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Experimental study and numerical simulation of the
injection stretch/blow molding process
Fabrice Schmidt, Jean-François Agassant, Michel Bellet
To cite this version:
Fabrice Schmidt, Jean-François Agassant, Michel Bellet. Experimental study and numerical simulation
of the injection stretch/blow molding process. Polymer Engineering and Science, 1998, 38 (9), p.1399-
1412. �10.1002/pen.10310�. �hal-00617038�
Expe
r
i
me
nta
I
Study
and
Nu
m
e
rica
I
Si
m
u
la
t
io
n
of
the Injection Stretch/Blow Molding Process
F.
M.
SCHMIDT,'**J.
F.
AGASSANT,2
dM.
BELLET2
'Ecole
des
Mines d'Albi-Carmaux
Campus
Jarlard
Route
de
Teillet
81
01
3
Albi
CT
Cedex
09,
France
2Ecole
des
Mines
de
Paris
06904 Sophia-Antipolis, Fhnee
CEMEF-URA
CNRS
rz~.
1374
The
injection stretch/blow molding process of
PET
bottles
is
a complex process,
in
which the performance of the bottles depends on various processing parameters.
Experimental work has been conducted on
a
properly instrumented stretch/blow
molding machine in order to characterize these processing parameters. The objec-
tive being a better understanding of the pressure evolution, preform free inflation
has been processed and compared with a simple thermodynamic model. In addi-
tion, a numerical model for the thermomechanical simulation of the stretch/blow
molding process has been developed. At each time step, mechanical and tempera-
ture 'oalance equations are solved separately on the current deformed configu~-
tion. Then, the geometry is updated. The dynamic equilibrium and the Oldroyd
B
constitutive equations are solved separately using
an
iterative procedure based on
a
fixed-point method. The heat transfer equation is discretized using the Galerkin
methlDd and approximated by
a
Crank-Nicholson's scheme over the time increment.
Succc:ssful free blowing simulations
as
well
as
stretchjblow molding simulations
have been performed and compared with experiments.
1)
InfTRODUCTION
1.1)
Presentation
of
the
Study
he injection strt:tch/blow molding process of
T
poly(ethy1ene terephtalate) bottles
is
a
three step
process
(as
sketched
in
m.
1):
first the
PET
resin is
injected in
a
tube-shaped preform
[
11,
then this amor-
phous preform
is
heated above the glass transition
temperature
[Z]
and h-ansferred inside
a
mold. Finally
the preform
is
inflated with stretch rod assistance
in
order to obtain the desired bottle shape
[3].
The performance
of
PET
bottles produced by this
process depends on three
main
processing variables:
the
initial
preform shape, the initial preform tempera-
ture, and the balance between stretching and blowing
rates. These parameters
will
induce the thickness dis-
tribution
of
the bottle
as
well
as
the
bid
orientation
and crystallinity, which in turn governs the
trans-
parency and the mechanical properties of the bottle.
This article will deal only with the last step of the
*Corresponding
author.
process, namely the stretching and blowing phase.
Our objective is to propose
a
general thermomechani-
cal approach that
is
able to take into account
vis-
coelastic constitutive equations for
PET
as
well
as
complex boundary conditions. A two-dimensional vo-
lumic finite element method has been developed,
which is able to capture the shearing effects especially
at
the contact zone between the moving stretching
rod
and the preform. Numerical results have been com-
pared with experiments performed on an instrument-
ed stretch/blow molding machine.
This
model
will
be
a
useful tool
in
order to optimize the processing para-
meters in order to obtain controlled thickness distrib-
ution
as
well
as
final
stress distribution.
1.2)
Literature
on
Blow
Molding
Roceu
A few models have been developed
[
1,
2)
in
order to
represent heat transfer inside an infrared oven, but
because of the complexity of the radiative transfer
in
a
transparent parison, the problem
still
remains open.
A
few experimental works refer to the experimental in-
vestigation of the kinematics of parison inflation. In
several papers
(3-6).
the authors have recorded the
POLYMER ENGINEERING AND SCIENCE, SEPTEMBER
1998,
Vol.
38,
No.
9
1399
F.
M.
Schmidt,
J.
F.
Agassant,
and
M.
BeUet
RECIPROCATING SCREW
n
MOLD
CLOSED
Rg.
1.
Description
of
the
injection
stretch/blow
molding
process.
inflation of free (or confined) parisons using high
speed video camera. In the case of confined parison
inflation, they have designed transparent molds.
