Interface development and encapsulation in simultaneous coinjection molding of disk. II. Two‐dimensional simulation and experiment

Two‐dimensional simulation and experimental studies of flow‐rate‐controlled coinjection molding were carried out. Skin polymer was injected first, and then both skin and core polymers were injected simultaneously into a center‐gated disk cavity through a two‐channel nozzle to obtain an encapsulated sandwich structure. The physical modeling and simulation developed, reported in Part I of this series, were based on the Hele–Shaw approximation and the kinematics of the interface to describe the multilayer flow, and the interface development was used to predict the skin/core distribution in the moldings. The effects of rheological properties and processing conditions on the material distribution, penetration behavior, and breakthrough phenomena were investigated. The predicted and measured results were found to be in a good agreement. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2310–2318, 2003     

Birefringence and interface in sequential co‐injection molding of amorphous polymers: Simulation and experiment

Modelings of the interface distribution and flow‐induced residual stresses and birefringence in the sequential co‐injection molding (CIM) of a center‐gated disk were carried out using a numerical scheme based on a hybrid finite element/finite difference/control volume method. A nonlinear viscoelastic constitutive equation and stress‐optical rule were used to model the frozen‐in flow stresses in disks. The compressibility of melts is included in modeling of the packing and cooling stages and not in the filling stage. The thermally induced residual birefringence was calculated using the linear viscoelastic and photoviscoelastic constitutive equations combined with the first‐order rate equation for volume relaxation and the master curves for the relaxation modulus and strain‐optical coefficient functions of each polymer. The influence of the processing variables including melt and mold temperatures and volume of skin melt on the birefringence and interface distribution was analyzed for multilayered PS‐PC‐PS, PS‐PMMA‐PS, and PMMA–PC–PMMA molded disks obtained by CIM. The interface distribution and residual birefringence in the molded disks were measured. The measured interface distributions and the gapwise birefringence distributions in CIM disks were found to be in a fair agreement with the predicted interface distributions and the total residual birefringence obtained by the summation of the predicted frozen‐in flow and thermal birefringence. POLYM. ENG. SCI., 55:88–106, 2015. © 2014 Society of Plastics Engineers     

Numerical study of nonisothermal polymer extrusion flow with a differential viscoelastic model

A numerical study of nonisothermal viscoelastic flow is conducted to investigate the complex flow characteristics of polymer melts in the extrusion process. A general thermodynamic model for the energy conversion related to viscoelastic fluid flow is introduced. The mathematical model for three‐dimensional nonisothermal viscoelastic flow of the polymer melts obeying a differential constitutive equation (Phan‐Thien and Tanner model) is established. A decoupled algorithm based on the penalty finite element method is performed on the calculation. The discrete elastic‐viscous split stress (DEVSS) algorithm, incorporating the streamline‐upwind Petrov‐Galerkin (SUPG) scheme is employed to improve the computation stability. Essential flow characteristics of polymer melts in the extrusion die for hollow square plastic profile is investigated based on the proposed numerical scheme with ignoring the outer thermal resource. The energy partitioning, which quantified the conversion of mechanical energy into thermal energy, is discussed. The effects of volume flow rate and die contraction angle upon the flow patterns are further investigated. POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers     

Reinforcing and toughening isotactic polypropylene through shear-induced crystallization and β-nucleating agent induced crystallization

In this article, iPP with β-nucleating agent was molded by sequential co-injection molding (SCIM), in which skin and core melt were injected into the mold cavity one after the other. The microstructure and mechanical properties of samples were investigated by polarized optical microscope (POM), wide angle X-ray diffraction (WAXD) and mechanical property test. Results show that plastic parts molded by SCIM have double shear layers due to twice shear induced by filling flow of skin and core melt. In the shear layers especially the layer at the overlap of skin and core material, shear promoted the formation of highly oriented structures (shish-kebabs) but inhibited the produce of β-form. In core layer of skin material and core layer of core material, β crystals are predominant. The combination of oriented structures (shish-kebabs) and β crystals endow iPP with high strength and toughness. This work demonstrates a new approach to achieve high-performance polymer materials based on general plastics by manipulation strategy for morphology and structure.     

Hydrodynamic analysis of negative flow in a spiral disc extruder

The flow of polymer melts in a rotating disc extruder is analyzed with a mathematical model for pressure flow and leakage flow (termed neg ative flow). It is assumed that the material is fully melted and exhibits Newtonian flow behavior under isothermal conditions for each element. Flow is evaluated in successive sections of the flow path and the final expression involves a computer-assisted numerical solution. Pressure flow, which is negative, is calculated by analyzing the situation in which the pressure gradient causes the extrudable material to flow back across the stationary disc. A simplified geometrical model is developed for numerical solution, assuming incompressible flow. Leakage flow is between the contours of the disc and the engaging interior face of the housing. The flow is also directed opposite to the drag component and is estimated by using parallel plate flow equations.     

