Available online at www.sciencedirect.com
annals of
NUCLEAR ENERGY
Annals of Nuclear Energy 35 (2008) 627–635
www.elsevier.com/locate/anucene
Fracture mechanical evaluation of an in-vessel melt retention scenario
M. Abendroth *, H.G. Willschütz, E. Altstadt
Forschungszentrum Dresden-Rossendorf, Bautzner Landstrasse 128, 01328 Dresden, Germany
Received 14 June 2007; accepted 6 August 2007
Available online 24 September 2007
Abstract
This paper presents methods to compute J-integral values for cracks in two- and three-dimensional thermo-mechanical loaded structures using the finite element code ANSYS. The developed methods are used to evaluate the behavior of a crack on the outside of an
emergency cooled reactor pressure vessel (RPV) during a severe core melt down accident. It will be shown, that water cooling of the
outer surface of a RPV during a core melt down accident can prevent vessel failure due to creep and ductile rupture. Further on, we
present J-integral values for an assumed crack at the outside of the lower plenum of the RPV, at its most stressed location for an emergency cooling (thermal shock) scenario.
Ó 2007 Elsevier Ltd. All rights reserved.
1. Introduction
The J-integral concept is widely known and used as a
tool to predict brittle and ductile fracture due to instable
or stable crack growth. A comprehensive study about the
two- and three-dimensional evaluation of the J-integral
under the presence of thermal fields and body loads is given
by Shih et al. (1986). But it is still a challenging task to
compute reliable J-integral values especially for threedimensional cracks in real structures using finite element
codes. A useful source which describes some of the computation difficulties of the J-integral is a report written by
Brocks and Schneider (2001).
The main computing problem, especially in the threedimensional case, is the integration of the field equations.
The integration volume is represented by finite elements
which should have a suitable shape and position to the
crack front for the integration. Then the integration is in
fact a summation of the requested values about all integration points of all elements inside the integration volume.
For such computations the finite element mesh has to fit
*
Corresponding author.
E-mail addresses: M.Abendroth@fzd.de (M. Abendroth), H.G.Willschuetz@fzd.de (H.G. Willschütz), E.Altstadt@fzd.de (E. Altstadt).
URL: www.fzd.de (M. Abendroth).
0306-4549/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.anucene.2007.08.007
not only to the needs for computing the boundary value
problem but also the needs for the J-integral computation.
Making those meshes is often difficult and therefore time
consuming.
The finite element code ANSYS provides some useful
path-commands, which allow a quite simple area or volume
integration over basic geometrical shapes. These shapes are
not bound on the topology of the finite element mesh.
The mesh independent J-integral computation was
developed to analyze cracks in RPVs. In our special case
we assume a severe accident, where the main cooling of
the reactor has failed, which can cause a core dry out
and a subsequent core melt down, as happened in the
TMI-2 accident (Rempe et al., 1994). Contrary to the
TMI-scenario we assume no internal cooling at all, therefore the molten parts of the core will form a melt pool in
the lower plenum of the RPV with internal heat sources
due to the decay of radioactive isotopes. The temperature
in the melt pool can reach 3000 K and cause melting of
the inner surface of the RPV. Where the RPV wall exceeds
temperatures of ca. 850 K it begins to creep and can fail
due to ductile rupture if the external cooling cannot be
established early enough.
One strategy to prevent vessel failure is an emergency
cooling with water on the outside of the vessel (external
flooding). Depending on the flooding time, this can result
628
M. Abendroth et al. / Annals of Nuclear Energy 35 (2008) 627–635
a sudden temperature drop (thermal shock) of the outer
surface of the vessel, which induces high thermal strains
and stresses. Those thermal shock phenomena were analyzed experimentally and numerically by different work
groups (Bass et al., 1982; Bass and Bryson, 1983; Sievers
and Höfler, 1986).
Here, we present results for a Konvoi RPV. The data for
the vessel material are very detailed. We use a data base
which includes temperature dependent stress–strain and
creep behavior, thermal expansion coefficient, thermal conductivity, specific heat, elastic modulus and density. In our
special case creeping was not taken into account since the
outer wall temperatures are below the creep temperature
range. For the core melt an effective conduction convection
model (ECCM) is used. It was developed by Bui (1998),
Dinh and Nourgaliev (1997) and describes the heat transport in a core melt pool by anisotropic and inhomogeneous
conduction. The finite element model of the lower head for
evaluating the temperature field and the viscoplastic behavior of the RPV wall was developed by Willschütz and Altstadt (2002), Willschütz (2006), Willschütz et al. (2005a),
Willschütz et al. (2005b), Willschütz et al. (2006).