These works represent
an
important contribution to
the analysis of parison inflation, but the technique
still
remains limited to simple mold geometries
(high
curvatures enhance visual distorsions). Experimental
work close to the stretch/blow molding process has
been performed on
a
well instrumented machine
at
Corpoplast company
(7):
the preform inflation has
been investigated using displacement sensors that are
located inside the mold, but the force exerted by the
polymer on the stretch
rod
has not been measured.
Finite element numerical simulations of the blow or
stretch/blow molding step have been extensively de-
veloped during the last decade.
Most
of
the models
as-
sume
a
thin
shell description of the parison. Warby
and Whiteman
(8)
as
well
as
Nied
et
aL
(9)
proposed
isothermal finite element calculations. These models,
first developed for the thermoforming process. have
now been applied to blow molding process. The rheo-
logical behavior is approached by
a
nonlinear-elastic
constitutive equation issued from the rubber-like
ma-
terials theory. Kouba
et
aL
(10) extended the previous
model to
a
viscoelastic fluid
(KF3KZ
constitutive equa-
tion). Several models use
a
volumic finite element ap-
-
MOLD
CLOSED
MOLD
OPEN
-
PART EJECT
U
11
EJECT
proach. In
1986,
Cesar de
Sa
(1
1)
simulated the blow-
ing process of glass parisons assuming
an
Arrhenius
temperature dependent Newtonian behavior. Chung
(12) carried out simulations of the
PET
stretch/blow
molding process using the
AE3AQUS@
sohare. The
model assumes the elasto-visco-plastic behavior and
thermal effects
are
neglected.
Poslinski
et
aL
(13)
in-
troduced nonisothermal effects in
a
simplified geome-
try.
In
order to take into account the phase change,
the latent heat of solidification
was
included in the
heat capacity of the material. Debbaut
et
aL
(14)
also
performed nonisothermal viscoelastic blow molding
simulations with
a
Giesekus constitutive equation,
but they presented numerical results
only
in the case
of
a
Newtonian fluid.
In
conclusion, the thin shell assumption, which
permits
3D
finite element computations, is often used
and commonly associated to the hyperelastic behavior
issued from solid elastic media. The finite element vo-
lumic approach issued from the blow molding of
glass
parisons is generally employed with liquid-We consti-
tutive equations
(Newtonian,
viscoelastic) and is limit-
ed
to 2D computations.
In
the stretch/blow molding
step, the contact between the stretch
rod
and the bot-
tom of the preform induces shear deformations
as
well
as
high and localized temperature gradients,
1400
POLYMER ENGINEERING
AND
SCIENCE, SEPTEMBER
ISSS,
Vd.
38,
No.
9
Experimental
Study
and
Numerical
Simulatto
*
n
of
the
Injection Stretch/Blow
Molding
Process
Stretching stage
which actually
just.@,
a
volumic approach in order to
obtain
an
accurate description of the deformation.
v,
(mm/s)
500
2)
EXPERIMENTAL
INVESTIGATIONS
2.1)
Inwentad
:Mold
of
a
StretchlBlow
Molding
Machine
Experiments were performed on
a
well-instrument-
ed mold at the Side1 Company
(1
5).
The dimensions of
the preform and of the mold are summarized
in
Table
1.
The instrumentaticln
is
described in
Fig.
2
the dis-
placement of the stretch rod
is
controlled and the
force exerted on the stretch rod
is
recorded versus
time using a force sensor. The blowing pressure
is
recorded versus timc: using a pressure sensor (the
pressure value
is
actiially different from the imposed
blowing pressure). Nine contact sensors at the mold
wall permit to identify the contact time between the
polymer and the mold.
The parameters asslxiated with the stretching stage
are the velocity of the stretch rod
u,,
which
is
applied
until the preform contacts the bottom of the mold,
and the preblowing step
(Rps
=
displacement of the
stretch rod before the, inflation pressure
is
imposed).
The parameters associated with the inflation stage are
Pps,
the maximum pre-blowing pressure (low-pres-
sure) imposed during
a
preblowing time
Dps
for initi-
ating the general shape of the bottle, and
Ps,
the ma-
imum blowing pressure (high-pressure) that
is
applied
during
a
blowing time
Ds
in
order to flatten the poly-
Preblowing stage
Table
1.
Dimensions
of
the Bottle Mold and
the
Preform.
