Modelling stretch blow moulding of polymer containers using
level set methods
Citation for published version (APA):
Groot, J. A. W. M., Giannopapa, C. G., & Mattheij, R. M. M. (2011). Modelling stretch blow moulding of polymer containers using level set methods. (CASA-report; Vol. 1127). Technische Universiteit Eindhoven.
Document status and date: Published: 01/01/2011
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EINDHOVEN UNIVERSITY OF TECHNOLOGY
Department of Mathematics and Computer Science
CASA-Report 11-27 April 2011
Modelling stretch blow moulding of polymer containers using level set methods
by
J.A.W.M. Groot, C.G. Giannopapa, R.M.M. Mattheij
Centre for Analysis, Scientific computing and Applications Department of Mathematics and Computer Science
Eindhoven University of Technology P.O. Box 513
5600 MB Eindhoven, The Netherlands ISSN: 0926-4507
PVP2010-25710
Modelling Stretch Blow Moulding of Polymer
Containers Using Level Set Methods
J. A. W. M. Groot C. G. Giannopapa R. M. M. Mattheij
Email: j.a.w.m.groot@tue.nl Email: c.g.giannopapa@tue.nl Email: r.m.m.mattheij@tue.nl
Dept. of Math. and Computer Science Eindhoven University of Technology
PO Box 513, 5600 MB Eindhoven The Netherlands
ABSTRACT
Stretch blow moulding is a widely used technique e.g. for the production of PET bottles. In a stretch blow moulding process a hot preform of polymer is simultaneously stretched and blown into a mould shape. The process takes place at a fast rate and is characterised by large deformations and temperature gradients. In this paper a computer simulation model for stretch blow moulding is presented. The model is based on finite element methods and uses a level set method to track the interfaces between air, polymer and stretch rod. The PET behaviour is modelled as a non-newtonian, isothermal fluid flow, based on a viscoplastic material model. An application presented is the stretch blow moulding of a realistic PET water bottle. The model is validated by verifying volume conservation.
KEY WORDS: stretch blow moulding, process simulation, level set methods, Non-newtonian fluid flow, finite element methods
Nomenclature
Br Brinkman number
dev deviatoric part
Fr Froude number Pe Péclet number Re Reynolds number cp specific heat [J kg−1K−1] g gravitational acceleration [m s−2] k modulus [Pa sm] Lc characteristic length [m]
m reciprocal of power-law index
p pressure [Pa]
t time [s]
Tp typical polymer temperature [K]
Tm typical mould temperature [K]
u flow velocity [m s−1]
Vc characteristic velocity [m s−1]
˙ε strain rate tensor [s−1]
˙¯ε strain rate [s−1]
λ thermal conductivity [W m−1K−1]
µ (dynamic) viscosity [kg m−1s−1]
µc characteristic viscosity [kg m−1s−1]
ρ density [kg m−3]
σ stress tensor [Pa]
¯
σ equivalent stress [Pa]
φ level set function
INTRODUCTION
Blow moulding is a technique that was invented thousands of years ago for the production of glass containers, e.g. bottles and jars. The automated blow moulding process as it is known today has seen rapid development during the last century, while at the same time the range of applications and diversity of materials has considerably increased. In spite of the fact that blow moulding has been used for many years, manufacturers still experience difficulties in optimising and controlling the process.
In polymer container manufacture three main blow moulding techniques can be distunguished: in-jection blow moulding, extrusion blow moulding and stretch blow moulding. In inin-jection blow moulding first a polymer preform is formed by injecting a polymer melt into a tube-shaped mould and subse-quently it is brought into another mould, where the final container is blown by inflating the preform with air. Injection blow moulding is usually used to manufacture small or wide-mouthed containers. In extrusion blow moulding the polymer melt is extruded in a preform shape before blowing it into the container shape. Extrusion blow moulding can be used for a wide variety of container shapes and has in general a high production rate. Finally, stretch blow moulding is a popular manufacturing technique for the production of so-called PET (polyethylene terephtalate) bottles and is subject of this paper.
Figure 1 shows a schematic drawing of the stretch blow process. Initially a preform is transferred on the stretch rod into a mould (Fig. 1(a)). The preform is typically produced by injection moulding a polymer melt. Then the preform is simultaneously stretched with the stretch rod and inflated with pressurised air (Fig. 1(b)-1(c)). Finally, the resulting container is cooled down and ejected from the mould.
