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.     

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     

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.     

Effect of water absorption and temperature gradients on polycarbonate injection moldings

Polycarbonate injection moldings have been conditioned for various times in (i) hot water (40, 60, 80, and 100°C) or (ii) in a temperature gradient (with hot surface/cold surface temperatures 80/25, 100/25, 120/35, and 140/60°C). Water absorption occurred in hot water and caused the formation of disc-shaped flaws, which were located at all depths within the bars and at all orientations. The presence of the flaws caused severe embrittlement and cracks were nucleated by them during uniaxial tensile testing. Residual stress levels were found to be diminished by hot water conditioning more than those in bars conditioned at the same temperatures in air. The sense of the residual stresses reversed in a bar that was allowed to cool slowly in the water bath, an observation attributed to desorption. It was generally found that the flaws near the surface healed on allowing the bars to stand in air at room temperature. Temperature gradient conditioning caused reversal of the sense of the residual stresses near to the hot surface at the two higher temperatures used and significant reduction in magnitude at the lower temperatures. Fracture nucleated at this surface during uniaxial tensile testing.     

The use of birefringence for predicting the stiffness of injection molded polycarbonate discs

Polycarbonate discs were injection molded with different sets of molding conditions. The parameters studied were the flow rate, melt- and mold-temperature. The discs were subjected to three point support flexural tests. Those tests are specially intended for injection molded discs because of their inherent non-flatness. The through-thickness molecular orientation was assessed by birefringence measurements along and across the flow direction using the wedge method. This method is ideal to measure the birefringence of materials that are difficult to cut with a microtome. The through-thickness stiffness of the discs was calculated from the measured birefringence distributions. A composite model of the disc was used in the Algor finite element method (FEM) package to simulate the flexural tests.     

The role of the interaction coefficient in the prediction of the fiber orientation in planar injection moldings

The mechanical properties of injection molded parts in glass reinforced materials are sensitive to processing. A successful design requires a good estimate of the product performance before production. Its performance is strongly affected by the fiber orientation field set up during processing. The fiber orientation pattern is complex and varies three‐dimensionally in the moldings. Some commercial simulation programs already allow the prediction of the fiber orientation induced during the flow by the associated stress field. The results from the simulations are dependent on a parameter accounting for the interactions between fibers during the flow, known as the fiber interaction coefficient. In this paper the effectiveness of the interaction parameter on controlling the predicted patterns of the fiber orientation is studied. This is done by comparing and analyzing the experimental data and the corresponding predictions.     

Melt viscosity and flow birefringence of polycarbonate

Melt viscosity and flow birefringence of bisphenol A-type polycarbonate were measured and analyzed by the application of rubber-like photoelastic theory. The melt viscosity in the Newtonian flow region increased with the molecular weight to the power of 3.4. In polycarbonate, the shear stress of the Newtonian flow region was to 10⁶ dyn/cm², whereas in PMMA it was at most 3 = 10⁵ dyn/cm². The flow birefringence δn has a linear relation with shear stress S, that is δn = 5.7 × 10^?10 S. The principal polarization difference of flow unit α₁ – α₂ was 1.62 × 10^?23 cm³, which was obtained by the application of the rubber-like elastic theory. In PMMA, it was 3.9 = 10^?25 cm³; about 1/40 of that was polycarbonate. The anisotropy of polarizability of the flow unit of polycarbonate was also about 40 times larger than that of PMMA. So the anisotropy reflected the large flow birefringence of the polycarbonate.     

