Three‐dimensional simulation of multi‐material injection molding: Application to gas‐assisted and co‐injection molding

This paper presents an overview of the results obtained at the Industrial Materials Institute (IMI) on the numerical simulation of the gas‐assisted injection molding and co‐injection molding. For this work, the IMI's three‐dimensional (3D) finite element flow analysis code was used. Non‐Newtonian, non‐isothermal flow solutions are obtained by solving the momentum, mass and energy equations. Two additional transport equations are solved to track polymer/air and skin/core materials interfaces. Solutions are shown for different thin parts and then for thick three‐dimensional geometries. Different operating conditions are considered and the influence of various processing parameters is analyzed.     

Three‐dimensional simulation of primary and secondary penetration in a clip‐shaped square tube during a gas‐assisted injection molding process

This article proposes a generalized Newtonian model to predict the three‐dimensional gas penetration phenomenon in the GAIM process, where the gas and melt compressibility are both taken into account and hence the primary and secondary penetrations in GAIM processes are able to be quantitatively predicted. Additionally, an incompressible model requiring no outflow boundary is also presented to emphasis the influence of gas compressibility on the primary penetration. Based on a finite volume discretization, the proposed numerical model solves the complete momentum equation with two front transport equations, which are employed to track the gas/melt and air/melt interfaces. The modified Cross‐WLF model is adopted to describe the melt rheological behavior. The two‐domain modified Tait equation is exploited to represent the melt compressibility, while a polytropic model is employed to express the gas compressibility. The proposed schemes are quantitatively validated by the gas penetration characteristics in a clip‐shaped square tube, where good prediction accuracy is obtained. The influences of five major molding parameters, such as the injection pressure, mold temperature, melt temperature, delay time, and melt material on the gas penetration characteristics in the same clip‐shaped square tube via the proposed numerical approach are extensively presented and discussed. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Three‐dimensional numerical simulation of injection molding filling of optical lens and multiscale geometry using finite element method

This article presents the development, verification, and validation of three‐dimensional (3‐D) numerical simulation for injection molding filling of 3‐D parts and parts with microsurface features. For purpose of verification and comparison, two numerical models, the mixed model and the equal‐order model, were used to solve the Stokes equations with three different tetrahedral elements (Taylor‐Hood, MINI, and equal‐order). The control volume scheme with tetrahedral finite element mesh was used for tracking advancing melt fronts and the operator splitting method was selected to solve the energy equation. A new, simple memory management procedure was introduced to deal with the large sparse matrix system without using a huge amount of storage space. The numerical simulation was validated for mold filling of a 3‐D optical lens. The numerical simulation agreed very well with the experimental results and was useful in suggesting a better processing condition. As a new application area, a two‐step macro–micro filling approach was adopted for the filling analysis of a part with a micro‐surface feature to handle both macro and micro dimensions while avoiding an excessive number of elements. POLYM. ENG. SCI., 46:1263–1274, 2006. © 2006 Society of Plastics Engineers     

Numerical simulation and experimental verification of the filling stage in injection molding

The linear low‐density polyethylene melt is described by the modified Cross model, the dependence of melt viscosity on temperature incorporated with the Arrhenius equation, and the Moldflow second‐order model in this investigation. The mass, momentum conservation, and constitutive equations are discretized and solved by using the iterative stabilized fractional step algorithm along with the Crank–Nicolson implicit difference scheme. The energy conservation equation is discretized with the characteristic Galerkin approach. The free surface of molten polymer flow front is tracked by the arbitrary Lagrangian–Eulerian (ALE) method. It is demonstrated that good agreement of the numerical predictions given by the proposed ALE method with the results obtained by the injection short‐shot experiments is achieved in the locations and shape of the melt front. Furthermore, when the melt front completely reaches the wall of the mold cavity, the horizontal velocity distribution of counterflow at the section near the finally filling wall is exhibited in the present simulation. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Three‐dimensional numerical analysis of injection‐compression molding process

