Polymer Testing 87 (2020) 106508
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Polymer Testing
journal homepage: http://www.elsevier.com/locate/polytest
Test Method
On the experimental measurement of fracture toughness in SENT
rubber specimens
Silvia Agnelli a, *, Winoj Balasooriya b, Fabio Bignotti a, Bernd Schrittesser b
a
b
Department of Mechanical and Industrial Engineering, University of Brescia, Via Branze 38, 25123, Brescia, Italy
Polymer Competence Center Leoben GmbH, Roseggerstrasse 12, 8700, Leoben, Austria
A R T I C L E I N F O
A B S T R A C T
Keywords:
Rubber
Toughness testing
Tearing energy
J-integral
SENT specimen
Digital image correlation
This work provides a direct comparison of several experimental approaches used in the literature to measure
fracture toughness of rubber of rubber using single edge notched in tension (SENT) specimens, with the final aim
to provide guidelines for an optimal testing procedure. Digital image correlation measurements were used to get
new insights into the fracture process. SENT is experimentally advantageous because of the simple preparation
from laboratory plates and the small amount of material required. The most common experimental approaches to
measure fracture toughness of rubber rely on the energy release rate, measured by the tearing energy or the Jintegral parameters. This work points out the importance of experimental conditions and test procedures: long
specimens and short notches are preferred, identification of fracture initiation from the front view is necessary,
strain energy density should not be evaluated from un-notched specimens at the critical stretch level, rather
alternative strategies are shown in this work.
1. Introduction
G¼
Elastomeric materials are nowadays widely used in many engineer­
ing components (as for example tires, seals, hoses), where their struc­
tural resistance is a fundamental condition to guarantee safety and
performance. Experimental testing of fracture resistance of rubber ma­
terials therefore provides useful information to engineers for the design
of such components and for material selection. Elastomer-based systems
are highly deformable non-linear viscoelastic materials, therefore their
fracture behaviour is usually characterized by global approaches based
on energy concepts, which do not require the knowledge of the stress
and strain fields around the crack tip.
Considering a body containing a stationary crack of area A, the en­
ergy balance is expressed as follows:
dUin
dA
dU dUdiss
¼
dA
dA
(1)
where Uin is the input energy (external forces’ work), U is the recover­
able elastic strain energy, and Udiss is the dissipated energy. Starting
from the balance in equation (1), Griffith [1] defined the energy release
rate (G), i.e. the energy dissipated during fracture per unit of newly
created fracture surface area at a fixed displacement (u):
�
dU��
dA�u
(2)
Fracture initiation occurs when the change of potential energy in
system (G) exceeds the amount of energy required to form new surfaces,
labelled Gc, which is a material characteristic. The first attempt to
“obtain a criterion for the tearing of a rubber vulcanizate, which is in­
dependent of the form of the test-piece” was done by Rivlin and Thomas
in 1953 [2], in which they extended the Griffith criterion [1] to rubbers.
They introduced the tearing energy T, representing the work expended
irreversibly per unit area of crack advancement (left hand side of
Equation (1)), and expressed it as a function of the uniform strain energy
density W0 (i.e. the strain energy density far from the crack) and the
crack length, a:
T¼
dUin
dA
dUpot
¼ kðλÞ⋅W0 ⋅a
dA
(3)
where k(λ) is a function of the elongation ratio λ. From Equation (3)
Rivlin and Thomas derived simplified semi-empirical equations for
simple extension tear, Single Edge Notched in Tension (SENT) and Pure
Shear (PS) specimen geometries, by testing rubbers characterized by a
substantially reversible elasticity, except at very large deformations in
the neighbourhood of the notch tip. However, technologically relevant
* Corresponding author.
E-mail address: silvia.agnelli@unibs.it (S. Agnelli).
https://doi.org/10.1016/j.polymertesting.2020.106508
Received 15 October 2019; Received in revised form 28 February 2020; Accepted 24 March 2020
Available online 30 March 2020
0142-9418/© 2020 Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
S. Agnelli et al.
Polymer Testing 87 (2020) 106508
rubbers are non-elastic materials, which dissipate energy during
extension due to viscous deformation and strain-induced crystallization
(only for specific elastomers, like NR). For these reasons the application
of the tearing energy simplified equations derived by Rivlin and Thomas
are limited [3].
Some years later, Rice [4] proposed the J-integral theory to char­
acterize the stress and strain field at the crack tip for non-linear mate­
rials of infinitesimal elasticity. J-integral and tearing energy are both
defined as the energy released for a unitary area crack advancement.
The equivalence of the J-integral and the tearing energy T was then
verified for highly extensible materials both mathematically (Chang [5])
and experimentally (Oh [6]). In spite of the non-elastic behaviour of
most rubbers, the path independence of J-integral could be verified both
experimentally [7] and numerically [8] and several authors proposed to
use the J-integral approach for the evaluation of fracture toughness of
rubbers [7–22].
The two most widely used specimen geometries for rubber fracture
toughness testing are the Pure Shear (PS) and the Single Edge Notched in
Tension (SENT) specimens (see Fig. 1). The advantage of SENT
compared to PS is that the specimens can be easily obtained from rubber
sheets, commonly produced in the testing laboratory, and easily clam­
ped. On the contrary, PS needs thicker edges and special clamps to avoid
specimen slip during the test, and therefore dedicated moulds are often
used to obtain this shape. Moreover, the total volume required for a
SENT specimen is smaller than in the case of PS specimens, because less
material is needed to clamp the specimens correctly. Therefore SENT is
the favourable choice when a restricted amount of material is available
for testing.
