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.     

Simple tools for fiber orientation prediction in industrial practice

In this paper, the two origins of the preferred orientation of fibers are first reviewed. We then propose a definition of what to call an oriented fiber from a practical point of view in the cementitious material field. Considering typical industrial flows and materials, we identify the dominant phenomena and orientation characteristic time involved in the fiber orientation process in the construction industry. We show that shear induced fiber orientation is almost instantaneous at the time scale of a typical casting process. We moreover emphasize the fact that shear induced orientation is far stronger in the case of fluid materials such as self compacting concretes. The proposed approach is validated on experimental measurements in a simple channel flow. Finally, a semi-empirical relation allowing for the prediction of the average orientation factor in a section as a function of the rheological behavior, the length of the fibers and the geometry of the element to be cast is proposed.     

Stereological measurement and error estimates for three-dimensional fiber orientation

A method is presented for measuring three-dimensional fiber orientation in fiber-reinforced polymers and placing confidence limits on the results. The orientations of individual fibers are determined from the elliptical intersections between the cylindrical fibers and a polished section. This can be done using either manual digitization or automated image analysis. Volume averages for the sample are computed using an orientation-dependent weighting function that corrects for the bias of an area-based sample. Equations are developed for nonuniform fiber lengths, using both number-average and weight-average measures of orientation. Sources of systematic, measurement, and sampling error are discussed and equations for sampling error and the propagation of measurement error are derived. The results use a second-rank tensor to characterize fiber orientation, but the error analysis can be applied to any type of orientation parameter. We implement the technique using manual digitization of optical micrographs. Our implementation accurately measures samples with known orientation, and produces identical results from two perpendicular sections of a glass fiber/nylon injection-molded sample.     

Analytical solutions for fiber orientation in 2-D flows of dilute suspensions

Analytical solutions for fiber orientation in dilute solutions are presented for both 2-D planar and axisymmetric flow. The viscosity is assumed to be independent of position along the flow direction, but varies through the thickness of the mold cavity. For the particular case of a laminate of two fluids, an analytical solution is derived. Based upon the assumption that the fluid adjacent to the mold wall exhibits reduced viscosity due to non-isothermal considerations, the fluid kinematics simplify, and an analytical solution to Jeffery's orientation equation is derived. Since the fiber orientation analysis is based on Jeffery's equation, it is valid only for dilute suspensions, i.e. for fiber volume fraction < 1/(fiber aspect ratio)². Qualitatively, the analytical results obtained provide superior correlation with experimental results, indicating that non-isothermal fluid flow may play an important role in the development of the fiber orientation distribution in the molded component.     

Numerical simulation of fiber orientation distribution in round turbulent jet of fiber suspension

The Reynolds averaged Navier–Stokes equation was solved numerically with the Reynolds stress model to get the mean fluid velocity and the turbulent kinetic energy in a round turbulent jet of fiber suspension. The fluctuating fluid velocity was described as a Fourier series with random coefficients. Then the slender-body theory was used to calculate the fiber orientation distribution and orientation tensor. Numerical results of mean axial velocity and turbulent shear stress along the lateral direction were validated by comparing with the experimental ones. The results show that most fibers are aligned with the flow direction as they go downstream, and fibers are more aligned with the flow direction within the region near the jet core. The fibers with high aspect ratio tend much easier to align with the flow direction, and the fiber orientation distribution is not sensitive to fiber aspect ratio when fiber aspect ratio is larger than 5. Fiber density has no obvious influence on the fiber orientation distribution and fiber orientation tensor. The randomizing effect of turbulence is insignificant in the regions near outside and jet core, and becomes significant in the region between outside and jet core. The randomizing effect increases with the increasing of the distance from the jet exit. Different components of fiber orientation tensor show a similar distribution pattern.     

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.     

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.     

Qualitative prediction of the effects of changes in spinning conditions on spun fiber orientation

A simple model, based on an average elongational rate, correctly predicts qualitatively the effects of changes in all spinning parameters on the orientation of fibers spun from viscoelastic melts. The model may be extended to any extrusion process with an elongational character.     

Effects of abrupt expansion geometries on flow‐induced fiber orientation and concentration distributions in slit channel flows of fiber suspensions

Flow‐induced fiber orientation and concentration distributions were measured in channel flows of fiber suspension. The test fluids used are a concentrated fiber suspension (CFS), a semidilute one (SDFS), and a dilute one (DFS). The channel has a thin slit geometry with a 1:16 expansion. In the present work, fiber orientation and concentration distributions are quantitatively evaluated by direct observation of fibers even in the CFS flow. It is found that the weak fiber–fiber interaction of the SDFS largely affects the fiber orientation in the flow with a sudden change such as in the expansion flow, while it is ineffective upon the fiber orientation in the flow without a sudden change such as in the far downstream region. Fiber concentration in the CFS has a flat distribution over a channel width in both the entrance region of the expansion and the downstream region. However, fiber concentration distributions in the SDFS and the DFS have a small and a large peak near the sidewall in the entrance region, respectively, due to the fiber‐wall interaction at the channel wall. These peaks, however, disappeared in the far downstream region after the fibers passed through the expansion. POLYM. COMPOS., 26:660–670, 2005. © 2005 Society of Plastics Engineers.     

