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     

Residual thermal stresses in injection molded products

Nonisothermal flow of a polymer melt in a cold mold cavity introduces stresses that are partly frozen-in during solidification. Flow-induced stresses cause anisotropy of mechanical, thermal, and optical properties, while the residual thermal stresses induce warpage and stress-cracking. In this study, the influence of the holding stage on the residual thermal stress distribution is investigated. Calculations with a linear viscoelastic constitutive law are compared with experimental results obtained with the layer removal method for specimens of polystyrene (PS) and acrylonitrile butadiene-styrene (ABS). In contrast to slabs cooled at ambient pressures, which show the well-known tensile stresses in the core and compressive stresses at the surfaces, during the holding stage in injection molding, when extra molten polymer is added to the mold to compensate for the shrinkage, tensile stresses may develop at the surface, induced by the pressure during solidification.     

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.     

Tensile stresses in the edges of injection moldings: Roles of packing pressure,machine compliance,and resin compression

The slow spontaneous development of cracks in the edges of injection moldings under “field” conditions has been observed for 30 years or more. While environmental stress cracking agents have long been implicated, the magnitude and distribution of the stresses associated with cracking have been obscure. The current study of these stresses involved polycarbonate as a model test material that was molded under systematically varied molding conditions. Surface tensile stresses, though rarely great enough alone to cause “dry” crazing or cracking were revealed through exposure to environmental stress crazing and cracking (ESC) agents. Using an old technique involving a set of calibrated ESC liquids, edge tensile stresses as great as 18 MPa were found in the edges of the moldings. Other, independent methods of stress assessment gave results in semiquantitative agreement with those of the ESC tests. Packing force, machine compliance, injection hold time, and mold flashing emerged as major variables either raising or mitigating stress levels. The root cause of the edge tensions is the mismatch in the times and pressures at which the skins and cores of moldings solidify. In short, skins quench at low pressure first, while cores solidify later during the packing stage. Upon release from the mold, elastic recovery of the core stretches the skin. More importantly, machine and mold compliances allow expansion of the part in the packing stage, during which certain areas of the skin are stretched. Solidifying the core during the packing preserves part of the skin extension as elastic strain. These effects are capable of outweighing the classical tendency of quenching to generate skin compression and core tension. A number of other effects, including release from the mold before the core has solidified, and flashing of the mold, have been found to limit the rise of skin tension.     

Solidification of thermoviscoelastic melts. Part 4: Effects of boundary conditions on shrinkage and residual stresses

The solidification of a molten layer of amorphous thermoplastic between cooled parallel plates is used to model the mechanics of part shrinkage and the buildup of residual stresses in the injection-molding process. Flow effects are neglected, and a thermorheologically simple thermoviscoelastic material model is assumed. The model allows material to be added to fill the space created by the pressure applied during solidification, so that this model can be used to assess packing-pressure effects in injection molding. The interactions between the mold surfaces and the solidifying material are accounted for by modeling different types of constraints through different model boundary conditions. For several sets of boundary conditions, parametric results are presented on the effects of the packing pressure—the pressure applied during solidification to counteract the effects of volumetric shrinkage of the thermoplastic—on the in-plane and through-thickness shrinkages, and on residual stresses in plaque-like geometries. Plaques that can shrink in the in-plane direction while in the mold are shown to shrink more and to have higher residual stresses than plaques that are fully constrained while in the mold. Although the results are presented in terms of normalized variables based on the properties of bisphenol-A polycarbonate, they can be interpreted for other amorphous thermoplastics such as modified polyphenylene oxide, polyetherimide, and acrylonitrile-butadiene-styrene.     