For SENT specimens, Rivlin and Thomas [2] recommended that a,
the notch length, shall be small compared to the specimen width (less
than 30%), so that the deformation in the bulk of the specimen is un­
affected by the presence of the notch. The width in turn is small
compared to the specimen length (at least double the width). Concern­
ing the geometry factor of equation (3), k(λ), Greensmith [23] proposed
the following form for SENT with short notches:
2π
kðλÞ ¼ 1=2
λ
therefore provide some guidelines for an optimal characterization of
fracture resistance with SENT specimens. In summary, the following
approaches are applied:
1) Calculation of the tearing energy with W0 taken from an un-notched
specimen at the same λ;
2) Calculation of the tearing energy with W0 taken from an un-notched
specimen at the stress level;
3) Calculation of the tearing energy with W0 taken from the loaddisplacement curve of the notched specimen;
4) Calculation of the J-integral parameter via the single specimen for­
mula, with some considerations on the geometry factor calibration.
2. Experimental details
The material tested was a commercial grade of Nitrile Butadiene
Rubber (NBR) filled with 40 phr of CB N347, provided as compression
moulded plates of 2 mm thickness. The density of the material is 1.218
� 0.005 g/cm3, hardness is 72 ShoreA, tensile stress at break and tensile
strain at break were 21 MPa and 450%, respectively, measured in uni­
axial tensile tests by the authors.
Single Edge Notched in Tension (SENT) specimens were cut from the
plates (see Fig. 1a) with the following dimensions: 2 mm thickness (B),
15 mm width (W), 160 mm total length (L), notch length (a) variable
from 0 mm (un-notched specimen) to 8 mm. The nominal a/W ratio of
notched specimens ranged from 0.15 to 0.5. The notch was inserted with
a sharp industrial blade, a Stanley 1992 N, in a single cut, without
removing material. The tip radius of the blade from SEM images was
equal to about 6 μm. The actual specimen width and thickness were
measured by a calliper before testing, whereas the actual a/W ratio was
obtained measuring the crack length a on the fractured surface by a
microscope. The clamp distance (L0) was set at a displacement of 100
mm. Furthermore, also some Pure Shear (PS) specimens were tested
with the following dimensions: W ¼ 80 mm, L0 ¼ 8 mm, B ¼ 2 mm, a ¼
15 mm.
Fracture tests were carried out with a Zwick Z001 universal testing
machine (Zwick Roell, Test expert, Ulm, Germany), equipped with a 1
kN load cell and hydraulic grips, at a crosshead speed of 200 mm/min
(and 15 mm/min for PS specimens). It is known that fracture resistance
of rubber is highly strain rate dependent, due to its viscoelastic nature.
Therefore the two test speeds were chosen in order to have the same
nominal strain rate in SENT and in PS specimens. The strain rate is
calculated as test speed over the clamp distance. In this work a strain
rate of 0.03 1/s was selected: this strain rate was already adopted in
previous works [18] and is in the quasi-static range of speeds. An optical
testing device (Mercury) with two cameras was placed in front of the
specimen, taking pictures at a rate of 10 fps. An image of the overall test
set-up is shown in Fig. 1b. The images allowed both the analysis of
strains on the specimen surface by the Mercury RT software (version 2.5,
2017) (Sobriety s.r.o., Ku�rim, Czech Republic) for DIC measurement,
and the identification of the onset of fracture. Pictures were synchro­
nized with the loading curve after the tests, by taking test start when the
first variation of distance between the clamps was observed.
In order to allow strain measurement, a fine pattern of white was
speckles was applied by a permanent spray on the specimen surface,
before performing the fracture tests. It is worth mentioning that engi­
neering strain (ε) is related to λ by the relationship λ ¼ ε þ 1.
Fig. 1c shows the evaluation of two types of strain. “Global strain”
(εglo) is calculated as engineering strain from the crosshead displace­
ment, ΔL:
(4)
The literature proposes several approaches to experimentally
calculate W0. In the most common approach [2,24,25], W0 is taken from
an un-notched specimen at the same λ of the notched specimen. Agnelli
et al. [26] proposed the use of stress rather than stretch ratio for the
comparison of notched and un-notched specimens, so that W0 is taken
from an un-notched specimen at the same stress level of the notched
specimen. For long specimens and short notches, the region of strain
energy density amplification around the notch is negligible compared to
the other regions of the specimen, so that W0 is taken directly from the
load-displacement curve of the notched specimen [27].
Nowadays, advanced optical strain measurement devices, such as
Digital Image Correlation (DIC) systems, allow the experimental mea­
sure of the strain field directly on a sample during the test. DIC is a fullfield strain analysis (FFSA) able to track and measure in 2D or 3D
changes in images. In principle, it compares speckle patterns structures
on the surface of the sample between two deformation states [28]. This
powerful facility allows the direct monitoring of W0 far from the crack,
as ideally required by Rivlin and Thomas [2]. In this work, DIC was used
to actually measure such W0 values, and the results are considered as
reference values for the comparison with other indirect approaches to
measure W0.
Finally, and under the hypothesis of a nonlinear-elastic material, the
fracture energy can also be calculated by the J integral parameter. This
parameter is defined as the strain energy release rate and can be
calculated with a single-specimen approach, provided that a geometry
factor is calibrated for the specimen geometry [18].
The aim of this work is to compare different experimental ap­
proaches to measure fracture resistance in SENT rubber specimens, and
εglo ¼
ΔL
L0
(5)
“Local strain”, εloc, is calculated from Mercury software over a
rectangular area selected far from the notch and the clamps, as shown
for example in Fig. 1d. Fig. 1c displays a sketch of the two types of strain.
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Polymer Testing 87 (2020) 106508
Fig. 1. a) geometry and dimensions of SENT specimen; b) picture of the test set-up; c) sketch of the specimen and of the characteristics used to measure strains; d)
image taken by DIC system to a sputtered specimen, with the blue area selected for measuring local strain; e) image taken by DIC system to a specimen during the test,
showing the vertical strain pattern and the area of interest (black rectangle).
