V - HZDR

Transcription

V - HZDR

FORSCHUNGSZENTRUM
ROSSENDORF
~
Mitglied der Wissenschaftsgemeinschaft Gottfried Wilhelm Leibniz
WISSENSCHAFTLICH-TECHNISCHE BERICHTE
FZR-353
August 2002
.[
_ -(....:.=?.!...::'~'?..:'-8;:--:;;':,:::::~
ISSN 1437-322X
Hans-Georg WHlschütz, Eberhard Altstadt
Generation of aHigh Temperature
Material DataBase and its Application to Creep
Tests withFrench or German RPV-steel
Herausgeber:
Forschungszentrum Rossendorf e.Y.
Postfach 51 01 19
0-01314 Dresden
Telefon +49 351 26 00
Telefax +49 351 2690461
http://www.fz-rossendorf.de/
Als Manuskript gedruckt
Alle Rechte beim Herausgeber
FORSCHUNGSZENTRUM ROSSENDORF
~
WISSENSCHAFTLICH-TECHNISCHE BERICHTE
FZR-353
August 2002
Hans-Georg Willschütz Eberhard Altstadt
J
Technical Report I Sachbericht
'Generation of a High Temperature
Material Data Base and its Application to C.reep
Tests with French or German RPV-steel
Erzeugung einer Materialdatenbasis für hohe Temperaturen und ihre
Anwendung auf Kriechversuche mit mit französischen und deutschen
ROB-Stählen
Reactor Safety Research-project No.: 150 1254
Project Title: Modelling of in-vessel retention after relocation of corium into the tower ptenum:evaluation
of the temperature field and of the visco-plastic deformation of the vessel wall
Reaktorsicherheitsforschung - Vorhaben Nr.: 150 1254
Vorhabenstitel: Beitrag zur Modellierung der Schmelzerückhaltung im ROB nach Verlagerung von Corium
in das untere Plenum: Berechnung des Temperaturfeldes und der visko-plastischen Verformung der
Behälterwand
Hinweis:
Das diesem Bericht zugrundeliegende Vorhaben wurde mit Mitteln des Bundesministeriums für Wirtschaft und Technologie unter dem Förderkennzeichen GRS 150
1254 gefördert. Die Verantwortung für den Inhalt dieser Veröffentlichung liegt bei den
Autoren.
Das Forschungszentrum Rossendorf e. V. und die Berichtersteller übernehmen keine Haftung für Schäden, die aufgrund von weiterführenden fehlerhaften Anwendungen der in diesem Bericht dargestellten Ergebnisse entstehen.
Generation and Application of a High Temperature Material Data Base
5
Abstract
Gonsidering the hypothetical core melt down scenario for a light water reactor (LWR)
a possible failure mode of the reactor pressure vessel (RPV) and its failure time has
to be investigated for adetermination of the loadings on the containment. Numerous
experiments have been performed accompanied with material properties evaluation,
theoretical, and numerical work/REM 1993/, ITHF 1997/, /GHU 1999/.
For pre- and post-test calculations of Lower Head Failure experiments Iike OLHF or
FOREVER it is necessary to model creep and plasticity processes. Therefore a Finite Element Model is developed at the FZR using a numerical approach which
avoids the use of a single creep law employing constants derived from the data for a
limited stress and temperature range.lnstead of this a numerical creep data base
(GOB) is developed where the creep strain rate is evaluated in dependence on the
current total strain, temperature and equivalent stress. A main task for this approach
is the generation and validation of the GDB. AdditionaUy the implementation of all
relevant temperature dependent material properties has been performed. For an
evaluation of the failure times a damage modelaccording to an approach of Lemaitre
is applied.
The validation of the numerical model is performed by the simulation ofand comparison with experiments. This is donein 3 levels: starting with the simulation of single uniaxial creep tests, which is considered as a 1O-problem.ln the nextlevelso
called "tube-failure-experiments" are modeled: the RUPTHER-14 and the "MPAMeppen"-experiment. These experiments are considered as 2D-problems. Finally the
numerical model is applied to scaled 3D-experiments, where thelower head of a
PWR is represented in its hemispherical shape, Iike in the FOREVER-experiments.
This report deals with the 1D- and 2D-simulations.
An interesting question to be soIved in this frame is the comparabiJity of the French
16MND5 and the German 20MnMoNi55 RPV-steeIs, which are chemicaJ)y neany
identical. Since these 2 steels show a similar behavior, it should be allowedon a Iimited scale to transfer experimental and numerical data from one to the other.
