modelling of the behaviour of pet in the glassy state and
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Modelling of the behaviour of PET in the glassy
state and prediction of the elastic behaviour at
room temperature
Benoît COSSON Luc CHEVALIER Gilles REGNIER
11/03/2009
2
Context of the study
Paramè t re s
t e c hno lo g iq ue s d u
p ro c é d é d e s o uff lag e
Te nue e n s e rv ic e
d e s bo ut e ille s
s o uff lé e s
Ev o lut io ns :
d e la g é o mé t rie d e la b o ut e ille
d e la mic ros t ruc t ure d u mat é riau
F
PV
pV P
Process parameters
Microstructure evolution
Resistance in use
3
Plan
� Viscoplastic modelling of PET linked to the microstructure (T>Tg)
� Homogenisation of elastic properties of PET (T<Tg)
� Simulations of stretch blow moulding process of PET bottles
� Conclusions
5
� MTS hydraulic press with oven regulated at 90°C.
� Thickness of specimen equal to 1 mm in order to have homogeneous temperature.
� 3 different traction velocities.
� 5 levels of displacement.
� Microstructure evolution
stopped by a liquid nitrogen jet.
� Crystallinity measured by
densitometry.
PET Arnite D00301 given by DSM.
Trial protocol
Viscoplastic modelling of PET linked to the microstructure (T>Tg)
6
Raw data for a traction velocity = 66 mm.s-1
Initial length of the specimen = 25 mm
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50 60 70 80 90 100
jaw displacement (mm)
measu
red
fo
rce
(N)
ep_26
ep_27
ep_30
ep_32
ep_35
ep_36
ep_37
ep_38
ep_42
ep_43
ep_44
ep_45
ep_46
ep_47
ep_53
ep_54
ep_59
ep_61
ep_63
ep_64
ep_68
ep_69
ep_70
ep_72
ep_73
ep_74
Viscoplastic modelling of PET linked to the microstructure (T>Tg)
7
Local measurement of strain
(a) Initial mark (b) Distorted mark
True elongation = Length of the distorted mark
Length of the initial mark
Test directionTest direction
Viscoplastic modelling of PET linked to the microstructure (T>Tg)
8
Initial strain rate = 0.33 s-1Initial strain rate = 1.1 s-1
Initial strain rate = 2.2 s-1
Viscoplastic modelling of PET linked to the microstructure (T>Tg)
Crystallinity %
Young m
odulu
s (G
pa)
9
Crystallinity evolution (based on the Avrami
model) [Ahzi et al., Doufas et al.]:
Orthotropic behaviour:
(MP
a.sm
)
0,14
y0
30,360,230,60,571,850,1
4Value
βXc∝pnmcbaparameter
Viscoplastic modelling of PET linked to the microstructure (T>Tg)
if
if for
10
Results for uniaxial tensile tests
Cauchy stress versus logarithmic strain
Crystallinity versus logarithmic strain
(MP
a ;
%)
0.33 s-1
1.1 s-1
2.2 s-1
80°C 85°C 90°C 95°C 100°C 105°C
Viscoplastic modelling of PET linked to the microstructure (T>Tg)
12
Homogenisation of elastic properties of PET (T<Tg)
(a) (b)
(c)
Various morphologies of PET crystals (a) lamella; (b) fiber structure; (c) spherolite
[J.A. Kulkarni et al.]
Microstructure of PET
13
θ
ϕ
Principal axisSecondary axis
Secondary axis
Solution the Eshelby’s problem for an elastic
inclusion in a infinite elastic matrix
Elastic tensor of the matrix
Elastic tensor of the inclusion
4th order identity tensor
Eshelby tensor function of the
inclusion shape factor
Homogenisation of elastic properties of PET (T<Tg)
14
Homogenisation model [L.J. Walpole] for N+1 phases
Homogenisation model for 1 matrix and 1 type of inclusion with an infinity of
directions [S. Fedrico et al.]
Volume fraction of each phase
One phase is given by one direction and one elastic tensor
Homogenisation of elastic properties of PET (T<Tg)
18
Complete simulations of the process (0.33 L et 2 L):
•Thermo-mechanical problem (heat transfer with
the mould and the stretch rod).
•Contact problem (with the mould and the stretch
rod).
•Initial temperature: 10°C for the mould, 40°C
for the stretch rod and close to 100°C for the
preform.
•Mould and stretch rod temperature are assumed
constant.
•40g preform for 2 L bottle.
•25g preform for 0.33 L bottle.
Simulations of stretch blow moulding process of PET bottles
Setting up of
preformStretch and pre-blow
Stretch and blow Blow and cooling
19
Elastic simulation using
homogenised properties
2L bottle
0.33L bottle
Simulations of stretch blow moulding process of PET bottles
20
Conclusion
� Viscoplastic modelling of PET behaviour with a link to the
microstructure evolution.
� Prediction of elastic properties of stretched PET.
Complete simulation of stretch blow moulding process.
Prospects
� Viscoelastic modelling.
� Inverse identification of the model parameters.
� 3D simulation of stretch blow moulding process.
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