短纤维增强熔体三维充模模拟及制品性能预测

基于气-液-固三相模型,给出了适用于三维流场的纤维质心虚拟速度、纤维平动与取向、动量交换源项的求解公式,建立了描述短纤维增强聚合物熔体充模过程的三维模型。采用同位网格有限体积法和Level Set界面追踪技术,实现了充模过程的三维动态模拟。并且,根据模拟计算出的平均取向角,提出了三维取向短纤维增强复合材料力学性能参数计算的一种简化模型。数值结果表明:三维模拟技术可有效反映注塑成型充模的流动过程和喷泉效应;纤维取向分析可量化显示纤维在型腔中的表层-芯层结构取向;弹性模量计算结果与实验结果吻合较好。     

Modeling and simulation of material distribution in the sequential co-injection molding process

In co-injection molding, the properties and distribution of polymers will affect the application of products. The focus of this work is to investigate the effect of molding parameters on the skin/core material distribution based on three-dimensional (3-D) flow and heat transfer model for the sequential co-injection molding process, and the flow behaviors and material distributions of skin and core melts inside a slightly complex cavity (dog-bone shaped cavity) are predicted numerically. The governing equations of fluids in mold are solved by finite volume method and Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm on collocated meshes, and the domain extension technique is employed in numerical method for this cavity to assure that the numerical algorithm is implemented successfully. The level set transport equation which is used to trace the free surfaces in co-injection molding is discretized and solved by the 5th-order Weighted Essentially Non-Oscillatory (WENO) scheme in space and 3rd-order Total Variation Diminishing Runger-Kutta (TVD-R-K) scheme in time respectively. Numerical simulations are conducted under various volume fraction of core melt, skin and core melt temperatures, skin and core melt flow rates. The predicted results of material distribution in length, width and thickness directions are in close agreement with the experimental results, which indicate that volume fraction of core melt, core melt temperature and core melt flow rate are principal factors that have a significant influence on material distribution. Numerical results demonstrate the effectiveness of the 3-D model and the corresponding numerical methods in this work, which can be used to predict the melt flow behaviors and material distribution in the process of sequential co-injection molding.     

夹芯注塑成型过程的计算机可视化模拟分析--材料粘度与工艺参数对芯层熔体穿透深度的影响

采用Moldflow公司MPI软件中的Co-injection分析模块，对夹芯注塑成型过程进行动态模拟分析；以揭示材料粘度以及工艺参数对夹芯注塑成型过程中芯层熔体穿透深度的影响规律。结果发现，芯层熔体穿透深度值随芯／壳层熔体粘度比R值的减小而增大，这主要与芯层和壳层熔体的相对流动能力有关；此外，在工艺参数中，改变熔体注射速度对芯层熔体穿透深度的影响较为突出，而模温和熔体温度对芯层熔体穿透深度的影响相对较弱。     

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.     

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     

A basic experimental study of sandwich injection molding with sequential injection

An experimental study of sandwich injection molding is reported which involves sequential injection of polymer melts with differing melt viscosity into a mold. In isothermal injection molding the relative viscosity of the two melts is the primary variable determining the phase distribution in the mold. Generally the most uniform skin-core structure occurs when the second melt entering the mold has a slightly higher viscosity than the first melt injected. Large viscosity inequalities lead to nonuniform skin thicknesses. The influence of blowing agents and non-uniform temperature fields on the extent of encapsulation is described. Temperature fields are very important especially if the first polymer melt injected has a greater activation energy of viscous flow (or a greater temperature dependence of the viscosity function).     

夹芯注塑成型过程的计算机可视化模拟分析--材料粘度与工艺参数对芯层分布及均匀性的影响

为了了解夹芯注塑的成型过程、探悉其成型机理，采用Moldflow公司MPI软件中的Co-injection分析模块，对夹芯注塑成型过程进行动态模拟分析，揭示材料粘度以及工艺参数对夹芯注塑成型过程中芯层分布均匀性的影响规律。结果表明，芯层物料分布均匀性随芯／壳层熔体粘度比R值的减小而提高，这主要与芯层和壳层熔体的相对流动能力有关。此外，在工艺参数中，改变熔体注射速度对芯层物料分布均匀性的影响较为突出，而模温和熔体温度对芯层物料分布均匀性的影响却相对较弱。     

气辅共注射成型工艺中气道布局影响的CAE研究

基于气体辅助共注射成型充填过程的控制方程,采用CAE方法研究了气道布局对气体辅助共注射成型工艺的影响。通过对几种气道布局的模拟结果对比发现,采用高粘度皮层低粘度芯层时,气道布局对材料分布影响很大,可以通过更换注射顺序来改善材料的分布;沿着浇口到远浇口模壁布置的气道,成型时所需的注塑压力最小,压力分布也较均匀;气体基本上沿着气道在熔体中穿透。     

气体辅助注射成型流动分析模型

根据气体辐助注射成型流动过程的特点，从流体力学基本理论出发，引入合理的假设和简化，建立了熔体流动和气体穿透的数学模型，并在边界条件中反映出气体穿透和表面张力对熔体充填流动的影响。     

A 3‐D finite element model for gas‐assisted injection molding: Simulations and experiments

To gain a better understanding of the gas‐assisted injection molding process, we have developed a computational model for the gas assisted injection molding (GAIM) process. This model has been set up to deal with (non‐isothermal) three‐dimensional flow, in order to correctly predict the gas distribution in GAIM products. It employs a pseudo‐concentration method, in which the governing equations are solved on a fixed grid that covers the entire mold. Both the air downstream of the polymer front and the gas are represented by a fictitious fluid that does not contributeto the pressure drop in the mold. The model has been validated against both isothermal and non‐isothermal gas injected experiments. In contrast to other models that have been reported in the literature, our model yields the gas penetration from the actual process physics (not from a presupposed gas distribution). Consequently, it is able to deal with the 3‐D character of the process, as well as with primary (end of gas filling) and secondary (end of packing) gas penetration, including temperature effects and generalized Newtonian viscosity behavior.     

