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Numerical and Experimental Investigation of
the Deformational Behaviour of Plastic
Containers
By D. Karalekas,* D. Rapti, G. Papakaliatakis and E. Tsartolia
University of Piraeus, GR-185 34 Piraeus, Greece
A numerical and experimental study was undertaken to investigate the
deformational behaviour of a plastic grooved container used to store agrochem-
ical solutions when loaded under columnar crush conditions. Finite element
analysis was implemented to calculate stresses and deformations at various
critical points of the container. A non-linear elastoplastic analysis was
performed, based on the ABAQUS FEM computer program. The results of the
stress analysis were coupled with a yield criterion to predict the initiation of
plastic deformation. The numerically obtained results are compared to those
obtained experimentally. It was found that the numerically calculated strains at
predetermined locations of the plastic container were in good agreement with the
experimentally measured ones. Copyright O2001 John Wiley & Sons, Ltd.
Received 5 December 2000; Accepted 29 August 2001
KEY WORDS: plastic bottle deformation; ®nite element analysis; columnar crushing load;
plastic bottle testing
INTRODUCTION
The use of blow-moulded polyethelene terephtha-
late (PET) plastic containers has become common-
place in the packaging of liquid substances.
Typical PET containers are formed by a process
in which an elongated tubular preform is heated
and expanded into conformity with the inside
surface of a mould cavity, thus producing a semi-
rigid thin-walled container. Since the container is
exposed to various pressures and forces during
production and use, it must be designed to
respond to such physical in¯uences while main-
taining the predetermined and desired con®gura-
tion.
1
The deformation behaviour that a plastic con-
tainer exhibits in its useful life is a function of the
shape, material characteristics, moulding process,
geometry and loading conditions.
2
Plastic bottles
are sensitive to externally and internally applied
loads, normally because their walls are not rigid
enough. In plastic commercial bottles with ¯exible
walls, loaded under crushing loading conditions, it
has been observed that they lose their wall
symmetry and hence column strength, which often
prevents stacking of the containers for display or
storage purposes. The resulting deformation can
be more pronounced in those less rigid areas of the
bottle, depending on the level of ductility that the
plastic material exhibits.
3
As a result of their shape
and production process characteristics, locally
induced strains may arise, even at quite low levels
PACKAGING TECHNOLOGY AND SCIENCE
Packag. Technol. Sci. 2001; 14: 185±191
DOI:10.1002/pts.549
Copyright 2001 John Wiley & Sons, Ltd.
* Correspondence to: D. Karalekas, University of Piraeus, GR-185 34 Piraeus, Greece.
Email: dkara@unipi.gr
Contract/Grant Sponsor: Hellenic General Secretariat for Research and Technology, Greece; contract/grant number: PAVE
97BE26.
of applied stress, leading to premature failure
under loading.
4
Using computer-based simulation
and analysis allows these challenges to be ad-
dressed early in the development process of new
moulded thermoplastic containers.
4±6
Modelling
techniques have been developed to predict the
performance of water-®lled containers in the drop
impact test.
7
In the this work, a numerical and experimental
study was undertaken to investigate the deforma-
tional behaviour of an empty plastic grooved
container used to store agrochemical solutions
when loaded under columnar crush conditions.
Finite element analysis of the plastic container was
implemented to predict and evaluate its overall
and local behaviour under compressive loading. A
non-linear elastoplastic analysis was performed,
based on the ABAQUS FEM computer program.
The deformed shape of the plastic container and
the resulting stresses and strains were determined
at various critical points. The results of the stress
analysis were coupled with a yield criterion to
predict the initiation of plastic deformation. The
analytical results for strain deformation were
compared to those obtained experimentally.
EXPERIMENTAL
PROCEDURE
The plastic container tested in the present inves-
tigation was a blown thermoplastic bottle made by
Argo SA. The plastic bottle is made of PET and
consists of a bottom portion, a neck portion and an
intermediate body portion with parallel, equally
spaced, circumferential reinforcing grooves. The
uniformity of the bottle wall thickness was
examined by cutting and measuring circumferen-
tial sections at various locations of the bottle. It was
found that wall thickness (0.3 mm) remained
uniform across the intermediate body section,
while it varied considerably (0.3±0.5 mm) at the
area where the neck connects to the intermediate
section and the bottom portion of the container.
