Fracture toughness specimens: 2-D vs 3-D finite element
modelling
STATE OF STRESS MODELLING BY 2-D FINITE ELEMENT ANALYSIS OF
FRACTURE TOUGHNESS SPECIMENS
Dražan Kozak1, Liliana Blaj2, Franjo Matejiček3
1 PhD, Assistant Professor, University of Osijek, Mechanical
Engineering Faculty, Trg I. B. Mazuranic 18, HR-35000 Slavonski
Brod, Croatia, Tel. +385 35 446 188, Fax: +385 35 446 446, E-mail:
[email protected]
2 PhD, Associate Professor, University “Polytechnica” of
Timisoara, Faculty of Mechanics, Bd. Mihai Viteazu No. 1, RO-1900
Timisoara, Romania, Tel. +405 619 7658, Fax: +405 629 3767, E-mail:
[email protected]
3 PhD, Professor, University of Osijek, Mechanical Engineering
Faculty, Trg I. B. Mazuranic 18, HR-35000 Slavonski Brod, Croatia,
Tel. +385 35 446 188, Fax: +385 35 446 446, E-mail:
[email protected]
Summary:
This paper should clarify some details related to finite element
(FE) analysis of the single edge notch bend (SENB) specimen with
X-shaped welded joint as an example. The specimen consists in a
complex geometry as well as material mismatch, what makes the FE
modelling more difficult. The main advantage of 2-D calculations is
the short time needed for the computation of any fracture
parameter, but it involves assuming the state of stress. This
depends on the thickness of the specimen, plane section position
and loading level. Plane strain state (PE) is very conservative
approach valid for thick structures only, while plane stress state
(PS) is appropriate in the case of thin specimens. The use of 3-D
finite elements is necessary for the specimens with medium
thickness or in the case when the symmetry of the specimen
according to the thickness is not present.
1. Introduction
Integrity assessment of structures where cracks may appear
during production or exploitation (f. i. welded structures)
presents imperative importance today. Fracture behaviour is usually
characterised by stress intensity factor K under linear-elastic
conditions or by crack opening displacement (COD) for
elastic-plastic materials. Also, J-integral as a most applied
parameter could be used for linear-elastic as well as
elasto-plastic material behaviour. The value of these parameters
may be determined analytically for very simple problems,
experimentally during relatively complex and expensive testing and
numerically by finite element packages, which is mainly most
practical.
A lot of conventional FE packages (f.e. ABAQUS, ADINA, ANSYS
etc.) have developed code for two-dimensional and/or
three-dimensional K and/or J-integral calculation. However, 2-D
finite element models demand assumption about the state-of-stress
that governs in the specimen. This is not questionable by very thin
structures where plane stress (PS) state prevails or by very thick
structures with plane strain (PE) state. But, which state of stress
is more appropriate for the structures with medium thickness?
Three-dimensional effects near a crack tip in a ductile three-point
bend specimen were investigated recently [6, 8, 9]. To reveal the
effects of stress states on crack-tip constraints many numerical
analyses have been produced and summarised in the works [1, 2, 3].
In a general three-dimensional configuration it is needed to
distinguish between [7]:
- the in-plane constraint, which is directly influenced by the
specimen dimensions in the direction of the growing crack, i.e. the
length of the uncracked ligament for straight through cracks, and
additionally by the global load configuration (bending or tension),
and
- the out-of-plane constraint, which is affected by the specimen
dimension parallel to the crack front, i.e. the specimen thickness
for straight through cracks.
In most cases the in-plane and out-of-plane constraint are mixed
in such a way that their effects cannot be separated, but the
conceptual difference should be kept in mind, at least, to
understand that the common characterisation as plane strain
condition is insufficient to describe three-dimensional stress
uniquely. However, it is fairly difficult to bring one unique and
precise conclusion. In any case, the decisions to do a plane stress
or plane strain analysis should not be subjective. It has to be
somehow quantified. An additional problem is the fact that level of
loading plays also the role by 2-D state-of-stress assignment. The
situation becomes more complex in the case of irregular shaped weld
joint with present different strength of base material related to
cap or root metal. One useful approach is so-called mixed
state-of-stress modelling proposed by Newman et al [7].
On the other hand, solid finite element modelling demands much
more CPU time and analyst experience, because 3-D modelling of
cracked structures is always connected to specific problems (e.g.
crack faces modelling, boundary conditions setting, etc.).
Processor working time is significant longer than in 2-D
calculations, but the obtained results are much closer to
reality.