Over the last few decades computer simulation models have significantly contributed to a better insight in and understanding of blow moulding processes and nowadays they are widely used for pro-cess optimisation. Computer simulation models can help to minimise undesired variations in the wall thickness and reduce the weight while maintaining the strength. They offer a good alternative for trial-and-error methods with expensive blow moulding equipment or complicated measurements during a moulding process, which takes place in a closed construction at a fast rate. Moreover, simulations can be used for comparison with measurements. The numerous papers on simulating the stretch blow mould-ing include references [1–8]. Various computational models have also been developed for modellmould-ing the forming of glass containers [9–14], thermoforming [15, 16] and extrusion blow moulding [6, 17–19].
The simulation model presented in this paper is based on finite element methods and uses a level set method to track the polymer-air interfaces. Finite element methods have been widely used for the modelling of blow moulding processes in literature. Finite element methods are usually coupled to interface tracking techniques, which attempt to find the interfaces implicitly and update the finite
preform mould
(a)
stretch rod pressurised air
(b)
container
(c)
Fig. 1. SCHEMATIC DRAWING OF A STRETCH-BLOW MOULDING PROCESS
element mesh as the interfaces evolve. The procedure of updating the mesh can become increasingly computationally expensive as the mesh size decreases or the mesh has to be updated more frequently. A major advantage of level set methods is that no re-meshing is required to distinguish between polymer and air as time progresses; the location of the interface can be marked by the so-called level set function instead [20–23]. Level set methods also have other attractive properties: they automatically deal with topological changes, can in general be used with high order of accuracy [24] and extend easily to three dimensions [25]. The level set method in this paper is also used to describe the motion of the stretch rod.
The objective of this paper is to create a robust and computationally efficient model to be used for industrial purposes which can accurately capture the stretch blow moulding process of polymer containers. The model takes as input information the preform shape, a uniform temperature distribution of the preform and a prescribed inlet air pressure. It computes the container shape, the products final wall thickness as well as the stress and thermal deformations the polymer undergoes during the process. The model is applied to the stretch blow moulding of a 2D axial-symmetrical PET bottle with a relatively complex geometry. The model is validated by verifying conservation properties.
RHEOLOGICAL BEHAVIOUR
Much research has been conducted on the rheological behaviour of polymers. Essentially, three different kinds of models have been introduced in literature to describe the mechanics of a polymer melt subject to inflation, namely hyperelastic, viscoelastic and viscoplastic models.
Regarding the short inflation time (∼ 0.5s), a hyperelastic constitutive relationship can be assumed [1, 26]. In particular, earlier papers propose isothermal, hyperelastic models, many of which were first developed for thermo-forming processes [1, 15, 27]. However, hyperelastic models have difficulties with proper material characterisation and the prediction of the time-dependent behaviour of the polymer during a blow moulding process [17, 26]. Moreover, in [28] it was observed that the behaviour of PET is highly rate dependent, which is an effect that hyperelastic models generally cannot deal with.
Viscoelastic and viscoplastic models take into account both strain hardening and strain rate effects. Viscoelastic models have been widely used for stretch blow moulding processes in literature. For ex-ample, in [29] a K-BKZ visco-elastic model was adopted to simulate the blow moulding process. In [3] a liquid-like visco-elastic constitutive equation of Johnson-Segalman type was used to describe the mechanical behaviour of PET during a stretch blow moulding process. The simulation results were
in good agreement with the experimental data. In [30] the Christensen model was modified into a visco-hyperelastic model. Finally, in [31] the Buckley-Jones model was used to model the rheological behaviour of PET during the stretch blow process. Viscoelastic models can also calculate the stress relaxation during stretch blow moulding, which is a dominant deformation mode in relatively slow de-formation processes, such as extrusion. However, because of the short time duration of the stretch blow process, the loss of accuracy as a result of omitting stress relaxation is marginal, while the computa-tional time can be significantly decreased [32]. This can be a motivation to employ a viscoplastic model. Another advantage of viscoplastic models is that they are generally very stable, whereas difficulties with convergence can be encountered when using hyperelastic or viscoelastic models [32]. Viscoplastic mod-els are mainly used for metal forming processes, but have not been used extensively for stretch blow moulding. Viscoplastic models for stretch blow moulding were suggested in [5, 33–35].
In addition, some different models have been proposed for stretch blow moulding. For example, an elasto-visco-plastic model was suggested in [2] and a neo-Hookean hyperplastic consitutive relationship was employed in [36]. For the latter model it was concluded that the model is in reasonable qualitative agreement with the experimental results, but the model failed to accurately predict the container shape.
