Mechanical behavior of notched specimens in plane strain
state
João Fonte-Boa
Department of Mechanical Engineering, IST, Technical University of Lisbon, Lisbon,
Portugal
Abstract
The objective of this thesis is to propose a specimen geometry able to isolate the plane strain
state. For that purpose experimental tests were performed, as well as computer simulations using the
ANSYS software.
The first step of the experimental phase was to place the specimen in the fatigue test machine and
submit it to a cyclic axial load until the failure of the specimen. Four types of specimen geometries
were tested with a center notch, having two of them circular notches with radius of 1mm and 2mm.
The other two geometries did not contain circular notches and presented a thickness of 2mm and
10mm. Through the fatigue tests, the crack propagation curves were obtained ("a Vs N") and the
propagation rate ("da/dN Vs ΔK"). These values were used to obtain the parameters of the Paris law
(C and m). The fracture surfaces were observed and presented the expected aluminum alloys
behavior, i.e., striation and coalescence of microcavities mechanisms.
In the computational phase the ANSYS software was used to perform simulations at two
dimensions with crack propagation in order to obtain the stress field in the crack front, the value of the
stress intensity factor (K) for several crack lengths and the corresponding values of the geometric
factor, Y. For the triaxiality parameter, it was found that the notches produce the major contribution in
the transition of state of plane stress for state of plane strain, because in the notches’ vicinity there is a
triaxiality peak (state of plane strain), stabilizing for lower values (state of plane stress) near the
specimen surface.
Keywords: triaxiality parameter, stress intensity factor, crack propagation, plane stress state,
plane strain state
1. Introduction
The fatigue crack propagation in metallic
alloys is a complex phenomenon, on this
account exist various micro mechanisms to
create damage (oxidation, and others) that can
be responsible for the cracks growth. The
crack propagation can be transgranular,
intergranular or mixed according to the
conditions that exist at the end of the crack,
owing to existence of a certain dominant
mechanism. Afterwards, exist various
macroscopic parameters, including the type of
load (stress range, frequency of load, stress
ratio, and others.), the material, the
environment (temperature and atmosphere)
and the geometry of the fractured component
(crack length, stress state), that control the
referred mechanisms and predict the
propagation of the crack.
The stress state clearly affects the
behavior of the alloys. A plane stress state has
a great influence in different phenomena, such
as, in the closure of the crack and in the
propagation of fatigue cracks due to high
temperatures. The differentiation between
plane stress state and the plane strain state is
essential in certain studies of material
behavior. The isolation of the plane stress
state is acquired testing thin specimen, while
the plane strain state is acquired increasing the
specimen thickness or introducing lateral
notches. However, the plane stress state is not
completely eliminated at the surface, which
makes the experimental work more expensive.
The lateral notches allow us to obtain relatively
thin specimen in plane deformation.
The present work pretends to accomplish
the execution of 4 fatigue crack propagation
tests for specific geometries, with the objective
of verifying the notch behavior in the transition
from plane stress state to plane strain state
taking in account a geometry that can isolate
the plane strain state. The tests will be done
with the following geometries: specimen not
notched with 2mm thickness (specimen 4);
specimen not notched with 10 mm thickness
(specimen 2); notched specimen with 12mm
thickness and 8mm notch (R=2mm) (specimen
3); notched specimen 12mm thickness and
10mm notch (R=1mm) (specimen 1). It is
noteworthy to mention that the tests of
specimen 1 to 4 had to be repeated due to the
fact that problems emerged during the first
test. In the present thesis the aluminum alloy
2017 with heat treatment T4 will be used as
study material. The test previously referred will
be performed with maximum loads of 31.3KN
for the thicker specimen (10mm). For the
specimen with an 8mm notch the maximum
load used will be 25.1KN, while for the thinnest
specimen (2mm) the maximum load will not
exceed 5.3KN.
According to Mirone [1], the analysis and
optimization of the plane deformation state is
done in certain specimen through the utilization
of certain parameters to quantify the stress
triaxiality. One of these parameters is defined
by equation (1).
Θ = �����
=� � ∙���� ��� ����
�√�∙����������
� ���������� ������������ �(1)
Equation (1) represents the result of the
ratio between the average hydrostatic stress
(��) and the equivalent Von-Mises stress
(���), where the values of ��� , � , �!! represent the stresses according to x, y and z
directions, respectively. According to Branco et
al. [2], the value of this parameter may vary
from zero for the pure plane stress states, until
5 or 6 for situations of plane deformation.
