Numerical simulation of blow molding—Viscoelastic flow analysis of parison formation

The simulation of the parison formation process in blow molding has been studied. The flow field was divided into two regions, namely, the extrudate swell region near the die lip and the parison formation region after the exit swell. In the swell region, we predicted the swelling ratio and residual stress distribution for high Weissenberg numbers for steady planar well using the 1-mode Giesekus model. In the parison formation region, the flow is assumed to be an unsteady unaxial elongational flow including drawdown and recoverable swell and is modeled using the 10-mode Giesekus model. We calculated the time course of parison length and thickness distribution, and compare the calculation results of parison length with experimental data. It was found that the predicted values agreed rather well with the experimental values. The calculation results could especially predict the shrink-back, which is the phenomenon where the parison length becomes shorter after the cessation of extrusion, and it was found tat this was caused by the recoverable swell of the parison, which depends on the tensile stress generation in the die. Various flow rates and die geometries were studied and confirmed the reliability and usefulness of the method.     

Numerical simulation of blow molding—prediction of parison diameter and thickness distributions in the parison formation process

In our previous study, we calculated the time course of parison length in the parison formation stage, but it could predict only the parison area swell. The next target in our study is to calculate the parison diameter and thickness swell. Annular extrudate swell simulation is necessary for the understanding of various kinds of swelling ratios in blow molding. We have examined three kinds of swells (outer diameter, thickness, and area swells) obtained from simulation results of annular extrudate swell, using the Giesekus model, and have developed a method of predicting parison outer diameter and thickness swell values. The predicted values of parison outer diameters are discussed in comparison with experimental data, and reasonable results are obtained by the proposed method. This prediction method could also be applied to the parison formation process using a parison controller. As a result, it is possible to predict approximately the whole process of parison formation by numerical simulation.     

A comprehensive experimental study and numerical modeling of parison formation in extrusion blow molding

Parison dimensions in extrusion blow molding are affected by two phenomena, swell due to stress relaxation and sag drawdown due to gravity. It is well established that the parison swell and sag are strongly dependent on the die geometry and the operating conditions. The availability of a modeling technique ensures a more accurate prediction of the entire blow molding process, as the proper prediction of the parison formation is the input for the remaining process phases. This study considers both the simulated and the experimental effects of the die geometry, the operating conditions, and the resin properties on the parison dimensions using high density polyethylene. Parison programming with a moving mandrel and the flow rate evolution in intermittent extrusion are also considered. The parison dimensions are measured experimentally by using the pinch-off mold technique on two industrial scale machines. The finite element software BlowParison® developed at IMI is used to predict the parison formation, taking into account the swell, sag, and nonisothermal effects. The comparison between the predicted parison/part dimensions and the corresponding experimental data demonstrates the efficiency of numerical tools in the prediction of the final part thickness and weight distributions. POLYM. ENG. SCI., 47:1–13, 2007. © 2006 Society of Plastics Engineers     

A modeling approach to the effect of resin characteristics on parison formation in extrusion blow molding

The most critical stage in the extrusion blow‐molding process is the parison formation, as the dimensions of the blow‐molded part are directly related to the parison dimensions. The swelling due to stress relaxation and sagging due to gravity are strongly influenced by the resin characteristics, die geometry, and operating conditions. These factors significantly affect the parison dimensions. This could lead to a considerable amount of time and cost through trial and error experiments to get the desired parison dimensions based upon variations in the resin characteristics, die geometry, and operating conditions. The availability of a modeling technique ensures a more accurate prediction of the entire blow‐molding process, as the proper prediction of the parison formation is the input for the remaining process phases. This study considers both the simulated and the experimental effects of various high‐density polyethylene resin grades on parison dimensions. The resins were tested using three different sets of die geometries and operating conditions. The target parison length was achieved by adjusting the extrusion time for a preset die gap opening. The finite element software BlowParison® was used to predict the parison formation, taking into account the swell and sag. Good agreements were found between the predicted parison dimensions and the experimental data. POLYM. ENG. SCI., 2009. Published by Society of Plastics Engineers     