2. J-integral evaluation
The following formulations are valid for a hyper-elastic
material, where the stresses rij are a function of a thermomechanical potential, which is the strain energy density
W.
oW
rij ¼
;
ð1Þ
oeij
Z
rij deij :
ð2Þ
W ¼
eij
Here, rij denotes the stress tensor, eij the total strain tensor.
The formulations can be used also for incremental theory
of plasticity under the following conditions. Local unloading is not allowed, all loading paths in the stress space are
supposed to remain radial so that the ratios of the principal
stresses do not change in time (Brocks and Schneider,
2001). The integration path or the integration area should
enclose the plastic zone. The crack faces are free of loadings and no body loads do exist.
Since we are interested only in mode I crack growth, we
define a local crack tip coordinate system, with the x1 axis
pointing in crack extension direction as it is depicted in
Fig. 1. Then we can simplify Eq. (3) into
Z
J 1 ¼ ðW d1j nj rij nj ui;1 ÞdC:
ð4Þ
C
The J-integral can be computed also by using an area integral (Shih et al., 1986).
Z
J 1 ¼ ðrij ui;1 W d1j Þq1;j dA:
ð5Þ
A
Here, qk is smooth vector function with the only nonzero
component q1
r
r
T
qk ¼ 1 ð6Þ
ð1; 0; 0Þ ; q1 ¼ 1 ;
r0
r0
where r denotes the radius away from the crack tip and r0
the radius of the circular integration area A. q1 at the crack
tip can be interpreted as a virtual crack extension (VCE).
Then, J1 is the released energy for a virtual unit length
mode I crack extension. Under the restrictions given at
the beginning of this section the value of J1 is independent
of the path C or since we restrict the area to be circular J1 is
independent of r0.
To maintain this path independence under the presence
of a thermal field a correction term is necessary (Shih et al.,
1986; Bass et al., 1982; Bass and Bryson, 1983; Hellen,
1975). We assume an isotropic thermal expansion coefficient a for the RPV material. Then the complete equation
for the J-integral becomes
Z
Z
J 1 ¼ ðrij ui;1 W d1j Þq1;j dA þ rii ah;1 q1 dA:
ð7Þ
A
A
The temperature gradient is denoted by h,1, so the product
with the thermal expansion coefficient gives the thermal
strain gradient eth
;1 ¼ ah;1 . For the presence of body loads
(gravity forces) or crack face loads (pressure) additional
terms are necessary (see Shih et al., 1986).
2.1. Two-dimensional J-integral for thermally stressed bodies
The J-integral in its path formulation is
Z
J k ¼ ðW djk nj rij nj ui;k ÞdC;
ð3Þ
C
where djk denotes the Kronecker symbol, ui the displacement vector, ui,k the derivative of ui in direction of k and
nj the outward pointing normal vector on the integration
path C. In general, the integration path C includes the
crack face parts C+ and C. Both parts must be considered
only if there are loads (e.g. pressure) on the crack faces,
which is not the case in our problem.
Fig. 1. Two-dimensional integration path around a crack tip.
M. Abendroth et al. / Annals of Nuclear Energy 35 (2008) 627–635
629
2.2. Axisymmetric evaluation of the J-integral for thermally
stressed bodies
We define an axisymmetric coordinate system as shown
in Fig. 2. The rotational symmetry axis is x2, x1 is the radial
coordinate and x3 the angular coordinate. The mode I Jintegral for the axisymmetric case is then (Shih et al., 1986)
Z
1
J1 ¼
½ðrij ui;1 W d1j Þq1;j x1 þ ðr33 e33 W Þq1 þ rii ah;1 q1 x1 dA;
R A
ð8Þ
R denotes the radial distance of the crack tip from the symmetry axis. The indices i and j range over the coordinates x1
and x2.
Fig. 3. Three-dimensional integration path/area around a plane crack
with a curved crack front.
2.3. Three-dimensional evaluation of the J-integral for
thermally stressed bodies
Fig. 3 shows a three-dimensional plane crack with a
curved crack front and the definition of a local crack tip
coordinate system with the n1 axis pointing normal to the
crack front in crack extension direction. The n2 axis is normal to crack faces and the n3 axis is tangential to the crack
front. s is the local crack front coordinate.