Another parameter of triaxiality (h) has also
been developed, however it won’t be used in
this work.
2. Experimental Details
The material used to perform the fatigue
tests was the aluminum alloy 2017-T4 heat
treated. The heat treatment T4 corresponds to
an uniform heating of the alloy, followed by a
hardening processed by aging at room
temperature (natural aging) until a stable
condition, according to [3]. The chemical
compositions, as well as the physical and
mechanical properties of this type of material,
are presented in Tables 1 and 2, respectively.
Table 1: Chemical composition of aluminum alloy 2017-T4 (% of mass per element).
Chemical composition [3]
Al 91.5 - 95.5 Cr <= 0.10 Cu 3.5 - 4.5 Fe <= 0.70 Mg 0.4 - 0.8 Mn 0.4 – 1 Si 0.2 - 0.8 Ti <= 0.15 Zn <= 0.25
Outros <= 0.15
Table 2: Physical and mechanical properties aluminum alloy 2017-T4.
Physical and mechanical properties [3]
"#$% 276 MPa "& 427 MPa Ρ 2.79 g/#'( E 72.4 GPa ) 0.33 *& 22%
The fatigue tests were performed,
according to the norm ASTM E647-T [4], using
the average stress and specimen of
conventional geometry M(T). In Figures 1 to 4
we can observe the dimensions and details of
each of the specimen used. The tests were
obtained from the longitudinal transversal
direction of a laminated plate (direction L-T).
Figure 1: Dimensions of specimen 1.
Figure 2: Dimensions of specimen 2.
Figure 3: Dimensions of specimen 3.
Figure 4: Dimensions of specimen 4.
The method implemented consisted in
introducing the specimen in the fatigue testing
machine and submitting it to a constant
amplitude loading until the final fracture,
introducing markings when possible. During
the markings the stress ratio was of 0.01, while
in the rest of the test it would be 0.4. The
objective would be to let the crack propagate
until around 4mm (measured with aid of a
lunette and comparator). At this time the first
marking would be performed during 1mm.
Then the specimen would return to the
propagation state in which the stress ratio is
equal to 0.4 until almost 9mm where the
second marking was made. At last, and if the
specimen hadn’t reached its final fracture, a
last marking would be performed around
14mm of crack length. It is yet necessary to
refer that, as the crack propagated notes were
taken of its length and the corresponding
number of cycles with the intuition of later
being able to elaborate the curves of
experimental "a Vs N".
After all the tests were performed
proceeded the measurement of the fracture
surface. The fracture surfaces were analyzed
in the scanning electronic microscopy (SEM)
with the purpose of being able to observe the
striaction, as well as the coalescence of the
microcavitities provoked by the fatigue. These
two phenomena are most common in ductile
materials as for instance the aluminum alloys.
After the experimental values of a and N
were registered. The graphs "a Vs N" or
propagation curve were built. Later the graphs
"da/dN Vs ΔK" were obtained in order to
determine the propagation velocity. To attain
the graphs of propagation velocity, two
methods were used (one in the specimen 4a
and 4b and the other in the rest of the
specimen). In the specimen 4a and 4b a
method that used polynomial regression of the
propagation curves was used, which later were
derived to obtain the propagation velocity
(da/dN). For the rest of the specimens the
method used consisted in using a function that
returns statistics that describe a linear
tendency that coincides with known data,
based on a straight line graph acquired by the
application of the minimal square method to
the known values. It is an incremental
polynomial method with 5 consecutive known
points. The value of ΔK was obtained with the
aid of equation 2, with the value of Y being
calculated through the expression 3.
Consequently the values for the curves "da/dN
Vs ΔK" were obtained. To reach the
parameters of the Paris law (C and m) the
author used a potential regression of the
previous curve under a logarithmic scale.
+, = - ∙ � ∙ √./ (2)
- = �sec 34567�� 8
(3)
All of the experimental tests were
performed in a servo-hydraulic fatigue
machine, with a load capacity of 100kN,
connected to a computer for data control and
acquisition. All of the experiments were made
at room temperature and with a frequency of
10Hz. The specimens were attached to the
machine with hydraulic bonds.
3. Numerical procedure
There are 4 different types of specimens
tested in this work. However, in the
computational analysis only 2 of them were
investigated. The specimens don’t have
circular notches, one of them has 10mm and
the other has 2mm of thickness. Nonetheless,
it was decided to do a 2 dimension simulation.