This paper analyses the differences in the crack tip opening
displacement CTOD (5) numerical calculation, if pure PS, pure PE
and mixed state-of-stress approach is applied on the SENB fracture
toughness specimen with medium value of thickness (in this case 36
mm). Value of CTOD (5) is also compared with that obtained by
experiment.
2. Plane stress and plane strain conditions
The stress or strain state is always in three dimension. But in
most cases, they can be simplified to either plane strain or plane
stress by ignoring either the out of plane strain or plane stress.
In a thin body generally, the stress through the thickness (z)
cannot vary appreciably due to the thin section. Because there can
be no stresses normal to a free surface, z = 0 throughout the
section and a biaxial state of stress results [5]. This is termed a
plane stress condition (see Fig. 1a). The material fractures in a
characteristic ductile manner, with a 45o shear lip being formed at
each free surface.
In a thick body, the material is constrained in the z direction
due to the thickness of the cross section and z = 0, resulting in a
plane strain condition (Fig. 1b). Due to Poisson's effect, a
stress, z, is developed in the z direction. Maximum constraint
conditions exist in the plane strain condition, and consequently
the plastic zone size is smaller than that developed under plane
stress conditions. The material from the centre of the component
however, is not free to deform laterally as it is constrained by
the surrounding material. Thus, the stress state tends to plane
strain (triaxiality) and fracture in this region is brittle.
Therefore, shear failure tendency in ductiles is negligible under
triaxial hydrostatic loading. The plane stress condition will
results in a higher out of plane shear stress than the plane strain
condition for a given maximum stress. Again, the shear stress would
promote yielding, not fracture. According to theory of elasticity,
the component of stress z in the thickness direction is defined
as:
state
PS
0
state
PE
)
(
=
+
=
z
y
x
z
s
s
s
n
s
(1)
In the same time, the component of strain z could be determined
from:
[
]
state
PS
)
(
state
PE
0
)
1
y
x
z
y
x
z
z
E
E
+s
s
n
e
s
(s
-n
s
e
-
=
=
+
=
(2)
z
x
B
thickness B
y
s
s
z
thick plate
no contraction
s
thin plate
free contraction
B
y
z
s
z
PE
s
PS
s
Fig. 1a) Three-dimensional stress state at the crack-tipFig. 1b)
Biaxial stress state
2.1 Plasticity zone
The plastic zone size rp by two-dimensional finite element
calculation is conditioned by assumed state of stress and hence
they are in very close interaction. Typical qualitative shape of
plastic zone for fracture toughness specimen with straight crack
front according to the thickness is presented on the Fig. 2a). The
crack tip material in the mid-plane of the specimen tries to
contract in the z direction, but is prevented from doing so by the
surrounding material. This is the reason why there the radius of
plastic zone is the smallest. On the Fig 2b) state-of-stress
variation depending on both thicknss of the structure and plane
section position is depicted.
Crack length
Uncracked
ligament
r
p
(PS)
r
p
(PE)
Plastic zone
r
p
=
r
p
(
z
)
z
Thickness
Crack length
Uncracked
ligament
(% PE)
on the surface
100% PE
in the middle
(% RN)
in the middle
Thin
-
walled structures
(dominant PS state)
Thick
-
walled structures
(dominant PE state)
100% PS
on
the surface
Thickness
Fig. 2a) Characteristic plastic zone shape
Fig. 2b) State-of-stress variation with thickness
Plane stress assumption is valid for very thin-walled
structures, while plane strain is predominant condition in
structures with large thickness. Plastic zone boundary as a
function of the angle in polar coordinate system with origin in the
crack-tip may be estimated as:
222
o
2
I
o
YS
()(1)3sincos whit
22
1
2
rrk
K
r
jj
j
ps
éù
=-+
êú
ëû
æö
=
ç÷
èø
(3)
where KI is stress intensity factor for the mode I of crack
opening, YS is often taken as the average of the yield and ultimate
strengths, which is referred to as the flow stress afterwards and
constant k = 0 (plane stress) or k = 2 (plane strain). This could
be illustrated graphically for =0,3 (Fig. 3).
1,25
y
/
r
o
x
/
r
o
1,0
plane
stress
0,83
0,16
0,37
plane
strain
crack
-
tip
Fig. 3 Plastic zone boundary under PS and PE condition ahead the
crack-tip
In most of real fracture problems with structures of medium
thickness, the state of stress is in transition between two
aforementioned states and it depends on the plastic zone size.
