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.     

Applications of a fiber orientation prediction algorithm for compression molded parts with multiple charges

An application of a finite element simulation of mold filling and predication of fiber orientation in fiber filled compression molded parts is presented. Three-dimensional thin-walled geometries are considered. Following a simulation of the filling process, a set of transort equations are solved to predict the locally planar orientation of short fiber composites. The final orientation states throughout the part provide the necessary information to obtain a locally orthotropic mechanical model of the composite. A sheet molding compound part with a multiple charge pattern is used to illustrate the generality of the algorithms developed for compression flow, fiber orientation, and property predications. Derivations of the orthotropic mechanical properties obtained from the fiber orientation results are outlined.     

Mechanical properties of short fiber reinforced thermoplastic composites —I. Elastic properties and predictions

Twin roll-mill and compression molding machines were used to process the unidirectional ply of short fiber reinforced thermoplastics (FRTP). FRTP laminates were prepared by compression molding of angle plies with the desired stacking sequences.The fiber length and orientation distributions in FRTP took place after processing. Therefore, a statistical distribution function such as WeiBull distribution function was applied to represent the existing fiber length distribution. The orientation distribution in FRTP was characterized by a single parameter exponential function. Elastic moduli of the unidirectional ply were predicted by the Halpin-Tsai equation where the fiber length distribution was introduced to the estimation. The overall elastic moduli of laminates were estimated based on the simulated laminate-plate method. A comparison of measured elastic moduli with theoretical predicted results from unidirectional ply and laminate was discussed in this study.     

Effects of fiber length and orientation distribution on the elastic modulus of short fiber reinforced thermoplastics

A method including the effects of fiber length and orientation distribution to predict elastic moduli of short fiber reinforced thermplastics (FRTP) is presented. The fiber length distribution in FRTP has an asymmetric character with a tail at the long fiber end. Statistical distribution functions such as Weibull or log-normal can be used to represent this kind of distribution. Orientation distribution of fibers in FRTP can be characterized by a single parameter exponential function, $F(\theta) = \frac{{1 - \lambda \theta }}{{1 - e^{ - \frac{\P}{2}\lambda } }}$. A large λ indicates a highly oriented material whereas small λ represents a quasi-isotropic material. As fiber length and orientation distribution functions have been characterized, the elastic moduli of FRTP can be predicted. First, the mean elastic moduli of unidirectional plies are predicted through the fiber length distribution. Then the stacking sequence of laminate is assumed to be as the fiber orientation distribution of FRTP, and the overall elastic moduli of FRTP are estimated based on the laminate-plate method.     

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.     

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     

Experimental study and calculations of short glass fiber orientation in a center gated molded disc

Short glass fiber orientation in a center gated molded disc of polyamide is studied using optical microscopy techniques. The very different orientation between the core and the surface of the molding is quantified with an orientation function. The influence of the molding conditions is investigated. A numerical scheme is used for modeling the mold filling with a viscous melted polymer. A computation method is introduced to describe the fiber movement during the flow. The theoretical results are in good agreement with the experimental ones. In particular, the very different orientation between the skin and the core of the disc is well predicted.     

A numerical simulation of short fiber orientation in compression molding

A computer simulation has been developed to predict the orientation of fibers in a thin, flat part that is compression molded from sheet molding compound. The simulation combines a finite element/control volume simulation of the mold filling flow, a second order tensor representation of the fiber orientation state and a finite element calculation for the transient orientation problem. Sample results and comparison with experiments are presented. Predictions compare favorably with experiments on SMC (sheet molding compound) plaques and a model suspension of nylon fibers and silicon oil.     

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 prediction of fiber orientation in injection molding

We develop a numerical method for calculating fiber orientation in the midsurface of a molded part of small thickness. Two-dimensional fiber orientation is predicted on the basis of either Jeffery's equation or a constitutive equation for the orientation tensor. The calculation is fully transient; it is performed on a time-dependent flow domain. The method is based on finite elements. Updated finite element meshes are generated at every instant of filling and allow one to perform an accurate calculation of the orientation even along the boundary of the flow domain. The method is applied to several examples in plane and three-dimensional geometries.     

Process induces fiber orientation: Numerical simulation with experimental verification

The performance of short fiber molded composite structures is determined uniquely by the properties of the molding material and the process induced fiber orientation. Consequently, the capability to accurately predict the fiber orientation distribution is of fundamental importance in computer-aided mold design. Methodology for the numerical prediction of fiber orientation during the mold-fill process is presented for a short glass fiber thermoset (57 percent phenolic resin, 10 percent calcium carbonate filler, and 33 percent glass fiber by volume). On the basis of a finite element flow characterization, Jeffery's orientation equation is numerically integrated along streamlines to calculate fiber orientation. Correlation of experimental and numerical results for an end-gated bar with a molded-in hole is reasonably good.     

