Birefringence in gas‐assisted tubular injection moldings: Simulation and experiment

The influence of the processing variables on the birefringence and polymer/gas interface distribution is analyzed for polystyrene moldings obtained by gas‐assisted injection molding (GAIM) under various processing conditions. The processing variables studied were: melt and mold temperatures, shot size, gas pressure, injection speed, and gas‐delay time. Measurements and viscoelastic simulations of the radial distribution of birefringence components, Δn and n_rr ? n_θθ, the variation of the average birefringence, 〈n_zz ? n_θθ〉, along the molding and polymer/gas interface along the length of spiral‐shaped tubular moldings are presented. The polymer/gas interface distribution and flow stresses were simulated using a numerical scheme based on a hybrid finite element/finite difference/control volume method. The birefringence was calculated from the flow‐induced stresses using the stress‐optical rule. Simulations qualitatively agreed with measurements and correctly described theeffect of the processing variables on the birefringence andthe polymer/gas interface distribution in GAIM moldings. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

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     

Frozen-in birefringence and anisotropic shrinkage in optical moldings: II. Comparison of simulations with experiments on light-guide plates

The thermally-, flow-induced and total birefringence components and anisotropic shrinkages in LGP moldings were simulated by using a combination of a CV/FEM/FDM technique nonlinear viscoelastic and photoviscoelastic constitutive equations and orientation functions, as described in Part I of this study. The simulated results were compared with measurements on LGP moldings of a polystyrene (PS) and two optical grade polycarbonates (PCs) OQ1030 and OQ3820 having low and high molecular weights. The thermally-induced birefringence was simulated by a combination of constrained and free cooling during molding. In LGP moldings of PS, the simulated thermally-induced birefringence indicated a minor variation with location in the mold plane, a parabolic shape in the core region and an increase towards the wall. Compared to the flow-induced birefringence, the thermal birefringence provided a minor contribution to the total transverse birefringence Δn₁₂. In LGP moldings of PCs, the simulated thermally-induced birefringence showed a significant variation with location in the mold plane, nearly constant value in the core region and high value in the wall region. In LGP moldings of both PCs, the contributions of the thermally- and flow-induced birefringence to the total transverse birefringence Δn₁₂ were significant. The effect of processing conditions on the development of the normal birefringence in LGP moldings of PCs was ranked from most to least: the packing pressure, mold temperature, melt temperature, injection speed and packing time. However, in LGP moldings of PS the packing time effect was significant due to a longer gate freezing time. Simulated and measured normal birefringence along the flow direction was in fair agreement, but simulations were unable to describe the observed birefringence maximum arising near the gate. The averaged luminance of LGP moldings exhibited some correlation with the averaged normal birefringence. LGP moldings of PC OQ1030 indicated a pronounced maximum in the simulated transverse flow birefringence in the core but a low value near the wall. In contrast, the LGP molding of PC OQ3820 showed a high simulated birefringence near the wall and a low value of maximum in the core. The simulated and measured total transverse birefringence in LGP moldings was in fair agreement. LGP molding of both PCs showed similar tendency in shrinkage variation with processing conditions. However, the thickness shrinkage was higher in LGP moldings of PC OQ3820. The effect of processing conditions on the development of shrinkage in LGP moldings of both PCs was ranked from most to least: the packing pressure, melt temperature, mold temperature, injection speed and packing time. In LGP moldings of PS, the thickness shrinkage slightly increased with increasing melt temperature and significantly increased with reducing packing time. A good agreement between the simulated and measured anisotropic shrinkages in LGP moldings at various processing conditions was observed.     

