A numerical investigation of the effect of preform length for the fabrication of 1.5Lt PET bottle through the injection stretch blow molding process

This study carries the numerical effort for the investigation of effect of preform length on the final product wall thickness distribution. For the investigation, three different preform length cases were taken under consideration. Preform A, preform B and preform C of length 144.75mm, 165.7mm and 186.65mm respectively. All the preforms were stretched up to a same critical point respect to mold length so that the axial deformation during blowing was fair for all the preform cases. Blowing conditions were the same for all cases. The stretching period for each case was set in accordance to the to the limit of critical stretching point. The mass of all preform cases was 58.33grams. It was found that preform B and C result in more uniform thickness distribution. The optimum results are given by preform C, since the resulting product appears the less spots with excess usage of raw material. The heavier bottle bottom region resulting from preform C enhances the steadiness of the bottle.


Introduction
Injection Stretch Blow Molding process is a widely used fabrication technique for the production of hollow plastic containers [1], [2] [3] [4] [5] [6] [7], [8]. It comprises the stretching and blowing at the same time, of a preheated preform. The preform is similar to a test tube. Both stretching and blowing take place in a mold, which has the shape of the desired bottle/container. Thus the blown preform takes the desired volume [9]. The contact between the blown preform and the cooler mold walls reduced the temperature of the blown preform and therefore solidification of plastic initiates. Poly(Ethylene Terephthalate) (PET) is the most common choice for bottle/container fabrication due to its good mechanical and barrier properties [3].
One of the most crucial parameters in Stretch Blow Molding (SBM) is the temperature distribution along the preform length. Temperature highly affects the consistency of the raw material and therefore influences the kinematics during stretching and blowing [1] [10]. An earlier research lists the effort of optimization of preform temperature distribution via infrared (IR) radiation preform reheating step [1]. The researchers implemented a finitevolume software for the simulation of the reheating step while the SBM simulation was employed in ABACUS. For the optimization of temperature distribution three optimization variables were taken into consideration corresponding to three temperature locations along the preform length. They used Cubic Hermite Interpolating Polynomial was to extract the optimization temperature between the three temperature locations [11]. The study indicated that the final bottle wall thickness distribution is 80% more uniform after the temperature optimization.
An earlier study implementing the Oldroyd B type constitutive model to simulate the behavior of PET during the SBM process [12]. The temperature balance equation was approximated by the Crank-Nicholson scheme. The study also involves experimental investigations. It was found that by increasing the preblow time delay, more material is transferred from the neck of the preform to its lower body which is in agreement with more recent studies [3]. The authors performed the simulations with isothermal and non-isothermal model. The numerical results obtained using the non-isothermal model were closer to the experimental SBM. In addition, during both simulations and experiments the final temperature distribution is slightly higher than the initial temperature distribution due to energy dissipation during SBM.
The commercial simulation package POLYFLOW has been implemented in another study for the investigation of blowing pressure and stretch rod velocity on the final thickness distribution along the surface of a 680ml PET bottle [13]. The SBM process was also investigated experimentally. The comparison between the experimental and simulation results revealed that the simulated thickness distribution follows the similar trend with the experimental.
Although, in contrast with the experimental results, the simulations indicated that the increase in blowing pr does not provide any change on the thickness distribution. The conclusions extracted from the experiments a the higher blowing pressure provides a slight difference on thickness distribution, especially on the middle bottle length [13].
The current effort deals with the numerical investigation of the effect of preform geometry on the final produc thickness distribution. More specifically three different preform length cases were taken under consideration preform length is a parameter that is has not been investigated before. The study also comprises the effort to ma the preform temperature as much as possible above the glass-rubber limit which is about 80°C [14]. Stretchi preform above this limit induces crystallization [14]. Stretching may also occur during the material deform while the blown preform fills the mold cavities. The amount of induced crystallization is influenced b deformation and strain-rate modes [14] [15] [16] [17]. The highest the percentage of crystals in the materi highest is the strength [18]. Figure 1 illustrates the symmetry plane of the 3D shell solution domain with the three preform length case solution domain consists of two half moving molds, the preform and small tip (red color) representing the s rod. At the initiation of the simulation the two half molds move towards the preform and provide the cla force. The lengths of the three preform length casespreform A, preform B and preform C-are 144.7 165.7mm and 186.65 mm respectively. Tin represents the initial temperature on the preform walls. Tin obtain allowing the three preforms to quench within the mold from 378K or 105°C for 3.5 seconds. During the real process, there is a short time delay before stretching and blowing. This time delay is often called 'preform co time [2]. In this study, it was assumed that the preform cooling time is 3.5seconds. The mold temperat represented by Ta. In an effort to maintain the temperature as longer as possible above the glass-rubber tran limit ̴ 80°C the mold temperature was set 343K or 70°C. The concept beyond this selection is to investigate th kinetics during the deformation mode while the material is constraint by the mold walls. In the actual SBM pr such mold temperature selection is expected to induces more crystals within the material [14], thus influenci strength performance of the bottle [18]. The stretch rod velocity is represented by Vs, which was -0.8m/s cases. Although the stretching period is different in each case so that at the end of the stretching process, the b of each preform case is located at the same point respect to the mold length. The reason is to obtain simila deformation during blowing for all cases, since the length of each preform case is different. Table 1 indicat stretching and blowing period for each case. The time delay presented in Table 1, is the time interval betwe initiation of each process and the beginning of whole SBM. The heat transfer between the preform and cooler walls is described by the conduction heat flux boundary condition shown in eq. 1.