There are two J-integral formulations for the threedimensional case. The first one (Brocks and Schneider,
2001; Amestoy et al., 1987) is a combination of a path
and an area integral
Z
Z
o
J 1 ðsÞ ¼ ðW d1j nj rij nj ui;1 ÞdC
ðWn3 ri3 n3 ui;1 ÞdA
C
AðCÞ on3
Z
þ
rii ah;1 dA:
ð9Þ
Fig. 4. Three-dimensional integration volume around a plane crack with a
curved crack front.
1
J 1 ðsÞ ¼
Da
Z
ðrij ui;1 W d1j Þq1;j dV þ
V
Z
rii ah;1 q1 dV :
V
ð10Þ
AðCÞ
A second (VCE) formulation (Shih et al., 1986) uses a
three-dimensional function for qk and a volumetric integration domain, as it is depicted in Fig. 4.
In both formulations the indices i, j and k range over the
coordinates n1, n2 and n3. In Eq. (10) q1 is a function of
n3 and the radial distance from the crack tip r, q2 = q3 = 0.
r
q1 ðn3 ; rÞ ¼ ð1 4n23 Þ 1 ð11Þ
r0
The integration domain is a cylindrical volume with a
length ds and a radius r0. The resulting virtual crack front
extension is a plane parabolic shaped area with the size
Z þds
2
Da ¼
q1 ðn3 ; r ¼ 0Þdn3
ð12Þ
ds
2
2.4. Area and volume integration using ANSYS
Fig. 2. Two-dimensional integration area around a crack tip for an
axisymmetrical problem.
The finite element code ANSYS supports line integration along defined paths. In two dimensions the area integration is approximated by a summation of n line
integrals along Ci, which are multiplied by the width of
the ring segments wi (see Fig. 5). The width of the
integration rings wi is in our case a constant value. It could
be useful, especially for finite element meshes, which show
a strong refining towards the crack tip, to choose an
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M. Abendroth et al. / Annals of Nuclear Energy 35 (2008) 627–635
5
8
ds1 ¼ ds3 ¼ ds; ds2 ¼ ds
9
rffiffi9ffi
3
nð1;3Þ ¼ ; nð2Þ ¼ 0
5
ð17Þ
ð18Þ
In three dimensions three area integrals at different n3 positions are computed, multiplied by the weights dsj and
added together. This integration along n3 is similar to a
one-dimensional Gaussian integration scheme. The positions nj and the weights dsj are given in the Eqs. (17) and
(18). The depth of the cylindrical integration volume ds
should be equal or smaller than the element size along
the crack front.
Fig. 5. Different integration paths for area integration with ANSYS.
increasing width away from the crack tip. Then, the width
of the innermost and outermost integration ring should fit
the smallest and biggest finite elements located inside the
integration region.
Z
n Z
X
ðÞdA ¼
ðÞdCi wi
ð13Þ
A
Z
ðÞdV ¼
V
i¼1
Ci
j¼1
i¼1
m X
n Z
X
ri ¼ ði 0:5Þ
wi ¼
r0
n
r0
n
ðÞdCij wi dsj
ð14Þ
Cij
ð15Þ
ð16Þ
3. Finite element models for the thermo shock analysis
3.1. Axisymmetric model of the RPV without a crack
Fig. 6 shows the axisymmetric FE-model of a Konvoi
RPV with a melt pool in the lower plenum. Since the study
is focused on the bottom head of the vessel, the coolant inand outlet nozzles, the holes for the control rods and all
screw connections are not included in the FE-model. For
the vessel 4-node structural elements are used. The element
size is constant in tangential direction of the lower head but
varies in radial direction to the wall, to be capable reproducing the expected high temperature and stress gradients.
For modeling the liquid melt pool the same 4-node
structural elements are used. The material data of the melt
Fig. 6. Finite element model of the RPV with a melt pool. The line indicated with P defines a path trough the RPV wall, which is used to map results on it.
M. Abendroth et al. / Annals of Nuclear Energy 35 (2008) 627–635
are taken from Willschütz (2006), Willschütz et al. (2005a).
