EXPERIMENTAL TESTS OF FATIGUE INDUCED
DELAMINATION IN GFRP LAMINATES
D. Tumino, G. Catalanotti, F. Cappello, B. Zuccarello
Dipartimento di Meccanica, DIMA
Università degli Studi di Palermo
90128 – Palermo, Italy
ABSTRACT
This work deals with the experimental analysis of the delamination phenomena in composite materials under different loading
conditions. Quasi-static and fatigue tests are performed on specimens made of glass-fibre reinforced plastic (GFRP). In particular,
experiments have been done under single fracture modes I and II (using standard DCB and ENF test configurations) and mixed
modes I+II (using the MMB test configuration) with several mode mixtures. Attention has been drawn on the relationship between
the parameters that describe the fatigue behaviour and the mode mixture acting during the crack propagation.
Introduction
The study of the behaviour of long-fibre composite materials is, nowadays, a well established discipline in the field of structural
materials. Although such materials have, day by day, a larger diffusion into industrial applications, the comprehension of the
behaviour under different load conditions is still under investigation. Among the several kinds of damage which composites can
be subjected to, the phenomenon of delamination is one of those that mostly draws the researcher’s attention. Considering
only plane cases, the single fracture modes are two: opening (mode I) and sliding (mode II); mixed modes I+II cases can be
also present. The case of crack propagation under quasi-static loads (when the applied load increases monotonically very
slowly) has been studied by several authors, both for single fracture modes and for mixed mode. A detailed formulation on the
test coupons commonly used in experiments can be found in [1] and [2]. While single modes I and II are usually obtained with
the Double Cantilever Beam (DCB) test and the End Notched Flexural (ENF) test [3], for the mixed mode I+II there are
different test configurations [4] (see fig. 1). The Mixed Mode Bending (MMB) test [5]-[7] is the super-position of the DCB and
the ENF tests and permits a fast change of percentage of mode I and mode II by a simple variation in the lever length c.
Another test configuration has also been used for mixed mode fracture: the Single Leg Four Point Bending (SLFPB) test,
developed and studied in [8], that is less versatile than the MMB test, but is easier to setup.
In quasi-static condition, crack propagates under single fracture modes when the Strain Energy Release Rate (SERR), G,
equals its critical value (or interlaminar fracture toughness) Gc. This critical value is a material property and can be different for
mode I and for mode II. It has been noted [9] that the critical SERR depends on the mode mixture φ = GII/G (where G is the
sum of GI and GII) and different criteria have been proposed to model the material behaviour at fracture as φ varies. In [9]
different models are compared and applied to experimental results on a carbon/epoxy material.
In general, the fatigue delamination of composites, caused by the cyclic application of loads, can be described with the Paris
approach. Following this method, the condition of a stable crack growth can be obtained when the instant SERR is greater
than a threshold value and lower than the fracture toughness. In a log-log diagram (da/dN versus Gmax) the stable zone is
m
described by a line whose equation is da/dN = B(Gmax) , where B and m are characteristics of the material and of the mode
mixture. Fatigue tests on different composite materials have been performed in [10] for single modes I and II and in [11],[12],
where the load ratio effect and the threshold values for the SERR have been studied. In particular, results for
graphite/thermoplastic resin in [11] lead to very high values for the Paris constants, suggesting that, for this material, a
threshold-based design is more realistic than a propagation-based one. Single and mixed mode cases have been studied in
[13] for a graphite/epoxy composite; a non monotonic trend of the Paris parameters with the mode mixture was observed. In
[14] the effect of the temperature has been also verified for the same material and it has been proven that the crack growth
rate increases with the temperature.
Semi-empirical monotonic models have been proposed in [15] and [16] to correlate the Paris parameters B and m to the mode
mixture φ, on the basis of experimental results on different materials. In [16] several mode mixtures have been analysed for
glass/epoxy composites; the model fits quite well with the peculiar behaviour of the tested composite, but could not work for
other materials (as in the case of the present work). In [17] three mode mixture have been studied
(φ = 0, 0.5 and 1) for carbon/epoxy material; although the non-monotonic model proposed to relate φ with the Paris parameters
can be considered of general validity, it is based on very few experimental data.