A unified K-BKZ model for residual stress analysis of injection molded three-dimensional thin shapes

The flow-induced and thermally induced residual stresses during injection molding of a thin part with complex geometries are predicted. The injection molding precess was considered to consist of a filling and a post-filling stage (packing coupled with cooling). Additionally, the analysis were applied to successive stages of the process. The model takes into account the viscoelasticity of the molding polymer, which has been neglected in most previous works, because of the complexity of its inclusion. A unified K-BKZ viscoelastic constitutive model, capable of modeling both the fluid-rubbery state and the glass state of amorphous polymers, was employed for simulating this problem. For the flow-induced residual stress predictions of the filling stage, a quasi-steady state approximation was employed for each element of the part, for the calculation of stress profile and subsequent stress relaxation after cessation of flowf. Stress calculations were provided for the thermally induced residual stress predictions of the post-filling stage. These explicit calculations led to the results of pressure and temperature distributions of the part during the post-filling stage into the viscoelastic constitutive model. Additionally, the pressure and asymmetric temeprature profiles of the post-filling stage were based on finite element packing analysis coupled with a boundary element cooling analysis of the molding process. Finally, the total residual stress in the part was obtained via superposition of the flow-induced and thermally induced residual stresses. An example is provided to demonstrate the entire concept. The results indicate that thermally induced residual stress is higher than the flow-induced residual stress by one to two orders of magnitude.     

Numerical prediction of residual stresses and birefringence in injection/compression molded center‐gated disk. Part II: Effects of processing conditions

The accompanying paper, Part I, has presented the physical modeling and basic numerical analysis results of the entire injection molding process, in particular with regard to both flow‐induced and thermally‐induced residual stress and birefringence in an injection molded center‐gated disk. The present paper, Part II, investigates the effects of various processing conditions of injection/compression molding process on the residual stress and birefringence. The birefringence is significantly affected by injection melt temperature, packing pressure and packing time. However, the thermally‐induced birefringence in the core region is insignificantly affected by most of the processing conditions. On the other hand, packing pressure, packing time and mold wall temperature affect the thermally‐induced residual stress rather significantly in the shell layer, but insignificantly in the core region. The residual stress in the shell layer is usually compressive, but could be tensile if the packing time is long, packing pressure is large, and the mold temperature is low. The lateral constraint type turns out to play an important role in determining the residual stress in the shell layer. Injection/compression molding has been found to reduce flow‐induced birefringence in comparison with the conventional injection molding process. In particular, mold closing velocity and initial opening thickness for the compression stage of injection/compression molding have significant effects on the flow‐induced birefringence, but not on the thermal residual stress and the thermally‐induced birefringence.     

Packing and discharge in injection molding

In a reciprocating-screw injection-molding machine, the screw or plunger forces the plastic into the mold. It remains in the forward position under pressure for a fixed time during which plastic flow into the mold or ‘packing’ takes place. After the timer runs out, the screw moves back while rotating thus releasing the pressure on the plastic in the mold. At this time, if the gate has not frozen, flow of plastic out of the mold or ‘discharge’ takes place. In this study, clear rigid PVC, poly (vinyl chloride), was molded with varying amounts of packing and discharge. Photoelastic stress patterns for parts observed between cross-polaroids suggested that packing and discharge give rise to high frozen stresses due to molecular orientation in the gate area. Mechanical strength tests on the molded parts show that these high stresses are a source of weakness. Short forward times for the plunger significantly improve the mechanical properties of the parts in the gate area and at the same time have a significant influence on part dimensions, especially in the gate vicinity. Laminations observed at the gate interface can also be reduced by controlling the extent of molecular orientation introduced by packing and discharge.     

Analysis of the packing stage in injection molding

An unconditionally stable explicit finite difference numerical scheme is used to determine the pressure distribution during the packing stage of a rectangular mold cavity. Different initial conditions arising from both an isothermal and nonisothermal mold filling analysis are considered in relation to subsequent packing behavior. The packing stage is of short duration, may be assumed to be isothermal, and gives rise to a more uniform pressure distribution within the mold cavity.     

