Application of full-field strain measurement and analysis for
polymer testing
Z. Major2, R. Steinberger1, Ch. Feichter1 and R.W. Lang1,2
(1) Polymer Competence Center Leoben GmbH
(2) Institute of Materials Science and Testing of Plastics
University of Leoben, A-8700 Leoben, Austria
ABSTRACT
The deformation and failure behavior of elastomer and thermoplastic polymer test specimens were investigated in
this paper over a wide loading rate range and under various loading conditions by optical non-contact methods. A
full-field image correlation test system (Aramis, GOM, Braunschweig, D) was used to determine strains along with
the temporal and spatial distributions both in uniaxial and in various multiaxial test conditions.
In uniaxial tensile tests the main goal of the application of full-field strain analysis (FFSA) was the determination of
Poisson’s ratio and volume strain values. Furthermore, for multiaxial deformation tests using disc type specimens
two main objectives was defined and investigated. While in inflation test adequate material law was determined
for elastomers using disc specimens exposed to biaxial loading, the main goal of the radial compression test of
disc was the verification of FE simulation for viscoelastic contact situations. Finally, fracture tests with additional
FFSA were carried out using a pure shear specimen configuration for elastomers and a small size double edge
notched tensile configuration for thermoplastic materials.
Summarizing of all above results, the non-contact full-field strain measurement and analysis provided novel,
unique information’s about the material behaviour and may successfully be used to determine more adequate
material laws for engineering polymers.
Introduction
Recently, full field optical techniques are increasingly appreciated as deformation, strain and stress analysis tools.
These new techniques offer high potential for material and component testing. Three main applications of the
non-contact, full-field strain analysis in the material testing are: (1) Simultaneous measurements of the
longitudinal and transverse strains in uniaxial experiments and the determination of the general Poisson’s ratio
over a wide deformation range; (2) Determination of the true stress-strain relationship from the linear visco-elastic
to the post-yield deformation regime and (3) Characterization of the local crack tip deformation behaviour in
different test fracture specimen configurations. Based on above methods more adequate material laws can be
derived and used in numerical simulations.
The 2D or 3D image correlation photogrammetry is substantially more robust and has a greater dynamic range
than other techniques such as laser speckle interferometry (ESPI) or the conventional Moire interferometry.
Based on these features the image correlation method can effectively be used to determine deformations and
strains both on a local or global scale and up to high deformations and up to high deformation rates [1].
On the laboratory test specimen level such non-contact full-field strain analysis (FFSA) methods may provide
more accurate strain information over a large deformation range, as an important aspect in testing elastomers and
thermoplastics at elevated temperatures. Applying such systems several effects associated with the contact
methods may also be avoided. Moreover, the verification of numerical simulation of components exposed to
mechanical loads requires proper test methods which provide both informations on global deformations as well as
local deformations and strains along with their distribution.
There are different scales for the material testing of polymers, such as basic polymer characterization, compound
(powder, granulates), test specimens and components. Furthermore, from the main objectives of the material
testing; (i) comparison of materials, selection for specific applications, permission and specification, (ii) quality
assurance and certificate (iii) material development, structure-property relationships and (iv) the definition of
material models, determination of parameters and implementation in FEM, especially latter can very efficiently be
supported by non-contact methods.
Hence, the main objective of this paper is to verify the applicability of non-contact full-field strain and temperature
analysis methods to polymer testing both on laboratory specimen level to determine material laws and
parameters. The applicability of the FFSA method is illustrated by several examples in the paper.
Experimental
Materials
A wide variety of engineering polymers, elastomers, cross-ply elastomer composites, unfilled and particle filled
thermoplastics, short and continuous fibre reinforced advanced composites are used in the experiments. The test
specimens were manufactured carefully by the company partners under quality assurance process control.