Length (mm) Inner Radius External Radius
(mm)
(mm)
Preform
125 9.275 13.025
Bottle
mold
31
0
44.3
44.3
p,
(Pa)
5
x
lo5
Dps
(s)
0.3
mer along the mold
wall.
The preblowing air-rate
Qps
and the blowing air-rate
Qs
are prescribed by the op-
erator but not measured.
Qpical values of the process parameters of the
stretch/blow molding step are referred
in
Table
2.
The
I
R,,
(mm)
1
Blowing stage
I
D,
(s)
1.5
force
sensor
preform
pressure
contact
senbor5
sensor
Flg.
2.
Description
of
the
<mnstrumented
mold
of
a
stretch/blow
molding
machine.
t
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
t(s)
pre
-
blowing
stage
Q.
3.
History
of
pressure
uersus
time.
POLYMER ENGINEERING AND SCIENCE, SEPTEMBER
1998,
Vol.
38,
No.
9
1401
F.
M.
Schmidt,
J.
F.
Agassant,
and
M.
Bellet
pressure
is
measured directly in the preform (see
Flg.
3).
In addition, short-shot bottles produced for the
target process are time-located on the recorded pres-
sure curve.
As
shown
in
Fig.
4, the measured stretching force
of
the rod versus time
starts
from zero (or from
a
very
450
400
350
300
5
.-
250
-
Y
2
200
150
100
50
0
Rps
=
40
mm
-+---
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
tb)
Flg.
4.
Measured
siretching force of
the
rod
versus
time.
Flg.
5.
Location
of
the
contacts
sensors
on
the
mold
waU
low value), and then the curve rises to
a
maximum
and decreases continuously. Note
that
when
Rps
in-
creases, the maximum of
the
curve increases. In pre-
vious papers
(16.
13,
we pointed out
that
the
increas-
ing
part and the decreasing part of
this
curve
may
be
related respectively to elastic and viscous phenomena.
The location
of
the contact sensors (from no
1
to no
9)
on the mold wall
is
indicated in
FXg.
5.
Recorded
contact times versus the location of contact sensors
are plotted in
Flg.
6
using the process parameters that
are referred in
Table
2.
When
the preblowing delay
Rps
is increased from
1
mm
to
40
mm,
all the contact
times between the polymer and the mold increase and
the
contact times are more homogenous in the central
part of the bottle. In addition,
if
we plot the measured
thickness distribution versus longitudinal coordinate
at
the end of the process for the two values of
Rps
(see
Fig.
7).
we note that
an
increase in the preblowing
0.55
1 I
I
I
1
I
I
I
I
0.5
p
,
Rps=lmm
-+--
Rps
=
40
mm
-+---
0.25
'
I
I
1
I
I
I
I
123456789
no
sensor
contact
--.-.I--_.
1
m.
6.
Contact
times
uersus
nurnber
of
contact
sensors.
I
I
I
I
0.31
0.32
I
1402
POLYMER ENGINEERING AND SCIENCE, SEPTEMBER
I-,
Vol.
38,
No.
B
Experimental
Study
and
Numerical
Simulation
of
the
Injection Stretch/Blow
Molding
Process
Fg.
8.
Diflerential
pressure
us.
time.
0
1
delay induces more material displacement from the
neck to the bottom of the bottle.
2.2)
Mecutuement
and
Calculation
of
the
htelnal
Reuolre
In fact, in industrial blowing tools, the inflation
pressure
is
only imposed and measured
in
the blow-
ing device upstream and not inside the preform; sig-
nificant differences may be observed between these
two
pressures. Let
us
consider now the free inflation
of
a
preform. The preform
is
heated
in
a
silicone oil
bath
in
order to obtain a uniform temperature distrib-
ution
(T
=
95"C,
100°C.
105°C).
A
"nominal" pressure
has been imposed to
a
constant value of
0.27
MPa
in
the upstream blowing device for each case and the
differential inflation pressure
Ap,
(t)
=
pa
(t)
-
po
(pa
(t)
inflation pressure,
po
atmospheric pressure
at
ambi-
ent temperature) is recorded versus time using
a
pres-
sure sensor (see
Fig.
8).
For each temperature, free
in-
flations were recorded using video camera. In
Fig.
9,
successive preforms duing free inflation are presented
at
T
=
105°C.