In this paper the viscoplastic model presented in [5, 37, 38] is used to describe the rheological be-haviour of the polymer. The model is based on the Levy-Mises flow rule:
dev(σ) =2
3 ¯ σ
˙¯ε˙ε, (1)
where the strain rate ˙¯ε and the equivalent stress ¯σ are given by
˙¯ε = r 2 3˙ε
:
˙ε, (2) ¯ σ= r 3 2dev(σ):
dev(σ). (3)where
:
is the double dot inner product, defined byT
:
T= tr(TT), (4)for any tensor T. In [5, 33] the material behaviour was determined by performing an uniaxial tensile test. From the test the following relation was deduced:
¯
σ= k(T )˙¯εm. (5)
In [35, 39] the G’Sell-WLF material model was proposed for the rheological behaviour of PET:
¯ σ= k0exp C1(T − Tref) C2+ T + Tref (1 − exp(−Aγ)) exp(BγC)˙¯εm, (6)
where γ is the cumulated strain rate. If constants A and B are disregarded, the uniaxial tensile test in (5) is obtained with k(T ) = k0exp C1(T − Tref) C2+ T + Tref . (7)
In (7) the WLF equation for the temperature dependence of the viscosity can be recognised [40]. Finally, substitution of (5) in (1) results in the isotropic, viscous polymer flow,
dev(σ) = 2µ˙ε, (8)
with non-newtonian viscosity
µ(˙¯ε, T ) = k(T )
3 ˙¯ε
m−1.
(9)
GOVERNING EQUATIONS
This section presents the governing equations for the stretch blow moulding process. These involve conservation of mass, momentum and energy of the polymer melt and air and the evolution of the polymer-air interfaces. A two-phase fluid flow formulation is considered, i.e. the governing equations describe the flow of both air and molten polymer.
Mechanics
The mechanics of the system can be described by the momentum and mass equations for an incom-pressible fluid:
ρdu
dt = ∇
·
σ+ ρg, (10)∇
·
u= 0, (11)where dtd := ∂
∂t+ u
·
∇ denotes the material time derivative. For isotropic, viscous fluids the constitutiveequation for the stress tensor is given by
σ= 2µ˙ε − pI, (12)
where the strain rate tensor relates to the flow velocity as
˙ε= 1
2 ∇u+ ∇u
T . (13)
System of equations (10-11) is written in dimensionless form in order to perform a quantitative analysis
of the problem. Consider a typical: velocity Vc, length scale Lc and viscosity µc. Then introduce the
dimensionless variables t∗:=Vct Lc, x ∗:= x Lc, u ∗:= u Vc, µ ∗= µ µc, p ∗:= Lcp µcVc. (14)
Superscript∗is used to indicate that variables and operators are in terms of the dimensionless variables.
the dimensionless variables (14) into the flow equations (10-11) and division by the order of magnitude
of the viscous term, µcVcL−2c , leads to the dimensionless flow equations
Redu ∗ dt∗ = ∇ ∗
·
(2µ∗˙ε∗) − ∇∗p∗−Re Frez, (15) ∇∗·
u∗= 0, (16) where Re= ρVcLc µc , (17) Fr= V 2 c gLc (18)are the Reynolds number and the Froude number, respectively. The dimensionless form is useful for assessing the order of magnitude of the different terms in (15) and is the basis for simplifications in the simulation model.
For the flow problem the following boundary conditions are imposed:
• no-slip conditions for the polymer melt and no-stress conditions for air on the mould wall, • no-slip conditions for the polymer melt and an inlet pressure for air at the mould entrance, • axial symmetry conditions on the axis.
Thermodynamics
The heat transfer in polymer, air and equipment is described by the heat equation for incompressible continua:
ρcp
dT
dt = −∇
·
q+ 2µ˙ε:
∇u. (19)If the heat transfer due to radiation is neglected, the heat flux q [W m−2] is the result of thermal
con-duction,
q = −λ∇T, (20)
In order to write (19) in dimensionless form, a dimensionless temperature distribution is introduced,
T∗:= T− Tm
Tp− Tm, (21)
where Tmis the typical temperature of the mould and Tpis the typical polymer temperature. Substitution
of the dimensionless variables (14) and (21) in the heat equation (19) leads to the dimensionless form,
PedT
∗
dt∗ = ∇
∗2T∗+ 2µ∗Br ˙ε∗
:
where Pe= ρ ¯cpVcLc λ , (23) Br= µcV 2 c λ Tp− Tm (24)
are the Péclet number and the Brinkman number, respectively. The heat transfer is discussed into more detail further on for the PET bottle simulation.