Test systems
-3
4
Various test systems were applied to load the specimens over a wide loading rate (10 to 10 mm/s), test
-2
2
frequency (from 10 to 5x10 Hz) and load level range (from 1 N to 100 kN). While for monotonic uniaxial tests
universal electromechanical testing machine (Instron 4505, High Wycomb, UK) was used, high rate
servohydraulic test systems (MTS 831.59, MTS Systems, MN, USA) were applied for the dynamic and fracture
experiments. In some cases, the tests were run on special multiaxial test systems (axial/torsion servo hydraulic
with 2 axis (MTS 359 Ax/Tors) and a universal micro-tribometer (UMT, CETR, Campbell, CA, USA) with 3 axis).
The high rate servo hydraulic testing machine along with the full-field analysis system is shown in Figure 1.
Figure 1. High rate servohydraulic test system with full-field strain (in the centre, black cameras) and full-field
temperature (right side, blue camera) analysis systems.
Although, different non-contact systems are available for the tests (video extensometer with edge detection,
image correlation system, ESPI, thermocamera system(s)), examples are shown only made by the image
correlation system (Aramis, GOM, Braunschweig, D) in this paper.
Test Methods
The applicability of the digital image correlation (DIC) based full-field strain analysis (FFSA) is demonstrated by
the following examples. First, the longitudinal and transverse strain distribution of uniaxial ISO tensile test
specimens is measured and analyzed over a wide loading rate range for various polymeric materials. Second,
disc type specimens were loaded either biaxial by internal pressure or radial in compression between two plates
and the strain distributions was analyzed in both cases. Finally, the strain distributions in two different fracture
type specimens are measured and subsequently the fracture behaviour was characterized.
Uniaxial tensile test
Both the longitudinal strain (εl) and the transverse strain (εtr) can simultaneously be measured during uniaxial
tensile tests from small up to high degree of deformation over a wide loading rate range for various thermoplastic
polymers using FFSA methods. The spatial strain distributions of longitudinal (εy) and transverse strains (εx) of a
tensile specimen are shown at yield and at immediately before the ultimate failure for PEEK in Figure 2.
(a)
(b)
(c)
(d)
Figure 2. Strain distribution of a tensile specimen for PEEK; (a) εy at yield, (b) εx at yield, (c) εy before
ultimate failure and (d) εx before ultimate failure.
While tensile modulus values can be calculated using only the longitudinal strain values, to calculate proper
Poisson’s ratio values both the longitudinal and the transverse strain values must be determined simultaneously
in the same material volume. Moreover, volume strain values are also calculated in two ways. First, using the
transverse strain values measured in the width under the assumption that the transverse strain equal in the width
and in the thickness direction and second, the transverse strain was also directly measured in the thickness
direction applying a mirrors in a special test set-up.
Multiaxial deformation experiments
One of the main advantages of the FFSA technique is the opportunity of the characterization of multiaxial strain
states and the determination of the various strain components. The following two examples demonstrate the
applicability of FFSA in biaxial deformation and strain measurements for engineering polymers. First, a rubber
disc specimen for biaxial tests is shown in Figure 3a. The specimen is used in an inflation type test, in a special
equipment (see Figure 3b), where the change of the gas pressure causes biaxial deformations.
Figure 3. Biaxial test; (a) disc type specimen from rubber and (b) test set-up with FSSA.
The spatial strain distribution of this specimen during the experiments is seen in Figure 4. The highest strain was
measured at the mid top of the disc specimen. Stress values were calculated according to the procedures
described in [2] and the results are used in two various applications described in the next chapter.
Figure 4. Strain distribution of a disc specimen loaded biaxial by internal pressure.
Second, disc specimens from thermoplastic engineering polymers were machined from 4 mm thick plates and
subsequently tested in radial direction under compression between two platens. The objective of these tests was
the characterization of the spatial strain distribution in the contact area and the determination the temporal change
(i.e., creep tests) of selected strain value. Strain distribution of a disc specimen loaded between two plates in
radial compression is seen in Figure 5a for major strain and in Figure 5b for minor strain values.