Three different parts may be observed
on
each curve:
a first part where the pressure rises to
a
maximum
(less
than
0.3
ma),
during which the polymer is not
inflated (the internal volume of the preform remains
constant);
a
second part where the pressure decreases contin-
uously to a minimum because the volume increases:
the last part of the curve where the pressure
in-
creases again because of the "strain-hardening" of the
material, which is
in
fact related to the development of
crystallinity under biaxhl stretching.
It
is
to
be
noted that the duration of these three
steps during free inflation
is
strongly dependent on
temperature. This experiment demonstrates that the
evolution of the intema pressure and the inflation of
the preform are highly coupled.
It
is
also to be noted
that the recorded internal pressure
is
significantly
dif-
2
3 5
6
7
9
10
time
(s)
ferent from the "nominal" pressure. In order to better
understand this pressure evolution, we develop here-
after
a
simple thermodynamic model.
As
sketched
in
Fig.
10,
we consider
that
air
flows
in
the "control vol-
ume"
V,(t)
at
an air-rate
q
with
a
velocity field, pres-
sure
pe
and
a
temperature
T,.
We assume that the
air-
rate
q
is
constant during the pre-blowing stage, which
results
in
the following relationship between the air
mass
&(t)
(occupying the volume
V,(t))
and
q:
dm,
q
=
__
=
cte
+
m,(t)
=
m,
+
qt
dt
where
m,
is
the
air
mass within the parison
at
time
t
=
0.
Using
the following assumptions:
no heat transfer between the air volume and the
surrounding medium,
air
is
an
ideal
gas,
the global energy balance during the time step
dt
over
the volume
Va(
t)
may be simplified
as
(1
8):
d
d
Te
dt dt
'a
--
(Ln(p,VY,))
=
-
(Ln(rnY,))
--
where
y
=
1.4
for
air.
In order to obtain
a
simplified re-
lationship, we assume
T,
=
T,,
which
is
consistent
with the assumption of
no
heat transfer with the sur-
rounding medium. Using
Eq
1
and
ma
=
pa
V,,
Equation
2
reduces to:
(3)
where
po
is
the
air
specific mass
at
time
t
=
0
(initial
ambient temperature). Knowing the volume
VJt)
(due
to parison inflation),
this
relation should provide the
pressure value
p,(t).
However, the experimental deter-
mination of the air-rate
q
is
very difficult. In order to
overcome
this
difficulty, we suggest that
q
should be
determined through an inflation test
at
constant vol-
ume
V,
(for example, using
a
prefonn which has not
been heated). Differentiating
Eq
3
with respect to time,
1403
POLYMER ENGINEERING
AiND
SCIENCE, SEPTMBER
1998,
Vol.
38,
No.
9
F.
M.
Schmidt,
J.
F.
Agassant,
and
M.
BeUet
Fig.
9.
Preformfree
injhbn
fl=
105°C).
t
=
3.E
s
we
obtain at
initial
time
t
=
0:
t
=
4.03
5
t
=
5.35
5
(4)
This
relationship has been introduced
in
the stretch/
blow molding finite element software
BLOWUP
(18).
Results
will
be
presented
in
Section
5.
Ap,(t)
will
be
determined
as
follows:
Once
the
specific
flow-rate
q
(or
Q
dpdt’s
It
=
/
has been
.-
a
inflation at
a
given flow-rate of
a
preform
that
has
not been heated and measurement of the
initial
slope
of
the recorded pressure curve,
POLYMER ENGINEERING AND SCENCE, SEPlEWER
la,
Vol.
38,
No.
9
experimentally determined, it
is
possible to express
the idlation pressure
Ap,(t):
1404
Experimental
Study
and
Numerical
Simulation
of
the Injection Stretch/Blow
Molding
Process
calculation of the initial internal volume of the pre-
computation of tht: internal volume of the preform
VJt) at each time step,
determination of Apa(t) using
Eq
5.
form
v,,
3)
BOUNDARY
CONDITIONS
The boundary conditions are presented
in
Fig.
11:
along the contact surface between the rod and the
preform
u
=
u,
(sticking contact)
T
=
T,
(prescribed temperature
at
the rod: note that
the temperature of the rod is not easy to measure)
along the internal mrface of the preform, which
is
not
in
contact with the rod
(U
.
n')
.
n'
=
-
Ap,(t)
(kVT)
.
n'=
-
&(T--
T,)
where
h,
is
the heat transfer coefficient between the
polymer and the
air
inside the parison; however, the
extracted heat
flux
car^
be generally neglected.
along the external surface of
the
preform, which is
in contact with the mold
v=o
T
=
T,
(prescribed temperature of the mold)
along the external surface of the preform, which is
not
in
contact with
the
mold
(g
.
n')
'
r;
=
0
(kVT) .
n'=
-
h,(T-
T,)
where
h,
is
the heat transfer coefficient with the
mold, which will vary continuously during the infla-
tion process.
