DEVELOPMENT OF A COMPRESSION TOOL
FOR POLYMERIC MATERIALS
M. Jerabek1), R. Steinberger1) and Z. Major2)
1) Polymer Competence Center Leoben GmbH, Parkstrasse 11, 8700 Leoben, Austria
2) Institute of Materials Science and Testing of Plastics, University of Leoben,
Franz-Josef-Strasse 18, 8700 Leoben, Austria
Abstract
Mechanical properties of polymers exhibit a strong time, temperature and pressure dependency. The former two have
extensively been investigated mostly by tensile testing whereas only little is known about the influence of pressure. This can
be analyzed by applying different compression test methods. For this purpose a compression tool was designed and uniaxial,
plane strain and multiaxial compression tests were performed. In this paper the several factors that may influence the result
are explained in detail. Furthermore an appropriate testing procedure is explained in order to measure the small as well as the
large strain behavior. The obtained results were compared to uniaxial tensile tests, where it was found out that both regimes
show a strong dependence on hydrostatic pressure.
Introduction
Extensive studies have been conducted to determine the time and temperature dependent tensile behavior of polymers. Only
little research work is available for their mechanical response dependent on hydrostatic pressure that is testing under pure
shear and especially under compression. This may be associated with the increased experimental difficulties in compression
testing and the extensive testing procedure to get the intrinsic material behavior under uniaxial, plane strain and multiaxial
stress states. It is well known that higher yield stresses in the compression regime compared to uniaxial tensile loading can be
attributed to the higher mean pressure in the specimen and thus to the reduced molecular mobility [1].
The knowledge of the constitutive equation dependent on hydrostatic pressure for polymers is of great practical interest for
contact problems or for finite element simulations of complex parts. In order to solve non-linear contact problems the values of
the multiaxial compression behavior such as stiffness and the onset of plastic deformation are important. Therefore the
motivation and objective of this research work was to establish a compression tool, which is capable to investigate the
materials response under arbitrary hydrostatic pressures.
For this purpose different experimental setups from uniaxial to plane strain and fully confined compression, found in literature,
were used. Unlike tensile testing, where the testing procedure is well developed, compression testing has still unsolved
problems, such as friction between the platens and specimen, specimen preparation and dimensions and specimen alignment.
In this paper the focus is on the uniaxial compression test with data reduction in the small strain and large strain regime. The
small strain regime represents the compressive modulus and the large strain regime the yield stress and the stress – strain
behavior up to final failure.
The material investigated in this study was a pure polypropylene homopolymer manufactured by Borealis GmbH Linz. The
several samples were cut out from injection-molded plates. The detailed dimensions used for the various setups will be
discussed in the respective section.
Method
All tests were run on an electromechanical driven universal testing machine Instron 4500 (Instron Deutschland GmbH). A
source of errors in compression tests may also be the testing machine. Under high compression loads the load pin of those
machines generally tend to deviate from the loading axis. This error cannot occur under tensile loading in which a pure uniaxial
stress state is guaranteed. One solution of this problem is the usage of a compression tool with aligning bars at each corner.
The designed tool used in this work can be seen in Figure 1 with the uniaxial compression configuration mounted. Due to the
four ball linings and highly accurate aligning bars a precise movement of the upper and lower compression plate is ensured.
This setup is capable to avoid any transverse forces or moments, which would manipulate the test result. The axial strain was
locally measured by means of a LVDT mounted between the two compression plates. In this work three different strain rates,
namely v1 – 8.7x10-3 s-1, v2 – 8.7x10-4 s-1and v3 – 8.7x10-5 s-1 were applied. All testing presented here was done at room
temperature.
Figure 1. Compression tool with the setup for the uniaxial compression test mounted. The four aligning bars at each corner can
be seen.
Uniaxial compression test setup
The uniaxial compression test configuration can be seen in Figure 1 with the cylindrical specimen in-between the two plates.
The lower plate consists of a spherical seat that is a self-adjusting tool [2] to correct for any geometrical divergence from the
ideal specimen shape. The length of the standard specimen was 12 mm with a diameter of 8 mm giving a L/D ratio of 1.5. This
was chosen because specimens longer then L/D>5 tend to buckle, between 2.5<L/D<5 shear failure may occur and 2<L/D<2.5
double barreling is the most preferable deformation and for short specimens L/D<1.5 friction plays the main role [3].