Generation and Application of a High Temperäture Material Data Base
6
Kurzfassung
Bezüglich eines hypothetischen Kernschmelzeszenarios in einem Leichtwasserreaktor ist es notwendig, mögliche Versagensformen des Reaktordruckbehälters sowie
Versagenszeiträume zu untersuchen, um die Belastung für das Containment
bestimmen zu können. Es wurden bereits eine Reihe von Experimenten durchgeführt, welche Erkenntnisse hierüber liefern sollen. Begleitend wurden in EinzeIversuchen Materialeigenschaften ermittelt, sowie theoretische und numerische Arbeiten
durchgeführt.
Für die Simulation von Experimenten zum Versagen der Bodenkalotte, wie OLHF
oder FOREVER, ist es notwendig, Kriechen und Plastizität zu berücksichtigen. Hierfür wurde am FZR ein Finite Elemente Model entwickelt, das die Verwendung von
einfachen Kriechgesetzen, die mit ihren angepassten Konstanten nur für begrenzte
Spannungs- und Temperaturbereiche gültig sind, umgeht. Stattdessen wird eine numerische Kriechdatenbasis angelegt, in der die Kriechdehnrate in Abhängigkeit von
der Gesamtdehnung, der Temperatur und der Vergleichsspannung abgelegt ist. Die
Hauptaufgabe für diese Vorgehensweise besteht in der Generierung und Validierung
der Kriechdatenbasis. Zusätzlich wurden alle relevanten temperaturabhängigen Materialeigenschaften mit entsprechenden Modellen in den Code eingegeben. Für die
Bestimmung der Versagenszeit wurde ein Schädigungsmodel nach einem Vorschlag
von Lemaitre implementiert.
Die Validierung des numerischen Models erfolgt durch die Simulation von und den
Vergleich mit Experimenten. Dies geschieht in 3 Stufen: zunächst werden einzelne
einachsige Kriechversuche nachgerechnet, was als 1D-Problem bezeichnet wird. In
der nächsten Stufe werden so genannte "Rohrversagensexperimente" simuliert: das
RUPTHER-14 und das "MPA-Meppen"-Experiment. Diese Experimnete werden als
2D-Probleme betrachtet. Schließlich kann das Modell auf skalierte 3D-Versuche angewendet werden, in denen die Bodenkalotte eines Druckwasserreaktors mit ihrer
halbkugelförmigen Geometrie wiedergegeben wird. Ein Beispiel hierfür sind die FOREVER-Experimente. Dieser Bericht behandelt die 1D- und 2D-Simulationen.
Eine wichtige Frage im Rahmen dieser Arbeit ist die Vergleichbarkeit des französischen Reaktordruckbehälterstahls 16MND5 und des deutschen 20MnMoNi55, weiche chemisch nahezu identisch sind. Da diese beiden Stähle ein ähnliches Verhalten
zeigen, sollte es in gewissem Umfang zulässig sein, experimentelle und numerische
Daten und Erkenntnisse zwischen beiden zu Übertragen.
7
Contents
Abstract
'•..... 5
Kurzfassung
6
List of Figures
'.........•.......•..... 8
Nomenclature............................................••................•.......•..............'. 10
Abbreviations
11
1.
Introduction
'.....................•................................•...... 12
2.
Material Properties of the Steel
14
2.1
Density
"'...•.•......•..........•..••.....•.......••......••...•.........•"'•...•••..•..•..••...•.••..•..•.•.... 14
2.2
Thermal Expansion Coefficient ..••....•.•....•••..••.....•...••.•.•••••.•••.•.•••.••••••.•.....15
2.3
Thermal c·onductiv·i.ty
2.4
Heat .capacity..........•....•.·....•.•...........•.............••.•...••....•..•.•••••.•••.•.••.••.•••.•••.••••••...•...16
2.5
Young'sModulus
16
2.6
P·lasticity
17
·••.•••.•• 1.6
111 .••
3.
Creep and Damage Modeling in the Transient Mechanical
Calculations......................................•..........••.•...•...•......•.........•• 21
4.
The Considered French 16MND5 and German 20MnMoNi55
Steels ..•.••,...............•....................•.....•..•...........•...;.'•..•••..•.••.•••'.••.•• 23
5.