Numerical prediction of residual stresses and birefringence in injection/compression molded center‐gated disk. Part I: Basic modeling and results for injection molding

The present study attempted to numerically predict both the flow‐induced and thermally‐induced residual stresses and birefringence in injection or injection/compression molded center‐gated disks. A numerical analysis system has been developed to simulate the entire process based on a physical modeling including a nonlinear viscoelastic fluid model, stress‐optical law, a linear viscoelastic solid model, free volume theory for density relaxation phenomena and a photoviscoelasticity and so on. Part I presents physical modeling and typical numerical analysis results of residual stresses and birefringence in the injection molded center‐gated disk. Typical distribution of thermal residual stresses indicates a tensile stress in the core and a compressive stress near the surface. However, depending on the processing condition and material properties, the residual stress sometimes becomes tensile on the surface, especially when fast cooling takes place near the mold surface, preventing the shrinkage from occurring. The birefringence distribution shows a double‐hump profile across the thickness with nonzero value at the center: the nonzero birefringence is found to be thermally induced, the outer peak due to the shear flow and subsequent stress relaxation during the filling stage and the inner peak due to the additional shear flow and stress relaxation during the packing stage. The combination of the flow‐induced and thermally‐induced birefringence makes the shape of predicted birefringence distribution quite similar to the experimental one.     

New approach to develop a 3D non-isothermal computational framework for injection molding process based on level set method

The simulation of three-dimensional (3D) non-isothermal, non-Newtonian fluid filling process is an extremely difficult task and remains a challenging problem, which includes polymer melt flow with free surface coupled with transient heat transfer. This paper presents a full 3D non-isothermal two-phase flow model to predict the complex flowinmelt filling process,where the Cross-WLFmodel is applied to characterize the rheological behavior of polymer melt. The governing equations are solved using finite volume method with SIMPLEC algorithm on collocated grids and the melt front is accurately captured by a high resolution level set method. A domain extension technique is adopted to dealwith the complex cavities, which greatly reduces the computational burden. To verify the validity of the developed 3D approach, the melts filling processes in two thin rectangular cavities (one of them with a cylindrical insert) are simulated. The predicted melt front interfaces are in good agreement with the experiment and commercial software prediction. For a case with a rather complex cavity, the dynamic filling process in a hemispherical shell is successfully simulated. All of the numerical results show that the developed numerical procedure can provide a reasonable prediction for injection molding process.     

基于气体穿透效果数值模拟的气体辅助注射成型工艺优化

对气体辅助注射成型工艺进行分析，阐述了气体辅助注射成型的关键技术要求在分析熔料流动、气体穿透物理模型的基础上，探讨了气体辅助注射成型数值分析的实现原理运用MPI／Gas模块对一T型支架进行了气体辅助注射成型CAE分析，模拟不同工艺条件下的气体穿透效果，确定了合理的工艺参数。     

A numerical simulation of the cavity filling process with PVC in injection molding

Filling cold mold cavities with hot polymer melts at high pressures is of great practical interest. The transport approach to this process of solving the general equations of change with suitable equations of state to describe the flowing material has been largely ignored. No analytic solution is possible, and the non-steady state flow adds a dimension which makes digital computation discouraging because of the core storage and execution time requirements. The mold filled in this simulation is a disk which hot polymer melt enters through a tubular entrance located at the center of the top plate. The tube is 2.54 cm. long and has a radius of 0.24 cm. The plate separation and outer radius of the disk cavity may be varied. A constant pressure applied at the entrance of the tube causes the flow. The cavity walls are kept at various low temperatures. The reported results are for rigid polyvinyl chloride (PVC). The general transport equations, i.e. continuity, momentum, and energy, for a constant density power law fluid are used to solve the flow problem. Convergence to the differential solutions is guaranteed but since a lower limit was imposed on the time increment by the core storage limit of the computer facilities (27K) and long execution times, all results are semiquantitative for the problem as stated. Using the results obtained it is possible to predict “fill times”. The formation of a frozen polymer skin as the cavity fills may be followed via the velocity profiles. The temperature profiles which reflect cooling and the amount of viscous heat generated provide the basis for studying resin thermal degradation effects. Finally, because so much of the total pressure drop is disispated in the entrance tube, and so much viscous heat is generated there, this study indicates that the design of the gate and runner system is perhaps the most important facet of success in mold filling.