The software used for this simulation was
ANSYS V11.0 and Microsoft Office Excel 2007
for the results analysis. The main objective of
this analysis was to determine the
computational stress intensity factor, the stress
distribution at the end of the crack and to study
the stress triaxiality in the specimen. The
behavior of the specimen was studied with
different crack lengths of 1mm spacing
between them. With this and with the help of
the ANSYS program a new value of ΔK was
acquired for each a, so that later a comparison
could be made with experimental values and to
permit the elaboration of the "Y Vs a"
by using expression 3. With the
graphs, an expression could now be developed
to calculate a value of numerical
of polynomial regressions of the curves
mentioned.
Relatively to the construction of the used
mesh, as well as the modeling of the specimen
by means of FEM the author had to take in
consideration various aspects and details
geometry and boundary conditions used refer
to only half of the specimen due to the existing
symmetrical conditions.
Firstly the KEYPOINTS were defined in the
ANSYS program, followed by the division of
specimen in 6 symmetrical disposed
In this work 3 types of mesh were studied
One more less refined and another one more
refined than that which was used for the final
analysis. The study of the mesh was done with
the initial crack length. To find the various
elements that constitute the mesh, the lines
that compose the geometry of the specimen
were divided in smaller lines. To perform the
study of the mesh convergence t
command (mesh energetic error) of ANSYS
was used, and the values of equivalent
Mises stress was obtained, having both
parameters converged to acceptable values
figure 5 we can observe the mesh used in the
critical zone of the problem (fro
crack). In this area of the specimen the mesh
was the most refined possible without causing
harm to the analysis time and quality of the
results. In the rest of the zones the mesh
refinement was less refined
compromising the quality of the results
could be made with experimental values and to
"Y Vs a" graphs
With the "Y Vs a"
expression could now be developed
numerical Y, as a result
of polynomial regressions of the curves
Relatively to the construction of the used
of the specimen
by means of FEM the author had to take in
consideration various aspects and details. The
geometry and boundary conditions used refer
to only half of the specimen due to the existing
were defined in the
followed by the division of
disposed areas.
In this work 3 types of mesh were studied.
and another one more
refined than that which was used for the final
analysis. The study of the mesh was done with
To find the various
elements that constitute the mesh, the lines
that compose the geometry of the specimen
To perform the
study of the mesh convergence the ERNORM
command (mesh energetic error) of ANSYS
equivalent Von-
stress was obtained, having both
parameters converged to acceptable values. In
figure 5 we can observe the mesh used in the
critical zone of the problem (front side of the
In this area of the specimen the mesh
was the most refined possible without causing
harm to the analysis time and quality of the
In the rest of the zones the mesh
less refined without
e results.
Figure 5: Detail of the front side of the crack
In respect to the type of element used
owing to the fact that the modeling is done in
2D the ANSYS manual [5
quadratic element PLANE183 of 8
type of element has an above average
behavior in irregular meshes as the one that
exists in the front side of the crack (F
The boundary conditions of the problem
are the areas in which the bonds are attached
to the specimen, which had a spec
due to the fact that they are zones that the
movement is severely restricted
to follow the suggestions of
which the inferior bond the movement is
restricted in all directions and in the superior
bond the movement is restricted only in the
horizontal direction (X-axis
specimen, the type of element used is the rigid
element MPC 184, because the
manual [5] advises this type of element for
undeformable areas (bond area
4. Results and
Initially only 4 tests were suppose
performed, but since two of them didn’t run as
expected, 6 were performed. However it was
decided not to present the results of specimen
1b for the reason that the corresponding
results were considerably
Detail of the front side of the crack.
In respect to the type of element used,
owing to the fact that the modeling is done in
[5] suggests the solid
PLANE183 of 8 nodes. This
type of element has an above average
behavior in irregular meshes as the one that
exists in the front side of the crack (Figure 5).
The boundary conditions of the problem
are the areas in which the bonds are attached
, which had a special attention,
due to the fact that they are zones that the
movement is severely restricted. It was chosen
to follow the suggestions of Serrano [6], in
which the inferior bond the movement is
restricted in all directions and in the superior
nt is restricted only in the
axis). In this zone of the
specimen, the type of element used is the rigid
because the ANSYS
dvises this type of element for
bond area).
