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     

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.     

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 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.     

Birefringence in injection‐compression molding of amorphous polymers: Simulation and experiment

The influence of the processing variables on the residual birefringence was analyzed for polystyrene and polycarbonate disks obtained by injection‐compression molding under various processing conditions. The processing variables studied were melt and mold temperatures, compression stroke, and switchover time. The modeling of flow‐induced residual stresses and birefringence of amorphous polymers in injection‐compression molded center‐gated disks was 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 frozen‐in flow stresses in moldings. The filling, compression, packing, and cooling stages were considered. 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 Young's relaxation modulus and strain‐optical coefficient functions. The residual birefringence in injection‐compression moldings was measured. The effects of various processing conditions on the measured and simulated birefringence distribution Δn and average transverse birefringence <n_rr?n_θθ> were elucidated. Comparison of the birefringence in disks manufactured by the injection molding and injection‐compression molding was made. The predicted and measured birefringence is found to be in fair agreement. POLYM. ENG. SCI., 2013. © 2013 Society of Plastics Engineers     

Prediction of residual stress and viscoelastic deformation of film insert molded parts

Film insert molding (FIM) has been modeled numerically to predict residual stress and viscoelastic deformation of the part. Nonisothermal three dimensional flow analysis for filling, packing, and cooling stages was carried out by using a commercial software. It was assumed that the inserted film was solid throughout the entire molding procedure although remelting could occur at the interface with the substrate. The flow analysis results, e.g., temperature, stress, and density distribution in the substrate domain, were transported to a finite element stress analysis program for viscoelastic stress analysis. Deflection of the FIM part was obtained as soon as the part was ejected from the mold by assuming isotropic elastic material. The residual stress distribution in the FIM part was acquired by removing the constraints along the boundary of the molded part. Viscoelastic deformation of the FIM part was predicted by performing viscoelastic stress analysis in order to understand long term behavior of the FIM part when exposed to room temperature. Durability of automotive and electronic parts produced by the film injection molding can be predicted by the procedure adopted in this study. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Integrated numerical modeling of the blow molding process

The numerical modeling of the extrusion blow molding of a fuel tank is considered in this work. The integrated process phases are consecutively simulated, namely, parison formation, clamping, and inflation, as well as part solidification, part deformation (warpage), and the buildup of residual stresses. The parison formation is modeled with an integral type viscoelastic constitutive equation for the sag behavior and a semi-empirical equation for the swell behavior. A nonisothermal viscoelastic formulation is employed for the clamping and inflation simulation, since parison cooling during extrusion strongly affects the inflation behavior. Once the parison is inflated, it solidifies while in the mold and after part ejection. Warpage and residual stress development of the part are modeled with a linear viscoelastic solid model. Numerical predictions are compared with experimental results obtained on an industrial scale blow molding machine. Good agreement is observed. A process optimization based on a desired objective function, such as uniform part thickness distribution and/or minimal part weight, is performed. The integrated clamping, inflation, and cooling stages of the process are considered. The optimization is done by the systematic manipulation of the parison thickness distribution. Iterations are performed employing a gradient based updating scheme for the parison thickness programming, until the desired objective of uniform part thickness is obtained.     

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.

     

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.     

Evaluation of residual thermally induced stresses in the cooling of polymer melt via transfinite element computations

The present paper describes the evaluation of nonlinear thermally induced residual stresses in the cooling of polymer melt during injection molding of plastic components. The computational methodology adopted is based on the transfinite element approach, which is a hybrid scheme as it combines transform methods and classical Galerkin schemes with finite element formulations to preserve the modeling versatility. The applicability of the proposed formulations for understanding the physics and the nature of the nonlinear thermally induced stresses in the solidifying process of a sample amorphous polystyrene specimen demonstrates the basic capabilities and potential of the methodology. Results obtained agree qualitatively well with earlier research studies and experimental findings relevant to thermally induced residual stresses in the injection molding of plastic components.     

Analysis of the packing stage of a viscoelastic melt

The packing stage starts at the end of mold filling. During this stage, additional material is forced into the mold to compensate for the shrinkage during subse-quent cooling. Underpacking results in molded parts with dimensional variation. Overpacking causes flash at the parting lines, stick during ejection, and excess residual stresses resulting in warpage. The packing stage is thus extremely important in the determination of the final quality of the product. Despite its importance, analysis of the packing stage has been relatively ignored, particularly the viscoelastic effect. In this work, the analysis of the isothermal packing stage is presented for a Maxwell fluid. A set of governing equations is derived for a two-dimensional mold and solved using the Galerkin finite element method. In addition to the distribution of velocity and pressure, the model predicts the stresses in the planar direction, which could be used for subsequent calculation of the residual stresses.     