In this work experiments of fatigue crack propagation on unidirectional GFRP have been performed under single and mixed
fracture modes. Preliminary quasi-static tests have been done to calculate the fracture toughness of the material. For the
analysed material, the accordance between the monotonic and non monotonic criteria with the experimental results, has been
verified.
l max
v,P
l min
l
l
a
l
a
c
v,P
v,P
v,P
SLFPB
Figure 1. Test configurations for single and mixed fracture modes
Material tested
The material used is a glass/epoxy composite manufactured by the hand lay-up technique. It consists of 12 laminae of dry
unidirectional fabric stacked together with an epoxy resin. In the half-thickness of the laminate a short strip of anti-adhesive
(Mylar®) which standard thickness is about 10 μm, has been inserted, with the aim to create a pre-crack in the specimens.
The cure of the resin has been obtained with a first period (12 hours) at room temperature followed by a second period (12
hours) in the oven at 60°C. During the entire period of curing a slight pressure was applied to the laminate. After the curing
process, the fibre weight fraction Wf has been calculated by measuring the weight of the composite and knowing the weight of
3
3
the fibres. It results Wf = 40%. Then, knowing the density of glass fibres (ρf = 2.5 g/cm ) and matrix (ρm = 1.07 g/cm ) the
3
density of the composite can be calculated (ρc = 1.43 g/cm ) and the fibre volume fraction via the relation [18]:
Vf =
ρc
W = 26%
ρf f
(1)
The reason for the low value of Vf can be found in the manufacturing process, where no vacuum techniques have been
adopted, and in the particular morphology of the dry patches of fibres, that consists of well-separated bundles (see also figure
2.a). The gap between bundles is filled with the resin during lamination resulting in a matrix excess into the composite.
Preparation of the specimens
Specimens have been cut from the plate following the standard ASTM D3039 for tensile test, the ASTM D790 for flexural test
and the standard ASTM D4255 for the rail shear test. Each specimen has been instrumented with resistance gauges to
measure the longitudinal and the transversal strain. Tests have been carried out with an electro-mechanical testing machine
with a 20 kN capacity load cell, under displacement control. Results of the tests are summarised in table 1.
TABLE 1. Material properties.
Material
E-glass/Epoxy
EL [GPa]
21
ET [GPa]
6
νLT
0.28
GLT [GPa]
1.6
Specimens for delamination tests have been machined from the composite plate following the indications of the standard
ASTM D5528. Width and thickness of the specimens are the same for all the tests performed in this work. In particular, a width
Bw = 20 mm and a total thickness 2h = 4.7 mm (where h is the thickness of one arm of the specimen after the crack
propagation) have been measured. Each specimen has been painted in its lateral face with a matt white colour and marks
have been drawn at regular intervals (1 mm).
Except the ENF test, for both DCB and MMB tests (where a mode I component is present) hinges have been glued to the precracked ends of the specimens using a cyanoacrylate fast-curing glue (see fig. 2.b). Because of the high values of loads
applied to the hinges, premature debonding between hinge and specimen was observed during the linear part of the loading
curve. This issue has been solved with a more accurate preparation of the surfaces glued together: surfaces were initially
roughed with sand paper and then cleaned with degreasing agents.
(a)
(b)
Figure 2. Close-up on the fibres (a) and the DCB specimen (b).
Quasi-static tests
Quasi-static delamination tests have been performed with an electro-mechanical testing machine with a 2 kN capacity load
cell, under displacement control. The displacement, v, of the cross-head and the load, P, measured by the load cell have been
recorded. The crack length, a, has been evaluated by optical observation of digital photos of the lateral face of the specimen
taken with a high resolution Nikon camera equipped with a macro lens. Average dimensions of the specimens used for the
tests are summarised in table 2.
TABLE 2. Specimen dimensions [mm].
Test
DCB
MMB (φ = 0.25)
MMB (φ = 0.5)
MMB (φ = 0.75)
ENF
Mid-span length l
75
75
75
55
Pre-crack a0
40
38
46
52
30
Lever length c
125
66
45
-
Data reduction
Figure 3 shows the typical load-displacement curves for DCB, ENF and MMB tests performed under monotonic loads. For the
DCB test it is easy to distinguish the linear region from the softening region of the diagram. The first one corresponds to a
strain energy increasing process where the crack doesn’t grow, the second one corresponds to the strain energy release
process where the crack propagates and load decreases.