Despite the fact that highly polished plates and a lubricant were used friction is always evident in compression testing and will
influence the test results particularly at higher strains. To this end the so-called Cook and Larke method [4] was applied.
Specimens with different L/D ratios were prepared and tested up to 50% axial strain. In accordance with the key assumption of
Cook and Larke the stress at a certain strain should decrease with higher L/D ratios since friction does only occur at the end
surfaces of the specimen. Thus the longer the specimens are the less pregnant the role of friction. By extrapolating the various
stress levels obtained via different heights of the specimens to infinite length gives rise to the intrinsic material stress – strain
response. The variation of the L/D ratio should be reached with different specimen lengths at constant diameters to provide the
same stress distribution due to friction within the specimen. Changes in the diameter may also change the stress state within
the specimen.
Another method to account for friction is the use of PTFE tapes stuck on the end surfaces of the specimen. These tapes can
be strained up to several 100 per cent. In fact a homogeneous deformation of the specimen up to 40% axial strain could be
obtained reflecting the low coefficient of friction between PTFE and steel. Another possibility to overcome friction may be the
use of small indentations at the ends of the specimen filled with lubricant [5]. Besides the advantage of having a homogeneous
deformation up to higher strain levels additional stresses emerge at the grooves and the modulus calculation is made
impossible. However, this method was not applied in this research work.
Another problem on which one may struggle is the accurate and reliable measurement of the compressive modulus. Since the
strain range at which the compressive modulus should be calculated in accordance with the ISO 604 [6] is equivalent to the
tensile strain range that is 0.0005 – 0.0025 strain any initial misfits result in an error of the obtained modulus value. For this
purpose special attention was given to the preparation of the specimen that the specimen axis is perpendicular to the end
surfaces and the end surfaces parallel to each other.
Data Reduction
The deformation and force is measured via LVDT and load cell, respectively. The axial strain is calculated according to
Equation (1)
ε=
l
l0
(1)
where
l = actual length
l0=original specimen length
The nominal axial stress is calculated via the original cross section of the specimen with Equation (2)
σ=
F
A0
(2)
in which
F = Force
A0 =original cross section
Results and discussion
Large strain behavior
Stress – strain curves at different strain rates are shown in Figure 2. It can be seen that as expected higher strain rates yield to
higher yield stresses. This is common for all time dependent materials. The velocity dependence of the coefficient of friction
can also be observed in the post yield hardening of the material. At high deformation rates friction between the platens and the
specimen is low representing a lower strain hardening obvious for v1. At low deformation rates the impact of friction is
becoming more important and results in a significant strain hardening and overestimation of the material. This can be observed
in the crossing point between the stress – strain curves of v1 and v2. Barreling of the specimens start to develop at around
10 % axial strain. Hence data beyond the yield strain do not represent true material behavior and needs to be corrected to
lower stress levels as will be shown.
100
axial stress, MPa
80
60
40
v1
v2
v3
20
0
0,0
0,1
0,2
0,3
0,4
0,5
axial strain, Figure 2. Stress – strain curves tested at three strain rates v1, v2 and v3.
An appropriate method to correct for frictional effects is the Cook and Larke method [4]. This was done at the second strain
rate for three different specimen lengths, as displayed in Figure 3. It is obvious that extrapolation to infinite lengths result in a
significant stress decrease. It is worth noting that up to yield point practically the true material stress – strain curve is
determined and only if the large strain behavior is of interest one may consider the Cook and Larke method. Another possibility
as already mentioned is the used of a PTFE tape. A result is also shown in Figure 3 indicating that this setup gives rise to the
intrinsic material behavior since it is closely related to the Cook and Larke result. Moreover no inhomogeneous deformation of
the specimen could be detected using this tape. The determination of the modulus on the other hand might be difficult since
the tape itself undergoes some amount of deformation. In the present study tests run with PTFE lead to lower modulus values
than measured without the tape.
100
axial stress σ, MPa
80
60
40
L/D=1
L/D=1.5
L/D=2
Cook and Larke Correction
L/D 1.5 - PTFE
20
0
0,0
0,1
0,2
0,3
0,4
0,5
axial strain ε, Figure 3. Results of the Cook and Larke correction for uniaxial compression test results obtained with specimens having
different L/D ratios. Also shown is the result of the specimen with the PTFE tape sticked on the end surfaces.
