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     

Residual birefringence in modified polycarbonates

The residual birefringence in quenched and injection‐molded specimens of bisphenol‐A polycarbonate (BAPC) homopolymer and its copolymers with substituted bisphenol‐A is investigated. The chemical modifications lead to a different stressoptical behavior in the melt and glass state, which generates differences in the residual birefringence of molded specimens. In this way the origins of the residual birefringence can be interpreted in a better way. In quenched samples it is found that the level of birefringence depends on the stress‐optical coefficient in the glassy state, but the unbalance of the birefringence distributions scales with the stress‐optical coefficient in the melt state. This supports the idea that transient thermal stresses present during vitrification induce molecular orientation, which is responsible for the unbalance of the distributions. The residual birefringence distributions in injection‐molded specimens all display a broad plateau in the core, as is usually observed in BAPC. The level of the plateau is found to scale with the stress‐optical coefficient of the melt state. This is a proof for the interpretation of this plateau being induced by transient thermal stresses during vitrification and not by residual stresses. It cannot be eliminated by optimizing molding conditions but only by drastically reducing the stress‐optical coefficient in the melt state.     

Numerical Modeling of Cooling Stage of Glass Molding Process Assisted by CFD and Measurement of Residual Birefringence

Process parameters of Precision Glass Molding (PGM) are often sought by Finite Element (FE) simulation. Mechanical as well as thermal boundary conditions (BCs) are necessary for FE simulation in which mechanical BCs are usually known or easily determinable. However, most of the thermal BCs are generally assumed in the FE simulation as they cannot be measured directly. The focus of this article is to propose a novel method for evaluating the thermal BC of glass–N₂ gas. FE simulations as well as thermal cycling experiments are carried out for a glass disk specimen for three different cooling rates. CFD analysis of N₂ flow in the PGM machine is performed to understand the heat extraction mechanism. Based on this, adhoc values for equivalent heat transfer coefficient (h_eqv) are obtained by lumped system analysis. A novel methodology is then proposed for obtaining accurate h_eqv values by measurement of integrated residual birefringence in glass using digital photoelasticity. FE simulation is repeated for different values of h_eqv until the integrated birefringence based on simulation matches with that of the experiment. For the same cooling rates, two aspherical glass lenses are molded and their residual birefringence is measured and compared with the glass disk specimen.     

Study on the blackening phenomenon of leaded glass during microgroove molding using nickel phosphorous mold

Precision glass molding (PGM) is a recently developed method to fabricate glass microgroove components. Lead glass is commonly used as an optical material due to its high refractive index and low transition temperature. A nickel-phosphorous (Ni–P) plated mold is traditionally employed in the PGM process for microstructures optics. However, leaded glass is subject to color change and can blacken during the PGM process, reducing the light transmittance of microgrooves. In this paper, an equation for the redox reaction between Ni and Pb is proposed, which is based on the diffusion of inner Ni atoms to the surface of the mold and the standard electrode potential of the Pb ions in leaded glass. A viscoelastic constitutive model of the glass is established to simulate the compression stress distribution during molding. Finally, the effects of molding pressure, molding temperature, and mold material on glass blackening are studied. The results show that the blackening of leaded glass is caused by Pb enriching the surface. The rise in molding stress and temperature increases the deformation of Ni–P plating, which promotes the diffusion of Ni atoms. By adding a titanium incorporated diamond-like carbon (Ti-DLC) coating, the deformation of the Ni–P plating during molding is suppressed, and the diffusion of Ni atoms can be prevented. In this way, the blackening of leaded glass can be prevented.     

Stress birefringence patterns in molten polymers during the mold-filling and cooling process

An experimental study has been carried out to better understand the phenomenon of stress buildup during the mold-filling process in the injection molding operation. For the study, a rectangular mold with two glass windows was constructed, so that stress birefringence patterns of molten polymers flowing into the mold could be photographed with the aid of a polariscope. As a feeding system, a 1-in. extruder was used attached to the mold with a 2-ft length of stainless steel tubing having a relief valve. In this way, the injection pressure (and injection velocity) was carefully controlled to ensure that the glass windows would not be damaged. The development of stress birefringence patterns during the mold-filling process was recorded on a movie film. It was observed that, in isothermal operation, when flow stopped after the mold was filled, stresses relaxed immediately because of the very slow cooling of the mold by ambient air. However, it was observed that, as cooling proceeded, stresses were gradually built up again in the mold. It was possible, therefore, to determine the residual stress in the mold, which originates from the cooling process alone.     