Numerical investigation of three-dimensional fiber suspension flow by using finite volume method

Fiber suspension flow is common in many industrial processes like papermaking and fiber-reinforcing polymer-based material forming. The investigation of the mechanism of fiber suspension flow is of significant importance, since the orientation distribution of fibers directly influences the mechanical and physical properties of the final products. A numerical methodology based on the finite volume method is presented in the study to simulate three-dimensional fiber suspension flow within complex flow field. The evolution of fiber orientation is described using different formulations including FT model and RSC model. The pressure implicit with splitting of operators algorithm is adopted to avoid oscillations in the calculation. A laminate structure of fiber orientation including the shell layer, the transition layer and the core layer along radial direction within a center-gated disk flow channel is predicted through a three-dimensional simulation, which agrees well with Mazahir’s experimental results. The evolution of fiber orientation during the filling process within the complex flow field is further discussed. The mathematical model and numerical method proposed in the study can be successfully adopted to predict fiber suspension flow patterns and hence to reveal the fiber orientation mechanism.     

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.     

The prediction of flow and orientation behavior of short fiber reinforced melts in simple flow systems

A model for the prediction of changes in fiber orientation in simple flows of fiber suspensions is proposed. Fiber interactions are modeled as randomizing forces over the rotation of fibers in closed orbits in simple shear. The resulting Fokker-Planck type convection-diffusion equation in orientation space is solved using a finite difference technique. The solution technique permits the use of periodic boundary condition for the convection-diffusion equation and different initial conditions for the orientation distribution. The model predictions for simple shear flow demonstrate the interaction between the structural changes and the bulk rheological properties. The effect of non-Newtonian fluid properties on the orientation distribution was also incorporated at the slow flow limit. Structural changes are assumed to be irreversible. The irreversibility is incorporated through an orientation distribution dependent diffusion coefficient.     

The role of the interaction coefficient in the prediction of the fiber orientation in planar injection moldings

The mechanical properties of injection molded parts in glass reinforced materials are sensitive to processing. A successful design requires a good estimate of the product performance before production. Its performance is strongly affected by the fiber orientation field set up during processing. The fiber orientation pattern is complex and varies three‐dimensionally in the moldings. Some commercial simulation programs already allow the prediction of the fiber orientation induced during the flow by the associated stress field. The results from the simulations are dependent on a parameter accounting for the interactions between fibers during the flow, known as the fiber interaction coefficient. In this paper the effectiveness of the interaction parameter on controlling the predicted patterns of the fiber orientation is studied. This is done by comparing and analyzing the experimental data and the corresponding predictions.     

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 prediction of flake orientation and surface color in injection molding of flake‐pigmented thermoplastics

The present study attempts to develop physical modeling and numerical simulation system for prediction of the surface color in injection molding of flake‐pigmented thermoplastic composites. Folgar–Tucker model along with the orientation tensor is employed to predict the orientation state of pigment flakes. A phenomenological relationship between the orientation state and the surface color is proposed to estimate the surface color and color defects from the orientation prediction result. Basic studies are carried out using simple geometries with a hole or rib structure. Also a qualitative comparison between the numerical prediction and the experimental result is carried out for a complex geometry having ribs and holes. The color defects such as flow marks and weld lines could be reasonably predicted using the developed modeling and simulation system. POLYM. COMPOS., © 2011 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     

Numerical analysis of injection molding of glass fiber reinforced thermoplastics. Part 2: Fiber orientation

Numerical predictions of fiber orientation during injection molding of fiber-filled thermoplastics are compared to measurements. The numerical work successfully describes the flow of fiber-filled plastic during injection molding, using finite-difference solutions for the transport equations and marker particles to track the flow front. The flow is modeled as a 2-D, non-isothermal, free-surface flow with a new viscosity model dependent upon temperature, pressure, and fiber concentration. The fiber orientation is based upon solution to the Fokker-Planke equation. The comparison demonstrates fair agreement between predicted fiber orientation and experimental results for slow and fast injection speeds. For the slow speed case at 10 and 20 wt% fibers, the numerical and experimental works show that the fibers are more random at the flow front than at the centerline, and that the fibers become more aligned as they flow from the gate to the midstream region. At fast injection speeds, the agreement between the numerical and experimental works is not as good as at slow injection speed. Possible explanations for the discrepancies are that the flow is assumed to be simple shear when injection molding is known to be a pressure-driven flow, the fibers have an initial orientation for the runner rather than the assumed random orientation, the fibers that were displayed from the camera were more oriented just behind the flow front (owing to the fast injection speed), and the orientation requires more than a 2-D video image to represent a 3-D fiber orientation.     

Rheological behavior and fiber orientation in slit flow of fiber reinforced thermoplastics

The flow behavior and fiber orientation in slit flow of a short fiber reinforced thermoplastic composite melt are investigated. A slit die with adjustable gap and interchangeable entrance geometries was designed and built. The slit die is fed by a single screw extruder. The bulk viscosity is calculated from the axial pressure profiles measured using three flush mounted pressure transducers. The effect of entrance geometry and gap dimensions on the fiber orientation and bulk flow behavior is specifically considered. A skin-core composite fiber orientation is observed in the thickness direction. Fibers are oriented in the flow direction and parallel to the walls in the skin region irrespective of the entrance geometry. Different fiber orientation distributions in the core region can be realized by using different entrance geometries. However, the changes in the core fiber orientation are not fully reflected by the measured viscosities, due to highly oriented skin layer. Exit pressures obtained by extrapolation of linear pressure profiles are found to be all positive, but dependent on the die geometry and entrance conditions, even for the unfilled melts.