Toward a viscoelastic modeling of anisotropic shrinkage in injection molding of amorphous polymers

A novel approach to predict anisotropic shrinkage of amorphous polymers in injection moldings was proposed using the PVT equation of state, frozen‐in molecular orientation, and elastic recovery that was not frozen during the process. The anisotropic thermal expansion and compressibility affected by frozen‐in molecular orientation were introduced to determine the anisotropy of the length and width shrinkages. Molecular orientation calculations were based on the frozen‐in birefringence determined from frozen‐in stresses by using the stress‐optical rule. To model frozen‐in stresses during the molding process, a nonlinear viscoelastic constitutive equation was used with the temperature‐ and pressure‐dependent relaxation time and viscosity. Contribution of elastic recovery that was not frozen during the molding process and calculated from the constitutive equation was used to determine anisotropic shrinkage. Anisotropic shrinkages in moldings were measured at various packing pressures, packing times, melt temperatures, and injection speeds. The experimental results of frozen‐in birefringence and anisotropic shrinkage were compared with the simulated data. Experimental and calculated results indicate that shrinkage is highest in the thickness direction, lowest in the width direction, and intermediate in the flow direction. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 2300–2313, 2005     

Theoretical and experimental studies of anisotropic shrinkage in injection moldings of semicrystalline polymers

A novel approach to predict anisotropic shrinkage of semicrystalline polymers in injection moldings was proposed using flow‐induced crystallization, frozen‐in molecular orientation, elastic recovery, and PVT equation of state. The anisotropic thermal expansion and compressibility affected by the frozen‐in orientation function and the elastic recovery that was not frozen during moldings were introduced to obtain the in‐plane anisotropic shrinkages. The frozen‐in orientation function was calculated from amorphous and crystalline contributions. The amorphous contribution was based on the frozen‐in and intrinsic amorphous birefringence, whereas the crystalline contribution was based on the crystalline orientation function, which was determined from the elastic recovery and intrinsic crystalline birefringence. To model the elastic recovery and frozen‐in stresses related to birefringence during molding process, a nonlinear viscoelastic constitutive equation was used with temperature‐ and crystallinity‐dependent viscosity and relaxation time. Occurrence of the flow‐induced crystallization was introduced through the elevation of melting temperature affected by entropy production during flow of the viscoelastic melt. Kinetics of the crystallization was modeled using Nakamura and Hoffman‐Lauritzen equations with the rate constant affected by the elevated melting temperature. Numerous injection molding runs on polypropylene of various molecular weights were carried out by varying the packing time, flow rate, melt temperature, and mold temperature. The anisotropic shrinkage of the moldings was measured. Comparison of the experimental and simulated results indicated a good predictive capability of the proposed approach. POLYM. ENG. SCI., 46:712–728, 2006. © 2006 Society of Plastics Engineers     

Theoretical and experimental studies of anisotropic shrinkage in injection moldings of various polyesters

A novel approach to predict anisotropic shrinkage of slow crystallizing polymers in injection moldings was proposed, using the flow‐induced crystallization, frozen‐in molecular orientation, elastic recovery, and PVT equation of state. In the present study, three different polyesters, polyethylene terephthalate, polybutylene terephthalate, and polyethylene‐2,6‐naphthalate (PEN), are used. The anisotropic thermal expansion and compressibility affected by the frozen‐in orientation function and the elastic recovery that was not frozen during moldings were introduced to obtain the in‐plane anisotropic shrinkages. The frozen‐in orientation function was calculated from the amorphous contribution based on the frozen‐in and intrinsic amorphous birefringence and crystalline contribution based on the crystalline orientation function determined from the elastic recovery and intrinsic crystalline birefringence. To model the elastic recovery and frozen‐in stresses related to birefringence during molding process, a nonlinear viscoelastic constitutive equation was used with the temperature‐dependent viscosity and relaxation time. Occurrence of the flow‐induced crystallization was introduced through the elevation of melting temperature affected by entropy production during flow of the viscoelastic melt. Kinetics of the crystallization was modeled using Nakamura and Hoffman‐Lauritzen equations with the rate constant affected by the elevated melting temperature. Numerous injection molding runs were carried out by varying the packing time, packing pressure, flow rate, melt and mold temperature, and anisotropic shrinkage of moldings were measured. The experimental results were compared with the simulated data and found in a fair agreement. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 3526–3544, 2006     

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.     