RUPTHERpost test calculation
27
6.
MPA-Meppen post test calculation
29
7.
Conclusions .............•........•.•.........••••••...•••..............•••••.•.••..••••• 32
8.
References ...................••..•.........•.
9.
Acknowledgement ....•...•.•..••............•..••.•..•.•••••••.:
10.
AJ)Il~rlcti)(••••••••..••..•..••••••..••••••.•••••••••••••••.••••••••••••••••••••••••••••••••••• ~!i
1iI • • • • • • • • • • • • • • • • • • • • • • • • '• • • • • • • • • • • • • • • • • • • •
'•••••.•
111 • • • • •
33
34
Generation and Application of a High Temperature Material Oata Base
8
List of Figures
Figure 1: Principal experimental setup of FOREVER - not to scale
12
Figure 2: Temperature dependent density
14
Figure 3: Temperature dependent mean thermal expansion coefficient.
15
Figure 4: Temperature dependent thermal conductivity
16
Figure 5: Temperature dependent heat capacity
16
Figure 6: Temperature dependent Young's Modulus and yield stress and true
ultimate stress as measured in tensile tests
17
Figure 7: Plasticity curves and model at 800 Q C
18
Figure 8: Stress-temperature range covered by the 16MN05-based COB
23
Figure 9: Comparison of uniaxial creep tests at 700°C
24
Figure 10: Comparison of the creep behavior of 16MN05 and 20MnMoNi55 with the
25
applied ANSYS COB at 800°C and 65MPa
Figure 11: Principal configuration of the RUPTHER-14 experiment [mm].
27
Figure 12: Example of resulting ANSYS deformation at failure [m].
27
Figure 13: Loading history of RUPTHER-14 and comparison of the measured and
calculated diameter increase
28
Figure 14: Principal scheme of the MPA-Meppen test [mm]
29
Figure 15: Calculated displacement at failure [m]. (Tmax=998K)
29
Figure 16: Loading history of MPA-Meppen test and comparison of the measured
and calculated radius increase
30
Figure 17: Comparison of the radius development during the last stage of the MPAMeppen test.
30
Figure 18: Engineering stress-strain curves of 16MN05 (REVISA-tests)
35
Figure 19: True stress-strain curves of 16MN05 (REVISA-tests)
35
Figure 20: Measured and modeled Stress-strain relations at 20°C
36
36
37
37
38
Figure 25: Measured and modeled Stress-s,train relations at 700°C
38
39
39
Figure 28: Measured and modeled Stress-strain relations at 11 OO°C
.40
Generation and Application of a High Temperature Material Data8ase
9
.40
Figure 30: Measured and modeled Stress-strain rel,ations at 1300°C
41
Figure 31: Comparison of uniaxial creep tests and calculation at 600°C
.41
.42
.42
.43
Figure 35: Comparison of uniaxial creep tests and calculation at 11 OO°C..........•.....43
44
.44
-=G:..:e:..:...:n~e.:....:ra.:.....ti:..:.o:...:..n. =a.:. . :n.: .d..:...A.:!:p-l:.p..:.:..lic.:....:a.:....:ti~o.:..:.n-=o..:..f ..::.a..:.H..:.::ig~h..:...T..:...e..:...m..:...:.!:..pe.:.:r-=a=tu:.:..re::.....:.:.M:...:..a.:.....te:....r.:.:..ia 1_D..:...ata B:. :a:.:. : s:. ,:.e
Nomenclature
Latin Symbols
A
[ m2 ]
cp
[J/kgK]
[ ]
[ ]
[Pa]
[N]
[ ]
[ m]
[-]
[ Oe]; [K]
[ K]
[ s ]; [ min ]; [ h ]
[s]
D
AD
E
F
i
L
Rv
T
AT
t
At
V
-
-
[ m3 ]
area
specific isobaric heat capacity
damage parameter
damage parameter increment
Young's modulus
force
counter
length, distance
triaxiality function
temperature
temperature difference
time
time step
volume
Greek Symbols
cx.