Evolution of the interfaces: a level set method
A level set method is used to capture the interfaces in the two-phase fluid flow problem. Level set methods are based on an implicit formulation of the interfaces by means of so-called level set functions, which enables the two-phase fluid flow problem to be solved on a fixed mesh in the flow domain. While the governing equations are formulated in the whole flow domain, level set methods can be used to differentiate between material properties.
Level set methods seem to be attractive for this problem because the interfaces are accurately cap-tured, topological changes are naturally dealt with and complicated re-meshing algorithms are avoided. The latter is particularly an issue for blow moulding processes, since a moving mesh can become rapidly distorted during a simulation because of the large deformations. As a result the mesh would have to be updated frequently, which can become increasingly computationally expensive. Other advantages of level set methods are a relatively easy generalisation to three dimensions and straightforward calcula-tion of properties of the interfaces, such as the normal and curvature. A drawback of level set methods is that they are in general not conservative. However, in [13] a change in mass of less than 1% during the glass blow moulding process simulations is reported, which can even be further improved by using higher order time integration schemes or by taking smaller time steps.
The basic idea of level set methods is to embed each moving interfaces between the polymer, air and stretch rod as the zero level set of a level set function φ. The equation of motion of the interfaces follows from the fact that the material derivative of the level set function is equal to zero:
dφ
dt =
∂φ
∂t + u
·
∇φ = 0. (25)Initially, the level set function is defined as the signed Euclidean distance function to the interfaces. The flow velocity u is found by solving flow problem (15-16) and boundary conditions. Each polymer surface corresponds to the zero level set of one level set function, which means two level set problems have to be solved to capture both interfaces. Furthermore, to completely avoid moving mesh algorithms, also the surface of the stretch rod is described by a level set function. However, the level set problem
for the stretch rod moving with constant velocity ur = Vrez is trivial, as
φr(x,t) = φr,0(x + urmin{t − t0,tstretch− t0}), (26)
where φr(x,t) is the level set function corresponding to the stretch rod at position x and time t, tstretchis
the stretch time, t0is the time at which the stretch rod starts moving and
In conclusion, three level set functions are used to describe the evolution of the moving interfaces:
φifor the inner polymer surface, φofor the polymer surface and φr for the stretch rod surface. Level set
functions φiand φoare found by solving (25) and φr is given by (26). Figure 2 gives an overview of the
continuum domains and the corresponding signs of the level set functions. The continuum domains are defined as follows: air : max{min{φi, φo}, φr} < 0, polymer : min{φi, φo} > 0, stretch rod : φr> 0. φi< 0 air φi> 0 φo> 0 φo< 0 air st re tc h ro d φ r = 0 polymer φr>0 φr< 0 φi= 0 φo= 0
Fig. 2. SIGN OF THE LEVEL SET FUNCTIONS
One of the difficulties encountered in level set methods is maintaining the desired shape of the level set function. The flow velocity does not preserve the signed distance property, but may instead considerably distort and stretch the shape of the function, which eventually leads to additional numerical difficulties [20, 41]. To avoid this the evolution of the level set function is stopped at a certain point in time to rebuild the signed distance function. This process is referred to as re-initialisation. In this paper a triangulated fast marching method is used [20, 42]. Fast marching methods build the signed distance function outward starting from a narrow band around the zero level set and subsequently marching along the nodes. Further details about the fast marching algorithm used can be found in [13, 43, 44].
DISCRETISATION METHOD
A Galerkin Finite Element Method is employed for the discretisation of the governing equations. The 2D axial-symmetrical finite element model has been implemented in COMSOL 3.5 with MATLAB. Each time step the system of equations is solved using COMSOL 3.5, while the re-initialisation of the level set functions is done in MATLAB between successive time steps. The level set problems are solved using the convection-diffusion application mode in COMSOL 3.5. First order elements have been used for the spatial discretisation: Mini-elements for the flow problem and Lagrange elements for the other problems [45–47]. For the temporal discretisation an IDA scheme has been used [48], which employs a
variable-order variable-step-size BDF method. The discretised system of equations is solved using the BiCGstab method with a geometric multigrid method as a preconditioner [49].