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Polymer Testing 87 (2020) 106508
The interested area was selected ~30 mm from the notch and ~20 mm
from the clamp. Fig. 1e shows a DIC image of vertical strain: the inter­
ested area (black rectangle) is placed in a region of homogeneous
strains, not influenced by the clamps. The strain is measured as Lan­
grangian Finite strain. At high strain levels, the Lagrangian strains can
become much larger than engineering strains due to the higher order
term. However, in this work strains far from the notch don’t exceed
40%, and in this range the two types of strain are equal.
test, F, as F/(B*W). W0 measured by Equation (6) with εloc is termed W0,
loc,notch, and this value is used as the reference to check the reliability of
other approaches.
3.1.1. Determination of W0 from an un-notched specimen
In the case of a/W < 0.2, as recommended by Rivlin and Thomas, the
cut introduced into the sample is such that W0 does not vary significantly
compared to an un-notched specimen at the same stretch level, and a
good estimation of W0 at the global strain of interest can be obtained
from stress-strain relationship obtained from a rubber strip. Therefore,
most commonly in the literature [2,22,24,25], the W0 needed for the
calculation of T at a specific global stretch level is obtained by testing an
un-notched specimen, with the same configuration and geometrical di­
mensions as the notched one. This approach provides an approximation
of the actual W0, which should be acceptable under the conditions
indicated by Rivlin and Thomas. In this work tests will be implemented
using specimens with a notch length to width ratio exceeding 20%, in
order to explore the limits of this approach.
From the load-displacement curve of the un-notched specimen, en­
gineering stress and engineering strain are calculated as global param­
eters by dividing the force by the section area and the displacement by
the clamp distance, respectively. These parameters allow us to calculate
W0,ε,un-notch from the un-notched specimen, using Equation (6).
Fig. 3a shows the results of W0,ε,un-notch plotted as a function of W0,loc,
notch for some specimens with different a/W ratios. Some of the curves
are interrupted due to the specimen break. The black line is the bisector
where W0,ε,un-notch equals W0,loc,notch, drawn as a guideline for the eyes.
According to the approximation of Rivlin and Thomas, W0,ε,un-notch
should be equal to W0,loc,notch, at least for short notches. As depicted, the
experimental curves are approximately straight lines, and they all lie
above the bisector. With increasing the notch length, W0,ε,un-notch over­
estimates W0,loc,notch.
Using the scheme in Fig. 3b, the deviation can be explained consid­
ering two specimens, with the same geometry except for the notch,
globally stretched up to the same level (same ΔL). The strain (εglo) is
uniform in the un-notched specimen, throughout the specimen length. In
the notched specimen, the local extension of the material will concen­
trate in a region around the notch; therefore to compensate this far from
the notch the local extension will be lower than in the un-notched
specimen. Consequently, also the local strain (εloc) will be lower,
depending on the notch length. Since the constitutive behaviour of the
material is the same, a lower strain corresponds a to a lower stress level,
and consequently also a lower W0. Therefore, an increasing notch leads
to the higher W0,ε,un-notch with respect to W0,loc,notch as experimentally
observed.
Agnelli et al. [26] proposed that a more precise estimation of the
strain energy density far from the crack from the loading curve of an
un-notched specimen, is obtained by the comparison of the two speci­
mens at the same stress level, rather than at the same stretch ratio. As a
matter of fact, provided that the SENT specimen is sufficiently long, the
stress state far from the notch is simple extension. Therefore, when
stretched up to the same load level, the stress in the notched specimen
far from the notch (σnotched) equals the stress in an un-notched specimen
(σun-notched) with the same net section (A0). Since the stress-strain rela­
tionship obtained in simple extension is unique to the material, the re­
gion far from the crack in the SENT specimen is characterized also by the
same strain and W0,σ,un-notch value as in the un-notched specimen
(Fig. 4).
Also in this case, the relationship between W0,σ,un-notch and W0,loc,
notch is nearly linear. The scatter is lower than in the comparison at the
same stretch level, but without a clear trend of the curves with the a/W
ratio. This scatter is related to the scatter in the stress-strain curves of the
material. As a matter of fact, stress-strain curves in uniaxial extension
can be obtained by plotting σnotched and εloc for notched specimens, and
σun-notched and εglo for un-notched specimens. Although in principle they
should be perfectly overlapped, the experimental curves obtained
3. Results
In the following, (i) different approaches are shown, which allow the
evaluation of the strain energy density W0, required to calculate T; (ii)
the calculation and the results of the J parameter will be reported; (iii) a
comparison of the fracture resistance parameters, T and J, will be pro­
vided. All the results are calculated starting from the same set of
experimental load-displacement curves, shown in Fig. 2. The a/W ratio
of each specimen is displayed in the legend. Moreover, the fracture
initiation points optically detected from pictures are displayed as circles.
It is worth pointing out that initiation points do not coincide with the
maximum point, after which catastrophic failure occurs. This is a very
common behaviour in rubber, related to the mechanical hysteresis of
rubber at very high strains. In a purely elastic material without hyster­
esis, catastrophic fracture would occur as soon as initiation occurs.
Instead, in most rubbers, crack propagation causes relaxation of a highly
stretched region around the crack tip. The relaxation is governed by the
unloading branch of the stress-strain curve of the material, and in­
fluences the stress at the new tip. Due to hysteresis, the stress at the tip
may be substantially lower than in a purely elastic material. This can
explain why rubber show a region of stable crack propagation, where the
higher is the hysteresis, the slower is the crack propagation [29].
3.1. Evaluation of T parameter
W0 in Equation (3) is the strain energy density in the bulk of the
specimen, i.e. far from the notch [2,27] and it is defined as shown in
Equation (6), where σ and ε are the stress and strain, respectively.