Effect of hydrogen bonding on the rheology of polycarbonate/organoclay nanocomposites

The linear dynamic viscoelastic properties and non-linear transient rheology of polycarbonate (PC)/clay nanocomposites were investigated at temperatures ranging from 240 to 280 °C. For the study, nanocomposites of PC and natural montmorillonite (Cloisite Na⁺) or chemically modified clay (Cloisite 30B) were prepared by melt blending in a twin-screw extruder. Cloisite 30B is a natural montmorillonite modified with methyl, tallow, bis-2-hydroxyethyl, quaternary ammonium chloride (MT2EtOH). In both PC/Cloisite Na⁺ and PC/Cloisite 30B nanocomposites the concentration of clay was varied from 2.3 to 4.3 wt%. In situ Fourier transform infrared (FTIR) spectroscopy results show that at temperatures ranging from 30 to 280 °C the carbonyl groups in PC and the hydroxyl groups in MT2EtOH of Cloisite 30B in PC/Cloisite 30B nanocomposites formed hydrogen bonds, while no evidence of hydrogen bonding was observed in the PC/Cloisite Na⁺ nanocomposites. There are no discernible sharp reflections in the X-ray diffraction (XRD) patterns of PC/Cloisite 30B nanocomposites, after Cloisite 30B having the d₀₀₁ spacing of 1.85 nm was mixed with PC, whereas the d₀₀₁ spacing changes little (1.17 nm) before and after the mixing of Cloisite Na⁺ to PC. Transmission electron microcopy (TEM) images show that organoclay platelets are well dispersed in PC/Cloisite 30B nanocomposites, while the untreated clay platelets are poorly dispersed in PC/Cloisite Na⁺ nanocomposites. The observed differences in XRD patterns and TEM images between the two nanocomposite systems are explained by in situ FTIR spectroscopy. The results of rheological measurements (linear dynamic viscoelasticity, non-linear transient shear flow, and steady-state shear flow) support the conclusions drawn from the results of XRD, TEM, and FTIR spectroscopy.     

Structure and properties of injection moldings of polypropylene/polystyrene blends

A homoisotactic polypropylene (PP) was melt blended with 0–30 wt % of three kinds of polystyrene (PS) with melt flow indexes lower than, similar to, and higher than that of PP. The blends were injection molded at cylinder temperatures of 200–280°C, and the structure and properties of the injection moldings were studied. With PS blending, although the PP molding whitened, no surface defect such as layer peeling and pearl-like appearance occurred. The rigidity and dimensional accuracy of the molding improved without much deterioration in impact strength and heat resistance. At the same time the fluidity also improved. The injection moldings of PP/PS blends did not show clear skin/core structure under a polarizing microscope. The degrees of crystallinity and crystalline c-axis orientation decreased with PS blending. PS particles were the smallest when the ratio of the viscosity of the PS to that of PP at molding shear rate was slightly lower than unity. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 1015–1027, 1997     

The thermomechanical environment and the mechanical properties of injection moldings

Axisymmetric specimens were injection molded in a propylene copolymer with systematic variations of the melt and mold temperatures and the injection flow rate, in a total of 15 different processing conditions. From computer simulations of the mold filling stage using commercially available software packages, two thermomechanical indices were calculated. They aim at evaluating the level of orientation of the skin and the degree of crystallinity of the core layers. Assuming that these morphological features determine the mechanical response of the moldings, the thermomechanical indices were weighted by the relative thickness of the skin and core layers. The tensile behavior of the moldings was assessed at two velocities of 3.3 × 10^?5 (2 mm/min) and 3 m/s. The mechanical properties studied were the initial modulus, the yield stress and the strain at break. The relationships between the weighted thermomechanical indices and these mechanical properties were analyzed from 3D response surfaces obtained by polynomial fittings. Globally, a marked effect of the strain rate on the mechanical response along with a distinct sensitivity on the weighted thermomechanical indices was found. At high strain rates the microstructural differences were enhanced. The dependence of the yield stress on the thermomechanical indices was not significantly affected by the strain‐rate. However, the strain‐rate dependence of the other mechanical properties was strongly influenced by the initial microstructural state. Furthermore, the maximization of different mechanical properties could not be made simultaneously due to their distinct microstructural dependences. The concept of the thermomechanical indices is evidenced as a simple, valid and valuable tool to establish straightforward relationships between the processing and the mechanical behavior. Polym. Eng. Sci. 44:1522–1533, 2004. © 2004 Society of Plastics Engineers.     

