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.     

注塑成型充填过程的可压缩流动分析

注塑成型过程中,熔体在型腔中的流动和传热对制品质量性能有重要的影响.为了预测注塑制品的收缩、翘曲和力学性能,精确预测充填过程的流动及传热历史是十分必要的.本文考虑熔体的可压缩性及相变的影响,将充填过程中熔体的流动视为非牛顿可压流体在非等温状态下的广义Hele-Shaw流动.采用有限元/有限差分混合方法求解压力场和温度场,采用控制体积法跟踪熔体流动前沿,并应用Visual C++实现了注塑充填过程的可压缩流动分析.为了保证能量方程各项在单元内边界的连续性,结点能量方程各项由单元形心处的离散值加权平均获得,因而,能量方程在计算区域内整体求解.对两个算例进行了分析,模拟结果与实验结果的对比,验证了本文数值算法及程序.     

Optimization and numerical simulation analysis for molded thin‐walled parts fabricated using wood‐filled polypropylene composites via plastic injection molding

Plastic injection molding is discontinuous and a complicated process involving the interaction of several variables for control the quality of the molded parts. The goal of this research was to investigate the optimal parameter selection, the significant parameters, and the effect of the injection‐molding parameters during the post‐filling stage (packing pressure, packing time, mold temperature, and cooling time) with respect to in‐cavity residual stresses, volumetric shrinkage and warpage properties. The PP + 60 wt% wood material is not suitable for molded thin‐walled parts. In contrast, the PP + 50 wt% material was found to be the preferred type of lignocellulosic polymer composite for molded thin‐walled parts. The results showed the lower residual stresses approximately at 20.10 MPa and have minimum overpacking in the ranges of ?0.709% to ?0.174% with the volumetric shrinkage spread better over the part surface. The research found that the packing pressure and mold temperature are important parameters for the reduction of residual stresses and volumetric shrinkage, while for the reduction of warpage, the important processing parameters are the packing pressure, packing time, and cooling time for molded thin‐walled parts that are fabricated using lignocellulosic polymer composites. POLYM. ENG. SCI., 55:1082–1095, 2015. © 2014 Society of Plastics Engineers     

Development of density distributions in injection molded amorphous engineering plastics. Part II

The experimental results obtained on the gapwise density distributions of freely quenched and injection molded specimens of two engineering thermoplastics presented in Part I of this paper were compared with simulation results. The effect of the thermal history on the density development in the freely quenched samples was investigated by employing the fictive temperature concept in conjunction with the experimentally determined material characteristics. The density distribution in freely quenched specimens of poly(ether imide) could be readily predicted. The combined effects of the cooling rate and the pressure history on the density distributions of injection molded samples were also investigated. A phenomenological model was developed to combine the effects of thermal and pressure history on the density distribution. Overall, the predicted results for injection molded specimens agreed well with the experimental results.     

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.     

双组分注射成型件体积收缩的数值模拟研究

以ABS为第一次成型的内嵌件材料,PP为第二次成型的外嵌件材料,通过对双组分注射成型的数值模拟,系统研究了熔体注射温度、模具温度、注射时间、保压时间和冷却时间等工艺参数对其平均体积收缩率的影响规律,并基于流变学理论,揭示了其影响机理。结果表明,随着熔体注射温度和模具温度的升高,双组分注射成型制品的体积收缩增加,而随着注射时间、保压时间和冷却时间的增加,其平均体积收缩率减小。     

Distribution of some physical properties in injection-molded thermoplastic parts

During the injection molding process, moldings undergo shear and elongational stresses. They are also exposed to thermal gradients of varying intensity. Invariably, molded parts, or at least some sections thereof, freeze before the polymer chains can relax to a random, non-oriented configuration. As a result, injection molded parts contain frozen strains and exhibit anisotropic physical properties. In the present work, a variety of experimental techniques have been employed to determine the three-dimensional variation of the following properties of injection-molded, thermoplastic, rectangular parts: density, heat shrinkage, birefringence, and tensile strength.     

Predicting surface defects in injection molded PVC components

Surface defects in injection molded PVC parts have long been analytically unpredictable. These defects are typically caused by thermal instability and flow instability of the material. There exists a need to analytically predict these defects through the use of mold filling simulation. This paper documents an experimental approach to predicting surface defects on injection molded PVC parts through the use of material characterization, mold filling simulation correlation, and verification tests.     

Feasibility study of thin microinjection molded components

The trend toward the miniaturization of parts has created a strong demand for the manufacturing of precision‐molded miniature polymeric components, due to their high productivity and cost‐effectiveness. The objective of this study is the investigation of the filling behavior and dimensional accuracy of thin microinjection‐molded components using chemical blowing agents and wood fibers. In order to investigate the dimensional stability of the miniature molded parts, a micromold was designed and manufactured using a precision micromilling machine. The flow pattern of the thin molded components was experimentally investigated using different materials: pure linear low‐density polyethylene (LLDPE), foamed LLDPE, and wood fiber LLDPE composite. The results indicate that viscosity significantly affects the flow patterns. Filling behavior of the molded parts was also investigated using commercial flow software. Dimensional accuracy and shrinkage of the molded parts were measured using various gauges. Controlling the cell size, cell density, and distribution of foamed parts was especially difficult for thin micro components; however, the results showed that use of chemical blowing agents can improve the flow ability of the thin components in the microinjection molding process. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Reducing residual stresses in molded parts

Means of reducing the flow-induced residual stresses in injection molded parts through optimization of the thermal history of the process are presented. An approach through the use of a passive insulation layer with low thermal inertia on the cavity surface was investigated. The passive insulation layer prevents the polymer melt from freezing during mold filling and allows the flow-induced stresses to relax after the filling. The criteria for the optimal thermal properties and the required thickness of the layer are presented. A numerical simulation model of non-isothermal filling and cooling of viscoelastic materials was also used to understand the molding process and to evaluate this approach. This model predicts the stress development and relaxation in the molding cycle. Both simulation and experimental results show that the final stresses in the molded parts can be reduced significantly with the use of an insulation layer. This technique can also be applied to other molding or forming processes in order to decouple the material flow and cooling process for minimum residual stresses in the molded parts.     

