele-Shaw flow of a non-Newtonian fluid and analyzed by using a finite element method. To define a degree of fiber orientation, an orientation parameter is calculated from the distribution function against a typical orientation angle. Computed orientation parameters were compared with measured thermal expansion coefficients for molded square plates of glass-fiber-reinforced polypropylene. A good correlation was found.     

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.     

Numerical and experimental investigations on polymer melt flow phenomenon in a vario‐thermal mold cavity

Mold temperature is one of the key factors affecting the morphology and quality of plastic parts. This article explores the melt flow phenomena in a vario‐thermal mold cavity. A coupled numerical method, considering the conjugate heat transfer between the mold and melt, is developed for the melt flow simulation. Mold temperature variations and melt flow phenomena for short shot injection in an electrical heated mold cavity are numerically studied and verified by experiments. The results indicate that the melt flow length and cavity filling ratio increase significantly with the elongation of the preheating time before injection. Melt filling ratio increased nearly linearly with the increasing of electric heating time. The smaller the injection pressure is, the bigger the relative filling ratio increment is. Therefore, polymer melt can flow much longer or the mold cavity can be filled up with a smaller injection pressure when the cavity is preheated. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45193.     

Edge effect in RTM processes under constant pressure injection conditions

In resin transfer molding processes, the edge effect caused by the nonuniformity of permeability between fiber preform and edge channel may disrupt resin flow patterns and often results in the incomplete wetting of fiber preform, the formation of dry spots, and other defects in final composite materials. So a numerical simulation algorithm is developed to analyze the complex mold‐filling process with edge effect. The newly modified governing equations involving the effect of mold cavity thickness on flow patterns and the volume‐averaging momentum equations containing viscous and inertia terms are adopted to describe the fluid flow in the edge area and in the fiber preform, respectively. The volume of fluid (VOF) method is applied to tracking the free interface between the two types of fluids, namely the resin and the air. Under constant pressure injection conditions, the effects of transverse permeability, edge channel width, and mold cavity thickness on flow patterns are analyzed. The results demonstrate that the transverse flow is not only affected by the transverse permeability and the edge channel width but also by the mold cavity thickness. The simulated results are in agreement with the experimental results. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Prediction of fiber orientation in a rotating compressing and expanding mold

In the rotating/compressing/expanding mold (RCEM), one mold wall can expand, compress, and rotate during injection molding, thus offering opportunities to control the thermomechanical history of a polymer and its microstructure. A computer simulation of flow and fiber orientation in RCEM was developed. The predictive model extends the generalized Hele‐Shaw formulation to account for compression/expansion and rotation of the mold wall, and uses the Folgar–Tucker model for fiber orientation predictions. A 20% GF polypropylene was molded under various molding conditions. The predicted fiber orientation distributions were compared with experiments. The model compares favorably with experiments, provided that the fiber orientation equation is modified by a strain‐reduction factor that slows the transient development of fiber alignment. The effect of fountain flow on orientation must also be included to correctly predict fiber orientation near the mold walls, mainly for the case of stationary and linear motions of the mold surface. Compression or expansion of the mold has only a small effect on fiber orientation, but rotation of the mold dramatically changes the orientation, causing fibers to align in the tangential direction across the entire thickness of the molding. This rotation action perturbs the fountain flow and becomes the dominant factor affecting fiber alignment across the entire cavity thickness. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

Effect of packing pressure on fiber orientation in injection molding of fiber‐reinforced thermoplastics

Injection molding of fiber‐reinforced polymeric composites is increasing with demands of geometrically complex products possessing superior mechanical properties of high specific strength, high specific stiffness, and high impact resistance. Complex state of fiber orientation exists in injection molding of short fiber reinforced polymers. The orientation of fibers vary significantly across the thickness of injection‐molded part and can become a key feature of the finished product. Improving the mechanical properties of molded parts by managing the orientation of fibers during the process of injection molding is the basic motivation of this study. As a first step in this direction, the present results reveal the importance of packing pressure in orienting the fibers. In this study, the effects of pressure distribution and viscosity of a compressible polymeric composite melt on the state of fiber orientation after complete filling of a cavity is considered experimentally and compared with the simulation results of Moldflow analysis. POLYM. COMPOS. 28:214–223, 2007. © 2007 Society of Plastics Engineers     