-n
4)
NUMERICAL
RESOLUTION
4.1)
Thermomechpnlcal
Equations
The numerical simulation of the stretch/blow mold-
ing
of an incompressible viscoelastic fluid (Oldroyd
B
type) consists in solving the following set of equations
on the domain
R
occupied by the preform:
where
g
=
-p'i
+
2rlsi
+
7
(6)
p(7-G)
=
V
.
v.r;'=o
(7)
I
with
the above-mentioned boundary conditions. In
this
model, the mechanical equations
(Eqs
6
to
8)
and
the temperature balance equation
(Eq
9)
are solved
separately on the deformed configuration
R"
at cur-
rent time step
t,,
(see
%.
12).
The current values of
the
velocity vector
i?',
the pressure
p'"
and the extra-
stress tensor
7"
are determined
first.
Then the tem-
perature field
?'
+
is
computed. Finally, the geome-
try
is
updated from
R"
to
R"
+
using the 2nd order
explicit Euler rule:
Rg.
10.
Volumefree
blowing
at
a
constantjlow
rate.
RADIAL
SYMMFTRY
;j
I
AXIAL
+I
I
I
I
I
I
I
SYMMEfRY
;\
BOTTLE
-----
PREFORM
Rg.
11.
Boundary
conditions.
MOLD
/-
POLYMER ENGINEERING AND SCIENCE, SEPTEMBER
1998,
Yo/.
38,
No.
9
1405
F.
M.
Schmidt,
J.
F.
Agassant,
and
M.
BeUet
4.2)
Remolution
of
the
Machanid
Equation8
The resolution method is summarized hereafter.
Full details about the numerical algorithms are given
elsewhere (16,
17).
4.2.1)
Splitting
Technique
At
each time step, an iterative procedure based on
a
fixed-point method is used in order to solve
EQuations
6
to
8.
The first sub-problem, called the "Generalized
Stokes Problem" (GSP), deals with
an
incompressible
Newtonian fluid flow, perturbed by
a
known
extra-
stress tensor
1
computed at the previous fixed-point
iteration
(k-u
(Equations
6
and
7).
The second sub-
problem consists
in
determining the components of
the extra-stress tensor
1
for
a
known
velocity field by
solving the time-discrekd constitutive equation
(Eq
8).
The procedure
is
repeated until convergence.
4.2.2)
Spatial
Discretization
The domain
Q
is
approximated by
a
set of 6-node
n=l
tn
=O
m
I
I
isoparametric triangles
Th
(quadratic element, see
m.
13),
which are deflned by the shape functions
$k.
The
nodal velocity field is expressed in term of the compo-
nent
uk
of
the nodal velocity vectors with the same
shape functions. The pressure is constant by element.
Using
the Galerkin method, the discretized equations
of GSP at current time
t,
lead to the following system:
+-++
where the matrix
A,
B
and the vytop
V,
P,
F
are given
elsewhere (16). In order to find
V,P.
we use
an
itera-
tive scheme derived
from
Uzawa's
algorithm (1
6).
The
bounded set of
linear
algebraic equations is solved by
a
direct Crout decomposition.
4.2.3)
Viscoelastic Equation
As
the different integrals in
Equation
11
are evaluat-
ed
by
the Gauss-Legendre point integration rule, the
components of the current
extra-stress
tensor
xn
are
needed only
at
the Gaussian points of each element.
Consequently, the tensorial equation
(Eq
8)
is solved
at
a
local level; it reduces to
a
(4
x
4)
linear
algebraic
system.
where the matrix
K,
and the vectors
2u,
2"
are defined
elsewhere (18). The set of linear algebraic equations
(Eq 13) is solved
by
a
direct Gauss method.
4.3)
Thermal
Bplpnce
Equation
The time differential equation
(Eq
9)
is approximat-
ed by
a
Crank-Nicholson's scheme over the time in-
tn+l=
tn
+
Atn+l
n=n+l
-
I
geometry
f
Constant
pressure
0
Velocity, Temperature
I
Flg.