The melt pool has different layers, each represented by different material data, to account for the inhomogeneous
heat transfer inside the melt pool. During the solution
the melt pool elements can change their material state
depending on the temperature distribution in the pool.
The melt pool elements are connected to the vessel via contact elements, which allow heat transfer from the melt to
the vessel wall. Additionally, radiation elements are used
to consider the heat radiation inside the vessel (see Fig. 7).
The melting of the vessel wall is modelled within the
temperature dependent material data. If an element reaches
the material liquidus temperature, the strength properties
are set to almost zero values and the thermal properties
change to those of liquid metal.
The external cooling is modeled by a temperature dependent heat transfer function at the outside of the vessel.
Here, we use the Nukijama-curve (Nukijama, 1934), which
characterizes the heat transfer from a heated horizontal
plane to an upper water layer. The heat flux depends on
the temperature difference between outer vessel surface
and surrounding water. The water is assumed to have a
temperature of 373 K.
Since the elements (solid182) do not allow direct
thermal–mechanical coupling, a sequentially coupled simulation is performed (Willschütz et al., 2006). The simulation
is split up into predefined time steps. For each time step a
transient thermal solution is obtained. The subsequent
mechanical solution uses the spatial temperature field as
a body load to compute the thermal strain field and the
resulting stress field. The next time step starts with another
thermal solution with the state at the end of the former
time step as starting conditions. This time splitting is necessary to account for the deformation due to the thermal
strains and the phase changes, which occur in the melt.
The phase changes are modeled by switching between dif-
106
5
.
q [W/m2]
10
4
10
103
I
102
0
10
II
III
1
10
ΔT [K]
IV
10
2
3
631
ferent material models. Table 1 shows the boundary and
starting conditions for the simulation.
3.2. Axisymmetric model of the RPV with a circumferential
crack
A second axisymmetric model contains a circumferential
crack at the most stressed location at the outside of the
model (see Fig. 8). The solution strategy is the same as
described in the subsection above. Additional postprocessing is done using the formulas from Sections 2.2 and 2.4 to
compute the J-integral.
3.3. 3D submodel with a semi elliptical surface crack
Since a circumferential crack as described in Section 3.2
is very unlikely, a three-dimensional submodel with a semi
elliptical surface crack has been developed. The location of
the submodel is indicated in Fig. 9. The displacements for
the cut boundaries and the temperature field are taken
Table 1
Initial and boundary conditions for the simulation
Initial conditions for the thermal solution
Homogeneous wall temperature
Homogeneous melt temperature
h0wall ¼ 600 K
h0melt ¼ 3000 K
Boundary conditions for the thermal solution
Total heat generation in the melt at t = 0
Heat radiation emission coefficient
Heat flux to external water (flooded)
Heat convection to the containment (not
flooded)
q_ 0gen ¼ 1 MW=m3
e = 0.75
_
qðhÞ,
Nukijama-curve
a = 10 W/m2 K s
Tbulk = 323 K
Boundary conditions for the structural solution
Temperature field
Internal pressure
External displacements (symmetry)
hmech(x, t) = htherm(x, t)
p = 2.5 MPa
ux(x = 0) = 0
ANSYS 10.0
HFLU
PLOT NO. 1
-460161
-409539
-358918
-308296
-257674
-207053
-156431
-105809
-55188
-4566
TEMP
PLOT NO. 1
87.893
424.794
761.695
1099
1435
1772
2109
2446
2783
3120
10
Fig. 7. (left) Heat flux over temperature difference between vessel surface and surrounding water (Nukijama-curve (Nukijama, 1934)). I – convective
boiling, II – stable, III – instable bubble boiling, IV – film boiling (pure radiation), (right) heat flux (arrows) and temperature distribution (colored
contours) for the lower head of the RPV.
632
M. Abendroth et al. / Annals of Nuclear Energy 35 (2008) 627–635
ANSYS 10.0
S1
PLOT NO. 1
-.710E+08
.947E+08
.260E+09
.426E+09
.592E+09
.757E+09
.923E+09
.109E+10
.125E+10
.142E+10
ANSYS 10.0
S1
PLOT NO. 1
-.710E+08
.947E+08
.260E+09
.426E+09
.592E+09
.757E+09
.923E+09
.109E+10
.125E+10
.142E+10
Fig. 8. Maximum principal stress (Pa) for the axisymmetric model of the RPV with an circumferential surface crack.