Results and Discussion
were supposed to be
performed, but since two of them didn’t run as
expected, 6 were performed. However it was
decided not to present the results of specimen
1b for the reason that the corresponding
y bad.
Figure 6: Propagation curves of fatigue
Through the observation of Figure 6 it is
possible to verify that the test where the
velocity growth of the crack was higher in
specimen 2, followed by specimen 4b, then
specimen 1a, then 4a, and finally specimen 3
Even though specimens 4a and 4b were
identical, it is possible to verify that the first has
9: (number of initiation cycles) higher
second one, i.e. the crack takes longer to
begin propagating in specimen 4a
the specimens 1a and 4b, with thicknesses of
12 mm and 2mm respectively, it was possible
to verify that these suffered a final fracture with
a very similar number of cycles
fact that the length of the crack
than 4b. The specimens 1a, 2, 4a and
a higher N in the initiation phase and a
in the propagation phase, comparatively to
specimen 3.
Figure 7: Curves "da/dN Vs
0
5
10
15
20
25
0 1000000 2000000
a (
mm
)
N
5,00E-07
5,00E-06
5,00E-05
1 10
da
/dN
(m
m/c
ycl
e)
ΔK (MPa*m1/2)
fatigue tests.
Through the observation of Figure 6 it is
possible to verify that the test where the
velocity growth of the crack was higher in
specimen 2, followed by specimen 4b, then
a, then 4a, and finally specimen 3.
Even though specimens 4a and 4b were
identical, it is possible to verify that the first has
higher than the
i.e. the crack takes longer to
begin propagating in specimen 4a. Considering
with thicknesses of
it was possible
to verify that these suffered a final fracture with
a very similar number of cycles, despite the
is much larger
1a, 2, 4a and 4b have
in the initiation phase and a lower N
comparatively to
/dN Vs ΔK".
It was from the graphs of Figure 7 that the
parameters "C" and "
(expression 4) were obtained
parameters were obtained with potential
regressions. The ideal situation would be to
have residues as close as possible to the
Table 3 will present all of the referred data
Relatively to the graph analysis it is
feasible to observe that the
curves in Figure 7 have a very
behavior, except for specimen
part. In other words, in all of studied case
cracking velocity was quite identical
;5;< = =
Table 3: Summary of the parameters of the Paris law of the various tests
C
Specimen 1a 2.7515e-9Specimen 2 1.5745e-11Specimen 3 1.1466e-9Specimen 4a 1.4621e-10Specimen 4b 2.1225e-7
The values of C and
author are in the range provided by the theory,
mainly the value of m,
located between 2.7 and 4.
occur due to the fact that the error of the
square of the residue (>8) tests. In test 3 it doesn´t reach
reflected in the results that don’t
reality accurately.
Relatively to the fracture surfaces
chosen only specimen 3,
aspects to be studied are visible
Figure 8: Fracture surface of specimen 3
2000000
Specimen 1a
Specimen 2
Specimen 3
Specimen 4a
Specimen 4b
10
Specimen 1a
Specimen 2
Specimen 3
Specimen 4a
Specimen 4b
Markings
It was from the graphs of Figure 7 that the
"m" of Paris Law
were obtained. These
parameters were obtained with potential
The ideal situation would be to
have residues as close as possible to the unity.
will present all of the referred data.
Relatively to the graph analysis it is
feasible to observe that the all of the presented
curves in Figure 7 have a very similar
except for specimen 4b in its final
l of studied cases the
velocity was quite identical.
∙ ∆+@ (4)
Summary of the parameters of the Paris law of the various tests.
M &A
9 5.0577 0.96054 11 8.1443 0.94413 9 4.9194 0.89123 10 6.8140 0.91104 7 2.3419 0.95581
and m attained by the
author are in the range provided by the theory,
, since it should be
4. Such an event may
occur due to the fact that the error of the
) is quite high in some
test 3 it doesn´t reach 0.9, which is
reflected in the results that don’t replicate the
fracture surfaces it was
3, since the principal
aspects to be studied are visible.
: Fracture surface of specimen 3.
Zone 1
Zone 2
The fracture surfaces are representative of
the different types of fractures due to fatigue
and in them it is possible to identify two distinct
regions, as well as the markings, labeled in
Figure 8.
There are 2 identified zones in the fracture
surfaces. Zone 1 is a smooth region with a
silky and bright aspect, caused by the contact
of the crack surfaces during the propagation
phase [7]. The second region identified by the
fracture surfaces have a more irregular aspect
than the first, much less bright, presenting
various irregularities. In this zone occurs the
final fracture of the specimen when the
transversal section (not cracked) it is not able
to support the applied stress.