The bottles were tested under compression
along their long axis of symmetry using a Zwick
Z010 testing machine. The containers were loaded
at a constant cross-head rate of 25 mm/min until
failure. The testing method is fully described at
ASTM D2659-95.
8
A typical load vs. compressive
displacement curve is drawn in Figure 1. Particu-
lar care was taken in the selection of the bottle
specimens as well as in their alignment, since
determination of its deformation under loading is
particularly sensitive to the effects of specimen
non-uniformity or improper specimen positioning.
The specimens were free of obvious defects, such
as rocker bottoms or bent necks, and were aligned
between the compression platens in such a way
that the axis of crushing coincided with the centre
line of the movable member of the testing machine.
Strain gauge techniques were used to obtain the
induced strain ®elds as a result of the exhibited
deformation under compressive loading. Strains
along the direction of the applied load were
measured with single foil gauges mounted at
various positions of the bottle sidewall, as illu-
strated in Figure 2. The mechanical properties of
the formed PET were obtained by testing in
tension specimen coupons. A typical load vs.
elongation curve of the formed PET material is
shown in Figure 3.
COMPUTATIONAL
APPROACH
An analysis based on ®nite element methods was
used to solve the boundary value problem of the
plastic container and to evaluate its overall and
Figure 1. Load vs. compressive displacement curve of plastic
container under crushing loading.
Copyright O2001 John Wiley & Sons, Ltd. 186 Packag. Technol. Sci. 2001; 14, 185±191
D. KARALEKAS ET AL.
local behaviour under compressive loading. A
non-linear elastoplastic analysis was performed,
based on the ABAQUS standard ®nite element
program. Four-node axonosymmetric elements,
2856 in total, were employed to construct the mesh
of the modelled pro®le. The location of the node
elements along the modelled pro®le is shown in
Figure 4. The actual wall thickness of the neck,
intermediate and bottom sections, along with the
experimentally obtained mechanical properties of
the PET material, were input in the analysis. The
model was compressed, at a constant rate of
0.16 mm/s, up to a de¯ection of 14.416 mm,
calculating the values of stress, strain and dis-
placement at the four nodes of every element. In
addition, the total strain energy, involved in
change of its shape and volume, was also
calculated.
The results of the stress analysis were coupled
with the von Mises' yield criterion to predict for
Figure 2. Schematic representation of strain gauge location.
Figure 3. Load vs. elongation curve of formed PET material.
Figure 4. Location of node elements along the modelled
pro®le.
Figure 5. Discretization of modelled pro®le when unloaded.
Copyright O2001 John Wiley & Sons, Ltd. 187 Packag. Technol. Sci. 2001; 14, 185±191
DEFORMATIONAL BEHAVIOUR OF PLASTIC CONTAINERS
plastic deformation. The equivalent stress,
eff
was
computed by the following equation:
eff 1
2
p
122232312
q
1
In Figure 5 the discretization of the modelled
container is presented in the unloaded state and in
Figure 6 under compressive loading. The details of
the base and of a representative reinforcing groove
section are also shown. For these bottle sections
and for an applied compressive displacement of
14.416 mm, the obtained contours of
eff
across the
bottle thickness are plotted in Figure 7. The
corresponding contours of elastic strain energy
are presented in Figure 8.
RESULTS AND DISCUSSION
The formed PET material, when tested under
tension, exhibits an elastoplastic, highly ductile
behaviour, as seen from Figure 3. The modulus of
elasticity was obtained to be E= 1890 N/mm
2
, the
yield stress
ys
= 66 N/mm
2
and the ultimate
failure stress
u
= 134.5 N/mm
2
.
The deformational behaviour of the plastic
bottle under investigation is characterized by
pronounced wall deformation (panelling) under
crushing loading. From Figure 1 is obtained that
the bottle starts to deform when a maximum load
of 355 N is reached, corresponding to 5.24 mm
applied displacement. At that crushing load, the
less rigid curved areas of the bottom section of the
intermediate body start to collapse. The load-
carrying capability of the bottle decreases even
further as inward buckling (folding) of the side-
wall starts to take place, forming a triangular
shape folding pattern. The resulting triangles
increase in number, with applied crushing dis-
placement eventually ®lling the circumferential
areas located in between the reinforcing rings. An
Figure 6. Discretization of modelled pro®le when loaded.
Figure 7. FEM obtained
eff
contours across the bottle thickness. (a)
Reinforcing groove section. (b) Bottom section.
