EXPERIMENTAL AND THEORETICAL STUDY OF THE DAMAGE ONSET IN
BIAXIAL CRUCIFORM SPECIMENS UNDER STATIC AND HYSTERESIS
LOADING
E. Lamkanfi a,1, C. Ramault2, A. Makris2, W. Van Paepegem1, J. Degrieck1,
D. Van Hemelrijck2 and H. Sol2
1
Department of Mechanical Construction and Production, Ghent University,
Sint-Pietersnieuwstraat 41, B-9000 Ghent, Belgium.
2
Department of Mechanics of Materials and Construction, Free University of Brussels,
Pleinlaan 2, B-1050 Brussels, Belgium.
ABSTRACT
In this paper an attempt is made to prove that the load level at which failure is initiated in a biaxial loaded specimen is very
close to the actual failure load. The digital image correlation method and the finite element method, in combination with the
ultrasound phased array technique, are used to get a better understanding in the onset of the failure mechanisms in fibre
reinforced plastics (FRP) such as glass reinforced epoxy. It is shown that the failure mechanisms of these FRP, with a specific
stacking sequence that is widely used in the windturbine industry, start in a very late stage, approximately around 80% of the
failure load, regardless of the fact that the load distribution is applied in one or two directions. No large difference is observed
in the damage initiation load for a linear increase of the applied load compared with a hysteresis loading approach. Through
implementation of the problem in a finite element model, it is shown that the digital image correlation results correspond very
well with the numerically found strain fields. The ultrasound scans made of the central milled out zone do not expose large
differences with a scan of an unloaded specimen. This confirms the conclusion of the late onset of damage during a loading
cycle and leads in this way to very sudden failure of the specimen in the last 20% of the failure load.
Introduction
During the last decades, the use of fibre-reinforced composites has largely increased and currently, these materials are used
in almost every industrial sector. Yet, current research shows a number of important shortcomings, both in the experimental
and theoretical domain. Standard mechanical tests on uniaxially loaded specimens appear unsatisfactorily for an accurate
description of the mechanical behaviour of these materials. A biaxial loading approach should give a better representation. In
the past, different techniques were developed for creating a biaxial loading state. Anticlastic bending of thin rhomb plates and
tension/torsion of thin-walled tubes are just two out of a series of possible solutions [1-3]. A recent alternative technique is the
loading of a cruciform specimen (Fig. 1 and Fig. 2) along its two orthogonal directions. This shows a lot of advantages
compared to the other methods [4-6].
Another key issue is the detection and monitoring of damage in these materials. From static biaxial tests it appeared from the
European Optimat Blades project [7] that complex stacking sequences can give rise to delaminations starting from the corners
of the cruciform and growing to the central zone. However the time of onset of this kind of damage occurs in a very late stage
of the failure loading. This means that the failure of the biaxial loaded specimen occurs very suddenly, when the loading forces
are very close to failure loads of the specimen.
In this paper it will be shown that no difference in the load level for initiating damage is observed when the specimen is loaded
linearly or when it undergoes several loading-reloading cycles. To prove this, a numerical-experimental approach is chosen,
where experimental results will be conducted and confirmed by the use of the finite element method. This method will also be
used to affirm the results obtained with the ultrasonic phased array and the digital image correlation technique. So in the
following paragraphs, first a short description of the test-set up and the biaxial specimen will be given. Next the instrumentation
techniques used during the loading of the cruciform are described. First the digital image correlation technique together with
the obtained results will be overviewed. Next the principle of the ultrasonic phased array is explained shortly together with the
scans made with this technique on the cruciform specimen. Finally, in a last paragraph, the experimental observed images and
a
Author to whom correspondence should be addressed : [email protected]
scans will be motivated by the implementation and the discussion of a finite element method. It will be shown that
experimentally measured loads where damage is initiated match very well with those found with the numerical model.
Experimental techniques
Test set-up
The biaxial test set-up, shown in Fig. 1, is developed at the Free University of Brussels (VUB) and has a capacity of 100 kN in
each perpendicular direction. With this test rig only experiments in tension can be conducted, because hinges were used to
connect the specimen to the load cells and the servo-hydraulic cylinders to the test frame. This is a necessary measure
because when failure or slip in one arm of the specimen occurs, sudden radial forces could seriously damage the load cells
and the servo-hydraulic cylinders. The applied loads can vary statically or dynamically up to a frequency of 20 Hz. To avoid
bending moments in the specimen the centre point of the cruciform may not move. Otherwise a non-symmetric strain
distribution will be created in the center zone of the specimen.
Figure 1. The biaxial test set-up.