̇= − ∇
Where, k is the thermal conductivity of mold material (for aluminum k = 205 W mK ) and T is the temperature diffe between the preform and the mold walls. Once the preform touches mold walls, the motion of the mate constrained by the sticking boundary condition imposed on the mold walls. The sticking boundary condition slip) obtains due to the force exerted by the blown preform. The sticking boundary condition is also used earlier SBM study [12].  Table 1. SBM simulation process parameters

Mesh, material model and initial SBM simulation conditions
The non-isothermal viscoelastic behavior of PET has been modeled using then KBK-Z model provided in ANSYS POLYFLOW. The material parameters were taken by earlier SBM and experimental studies. [13], [19]. ANSYS POLYFLOW has also been employed for the investigation of PET SBM by another study [13]. The initial discretized domain consists of 270735, 270857 and 271016 finite elements for the case of preform A, B and C respectively. For more accuracy, mesh refinement has been imposed at the preform contact regions. Figure 2 shows the discretized domain of each preform case. The initial preform temperature obtained by preform cooling as referred in section 2.1 has been predicted using the Eulerian approach for the solution of heat transfer equations.
The Eulerian approach has also been used for the solution of the constitutive equations that govern the kinetics of PET during SBM process. Figure 3 indicates the thickness of each preform case temperature after preform cooling and temperature after preform cooling. Each preform weighs 58.33grams. To eliminate the effect of variable thickness distribution each preform has uniform length. Each preform has the same thickness(1.5mm) at the uppermost region which is the region that molds clamp the preform. This region also contains the threads for the bottle cover and obviously is the thickest region of a bottle. To maintain the same mass for all the preform cases, the neck to the lowest bottom region of preform A has thickness 3.427mm while its counterparts preform B and C have thickness 3.015mm and 2.63mm respectively.

Results and discussion
Figures 4-6 indicate the thickness, strain rate and stresses contours after the end of stretching process for preform A, B and C. In all cases preblowing initiates in a short time interval before the end of stretching process. It can be observed that the preform A has the grater regions with the less thickness. The less extent of the region with the less thickness after the end of the stretching process belongs to preform C.