. On behalf of the thicker specimens, such
as specimen 3, the propagation line tends to
be curved and this fact is accentuated as we
head towards the interior of the specimen. This
happens due to, in the case of the thinner
specimens, the probable plane stress state of
the specimen due to the fact that it has only
2mm of thickness. In the case of the thicker
specimens the propagation lines tend to curve
as it advances to the interior of the specimen,
owing to the fact that the specimen is close to
the plane strain state. Close to the surface of
the specimen the fact that the lines don´t have
an accentuated curvature is due to the plane
stress state that occurs at the surface of the
specimen.
Figure 9, which was taken from the
scanning electronic microscope shows the two
most common phenomenon in ductile
materials (coalescence of microcavities and
striaction), as is the case of the aluminum
alloys.
Figure 9: Striation and coalescence of microcavities.
The computational analysis was performed
with the goal of developing a three-dimensional
numerical model that would simulate the
automatic propagation of the cracks and
subsequently compare the acquired results
with the experimental ones. However, after
various tries and intensive research on the field
of study, the author concluded that his
implementation is quite complex and would
involve a three-dimensional analysis. Owing to
the lack of time for the execution of the
computational part it was decided by the
author that only two-dimensional computational
analysis would be performed to specimens 4a
and 4b and to specimen 2.
Focusing on the value of ΔK only the
values of specimen 4a will be presented, since
the remaining results (2 and 4b) follow a quite
similar tendency relatively to the results of
specimen 4a.
Coalescence of microcavities
Striaction
Figure 10: Comparison of curves ΔK Vs a of specimen 4a.
Analyzing the figure 10 it is possible to
verify a certain discrepancy between the
experimental and computational values, more
accentuated as the length of the crack
increases. Such a discrepancy has an
associated error of 44.5% at the beginning and
44.3% at the end. The error of this specimen
between the computational and experimental
values is high; however it is the lowest of the
three that were studied. Despite this
discrepancy, it’s possible to verify that the
format of the curves, experimental and
computational, has a similar development.
Figure 11 shows the development of the Y
value with the crack growth for the specimen
4a. Through observation of figure 11 it was
found that the experimental and computational
curves don’t coincide, or even close, with
errors in the magnitude of 50%. This high error
occurs probably due to the fact that the
analysis was done in two dimensions.
However, both curves have a quite identical
behavior, with a decline in the initial part, and
as the crack propagates that decline increases,
which agrees with the theory provided for this
type of analysis. To obtain the graph of the
experimental part expression 4 was used, with
a central crack of length 2a in a finite plate of
width W, according to [7]. The computational
curve was acquired by using expression 3. The
value of ΔK used was obtained from the finite
element program ANSYS, being the rest of the
values the same, either for the experimental
part either for the computational part.
Figure 11: Graph "Y Vs a" of specimen 4a.
Finally a polynomial regression of third
order was elaborated to the computational
curve to obtain an expression for the
geometrical factor of stress intensity (Y). The
regression (expression 5) was attained with a
fairly reduced residue (>8 = 0.9866).
- = �−9,1009 × 10J�/� + �4,1135 × 10��/8 −
16,251 × / + 2,0421 (5)
As seen in Figure 12, an expressive
variation appears of the equivalent stress of
Von-Mises in the notch surroundings, i.e.
approximately around the 3.5mm. However, as
we go along the width of the specimen towards
its exterior it is possible to verify a tendency of
the stress value to the remotely applied load
(63,5MPa in the case of specimen 4a).
Figure 12: Distribution of Von-Mises stresses at the front side of specimen 4a.
In relation to the triaxiality parameter we
can observe the results of Figure 13. As it can
be seen in Figure 13 the triaxiality parameter
increases significantly near the notch root, and
0
5
10
15
3 5 7 9
ΔK
(M
Pa
*m
1/2
)
a (mm)
ΔK Vs a
Experimental
Computational
0
1
2
3
0 0,002 0,004 0,006 0,008
Y
a (m)
Y Vs a
Computational
Experimental
0
1000
2000
3000
4000
0 10 20 30Vo
n-M
ise
s st
ress
(MP
a)
Width of specimen(mm)
Evolution of Von-Mises stress
then tends to converge to a minimum value,
that can be verified in the rest of the specimen.