For the ENF test, different parts can be pointed out: in the first linear one the load increases and the crack doesn’t grow, then,
near the maximum point, the crack starts to propagate slowly; after the maximum point, the crack propagates very fast and the
load decreases; in the last part the crack passes the mid-span length and the load increases again.
Similar considerations to those relative to the ENF test can be done for the MMB tests, although curves in figure 3.c show
results from test stopped soon after the maximum point has been reached.
Simplified and more efficient data reduction theories [2]-[6] can be found in literature to obtain the Strain Energy Release Rate
from the recorded data. Taking into account spurious phenomena like rotations of the arms in correspondence of the crack tip,
or shear deformations, the data reduction theory suggested in [13] is adopted. In this theory the components in mode I and in
mode II of the total strain energy released can be found (for DCB, ENF and MMB) via the relationships:
PI2 (a + Δ )
BW E L I H
2
GI =
(2)
and
GII =
3PII2 a 2
64 BW E L I H
⎛
EL h 2 ⎞
⎜1 +
⎟
⎜ 9 KG a 2 ⎟
LT
⎝
⎠
where IH is the moment of inertia of half-thickness of the specimen, Δ is a correction factor of the crack length a given by:
(3)
⎡⎛ E
Δ = h ⎢⎜⎜ L
⎢⎣⎝ 6 ET
1/ 4
⎞
⎟⎟
⎠
+
EL ⎤
⎥
GLT ⎥
⎦
1
2π
(4)
K = 5/6 is the shear factor.
For the single mode tests, loads can be simply taken from the value, P, measured by the load cell; for the DCB test eq. (2) is
used and PI is the load applied at the hinges, whereas for the ENF test eq. (3) is used and PII is the load applied by the pin in
the mid-span length of the specimen. For the MMB test, loads in eq. (2) and (3) can be evaluated via the following formulas:
3c − l
P
4l
c+l
P
PII =
l
PI =
90
(6)
800
(a)
80
250
(b)
700
(c)
φ = 0.75
200
70
600
60
500
40
150
P [N]
50
P [N]
P [N]
(5)
400
φ = 0.5
100
300
30
200
20
0
φ = 0.25
50
100
10
0
5
10
15
20
25
30
35
40
0
45
0
2
v [mm]
4
6
8
10
12
14
0
0
5
10
v [mm]
15
20
25
30
v [mm]
Figure 3. Load-displacement plots for DCB (a), ENF (b) and MMB (c) tests.
In figure 3 the circles indicates the loads used to the evaluation of the SERR that have been selected in accordance with the
ASTM D5528. Table 3 summarises the critical values of the total SERR for the different value of the mode mixture φ. These
critical values are quite different with respect to those reported in [16] but are in good agreement with data reported in [10] for
a similar material.
TABLE 3. Critical values of SERR [N/mm].
Mode mixture φ
0
0.25
0.5
0.75
1
Test
DCB
MMB
MMB
MMB
ENF
GIcφ
1.25
1.14
0.97
0.60
0
GIIcφ
0
0.38
0.97
1.81
3.6
Gc
1.25
1.52
1.94
2.41
3.6
For the DCB and ENF tests, the resistance curves, i.e. the SERR as a function of the actual crack length, are plotted in figure
4. In details, figure 4.a shows the resistance curve calculated for the DCB test; the critical value of the SERR in table 3 is
located, in figure 4.a, at the beginning of the curve, when the crack starts to grow. The curve has a monotonic trend and
doesn’t show an horizontal asymptote. This behaviour is due to fibre-bridging phenomena in front of the crack tip that are
evident after few millimetres of crack propagation. The fracture toughness is calculated at the very beginning of the curve,
when fibre-bridging phenomena are not present yet.
Resistance curve for the ENF test is shown in figure 4.b; it can be seen how, in the first phase, the SERR increases with the
crack length; at this stage the load increases with the displacement in figure 3.b. The maximum value of load corresponds to a
crack length of 40 mm, then the test becomes unstable and the crack suddenly reaches the mid-span length of the specimen.
The energy released can be considered constant with the crack length for a > l, as shown in figure 4.b.