Y
Z
X
ANSYS 10.0
SEQV
PLOT NO. 1
422193
.733E+08
.146E+09
.219E+09
.292E+09
.365E+09
.437E+09
.510E+09
.583E+09
.656E+09
ANSYS 10.0
TEMP
PLOT NO. 1
452.771
755.019
1057
1360
1662
1964
2266
2569
2871
3173
Z
Y
X
Fig. 9. (left) Temperature field for the 2D axisymmetric model and (right) 3D submodel with the semi elliptical surface crack and resulting equivalent
stress (Pa) distribution.
4. Results
4.1. Axisymmetric model of the RPV without a crack
100
with flooding
without flooding
90
remaining vessel wall thickness [%]
from the solution of the model described in Section 3.1.
Since the transient temperature field is already known from
the axisymmetric solution, only the mechanical solution
has to be obtained. The two methods described in the Section 2.3 and the 3D-integration from Section 2.4 are used
to compute the J-integral along the three-dimensional
crack front.
80
70
60
50
40
30
If an external flooding of the vessel can not be established, a large part of the inner wall of the lower head of
the RPV will melt. The remaining wall thickness would
be below 25% of the original thickness, as can bee seen in
Fig. 10. The symbols in this plot indicate the time steps
of the computation. The steps in the diagrams occur from
the post processing. As remaining wall all elements are
counted with a temperature below the material liquidus
temperature. Each step corresponds to an element boundary. The remaining wall reaches temperatures where the
material will creep rapidly and fail due to ductile rupture.
The time to failure depends strongly on the material creep
20
0
2
4
6
8
10
time [hours]
Fig. 10. Remaining RPV wall thickness for the cooled and the uncooled
scenario without consideration of the mechanical response.
properties as reported in Willschütz (2006), Willschütz
et al. (2006).
If a vessel flooding can be established, only 35% of the
wall will melt (see Fig. 10). At the outside of the remaining
wall the temperatures are below the creep temperature of
M. Abendroth et al. / Annals of Nuclear Energy 35 (2008) 627–635
wall surface and after 100 s (see Fig. 12) it reaches magnitudes above the critical JIc, which means that ductile crack
growth will occur. However, the assumption of a circumferential crack is rather unrealistic. Therefore in the next
subsection we assume a semi elliptical surface crack.
4.3. 3D submodel with a semi elliptical surface crack
The crack considered here has a depth of a = 15 mm
and a depth/width ratio of a/c = 0.3. Fig. 13 shows the
equivalent stress around the crack front. As expected we
find a stress concentration at the crack tip. Fig. 14 shows
the J-integral values computed with the two methods outlined in Section 2.3. In general, we have a similar run of the
curves as for the axisymmetric crack but the maximum values do not exceed the critical JIc value. The J-integral values increase for larger angular positions of u but do not
vary much for angular positions of u > 30. The differences
500
400
J1 [N/mm]
the material. The assumed inner pressure of 25 bar does
not cause stresses above the ultimate tensile strength. For
the given scenario a flooded vessel will not fail.
In the following we concentrate on the cooled (flooded)
scenario. The cooling water is assumed to surround the
whole vessel from the beginning t = 0 s. A possible slow
flooding with an in time increasing water level is not considered here.
On the left side of Fig. 11 the temperature distribution
through the vessel along the path P is plotted for different
times. At the beginning the inner wall temperature is equal
to the melt temperature and we see a very inhomogeneous
temperature field and a temperature gradient decreasing in
time.
But if we concentrate on the outer surface (x =
149 mm), we find a temperature gradient rising with time,
with its maximum around at 3600 s. This temperature gradient causes the large magnitudes of the hoop stress and ry
stress (tangential to the RPV wall, in meridian direction) at
the outside of the vessel, which is shown on the right side of
Fig. 11. The complementary ry-compression stresses are
found in the middle of the RPV wall. The value of these
compression stresses decrease towards the inner wall surface, where the material looses its stress carrying capacity
(strength) due to the high temperatures, which are close
to or above the melting point of the RPV material.
The largest stress values are found in a region where the
vessel has a weld line, which are known as typical (or most
likely) locations for cracks. Therefore, further investigations are necessary.