13.
Mesh
of
the
preform
and
P2-PO
element
1406
POLYMER
ENGINEERING AND SCIENCE, SEPTEMBER
lssS,
Vol.
38,
No.
9
Experimental
Study
and
Numerical
Simulation
of
the
Injection Stretch/Blow
Molding
Process
crement
At,,.
Using Galerkin method, the discretized
equation
(Eq
9)
at current time
t,,
leads to the follow-
ing
system:
$"A
I
-
$"
$n+1
+
5ll
~
C*(
A~
)+K*/-)iS*=O
(14)
The capacity+Tatrix
C:,
the conductivity
matrix
K,
and
the vectors
T.
S
are defrned below:
4
+
JakV
YkV
9,dv
1
S,=
-lnhaTa.YldS- h,T;Vr,ds+IWVr,dv
n
Each matrix
Mx
(=
C*,
K*,
$)
takes the following form:
(15)
3
1
2
2
which results from
a
linearized technique (19)
in
order
to avoid
an
iterative resolution of
Eq
14.
Only
the non-
reversible part of
the
strtss
tensor
4"
(viscous
part)
con-
tributes
to
the dissipated energy
W.
1r.
M*
~
~-
MK-
~n-1
W
=
Tiv
:
=
2(qs
+
q,)b
:
E
=
2q
:
t
'.
=0.65s
Flg.
14.
Intermediate
1)ubble
shapes
(T
=
105°C).
Table
3.
Processing and Rheological Parameters for
Free
Inflation at
T
=
105°C.
Process Parameters Rheological Parameters
(bars)
(MPals)
2.58
The linear system
(Eq
14)
is
solved by a direct Crout
decomposition.
4.4)
Variation
of
Viscosity
With
Temperature
The
empirical relation proposed by Ferry
et
aL
(20)
accounts for rapid variation
of
the viscosity between
the
glass
transition
Tg
and
Tg
+
100°C.
-
C:(T-
;)
where
'2:
=
8.38
R'
and
Cz
=
42.39
K
(21).
t
=
0.27s
u
t
=1.5s
Rg.
15.
Intmmedmk
'
bubble
shapes
(T
=
105"C,
8,
=
125%).
1407
POLYMER
ENGINEERING
AND
SCIENCE, SEPTEMBER
1998,
Vol.
38,
No.
9
F.
M.
Schmidt,
J.
F.
Agassant,
and
M.
Bellet
0,3
-
0.25
z
z
g
0‘2
2
5
0,15
2
0.1
g
0.05
6
0
L
-
m
_C___--r--r---
Computed
-
Measured
----.
-
Computed
-
Measured
-----
Q.
16.
Diimeniial
injlation pressure
uers~ls
time.
6)
APPLICATIONS
6.1)
PratarmFreebnption
Let
us
proceed to free inflation simulations at
T
=
105°C
in
order to compare the computed differential
inflation pressure to the measured one (see
Seetion
2.2).
Processing parameters are given in
Table
3.
Viscoelastic parameters have been adjusted
in
order
to obtain the same maximum pressure. We assume
that the relaxation time remains constant.
It
appears
immediately
in
Rg.
14
that the expansion of the pre-
form and especially the radial expansion is unlimited.
This problem, which is not observed experimentally,
occurs because the strain-hardening phenomenon of
the material, related to the development of crystallini-
ty under biaxial stretching, is not taken into account
in the numerical model, and this problem has not
Flg.
17.
Intermediate
bottle
shapes.
n
t=Os
Table
4.
Rheological Parameters for StretchiBlow Molding.
84.2 0.05 2.5 0.1
Table
5.
Typical Values for the
Physical Propefliesfor
the
PET.
Physical Propsrties Typical Value
1336
0.25
cp
(kJ/kg.K)
at
23°C
at
80°C
at
100°C
at
200°C
1.13
1.42
1.51
1.88
been addressed
in
this
paper.
Introducing
a
viscosity
dependent on the generalized
strain
E
=
,bdz
as
proposed by
GSell(22):
t
strain
-
hardening
tm
where
Eo
is
a
reference value, leads to
limit
the expan-
sion
of
the preform (see
Fig.
15).
In that case, the
computed differential inflation pressure and the mea-
sured one are plotted
in
Fig.
16.
We note that the
agreement is
fair
between the
two
curves except
in
the
t=0.36s
t
=
0.4
s
t
=
0.45
s
1408
POLYMER ENGINEERING AND SCIENCE, SEP7EMBER
lS@E,
Vol.