Z
W0 ¼ σ:dε
(6)
In this work, W0 could be determined measuring the strain far from
the notch through DIC analysis. The local strain far from the notch is
experimentally measured by optical DIC measurements, and is defined
as εloc. Since the stress far from the notch in a SENT specimen is uni­
formly distributed, it is calculated from the load recorded during the
Fig. 2. Load-displacement curves of SENT specimens. The point of fracture
initiation (full circle) is displayed on the curves. The legend reports the nominal
a/W of each curve.
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Polymer Testing 87 (2020) 106508
Fig. 3. a) W0,ε,unnotch vs W0,loc,notch for specimens with different a/W ratio (displayed in the legend); the black line is the bisector; b) Scheme to explain why W0,ε,
unnotch overestimates W0,loc,notch.
showed some differences. For example, in Fig. 4c two curves are plotted,
one of a notched and one of an un-notched specimen, revealing a clear
difference between them. The blue area highlights the difference in
terms of strain energy density of the two curves at the same strain level,
whereas the green area highlights the difference in terms of strain en­
ergy density of the two curves at the same stress level. The difference in
terms of W0 between the two curves is much larger compared at the
same stress level, rather than at the same strain level, and this further
magnifies the scatter in the results for W0,σ,un-notch.
specimen) is higher than the local one, as explained in paragraph 3.1.1.
The overestimation of W0,glo,notch with respect to W0,loc,notch is smaller
than in the case of W0,ε,un-notch because in this last case not only the
strain, but also the stress is overestimated.
This result will depend also on the specimen length: it is reasonable
to think that reducing the length (L0) the strain amplification region will
have a higher influence on the correct calculation of the global strain,
and consequently W0,glo,notch will differ more from W0,loc,notch. In order
to virtually analyse the effect of L0/W ratio on W0,glo,notch, the global
strain was calculated by DIC over areas of decreasing length and sym­
metric to the notch, as if the specimen had virtually a shorter length. The
areas are drawn on the images captured during the test, as schematically
drawn in Fig. 6a, and the length (Li) and global strain (εglo,i ¼ ΔLi/Li) are
calculated by the software tool. The global strains obtained are used to
calculate W0,glo,notch,i. In order to provide an overview of such results,
Fig. 6b reports W0,glo,notch,i for several specimens with different a/W
ratio, at a fixed W0,loc,notch equal to 100 kJ/m3.
The graph 6b summarizes the virtually obtained influence of spec­
imen length on the global strain energy density, W0,glo,notch,i, in differ­
ently notched specimens and compared at W0,loc,notch ¼ 100 kJ/m3. It
shows stable W0 values similar to the reference even with ~15 mm
virtual length (Li/W ¼ 1) for small notches (a/W ¼ 0.14). However, with
increasing the a/W ratio, a higher specimen length is necessary to obtain
stable W0. Therefore, at virtual specimen length of 80 mm (Li/W ¼ 5)
each tested specimen delivers a stable W0,glo,notch,i close to the reference
3.1.2. Determination of W0 from the load-displacement curve of the
notched specimen
When SENT specimens have a high L0/W ratio, and a low a/W ratio,
the strain energy density is approximately uniform through all the
specimen, and can be calculated directly from the global stress (σnotched)
and strain (εglo) of the notched specimen from the load and displacement
data [27].
The strain energy density obtained directly from the global param­
eters is termed here W0,glo,notch, and the results for several specimens are
reported in Fig. 5 versus W0,loc,notch. Also in this case, the experimental
curves of Fig. 5a are approximate lines. W0,glo,notch is very similar to W0,
loc,notch, particularly for short notches, but the longer the notches the
more W0,glo,notch overestimates W0,loc,notch. This discrepancy is attrib­
uted to the fact that at the same level of σnotched far from the crack, the
global strain (an average over the not uniform strain levels in the
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Polymer Testing 87 (2020) 106508
Fig. 4. a) Scheme to explain the reason for the comparison
of notched and unnotched specimens at the same load level;
b) W0,σ,unnotch vs W0,loc,notch for specimens with different a/W
ratio (displayed in the legend); the black line is the bisector;
c) stress strain curves of two selected specimens: a notched
one (σnotched and εloc) and an unnotched one (σunnotched and
εglo); the blue area and the green highlight the difference in
terms of strain energy density of the two curves at the same
strain or at the same stress level, respectively.
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Polymer Testing 87 (2020) 106508
Fig. 5. a) W0,glo,notch vs W0,loc,notch for specimens with different a/W ratio (displayed in the legend); the black line is the bisector; b) Scheme to explain why W0,glo,
notch overestimates W0,loc,notch (dashed curve represents the stress-strain relationship with εglo).
value. With a larger notch size, a greater stress concentration around the
notch and subsequently, higher strain amplification around notch is
expected. Therefore, in these same stress conditions, higher strains
result in higher W0,glo,notch,i with shorter specimen lengths.
included in the standard deviation band. W0,glo,notch results are in very
good agreement with the W0,loc,notch values. The scatter increases with
increasing the stretch level, but the average value keeps centred in the
reference level, much more than the other W0. This is due also to the
sufficiently high L/W ratio (higher than 5), as commented in paragraph
3.1.2.
From the overview of results shown in Fig. 7, it seems that the best
approach for the specimens adopted in this work is the calculation of W0
values from global parameters of the notched specimen. This provides
also a practical advantage since this method removes the need for testing
an un-notched specimen.
3.1.3. Comparison of W0 results from different experimental methods
Three different approaches for the calculation of W0 in Equation (3)
are put forward in this work, and are applied to the same set of exper­
imental curves obtained from specimens with different a/W. In order to
compare the results, three levels of W0,loc,notch have been selected (100,
300 and 500 kJ/m3), and the corresponding W0,ε,un-notch, W0,σ,un-notch
and W0,glo,notch are calculated for each specimen. The average values
over all the tested specimens are reported in Fig. 7. It is worth recalling
that W0,loc,notch is considered as the best estimation of W0 in the bulk of
the specimen (far from the crack) to be used in Equation (3), and is taken
therefore as the reference level.