633
300
200
100
4.2. Axisymmetric model of the RPV with circumferential
crack
0
0
The only additional information obtained from this
model is the stress intensity at the crack tip. The crack
depth is a = 15 mm. The computed J-integral values rise
very steeply during the temperature drop down of the outer
3500
500
300
200
1500
2400
3000
3600
after 1 sec.
after 10 sec.
after 100 sec.
after 158 sec.
after 1000 sec.
after 3600 sec.
after 36000 sec.
400
2000
1800
Fig. 12. Value of the J-integral over time computed with the method of
Shih et al. (1986) for the axisymmetric model containing the circumferential surface crack.
y-stress [MPa]
temperature [K]
2500
1200
t [sec]
after 1 sec.
after 10 sec.
after 100 sec.
after 1000 sec.
after 3600 sec.
after 36000 sec.
3000
600
100
0
-100
1000
-200
500
-300
0
-400
0
20
40
60
80
100
x-coord [mm]
120
140
16
0
20
40
60
80
100
120
140
160
x-coord [mm]
Fig. 11. (left) Temperature profile through the RPV wall along the path P for different times and (right) ry – stress tangential to the RPV wall along the
path P for different times.
634
M. Abendroth et al. / Annals of Nuclear Energy 35 (2008) 627–635
ANSYS 10.0
SEQV
PLOT NO. 1
.184E+09
.233E+09
.282E+09
.331E+09
.380E+09
.430E+09
.479E+09
.528E+09
.577E+09
.626E+09
Z
ANSYS 10.0
SEQV
PLOT NO. 1
.184E+09
.233E+09
.282E+09
.331E+09
.380E+09
.430E+09
.479E+09
.528E+09
.577E+09
.626E+09
Z
Y
Y
X
X
130
130
120
120
110
110
100
100
90
90
80
80
J1 [N/mm]
J1 [N/mm]
Fig. 13. Equivalent stress (Pa) distribution around the semi elliptical surface crack; (left) view onto the symmetry plane where the deepest point of the
crack is u = 90 and (right) view onto the outer surface u = 0.
70
60
50
3.75 deg
18.75 deg
33.75 deg
48.75 deg
86.25 deg
J1c
40
30
20
10
70
60
50
3.75 deg
18.75 deg
33.75 deg
48.75 deg
86.25 deg
J1c
40
30
20
10
0
0
0
250
500
750
1000
1250
1500
t [sec]
0
250
500
750
t [sec]
1000
1250
1500
Fig. 14. Value of the J-integral over time for different positions along the crack front of the semi elliptical surface crack; (left) computed with Eq. (9) and
(right) computed with Eq. (10). See Fig. 15 for the definition of the angular position u.
Fig. 15. Elliptical crack front with coordinate s(u) and definition of ~
q
which is in plane with the crack faces and normal to the crack front.
between the both J-integral computation methods can be
neglected.
5. Discussion
The crack propagation behavior in the lower head of an
externally cooled RPV during a core melt down accident
was evaluated by finite element analysis. The J-integral
was calculated for a simplified 2D axisymmetric analysis
and with two methods for 3D analysis.
In the 2D calculation a crack over the whole perimeter is
assumed, whereas in the 3D calculations a more realistic
semi elliptical crack with an aspect ratio of a/c = 0.3 was
used. Consequently, in the 2D calculation the radial
displacements are much higher than in the 3D case, where
the crack is stabilized by the surrounding material.
Therefore, the crack opening in the 2D calculation is
approximately 10 times of that in the 3D calculation. In
conclusion the J-integral is considerably overestimated by
the simplified 2D axisymmetric crack model. The J-values
obtained from the 3D crack model are about 20% below
the critical value of JIc = 122 N/mm for the RPV steel.
For the calculated scenario the semi elliptical surface crack
would not propagate. However, this result does not guarantee that the RPV will not fail in other in vessel retention
(IVR) scenarios.
One uncertainty is the ablation model of the RPV wall.
In the presented investigation is was assumed that the wall
M. Abendroth et al. / Annals of Nuclear Energy 35 (2008) 627–635
elements are eroded at the melting temperature of the steel.
However, the METCOR experiments (Bechta et al., 2006)
have shown that the steel ablation at the interface between
corium and vessel steel is not only a thermal phenomenon.
Corrosion processes and the formation of eutectics lead to
the erosion of the vessel steel at temperatures that are significantly lower than the melting temperature of steel.
Therefore, the remaining wall thickness could be lower
than in the presented analysis, which could lead to higher
J-values for the assumed crack.
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