Plane strain conditions exist at the boundary if the plastic zone
is small compared to the thickness, but the stress state is
predominantly plane stress if the plastic zone is greater than half
the specimen thickness. One can conclude that state-of-stress is
mixed where it changes from plane strain at the tip to plane stress
state at a critical distance rc from the tip. Thus, the critical
distance from the crack tip at which conditions of plane stress
dominate depends on the specimen thickness.
2.2 Mixed state-of-stress
The idea of modelling state-of-stress as a combination of PE in
the core around the crack-tip and PS out of that core was proposed
by Newman et al [7] using standard compact tension (CT) specimen.
However, the criteria to define the size and position of the
rectangular region where the PE governs were unclear. This approach
was more inaccurate in the case of stable crack growth, because the
dimensions of fixed PE core were constant. Obtained results were
better than earlier, but with lack of mathematical and physical
explanation. It was interesting that very small PE region about the
crack-tip influenced very hard the results. Namely, the area of
this region was only 1% and 2,5% for CT and SENB specimen,
respectively related to whole area of the specimen plane. The
position and size of the plane strain core on example of CT
specimen is presented on the Fig. 4.
crack
-
tip
0,125
W
0,05
W
a
0
W
-
a
0
1/2 of CT specimen
PS
PE
Plastic zones by
maximum
force
0,6
W
0,2
B
B
=25,4 mm
W
=50,8 mm
a
0
/
W
=0,65
Fig. 4 Plane strain (PE) core around the crack-tip [7]
Newman's approach was extended by Kozak et al [4] defining PE
region shaped and sized as a plastic zone around the crack-tip.
Both, PE region size and PE region shape should be modified during
successive increasing of the loading level. Namely, material in
plastic zones hardened with the factor of approximately
e
3
R
×
, so an assumption of PE condition there has a physical
meaning.
2.3 In-plane and out-of-plane constraints
The relatively thin plates (25 mm thickness and less) used in
ships and bridges do not develop significant constraint through the
thickness and are therefore in a state of plane stress. The
structure thickness larger than 25 mm may more influenced crack tip
stress field. The constraint can be literally defined as a
structural obstacle against plastic deformation which is induced
mainly by the geometrical and physical boundary conditions but can
also be due to mismatch of material properties in a heterogeneous
joint [10]. The in-plane constraint is associated with the boundary
conditions and in-plane geometry of the plane, while the
out-of-plane constraint is mainly caused by the stress component z
[1].
The overall structural conditions determine the local triaxility
of stresses, commonly defined as the ratio of the hydrostatic mean
stress to the von Mises equivalent stress in the specimen [2]:
(
)
(
)
(
)
1
22
2
2
1
()
3
1
2
xxyyzz
xxyyxxzzyyzz
k
sss
ssssss
++
=
éù
-+-+-
êú
ëû
(4)
where xx, yy and zz are the stresses in the x, y and z
directions, respectively. In this sense, stress triaxility
magnitude may be understood as a local constraint. Very often in
use is ratio z/(x+y), which implies whether the stress state is
similar to the plane strain state or the plane stress state. This
ratio is mainly uniform over most of the specimen thickness (along
the crack front) and drops to zero very near the free surface. Its
value should be about 0,28 in the interior of the specimen for the
elastic case and approaches 0,47 with increasing plastic
deformation. Both parameters show in the rule the same tendency of
the material responses. The stress triaxility is a description of
the 'easiness' of the plastic deformation. Greater value of stress
triaxility parameter means greater constraint and the stress state
closer to the plane strain. According to the references, for the
parameter of stress triaxility greater than 2,5, it is reasonable
to suppose significant out-of-constraint and plane strain stress
state.
3. Numerical example
Fracture toughness specimen with homogeneous X - weld joint was
notched in the middle. The cross section of the specimen is
BxB(W)=36x36 mm. Base material (BM) of the specimen is high
strength low alloy (HSLA) steel with yield strength (YS = 712 MPa)
lower than weld metal (WM). Strength yield mismatch factor was
about M=1,22. The ratio of the crack length and specimen width was
a/W=0,27.