3
4.5
(a)
2.8
(b)
4
2.6
3.5
2.2
GII [N/mm]
GI [N/mm]
2.4
2
1.8
1.6
3
2.5
2
1.4
1.5
1.2
1
40
42
44
46
48
50
52
54
56
58
1
60
30
35
40
a [mm]
45
50
55
60
65
70
a [mm]
Figure 4. Resistance curve for DCB (a) and ENF test (b)
The optimal resistance criterion that describes this material can be found by plotting the points in table 3 on a plain
(G
φ
IIC
) (
)
φ
/ G IIC , GIC
/ GIC . Following the generalised power criterion proposed in [9], the equation that describes the resistance
of a material under mixed mode is:
φ
⎛ GIC
⎜
⎜G
⎝ IC
α
⎛ Gφ
⎞
⎟ + ⎜ IIC
⎜G
⎟
⎝ IIC
⎠
β
⎞
⎟ =1
⎟
⎠
(7)
In figure 5 the experimental points are drawn together with the equation (7) obtained by the best-fitting procedure implemented
in Matlab® environment. It is seen that, although the curve fitting gives α = 1.21 and β = 0.84, the approximation obtained by
using α = β = 1 (linear resistance behaviour) can be also used in practice (the difference between the two lines is negligible).
mode mix = 0.25
mode mix = 0.5
mode mix = 0.75
power int.
linear int.
1
GφI /GIc
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
GφII/GIIc
Figure 5. Fracture domain
Fatigue tests
Fatigue tests have been performed by using a MTS servo-hydraulic testing machine, equipped with a in-house made 1 kN load
cell. Both displacement and load control have been used to carry out the experiments. Similarly to quasi-static tests, the crack
length is measured via optical observation of high resolution digital photos. Typical loading frequency was 2 Hz, but in some
cases it was properly lowered because of resonance phenomena of the hydraulic circuit. Due to this problem, the mixed mode
experiments have been carried out by the SLFPB test that requires small displacement of the actuator. After some
modifications to the hydraulic circuit of the machine, experiments with the MMB test have also been done and two further
mode mixtures (φ = 0.25 and φ = 0.75) have been analysed. All the output files given by the MTS software have been postprocessed in Matlab® environment. A constant load ratio R = Pmin/Pmax = 0.1 was adopted.
DCB and ENF fatigue tests have been carried out under load control. In order to obtain a wide interval of variation for the
SERR, specimens were analysed with different initial crack lengths and/or under different load levels. For both the DCB and
the ENF test under load control, the crack rate is rising with cycles up to sudden failure in proximity of the critical value of the
static toughness Gc.
The components of the total energy released estimated from the SLFPB data are given by the following relationships:
GI = b11nλ− 3 4 Φ 2
(8)
GII = b11nλ
(9)
−1 4
Θ
2
where:
3
nh3
Φ = λ3 8 M
9
4nh3
, Θ = λ1 8 M
(10)
and
n=
ρ +1
2
, ρ=
2b12 + b66
2 b11b22
, λ = b11 b22
(11)
being M the moment (per unit width) at the crack tip and bij the terms of the generalised Hooke law. By substituting of eqs. (10)
and (11) into eqs. (8) and (9) a mode mixture φ = 0.43 is obtained.
To plot the fatigue plots (da/dN vs. Gmax) the crack length with cycles, a(N), and the maximum load with cycles, Pmax(N), have
been recorded; the crack length is obtained from the digital photos and the load is given by the testing machine software. The
experimental data of the crack length are fitted with power or exponential curves and the derivative da/dN has been calculated
analytically from the fitting curve. The instant value of Gmax is evaluated from the load, Pmax(N), and the current crack length,
a(N), via equations (2) and (3). In figure 6 and 7 the crack growth rate is plotted versus the maximum value of the total SERR
for the tests performed. Power laws have been adopted to interpolate the data. In some cases (see for example the curve φ =
0.25), when Gmax approaches to the static toughness Gc the resulting curve becomes too steep; these points have been
excluded from the interpolation procedure.
Average Paris parameters for the tests are summarised in table 4 and plotted in figure 8. It is easy to notice that the two
parameters change with the mode mixture in a different manner. The intercept B increases monotonically with φ while the
slope m has low values in correspondence of the single fracture modes and a maximum value in proximity of φ = 0.5.
