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.     

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 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.     

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.     

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.     

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.     

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.     

A finite element/control volume approach to mold filling in anisotropic porous media

Mold filling in anisotropic porous media is the governing phenomena in a number of composite manufacturing processes, such as resin transfer molding (RTM) and structural reaction injection molding (SRIM). In this paper we present a numerical simulation to predict the flow of a viscous fluid through a fiber network. The simulation is based on the finite element/control volume method. It can predict the movement of a free surface flow front in a thin shell mold geometry of arbitrary shape and with varying thickness. The flow through the fiber network is modeled using Darcy's law. Different permeabilities may be specified in the principal directions of the preform. The simulation permits the permeabilities to vary in magnitude and direction throughout the medium. Experiments were carried out to measure the characteristic permeabilities of fiber preforms. The results of the simulation are compared with experiments performed in a flat rectangular mold using a Newtonian fluid. A variety of preforms and processing conditions were used to verify the numerical model.     

Analysis of resin transfer/compression molding process

Resin transfer/compression molding (RT/CM) is a two-step process in which resin injection is followed by mold closing. This process can enhance the resin flow speed and the fiber volume fraction, as well as reducing the mold filling time. In this study, a simulation program for the mold filling process during RT/CM was developed using the modified control volume finite element method (CVFEM) along with the fixed grid method. The developed numerical code can predict the resin flow, temperature, pressure, and degree of cure distribution during RT/CM. The compression force required for squeezing the impregnated preform can also be calculated. Experiments were performed for a complicated three-dimensional shell to verify the feasibility of the RT/CM process and the numerical scheme. The compression force and the compression speed were measured. A close agreement was found between the experimental data and the numerical results. The resin front location obtained from a short shot experiment was compared with the numerical prediction. Again, a close agreement was observed. In order to demonstrate the effectiveness of the numerical code, simulations were performed for more complicated process conditions with anisotropic permeability of the preform at higher fiber volume fractions.     

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     

Fiber orientation in simple injection moldings. Part I: Theory and numerical methods

This paper sets out the theory and numerical methods used to simulate filling and fiber orientation is simple injection moldings (a film-gated strip and a center-gated disk). Our simulation applies to these simple geometry problems for the flow of a generalized Newtonian fluid where the velocities can be solved independently of fiber orientation. This simplification is valid when the orientation is so flat that the fibers do not contribute to the gapwise shear stresses. A finite difference solution calculates the temperature and velocity fields along the flow direction and through the thickness of the part, and fiber orientation is then integrated numerically along pathlines. Fiber orientation is three-dimensional, using a second-rank tensor representation of the orientation distribution function. The assumptions used to develop the simulation are not valid near the flow front, where the recirculating fountain flow complicates the problem. We present a numerrical scheme that includes the effect of the fountain flow on temperature and fiber orientation near the flow front. The simulation predicts that the orientation will vary through the thickness of the part, causing the molding to appear layered. The outer “skin” layer is predicted only if the effects of the fountain flow and heat transfer are included in the simulation.     

A model of compression mold filling

A model is proposed for the flow, reaction, and heat transfer during compression molding of thin, flat parts. The isothermal Newtonian version of the model is implemented using the finite element method, and is capable of handling arbitrary planar geometries. Automated mesh expansion and boundary condition modification allow the simulation to run without operator interaction. The model accurately predicts mold filling pattern for non-Newtonian and non-isothermal flows.     

树脂传递模塑充填过程的数值模拟

树脂传递模塑成型（RTM）工艺是在一定温度及压力下把低黏度的树脂注入预先置有增强纤维的模具中,然后固化成型的一种复合材料液体成型方法。本文建立了RTM工艺充模过程的数学模型,并采用有限元/控制体积法实现了对复杂薄壁构件的充填模式、压力场和速度场的模拟。     

Numerical prediction of three-dimensional fiber orientation in Hele-Shaw flows

A numerical technique is developed to determine the three-dimensional fiber orientation in complex flows. The fiber orientation state is specified in terms of orientation tensors, which are used in several constitutive models. This method is applied to quasi-steady state Hele-Shaw flows in order to predict the flow-induced fiber orientation during injection molding at zero volume fraction limit. At the inlet, a number of fibers are introduced at a specified rate into the flow and each fiber location is traced during the mold filling. Along these determined paths, the independent components of fourth order orientation tensors are solved, describing the orientation state. The numerical grid generation technique, which is suitable for complex mold shapes, is employed for the flow solution. Orientation ellipsoids are calculated from the second order tensors and are used to present the fiber orientation results. The numerical solutions are obtained for channel and converging flows. Planar, longitudinal, and transverse orientation results are generated from the orthogonal projections of the orientation ellipsoids.     

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.     

Simulation of the injection process in resin transfer molding

A simulation based on Darcy's law for modeling mold filling in resin transfer molding has been developed. The simulation uses a new Flow Analysis Network (FAN) technique to predict and track the movement of the free-surface, and a finite element method to solve the governing equation set for each successive flow front location. A variety of element types have been incorporated into the simulation, enabling modeling of flow for a variety of conditions of industrial interest including runner distribution systems, “2.5-D” shell geometries, and fully 3-D flows. The FAN technique developed here has two main benefits: it enables conservation of mass, even for highly distorted element shapes, and also, allows elements of different dimension to be simultaneously used in a single simulation. At present, the simulation predicts flow front position as a function of time, and the pressure distribution during the filling process for a number of inlet gating conditions. A number of examples are presented and discussed to highlight the simulation's capabilities, including the filling of a complex automotive part.     

基于SPH方法的微注射成型数值模拟

基于无网格方法和黏性本构方程,开展微注射成型数值模拟的研究。采用光滑粒子流体动力学的粒子近似法离散N-S 控制方程组,求解速度场、压力场、温度场等物理场的变化规律。以应用于生物医学领域带有细微针头的聚合物微针为例,进行充型过程的数值模拟,模拟结果与实验结果基本一致。     

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     

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.     

Injection molding of unsaturated polyester compounds

A bulk-molding compound made of unsaturated polyester resin, glass fiber, calcium carbonate fillers, and low profile additives is studied. The viscosity of the compound in the absence of cure reaction is measured by capillary rheometry. The compound exhibits a shear-thinning behavior. Injection molding in a rectangular plaque equipped with pressure transducers shows that the crosslinking reaction can begin during mold filling for low flow rate or high mold temperature. Fiber orientation in the plaque is complex as the reinforcement appears under two aspects, bundles or filaments. Their lengths and orientations are different. A layered structure throughout the thickness is observed at the mold entrance, whereas the orientation becomes progressively unidirectional in the plaque. Two fiber-free layers near the the mold walls are observed. A numerical simulation of mold filling assuming inelastic non-Newtonian kinetic dependent behavior is presented. The results agree well with pressure measurements. A simplified decoupled fiber motion calculation is finally proposed. A qualitative explanation of the basic phenomena which induce fiber orientation is presented.