Predicting shrinkage and warpage of fiber-reinforced composite parts

One major problem that arises in the design of plastic parts, especially those that are fiber reinforced, is the change of shape and dimension as a result of shrinkage and warpage. These material inhomogeneities are caused by flowinduced fiber orientation, curing, poor thermal mold lay-out, and other processing conditions. This paper presents a simulation that predicts shirnkage and warpage of 3-D compression molded fiber reinforced composite parts. The simulation represents the structure with the 3-noded shell elements used in mold filling simulations. The calculated results indicate that fiber orientation strongly affect the final properties, which vary with different chage locations, have a significant effect on warpage. Unsymmetric curing, caused by uneven mold temperatures, could lead to a thermal moment that could possibly help reduce warpage.     

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     

Effects of flow induced orientation of ferromagnetic particles on relative magnetic permeability of injection molded composites

Composite samples consisting of ferromagnetic asymmetric particles incorporated into a polyolefin binder were injection molded using custom designed molds which produced preferential fiber orientations. The relative magnetic permeability values of the composites were measured as a function of the filler volume fraction, injection rate, gate diameter, temperature, aspect ratio of the fibers, and fiber orientation. Fiber orientation was affected by the molding conditions and controlled the relative magnetic permeability of the composites. The degree of fiber orientation was significantly affected by the size of the opening (gate) to the mold, or by the mold geometry going from an edge-gated cylindrical to a center-gated disk cavity. Relative permeability values of the composites were observed to increase when the fiber orientation and the applied field were parallel to one another. For instance, highly aligned composite samples exhibited up to 30% greater relative permeability values compared to those samples which exhibit fiber orientation distributions approaching a random distribution. To our knowledge this is the first study that provides data linking the fiber orientation distribution functions of ferromagnetic asymmetric particles to the relative magnetic permeability values of injection molded composites.     

Integrated simulation to predict warpage of injection molded parts

Injection molding analysis programs were developed for CAE (Computer Aided Engineering) in injection molding of thermoplastics. The programs consist of mold cooling, polymer filling-packing-cooling, fiber orientation, material properties and stress analyses. These programs are integrated to predict warpage of molded parts by using a common geometric model of three dimensional thinwalled molded parts. The warpage is predicted from temperature difference between upper and lower surfaces, temperature distribution, flow induced shear stress, shrinkage, and anisotropic mechanical properties caused by fiber orientation in the integrated simulation. The integrated simulation was applied to predicting warpage of a 4-ribbed square plate of glass fiber reinforced polypropylene for examination of its validity. Predicted saddle-like warpage was in good agreement with experimental one.     

Volumetric effects in the injection molding of polymers

Density and shrinkage measurements have been performed in quenched and molded slabs from polystyrene (PS) and poly (methylmethacrylate) (PMMA). Various processing conditions have been employed and their effect on density and shrinkage variation in the final parts, as well as volumetric aging vs. Elapsed time at room temperature, have been elucidated. A numerical simulation of the density variation in quenched parts and their aging has been performed by using first-order rate theory for volumetric changes in conjunction with solving the transient one-dimensional heat-conduction equation with a convective heat-transfer boundary condition at surface. A numerical simulation of the shrinkage in molded parts has been carried out by using the equation of state with a simultaneous solving of the governing equations for one-dimensional mold filling during the cavity filling stage followed by transient one-dimensional conduction during packing and cooling stages. Predicted results for density and shrinkage are compared with experimental data.     

Reaction injection molding process of glass fiber reinforced polyurethane composites

Structural reaction injection molding (SRIM) was used to produce polyurethane composites containing random continuous glass fiber mats. A long rectangular mold was used to carry out the SRIM experiments. 4,4′‐diphenylmethane diisocyanate and poly(propylene oxide) triol were used to formulate a thermoset polyurethane system. Dibutyltin dilaurate was used as a catalyst. A second order Arrhenius equation described the PU polymerization kinetic data obtained from the adiabatic temperature rise measurement. A viscosity as a function of temperature and conversion was developed using rheometer data. The pressure rise at the gate was measured during filling. The flow behavior within the mold was described by Darcy's law and the Kozeny's equation. The temperature profile within the mold measured by thermocouples during filling and curing coincided fairly well with the simulation results. The thermal transient problem at the wall was solved using the overall heat transfer coefficient, and it was analyzed as a function of Biot number. The dimensional stability of the fiber reinforced PU parts was excellent compared to the pure PU parts.     

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.     

Analysis of the packing stage of a viscoelastic melt

The packing stage starts at the end of mold filling. During this stage, additional material is forced into the mold to compensate for the shrinkage during subse-quent cooling. Underpacking results in molded parts with dimensional variation. Overpacking causes flash at the parting lines, stick during ejection, and excess residual stresses resulting in warpage. The packing stage is thus extremely important in the determination of the final quality of the product. Despite its importance, analysis of the packing stage has been relatively ignored, particularly the viscoelastic effect. In this work, the analysis of the isothermal packing stage is presented for a Maxwell fluid. A set of governing equations is derived for a two-dimensional mold and solved using the Galerkin finite element method. In addition to the distribution of velocity and pressure, the model predicts the stresses in the planar direction, which could be used for subsequent calculation of the residual stresses.     

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.