Experimental investigation of contact heat transfer coefficients in nonisothermal glass molding by infrared thermography

Nonisothermal glass molding has recently become a promising technology solution for the cost-efficient production of complex precision glass optical components. During the molding process, the glass temperature and its temperature distribution have crucial effects on the accuracy of molded optics. In nonisothermal molding, the glass temperature is greatly influenced by thermal contact conductance because there is a large temperature difference between the glass and mold parts. Though widely agreed to be varied during the molding process, the contact conductance was usually assumed as constant coefficients in most early works without sufficient experimental justifications. This paper presents an experiment approach to determine the thermal contact coefficient derived from transient temperature measurements by using infrared thermographic camera. The transient method demonstrates a beneficially short processing time and the adequate measurement at desirable molding temperature without glass sticking. Particularly, this method promises the avoidance of the overestimated contact coefficients derived from steady-state approach due to the viscoelastic deformation of glass during the inevitably long period of holding force. Based on this method, the dependency of thermal contact conductance on mold surface roughness, contact pressure, and interfacial temperature ranging from slightly below-to-above glass transition temperature was investigated. The results reveal the dominance of interfacial temperature on the contact conductance while the linear pressure-dependent conductance with an identical slope observed for all roughness and mold temperatures. The accurate determination of the contact heat transfer coefficients will eventually improve the predictions of the form accuracy, the optical properties, and possible defects such as chill ripples or glass breakage of molded lenses by the nonisothermal glass molding process.     

Numerical Simulation for Injection Molding with a Rapidly Heated Mold,Part II: Birefringence Prediction

In the accompanying paper, Part I, the advantages of the rapid thermal response (RTR) molding process were investigated for thin-wall-mold filling by employing coupled analysis of flow and heat transfer. Besides the complete filling of the cavity, frozen-in molecular orientation is another major quality issue in thin wall molding. The frozen-in orientation causes residual stress and birefringence, and potential part distortion. The present work focuses on the prediction and visualization of birefringence in RTR-molded parts. To calculate birefringence, flow-induced residual stress is computed first and the stress-optical law is then applied. The simulation results show that the amount of molecular orientation, residual stress, and birefringence level considerably decrease in the RTR-molding process. The effect of the mold temperature on the level of birefringence was also studied and predicted birefringence patterns were compared with experimental results for a thin-walled rectangular strip. Both predicted and experimental patterns of birefringence are in agreement on the observation that the birefringence level diminishes significantly when the mold temperature is raised to above the glass transition temperature.     

Ring Compression Test for High‐Temperature Glass Using the Generalized Navier Law

Glass‐forming processes such as high viscosity extrusion and Precision Glass Molding take place at temperatures where slip between the glass and mold/die surfaces is known to occur. Characterization of the frictional forces that accompany interface slip are essential in computational simulations of these processes for prediction of pressing time or force, distortion of the part and possible wear of expensive mold surfaces. In this study, the generalized Navier law, where the interface shear stress, τ, is related to the relative sliding speed of the glass on the mold surface, v_s, by τ = kv_s^e, is used in simulations of the ring compression test to produce friction calibration curves. Contrary to the nonlinear form of the Navier law, the linear form, just like the Coulomb friction model, leads to calibration curves that are loading rate and material behavior independent. This independence is achieved by normalizing the Navier friction coefficient with the viscosity. Friction calibration curves for the normalized coefficient are characterized for the full range of interface conditions from no‐slip to no friction. The results showed an approximate one‐to‐one correspondence between the normalized Navier coefficient and the Coulomb friction coefficient for the full range of axial deformation in the ring compression test.     

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     

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.     

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.     

Precision Glass Molding: Validation of an FE Model for Thermo-Mechanical Simulation

In precision glass molding process, the required accuracy for the final size and shape of the molded lenses as well as the complexity of this technology calls for a numerical simulation. The current paper addresses the development of an FE model for thermo-mechanical simulation of the precision glass molding process including heating, pressing, and cooling stages. Temperature-dependent viscoelastic and structural relaxation behavior of the glass material are implemented through a FORTRAN material subroutine (UMAT) into the commercial FEM program ABAQUS, and the FE model is validated with a sandwich seal test. Subsequently, precision molding of several glass rings is performed at three different pressing temperatures, and the experimental deformation of the glass rings at the end of the molding is compared with the predicted ones from FE simulation. Furthermore, the transient and residual stress distribution inside the glass rings are calculated by the developed FE model, and the effects of some important process parameters such as interface friction and mold temperature on the FE results are assessed. The developed FE model can be employed to predict the deformation behavior, final size/shape, and the residual stress state inside the glass lenses in a precision glass molding process.     

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.     