[K
1
]
8
[-]
E
[S-1 ]
A
[W/mK]
v
p
cr
[-]
[kg/m 3 ]
[Pa]
thermal expansion coefficient
strain
strain rate
heat conductivity
Poisson's number
density
stress
Indices
o
cr
el
eqv
frac
h
inst
max
min
n
pi
ref
t
original, at the beginning
creep
elastic
equivalent
fracture, rupture
hydrostatic
instantaneous; current
maximal
minimal
nominal, engineering
plastic
reference
true
10
Abbreviations
CDB
CFD
FE
FOREVER
LWR
OLHF
RPV
PWR
UPF
Creep Data Base
Computational Fluid Dynamics
Finite Element
Failure Of REactor VEssel Retention
Light Water Reactor
OECD Lower Head Failure Program
Reactor Pressure Vessel
Pressure Water Reactor
User Programmable Feature
1.lntroduction
The hypothetical scenario of a severe accident with core meltdown and formation of
a melt pool in the lower plenum of a Light Water Reactor (LWR) Pressure Vessel
(RPV) can result in the failure of the RPV and the discharging of the melt to the containment. One accident management strategy could be to stabilize the in-vessel debris or melt pool configuration in the RPV as one major barrier against uncontrolled
release of heat and radionuclides.
To obtain an improved understanding and knowledge of the melt pool convection,
the vessel creep, possible failure processes and modes occurring during the late
phase of a core melt down accident the FOREVER-experiments (Failure Of REactor
VEssel Retention)
are currently being
performed at the Pressure Valve Power Supply Melt Injection Orifiee
Division of Nuclear
•i Pressure Vesseilld
Power Safety of
..", iit- i
the Royal Institute
~ !li
,
Ili
l~
!
of
Technology,
Stockholm
/SEH
1999/. These ex- I";"";'".....j.:o...:••
periments
are
simulating the behavior of the lower
head of the RPV
under the thermal
loads of a convecting melt pool
with decay heating, and under the
pressureloads that
the vessel experi=
ences in a depressurized
vessel
scenario (cf. Fig.
1). The geometrical scale of the
Weldlntl
experiments
is
1:10 compared to
HeaterRods
a prototypic LWR.
Due to the multi
BottomHead
axial creep defor16MND5
mation of the ves<.);'IIIIi.---t-Displaeement
sei with a non~Q:~~~.....
Transducers
uniform temperature field these
Thermocouples
experiments
are
on the one hand
an
excelfent Figure 1: Principal experimental setup of FOREVER - not to
scale.
~
':..
/,
_G_e_n_e_ra_t_io_n_a_n_d_A-!p~p_li_ca..:..:..t.:.:..;io:-n_o_f_a_-=H.:.::ig!..:..:h:-T:....:e:..:..m::..:.!p.:.:..;e:..:..r.:.:.at.:.:.u:..:....re:...:..:.M.:::a:.:.:te:.:r.:::ia:.:...1.:::.D.:.:.at.::a:.,.:B.:.:..;a=.:s:.:e:..........
13
source of data to validate numerical creep and damage models which are developed
on the basis of uniaxial creep tests. On the other hand the results of pre-test calculations can be used to optimize the experimental procedure and can help to make onsite decisions during the experiment.
Therefore an axisymmetric Finite Element (FE) model is developed based on the
multi-purpose code ANSYS/Multiphysics@. Using the Computational Fluid Dynamics
(CFD) module the melt pool convection is simulated and the temperature fjeld within
the melt pool and within the vessel wall is calculated. The transient structural mechanical calculations are then performed applying a creep model which takes into
account the large temperature, stress and strain variations.
A main task for the numerical creep model approach is the development and validation of the creep data base (CDB). The source for the CDB are uniaxial creep tests,
Iike the REVISA-experiments. The CDB includes the primary, secondary and tertiary
creep stages. In the calculation the creep strain rate is then evaluated in dependence
on the current total strain, temperature and equivalent stress.
Additionally the implementation of all relevant temperature dependent material properties has been performed. For an evaluation of the failure times a damage model
according to an approach of Lemaitre ILEM 19961 is applied.
The modeling approach and validation is done in 3 steps: starting with the simulation
of single uniaxial creep tests, which is considered as a 1D-problem. In the next level
so called "tube-failure-experiments" are modeled: the RUPTHER-14 and the "MPAMeppen"-experiment. These experiments are considered as 2D-problems. Finally the
numerical model can be applied to scaled 3D-experiments, where the lower head of
a PWR is representedin its hemispherical shape, Iike in the FOREVER-experiments..