Injection‐compression molding (ICM) process, combining conventional injection molding (CIM) process with compression molding, has been widely used in the manufacturing of optical media and optical lenses. Most of previous numerical studies regarding ICM process employ the Hele‐Shaw approximation, which is appropriate for thin cavity geometry only. This work presents a three‐dimensional numerical analysis system using a stabilized finite element method (FEM) and an arbitrary Lagrangian‐Eulerian (ALE) method for more rigorous modeling and simulation of ICM process of three‐dimensional geometry. The developed system is verified by comparing the results with existing experimental data as well as simulation data obtained from commercial software. Then, the system is adopted for simulations of ICM process of an optical lens, which is a practical example of three‐dimensional geometry. According to the simulation results, three‐dimensional flow characteristics are found to be significant especially during compression stage because of the squeezing nature of the flow. The results are then compared with those of CIM process, showing that ICM process results in reduced and more uniform distributions of the generalized shear rate and shear stress of the final part. Basic parametric studies are also carried out to understand effects of processing conditions, such as compression velocity and compression gap. POLYM. ENG. SCI.,2011. © 2011 Society of Plastics Engineers     

Three‐dimensional simulation on multilayer parison shape at pinch‐off stage in extrusion blow molding

We tried to predict the multilayer parison shape at pinch‐off stage in extrusion blow molding by nonisothermal and purely viscous non‐Newtonian flow simulation using the finite element method (FEM). We assumed the parison deformation as a flow problem. The Carreau model was used as the constitutive equation and FEM was used for calculation method. Multilayer parison used in this simulation was composed of high‐density polyethylene (HDPE) as inner and outer layers and low‐density polyethylene (LDPE) of which viscosity is five times lower than HDPE as a middle layer. We discussed multilayer parison shape in pinch‐off region. The results obtained are as follows; the parison shape of each layer was clearly visible in the pinch‐off during the mold closing. In addition, the distribution of parison thickness ratios for each layer was located for a large deformation near the pinch‐off region. The melt viscosity for each layer has an influence on the melt flow in the pinch‐off region. In a comparison with an experimental data of parison thickness ratios, the simulation results are larger than the experimental data. These simulation results obtained are in good agreement with the experimental data in consideration of the standard deviations. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

Numerical simulation on residual wall thickness of tubes with dimensional transitions and curved sections in water‐assisted injection molding

Residual wall thickness is an important indicator which aims at measuring the quality of water‐assisted injection molding (WAIM) parts. The changes of residual wall thickness around dimensional transitions and curved sections are particularly significant. Free interface of the water/melt two‐phase was tracked by volume of fluid (VOF) method. Computational fluid dynamics (CFD) method was used to simulate the residual wall thickness, and the results corresponded with that of experiments. The results showed that the penetration of water at the long straight sections was steady, and the distribution of the residual wall thickness was uniform. However, there was melt accumulation phenomenon at the dimensional transitions, and the distribution of the residual wall thickness wasn't uniform. Adding fillet at the dimensional transitions could improve the uniformity of the residual wall thickness distribution, and effectively reduce water fingering. Additionally, at the curved sections, the residual wall thickness of the outer wall was always greater than that of the inner wall, and the fluctuations of the residual wall thickness difference were small. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

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.     

Three‐dimensional nonisothermal simulation of a coat hanger die

We studied the nonisothermal flow of Carreau fluid in a coat hanger die. A general three‐dimensional finite volume code was developed for the purpose of flow analysis. The pressure distribution and velocity distribution were obtained in addition to the temperature distribution. The results illustrated that the highest temperature occurred more by the center of manifold than by the die‐lip region. In the regions where the die gap was small relatively, the wall temperature played a key role in the determination of the temperature distribution in the melt. However, in the manifold, the viscous dissipation was the key factor that determined the temperature distribution in the melt where the heat conduction was relatively poor because of the thicker gap. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101:2911–2918, 2006     

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.     