退火对注射成型PC制品力学性能的影响

注射成型的塑料光学制品应用日益广泛,但注射成型加工的聚碳酸酯制品通常有较大的残余应力,会对制品的光学性能、力学性能有负面的影响,而退火可减少/消除制品的残余应力。本文考察了退火对不同工艺条件下注射制品残余应力和力学性能的影响。研究的工艺条件包括三水平的变化的模具温度、熔体温度、保压压力、冷却时间等;残余应力的变化通过光弹实验的应力干涉条纹表示,力学性能的变化以拉伸强度、延伸率的变化表示。实验发现,退火前后,不同工艺条件下注塑PC制品拉伸强度平均提高4.5%,最大达9.0%;同时,断裂延伸率平均降低3%,最多减少14%。     

Solidification of thermoviscoelastic melts. Part II: Effects of processing conditions on shrinkage and residual stresses

The solidification of a molten layer of thermoplastic between cooled parallel plates is used to model the mechanics of part shrinkage and the buildup of residual stresses in the injection-molding process. Flow effects are neglected, and a thermorheologically simple thermoviscoelastic material model is assumed. The model allows material to be added to fill the space created by the pressure applied during solidification, so that this model can be used to assess packing-pressure effects in injection molding. Parametric results are presented on the effects of the mold and melt temperatures, the part thickness, and the packing pressure—the pressure applied during solidification to counteract the effects of volumetric shrinkage of the thermoplastic—on the in-plane and through-thickness shrinkages, and on residual stresses in plaque-like geometries. The packing pressure is shown to have a significant effect on part shrinkage, but a smaller effect on residual stresses. Packing pressure applied later in the solidification cycle has a larger effect. Mold and melt temperatures are shown to have a much smaller effect. The processing parameters appear to affect the through-thickness shrinkage more than the in-plane shrinkage. While the results are presented in terms of normalized variables based on the properties of bisphenol-A polycarbonate, they can be interpreted for other amorphous thermoplastics such as modified polyphenylene oxide, polyetherimide, and acrylonitrile-butadiene-styrene.     

Residual stress and viscoelastic deformation of film insert molded automotive parts

Complex automotive parts were produced by film insert molding and the ejected parts were annealed to investigate the viscoelastic deformation. Warpage of the part was predicted by numerical simulation of mold filling, packing, and cooling stages with non‐isothermal three‐dimensional flow analysis. The flow analysis results were transported to a finite element stress analysis program and the stress analysis was performed by using time‐temperature superposition principle to investigate viscoelastic deformation. Predicted residual stresses, viscoelastic deformation, and warpage showed good agreement with experimental results. Thermal shrinkage of the inserted film and relaxation of the residual stress affected the viscoelastic deformation of the part significantly during annealing. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Residual stresses and density gradient in injection molded starch/synthetic polymer blends

Residual stress distribution in injection molded starch/synthetic polymer blends was evaluated using the layer removal technique. The synthetic polymers in the blend were either polybutylene succinate (PBS) or polycaprolactone (PCL). The starch content ranged from 0 to 70% by weight in the PBS blend and was held constant at 70% in the PCL blend. The effects of various molding conditions, aging and starch content were investigated. The residual stress profiles were found to be parabolic in nature with surface compressive stresses and interior tensile stresses. Increasing the injection pressure and mold temperature decreased the tensile stresses but had no significant effect on the surface compressive stresses. Decreasing the packing pressure produced a significant decrease in the magnitude of residual stresses. Varying melt temperature and packing time did not significantly affect the residual stress distribution for the range of values investigated. The residual stresses relaxed with time, decreasing over a period of 57 days. The magnitude of residual stresses increased as the starch content in the PBS blends was varied from 0 to 70%. Density gradient measurements were made in a 70% starch/PBS blend. The density was found to be higher in the interior than at the surface with a steep gradient close to the surface. Varying the molding conditions had a complex effect on the average density and the density distribution.     