In the frame of this work the comparability of the French 16MND5 and the German
20MnMoNi55 RPV-steel is investigated. If these 2 steels show a similar behavior, it
should be allowed to transfer experimental and numerical data in a Iimited scale from
one to the other.
l
14
2. Material Properties of the Steel
For the considered tests a precise temperature dependent modeling of all relevant
material properties is necessary. Generally the material propelrties of the French
RPV-steel 16MND5 are considered. The material for the 16MND5-specimen, -tubes,
or -vessels investigated later was made by Kawasaki Steel, Japan IMON 1999/.
Each material property is stored in a table where the temperature ranges trom 275 K
to 1600 K with 54 equidistant (~T=25 K) temperature levels (MPTEMP-, MPDATAcommands). In the foUowing sections the material data applied in the Finite Element
Model is represented.
2.1
Density
Since inertia effects are not important in the considered tests until failure and the
simulations stop with tailure, the density influences the observed results in some calculations only slightly due to the deadweight of the structure, which depends on the
experimental setup.
The temperature dependent density generally decreases trom p=7850 kg/m 3 at room
temperature to p=7378 kg/m 3 at 1600 K. During the phase transformation, which is
for low carbon steels at low heating rates between Ac1=723 oe and AC3=830 oe and
which is modeled in the calculation trom 1000 K to 1100 K, there is a slight density
7900
-......
7800
......
~
7700
~
C)
=.
>.
~
I
............
""
~
7600
~ ..........- ----...
'"
Ul
C
4>
0
7500
7400
7300
250
350
450
550
650
750
-16MND5·steel
850
950
""'"
1"'-..
1050 1150 1250 1350 1450 1550 1650
Temperature [K]
Figure 2: Temperature dependent density.
~
_G_e_n_e_ra_t_io_n_a_n_d_A....:p'-!p_l_ic_a_tio_n_of_a_H~i9!...h_T.:....e.:....m~pe_r_a_tu_re..:......:.:M~a.:....te.:.:r.:....ia_I_D_a.:....ta.:.....::..B.:.:.as=-e=-·
15
increase with increasing temperature, Le. the structure is shrinking.
2.2 Thermal Expansion Coe'fficient
The thermal expansion coefficient is relevant for the simulation of structures with
temperature differences and/or transient temperatures during loading. The mean
thermal expansion coefficient a(T) shown in Fig. 3 is the average of the instantane~
ous expansion coefficient <linsteT) from the reference temperature to the actual tem~
perature. The relation is represented in the following equation:
T
fainst
(T) dT
a(T) :;:: -,T,=-,r
_
T-Tref
Eq.1
I.e., during the phase transformation between 1000 K to 1100 K the meanexpansion
coefficient just decreases, while the instantaneous expansion coefficient is negative.
During the heat up or cool down of a structure the different expansion behaviorin~
side and outside of the phase transformation can cause additional thermal stress
especially if there are large temperature differences within the structure.
18
-
16
~
~
15
~
=
9'
GI
0
I -16MND5-steel I
17
U
c
0
'jji
c
CIS
c.
><
w
ti
13
.c
12
E
GI
,-
14
t-
11
V
V
V- n
\\
'/
,,/
/
V
/
'\ /
V
V
\.."
J
10
250
350 450
550
650
150 850
950 1050 1150 1250 1350 1450 1550 1650
Temperature lK]
Figure 3: Temperature dependent mean thermal expansion coefficient.
16
2.3 Thermal conductivity
45
The temperature dependent
11 -16MND5-steel
thermal conductivity is reI40
quired if there are heat f1uxes
~
through the considered structure and the temperature field
"is evaluated by a thermal calculation prior to the mechanical calculation.
I~ ~ v V
25
As typical for ferritic/bainitic
low alloy steels the conductiv20
ity is around ",=40 WImK for
250 350 450 550 650 750 850 950 1050 1150 1250 1350 1450 1550
Temperature [KJ
low temperatures and decreases to 25 to 30 W ImK at
Figure 4: Temperature dependent thermal
high temperatures.
conductivity.
r./
"'t--
1\
1650
2.4 Heat capacity
The consideration of the
temperature dependent heat
capacity is necessary for
scenarios with transient temperature fields.
The capacity increases from
some cp=500 J/kgK at room
temperature to 800 J/kg at
the beginning of the phase
transformation. Ouring the
phase transformation the
heat capacity reaches values
1600
11
1400
1\
1200
11 \
:;;: 1000
~
:::!.