This tendency can be confirmed with the
visualization of the evolution of Θ in a plane
above the crack. Still the tendency of the
parameter Θ is to reach a peak of triaxiality
around the root of the notch, converging later
to a lower value (about half), corresponding to
a mixed state (plane stress and strain), but
closer to the plane stress state. This behavior
agrees with the theoretical fundamentals.
Figure 13: Evolution of triaxiality parameter of specimen 4a.
5. Conclusions
The main conclusions of this study were
the following:
Relatively to the experimental tests it is
significant to highlight that the obtained results
agree with the theory, with an exception of
curves "da/dN Vs ΔK", more specifically in the
values of the constants of the Paris law (C and
m). This fact occurs owing to the expression
used to calculate the geometric factor Y (see
equation 3), only for central notches, like the
ones used in the specimen of this thesis.
However, the effect of the circular notches is
not taken in consideration and therefore the
possible existence of this discrepancy with the
theory; According to the tonality of the fracture
surfaces (light or dark) that the beach mark
present are due to the different velocities of the
crack propagation. Zone 1 of Figure 8 presents
more irregularities than zone 1, since it is in
this zone that the final fracture occurs, coming
about in an instantaneous form. The
propagation line of the crack, in the thinner
specimens (4a and 4b) tends to be straight,
whereas in the thicker ones the curve tends to
curve as it advances towards the interior of the
specimen. This occurrence proves that in
thicker specimens the plane stress state is at
the surface of the specimen, evolving to a
plane strain state as we head towards the
interior of the specimen. The marking lines in
specimens 1 and 3 have a tendency to curve
more, since these specimens other than the
central notch, have a circular notch that
accentuates even more the plane strain state
in the interior of the specimen and makes the
plane stress state at the surface not as clear
as in the other cases, existing a state closer to
the plane strain state than to the plane stress
state. Consequently, the first conclusion is that
the ideal geometry is to isolate the plane strain
state is of M(T) specimens not very thick and
with circular notches.
Considering the computational analysis the
ΔK and the geometric factor Y values are
closer to the experimental values for small
crack lengths, increasing lightly the
discrepancy with the increasing of the crack
size. It is noteworthy that even though the
results have some discrepancy the evolution of
the graphs " ΔK vs a" and “Y vs a" have
identical developments. However, the values
obtained always have a high error, which is
probably due to the fact that the analysis was
done in two dimensions. The value of the
plastic radius had very reduced errors in the
experimental part, in the magnitude of 5%, of
0,3
0,4
0,5
0,6
0,7
0,00E+00 1,00E+01 2,00E+01
θ
Width of specimen(mm)
Evolution of triaxiality parameter
Parameter in the
crack line
Parameter above
the crack line
which in the computational part those errors
were much higher comparatively to the theory.
One of the plausible explanations for this fact
is that the simulations were only done in 2D. In
relation to the triaxiality parameter the results
obtained agree with what was expected, i.e. a
peak of triaxiality was observed at the
surroundings of the notch. This behavior
concurs with what was expected, since the
regions of the specimen away from the zone of
influence of the notch (in terms of Von-Mises
stress field) do not suffer any effect of triaxiality
imposed by this geometrical constrain. This
evolution of the triaxiality parameter confirms
the utility of the notches in the transition from
plane stress state to plane strain state. In a
region close to the notch one may have plane
strain state, of which as one gets away from
the end of the specimen a mixed stated is
verified, but closer to the plane stress state.
The geometries used were, in fact, able to
attain a state close to the plane strain state in
the region of crack propagation, as it was
demanded at the beginning of the dissertation.
The value acquired for the parameter Θ,
despite the fact that it does not approach the
theoretical values (5 or 6), it can already be
considered a plane strain state, since these
values can only be reached in a theoretical
situation, values of this magnitude are rarely
obtained.
References
[1] G. Mirone. Role of stress triaxiality in
elastoplastic characterization and ductile
failure prediction. Engineering Fracture
Mechanics, Vol. 74, pp. 1203-21, 2007.
[2] R. Branco, J. M. Silva, V. Infante, F.
Antunes and F. Ferreira. Using a standard
specimen for crack propagation under
plain strain conditions. International
Journal of Structural Integrity, Vol.1 No.4,
2010.
[3] http://www.matweb.com/
[4] ASTM. Standard terminology relating to
fatigue and fracture testing. ASTM E
1823, 1997.
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