Due to present symmetry only one half of the specimen was
considered by finite element analysis. Five planes through the
thickness have been modelled with different portion of the elements
in plane strain state (Fig. 5). Pure PS was assumed only to
specimen surface (plane A). As it is mentioned before, very small
percent of PE elements is sufficiently to be assigned to make model
more realistic. Here it amounts only 1% of PE elements in the
middle of the specimen (plane E). The PE distribution in the
interior of the specimen is unknown, so it were assumed 0,1% of PE
(plane B), 0,25% of PE (plane C) and 0,4% of PE (plane D).
a
0
=9,912 mm
100% PS on the
specimen surface
0
2
1
A
E
D
C
B
B
S
=144 mm
Portion of PE elements, %
E
D
C
B
A
0,5
1,5
Through thickness planes
1% of PE in the middle
of the specimen
B
=36 mm
Fig. 5 Planes A-E with different portions of elements in PE
stress state
The goal of such a modelling is to assess the influence of
different plane strain portions on the calculation of crack-tip
opening displacement CTOD (5). Measuring of the local CTOD (5)
displacement is characteristic for the specimens with present
materials dissimilarity. It is measured directly with the strain
gauge displaced for 2,5 mm from the crack-tip parallel to the
x-axis.
The coarse finite element mesh consisting of 8-node
isoparametric elements is depicted on the Fig. 6. Stress
concentration was assigned to the crack-tip after that mesh was
generated automatically. First row around the sharp crack were
singular elements. Total force has been distributed on two nodes to
reduce stress concentration on the place where the load acts.
Analysed region is enlarged in the Fig. 7 with the aim to show
whether elements were in PE conditions.
Fig. 6 Finite element mesh of the one half of the SENB
specimen
2
-
D FE model for the
MIDDLE of the
specimen (1 % PE)
0,25 % of
PE elements
0,1 % of
PE elements
uncracked ligament
crack tip
E
D
C
B
A
CTOD (
d
5
)
node
7,2 mm
Base material
Weld
Fusion line
0,4 % of
PE elements
1 % of
PE elements
2
-
D FE model for the
SURFACE of the
specimen (100 % PS)
Fig. 7 Finite element models with different portions of the
elements in the PE state
4. Results and discussion
CTOD (5) results with increasing loads for FE models with
different portions of PE elements are presented in the Fig. 8. It
is obviously that experimental value of CTOD (5) is closer to PS
solution for low loading levels, but force increasing causes
deviation experimental curve to PE solution. This is the evidence
that PE region size should not be constant during test simulation.
It is also very interesting that fracture toughness variation is
lower comparing the FE models with 1% of PE (plane E) and 100% of
PE, than FE models with 0,1% of PE (plane B) and 0,25% of PE (plane
C).
0
50
100
150
200
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
CTOD (
d
5
), mm
F, kN
Fig. 8 F-CTOD (5) curves for FE models with different portions
of PE elements
Note that only 0,1% of elements with assumed PE stress state
around the crack-tip is enough to model the problem more accurate
than FE model with pure PS or pure PE. If we assume PS state for
whole specimen, CTOD (5) displacement will be overestimated for
more than 30% for maximum loading. On the other hand using rigid
finite models with pure PE will underestimate the fracture
toughness for almost 50%.
It is valuable to present these results as curves, where CTOD
(5) is in function from the percent of PE elements, with F=const
(Fig. 9). Thus, better inclination of the experimental line from PS
to PE stress state with load increasing is visible. Hence,
realistic stress-strain distribution at the moment of crack
initiation or unstable fracture could be better presented. This is
very useful in the case when the reasons of the failure should be
investigated and explained, especially for the welded structures
with yield strength mismatch effect, where the crack path deviation
is possible. The yielding is usually directed from the material
with higher yield strength (weld metal in our case) to soft
material (base metal here), but highest maximum principal stress is
mainly just under the crack tip. Higher stresses are located in the
harder WM than in the softer BM. The stress will reach its peak
value at a distance less than two times the local CTOD.
Therefore, presences of the overmatched weld root pass effects
to stress-strain distribution at the vicinity of a crack tip. It
can be expected that an increasing of stresses in WM will prevent
from the risk of brittle fracture. If brittle fracture in WM does
not occurs, the initiation and growth of stable crack propagation
are governed by local plasticity in the base metal.