Residual thermal stresses in injection moldings of thermoplastics: A theoretical and experimental study

Internal stresses in injection molded components, a principal cause of shrinkage and warpage, are predicted using a three‐dimensional numerical simulation of the residual stress development in moldings of polystyrene and high‐density polyethylene. These residual stresses are mainly frozen‐in thermal stresses due to inhomogeneous cooling, when surface layers stiffen sooner than the core region as in free quenching. Additional factors in injection molding are the effects of melt pressure history and mechanical restraints of the mold. Transient temperature and pressure fields from simulation of the injection molding cycle are used for calculating the developing normal stress distributions. Theoretical predictions are compared with measurements performed on injection molded flat plates using the layer removal method on rectangular specimens. The thermal stress development in the thinwalled moldings is analyzed using models that assume linear thermo‐elastic and linear thermo‐viscoelastic compressible behavior of the polymeric materials. Polymer crystallization effects on stresses are examined. Stresses are obtained implicitly using displacement formulations, and the governing equations are solved numerically using a finite element method. Results show that residual stress behavior can be represented reasonably well for both the amorphous and the semicrystalline polymer. Similarities in behavior between theory and experiment indicate that both material models provide satisfactory results, but the best predictions of large stresses developed at the wall surface are obtained with the thermo‐viscoelastic analysis.     

Frozen-in birefringence and anisotropic shrinkage in optical moldings: I. Theory and simulation scheme

An unconditionally stable upwinding scheme was proposed to improve the efficiency of the viscoelastic simulation in molding of optical products using a CV/FEM/FDM technique. A significant computation time saving was achieved due to an elimination of subdivision of the time step as required in the conventional numerical scheme. The approach was applied to simulate the flow-induced birefringence and anisotropic shrinkage in disk moldings using a nonlinear viscoelastic constitutive equation, orientation functions and equation of state. The two-dimensional triangular finite element meshes were used in the disk cavity and the one-dimensional tubular elements were utilized in the delivery system. Good agreement was shown between the simulated pressure traces and flow birefringence in the molding using the unconditionally stable upwinding scheme of the present study and the conventional numerical scheme of the earlier study. In addition, an algorithm for simulation of the thermal stresses and birefringence in moldings using linear viscoelastic and photoviscoelastic constitutive equations was presented by combining constrained and free quenching approaches. The proposed numerical scheme for viscoelastic simulation of injection molding is more suitable for future commercial applications.     

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     

A thermoviscoelastic analysis of process‐induced internal stresses in thermoplastic matrix composites

A numerical tool for predicting the evolution of internal and residual stresses during the processing of thermoplastic matrix composites has been developed. Based on a finite element formulation, the model accounts for the anisotropy, vis‐coelasticity and heterogeneity of the materials and represents mechanisms of both stress generation and stress relaxation. The viscoelastic properties are described by a linear thermoviscoelastic formulation. The model allows the buildup of stresses during processing to be monitored, in particular when the material is cooling through its transition temperatures, and enables the prediction of stress release and the resulting part waipage on demolding. Its use is demonstrated for unidirectional and crossply polyetherimide/glass fiber (PEI/GF) laminates processed by compression molding, and the influence of cooling conditions on stress levels is shown.     

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.     

Incorporation of density relaxation in the analysis of residual stresses in molded parts

Thermo-rheologically/piezo-rheologically simple viscoelastic constitutive equations are adopted for the material behavior of a generic polystyrene, in both the deviatoric and dilatational domains, in order to investigate the effect of density relaxation on the development of the thermal residual stresses in a thin injectionmolded strip. A preliminary study is undertaken to assess the ability of the proposed dilatational viscoelastic constitutive equations to capture some of the density-relaxation behavior such as the isobaric volume relaxation following a sudden quench from above the glass-transition temperature and upon constant rates of cooling at different temperatures and pressures. In this preliminary study, different combinations of relaxation functions and shift factors are investigated. An appropriate combination is selected and used for the residual-stress analysis. The numerical simulation of the development of the stresses in a one-dimensional cavity qualitatively predicts the correct stress profile across the thickness of the molded part, as well as the dependency of this profile on some of the material properties and molding conditions. In general, the investigation presented in this paper suggests that density relaxation plays an important role in the development of residual stresses in molded parts.