Experimental studies on radial extrudate swell and velocity profiles of flowing PS melt in an electro‐magnetized die of an extrusion rheometer

This article investigates the radial extrudate swell and velocity profiles of polystyrene melt in a capillary die of a constant shear‐rate extrusion rheometer, using a parallel coextrusion technique. An electro‐magnetized capillary die was used to monitor the changes in the radial extrudate swell profiles of the melt, which is relatively novel in polymer processing. The magnetic flux density applied to the capillary die was varied in a parallel direction to the melt flow, and all tests were performed under the critical condition at which sharkskin and melt fracture did not occur in the normal die. The experimental results suggest that the overall extrudate swell for all shear rates increased with increasing magnetic flux density to a maximum value and then decreased at higher densities. The maximum swelling peak of the melt appeared to shift to higher magnetic flux density, and the value of the maximum swell decreased with increasing wall shear rate and die temperature. The effect of magnetic torque on the extrudate swell ratio of PS melt was more pronounced when extruding the melt at low shear rates and low die temperatures. For radial extrudate swell and velocity profiles, the radial swell ratio for a given shear rate decreased with increasing r/R position. There were two regions where the changes in the extrudate swell ratio across the die diameter were obvious with changing magnetic torque and shear rate, one around the duct center and the other around r/R of 0.65–0.85. The changes in the extrudate swell profiles across the die diameter were associated with, and can be explained using, the melt velocity profiles generated during the flow. In summary, the changes in the overall extrudate swell ratio of PS melt in a capillary die were influenced more by the swelling of the melt around the center of the die. Polym. Eng. Sci. 44:2298–2307, 2004. © 2004 Society of Plastics Engineers.     

Swell and distortions of high-density polyethylene extruded through capillary dies

The effect of varying the die entrance angle and the die length on extrudate swell and on the onset of extrudate distortion in capillary extrusion has been studied. Using theory from the literature, we have analyzed the contribution to the total pressure drop from the elongational and shear deformation in the entrance region, and from the capillary pressure drop in the land region of the die. From the contribution of the elongational deformation, we obtained an estimate for the elongational viscosity of the polymer. The same analysis was used to study the influence of the die geometry on the stick-slip instability. It is found that the elongational component at the inlet region mainly influences the extrudate distortions. The onset of the stick-slip instability occurs within 10% at a wall stress τ_w of 0.3MPa, where τ_w is calculated from expressions assuming fully developed flow. The variation around this average value is systematic with changes in die geometry, and the observed variations are probably due to the non-homogeneous pressure field in the die. We also propose a model for predicting extrudate swell. Input to the model are material parameters obtainable from oscillatoric measurements of the loss and storage modulus and residence times calculated from the geometry of the die. The swell model includes a fitting parameter that sets the overall scale of the swell.     

An experimental investigation of capillary extrudate swell in relation to parison swell behavior in blow molding

An experimental study was carried out to study and characterize the capillary extrudate swell and parison swell behavior in extrusion blow molding of two commercial blow molding grade high density polyethylene resins. The capillary extrudate swell behavior of these resins were determined employing a capillary rheometer and a special thermostatting chamber. Parison swell behavior was determined using an Impco A13-R12 reciprocating screw blow molding machine in conjunction with cinematography and pinch-off. The experimental conditions under which capillary extrudate and parison swell data can be related are elucidated. Excellent agreement is found between the area swell values determined on the basis of capillary and parison swell experiments.     

Isothermal swell of extrudate from annular dies; effects of die geometry,flow rate,and resin characteristics

An experimental study was made of the effects of die geometry and extrusion velocity on parison swell for three high-density-polyethylene blowmolding resins. Four annular dies were used: a straight, a diverging, and two converging dies. Diameter and thickness swells were measured as functions of time under isothermal conditions and in the absence of drawdown. This was accomplished by extruding into an oil having the same density and temperature as the extrudate. It was observed that 60 to 80 percent of the swell occurs in the first few seconds and that equilibrium swell is attained only after 5 to 8 minutes have elapsed. The diameter and thickness swells appear to be independent phenomena, as the relationship between them depends strongly on die design. The ranking of the resins in terms of the magnitude of the swell was found to be the same for all die geometries and extrusion rates used.     