Conformation of polycarbonate by flow and magnetic birefringence

Solutions of polycarbonate in chloroform and tetrahydrofuran have been used to make measurements of flow birefringence, magnetic birefringence and viscosity. The results are used with standard theories of the two effects to derive optical and magnetic polarizability anisotropies of the polymer's statistical segment. These anisotropies are then used to determine the average mutual orientation of the phenyl rings in the chain and the average number of monomer units per statistical segment.     

The V-notch at weld lines in polystyrene injection moldings

A major factor that weakens the weld line in injection moldings is the V-notch structure. Though the existence of a V-notch is well known, its depth variation with molding conditions has not been detailed. The aim of this paper is to clarify the V-notch structure and its effect on the strength of general purpose polystyrene injection moldings. A dog bone type tensile specimen with a weld line was molded under several molding conditions. The surface of the weld line was partially eliminated by cutting with a milling machine to seven levels of cut depth (D_c). As a result, the weld strength increased with D_c to about 50%. The relationship between the weld strength and D_c made it possible to determine the V-notch depth, which vas defined as the “depth of the weld line.” From these results, a hypothesis is proposed that the V-notch has a structure with a fine groove on the surface and a poorly bonded inner layer. This study considered the relationships among the weld strength, the depth of the weld line, and molding conditions.     

The structure of filled and unfilled thermotropic liquid crystalline polymer injection moldings

Studies of the microstructure and orientation in thermotropic liquid crystalline polymer injection moldings have been carried out using a variety of techniques to reveal the complex hierarchical structure. The effect of particle filler on the level of molecular orientation in the flow direction appears relatively weak, but at high filler contents, there is a marked disruption of coarse structure in the matrix. © 1993 John Wiley & Sons, Inc.     

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     

Generation of large residual stresses in injection moldings

Large residual stresses have been generated in injection molded bars by ejecting them prematurely and completing the cooling process by quenching into ice water or liquid nitrogen. The stress distribution formed under these conditions was found to be much closer to parabolic than is the case when the moldings cool conventionally. Limited testing on moldings made in this way indicated significant property enhancement and improved resistance to ultraviolet degradation.     

Determination of different morphological structures in PC/ABS open spiral injection moldings

The internal structure of injection molded polymer blends are complex and greatly affect the mechanical properties. In this work, the microstructure development was observed for a Polycarbonate (PC)/Acrylonitrile‐Butadiene‐Styrene (ABS) blend (60/40 wt% blend ratio) that was injection molded using an open spiral mold. The ABS‐rich phase was chemically etched out, leaving behind cavities of different shapes and sizes. With increasing depth, different morphological structures were observed due to the variation of temperature and shear profiles. The changes in morphology can be abrupt, especially at the regions closest to the external surface of the specimen, while a more gradual transition was observed with increasing specimen depth. Thus, a methodology is developed to segregate these structures into different and distinctive layers (skin, shear, intermediate, and core layers) corresponding to the state of shear flow, cavity pressure and distance from the gate. The thickness of these layers and the characteristics of the cavities (i.e. shapes and sizes) are believed to have a direct impact on the final mechanical properties of the moldings. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

PVC注塑件的密度与收缩

分析了PVC注塑件的密度特征和收缩特征,结果表明:PVC注塑件的密度及其分布与PVC注塑件的收缩相互影响。     

Morphology and thermal expansion in large HDPE injection moldings

Morphology and linear coefficients of thermal expansion (LCTE) within the wall of a large (10 kg) injection molded container were evaluated. The study employed polarized light microscopic birefringence techniques, differential scanning calorimetry, scanning electron microscopy (SEM), as well as thermal mechanical analysis to determine the LCTE anisotropy in the skin and core of the wall. A difference in crystallinity between skin and core was found, and a region with distinct lamellas was seen under SEM without sample etching. A large variability in anisotropy of the LCTE was found in the relatively thick (~700 μm) skin of the molding. The LCTE differences between skin and core were attributed to molecular orientation related to resin flow. LCTE anisotropy as an important source of residual stress in the transition zone between skin and core was confirmed by fractographic analysis. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47507.