Prediction of fiber orientation in the injection molding of long fiber suspensions

The properties of long glass fiber reinforced parts are highly dependent on the fiber orientation generated during processing. In this research, the orientation of concentrated long glass fibers generated during the filling stage of a center‐gated disk (CGD) mold was simulated. The orientation of the fibers was calculated using both the Folgar‐Tucker model and a recently developed semiflexible Bead‐Rod model. Rheologically consistent model parameters were used in these simulations, as determined from a previously proposed method, using a sliding plate rheometer and newly modified stress theory. The predicted CGD orientations were compared with experimentally measured values obtained from the parts. Both models performed very well when using model parameters consistent with the independent rheological study, and the results provide encouragement for the proposed method. Comparatively, the Folgar‐Tucker model provided slightly better orientation predictions up to 20% of the fill radius, but above 20% the Bead‐Rod model predicted better values of the orientation in both the radial and circumferential directions. The Folgar‐Tucker model, however, provided better orientation values perpendicular to the flow direction. Lastly, both models only qualitatively represented the orientation above 70% of the fill radius where frontal flow effects were suspected to be non‐negligible. The uniqueness of this research rests on a method for obtaining model parameters needed to predict fiber orientation which are independent of the experiments being simulated and a method for handling long semiflexible fiber suspensions. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers     

Thermal response of an electric heating rapid heat cycle molding mold and its effect on surface appearance and tensile strength of the molded part

Rapid heat cycle molding (RHCM) is a newly developed injection molding technology in recent years. In this article, a new electric heating RHCM mold is developed for rapid heating and cooling of the cavity surface. A data acquisition system is constructed to evaluate thermal response of the cavity surfaces of the electric heating RHCM mold. Thermal cycling experiments are implemented to investigate cavity surface temperature responses with different heating time and cooling time. According to the experimental results, a mathematical model is developed by regression analysis to predict the highest temperature and the lowest temperature of the cavity surface during thermal cycling of the electric heating RHCM mold. The verification experiments show that the proposed model is very effective for accurate control of the cavity surface temperature. For a more comprehensive analysis of the thermal response and temperature distribution of the cavity surfaces, the numerical‐method‐based finite element analysis (FEA) is used to simulate thermal response of the electric heating RHCM mold during thermal cycling process. The simulated cavity surface temperature response shows a good agreement with the experimental results. Based on simulations, the influence of the power density of the cartridge heaters and the temperature of the cooling water on thermal response of the cavity surface is obtained. Finally, the effect of RHCM process on surface appearance and tensile strength of the part is studied. The results show that the high‐cavity surface temperature during filling stage in RHCM can significantly improve the surface appearance by greatly improving the surface gloss and completely eliminating the weld line and jetting mark. RHCM process can also eliminate the exposing fibers on the part surface for the fiber‐reinforced plastics. For the high‐gloss acrylonitrile butadiene styrene/polymethyl methacrylate (ABS/PMMA) alloy, RHCM process reduces the tensile strength of the part either with or without weld mark. For the fiber‐reinforced plastics of polypropylene (PP) + 20% glass fiber, RHCM process reduces the tensile strength of the part without weld mark but slightly increases the tensile strength of the part with weld mark. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Prediction of fiber orientation in the thickness plane during flow molding of short fiber composites

Fiber orientations caused by the flow in the thickness plane during injection molding of short fiber reinforced polymer composites has been simulated. The Lagrangian scheme was employed for the finite element analysis. Flow fields were solved by using a penalty method with Uzawa's scheme and orientation fields were also solved by using the second order orientation tensor. A generalized Newtonian fluid whose rheological behavior is independent of fiber orientation was assumed. Automatic mesh generation using an elliptic grid generator was developed for quadrilateral elements. Mold filling and orientation analyses were performed for a cavity of rectangular cross section. To determine the orientation state in other cross-sectional geometries, numerical analyses were also performed for two different typical cross sections. As the result, orientation of short fibers in the flow field was analyzed qualitatively and quantitatively. According to the state of short fiber orientation in the thickness plane, the orientation field can be classified into three regions in the flow direction and three layers in the thickness direction. Orientation of short fibers was mainly influenced by elongational and shear flows. It was observed that critical values are present for upper limits of orientation. Effects of initial orientation at the inlet on the orientation field were examined.     