Influence of processing on quality of injection-compression-molded disks

A modified injection molding machine with a compression mechanism, and a mold with a movable wall and shut-off mechanism, were used to investigate the effects of processing parameters on the quality of injection-compression-molded polystyrene disks. The compression start-up time, compression force, melt temperature, and part thickness were selected processing parameters. The disk moldings were evaluated based on dimensional accuracy and birefringence. It is found that the compression start-up time affects packing time, and thus greatly affects the residual orientation. If the transition from packing to compression could start before peak cavity pressure, disks with low residual orientation could be obtained. High compression force improves part quality and reduces thickness. Since both compression-induced reduction and cooling-induced shrinkage are involved, the effects of temperature and thickness are not as straightforward as the trends in conventional injection molding.     

Thermal stresses and birefringence in quenched tubes and rods: Simulation and experiment

Measurements and simulations of the radial distribution of the thermal birefringence components, Δn and n_θθ ? n_rr, and the average birefringence, <n_zz ? n_θθ>, in free quenched tubes and rods of polystyrene (PS) and polycarbonate (PC) at different initial temperatures were carried out. The thermal stress and birefringence components were simulated 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 of polymers. The numerical procedures used to discretize the governing equations using finite difference method were described. The obtained numerical results provided the evolution of stress and birefringence components with time during and after quenching and an explanation of the measured residual birefringence distribution in quenched tubes and rods. It was also found that the thickness of the slices removed from the samples to measure the thermal birefringence components, Δn and n_θθ ? n_rr, was critical, in particular, when the initial temperatures were close to the glass transition temperature of polymers. With an increase of the initial temperature during quenching, a better agreement between the simulated and measured birefringence components was obtained. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers     

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.     

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.     

Linear viscoelastic and morphological description of multiphase systems affected by processing parameters

Influence of processing methods, in terms of comparing compression and injection moldings, on the rheological behavior of polycarbonate (PC)/acrylonitrile‐butadiene‐styrene (ABS) blends and PC/ABS/glass fibers composites is presented. Blend compositions and fiber content are considered as material variables. For blends, the effect of the processing route on the viscoelastic functions is evident only for low shearing frequencies. Injection molding created morphology with cocontinuous character, while compression molded blends have “relaxed” structure, where dispersed phase domains are several times larger than in injection molded ones. The glass fiber reinforcement led to the significant differences in viscoelastic properties of composites processed by injection and compression molding. Injected composites have both moduli always higher than compression molded. Also, fiber lengths are reduced more for compressing molding. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

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.     

Simulation of microstructure development in injection molding of engineering plastics

Mathematical models were developed to predict the various microstructural properties, including birefringece, residual stress, and density distributions, in the freely quenched compression molded samples as well as in the injection molded samples. To model the birefringence distribution in the injection molded samples, the BKZ type integral constitutive equation was employed to account for the nonisothermal stress relaxation, which takes place during the cooling stage of the molding cycle. The predicted birefringence agreed well with the experimental data near the mold walls. The residual stress distribution was modeled by the existing thermoelastic theory. The residual thermal stress distribution in the freely quenched samples was predicted very well by the model. However, the predicted residual thermal stresses in the injection molded samples were much larger than the measured ones. A phenomenological model to predict the density distribution in injection molded sample is proposed by including the effects of both cooling rate and the pressure on the density development. The predicted results agreed well with the experimental data.     