(a)
(b)
Figure 5. Strain distribution of a disc specimen loaded between two plates in radial compression; (a) major strain
and (b) minor strain.
Fracture tests using notched specimens
The presence of internal flows, notches or cracks results in a multiaxial strain state. To get more insight into the
fracture behaviour of engineering polymers, fracture tests with simultaneous FFSA were also performed. While
the classical fracture mechanics uses global parameters to calculate fracture parameters, the FSSA techniques
can provide data for a continuum mechanics based analysis of both the near filed (crack tip) and the far field
regime (specimen ligament). Hence, using FFSA a combination of these two main approaches and the
simultaneous application to material characterization is possible.
In the first example the characterization of the fracture behaviour of elastomers using pure shear specimens is
introduced. More information about this research task is found in the other paper of this conference [3]. The test
set-up along with the test system is shown in Figure 6.
Figure 6. Pure shear test set-up for fracture tests of elastomers with cameras for FFSA.
The pure shear specimen exhibits some advantages for applying in fracture experiments of elastomers as
described in [4]. The strain distribution of a FWPA specimen under monotonic loading both global as colour
scaled image and local in the mid line as a diagram are seen in Figure 7. It can be seen that after a high strain
gradient around the crack tip, the strain remains constant in the ligament.
Figure 7. Strain distribution of monotonically loaded pure shear test specimen at peak load for elastomer.
In the second example the characterization of the fracture behaviour of unfilled and filled thermoplastics (PP)
using double edge notched tensile (DENT) specimens is introduced. More information about this research task is
found in the following papers [5]. It must be mentioned, however, that the width of the specimen was only 8 mm
and the ligament was 5 mm and hence special objective had to have used to make high resolution images in the
vicinity of the crack tip. The strain distribution of a DENT specimen is seen in Figure 8.
(a)
(b)
Figure 8. Strain distribution of a monotonically loaded small size (W=8 mm) double edge notched tensile
specimen; (a) immediately before crack extension and (b) after crack extension.
Results and Discussion
Uniaxial tensile test
As one of the highest challenge is the determination of Poisson’s ratio values over a wide loading rate for various
engineering polymers [6], the test are focused on this problem and some selected results are shown in this paper.
Longitudinal strain and transverse strain curves of a PEEK tensile specimen at high loading rate are seen in
Figure 9a. The general the Poisson’s ratio changes with increasing longitudinal strain from 0.44 in the reversible
viscoelastic deformation range to 0.2 in the post-yield regime (see Figure 9b).
0,0
25
εtr/εl
longitudinal strain
15
10
5
0,2
0,3
0,4
0,5
transverse strain
0
PEEK
tensile test
6 m/s
0,1
Poissons's ratio
strain,
%
20
PEEK
tensile test
6 m/s
0,6
-5
0,000
0,005
0,010
time
t,
0,015
0,000
0,020
0,005
0,010
time
s
t,
(a)
0,015
0,020
s
(b)
Figure 9. Results of Poisson’s ratio measurements by FFSA at high loading rate (6 m/s); (a) longitudinal strain
and transverse strain curves of a PEEK tensile specimen and (b) Poisson’s ratio values from low to high
deformations.
The results of the experiments show that the determination of Poisson’s ratio values was possible with sufficiently
good quality up to a testing rate of 6 m/s, corresponding to a nominal strain rate of about 50 s-1 in unaxial tensile
tests. For more information about these tests and results please refer to [5].
Heterogeneous, filled polymer systems reveal a longitudinal strain level dependent volume change, especially in
the post-yield regime. Hence, to the proper characterization of the deformation and failure behavior a volumetric
strain analysis is necessary. Transverse strain vs. longitudinal strain curves for unfilled and glass sphere filled PP
tensile specimens along with Poisson’s ratio, ν values in the small strain range are depicted in Figure 10a.