Fig. 7 shows a clear trend of W0,ε,un-notch, which systematically
overestimates the reference values of W0, at any strain level. This was
already highlighted in paragraph 3.1.1, and Fig. 7 confirms that W0,ε,unnotch provides values higher than all the other W0 types. W0,σ,un-notch
provides values very close to W0,loc,notch at 100 kJ/m2, but with
increasing strain level the results move toward an underestimation. This
is probably related to the increasing scatter of results, as commented in
Paragraph 3.1.1. Compared to the other W0, W0,σ,un-notch values are
systematically the lowest, although the reference value is always
3.2. Evaluation of J parameter
The J-integral parameter was proposed by Rice for nonlinear elastic
materials [4]. The J parameter can be calculated by testing a single
specimen as shown in Equation (7) [30]. Where Uin is the external work
(area under the load-displacement curve) and η is a geometry factor,
which is specific to the specimen geometry. For example, for pure shear
specimens it is unitary, whereas for SENT specimens it is reported to be
lower than one [18,22,31,32].
J¼
ηUin
BðW aÞ
(7)
In this work η was experimentally calibrated for a proper calculation
7
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Polymer Testing 87 (2020) 106508
specimen J formula (equation (7)):
�
1 dU��
ηU
⋅ �
¼
J¼
B da u¼const: BðW aÞ
(8)
The η factor can thus be obtained from equation (8) as follows:
�
dU��
ðW aÞ
(9)
η¼
⋅
da �u¼const:
U
By testing specimens with different a/W ratio, from the geometry
dimensions and experimental load-displacement curves, all the param­
eters required for the calculation of η can be obtained. Starting from the
curves in Fig. 2, the energy U was calculated for each specimen at
different displacement levels, up to a maximum of 16 mm, to be sure that
the notch length (a) does not vary due to fracture propagation. U vs a
curves at fixed displacement were fitted with second degree polynomial
best fitting curves, as suggested by Dong et al. [34]. The values of η were
displacement-dependent: they decreased about 30% by increasing
displacement from 2 to 16 mm. This displacement dependency, already
observed by the authors also for other systems, was justified by Shahani
et al. [31] as an effect of the nonlinear elastic behaviour of rubber.
Nevertheless, all the values obtained from each specimen were averaged
over the considered displacement levels, and the final average values are
reported in Fig. 8 with standard deviation. The equation of the poly­
nomial best fitting curve is also displayed.
The results of this work show η increasing with a/W, starting from
0.2 at a/W ¼ 0.15 to 0.4 for a/W ¼ 0.5. These values are quite low
compared to those reported in the literature for SENT specimens: around
0.6 for specimens with 50 mm length, 2 mm thickness and 15 mm width
of “filled buna” rubber in Refs. [22], 0.9 for specimens with 50 mm
length, 2 mm thickness and 25 mm width of a mixture of natural rubber
and synthetic polyisoprene with 60 phr carbon black in Ref. [18], and
from 0.5 to 0.6 for specimens with 120 mm length, 12.5 mm thickness
and 30 mm width of butadiene rubber in Refs. [31]. Differences of the
geometry factor compared to literature results can be mostly attributed
to the different specimen dimensions used, although a numerical study
by Shahani et al. [31] reports also η is material-dependent for hypere­
lastic materials. This aspect should be investigated, but it is out of the
scope of the present work.
Fig. 6. a) SENT specimen with the areas of length Li over which several global
strains are calculated by DIC software; b) W0,glo,notch,i vs a/W calculated over
different virtual lengths Li (displayed in the legend), at a fixed W0,loc,notch ¼
100 kJ/m3.
3.3. Comparison of Jc and Tc results
Fracture resistance parameters, either Tc or Jc (where c stays for
critical), are evaluated by equation (3) or 7, respectively, at the point of
fracture initiation. The fracture initiation event is optically observed
from pictures showing the lateral surface of the specimen, a point of
Fig. 7. Comparison of W0,ε,unnotch, W0,σ,unnotch and W0,glo,notch averaged over
specimens with different a/W calculated at three different levels of W0,loc,notch
(100, 300 and 500 kJ/m3).
of the J parameter at fracture initiation point.
The geometry factor was determined according to a multi-specimen
procedure proposed by Landes and Begley [33]. Here only the principles
and the results are reported. For a detailed description of the application
of this procedure to elastomeric materials, please refer to the literature
[18,22,31,32].
To obtain an evaluation of the geometry factor, the strain energy
release rate at fixed displacement (equation (2)) is equated to the single
Fig. 8. Geometry factor, η, vs a/W. Values are averaged over displacement
levels. The line represents the polynomial best fitting curve, and its equation is
also reported.
8
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Polymer Testing 87 (2020) 106508
view necessary for DIC measurements. The points of fracture initiation
determined in this way are displayed on the load-displacement curves of
Fig. 2, and fracture resistance is calculated at such points.
As the final aim of this work is to analyse and compare several ap­
proaches for the measurement of fracture toughness, the most instruc­
tive information can be obtained by the direct comparison of the final
results of Tc and of Jc. Fracture toughness parameters obtained for each
specimen are plotted in Fig. 9a and b as a function of a/W ratio. Tc values
are termed Tc,loc,notch, Tc,ε,un-notch, Tc,σ,un-notch, Tc,glo,notch, depending
whether they are calculated from W0,loc,notch, W0,ε,un-notch, W0,σ,un-notch
or W0,glo,notch, respectively. Moreover, in Fig. 9c are reported also the
results of Tc,glo,notch, i.e. Tc values evaluated as Tc,glo,notch, but at a
fracture initiation observed from a frontal view, as described in the next
section.
The results of Tc and Jc are shown in two different graphs for a better
readability, and Tc,loc,notch values, displayed as black triangles, are re­
ported in both Fig. 9a and b as a reference since W0,loc,notch is taken as
the best estimation of W0 far from the notch.