A numerical method for solving the transient multidimensional population balance equation using an Euler-Lagrange formulation

A numerical method was developed to solve the population balance equation for transient multidimensional problems including particle-particle interactions. The population balance equation was written in a mixed Euler-Lagrange formulation which was solved using the discretization method that represents the number density function by impulse functions, an operator splitting method and a remeshing procedure for the internal variable that conserves the mass and the number of particles.This method was successfully tested against analytical and semi-analytical solutions for pure breakage, pure coalescence, breakage and coalescence, pure advection, advection with absorption, advection with binary uniform breakage and with constant or linear absorption. The method was also applied to a free-boundary transient one-dimensional gas-phase model in a bubble column reactor with simplified hydrodynamics. Accurate solutions were obtained for several simulation conditions for the bubble column, including gas absorption, bubble breakage, bubble coalescence and variable gas density effects. The results showed that the numerical method is adequate and robust for solving transient population balance problems with spatial dependence and particle-particle interactions.     

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 multiscale simulation of polymer processing using parameter-based bridging in melt rheology

To investigate the effect of molecular structure on macroscopic flow behavior of polymeric liquid, attempts have been made to embed the microscopic information into the flow simulation. Constitutive equation based on the theory of polymer dynamics is ideal but the theory is still under development. The CONNFFESSIT approach (where microscopic simulation is embedded into calculation grid in macroscopic simulation) is another promising direction but the computational cost is not practical yet. In this study, we propose another simple method using parameter-based bridging where the parameters for phenomenological constitutive equations in macroscopic flow simulation are obtained from coarse-grained molecular simulation. As an example, we performed a simulation of injection molding and examined the effect of molecular weight on warpage of the molded product. We used the primitive chain network simulation to calculate linear viscoelasticity of linear monodispersed polystyrenes from molecular weight. The obtained linear viscoelasticity was converted into the relaxation spectrum and into the flow curve to be used in the macroscopic simulations. From the flow curve, the parameters of an inelastic non-Newtonian constitutive equation were obtained and used for the simulation of filling process. The relaxation spectrum was used to calculate residual stress from the flow profile in the filling process. From the residual stress and thermal shrinkage, warpage of the product was obtained. For the examined thin plate product, significant change in the warpage direction was demonstrated according to the molecular weight of the material. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

ELIMINATING FLOW INDUCED BIREFRINGENCE AND MINIMIZING THERMALLY INDUCED RESIDUAL STRESSES IN INJECTION MOLDED PARTS*

Eliminating flow-induced birefringence and stresses and reducing thermally induced stresses in the injection molded parts have been studied using rapid thermal response (RTR) molding technique. In the RTR molding, mold surface temperature can be rapidly raised above T _g in the filling stage, while the normal injection molding cycle time is still maintained. Therefore, the melt can fill the cavity at temperatures above T _g, which enables the flow-induced stresses to relax completely in a short time after filling and before vitrification. Residual stresses and birefringence in a RTR molded strip specimen are compared with the conventional molded parts by applying layer removal method and retardation measurement. For the material (Monsanto® Lustrex Polystyrene) and process conditions chosen, the birefringence level decreased as the RTR temperature approached and exceeded the glass transition temperature until it almost disappeared at a RTR temperature of 180°C. Reduction of magnitude and shift of peak location were observed in the gapwise stress profile for RTR molded specimen.

     

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.     

注塑成型保压阶段的分析

本文主要研究二维矩形模腔的非等温、可压缩无定形聚合物的保压阶段。流体是广义牛顿型的，可压缩行为服从Ｔａｉｔ的ｐ—ｖ—Ｔ状态方程。本文在展示保压阶段速度、压力的分布，密度沿着厚度方向的变化的基础上，讨论了保压阶段压力和密度的分布对最终产品的内应力、收缩和翘曲的影响。研究结果表明，保压阶段是注塑成型过程中一个非常复杂的阶段，其压力、温度、速度、密度的变化强烈地依赖于熔体的粘度和模腔的边界条件     

熔接痕位置预测及优化技术研究进展

综述了熔接痕位置预测、优化和控制技术的研究进展,介绍了填充过程熔接痕形成的数学模型。对数值模拟技术、数值模拟技术结合数学规划理论、阀式浇注和大型注射成型制品多浇口进料顺序控制技术等3种技术的分析流程、预测方法和应用实例进行了详细介绍,其中基于数值模拟技术和数学规划理论结合的熔接痕位置确定新算法是行之有效的熔接痕位置优化技术,已成为当前研究热点。随着该技术的日趋成熟,应用范围将逐渐增大。而阀式浇注和大型注射成型制品多浇口进料顺序控制技术的实施可以成功避免注塑件熔接痕的出现,在大型零件生产中具有广阔的应用前景。     

注塑冷却的数值模拟

以注塑制品的温度变化为对象,考虑了注塑制品出模后的冷却过程。系统地对注塑模具的冷却过程以及制品在注塑模具内和出模后的冷却过程进行集成分析。建立了冷却过程的数学模型,并采用边界元法和有限差分法求解成型过程中模具的温度分布和制品在模具内和出模后的温度分布。