Solidification of thermoviscoelastic melts. Part 3: Effects of mold surface temperature differences on warpage and residual stresses

The solidification of a molten layer of amorphous thermoplastic between cooled parallel plates is used to model the mechanics of part warpage in the injection-molding process. Flow effects are neglected, and a thermorheologically simple thermoviscoelastic material model is assumed. The model allows material to be added to fill the space created by the pressure applied during solidification so that this model can be used to assess packing-pressure effects in injection molding. Parametric results are presented on the effects of the mold temperatures and the packing pressure—the pressure applied during solidification to counteract the effects of volumetric shrinkage of the thermoplastic—on the in-plane and through-thickness shrinkages, on warpage, and on residual stresses in plaque-like geometries. The packing pressure is shown to have a significant effect on part warpage. While the results are presented in terms of normalized variables based on the properties of bisphenol-A polycarbonate, they can be interpreted for other amorphous thermoplastics, such as modified polyphenylene oxide, polyetherimide, and acrylonitrile-butadiene-styrene.     

Orientation in injection molded polystyrene

The ultimate properties of injection-molded thermoplastics articles are controlled to a large extent by flow and heat transfer phenomena that take place during the injection-molding process. In fact, the thermo-mechanical history of the melt during the molding process leads to a non-uniform distribution of many of the critical properties of the molding. Birefringence has been employed as an indirect measure of the distribution of frozen stresses or strains in amorphous polymers. The present study employs birefringence to study the development of frozen stresses in injection-molded polystyrene. In general, orientation in the flow direction is much greater than the orientation in the transverse direction of the moldings. In the vicinity, of the gate, where mold filling is characterized by spreading radial flow of the melt, the hoop stresses (planar deformation) at the melt front give rise to high orientation in the transverse direction. It appears that relaxation phenomena are not very important during the filling stage; however, they become more, important in the packing and pressure holding stages. With the aid of the appropriate rheo-optical relationship, it is shown that the distribution of frozen-in orientation in injection-molded polystyrene may be estimated on the basis of data relating to pressure variations during the filling stage.     

Analysis of filling,packing, and cooling stages in injection molding of disk cavities

This research tried to simulate three stages of injection molding cycles (filling, packing, and cooling) for polypropylene. The cavity used was a center-grated disk-shaped mold. During the filling stage, we assumed the polymer fluid obeyed the CEF equation and flowed nonisothermally. The packing stage was represented by isothermal flow of Newtonian fluid, and, during cooling stage, we took into account the effect of pressure drop on the energy balance. By finite difference method, we could solve the partial differential equations numerically. The results showed. (1) Elastic effect was not significant at the filling stage. (2) Pressure buildup in the cavity was very quick at the packing stage. (3) At the cooling stage, temperatures predicted by taking into account pressure drop were lower than those without considering pressure drop. In addition, the influences of mold temperature, flow rate, and inlet melt temperature on the three stages of injection molding process were discussed.     

Residual stresses,shrinkage, and warpage of complex injection molded products: Numerical simulation and experimental validation

A numerical simulation model for predicting residual stresses and residual deformations which arise during the injection molding of thermoplastic polymers in the post-packing stage has been developed. A thermoviscoelastic model with volume relaxation is used for the calculation of residual stresses. The finite element method employed is based on the theory of shells as an assembly of flat elements. This theory is well suited for thin injection molded products of complex shape. The approach allows the prediction of residual deformations and residual stresses layer by layer like a truly three-dimensional calculation, while reducing the computational cost significantly. The hole drilling technique is used to measure the residual stresses across the thickness of the product. A three-dimensional laser digitizing system, an image processing technique and a dual displacement transducer system are used to measure the warpage. Experiments are carried out on polycarbonate and high density polyethylene parts. Numerical results are in qualitative agreement with experimental observations, i.e., the skin of the box is surrounded by a compressive region while the core region is in traction. The trend of both the experimental and the predicted residual stress profiles is close. Different examples are presented to illustrate the influence of the geometrical complexity of the shape on the final deformations and residual stresses. The influence of the mold temperature on residual stresses and warpage is also analyzed.     

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