Generally, the results show a remarkable scatter. For example, the
average value of Tc,loc,notch is 16 � 3 kJ/m2, i.e. a scatter of 20%, which,
however, is not unusual for fracture tests, also considering the limited
amount of data available. Both Tc,ε,un-notch and Tc,σ,un-notch are very close
to Tc,loc,notch at small a/W. Increasing a/W, particularly at a/W > 0.3,
Tc,ε,un-notch tends to overestimate Tc,loc,notch, reflecting the same
Fig. 9. a) Tc,loc,notch, Tc,ε,unnotch, Tc,σ,unnotch vs a/W; b) Tc,loc,notch, Jc, Tc,glo,notch vs a/W; c) Tc,glo,notch and Tc,glo,front vs a/W; d) scheme of areas ahead of the notch tip
where strains are measured by DIC, at increasing distance from the edge; e) local strain measured by DIC for two specimens with a/W ¼ 0.15 and 0.5, at frac­
ture initiation.
9
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Polymer Testing 87 (2020) 106508
behaviour of W0. As mentioned in sections 3.1.1 and 3.1.3, Tc,ε,un-notch is
not recommended because of its intrinsic energy overestimation. Tc,σ,unnotch data follow the same trend and are very close to Tc,loc,notch at any a/
W. Small differences between the two parameters are, however, lower
than the data scatter.
Fig. 9b shows that Tc,glo,notch is also very similar to Tc,loc,notch for a/W
lower than 0.3, and it tends to overestimate Tc,loc,notch for larger a/W,
but the difference is still smaller than the data dispersion. Finally, Jc is
very close to Tc,loc,notch for a/W larger than 0.25, whereas it over­
estimates Tc,loc,notch for very short notches. A possible reason could be
attributed to the geometric factors, both of the tearing energy (k(λ) is
obtained from the literature) and of the J integral (η is obtained by in­
terpolations, and the results can be less reliable at the extreme regions,
with the smallest and largest notches). However, this aspect should be
better investigated to find a proper explanation.
Globally, the results show a slight decrease with increasing a/W,
particularly for a/W > 0.4. This effect for long notches could be related
to the limited ligament length (the remaining net section after notching),
which interferes with the strain intensification region around the notch
tip. In order to check this hypothesis, DIC was used to measure strain in
small regions ahead of the notch tip. A scheme for the pattern of mea­
surement areas is sketched in Fig. 9d. The results of such measurements
are reported in Fig. 9e for two specimens with a/W ¼ 0.15 and 0.5, at a
stretch level corresponding to fracture initiation. As can be observed, for
both specimens the strains are higher close to the notch tip (right hand
side of the plot), and decrease close to the specimen edge (left hand side
of the plot). Whereas for the shortest notch the strains are almost con­
stant close to the edge, for the longest notch the strains do not reach a
stable region, supporting the hypothesis of a border effect on the frac­
ture toughness measurement.
frontally or laterally. It is clear that the frontal view allows to detect very
early fracture initiation, in its primitive stage. A comparison of Tc,glo,
notch values, obtained from lateral (Tc,glo,notch) or frontal (Tc,glo,front)
view, is reported in Fig. 9c. It is clear that the lateral view leads to much
higher values than a frontal view, differently from PS specimens.
However the trend of values with a/W is very similar to lateral values: Tc
is slightly higher at low a/W values, and decreases for a/W values higher
than 0.5. Between 0.2 and 0.5 of a/W, Tc,glo,front is quite stable with an
average value of 2.3 � 0.1 kJ/m2.
Therefore Tc results evaluated from the front view are closer to the
reference values of PS than Tc evaluated from the lateral view. This
experiment points out that much care should be given to the detection of
initiation in the case of SENT, since lateral view and front view give very
different results.
4. Conclusions
In this work, a systematic comparison of various literature ap­
proaches to the measurement of fracture toughness of rubbers with
SENT specimens is presented. SENT geometry was chosen because of its
experimental simplicity, both in the specimen preparation and testing.
Additionally, DIC measurements of strains allowed the verification of
correct values of strain energy density far from the notch, necessary for
tearing energy calculations. The results point out that:
- The specimens with a high L0/W ratio allow a correct measure of Tc
without the use of additional specimens to obtain W0;
- W0 measured from un-notched specimens at the critical stretch ratio
provides an overestimation of energy values, except for very short
notches (a/W < 0.25). Although it is the most common approach
used in the literature, it turned out to be the most inaccurate;
- Tc and Jc parameters provide comparable results;
- In SENT specimens, fracture initiation is better observed from a front
view.
3.4. Comparison with fracture toughness obtained by pure shear
specimens
In order to further investigate whether the fracture toughness values
represent an intrinsic property of the material, Jc values were obtained
by testing PS specimens and were used as reference values for a com­
parison. PS specimens were chosen because of the well established
approach: equation (7) allows us to obtain Jc values with η factor equal
to 1, as demonstrated both analytically [9] and experimentally [32].
Another advantage of such geometry is that the energy release rate
applied does not depend on the notch length. By contrast, PS geometry
needs specific moulds and clamps to host the large width and high forces
generated during the test.
The first experiments on PS revealed Jc values equal to 1.6 � 0.4 kJ/
m2, i.e. values much lower than those measured from SENT specimens.
In this case, fracture onset was observed from the lateral side of the
specimens, as they were for SENT specimens.
It was hypothesized that the lateral view could be misleading for
obtaining a real fracture initiation. In fact, from the lateral side, events
such as increase in fracture propagation rate, or in the notch tip radius
expansion, can be observed. This approach was, however, used to allow
monitoring strains by DIC on the lateral surfaces and monitor fracture
initiation on the same specimen.