1
6
0
filled PP
%
5
Ve,
4
ν=0.406
-2
volume strain
transverse strain
εt,
%
ν=0.39
-1
-3
filled PP
-4
unfilled PP
3
2
unfilled PP
1
-5
0
-6
-2
0
2
4
6
8
10
12
longitudinal strain εl,
(a)
14
%
16
18
20
-2
0
2
12
14
longitudinal strain εl,
4
6
8
10
%
16
18
20
(b)
Figure 10. Comparison of the unfilled and filled material behavior based on FFSA; (a) transverse strain vs.
longitudinal strain curves and (b) volume strain curves for unfilled and glass sphere filled PP tensile specimens
along with Poisson’s ratio, ν values in the small strain range.
Finally, volume strain was calculated for both the unfilled and the glass sphere filled PP and the results are
depicted in Figure 10b. for comparison.
Multiaxial deformation experiments
The hybrid method applied for determining the material laws and parameters for these laws also use the FFSA as
an experimental tool [2, 4]. Three different specimen configurations (uniaxial, plane strain and biaxial) are tested
and the results are fitted in the FE software tool (Abaqus). The application of FFSA technique especially become
of high importance for the biaxial experiments. The nominal stress-strain curves of an SBR elastomer for the three
configuration introduced above are depicted in Figure 11. The quality of the parameters depends highly on the
strain range applied in the experiments and the precisity of the determination of strain values. These hyperelastic
material laws may later be applied for determining the stress field of cracked specimens or in component
simulations.
16
uniaxial test data
planar test data
biaxial test data
calculated data (Ogden)
14
nominal stress, N/mm²
12
SBR elastomer
10
8
6
4
2
0
0,0
0,2
0,4
0,6
0,8
1,0
nominal strain
Figure 11. Nominal stress-strain curves of an SBR grade rubber in uniaxial, plane-strain and biaxial tests.
As engineering polymers are increasingly used in many technical applications in contact with other materials, the
characterization of the contact area is both of theoretical and practical importance. As well known, due to their
inherent viscoelasticity, engineering polymers reveal highly-non-linear, time and temperature dependent
deformation behaviour. In spite of these facts, hardly any data exist to describe the viscoelastic contact of polymer
–polymer or polymer-metal pairs in different contact situations. Hence, a comprehensive characterization of
various contact geometries and for various materials was performed and analyzed in a research work described
in [7]. Two examples of the results of these tests under creep conditions are shown in Figures 12. While the Major
strain distributions of disc specimens both in loading direction (section 0) and transverse direction (section 1)
under creep loading condition are shown in Figure 12a and the Minor strains are seen in Figures 12b in similar
manner.
(a)
(b)
Figure 12. Strain distribution of a compression loaded disc specimen under creep condition (Section 0: in load
direction and Section 1 transverse direction); (a) Major strain and (b) Minor strain.
Similar tests were performed under monotonic and under combined loading conditions. The combined loading
was realized so, that the discs were first loaded statically by constant force until 24 hours (creep and flattening
phase) and subsequently rolling motion was enforced due to the friction and by the linear movement of the
compression platens. These detailed experimental backgrounds along with the results are described elsewhere
[7].
Fracture tests using notched specimens
Based on the full-field strain images, strain values determined experimentally at increasing deformation values
were determined are depicted in Figure 13. Furthermore, the material laws determined by previous experiments
(see Figure 13 and section multiaxial deformation) to describe the highly non-linear complex hyperelastcic type
deformation behaviour of elastomers were used in the FE simulations. A comparison of the major strain values of
monotonically loaded pure shear test specimen at increasing global deformation levels are shown in Figure 13a
FFSA and in Figure 13b for FE simulation. While an excellent agreement was found between the measured
(FFSA) and the calculated (FE simulation) strain values in the specimen ligament (about 2 mm distance from the
crack tip), approximately 10 to 20 % difference was obtained in the crack tip near field regime. It was assumed
that the due to the limited strain range in the first version of the biaxial tests described above, the material law
was not precise enough to reflect high strain fields.