38,
No.
9
Experimental
Study
and
Numerical
Simulation
of
the Injection Stretch/Blow
Molding
Process
last part. The computed preform inflation remains,
however, significantly different from the free inflation
that
has
been recorded using video camera
(&.
9).
5.2)
Setmp
of
a
Real
Stretch/Blow
Molding
R0CG.I)
We study now
a
s
tretch/blow molding operation.
The geometries of the bottle mold and of the preform,
the processing parameters have been previously refer-
enced in
FQ.
5,
Table
1,
and Table
2,
respectively (see
Section
2.1).
The initial mesh
of
the preform has
been shown in
Fig.
j3.
For this thermomechanical
simulation, we use the experimental pressure that
has been plotted
in
Fig.
3
(i.e. the pressure is not cal-
culated using
Eq
5).
The viscoelastic rheologid para-
meters
(Table
4)
have been determined by
fitting
on
the traction force of
an
amorphous
PET
sample, in-
jected in the same conditions as the tube shaped pre-
500
7
I
I
I I
1
Non-isothermal-
Isothermal
-
- -
-.
experimental
~-
,_---___
350
form
(18).
Typical values for the physical properties of
the
PET
are referenced
in
Table
5.
The value of the
heat transfer coefficient between the
air
and the poly-
mer is considered to be
!-+,
=
10
W/K.m2.
A
high value
for the heat transfer coefficient between the mold and
the polymer
h,,,
=
500
W/K.m2 has been applied
at
the
interface between the preform and the mold after con-
tact.
The
initial temperature of the preform
is
100°C.
Besides, it should be noted that the internal and the
0
0.05
0.1
0.15
0.2
0.25 0.3
0.35
tb)
Hg.
18.
Measured
am!
computed
siretch
rod
us.
time.
h
E
E
v
3
2.5
2
1.5
1
0.5
0
non-isothernial
-
isotherm31
dz
ta
-
i-
-
-
1
non-isothernial
,hti
herma1
-
experimental
dz
ta
-
i-
-
-
I
I
I
I
I
I
I
I
\
\
--_
__---_
'---,,-4:----.~---,
------
I
I
I
I
0
50
100
150
200
250
300
350
w-1
I----------
Flg.
20.
Temperature
distribution
at
the
end
ofthe
process.
\-
3
Fig.
19.
Thickness
distrihution
at
the
end
of
the
process.
POLYMER ENGINEERING
AND
SCIENCE,
SEPTEMBER
1998,
Vol.
38.
No.
9
1409
F.
M.
Schmidt,
J.
F.
Agassant,
and
M.
Bellet
.A
-B
external heat transfer coefficients are assumed to be
the same.
lplsure
17
presents intermediate bottle shapes from
the beginning to the end of the process. The computed
isothermal and nonisothermal stretching force exerted
on the stretch rod
vs.
time
are
quite equivalent (see
Rg.
18).
This result
was
expected because heat
trans-
fer becomes important
only
when the outer surface of
the preform reaches the inner surface
of
the mold and
on
a
small area of the bottom of the preform that
is
in
contact with the rod. The nonisothermal stretching
force is lower
than
the isothermal one. This
is
due to
F@.
21.
Temperature
distribution
along
material
lines.
h
u
K
110
100
90
80
70
60
50
40
30
L
"
I
I
I
1
I
I
I
0
0.2
0.4
0.6
0.8
1
?-
Inner surface
(b>
?-
Outer surface
1410
POLYMER ENGINEERtNG AND SCIENCE, SEPEMBER
1998,
Vol.
38,
No.
9
Fg. 22.
Comparison
of
the
contact
times.
0.5
0.48
0.46
0.44
0.42
Y
0.4
0.38
0.36
0.34
0.32
0.3
0.28
h
Experimerital
Study
and
Numerical
Simulation
of
the
Injection Stretch/Blow
Molding
Process
Inner surface Outer surface
1
2
3
45
6
7
8
9
No
Capt.
T
1'
the dissipation energy related to high deformations,
which increases the temperature locally. The compari-
son between the computed thickness distribution and
the experimental data at the end of the process is
shown
in
Flg.
19.
The agreement
is
better with
a
non-
isothermal model than with an isothermal one.
The temperature di:jtribution at the end of the pro-
cess
is
represented
in
Fig.