Three‐dimensional simulation of microchip encapsulation process

A finite element simulation of moving boundaries in a three‐dimensional inertiafree, incompressible flow is presented. A control volume scheme with a fixed finite element mesh is employed to predict fluid front advancement. Fluid front advancement and pressure variation in a flow domain similar to the mold cavity used for microchip encapsulation are predicted. The predicted fluid front advancement and pressure variation are in good agreement with the corresponding experimental results. As the difference in the thicknesses of mold cavities above and below the microchip is changed, the weld line location and pressure variation during mold filling are found to change significantly.     

Determination of the heat transfer coefficient from short‐shots studies and precise simulation of microinjection molding

The filling process of a micro‐cavity was analyzed by modeling the compressible filling stage by using pressure‐dependent viscosity and adjusted heat transfer coefficients. Experimental filling studies were carried out at the same time on an accurately controlled microinjection molding machine. On the basis of the relationship between the injection pressure and the filling degree, essential factors for the quality of the simulation can be identified. It can be shown that the flow behavior of the melt in a micro‐cavity with a high aspect ratio is extremely dependent on the melt compressibility in the injection cylinder. This phenomenon needs to be considered in the simulation to predict an accurate flow rate. The heat transfer coefficient between the melt and the mold wall that was determined by the reverse engineering varies significantly even during the filling stage. With increasing injection speed and increasing cavity thickness, the heat transfer coefficient decreases. It is believed that the level of the cavity pressure is responsible for the resulting heat transfer between the polymer and the mold. A pressure‐dependent model for the heat transfer coefficient would be able to significantly improve the quality of the process simulation. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Glass fiber-filled thermoplastics. II. Cavity filling and fiber orientation in injection molding

Mold filling of a rectangular cavity of three different thick nesses fed from a reservoir is studied for unfilled and glass fiber-filled polypropylene and polystyrene. The shapes of flow fronts studied by short-shots are affected predominantly by the thickness of the cavity with other parameters playing a less important role. Pressure drop versus volumetric flow rate inside the thinnest cavity is studied experimentally and predictions are made from a computer simulation of mold filling. The orientation of fibers in the cavity is examined using a reflect-type microscope and the orientation is found to depend on cavity thickness, melt temperature, fiber content, and to a lesser extent, on volumetric flow rate. In the thinnest cavity, where the flow is quasi-unidirectional, the fibers remain in the plane of flow oriented either along the flow direction or perpendicular to it, except in the region near the flow front, where they follow a “fountain” flow behavior.     

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.     

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.     

In‐line monitoring of the injection molding process by dielectric spectroscopy

In recent years, electrical techniques like microdielectrometry have increasingly been utilized for their ability to continuously monitor, in a nondestructive way, the advancement of the reaction of thermoset resins under cure. This paper discusses an extension of this technique for the “in‐situ” monitoring of the crystallization of thermoplastics applied during an injection molding process. Electric sensors were positioned at the walls of the mold cavity so that an analysis of the volume dielectric properties of material during the filling, the post‐filling, and the cooling steps could be carried out. Poly(vinylidene fluoride) was chosen for this study. A correlation between the evolution of the dielectric parameters and the succession of the steps in this process was undertaken. The dielectric response was sufficiently sensitive to identify the steps of the closing of the mold, filling, post‐filling, cooling, and ejection of the part. In addition, information concerning the crystallization phenomenon near the wall or in the middle of the sample was collected. The gradual filling of the cavity of the mold was also identified by dielectric measurements. The temperature dependence of dielectric properties of the sample was beneficial in evaluating the increase of the temperature of the mold with the succession of injection cycles. The influence of the packing pressure has been clearly identified and confirms the usefulness of the dielectric method as a probe for detecting the shrinkage of the part during the optimization phase of the machine parameters. The dielectric method detailed herein provides a new non‐invasive technique and could be applied to a closed‐loop control of the injection molding process.