~
800
~
600
~
-16MND5.stoo'_1
/
:-
400
..I---"'" I--
1\
V
~
200
o
~
~
~
~
~
~
~
~
l*l_mO~N~l~~~
Temperature [K]
of 1400 J/kgK and after that it Figure 5: Temperature dependent heat capacity.
is around 600 J/kgK. The latent heat of fusion for the melting process is not modeled because the melting point
is above the considered temperature range.
2.5 Young's Modulus
The temperature dependent behavior of the Young's modulus is shown in Figure 6.
For comparison the Young's modulus is plotted to the right axis and the yield stress
and the true ultimate stress are plotted to the left axis. The Young's modulus starts
at room temperature with E=199 GPa. All properties are declining with increasing
temperature, but have the steepest decline around 900 K.
_G_e_n_e_ra_t__
io_n_a_n_d_A.. . !pc:. . !p:. .:.l:. .:.ic. : . :at.: .:. io:. :n. ;. . : ,.of:. . .a: . . :. .H;.: : i9:!.:. h:. . .T.:. .:e=..:m;2:.pe=.:r:.,=:a=:tu: :,.re=..:. :M.: a:.:.te: :.:r.: ia:.:. I. =D:.;:a: .:ta:. . .=B,: : as:: .:e: :. .-
17
800
240
-tr- Yield Stress or SigO.2% [MPa]
~ True Ultimate Stress [MPa]
700
.::1
~
600
,
~
500
';'
0-
::
;: 400
tn
f
-".
~-
(;j
300
--
-+- Young's Modulus [GPa]
180
~
\
~
"'l!>"
200
';'
150
\\
.\\
t!;
....
tn
:::s
120
:go
:E
,tn
90
~'
g>
:::s
o
>60
",\ ~
100
~
~~
........ ~
30
""l!!l
o
200
210
0
300
400
500
600
700
800
900 1000 1100 1200 1300 1400 1500 1600
Temperature [K]
Figure 6: Temperature dependent Young's Modulus and yield stress and true
ultimate stress as measured in tensile tests.
2.6 Plasticity
Additionally to the creep model described later a plastieity model is used to be able
to model prompt failure. In addition to creep, whieh is time dependent,it is necessary
to model plastieity, whieh takes place instantaneously.ln fact, both phenomena can
not be distinguished clearly in all cases, but to be conservative forall scenarios both
deformation and failure criteria areincluded.
For the plastieity the multilinear isotropie hardening model of the ANSYScode is
used (MISO-option). For 12 temperature levels from room temperature to 1600 K the
plasticity is represented by a curve consisting of 5 linear seetions. The straingiven in
the curve is the total strain, including elastic strain, but no thermal strain.. For an
overview Figure 18 in the appendix presents the engineering stress-strafn curves of
all REVISA tensile tests.
As an example Figure 7 represents the relations at 800 oe. The dotted blackcurve
shows the modeled stress-strain relation of the code. The plasticity in the FE model
is a prompt plasticity, Le. if the stress reaches a certain value at a time the corre"
sponding strain is modeledinstantly. Contrary to this the tensUe tests in Ihe REVISA
program were performed at a constant nominal or engineering strafn rate of
E=1 %/min for tests below 1000 °C (test specimenlength: 50 mm, displacement
oe
rate: 0.5 mm/min} and 1.176 % for 1000
and higher (test specimen length:
85 mm, displacement rate: 1.0 mm/min). The following explanations are oriented to
uniaxial tensile tests with cylindrical test specimen.
The blue curve in Figure 7 shows the measured values of the engineering or nominal
stress-strain relation. The engineering I nominal stress is defined as:
Eq.2
Where F(t} is the current measured force and A o the original cross sectional area.
And the engineering strain is calculated by:
8
n
=
L(t)-Lo
L
Eq.3
o
With L(t} and Lo as the current and originallength of the specimen, respectively. For
small strains the accuracy of these engineering values is sufficient, but for large deformation analysis the natural strain and the true stress are needed. The natural or
true strain increment is defined as:
ds = dL
Eq.4
L
t
The integration from the original length Lo. where 8=0, to the actual length L(t} provides the true strain:
140
100
/
2!.