Thermal birefringence in freely quenched multilayered slabs of amorphous polymers: Experiment and simulation

The simulation of the gapwise distribution of the thermally‐induced residual birefringence and stresses in freely‐quenched PS‐PC‐PS and PC‐PS‐PC multi‐layered slabs in water was carried out to calculate the gapwise distribution of the transient and residual birefringence. The modeling was based on the linear viscoelastic and photoviscoelastic constitutive equations combined with the first‐order rate equation for volume relaxation. The master curves for the Young's relaxation modulus and strain‐optical coefficient functions obtained earlier for PS and PC were used in the simulations. The obtained numerical results provided the evolution of the thermally‐induced stress and birefringence with time during and after quenching. The predicted gapwise residual birefringence distribution in these slabs was found to be in a fair agreement with the measured results. In addition, the gapwise distribution of the thermally‐induced residual birefringence in the multi‐layered PS‐PMMA‐PS, PMMA‐PS‐PMMA, PMMA‐PC‐PMMA, and PC‐PMMA‐PC slabs quenched from different initial temperatures was measured. Explanations were provided for the observed gapwise distribution of the thermal residual birefringence in each layer of these slabs including the effect of the initial temperature. POLYM. ENG. SCI., 54:2097–2111, 2014. © 2013 Society of Plastics Engineers     

Flow‐induced crystallization in the injection molding of polymers: A thermodynamic approach

The prediction of the crystallinity and microstructure that develop in injection molding is very important for satisfying the required specifications of molded products. A novel approach to the numerical simulation of the skin‐layer thickness and crystallinity in moldings of semicrystalline polymers is proposed. The approach is based on the calculation of the entropy reduction in the oriented melt and the elevated equilibrium melting temperature by means of a nonlinear viscoelastic constitutive equation. The elevation of the equilibrium melting temperature that results from the entropy reduction between the oriented and unoriented melts is used to determine the occurrence of flow‐induced crystallization. The crystallization rate enhanced by the flow effect is obtained by the inclusion of the elevated equilibrium melting temperature in the modified Hoffman–Lauritzen equation. Injection‐molding experiments at various processing conditions were carried out on polypropylenes of various molecular weights. The thickness of the highly oriented skin layer and the crystallinity in the moldings were measured. The measured data for the microstructures in the moldings agree well with the simulated results. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 95: 502–523, 2005     

Modeling and experimental study of birefringence in injection molding of semicrystalline polymers

The prediction of birefringence developed in injection moldings is very important in order to satisfy required specification of molded products. A novel approach for the numerical simulation of the flow-induced crystallization and frozen-in birefringence in moldings of semicrystalline polymers was proposed. The approach was based on the calculation of elastic recovery that becomes frozen when the flow-induced crystallization occurred. The flow effect on the equilibrium melting temperature elevation due to the entropy reduction between the oriented and unoriented melts was incorporated to model crystallization. To find the entropy reduction and the frozen-in elastic recovery during crystallization, a non-linear viscoelastic constitutive equation was used. From the ultimate elastic recovery the crystalline orientation function was calculated. The crystalline and amorphous contributions to the overall birefringence were obtained from the crystalline orientation function and the flow birefringence, respectively. The birefringence profiles were measured and predicted in moldings of polypropylenes of different molecular weights obtained at various melt temperatures, injection speeds, holding times and mold temperatures. The resulting predictions were in fair agreement with corresponding experimental data.     

Birefringence prediction of optical media

The flow and thermally induced birefringence of injection‐compression molded optical media such as compact discs and digital video discs is predicted by applying a stress‐optical rule to the flow and thermally induced stresses, which are estimated with a viscoelastic material model integrated into a non‐isothermal compressible flow simulation. The resulting model considers flow and cooling induced molecular orientation, and the transient effect of thermal stress and pressure. Contrary to previous research for polystyrene, the validated results indicate that, for polycarbonate, the magnitude of the thermally induced birefringence is comparable to the flow induced birefringence. Simulation results of the flow and thermally induced in‐plane birefringence for compact‐disc‐recordable moldings with an optical grade of polycarbonate compared well with experimental observations at different mold and melt temperatures. Both simulation and experiments indicate that mold and melt temperatures have a significant effect on the level of birefringence; increasing mold or melt temperature significantly reduces the birefringence. Polym. Eng. Sci. 44:814–824, 2004. © 2004 Society of Plastics Engineers.     

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.