20
at
different locations
(bottom of the bottle, details of the mold, neck of the
bottle). The contact between the stretch rod and the
bottom of the preform
as
well
as
the contact between
the bottle mold and the outer surface of the preform
induces high temperature gradients throughout the
thickness (maximum
50°C),
which just@ the volumic
approach
in
order to obtain
an
accurate description of
the temperature distribution. More enlightening
is
to
plot the temperature distribution along three material
lines, which are located, respectively,
at
the neck of
the preform
(yA
=
290
mm), at the center of the pre-
form
(y,
=
250
mm),
and at the bottom of the preform
(x,
=
6.9
mm) (see
F'ig.
214.
For each material line,
the temperature distribution
is
represented vs. the
nondimensional cumlinear coordinate
s
in
the thick-
ness direction
(Rg.
21
b).
We
note that the temperature
increases from
the
upper material line
(A)
to
the lower
one (C). This
is
due
1.0
the expansion of the preform,
which occurs from the neck to the bottom of the bot-
tle.
So,
the contact between the preform and the mold
occurs later for line
C
than for line
A.
More interesting
is
that
the temperature distribution along
line
C
at
the end of the process is partly higher
than
the
initial
temperature (see dashed line), which
is
related to the
energy dissipation during inflation. This phenomenon
has been observed experimentally.
Contact times versus location of contact sensors for
the isothermal model are plotted in
Flg.
22
and com-
pared with experiments. Contact times computed
using Oldroyd
B
model are closer
than
the Newtonian
one. Consequently, it appears that the kinetic of con-
tact
(and consequently the kinetic of blowing) depends
on the rheological behavior.
6)
CONCLUSION
Experiments have been conducted on
a
well-instru-
mented stretch blow molding machine: stretching
forces
as
well
as
contact times between the polymer
and the mold have been recorded. The bottle thick-
ness distribution has been measured for various pro-
cessing
parameters.
A
coupled model for the thermodynamic of the
air
and for the thermomechanical idation of the parison
has been proposed.
A
finite element model and a
vis-
coelastic differential constitutive equation have been
used. Viscous dissipation,
as
well
as
the temperature
gradient between the mold and the molten polymer,
has been considered. The comparison between experi-
mental and numerical rod stretching forces
is
fair.
The discrepancy
is
more important when considering
the thickness distribution and the contact kinetic.
Further developments
will
necessitate
a
better
un-
derstanding of the rheology of
PET
during the stretch
blow molding operation (amorphous, i.e., liquid at the
beginning
of the process, and semicrystalline, i.e.,
solid
at
the end of the process).
ACKNOWLEDGMENT
This research was supported by Side1 Company and
the Rench 'Ministere de
la
recherche"
(MHT
no
9OA
136).
POLYMER
ENGINEERIA'G AND SCIENCE,
SEPTEMBER
1998,
Vol.
38,
No.
9
1411
CP
Fh
9'
h,
I
k
- -
r'
1-3
i
=
-(Vu
=2
*k
r
R
F.
M.
Schmidt,
J.
F.
NOMENCLATURE
heat capacity
gravity
heat transfer coefficient between
air
and
polymer
heat transfer coefficient between mold/
stretch
rod
and polymer
identity tensor
heat conductivity
unit outward nod vector
number of nodes
arbitrary pressure
velocity field
discrete velocity field
assembly of
the
nodal velocity components
assembly of the nodal pressure vector
assembly of the nodal applied forces
time
temperature field
assembly of the nodal temperature field
temperature of the mold
temperature of
the
air
coordinate vector
discrete coordinate vector
coordinate vector
at
time
I?,,
+
(tf.V)[.]
-
VZ.[.]
-
[.].'VG
upper convective time derivative
acceleration field
+
'VV')
rate of
strain
tensor
associated with
total viscosity
viscous
part
of
the
total viscosity
viscoelastic part of the total viscosity
viscosity
at
glass
transition temperature
relaxation time
specific
mass
specific
mass
at
glass
transition temperature
Cauchy
stress
tensor
extra-stress
tensor
shape functions
boundary of the domain
R
part of the boundary
r
that
is
not
in
con-
tact
with
the rod
part
of the boundary
r
that
is not in contact
with the mold
domain occupied by the preform
Agassant,
and
M.
Bellet
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1.
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POLYMER ENGINEERING AND SCIENCE, SEPTEMBER
W&?,
Vol.
38,
No.
9
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