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.     

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     

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.     

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.     

Effects of molding conditions on properties of injection-molded polycarbonates

Statistically designed experiments were carried out to study the effects of molding conditions on the properties of two types of polycarbonate, which were synthesized by the solvent process and the melt process, respectively. The properties tested in this study were classified into two groups with respect to the effect of molding conditions. One, which included birefringence, heat shrinkage at 180°C, and surface resistance to Taber abrasion, was mainly affected by stock temperature and was slightly affected by holding pressure. The other, which included resistance to solvent crack, Rockwell hardness, density, and heat shrinkage at 120°C, was affected by mold temperature and holding pressure. Mechanically isotropic moldings with a low degree of frozen orientation could be molded at a high stock temperature and at a low holding pressure, where stock temperature was more effective than holding pressure. Moldings with low residual stresses could be molded at a high mold temperature and at a low holding pressure. Essentially there was no difference in the molding conditions and properties by the method of synthesis. However, under the same molding conditions polycarbonate synthesized by the melt process gave a higher degree of frozen orientation and somewhat more rigid moldings.     

Distribution of some physical properties in injection-molded thermoplastic parts

During the injection molding process, moldings undergo shear and elongational stresses. They are also exposed to thermal gradients of varying intensity. Invariably, molded parts, or at least some sections thereof, freeze before the polymer chains can relax to a random, non-oriented configuration. As a result, injection molded parts contain frozen strains and exhibit anisotropic physical properties. In the present work, a variety of experimental techniques have been employed to determine the three-dimensional variation of the following properties of injection-molded, thermoplastic, rectangular parts: density, heat shrinkage, birefringence, and tensile strength.     

Orientation in injection molded polystyrene

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

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     

Shrinkage anisotropy in fiber reinforced injection molded products

This paper includes a systematic study of the effect of fiber concentration and molding conditions on fiber orientation and shrinkage in injection molded composites. Closed-form expressions were derived to relate shrinkage and internal stresses to the molding pressure and fiber orientation. The shrinkage predictions were seen to agree well with experimentally measured shrinkages.     

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.     

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.     

Investigation of melt manipulation phenomena during injection molding via in situ birefringence observation

This study investigates the effects of melt manipulation on the development of molecular orientation during injection molding processing. Vibration‐assisted injection molding (VAIM), a particular method of melt manipulation, is a variation of conventional injection molding in which oscillatory energy is imparted to the polymer melt by vibrating the injection screw axially during the injection and packing stages of the molding cycle. Previous studies have shown that this process positively affects the tensile strength of polystyrene parts, but that the magnitude of the increase is dependent upon the processing parameters. Observation of birefringence patterns in VAIM processed samples show a significant impact on molecular orientation. A specially designed mold and associated image capture system has been developed and is used in this study to record the birefringence patterns of the polymer melt within the cavity during processing. Observation of birefringence shows that orientation develops primarily during post‐vibration packing of the part and not during the vibration phase as previously thought. The observed effects of process parameters such as melt temperature, packing pressure, and vibration duration are discussed. POLYM. ENG. SCI. 46:1691–1697, 2006. © 2006 Society of Plastics Engineers     

Effect of process conditions on birefringence development in injection-molded parts. I. Numerical analysis

Analysis of the injection-molding process based on Leonov viscoelastic fluid model has been employed to study the effects of process conditions on the residual stress and birefringence development in injection-molded parts during the entire molding process. An integrated formulation was derived and numerically implemented to solve the nonisothermal, compressible, and viscoelastic nature of polymer melt flow. Simulations under process conditions of different melt temperatures, mold temperatures, filling speeds, and packing pressures are performed to predict the birefringence variation in both gapwise and planar direction. It has been found that melt temperature and the associated frozen layer thickness are the dominant factors that determine the birefringence development within the molded part. For a higher mold temperature, melt temperature, and injection speed, the averaged birefringence along gapwise direction is lower. The birefringence also increases significantly with the increased packing pressure especially along gate area. The simulated results show good consistency with those measured experimentally. © 1995 John Wiley & Sons, Inc.     

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     

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

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

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

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

Comparison of structure development in injection molding of isotactic and syndiotactic polypropylenes

A comparative study of the crystallization and orientation development in injection molding isotactic and syndiotactic polypropylenes was made. The injection molded samples were characterized using wide angle X‐ray diffraction (WAXD) techniques and birefringence. The injection molded isotactic polypropylene samples formed well‐defined sublayers (skin, shear and core zones) and exhibited polymorphic crystal structures of the monoclinic α‐form and the hexagonal β‐form. Considerable amounts of β‐form crystal were formed in the shear and core zones, depending on the injection pressure or on the packing pressure. The isotactic polypropylene samples had relatively high frozen‐in orientations in the skin layer and the shear zone. The injection molded syndiotactic polypropylene exhibited the disordered Form I structure, but it did not appear to crystallize during the mold‐filling stage because of its slow crystallization rate and to develop a distinct shear zone. The core zone orientation was greatly increased by application of high packing pressure. The isotactic polypropylene samples exhibited much higher birefringence than the syndiotactic polypropylene samples at the skin and shear layers, whereas both materials exhibited similar levels of crystalline orientation in these layers.