Therefore, some fracture tests were repeated and fracture initiation
was monitored frontally, by coating the notch surfaces with a white
talcum powder, to contrast with the black colour of the rubber. By
looking frontally at the notch root, the new black fracture surface can be
distinguished from the white notch surface, and fracture initiation is
taken conventionally at a crack tip opening displacement equal to 0.1
mm, as more extensively described in Ref. [26].
Two PS specimens were tested in this way, and the result was Jc ¼
1.4 � 0.2 kJ/m2, practically equal to the results obtained from the
lateral view. In the case of the SENT specimen, the two approaches gave
very different results. Fig. 10 shows the load-crosshead displacement
curves of the SENT specimens and the initiation points, observed
The result of this work show also some geometry effects, which are
confined to the case of the shortest and longer notches. Since also other
authors pointed out the effect of geometry on fracture toughness mea­
surement for SENT specimens [22,31], it is worth further investigating
the effect of the specimen dimensions. The identification of a minimum
size to obtain intrinsic properties, also in relationship to dissipation
properties of the material, could make the fracture toughness mea­
surement of rubber more reliable. This will be the focus of future works.
Fig. 10. Load-crosshead displacement curves of SENT specimens with a/W ¼
0.25. The points of fracture initiation observed frontally (red square) or later­
ally (blue circle) are displayed on the curves.
10
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Polymer Testing 87 (2020) 106508
Data availability
[12] N.A. Hocine, M.N. Abdelaziz, A. Imad, Fracture problems of rubbers: J-integral
estimation based upon η factors and an investigation on the strain energy density
distribution as a local criterion, Int. J. Fract. 117 (1) (2002) 1–23, https://doi.org/
10.1023/A:1020967429222.
[13] N.A. Hocine, M.N. Abdelaziz, A new alternative method to evaluate the J-integral
in the case of elastomers, Int. J. Fract. 124 (1/2) (2003) 79–92, https://doi.org/
10.1023/B:FRAC.0000009301.54681.ae.
[14] K. Reincke, W. Grellmann, R. Lach, G. Heinrich, Toughness optimization of SBR
elastomers – use of fracture mechanics methods for characterization, Macromol.
Mater. Eng. 288 (2) (2003) 181–189, https://doi.org/10.1002/mame.200390011.
[15] K. Reincke, W. Grellmann, G. Heinrich, Investigation of mechanical and fracture
mechanical properties of elastomers filled with precipitated silica and nanofillers
based upon layered silicates, Rubber Chem. Technol. 77 (4) (2004) 662–677,
https://doi.org/10.5254/1.3547843.
[16] L. Agostani, F. Briatco Vangosa, C. Marano, M.E. Rink Sugar, Application of
Fracture Mechanics to Organoclay Modified Styrene-Butadiene Rubber, 2006,
pp. 411–444.
[17] G. Ramorino, C. Andreana, O. de Feo, T. Ricco, Fracture resistance of natural
rubber/layered silicate nanocomposites. Application of J-testing method, in:
Proceedings of the 13th International Conference on Deformation, Yield and
Fracture of Polymers, Kerkrade, Netherlands, 2006, pp. 505–507.
[18] G. Ramorino, S. Agnelli, R. de Santis, T. Ricc�
o, Investigation of fracture resistance
of natural rubber/clay nanocomposites by J-testing, Eng. Fract. Mech. 77 (10)
(2010) 1527–1536, https://doi.org/10.1016/j.engfracmech.2010.04.021.
[19] C. Marano, M. Boggio, E. Cazzoni, M. Rink, Fracture phenomenology and
toughness of filled natural rubber compounds via the pure shear test specimen,
Rubber Chem. Technol. 87 (3) (2014) 501–515, https://doi.org/10.5254/
rct.14.86950.
[20] F. Camimi, R. Calabr�
o, F. Briatico-Vangosa, C. Marano, M. Rink, Toughness of
natural rubber compounds under biaxial loading, Eng. Fract. Mech. 149 (2015)
250–261, https://doi.org/10.1016/j.engfracmech.2015.08.003.
[21] F. Caimmi, R. Calabr�
o, F. Briatico-Vangosa, C. Marano, M. Rink, J -Integral from
full field kinematic data for natural rubber compounds, Strain 51 (5) (2015)
343–356, https://doi.org/10.1111/str.12145.
[22] M. Torabizadeh, Z.A. Putnam, M. Sankarasubramanian, J.C. Moosbrugger,
S. Krishnan, The effects of initial crack length on fracture characterization of
rubbers using the J-Integral approach, Polym. Test. 73 (2019) 327–337, https://
doi.org/10.1016/j.polymertesting.2018.11.026.
[23] H.W. Greensmith, Rupture of rubber. X. The change in stored energy on making a
small cut in a test piece held in simple extension, J. Appl. Polym. Sci. 7 (3) (1963)
993–1002, https://doi.org/10.1002/app.1963.070070316.
[24] C. Creton, M. Ciccotti, Fracture and adhesion of soft materials: a review, Rep. Prog.
Phys. 79 (4) (2016) 46601, https://doi.org/10.1088/0034-4885/79/4/046601.
[25] R. Sto�cek, O. Kratina, I. Ku�ritka, Focus on future trends in experimental
determination of crack initiation in reinforced rubber, Chem. Listy 108 (1) (2014)
71–77.
[26] S. Agnelli, F. Baldi, T. Ricc�
o, A tentative application of the energy separation
principle to the determination of the fracture resistance (JIc) of rubbers, Eng. Fract.
Mech. 90 (2012) 76–88, https://doi.org/10.1016/j.engfracmech.2012.04.020.
[27] G.J. Lake, C.C. Lawrence, A.G. Thomas, High-speed fracture of elastomers: Part I,
Rubber Chem. Technol. 73 (5) (2000) 801–817, https://doi.org/10.5254/
1.3547620.
