Thermoforming of cut sheets is extensively used in the industry for various commercial applications. In this process, the sheet is heated to a softened state and subsequently deformed into the mould due to an applied pressure, a vacuum, a moving plug or a combination of these media. The thermoforming-process market is expanding to complex geometries and to a list of potential materials. In this work, I use a no isothermal hybrid approach which combines the dynamic finite element method and the thermodynamic law of perfect gases to study the effect of the temperature of the air flow on the blowing of a thin, isotropic and incompressible thermoplastic membrane. The viscoelastic behaviour of the K-BKZ model is considered. The Lagrangian formulation together with the assumption of the membrane shell theory is used. The numerical validation is performed by comparing the obtained results with the theoretical results for the HDPE grade. Moreover, the effect of the temperature on the thickness and stresses distribution is presented.

1.
Wiesche S. A., Industrial thermoforming simulation of automotive fuel tanks, Applied Thermal Engineering, 2004, p. 2391–2409.
2.
A. Yousefi, R. Diraddo, A. Bendada, Simulation of the Mobile Preform Reheat in Injection Stretch Blow Moulding, PPS-17 The Polymer Processing Society, CD- ROM proceedings, Montreal, Canada, May 21–24, 2001, pp. 134–146.
3.
Warby
M. K.
,
Whiteman
J. R.
,
Jiang
W. G.
, and al,
Finite element simulation of thermoforming processes for polymer sheet
.
Mathematics and computer in simulation
Vo.
61
,
2003
, pp.
209
218
.
4.
Erchiqui F., Bendada A., Godard F., Gakwaya A., Thermodynamical approach for modeling of free inflation of the closed thin hyperelastic structure International Association of Science and Technology for Development-IASTED459-043, Modeling and Simulation, Cancun, Mexico, May 18–20 (2005)
5.
Laroche D., Erchiqui F., 3D modelling of the blow moulding process Simulation of Materials Processing: Theory, Methods and applications, Hue´tink & Baaijens (eds) 1998, Balkema, Rotterdam, ISBN 90 5410 970 X, pp. 483–488.
6.
Erchiqui F., Derdouri A., Gakwaya A., Verron E., Analyse expe´rimentale et nume´rique en soufflage libre d’une membrane thermoplastique, Entropie, No. 235/236, 2001, pp. 118–125.
7.
Verron
E.
,
Marckmann
G.
and
Peseux
B.
,
Dynamic inflation of Non-Linear Elastic and viscoelastic rubberlike membrane
,
International Journal Numerical Methods Engineering
, Vol.
50
,
2001
, pp.
1233
1251
.
8.
Erchiqui
F.
,
Diri
D.
Mode´lisation du comportement des polyme`res thermoplastiques par une approche combinant la me´thode dynamique des e´le´ments finis et la loi des gaz parfaits
.
Revue des composites et des mate´riaux avance´s
. Vol.
13
, No.
1
,
2004
, pp.
99
114
.
9.
Erchiqui
F.
,
Gakwaya
A.
and
Rachik
M.
Dynamic finite element analysis of nonlinear isotropic hyperelastic and viscoelastic materials for thermoforming applications
.
Polymer engineering & science
, Vol.
45
, No.
1
,
2005
, pp.
125
134
.
10.
Zienkiewicz O. C. and Taylor R.L; The Finite Element Method; Fourth edition, McGraw-Hill, Vol. 1 and Vol. 2, 1991.
11.
Bernstein
B.
,
Kearsley
E. A.
,
Zapas
J.
A Study of stress relaxation with finite strain
,
Trans. Soc. Rheol.
Vol.
VII
,
1963
, p.
391
410
.
12.
Wagner
M. H.
,
Network theory of polymer melts
,
Rheology Acta
, Vol.
8
,
1979
, pp.
33
50
13.
Dokainish
M. A.
,
Subbaraj
K.
,
A survey of direct time-integration methods in computational structural dynamics
.
Comput. Struct.
, Vol.
32
, No.
6
,
1989
, pp.
1371
1386
.
14.
Lodge A. S., Elastic liquids, Academic Press, London, 1964.
15.
Papanastasiou
A. C.
,
Scriven
L. E.
,
Macosko
C. W.
,
An integral constitutive equation for mixed flows: viscoelastic characterization
.
J. Rheol.
, Vol.
27
,
1989
, pp.
387
410
.
16.
Ferry J. D., Viscoelastic properties of polymer, John Wiley & Sons, 1980.
17.
Macosko C. W., Rheology: principles, measurements and applications, John Wiley & Son, 1994.
18.
Laun
H. M.
Rheological Acta
, vol.
17
,
1978
, pp.
404
404
.
19.
Wagner
M. H.
,
Elongational behaviour of polymer melts in constant elongation-rate, constant tensile stress, and constant tensile force experiments
,
Rheologica Acta
, Vol.
18
,
1979
, pp.
681
692
.
20.
Osaki
K
,
On the damping function of shear relaxation modulus of entangled polymers
.
Rheol Acta
, Vol.
32
,
1993
, pp.
429
437
.
21.
Fulchiron R., Verney V., Marin G., Determination of the elongational behavior of polypropylene melts from transient shear experiments using Wagner’s model. Journal of Non-Newtonian Fluid Mechanics, (1993), pp. 48–49.
22.
F. Erchiqui, D. Laroche ≪Mode`le de Lodge 3D quasi-incompressible≫, IMI99-50202-79857-C CNRC, 1999.
This content is only available via PDF.
You do not currently have access to this content.