0,0
0,1
0,2
0,3
0,4
Fig. 9 CTOD (5) results for FE models with different portions of
PE elements by F = const
5. Conclusions
Details of state-of-stress assigning by two-dimensional finite
element (FE) analysis of the single edge notch bend (SENB) specimen
with X-shaped welded joint as an example were considered. Both,
complex geometry and materials dissimilarity makes the FE modelling
more difficult. An assumption of pure plane stress or pure plane
strain state is valid for only very thin and very thick structures,
respectively. In this paper fracture toughness specimen with medium
thickness was analysed (B=36 mm). Therefore, mixed state-of-stress
approach is necessary. To this purpose, new improved approach was
proposed, which foreseen plane strain state in the region where von
Mises equivalent stress overcomes yield strength of the material
and plane stress state out of this region. This is proven comparing
experimental measured CTOD (5) displacements with the same obtained
by five FE models with different portion of elements in PE state
around the crack-tip. Portion of PE elements depends on the
position of the model through the thickness of the specimen. It is
evident that significantly low part of elements with assumed PE
state (lower than 0,1%) plays decisive role on the numerical
results. Also, the state-of-stress in the vicinity of the crack-tip
varied from PS to PE as the force increases.
Acknowledgements
The authors gratefully acknowledge to Ministry of Science and
Technology of Republic of Croatia for support to their
investigations sponsored in the research project 0152-018.
6. References
[1]Guo, W., Three-dimensional analyses of plastic constraint for
through-thickness cracked bodies, Engineering Fracture Mechanics,
62, 1999, pp 383-407
[2]Henry, B.S. and Luxmoore, A.R., The stress triaxility
constraint and the Q-value as a ductile fracture parameter,
Engineering Fracture Mechanics, Vol. 57. No. 4, 1997, pp
375-390
[3]Kolednik, O. and Shan G.X. and Fischer F.D., Geometry and
size effects in ductile fracture – FEM studies and theoretical
considerations, IUTAM Symposium on Nonlinear Analysis of Fracture,
Kluwer Academic Publishers, 1997, pp 43-52
[4]Kozak, D., Gubeljak, N., Rak, I., Modified numerical
modelling of fracture behaviour of weld joint in ductile-to-brittle
temperature transition region, Materials and technologies, Vol. 32
(5), 1998, pp 337-342
[5]Matejiček, F. and Kozak, D., Some Remarks About 2-D and 3-D
Finite Element Modelling of Fracture Toughness Specimens with
Material and Geometric Mismatch, Proceedings of the 2nd
Slovenian-Japanese joint Seminar 'Welding Fracture Mechanics and
Dynamic Loading', Bohinj, 2001, pp 1-8
[6]Narasimhan R., Rosakis, A.J., Three-dimensional effects near
a crack tip in a ductile three-point bend specimen: Part I–A
Numerical investigation, Journal of Applied Mechanics, Vol. 57,
1990, pp 607-617
[7]Newman Jr., J.C., Booth, B.C. and Shivakumar, K.N., An
elastic-plastic finite-element analysis of the J-resistance curve
using a CTOD criterion, Fracture Mechanics: Eighteenth Symposium,
ASTM STP 945, ASTM, Philadelphia, 1988, pp 665-685
[8]Raftopoulos, D.D., Huang, Z., Konsta-Gdoutos, M. and Gdoutos
E.E., Evaluation of the three-dimensional region around a crack tip
by caustics, Int. J. of Fracture, 98, 1999, pp 343-350
[9]Rosakis, A.J. and Ravi-Chandar K., On Crack-Tip Stress State:
An Experimental Evaluation of Three-Dimensional Effects, Int. J. of
Solids and Structures, Vol. 22, No.2, 1986, pp 121-134
[10]Yuan, H. and Brocks, W., Quantification of constraint
effects in elastic-plastic crack front fields, J. Mech. Phys.
