MODELING AND SIMULATION OF THE INFLATION STEP IN THE TWO-STAGE GITBLOW-PROCESS

Transcription

1 MODELING AND SIMULATION OF THE INFLATION STEP IN THE TWO-STAGE GITBLOW-PROCESS Elmar Moritzer, Björn Landgräber, Yannick Martin, Paderborn University, Kunststofftechnik Paderborn (KTP), Germany Stefan Seidel, Bond-Laminates GmbH, Brilon, Germany Abstract The innovative two-stage GITBlow process combines the advantages of injection molding and blow molding. This is achieved by producing a preform using gasassisted injection molding, which is then inflated by a second gas injection within a larger cavity in the same mold. The components obtained have a large volume/wall thickness ratio, while, at the same time, featuring elements that are typical of injection molded parts, e.g. ribs. This paper presents the simulation of the inflation behavior under consideration of inhomogeneous preform temperature. For this purpose, a spring-dashpot model is developed to describe the viscous and viscoelastic behavior of the plastic material. The findings obtained in the simulations are then verified with experimental results. Introduction In the area of plastics processing, special processes to generate complex components with a design that fits a specific application are becoming increasingly important. In addition, technical challenges change dynamically as customer requirements grow constantly, calling for continuous innovation and development of the existing technologies and new processes. The demand for complex, thin-walled hollow structures with functional geometries is on a constant rise. GITBlow combines high accuracy in the reproduction of surface details as well as the short cycle times of gas injection molding to the production of complex thin walled hollow spaces, which is a feature typical of blow molding. In this process, first a preform is produced by gas-assisted injection molding (GAIM). In the following step, this preform is then inflated further by a second gas injection, while remaining inside the same mold (Fig. 1). Figure 1. Near-production GITBlow prototype part (left: preform; right: finished part) This generates a large, enclosed and thin-walled hollow space, which cannot be produced by mere gasassisted injection molding, due to restrictions in the attainable wall thicknesses [1]. The freedom of design for possible component geometries, however, is restricted in blow molding. For example, it is impossible to produce functional elements such as ribs or connector elements. They have to be connected to the blow molded parts in a downstream joining process. The GITBlow process makes up for these downsides. By combining the two processes, it allows for the production of components with local thinwalled hollow spaces and functional geometries connected. The technique s dimensional accuracy is typical of injection molding processes. Considering process control, the two stages of gas injection and blow molding are carried out at different times (Fig. 2). The upper of the two mold cavities shown in the figure features the preform geometry. Subsequently to the generation of a preform by GAIM, the mold is opened. A rotary table transfers the preform into the larger cavity (the lower of the two cavities). A second gas injection takes place here, inflating the component. At the same time, a new preform is made in the smaller cavity. SPE ANTEC Anaheim 2017 / 1549