-2
-1
10
10
(b)
δa/δN [mm/cycle]
δa/δN [mm/cycle]
(a)
spec 1
spec 2
spec 3
-3
10
-4
10
0.25
spec 1
spec 2
spec 3
-2
10
-3
0.5
Gmax [N/mm]
0.75
1
1.25
10
0.1
1
Gmax [N/mm]
Figure 6. Crack growth rate versus Gmax for DCB tests (a), and ENF tests (b).
2
3
-2
-2
10
10
(b)
spec 1
spec 2
spec 3
δa/δN [mm/cycle]
δa/δN [mm/cycle]
(a)
-3
10
-3
10
mode mix 0.25
mode mix 0.75
-4
10
-4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
10
1.3 1.4 1.5
0.5
0.6
0.7
Gmax [N/mm]
0.8
0.9
1
1.1
1.2
1.3 1.4 1.5
Gmax [N/mm]
Figure 7. Crack growth rate versus Gmax for SLFPB tests (a), and MMB tests (b).
TABLE 4. Paris parameters.
Mode mixture φ
0
0.25
0.43
0.75
1
Test
DCB
MMB
SLFPB
MMB
ENF
Test control
Load
Displacement
Displacement
Displacement
Load
Paris param.B
2.4E-3
9.0E-4
3.3E-3
5.7E-3
6.7E-3
Paris param.m
0.42
3.09
4.43
3.3
0.7
Parameters B and m can be related to the mode mixture by using the curve that fits the experimental data. Due to the
particular distribution of the points in the diagrams, a quadratic curve can be used for both parameters. Three constants must
be fixed for the curve B(φ) and for the curve m(φ). The curve are expressed as follows:
B(φ ) = − k Bφ 2 + (BII − BI + k B )φ + BI
(12)
m(φ ) = −k mφ + (mII − mI + k m )φ + mI
2
(13)
It is to be noted that BI, mI and BII, mII are the intercept and the slope of the fatigue plots for single mode I and single mode II,
respectively, whereas kB and km are given by the best fitting (see figure 8.a and 8.b) procedure of data. This best fit procedure
provides: kB = -5.15E-3, km = 15.45. In the same figures 8, also models given in [15] and [16] are plotted. It is seen how the
model proposed by Dahlen et al. works for the variation of the intercept B but fails for the slope m. Also the model proposed by
Kenane et al. works in predicting the variation of the intercept, whereas this model is not able to describe the behaviour of the
slope.
6
0.014
(a)
(b)
Experiments
0.012
Quadratic interp.
Experiments
Quadratic interp.
5
Dahlen & Springer
Dahlen & Springer
0.01
Kenane & Benzeggagh
4
B
m
0.008
3
0.006
2
0.004
1
0.002
0
0
0
0.2
0.4
φ
0.6
0.8
1
0
0.2
0.4
φ
0.6
0.8
Figure 8. Influence of the mode mixture φ on the intercept (a) and on the slope (b) of the Paris plot.
1
Conclusions
Quasi-static and fatigue delamination experiments have been performed in this work on a glass/epoxy unidirectional
composite. The material has been manufactured with the hand lay-up technique. Using different experimental configurations,
single and mixed fracture modes (opening, shearing and a mix of them) have been analysed under quasi-static and fatigue
loading. Taking into account the experimental results obtained, the following remarks can be here summarised.
o Fracture toughness values from quasi-static tests are quite high for this material, but they can be compared with other
found in literature. Resistance curves show that in mode I the energy required for the crack propagation increases
with the crack length; this phenomenon doesn’t appear in mode II.
o Fatigue Paris parameters (intercept and slope) that characterise the stable crack propagations depend on the mode
mixture; in particular the experimental results show that the intercept increases with the mode mixture whereas the
slope takes a maximum near to φ = 0.5.
o A simple quadratic model can be used to describe this dependency, whereas other monotonic models found in
literature fail when applied to the material analysed.
Future developments of the work include the analysis of cases where the mode mixture changes during the crack propagation,
in order to verify the quadratic interpolation model under more realistic loading conditions. Furthermore, a study on other
composite materials is going to be performed to assess the role of fibres and matrix on the material behaviour under fatigue
loading.
Acknowledgments
The authors would like to thank Mr. Giuseppe Giacalone and Mr. Giacomo Cerami (DIMA Laboratory) for the technical support
given to the realization of the experimental tests.
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