Cruciform specimen
The fibre reinforced plastic (FRP) used in the biaxial configuration, shown in Fig. 2, is a glass epoxy manufactured by LM
Glasfiber (Denmark) using the RTM technology. This composite, that is widely used in the wind turbine industry for the
construction of rotor blades, has a [(±45/0)4/±45] stacking sequence (Fig. 2 and Fig. 3). The [±45] plies contain a non-woven
glass roving in two layers with one layer in +45° and one layer in -45°. Since the [±45] plies are considered as internally
symmetric, a symmetric configuration is obtained. The [0] plies contain a non-woven unidirectional glass roving with a minor
amount of off-axis reinforcement. The laminate is post-cured at 80°C for four hours and the surface of the laminates is
manufactured with a peel-ply surface giving a thin slightly rough surface. In the center of the laminate, one group of [±45/0] at
each side of the specimen, is milled away. The laminate has in zone 1 (see Fig. 2) a thickness of 6.57 mm and in zone 2 a
thickness of 3.59 mm.
Figure 2. The geometry of the cruciform specimen together with the dimensions and the stacking sequence.
Figure 3. The stacking sequence of zone 1 (see also Fig. 2) in the cruciform arms.
Digital image correlation technique
Due to the complex specimen geometry, the relation between the externally applied loads in the arms of the cruciform
specimen and the resulting stress field in the centre of the specimen cannot be determined analytically. The use of strain
gages or an extensometer are not sufficient because of the average value of the deformation along their gage length. And
because of the fact that it is very difficult to realize a uniform stress and strain distribution in the biaxially loaded centre, the
strain field is experimentally measured with the Digital Image Correlation Technique (DICT) [8]. The principle behind this
technique is based on a comparison of images taken at different loading steps. First a random speckle pattern is applied onto
the surface of the cruciform. Then a Charge Couple device (CCD) camera acquires images from the area of interest on the
surface of the specimen in the undeformed and deformed states. In our experiments two cameras were used (Fig. 4) to
measure both the in-plane and the out of plane displacements in the zone where the surface is milled out. The obtained high
resolution images are correlated to determine the deformations by tracking the specific movement of these greyscale patterns
relative to their original positions. And finally some advanced mathematical procedures are applied to these deformations to
calculate the surface strains.
Figure 4. The principle behind the digital image correlation technique
Phased Array technique
To yield information about the initiation and the kind of damage during a mechanical test of a cruciform specimen, acoustic
techniques can be very useful. In this paper the ultrasound phased array technique is used for damage comparison of
specimens loaded in one or two directions and in a statical or cyclical way. This technique is based on the detection of waves
at a straight angle that are sent to and reflected by the specimen. The experiments performed with this method are done with a
lineair array consisting of 64 ultrasound probes (Fig. 5), possible to be steered individually. By the use of a water column or
water jet, the measurement can also happen without removing the specimen from the set-up. This technique is specially suited
for thickness measurements, for defect detection and for determining the depth of a defect. It is also well-suited for detecting
distributed air inclusions, such as delaminations and porosity in laminates.
Figure 5. Scanning principle of the ultrasonic phased array
Finite element method
This method will be used in the following paragraphs as a verification method for the experimental obtained results. The
implementation of a model will make it possible to compare the strain fields on the surface of the cruciform specimen obtained
by the digital image correlation technique and the calculated linear elastic strain fields. This will give an affirmation of the fact
that there is a minor influence on these fields regardless it is loaded statically or cyclically. A shell model of the cruciform will
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be implemented in the commercial FEM package ABAQUS .
Results
First the results of the digital image correlation technique are discussed. Next the scans made with the phased array technique
will be examined. And finally the results from the finite element model are compared with the strain fields obtained with the
DICT.
Digital image correlation
The experiments that have been done with the biaxial test set-up can be divided into two loading schemes : a static and a
cyclic. For each of these two schemes a uniaxial and a biaxial loading test, with a load ratio of 3.85/1, has been performed.
The largest load Fx is always applied along the dominant [0]° fibre direction. This direction, which corresponds with the x-axis,
is shown in Fig. 6.
Figure 6. The coordinate system and the [0°] fibre direction used for a cruciform specimen.
From the experiments done by Smits et al. [9] it is known that this biaxial FRP specimen fails under a biaxial load of Fx/Fy=46.2
kN/12 kN. The images that are shown in this section correspond with approximately 83% of this biaxial failure load. This
means that when the specimen is loaded biaxially, 38.5 kN is applied in the [0]° direction and 10 kN in the [90]° direction. In
the case of a uniaxially loaded specimen only the 38.5 kN is put along the horizontal x-axis. It can be clearly seen from Fig. 7
and Fig. 8 or from Fig. 9 and Fig. 10 that when the load is applied statically or cyclically, no major differences are perceptible in
the strain fields (εxx, εxy, εyy). The differences observed between the uniaxial and the biaxial performed tests are purely due to
the loading difference (uniaxial versus biaxial). The reason why the εyy uniaxial strain field is very different from the biaxial one,
is due to the fact the 90° direction is left unloaded in the uniaxial case. The shear strain εxy in the biaxial case is more distinct
in the biaxial case compared to the one in the uniaxial case. For the εxx strain field, no remarkable changes are observable.