Overall numerical simulation of extrusion blow molding process

This paper focuses on the overall numerical simulation of the parison formation and inflation process of extrusion blow molding. The competing effects due to swell and drawdown in the parison formation process were analyzed by a Lagrangian Eulerian (LE) finite element method (FEM) using an automatic remeshing technique. The parison extruded through an annular die was modeled as an axisymmetric unsteady nonisothermal flow with free surfaces and its viscoelastic properties were described by a K‐BKZ integral constitutive equation. An unsteady die‐swell simulation was performed to predict the time course of the extrudate parison shape under the influence of gravity and the parison controller. In addition, an unsteady large deformation analysis of the parison inflation process was also carried out using a three‐dimensional membrane FEM for viscoelastic material. The inflation sequence for the parison molded into a complex‐shaped mold cavity was analyzed. The numerical results were verified using experimental data from each of the sub‐processes. The greatest advantage of the overall simulation is that the variation in the parison dimension caused by the swell and drawdown effect can be incorporated into the inflation analysis, and consequently, the accuracy of the numerical prediction can be enhanced. The overall simulation technique provides a rational means to assist the mold design and the determination of the optimal process conditions.     

Experimental and theoretical investigation of extrudate swell of polymer melts from small (length)/(cross-section) ratio slit and capillary dies

An experimental and theoretical study is presented of extrudate swell from short capillary and slit dies. The polymer melts studied were polystyrene and polypropylene. The swell from slit dies is greater than the swell from capillaries. Decreasing die entry angle for capillary dies decreases swell. The argument is made that elongational How existing in the die entry region and for short dies determines extrudate swell. Dimensional analysis arguments are used to relate extrudate swell to a Weissenberg number based on elongational flow at the die entrance and the detailed die geometry. Correlations are developed. The theoretical study is based on unconstrained elastic recovery following elongational How through the die entrance region.     

A parallel coextrusion technique for simultaneous measurements of radial die swell and velocity profiles of a polymer melt in a capillary rheometer

This article proposes a new experimental technique to simultaneously measure radial die swell and velocity profiles of polystyrene melt flowing in the capillary die of a constant shear rate rheometer. The proposed technique was based on parallel coextrusion of colored melt‐layers into uncolored melt‐stream from the barrel into and out of the capillary die. The size (thickness) ratio of the generated melt layers flowing in and out of the die was monitored to produce the extrudate swell ratio for any given radial position across the die diameter. The radial velocity profiles of the melt were measured by introducing relatively light and small particles into the melt layers, and the times taken for the particles to travel for a given distance were measured. The proposed experimental technique was found to be both very simple and useful for the simultaneous and accurate measurement of radial die swell and velocity profiles of highly viscous fluids in an extrusion process. The variations in radial die swell profiles were explained in terms of changes in melt velocity, shear rate, and residence time at radial positions across the die. The radial die swell and velocity profiles for PS melt determined experimentally in this work were accurate to 92.2% and 90.8%, respectively. The overall die swell ratio of the melt ranged from 1.25 to 1.38. The overall die swell ratio was found to increase with increasing piston speed (shear rate). The radial extrudate swell profiles could not be reasoned by the shear rate change, but were closely linked with the development of the velocity profiles of the melt in the die. The die swell ratio was high at the center (～1.9) and low (～0.9) near the die wall. The die swell ratio at the center of the die reduced slightly as the piston speed was increased. Polym. Eng. Sci. 44:1960–1969, 2004. © 2004 Society of Plastics Engineers.     