Figure 4. Thickness contours after the end of stretching process for the three numerical cases (Preform A, B and C)
From Figures 4-6 it can be noticed that the extent of the preform volumes after the end of the stretching process is described by a trend characterized by the length of the preforms. Preform A has the greater volume while preform C has the less volume. This can be explained by Figure 5. The highest strain rate values obtain on the wall of preform A as an indication that more material migrates from the upper regions to the lower regions of preform during the stretching process. The highest strain rate values at the center of preform A indicate resulting from the transverse deformation due to preblowing. Since the preform C has greater extent of thicker regions after the stretching process, allow less deformation during the stretching preblowing. In Figure 5, it is clearly shown that at the end of stretching process preform C has the lowest strain rate values. As indicated in Figure 6, the stresses follow similar trend with the strain rate contours. The highest stresses values obtain at the center of preform A due to the high deformation rate. for preform A, B and C Figure 7a shows the resulting bottle with the thickness contours for each examined preform case. In cases the thickness distribution is more uniform at the center of the bottle body. Although as the preform length increases A-C the thickness on the uppermost region of the bottle decreases while the opposite happens at the lowermost region of the bottle resulting in generally more uniform distribution along the entire bottle for case C. Figure 7b represents the thickness contours on the bottom of the bottle. As the initial length of the preform increases the pointless material concentration at the center of the bottom is being reduced. In addition, the increase on the preform initial length increases the material concentration at the side bottom walls increasing the inherent and therefore the steadiness of a filled bottle. Figure 8 indicates the plot of thickness distribution as function of the bottle length. The reduction on the material concentration at the center of the lowermost bottle region for case C can be noticed at the beginning of the chart. Furthermore, the reduction of thickness at the neck of the bottle as the initial preform length increases is also observed. The general conclusion that can be extracted from the chart is that preform B and C the thickness is distribution follows similar trend. Although case C seems to be the optimum due to the reduction of the excess material concentration at the center of the lowermost region and to the increase of the thickness at the bottom side walls. Since case A has the thicker regions after the end of the stretching process, it is more readily deformed during the bi-axial pressure loading. The higher strain rate at the side bottle walls for the selected time step indicates that the higher deformation rates take place earlier for the case A. A worthing observation is that at case C, once the preform touches the mold side walls, it also touches the lowermost wall of the mold at the same time. In the case of preform A, the material touches the side walls firstly. From this observation in can be concluded that the thicker preform after the end of the stretching process expands more uniform in both transverse and axial directions. The regions with the highest stresses values presented in Figure 10 occupy almost the same area for the case B and C. Similar to Figure 9 the highest stresses values obtain in case A where the material is deformed at higher rates. The axial length of the mold is 306mm. Therefore, preform cases A, B and C have the 47.3%, 54,15% and 60.99% of the mold length respectively. As a conclusion it can be said that the optimum case of preform length is 60.99% of the mold length. Although this statement requires further investigation, because the desired characteristics of a bottle are affected by a combination of parameters including the process conditions (stretch rod velocity, preblow and blowing pressure and preform and mold temperatures).

Conclusions
The effect of preform length on a 1.5Lt PET bottle wall thickness distribution has been investigated numerically. For the simulation three preform case were taken under consideration. The preform length examined are 144.75mm, 165.7mm and 186.65mm which are the 47.3%, 54.15% and 60.99% of the axial mold length. The mass remained equal to 58.33gr for all cases. All the cases were stretched up to the same axial location respect to the mold length in an effort to eliminate the effect of the axial deformation during the blowing process since the preform cases have different length. It was found that the in cases the thickness distribution along the bottle length is described by a similar trend. In all cases it was observed that the thickness distribution on the main bottle body was uniform.
Although the final product obtained in cases B and C is characterized by a more uniform material concentration along the entire bottle length. Further, the increase of preform length implies in less material concentration on the bottle neck while the opposite happens on the bottom side walls which is desirable since it enhances the steadiness of filled bottle. A disadvantage of SBM process is that during stretching material is accumulated at the center of the bottom region. This material concentration does not avail in anything. Thus the reduction of the material concentration at that area is an optimization parameter on the reduction of the bottle weight without influencing is mechanical performance. The simulation results indicated that the concentration of material at the center of the bottom is being reduced with the increase of initial preform length. Summarizing the above, the most optimum preform length is 60.99% of the axial mold length. Although this statement requires further investigation since the material distribution along the bottle length is described by a function SBM parameters such as stretching and blowing conditions and governing temperatures.