2 Figure 2. Schematic diagram of the two-stage GITBlow process. As part of the complete process simulation, this paper describes the aspect of the inflation behavior during the second stage of gas injection. Modeling Aspects For the two-stage process under investigation, a characteristic wall thickness distribution is obtained for all materials and operating points. Temperature differences over the component cross-section lead to local differences in inflating behavior. Hot spots in the lateral section of the component cause it to stretch more severely there than in the upper section. Material stretching is more pronounced in the lateral areas than in the top, because stretching resistances differ in these cross-sectional areas. As a result, top walls are thicker than side walls. To describe the forming processes for blow molding and thermoforming applications, CFD simulations are frequently applied in practical use. The basic mechanisms are very similar to those of the GITBlow process [2]. Fig. 3 shows the result of an inflation simulation using the CFD-Software Ansys Fluent for a two-stage GITBlow process. However, this simulation leads to the reverse case: Walls are thicker on the sides than on the top. The CFD simulation fails to consider the plastic s solid state properties, i.e. material data does not take into account the viscoelastic behavior at low temperatures. For blow molding and thermoforming applications, these properties are irrelevant, because the preforms are heated homogeneously and to a level significantly higher than minimum forming temperature. Using the GITBlow process, however, some areas of the cross-section are heated to a level that is very close to minimum forming temperature, or, in some cases, even below. These cooler sections prevent viscous flow. It is therefore crucial for the inflation simulation take the solid state properties of the materials into consideration. This is why a mere viscous material model such as is used in the CFD simulation mentioned above is unsuitable to simulate inflation in this case. Physically speaking, viscous flow means slippage of molecular chains on each other. In case of insufficient heat, the molecular chains are less flexible, which prevents slippage, because some sections of the molecules are branched to each other. Severe forming resistances are obtained, caused, in part, by elongation of the molecule chains themselves. Stretched molecule chains can be elastically resilient, which leads to the viscoelastic behavior characteristic of thermoplastics. Creeping and stress relaxation are the results of this material behavior. While temperatures during inflation are extraordinarily low in the GITBlow process as compared to classical forming techniques, the main factor to determine forming is viscoelastic material behavior. However, temperatures at the component interior may be very high (Fig. 4), which is why viscous material properties have to be considered just as well. To make a precise statement about the temperature-related material properties of the material at the time of inflation, the preform half to be considered is divided into identical angle sections, in a first step. Figure 3. Component wall thickness comparison of CFD- Simulation and experimental data Figure 4. Measuring points for temperature and wall thickness investigations By means of FEM calculation using the Abaqus simulation software, average temperatures are determined SPE ANTEC Anaheim 2017 / 1550

3 for the defined positions. This has to be done for the specific material and operating point, in order to predict the respective inflating result for the parameter combination under consideration. For the detailed findings and boundary conditions underlying this simulation, see [3]. In view of the temperature gradients existing over the preform cross-section, there are two options of segmentation. Dividing the preform wall radially along the contour provides information on the way temperature develops over the circumference. Because of the hotspot in the lateral wall, average wall temperature decreases continuously until top position 9. Along with this, deformation resistance continuously increases from position 1 to 9. As a result, the characteristic wall thickness distribution (wall thickness increasing from the side walls to the top section), as described, is to be expected in the inflated component. Dividing the preform wall into inner and outer segments, however, shows that, in some areas, the plastic s temperature is significantly higher on the inside than on the outside. It can therefore be stated that the deformation behavior during inflation is mainly determined by viscous processes on the inside and by viscoelastic processes on the outside. There is mutual interaction, though, between these two deformation processes due to the fact that loads acting upon inner and outer walls can only be parallel. External load (i.e. inflating pressure) logically always causes a line load over the entire wall thickness. To reproduce these inter-relations in a model theory, the spring-dashpot model presented in Fig. 5 is established. It links the viscous to the viscoelastic aspects of plastic via a parallel connection. Figure 5. Three-Parameter-Model for micromechanical material behavior in the blow molding step of the GITBlow process the exterior, making the material mainly viscoelastic. While per definition viscosity can be described as a single dashpot, the MAXWELL model represents a way to describe a material behavior that is elastic and viscous. Composed of spring and damper units in a series connection, this model is linked to the preform exterior, while the single dashpot describes the forming behavior on the interior side. While both layers of the wall are stretched via the same path during inflation, the individual models are arranged in a parallel connection. The spring-damper model presented is a so-called three-parameter model. Its structure is similar to that of, e.g., the VOIGT-MAXWELL model with its dashpot connected in series with a parallel connection consisting of spring and damper. The VOIGT-MAXWELL model usually serves to describe creep and creep recovery behavior [4]. The viscosity at zero shear rate is defined as the damping coefficient η 0 of the single dashpot. The storage modulus (degree of the elastic shares of deformation) represents the spring constant E Sp. The loss modulus is the second damping coefficient η V as a measure of the plastic shares of deformation in the material [4]. According to the basic equations of the individual elements, the following differential equation is obtained [5], which connects exterior load σ to the total elongation ε resulting: σ + E Sp η V σ = η 0 ε + η V+η 0 η V E Sp ε (1) In this equation, σ is defined as input variable, i.e. the tensile stress in circumferential direction of the preform, resulting from the inflating pressure. As output variable, i.e. the elongation caused by the load, ε is defined. Parameter η 0 stands for the (zero-) extensional viscosity obtained from the TROUTON relation and the temperature displacement calculated with the WLF equation. The storage modulus E replaces parameter E Sp, while the loss modulus E replaces η V. Storage and loss modulus are the real and imaginary parts of the complex dynamic E-modulus. They are determined in a dynamic three-point bending test at constant load frequency and at different temperatures. The storage and loss modules for a SBS material are presented over temperature at 1 Hz and 10 Hz test frequencies in Fig. 6. The model concept underlying this structure corresponds to the situation as described above. On the inside of the preform, the plastic material has a higher temperature, because the heat cannot flow into the mold within the defined cooling time as a result of low heat conductivity. In a first approximation, material behavior is perfectly viscous here. The temperatures of the plastic material range around minimum forming temperature on SPE ANTEC Anaheim 2017 / 1551