Effect of molecular structure on extrudate swell behavior for different thermoplastic melts in an electro‐magnetized die

The extrudate swell ratio of five different thermoplastic melts flowing in a constant shear rate rheometer having a capillary die with and without application of magnetic field was studied. The effects of the magnetic flux direction and density, die temperature, and wall shear rate on the extrudate swell and flow properties were investigated. The experimental results suggested that an increasing wall shear rate increased the swelling ratio for the polystyrene (PS), LLDPE, and PVC melts, but the opposite effect was observed for the ABS and PC melts. The extrudate swell ratio for the PS, ABS, PC, and LLDPE melts decreased with increasing die temperature, the effect being reversed for the PVC melt. Thermoplastic melts having high benzene content in the side‐chain and exhibiting anisotropic character were apparently affected by the magnetic field, the extrudate swell ratio increasing with magnetic flux density. The effect of the magnetic field on the extrudate swell ratio decreased in the order of PS → ABS → PC. The extrudate swell ratio for the co‐parallel magnetic field system was slightly higher than that for the counter‐parallel magnetic field system at a high magnetic flux density. POLYM. ENG. SCI., 47:270–280, 2007. © 2007 Society of Plastics Engineers.     

Extrudate swell from slit and capillary dies: An experimental and theoretical study

A comparative experimental study of extrudate swell from long slit and capillary dies is reported for rheologically characterized polystyrene and polypropylene melts. Generally extrudate swell from a slit is greater than that from a capillary die. At low die wall shear rates it goes to a value of about 1.2 as opposed to about 1.1 found for capillary dies. The onset and character of extrudate distortion have been studied. The experimental results are compared with theories of swell based on unconstrained recovery from Poiseuille flow in these geometries. A detailed analysis of such theories of extrudate swell based on the original work of Tanner has been carried out. The analysis is placed in a more general form which should be valid for a range of die cross-sections.     

Numerical simulation of a single-screw plasticating extruder

A fully-predictive steady-state computer model has been developed for a single-screw plasticating extruder. Included in the model are a model for solids flow in the feed hopper; a variation of the Darnell and Mol model for the solids conveying zone; a variation of Tadmor's melting model for the melting zone; an implicit finite difference solution of the mass, momentum, and energy conservation equations for the melt-conveying zone of the extruder and die; and a predictive correlation for the extrudate swell at the die exit. A temperature- and shear-rate-dependent viscosity equation is used to describe the melt-flow behavior in the model. The parameters in the viscosity equation are obtained by applying regression analysis to Instron capillary rheometer data. Given the material and rheological properties of the polymer, the screw geometry and dimensions, and the extruder operating conditions, the following are predicted: flow rate of the polymer, pressure and temperature profiles along the extruder screw channel and in the die, and extrudate swell at the die exit. The predictions have been confirmed with experimental results from a 11/2 in. (38 mm) diameter, 24:1 L/D single-screw extruder with a 3/16 in. (4.76 mm) diameter cylindrical red die. High- and low-density polyethylene resins were used.     

Effect of die gap width on annular extrudates by the annular extrudate swell simulation in steady-states

We calculated the steady-state annular extrudate swell of polymer melts through flow geometries encountered in processes used to control parison thickness. A streamline-upwinding finite element method with an under-relaxation for the rate of deformation tensor was used. The Giesekus model was employed as the constitutive equation. An operation that widens the die gap is appropriate for the control of parison thickness corresponding to the change of die gap width. However, a control process that decreases the die gap width is not useful, because the parison thickness does not correspond to the die gap width. Furthermore, thickness swells change strikingly with the Weissenberg number. It is difficult to control the parison outer diameter in the case of a converging die, because the change of the outer diameter swell becomes large with increasing Weissenberg number. In the case of a diverging die, the changing value of the outer diameter swell is smaller than that in the case of a converging die.     