Small strain behavior
Besides the yield and irreversible behavior also the reversible behavior of polymers is of particular interest. Compared to the
tensile modulus obtained in the tensile test one may calculate the compressive modulus from the compression test. Again,
applying different test methods also a compressive modulus dependent on hydrostatic pressure can be determined. In
literature only few data on the modulus is available. This can be explained with the difficulties one has to struggle with to get
useful results. The first prerequisite to measure reliable modulus values is an accurate specimen preparation to ensure a
perfect fit between the specimen and the compression platens to avoid any initial misfits. But, however, also this may not by
default deliver the desired result as can be seen in Figure 4. Here the first 2 % strain are plotted for the uniaxial compression
test. The range where the compressive modulus is calculated is also plotted. It is obvious that if this range is taken for the
modulus determination a tremendous error and underestimation of the material would be done. After 0.5 % strain the
specimen is in full contact with the compression platens and the stress starts to increase.
v1
v2
v3
cubic splines
axial stress σ, MPa
40
30
Compressive modulus range
according to ISO 604
20
10
0
0,00
0,01
0,02
axial strain ε, Figure 4. Depiction of the small strain range of several uniaxial stress –strain curves. Cubic splines are also plotted in the
diagram.
stress - strain derivative, MPa
For this purpose the best value for the modulus is the highest slope of the stress –strain curve. In order to calculate the
derivative some kind of smoothing of the experimental data has to be done. It turned out that the best method to do so without
manipulating the raw data is the use of cubic splines also plotted in Figure 4. Cubic splines enable to remove the scatter of the
data without changing the overall trend of it. Subsequently these splines were derived as shown in Figure 5. Then the
maximum of the derivative was determined and a linear regression procedure was applied taking all values within the limit
±0.001. This ensures that the length of the strain range used for the modulus calculation is according to ISO 604.
It is apparent that the highest modulus values do not occur at the very beginning of the test but shortly beyond 0.5 % strain.
The length of the specimen in this investigation was 12 mm, thus 0.5 % of 12 mm are 60 µm. In the ISO standard the
specimen used for compressive modulus determination shall be 50 long. This means that the lower limit of the calculation
range starts at a deformation of 25 µm. Since it is very hard to reach this objective we suggest the described procedure for the
calculation of the compressive modulus. Furthermore the same specimen can be used to determine the stiffness and strength
of the material. However, the strain rate dependence of polypropylene can also be seen in Figure 5 where higher strain rates
give higher modulus values.
2500
2000
1500
1000
Uniaxial Compression Test
v1
v2
v3
500
0
0,00
0,01
0,02
axial strain ε, -/Figure 5. Derivative of the stress – strain plotted in Figure 4 to calculate the compressive modulus.
2500
modulus, MPa
2000
1500
Compressive Modulus
Tensile Modulus
1000
500
0
-5
10
10
-4
10
-3
10
-2
10
-1
crosshead speed, Figure 6. Comparison of the compressive and tensile modulus at three strain rates.
In order to compare these results with other test methods to prove the dependence of the modulus on hydrostatic pressure
tensile tests were conducted at the same strain rate. The result is shown in Figure 6. Obviously the whole stress – strain curve
is dependent on hydrostatic pressure. Not only the yield stress, which is the content of most studies, but also the modulus is
apparently influenced by molecular mobility and thus pressure affects the overall mechanical performance of polymers.
Conclusions
Uniaxial compression and tensile tests were applied on polypropylene. It was shown that in the former method localization that
is inhomogeneous deformation of the specimen does influence the result. Appropriate choice of specimen dimension and
testing conditions are of crucial importance to get true material properties. To investigate the uniaxial behavior of polymers we
would recommend to use the Cook and Larke method in which the influence of friction can be calculated or using the PTFE
tape. Otherwise at large strains friction may increase the observed stress levels more than 20 %. This in turn would lead to an
overestimation of the strength of the material.
In the pre-yield range an applicable and reproducible procedure was explained to obtain compressive modulus values avoiding
errors due to initial effects coming from misfits between the specimen and the compression platens. Furthermore it was shown
that pressure shifts the whole stress – strain curve to higher stress values since also the compressive modulus representing
the small strain behavior is significant higher than the tensile modulus.
Acknowledgements
The research work of this paper was performed at the Polymer Competence Center Leoben GmbH (PCCL, Austria) within the
framework of the Kplus-program of the Austrian Ministry of Traffic, Innovation and Technology with contributions by the
University of Leoben and Borealis GmbH. The PCCL is funded by the Austrian Government and the State Governments of
Styria and Upper Austria.
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