4 thickness of the inflated component was determined. Considering the preform symmetry, the inflated area, is divided in circumferential direction into 9 segments of the same shape. Fig. 7 presents this for the preform of the two-stage process. Figure 6. Temperature-dependent storage modulus E and loss modulus E (material: SBS) The diagram shows a pronounced drop in curvature between 100 and 120 C, which marks the glass transition temperature of the amorphous plastic. Dynamic threepoint measurement provides information on the storage and loss modules dependence on temperature, in addition to the frequency-related dynamic behavior of the material examined. Increasing the frequency causes the phases of the module curves to shift to the right, i.e. in the direction of increasing temperature. The measuring frequency is a characteristic value of deformation rate here [6]. Applying the GITBlow process, high stressing rates are obtained as inflating pressures rise. For the inflating pressures usually applied in GITBlow molding (between 5 and 20 bar), the deformation rate obtained is best approximated with a 1 Hz measuring frequency. In the following step, the elongation (ε) of the preform obtained is divided into several segments and defined as the relative share in total elongation. To standardize the effects of the characteristic values E, η 1 und η 2 for this investigation, the measured parameters are normalized to make them suitable for analytical calculation. For example, input and output values σ und ε are to be considered as dimensionless, which is why there is no need to convert the inflating pressure set into the stress generated inside the preform wall. In a preliminary step, the differential equation of the 3-parameter model set up (equation 1) is solved in a way that makes it possible to calculate the dependency of elongation ε on stress σ via a transfer function G: G = ε σ = s+ E η1 η 2 s 2 +E (η 1+η2 ) s η1 The transfer function G now allows for analytic calculation of the elongation response to any time-related stress signal. Due to the parameters employed, this elongation response is highly dependent on temperature. This is why the preform wall cannot be considered as a whole, because the average temperature changes significantly in circumferential direction, which has been shown in temperature simulation (Fig. 4). The preform is therefore divided into segments. The number of measuring points is the same as established when the wall (2) Figure 7. GITBlow-Preform partitioning Prior to the calculations, the geometry of the gas bubble is set. The average temperatures prevailing at the respective measuring positions 1 to 9 had been determined in temperature simulation and are then related to the respective spring-damper models. Using this model, the geometry does not need to be meshed into volume or area elements. In mathematical terms, this is a one-dimensional calculation. Acting homogeneously over the entire interior wall of the preform, the inflating pressure causes inner load that applies tension to the individual preform segments. This tensile load is applied to the individual 3- parameter models at a certain angle. This angle can be neglected, though, because the stress is assumed as dimensionless for the calculations and because the segments have the same angles to each other, i.e. loads are the same for all segments. Experimental Validation In order to validate the simulation results, a way must be found to directly compare simulation to real measured values. Measuring real GITBlow components, wall thicknesses are determined in defined measuring spots, whereas simulation presents relative elongations of the individual preform segments. An analytical approach serves to conduct the necessary conversion. The simulated relative elongation ε i,rel for segment i is related to the known total elongation, in a first step. This terms refers to enlargement of the outer preform contour to the final component. The length of the outer contour of the preform (s Preform) stretches to reach the length of the outer contour of the component s Part. This is the real elongation (HENCKY elongation) of the hollow space wall. The relative elongation ε i,rel thus leads to the real, i.e. absolute elongation of each single preform segment. Due to the plastic s volume and mass continuity, this elongation in SPE ANTEC Anaheim 2017 / 1552