[28] M. Jerabek, Z. Major, R.W. Lang, Strain determination of polymeric materials using
digital image correlation, Polym. Test. 29 (2010) 407–416, https://doi.org/
10.1016/j.polymertesting.2010.01.005.
[29] G.J. Lake, A.G. Thomas, The strength of highly elastic materials, Proc. R. Soc. A
300 (1967) 108–119, https://doi.org/10.1098/rspa.1967.0160.
[30] J.R. Rice, P.C. Paris, J.G. Merkle, Some further results of J-integral analysis and
estimates, in: Kaufman (Ed.), Progress in Flaw Growth and Fracture Toughness
Testing, 1973, pp. 231–245 [publisher not identified], [Place of publication not
identified].
[31] A.R. Shahani, H. Shoostar, M. Baghaee, On the determination of the critical Jintegral in rubber-like materials by the single specimen test method, Eng. Fract.
Mech. 184 (2017) 101–120, https://doi.org/10.1016/j.engfracmech.2017.08.031.
[32] S. Agnelli, F. Baldi, F. Bignotti, A. Salvadori, I. Peroni, Fracture characterization of
hyperelastic polyacrylamide hydrogels, Eng. Fract. Mech. 203 (2018) 54–65,
https://doi.org/10.1016/j.engfracmech.2018.06.004.
[33] D. Landes, J.A. Begley, The effect of specimen geometry on JIC, 31 Aug.-2 Sept.
1971, in: H.T. Corten, J.P. Gallagher (Eds.), Fracture Toughness, Proceedings of the
1971 National Symposium on Fracture Mechanics: Proceedings of the 1971
National Symposium on Fracture Mechanics, University of Illinois, UrbanaChampaign, Ill, American Society for Testing and Materials, Philadelphia, Pa.,
1972, 24-24-16.
[34] B. Dong, c. Liu, Y. Wu, Fracture and fatigue of silica/carbon black/natural rubber
composites, Polym. Test. 38 (2014) 40–45, https://doi.org/10.1016/j.
polymertesting.2014.06.004.
The raw/processed data required to reproduce these findings cannot
be shared at this time due to technical or time limitations.
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgements
Erwin Mach Gummitechnik is gratefully acknowledged for providing
the rubber material used for the investigation. This research work was
performed at the Polymer Competence Center Leoben GmbH (PCCL,
Austria) and within the COMET-modul “Polymers4Hydrogen” within
the framework of the COMET-program of the Federal Ministry for
Transport, Innovation and Technology and Federal Ministry for Econ­
omy, Family and Youth, with contributions by the Department of
Polymer Engineering and Science (Montanuniversitaet Leoben). The
PCCL is funded by the Austrian Government and the State Governments
of Styria, Lower Austria and Upper Austria.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.polymertesting.2020.106508.
References
[1] A.A. Griffith, The phenomena of rupture and flow in solids, Phil. Trans. Math. Phys.
Eng. Sci. 221 (582–593) (1921) 163–198, https://doi.org/10.1098/
rsta.1921.0006.
[2] R.S. Rivlin, A.G. Thomas, Rupture of rubber. I. Characteristic energy for tearing,
J. Polym. Sci. 10 (3) (1953) 291–318, https://doi.org/10.1002/
pol.1953.120100303.
[3] M. Klüppel, G. Huang, B. Bandow, Evaluation of tearing energy of elastomer
materials, Kautsch. Gummi Kunstst. 61 (12) (2008) 656–659.
[4] J.R. Rice, G.F. Rosengren, Plane strain deformation near a crack tip in a power-law
hardening material, J. Mech. Phys. Solid. 16 (1) (1968) 1–12, https://doi.org/
10.1016/0022-5096(68)90013-6.
[5] S.-J. Chang, Path-independent integral for rupture of perfectly elastic materials,
J. Appl. Math. Phys. 23 (1) (1972) 149–152, https://doi.org/10.1007/
BF01593213.
[6] H.L. Oh, A simple method for measuring tearing energy of nicked rubber strips, in:
J.R. Rice (Ed.), Mechanics of Crack Growth, ASTM International, 100 Barr Harbor
Drive, PO Box C700, West Conshohocken, PA, 1976, pp. 104–114, 19428-2959.
[7] H. Liu, R.F. Lee, J.A. Donovan, Effect of carbon black on the J -integral and strain
energy in the crack tip region in a vulcanized natural rubber, Rubber Chem.
Technol. 60 (5) (1987) 893–909, https://doi.org/10.5254/1.3536163.
[8] N.A. Hocine, M.N. Abdelaziz, H. Ghfiri, G. Mesmacque, Evaluation of the energy
parameter J on rubber-like materials: comparison between experimental and
numerical results, Eng. Fract. Mech. 55 (6) (1996) 919–933, https://doi.org/
10.1016/S0013-7944(96)00046-X.
[9] B.H. Kim, C.R. Joe, Single specimen test method for determining fracture energy
(JIC) of highly deformable materials, Eng. Fract. Mech. 32 (1) (1989) 155–161,
https://doi.org/10.1016/0013-7944(89)90213-0.
[10] H. Ghfiri, M.N. Abdelaziz, G. Mesmacque, Experimental determination of J on
rubbery materials: influence of finite dimensions, Eng. Fract. Mech. 44 (5) (1993)
681–689, https://doi.org/10.1016/0013-7944(93)90197-Z.
[11] M. Na€It-Abdelaziz, H. Ghfiri, G. Mesmacque, R.G. Nevi�ere, The J integral as a
fracture criterion of rubber-like materials: a comparative study between a
compliance method and an energy separation method, 19428-2959, in: F.
E. Erdogan (Ed.), Fracture Mechanics: 25th National Symposium Entitled "Fracture
Mechanics: New Trends in Fracture Mechanics" Papers, ASTM International, 100
Barr Harbor Drive, PO Box C700, West Conshohocken, PA, 1995, 380-380-17.
11