PET BOTTLE SIMULATION
In this section the stretch blow moulding process of a PET (polyethylene terephtalate) bottle is considered. First the governing equations are simplified based on a quantitative analysis of the process. Then the simplified model is applied for the simulation of the stretch blow moulding process. Finally, the results of the simulations are discussed. Table 1 depicts typical values for the simulation, which are also used for the analysis.
Quantity Symbol [Unit] Value
PET Air Characteristic length Lc [m] 1.00 · 10−2 Characteristic velocity Vc[m s−1] 1.00 · 10−1 Viscosity µ[kg m−1s−1] 1.00 · 105 1.00 · 10−5 Density ρ[kg m−3] 1.20 · 103 1.00 Thermal conductivity λ[W m−1K−1] 0.24 1.00 · 10−2 Specific heat cp[J kg K−1] 1.05 · 103 1.00 · 103
Inlet pressure pin[Pa] 1.0 · 106
Polymer temperature Tp[K] 3.73 · 102 2.98 · 102 Mould temperature Tm[K] 2.83 · 102 Rod temperature Tr[K] 3.13 · 102 Reynolds number Re [-] 1.20 · 10−5 1.00 · 102 Froude number Fr [-] 1.02 · 10−1 Péclet number Pe [-] 5.25 · 104 1.00 · 102 Brinkman number Br [-] 4.63 · 102 6.67 · 10−7
Table 1. TYPICAL VALUES FOR STRETCH BLOW MOULDING APETBOTTLE
Quantitative analysis of stretch blow model
First a quantitative analysis of the rheological behaviour of the PET melt is performed. The Deborah number De measures the ratio of elastic forces to viscous forces. For stretch blow moulding of PET the Deborah number is given by
De= τpin
µ ∼ 1, (28)
where τ= 0.1 is the typical relaxation time of PET [3]. Thus, the elastic forces are of the same order
T = 373K is σy= 10 MPa [50, 51]. For comparison the typical stress during stretch blow moulding is
σc= µc
Vc
Lc = 1 MPa. (29)
Thus, the isotropic yield criterium σc≤ σyis barely satisfied, that is, the typical stress for stretch blow
moulding is close to the elastic limit. It can be concluded that the rheological behaviour is elasto-visco-plastic. On the other hand, the choice of a viscoplastic material model is not unreasonable, particularly in view of modelling simplifications by disregarding the elastic effects.
Consider the dimensionless form of the flow equations (15-16). Obviously, the orders of magnitude
of the inertia forces (Re ∼ 10−5) and the gravitational forces (ReFr ∼ 10−4) are small for PET. This
indicates that the flow problem for PET is dominated by viscous forces only. However, this is clearly not the case for air. In order to simplify the governing equations in the whole domain, air is replaced by
a fictitious fluid with the same physical properties as air, but with a much higher viscosity, e.g. µair= 1.
Then the Reynolds number of the fictitious fluid (Re ∼ 10−3) is small enough to reasonably neglect the
influence of the inertia and gravitational forces. On the other hand, the viscosity of the fictitious fluid is still much smaller than the viscosity of glass, so that the pressure drop in the air domain is negligible compared to the pressure drop in the glass domain [13, 52, 53]. As a result the momentum equation for both PET and fictitious fluid can be described by the Stokes flow equations.
Next consider the dimensionless form of the heat equation (22). The Péclet number is large for both PET and air, which indicates that the contribution of conduction to the heat transfer is much smaller than the contribution of convection. The Brinkman number is moderately large for PET, but still a few orders
of magnitude smaller than the Péclet number. The Brinkman number of the fictitious fluid (Br ∼ 10−2)
is considerably larger than the Brinkman number of air, but still small compared to the Péclet number. It can be concluded that also the influence of dissipation on the heat transfer is marginal compared to
convection. Moreover, the Graetz number Gz is large (Gz= 14πρVcLccp/λ ∼ 8.6 · 103), so that also
thermal conduction towards the wall is negligible. Thus the heat transfer is convection dominated, hence the temperature is preserved along streamlines. This means that if the initial temperature of the fictitious fluid and PET is uniform, it will remain uniform. Based on the assumption that the temperature distribution of PET is uniform, the heat equation is omitted in the simulation and the coefficient k in (5) is treated as a constant.
In conclusion, the system of governing equations for the stretch blow moulding process of the PET
bottle are (∗is omitted):
∇
·
2µ˙ε = ∇p ∇·
u= 0 dφi dt = 0 dφo dt = 0, (30)The governing equations hold for the fictitious fluid, PET and the stretch rod. For the stretch rod an
artificial viscosity µr is imposed, which is much larger than the viscosity of PET, so that the strain rate
Results
The stretch blow moulding of a 2D axial-symmetrical PET bottle is simulated. The height of the bottle is 21.6 cm, the radius of the bottle is 1.5 cm at the neck to 3.15 cm at the widest part. Figure 3 shows a typical mesh for the stretch blow moulding simulation.
