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

4

Viscoplastic modelling of PET linked

to the microstructure (T>Tg)

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)

11

Homogenisation of elastic properties

of PET (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)

15

Homogenisation of elastic properties of PET (T<Tg)

with

with

16

βe=2

α=5

Homogenisation of elastic properties of PET (T<Tg)

[G.C. Rutledge]

crystal

17

Simulations of stretch blow moulding

process of PET bottles

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.