Experimental studies on extrudate swell behavior of PS and LLDPE melts in single and dual capillary dies

Extrudate swell behavior of polystyrene (PS) and linear low‐density polyethylene (LLDPE) melts was investigated using a constant shear rate capillary rheometer. Two capillary dies with different design configurations were used, one being a single flow channel and the other being a dual flow channel. A number of extrudate swell related parameters were examined, and used to explain the discrepancies in the extrudate swell results obtained from the single and dual flow channel dies, the parameters including output rate and output rate ratio, power law index, wall shear rate, wall shear stress, melt residence time, pressure drop induced temperature rise, flow channel position relative to the barrel centerline, and the flow patterns. It was found in this work that the power law index (n value) was the main parameter to determine the output rate ratio and the extrudate swell between the large and small holes for the dual flow channel die: the greater the n value the lower the output rate ratio and thus decreased extrudate swell ratio. The differences in the extrudate swell ratio and flow properties for PS and LLDPE melts resulted from the output rate ratio and the molecular chain structure, respectively. The extrudate swell was observed to increase with wall shear rate. The discrepancies in the extrudate swell results from single and dual dies for a given shear rate were caused by differences in the flow patterns in the barrel and die, and the change in the melt velocities flowing from the barrel and in the die to the die exit. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1713–1722, 2003     

Experimental study on extrudate swell and die geometry of profile extrusion

The objective of this study was to determine the die swell behavior of a polymer melt and to design a die for forming a polymeric extrudate with a desired shape using profile extrusion. Polystyrene pellets were chosen to perform the profile extrusion experiments. First, the polystyrene pellets were melted and pushed through a quarter ring profile. The profile of the swelled extrudate agreed with the numerical predictions. A modified die was designed to produce a quarter ring profile extrudate based on the direct extrusion problem (DEP) prediction. Polystyrene pellets were also melted and pushed through the modified die. The experimental results were close to the computational results. The melting temperature, die length, and melting residence time affect die swell behavior. The die swell ratio becomes smaller as the melting temperature and melting residence time are increased. As the die length is increased, the die swell ratio is lowered. According to the die geometry predictions, an extrudate with the desired profile can be made precisely.     

Effect of die temperature on the flow of polymer melts. Part II: Extrudate swell

The effect of die wall temperature on the extrudate swell of polymer melts flowing through dies with single and dual circular channels was studied. Extrudate swell was measured at constant flow rates using an Instron capillary rheometer with a modified die section. It was found that under isothermal conditions, extrudate swell plotted against the average wall shear stress gave rise to a temperature independent correlation for polystyrene. Under non-isothermal conditions, such a correlation did not exist, which might be due to the change of wall shear stress in the axial direction. The extrudate swell in the non-isothermal cases can be better correlated with the wall shear stress at die exit. For the two-hole die, changes of die wall temperature varied both the flow rate ratio and the extru date swell ratio. The latter is, however, much less sensitive to the die wall temperature than the former.     

Swell of extrudate from an annular die

Diameter and thickness swells have been measured as functions of time and wall shear rate for three high density polyethylenes at 170°C and one polypropylene at 190°C. By extruding into an oil having the same temperature and density as the extrudate, it was possible to measure isothermal swell in the absence of drawdown. Seventy to 80 percent of the swell occurs in the first one or two seconds, while several minutes are required to reach an equilibrium state. Relationships between various swell parameters, including parison weight swell and capillary extrudate swell, are examined. Important differences between the behavior of the polyethylenes and that of the polypropylene are noted.     

Foam extrusion characteristics of thermoplastic resin with fluorocarbon blowing agent. I. Low-density polyethylene foam extrusion

An experimental study was conducted to investigate the foam extrusion characteristics of low-density polyethylene resin. For the study, we used dichlorotetrafluoroethane and dichlorodifluoromethane as blowing agent and talc as nucleating agent. In the study, we investigated the effects of processing and material variables on the foam extrusion characteristics, namely extrudate swell behavior, foam density, and cell morphology. It was found that an inverse relationship exists between the extrudate swell ratio and the foam density. Also investigated was the effect of die geometry (theL/D ratio, D_R/D ratio, and entrance angle) on the foam extrusion characteristics of low-density polyethylene resin. Suggestions are made on the experimental technique that may be useful in selecting resins for foam extrusion operation. Also suggested are guidelines for selecting an optimum die geometry that would produce good quality foams of low-density polyethylene.