Copyright O2001 John Wiley & Sons, Ltd. 188 Packag. Technol. Sci. 2001; 14, 185±191
D. KARALEKAS ET AL.
image of the deformed container during experi-
mental testing is presented in Figure 9.
The experimentally obtained strains are plotted
as a function of applied compressive displacement
in Figure 10. It is seen that the lower section of the
sidewall is strained the most, while the magnitude
of the measured strains drop considerably when
folding of the bottom section starts to take place.
The numerically obtained strains along the bottle
long axis, at an applied compressive displacement
of 14.416 mm, are plotted in Figure 11. Their
magnitude remains well below the yield strain
(3.5%) of the formed material tested in tension and
they are in good agreement with these measured
experimentally at the three locations of the bottle
sidewall, as seen in Figure 2. Speci®cally at
location (a), the numerically obtained strain in
the long direction was calculated to be 2560 me
while the corresponding experimental one was
measured to be 2280 me. Their correlation is
considered satisfactory, since parameters such as
expected anisotropy of the formed material (in the
long and hoop directions) and non-uniformity of
the wall thickness in the intermediate section
Figure 8. FEM obtained elastic energy contours across the bottle thickness.
(a) Reinforcing groove section. (b) Bottom section.
Figure 9. Deformational behaviour of plastic container under
crushing loading.
Figure 10. Variation of experimentally obtained strains (e),
along the bottle long axis, as a function of applied
compressive displacement.
Copyright O2001 John Wiley & Sons, Ltd. 189 Packag. Technol. Sci. 2001; 14, 185±191
DEFORMATIONAL BEHAVIOUR OF PLASTIC CONTAINERS
could not be taken into account in the numerical
analysis performed.
In Figures 12 and 13, the von Mises' calculated
equivalent stress and elastic strain energy along
the bottle height are respectively plotted, both
reaching their maximum value at the same section
of the plastic container. It is seen in Figure 12 that
the maximum calculated value for von Mises'
stress reaches the experimentally obtained yield
stress of the formed material, thus indicating the
initiation of plastic deformation. However, a
signi®cant drop in the magnitude of the calculated
values, at the initially most strained lower section
of the bottle, results when the wall thickness of the
intermediate body section is increased from
0.3 mm to 0.5 mm.
Figure 12 shows that the resulted stresses at the
intermediate reinforced section of the plastic
container exhibit identical variations. The calcu-
lated stresses in between the reinforcing ring areas
are of low magnitude, while they increase con-
siderably at the tip of the rings. The corresponding
ones arising at the thicker threaded neck are, as
expected, of low magnitude, increasing gradually
across the section that connects the neck to the
intermediate portion. However, the resulting
stresses at the neck-intermediate area are of lower
magnitude when compared to those calculated at
the bottom section. This numerically derived
conclusion is fully veri®ed by the experimentally
obtained strains shown in Figure 10.
SUMMARY AND
CONCLUSIONS
A numerical analysis combined with an experi-
mental study was undertaken to investigate the
deformational behaviour under loading of a plastic
grooved container. Stresses and strain distribu-
tions were calculated at critical points of the
container. It was found that the most stressed area
of the container is the bottom portion of the
intermediate body section, exhibiting stress values
Figure 11. Variation of calculated strain (e), along the bottle
long axis, at a compressive displacement of 14.4 mm.
Figure 12. Variation of von Mises' equivalent stress (
eff
),
along the bottle long axis, at a compressive displacement of
14.4 mm.
Figure 13. Variation of elastic strain energy, along the bottle
long axis, at a compressive displacement of 14.4 mm.
Copyright O2001 John Wiley & Sons, Ltd. 190 Packag. Technol. Sci. 2001; 14, 185±191
D. KARALEKAS ET AL.
that exceed the yield stress of the PET material.
The numerically calculated strains at predeter-
mined locations of the plastic bottle sidewall were
in good agreement with the experimentally
measured ones. It was demonstrated that although
speci®c fabrication parameters of the plastic
container could not be incorporated in the per-
formed analysis, ®nite element analysis could be
implemented reliably in its early design phases to
evaluate its performance under crushing loading.
ACKNOWLEDGEMENTS
This work was supported in part by the Hellenic
General Secretariat for Research and Technology (Con-
tract No. PAVE 97BE26).
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DEFORMATIONAL BEHAVIOUR OF PLASTIC CONTAINERS