No‐flow temperature in injection molding simulation

Most injection molding simulation packages use the no‐flow temperature (NFT) as a means of determining whether the polymer flows or is solid. The NFT is not well defined, and a standard method for measuring it does not exist. A sensitivity analysis of the filling stage has been carried out with two different packages [VISI Flow (Vero Software Limited, Gloucestershire, UK) and Moldflow (Autodesk, Inc., San Rafael, CA)] to estimate the influence of the NFT on the main processing parameters. The NFT has a large influence on the thickness of the frozen layer, but it does not appreciably affect the filling pressure. Because the NFT affects the frozen layer, an effect on the estimation of shrinkage and warpage is expected. Software packages have also been compared, and similar simulations have been found to produce contrasting results. A simple correlation for NFT estimation, derived from the Cross–Williams–Landel–Ferry equation, is proposed for both amorphous and semicrystalline polymers. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Graphene coating assisted injection molding of ultra‐thin thermoplastics

High strength light weight parts are critical for the development of new technologies, particularly electronic devices, such as laptop computers, smart phones, and tablet devices. Injection molded plastics and composites are excellent choices for mass producing such parts. As the part thickness decreases from traditional injection molding (>2 mm thickness) to thin wall molding (～1 mm thickness), and lastly, to ultra‐thin wall molding (<0.5 mm thickness), avoiding incomplete filling (short shots) becomes more challenging. Even though, methods exist today for molding thin‐wall plastic parts (i.e., fast heating/fast cooling injection molding), they require multiple steps resulting in a noncost efficient process. In this article, we demonstrate the technical feasibility of using graphene coating to facilitate flow, by promoting slip at the mold walls. We evaluate the influence of coated and uncoated mold inserts on fiber orientation. We present experimental results using un‐reinforced polypropylene and a 40% by weight carbon fiber reinforced polycarbonate/acrylonitrile butadiene styrene. POLYM. ENG. SCI., 55:1374–1381, 2015. © 2015 Society of Plastics Engineers     

Numerical simulation on residual thickness of pipes with curved sections in water‐assisted co‐injection molding

The residual thicknesses of the skin and the inner layers are important quality indicators of water‐assisted co‐injection molding (WACIM) process or overflow WACIM (O‐WACIM) parts. At the curved section, the residual thicknesses change significantly. A numerical simulation program based on the computational fluid dynamics method was developed to simulate the O‐WACIM process. After the numerical simulation program was validated with the experimental results, it was used to study the effects of the bending radii and bending angles on the residual thicknesses of the skin and inner layers of O‐WACIM parts. The results showed that the penetration of the inner melt and water was always close to the inner concave side due to the higher local pressure gradient and temperature. The effects of processing parameters on the residual thicknesses of the skin and inner layers were investigated using the orthogonal simulation method. It was found that the residual thicknesses of the skin/inner layer at the inner concave/outer convex side are mainly influenced by different parameters. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42468.     

Computer simulation of the filling process in gas‐assisted injection molding based on gas‐penetration modeling

Gas‐assisted injection molding can effectively produce parts free of sink marks in thick sections and free of warpage in long plates. This article concerns the numerical simulation of melt flow and gas penetration during the filling stage in gas‐assisted injection molding. By taking the influence of gas penetration on the melt flow as boundary conditions of the melt‐filling region, a hybrid finite‐element/finite‐difference method similar to conventional‐injection molding simulation was used in the gas‐assisted injection molding‐filling simulation. For gas penetration within the gas channel, an analytical formulation of the gas‐penetration thickness ratio was deduced based on the matching asymptotic expansion method. Finally, an experiment was employed to verify this proposed simulation scheme and gas‐penetration model, by comparing the results of the experiment with the simulation. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 2377–2384, 2003     

Water‐assisted injection molding of thermoplastic materials: Effects of processing parameters

The objective of this study was to experimentally investigate the effects of various processing parameters on the water‐assisted injection molding of thermoplastic materials. Experiments were carried out on a lab‐developed water‐assisted injection molding system, which included a water pump, a water injection pin, a water tank equipped with a temperature regulator, and a control circuit. Two types of water injection pins designs were proposed to mold the parts. After molding, the lengths of water penetration in molded parts were measured. The effects of different processing parameters on the lengths of water penetration were determined. It was found that the shrinkage rate and the viscosity of the polymeric materials, and the void shapes of the hollowed cores mainly determined the water‐penetration lengths in molded products. In addition, a comparison has been made between the parts molded by water assisted injection molding and gas‐assisted injection molding. It was found that water‐assisted injection molded parts exhibit less uniform void sizes along the water channel. The cycle time for water‐assisted injection molded parts was shorter than that of conventional injection molded parts and gas‐assisted injection molded parts.     