5 longitudinal direction causes transverse contraction. This Poisson s ratio ν, which describes the ratio between transverse and longitudinal elongation is constant by approximation at the high temperatures prevailing during inflation (above glas transition temperature, i.e. within forming temperature range), assuming the value of 0.5, which is the maximum value that is possible in mathematical-physical terms [7]. Related to the preform wall thickness in position i (d i,preform), which is deducted from the gas bubble s preset geometry, the component s wall thickness (d i,part) in the respective measuring spot is obtained. Mathematically, this proceeding can be summarized as follows: d i,part = d i,preform [1 ν ε i,rel ( s Part s Preform 1)] (3) The relative elongation ε i,rel presented here results from calculation with the 3-parameter model introduced before. Fig. 8 shows the result obtained in a comparison between standard wall thicknesses that is determined experimentally and those calculated in simulations, for an operating point of the two-stage GITBlow process. Calculated and measured wall thicknesses are normalized to the respective average value. This improves comparability of the simulation results for different types of material. Discussion The deviations that exist between simulation and reality, as can be seen in the diagram above, are located in the lower lateral areas (measuring points 1 and 2) and in the top (measuring points 7 to 9). With all operating points, these deviations are very small. They are caused by the fact that adhesion mechanisms are neglected, taking place between the plastic and steel, as well as between the individual plastic elements. Moreover, the temperatures prevailing inside the preform cannot be validated, which is why uncontrollable deviations between simulation and reality might exist here. The simulated wall thickness is too high on the sides, and too low at the top, which may also be a result of the plastic s cooling behavior while being inflated. This issue is not considered by the employed spring-damper model, because it is unknown at present, where exactly the plastic material meets the surface of the inflation cavity. Generally speaking, the error sources described can be neglected, though. This is because, regardless of these simplifications, simulation provides an excellent approximation of real conditions. To find out whether the model is universally valid, more experimental research should be conducted to investigate other starting materials, as well. The model could also be enhanced to minimize the systematic deviations, most of all in components sections 1, 2 and 7 9. For this purpose, further investigations are necessary to determine, e.g. wall temperature in the preform geometry. Conclusions Figure 8. Component wall thickness comparison of Three- Parameter-Model simulation and experimental data The simulation results obviously represent a good approximation of real wall thickness distribution. For the presentation chosen, the symmetry of the component cross-section is considered. However, while doing so, it is important to make sure the preform wall thickness, node temperatures and component wall thickness are determined for the same cross-section halves. For all other operating points investigated, the calculated wall thicknesses differed only insignificantly from the real measured values, too. From the findings presented, it becomes obvious that model accuracy of the three-parameter model established is sufficient for the material under examination (SBS) as well as for the different operating points. In contrast to conventional CFD simulation, the model is able to substantially improve the agreement with experimental investigations for the GITBlow process. Acknowledgement The results presented here were obtained in the context of the research project MO 685/15-1, sponsored by the Deutsche Forschungsgemeinschaft (DFG). We would like to thank the DFG for their support. References 1. E. Moritzer, Phänomenorientierte Prozess- und Formteiloptimierung von thermoplastischen SPE ANTEC Anaheim 2017 / 1553

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