21.6c m 1.5cm 3.15cm 21.6c m
Fig. 3. TYPICAL MESH FORPETBOTTLE
Figure 4 shows the preform and initial position of the rod. The stretch rod is initially positioned at a
height h0 of 9.72 cm from the bottle mouth. The radius r0 of the stretch rod is 0.375 cm. At t= t0the
rod starts moving from this position with constant speed Vr. The level set function for the stretch rod in
terms of 2D axial-symmetrical coordinates(r, z) is
φr(r, z, t) = r0− r, if ˜z(z, t) ≥ 0, p r2+ ˜z2(z, t), if ˜z(z, t) < 0, (31) where ˜z(z, t) = z +Vrmin{t − t0, tstretch− t0} − h0. (32)
A disadvantage of modelling the motion of the stretch rod by a level set function is that automatically a no-slip condition is imposed on the stretch rod boundary, which is not always realistic or desirable. One way to allow some slip is to define a gradual transition of the viscosity over the stretch rod boundary.
The stretch time tstretch can either be given manually or is determined by the simulation model. In the
latter case the stretching is stopped when the polymer hits the bottom of the mould. This method is used for the simulations.
In [5, 54] the material parameters m= 0.54, k = 292529 are given for the uniaxial tensile stress test
0.25cm 9.72c m PET stretch rod PET air
Fig. 4. PREFORM AND INITIAL POSITION OF THE ROD FOR THE
SIMULATION 10−2 10−1 100 101 102 104 105 106 µ [k g m − 1 s − 1 ] ˙¯ε [s−1]
Fig. 5. NON-NEWTONIAN VISCOSITY FOR UNIAXIAL TENSILE STRESS TEST
Figure 6 shows results of the stretch blow moulding simulations for a PET bottle at different times
for inlet pressure pin = 1 MPa. First only air is blown inside without stretching. Then at t = 0.1 s
the stretch rod starts moving with speed Vr = 0.45m s−1. The white arrows depict the flow velocity
vectors. As expectable in stretch blow moulding, the polymer form first bulges at the top, while the bottom is stretched, then the bulging gradually extends to the bottom. The bottle in Fig. (6(f)) has an almost uniform thickness, with a minimum of approximately 1 mm at the bottom part and a maximum of slightly more than 3 mm at the neck part. This matches with the thickness profile of a realistic water bottle, which has an almost uniform thickness of 1.5 mm.
In order to assess the accuracy of the simulation model presented in this paper, the glass volume conservation is verified. Figure 7 shows the percentage volume change in time. The volume change has a maximum of 2.5%. The volume conservation can be further improved using smaller time steps and higher mesh quality. This phenomenon was also observed in [13, 14, 43, 55].
(a)t= 0.1S (b)t= 0.2S (c)t= 0.3S
(d) t= 0.4S (e)t= 0.5S (f)t= 0.62S
Fig. 6. STRETCH BLOW MOULDING PROCESS FOR PETBOTTLE
WITHpin= 1 MPaANDVr= 0.45m s−1 AT DIFFERENT TIMES.
CONCLUSIONS
This paper presents the development of a computer simulation model for the stretch blow moulding process of polymer containers. The model is based on finite element methods and uses a level set method to track the interfaces between polymer and air. The rheological behaviour of the polymer is described by a viscoplastic model.
The model was used to simulate the stretch blow moulding of a 2D axial-symmetrical PET bottle. It was verified that the polymer flow can be described by the non-newtonian, isothermal Stokes equations. The results showed that the model is robust and gives a good representation of the stretch blow moulding process. The model was validated by verifying the volume conservation. The method gave a volume
0 0.1 0.2 0.3 0.4 0.5 0.6 −2 −1.5 −1 −0.5 0 0.5 1
% glass volume change
time [s]
Fig. 7. Volume conservation of the stretch blow moulding process for the PET bottle using the IDA time discretisation scheme with time step
5 · 10−4.
change of less than 2.5% for the simulations of the PET bottle stretch blow moulding. This gives confidence that the model can be used for industrial practice. Optimisation of the bottle thickness will be a next step in the development. Comparison between the simulations and experiments or a viscoelastic model would also be a future consideration.
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