70
70
0,0 mm
0,6 mm
1,0 mm
1,5 mm
2,1 mm
2,8 mm
60
55
Major Strain, %
50
45
60
55
50
40
A72539, r = 2 mm
35
0.0
0.6
1.0
1.5
2.1
2.8
65
Major Strain, %
65
30
25
20
45
mm
mm
mm
mm
mm
mm
40
A72539, r = 2 mm
35
30
25
20
15
15
10
10
5
5
0
0
2
4
6
8
10
12
0
14
0
Distance, mm
2
4
6
8
10
12
14
Distance, mm
(a)
(b)
Figure 13. Comparison of the major strain distributions of monotonically loaded pure shear test specimen at
increasing global deformation levels; (a) FFSA and (b) FE simulation.
To characterize the fracture behaviour on a micro-scale, in-situ tensile tests were performed in a scanning
electron microscope using both unnotched and notched specimens [7]. To support these experiments FSSA of
the DENT specimens were separately carried out. The main goal was to exactly determine strain values both in
the vicinity of the crack tip and in the mid of the ligament. Load-time curves are shown in Figure 14a and strain
time curves in Figure 14b for monotonically loaded DENT specimens for PP tested in in-situ SEM experiments.
500
100
DENT for in-situ SEM
0.01 mm/s
23 °C
PP(H)
80
N
400
ligament
crack tip
60
strain %
load
F,
300
200
20
PP(H)-GB
100
40
0
0
-25
0
25
50
time
75
t,
100
s
125
150
-25
0
25
50
time
75
t,
100
125
150
s
(a)
(b)
Figure 14. Results of DENT tests; (a) load-time curves and (b) strain-time curves of a monotonically loaded small
size (W=8 mm) double edge notched tensile specimens for unfilled and filled PP.
Conclusions
•
FFSA technique was successfully applied to a wide variety of material testing problems for engineering
polymers.
•
In addition to the standardized determination of tensile modulus values in uniaxial tensile tests, Poisson’s
ratio and volume strain values were also determined for various engineering polymers. Furthermore, the
determination of these values was possible over a wide loading rate range.
•
In multiaxial deformation tests (biaxial inflation and compression contact with disc specimens) the strain
components and the spatial and the temporal distribution of these components was successfully determined
and analyzed. While material laws were determined over a wide strain range in biaxial inflation experiments
for elastomers, the contact strain situation was analyzed and compared with the results of FE simulation in
the compression plate tests.
•
In fracture tests both the near field and the far field strain distribution was reliably determined and used in
further fracture mechanics analysis. Finally, based on the materials laws determined using FSSA
experiments numerical simulations were also carried out and the experimental and simulation values were
compared.
Acknowledgement
The investigations described in this paper were performed at the Polymer Competence Center Leoben GmbH
within the Kplus-programme of the Austrian Ministry of Traffic, Innovation and Technology. The funding within this
programme by the Governments of Austria, Styria and Upper Austria is gratefully acknowledged.
References
[1]
[2]
[3]
[4]
[5]
[6]
GOM User Meeting 2006, Technical Bulletin, Braunschweig, D.
Ch. Feichter, Z. Major and R.W. Lang, 2007, submitted to Journal of Testing and Evaluation.
Z. Major, K. Lederer, R.W. Lang, 282 paper id. ICEM 13.
Ch. Feichter, Z. Major and R.W. Lang, 2006, Strain 42, pp. 299-304.
E. Wang, 2007, Bachelor thesis, University of Leoben.
R. Steinberger, M. Jerabek, Z. Major and R.W. Lang, 2006, 13th International Conference on Deformation,
Yield and Fracture of Polymers, Conf. Proceedings, April 11-14, Kerkarde, NL.
[7] M. Berer, 2007, Diploma thesis, University of Leoben.