Solids, Vol. 46, No. 2, 1998, pp 219-241
5 by experiment
5 calculated by FEA
100%
Planes:
E
D
C
B
A
0 %
0,4%
1%
Portion of
PE elements:
0,25%
Analysed
region
F/3
F/6
y
x
crack-tip
0,1%
Unstable fracture during experiment
Fracture toughness variation between FE models with 0,1% of PE
and 0,25% of PE
Fracture toughness variation between FE models with 1% of PE and
100% of PE
100% PS on the specimen surface
5 calculated by FEA
5 by experiment
middle of the specimen
surface of the specimen
Fmaks = 173 kN
F = 135 kN
F = 100 kN
F = 60 kN
Planes:
A
B
C
D
0,25%
0,1%
0 %
CTOD (5), mm
0,4%
PE portion:
E
1%
_1113745792.doc
Thickness
Crack length
Uncracked
ligament
z
Plastic zone
rp = rp (z)
rp (PS)
rp (PE)
_1114270210.doc
0,05W
a0
0,125W
W-a0
crack-tip
1/2 of CT specimen
PS
PE
Plastic zones by maximum force
0,6W
0,2B
B=25,4 mm
W=50,8 mm
a0/W=0,65
_1114271299.unknown
_1114276261.doc
B
a0=9,912 mm
A
D
C
S=144 mm
D
E
E
Portion of PE elements, %
B
C
B
A
0
0,5
1
1,5
2
Through thickness planes
100% PS on the specimen surface
1% of PE in the middle of the specimen
B=36 mm
_1114275969.doc
E
D
C
B
A
crack tip
uncracked ligament
CTOD (5) node
7,2 mm
Base material
Weld
Fusion line
0,1 % of
PE elements
0,25 % of
PE elements
0,4 % of
PE elements
1 % of
PE elements
2-D FE model for the SURFACE of the specimen (100 % PS)
2-D FE model for the MIDDLE of the specimen (1 % PE)
_1114270760.unknown
_1113748343.unknown
_1113750130.doc
1,25
y/ro
x/ro
1,0
plane
stress
0,83
0,16
0,37
plane
strain
crack-tip
_1113746055.doc
Thickness
Crack length
Uncracked
ligament
Thick-walled structures (dominant PE state)
Thin-walled structures (dominant PS state)
(% PE)
on the surface
(% RN)
in the middle
100% PE
in the middle
100% PS
on the surface
_1061843792.unknown
_1113727258.doc
PE
z
z
y
B
free contraction
thin plate
no contraction
thick plate
z
y
thickness B
B
x
z
PS
_1021292922.xls
Chart1
00.0150.01480.01430.0140.01250.0145
0.01170.026780.023660.022620.022360.0210.02288
0.01940.0380.0360.03330.0330.030.0335
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0.10.150.1150.0920.090.0730.095
0.1350.32240.21060.13780.12870.10.1469
0.2285
d5 eksperimentalno
0%RD
0,1%RD
0,4%RD
1%RD
100%RD
0,25%RD
CTOD (d5), mm
F, kN
0
39.986
39.986
39.986
39.986
39.986
39.986
39.986
60.206
60.206
60.206
60.206
60.206
60.206
60.206
80.282
80.282
80.282
80.282
80.282
80.282
80.282
100.49
100.49
100.49
100.49
100.49
100.49
100.49
119.96
119.96
119.96
119.96
119.96
119.96
119.96
135.44
135.44
135.44
135.44
135.44
135.44
135.44
149.99
149.99
149.99
149.99
149.99
149.99
149.99
173.66
173.66
173.66
173.66
173.66
173.66
173.66
Sheet1
LOAD, kNdelta5-exp0% RD-MKE0,1% RD0,25% RD0,4% RD1% RD100%
RD
0.0000.000000
39.9860.0117000.0150000.0148000.0145000.0143000.0140.012500
60.2060.0194000.0267800.0236600.0228800.0226200.022360.021000
80.2820.0329000.0380000.0360000.0335000.0333000.0330.030000
100.4900.0510000.0546000.0455000.0416000.0403000.04030.037500
119.9600.0745000.0760000.0650000.0550000.0540000.05350.049000
135.4400.1000000.1027000.0847600.0717600.0676000.06630.059000
149.9900.1350000.1500000.1150000.0950000.0920000.090.073000
173.6600.2285000.3224000.2106000.1469000.1378000.12870.100000
Sheet1
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0
d5 eksperimentalno
0%RD
0,1%RD
0,4%RD
1%RD
100%RD
0,25%RD
CTOD (d5), mm
F, kN
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
_1061843291.unknown
_1021387695.xls
Chart2
0000
1111
2222
3333
4444
F=173kN
F=60kN
F=135kN
F=100kN
0.3224
0.1027
0.02678
0.0546
0.2106
0.08476
0.02366
0.0455
0.1469
0.07176
0.02288
0.0416
0.1378
0.0676
0.02262
0.0403
0.1287
0.0663
0.02236
0.0403
Sheet1
Ravnina60.000000100.000000135.000000173.000000
0.0000.0267800.0546000.1027000.322400
1.0000.0236600.0455000.0847600.210600
2.0000.0228800.0416000.0717600.146900
3.0000.0226200.0403000.0676000.137800
4.0000.022360.04030.06630.1287
Sheet1
0000
0000
0000
0000
0000
&A
Page &P
F=173kN
F=60kN
F=135kN
F=100kN
CTOD (d5), mm
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