Three‐dimensional simulation of thermoforming process and its comparison with experiments

Three‐dimensional solid element analysis and the membrane approximated analysis employing the hyperelastic material model have been developed for the simulation of the thermoforming process. For the free inflation test of a rectangular sheet, these two analyses showed the same behavior when the sheet thickness was thin, and they deviated more and more as the sheet thickness increased. In this research, we made a guideline for the accuracy range of sheet thickness for the membrane analysis to be applied. The simulations were performed for both vacuum forming and the plug‐assisted forming process. To compare the simulation results with experiments, laboratory scale thermoforming experiments were performed with acrylonitrile‐butadiene‐styrene (ABS). The material parameters of the hyperelastic model were obtained by uni‐directional hot tensile tests, and the thickness distributions obtained from experiments corresponded well with the numerical results. Non‐isothermal analysis that took into account the sheet, temperature distribution measured directly from the experiments was also performed. It was found that the non‐isothermal analysis greatly improved the predictability of the numerical simulation, and it is important to take into account the sheet temperature distribution for a more reliable simulation of the thermoforming process.     

Residual wall thickness of water‐powered projectile‐assisted injection molding pipes

Water‐powered projectile‐assisted injection molding (W‐PAIM) is an innovative molding process for the production of hollow shaped polymer parts. The W‐PAIM utilizes high pressure water as a power to drive a solid projectile to displace the molten polymer core to form the hollow space. The residual wall thickness (RWT) and its distribution are the important quality criteria. The experimental and numerical investigations were conducted. Experimental specimens showed that the RWT of a W‐PAIM pipe was much thinner than that of a water‐assisted injection molding pipe. The cross‐section size of the projectile defined the basic penetration section size. The software FLUENT was used to obtain the instantaneous distributions of the flow field, which revealed the forming mechanism of the RWT. The experiments indicated that the processing parameters, such as melt temperature, melt injection pressure, mold temperature, and water injection delay time had obvious effects on the RWT, while the water pressure had little effect on it. The RWT of curved pipes was thin at the inner concave side while thick at the outer convex side. The RWTs at the bend portion are influenced by the deflection angle and bending radius, which is due to the pressure difference between the two sides. POLYM. ENG. SCI., 59:295–303, 2019. © 2018 Society of Plastics Engineers     

Simulations of a full three‐dimensional packing process and flow‐induced stresses in injection molding

Numerical investigations of a full three‐dimensional (3D) packing process and flow‐induced stresses are presented. The model was constructed on the basis of a 3D nonisothermal weakly compressible viscoelastic flow model combined with extended pom‐pom (XPP) constitutive and Tait state equations. A hybrid finite element method (FEM)–finite volume method (FVM) is proposed for solving this model. The momentum equations were solved by the FEM, in which a discrete elastic viscous stress split scheme was used to overcome the elastic stress instability, and an implicit scheme of iterative weakly compressible Crank–Nicolson‐based split scheme was used to avoid the Ladyshenskaya–Babu?ka–Brezzi condition. The energy and XPP equations were solved by the FVM, in which an upwind scheme was used for the strongly convection‐dominated problem of the energy equation. Subsequently, the validity of the proposed method was verified by the benchmark problem, and a full 3D packing process and flow‐induced stresses were simulated. The pressure and stresses distributions were studied in the packing process and were in agreement with the results of the literature and experiments in tendency. We particularly focused on the effects of the elasticity and pressure on the flow‐induced stresses. The numerical results show that normal stress differences decreased with incremental Weissenberg number and increased with incremental holding pressure. The research results had a certain reference value for improving the properties of products in actual production processes. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012