These observations of the strain fields will be compared in the following with the finite element calculations in order to have an
affirmation.
Figure 7. The strain fields εxx (left), εxy (middle) and εyy (right) from a static-uniaxial loading state with load ratio Fx/Fy=38.5/0
Figure 8. The strain fields εxx (left), εxy (middle) and εyy (right) from a cyclic-uniaxial loading state with load ratio Fx/Fy=38.5/0
Figure 9. The strain fields εxx (left), εxy (middle) and εyy (right) from a static-biaxial loading state with load ratio Fx/Fy=38.5/10
Figure 10. The strain fields εxx (left), εxy (middle) and εyy (right) from a cyclic-biaxial loading state with load ratio Fx/Fy=38.5/10
Finite element model
Next to these experiments, some finite element simulations have been conducted to get a better insight in the experimental
obtained strain fields. The FEM calculations of the FRP cruciform are based on the Classical Lamination Theory. The finite
element simulations were performed with the commercial software ABAQUSTM. The model is implemented with the same layup and geometry as the FRP shown in Fig. 2, using SR4 shell elements (see Fig. 11). These elements are 4-node doubly
curved thin elements for finite membrane strains. In each of the 4 nodes six degrees of freedom are defined : the translations
and the rotations in the nodal x, y and z directions. The applied loads, in the case of a biaxial loaded cruciform, are the same
as those in the performed mechanical tests, i.e. Fx/Fy= 38.5 kN/10 kN, where the greatest load is applied in the horizontal
direction. This direction correspond with the x-axis in Fig. 6 and with the 1-axis in Fig 11.
Figure 11. SR4 shell elements in the cruciform model.
The strain fields obtained with this numerical method are shown in Fig. 12 and Fig. 13. In Fig. 12 a uniaxial model is
considered where the load is applied only in the 1-direction and in Fig. 12 a biaxial model is used with loads in the two
directions. Comparison of these results with the corresponding ones from the DICT, shows that the strain εxy and εyy are very
similar. This is the case for the uniaxial as well as for the biaxial experiments. However, the strain in the 1-direction εxx differs
slightly from the DICT images, because the material model used in the finite element analysis is linear elastic without any
incorporated damage initiation and propagation law. But the fact that there is an observable difference in the εxx strain, means
that some damage is initiated around the load level of 80% of the failure load.
Figure 12. The strain fields εxx (left), εxy (middle) and εyy (right) from a static-uniaxial loading state with load ratio Fx/Fy=38.5/10
Figure 13. The strain fields εxx (left), εxy (middle) and εyy (right) from a static-biaxial loading state with load ratio Fx/Fy=38.5/10
Phased array technique
The use of the phased array technique will help us to have an idea of the influence the loading scheme has on the initiated
damage at approximately 80% of the failure load. The ultrasound waves are generated by an Omniscan MX PA from RD-Tech
which is connected to a 5MHz linear array probe. The propagation direction of the waves is parallel with the normal on the
surface of the cruciform. On the sectorial scans shown below, the central milled out zone (see Fig. 2) with the skew edges, is
clearly visible. This technique is focused on this central area, because the damage is expected to begin, due to the biaxial
loading condition, somewhere in this weaker biaxially loaded zone. As seen in the European Optimat Blade project [7] the
cruciform will start to delaminate from its corners. This was also observed during the tests performed on the different
cruciforms around 80% of the failure load. In Fig. 14 a scan of an unloaded specimen is showed, which will be used as a
reference scan. Comparison of this reference scan and those from the cruciforms subjected to the four different loading
schemes (Fig. 15 and Fig. 16), shows that it is difficult to distinguish them.
Figure 14. Sectorial scan of an unloaded specimen.
This means that up to 80% of the failure load, no large changes in the scans are observable. Therefore an explicit indication is
given that during the last 20% of the loading up until the failure load, the damage will grow very quickly making an online
monitoring of the damage difficult.
Figure 15. Sectorial scan of an uniaxial (left) and a biaxial (right) statically loaded specimen.
Figure 16. Sectorial scan of an uniaxial (left) and a biaxial (right) cyclically loaded specimen.
Conclusions
The late onset of damage of a cruciform FRP that is widely used in the windturbine industry is proven in this paper. After a
brief introduction, the experimental and numerical methods used for showing this late onset are briefly explained. The results
from the DICT images show no major differences in the strain fields (εxx, εxy, εyy) for the statically and cyclically performed
tests. These images correspond to a large extent with the numerically found strain fields, through the implementation of a
lineair elastic finite element model. The ultrasound scans made from the central milled out zone of the cruciform show minor
differences in the reflected signal of the waves. After comparison with a scan of an unloaded specimen, one can therefore
conclude that the loading of the specimens up to 80% does not initiate much damage.
Acknowledgments
The authors gratefully acknowledge the support for this research by the Fund for Scientific Research - Flanders (FWO).
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