Measured orientation and internal stress distributions in melt-spun fibers

In this investigation, experimentally measured radial birefringence profiles are compared to internal stress distributions as predicted by a mathematical model. A direct indicator of the degree of molecular orientation, fiber birefringence, is found to correlate well with the stress distributions as calculated from radial temperature variations. In an initial study of glass fibers, no radial birefringence profiles are found, indicating that any residual stresses present are small. In polystyrene fibers, however, large radial variations in birefringence are observed and are shown to be directly related to the calculated internal stresses.     

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     

Interfacial Bonding and Friction in Silicon Carbide [Filament]-Reinforced Ceramic- and Glass-Matrix Composites

Interfacial shear strength and interfacial sliding friction stress were assessed in unidirectional SiC-filament-reinforced reaction-bonded silicon nitride (RBSN) and borosilicate glass composites and 0/90 cross-ply reinforced borosilicate glass composite using a fiber pushout test technique. The interface debonding load and the maximum sliding friction load were measured for varying lengths of the embedded fibers by continuously monitoring the load during debonding and pushout of single fibers in finite-thickness specimens. The dependences of the debonding load and the maximum sliding friction load on the initial embedded lengths of the fibers were in agreement with nonlinear shear-lag models. An iterative regression procedure was used to evaluate the interfacial properties, shear debond strength (T _d ), and sliding friction stress (T _f ), from the embedded fiber length dependences of the debonding load and the maximum frictional sliding load, respectively. The shear-lag model and the analysis of sliding friction permit explicity evaluation of a coefficient of sliding friction (μ) and a residual compressive stress on the interface (σ₀). The cross-ply composite showed a significantly higher coefficient of interfacial friction as compared to the unidirectional composites.     

玻璃吹制成型熔体与模具传热耦合模拟

玻璃吹制成型过程中熔体与模具接触时间短,热交换迅速、剧烈,同时玻璃的黏度对温度极其敏感,微小的温度波动将会引起黏度的剧烈改变,并最终决定制品的厚度分布,因此熔体与模具传热的耦合求解是十分必要的。鉴于此,本文在熔体与模具接触面上引入了界面单元来处理接触面热阻区的热传递问题,建立了熔体流动与模具温度场耦合模拟的控制方程,完成了算法编制,实现了熔体流动与模具温度场的耦合模拟。算例证明,与耦合传热算法相比迭代结果不足以满足吹制成型对温度场准确性的要求;通过模拟与实验对比,在连续生产条件下模具绝大部分的温度保持稳定,但与熔体接触的型腔壁的温度却有大幅的周期性变化;模拟的最终产品壁厚较准确地反映了产品的实际壁厚分布,准确度达到88%以上。     

Development of polymer‐molding‐releasing metal mold surfaces with perfluorinated‐group‐containing polymer plating

The polymer‐molding‐releasing properties of metal molds were found to be related to the following factors: (1) interfacial chemical bonding between the surfaces of polymers and metal molds and (2) a friction force or friction coefficient between polar substances and/or low‐molecular‐weight components in the polymers and physical factors on mold surfaces. We theoretically and experimentally confirmed that metal molds with good polymer‐molding‐releasing properties had very small surface free energies. We also proved that the surface free energies in the resulting polymer moldings were lower than before shaping. The molding releasing properties improved with decreasing friction force and friction coefficient between the surface of polymers and metal molds and with decreasing surface free energy. To obtain metal molds with lower surface free energies, we developed a polymer plating method with perfluorinated‐group‐containing triazine dithiol. The Metal mold treated by polymer plating had lower critical surface tension (7.5 mJ/m²) than Teflon (18 mJ/m²), indicating that the surface consisted of CF₃ ? groups. The treated mold showed excellent durability in its releasing properties, which was better than that of the untreated mold. This technique was developed for the production of molds for the Fθ lens and the naturally bright focusing screen. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 2549–2556, 2003     

Viscosity Measurement by Cylindrical Compression for Numerical Modeling of Precision Lens Molding Process

Cylindrical compression tests were conducted on two different optical glass grades for determining the high-temperature viscosity and elastic parameters. Numerical simulations of the compression tests and the precision lens molding process were performed by incorporating the data obtained from the compression tests using a commercial finite-element method program. Excellent agreement between the viscosity data from the compression test and the beam bending test was obtained, and a good comparison between the measured and predicted deformation load results was also observed. Further issues that have emerged from this research that would be relevant to the ongoing research on the numerical modeling of the precision aspherical lens molding process include determination of high-temperature elastic properties of glass (i.e. elastic and shear modulus) and friction characterization at the glass–mold interface.