80
'jji
0»
~
60
CI)
40
20
,/
,/
17
~\
/
~,/
l e:;........
al
1ft
1ft
/
L,...--
~
---- r--
- - ---~
stress- elatior fromtE nsile tE stuntil
~
y
MISO- urve e cordin totru strein
\0:
~%tru
strein
~
V
==-' - - t
,
0
end 0 MISO urve
corre ponds
true r pture 5 ~ein
VI
~
r-- """""-
:--- r--
:----
r-- r--
r-. r--
---
Iotal de ormati nof1. P%
defon ation fO.2%
en( ofpur efesti defon ation
o
o
-
-
0
trein "ultim ten StrE ssou. ISO-CL rve
orresppndst( truest ein at naximu
rue StrE ssob~ erved
............
, 'Q"~" ,'Q'"
,/
/ .J
';'
c.
..,.,..
J
120
ulti mete s ess of MISO- urve C rrespe nds
to Inaxim mtrue tress bservE dinen test
5
10
15
20
25
--REVISA 800°C Eng. StrainJStress epsdot=1.0%/min
REVISA 800°C True StrainJStress
.. ANSYS MISO 800°C
---20MnMoNi55 Eng. StrainJStress epsdot=2.5%/min
---20MnMoNi55 Eng. StrainJStress epsdot=50%/min
-REVISA 65MPa Creep Test True Strain/Stress
30
35 40 45
Strain eps f'kl
Figure 7: Plasticity curves and model at 800o
e.
50
55
60
65
10
15
80
_G_e_n_e_ra_t-:io..;,.n-:a:....n.:..:d;....:A-:!pl:..!p:..:.':..::ica~t.::..io:...:n..:...o.::..f:....:a::.....:...H:..:.ii 9i!.:.h:..-T.:..:e:.:m.:.,:pce=.:r.=a=tu:.:..re::...:.:M.:.:a:::te:::.,:r.:.:ia::.'.=D:.::,a:::ta=-B::.a::::s:::,:e::-
19
Eq.5
To get the true stress the instantaneous cross sectional area A(t) has to be considered:
0"
t _ F(t)
Eq.6
t( ) - A(t)
Usually the volume change due to p/asticity or creep is negligible, Le., the voJume at
any time during the plasticity or creep process is constant (except for tertiary creep,
which is not considered here) after unloading the structure, so that there is no e/astic
volume change. This means, that the original vo/ume Vo of the unloaded structure is
the actual volume V(t) subtracted by the elastic volume change Vel:
Eq.7
Vo = V(t) - Ve1(t) = A o ' L o
For the elastic volume change following relation applies:
Ve1 = Lo(1+8el)·Ao(1-v'8el)2-Lo ·Ao
Eq.8
Usually the elastic strain is rather small «0.5 %, cf. Figure 16), also for large total
strains. Therefore the elastic volume change can be neglected and equation 7 reduces to:
Eq.9
Vo = A o . L o Rl A(t) -L(t)
Using equations 6, 9 and 3 the true stress becomes:
(t)=L(t).F(t) =(1+8
0"
t
L
o
A
)'0"
n
n
Eq.10
0
And finally using eq. 5 the true stress is defined as:
O"t(t) = eSl -O"n
Eq.11
P/otting the true stress against the true strain gives the red curve in Figure 7 (cf. also
Figure 19 in the appendix). It is visible that the true stressis higher than the
engineering stress at the same strain. At the maximum of the true curve the start of
necking can be assumed. I.e., the true stress at the smallest cross areais higher
than the ca/culated true stress with an assumed homogeneous deformation of the
specimen. On the other hand the true rupture strain is smaller than the engineering
rupture strain. But both figures of the true curve - stressand strain -are assumed as
conservative.
During the post-test ca/cu/ations of all REVISA creep tests ISAI 19981 it was observed that the conservative theoretical true stress calculated for the experimental
measurement according to equation 11 at the end of the highest load creep tests can
be clearly higher than the values from the tensUe tests. For the800°Clevel this is
shown in Figure 7 by the continuous black curve (REVJSA 65MPa Creep Test) which
Generation and Application of a High Ternperature Material Data Base
reaches a true stress value of more than 120 MPa contrary to only some 80 MPa in
the tensile test.
The reason is the deformation velocity: at high deformation velocities the resistance
of the material is higher than at low deformation velocities. This can be seen fram
experimental results for the German 20MnMoNi55 steel, which is assumed to be
similar to the French 16MND5 as explained later.
The 800 oe tensile tests for the German steel were performed at 2 different strain
rates: 2.5 %/min and 50 %/min. The measured values for the engineering yield
stress and the ultimate stress are given in Figure 7. Since the s,train rate of the REVISA tensile tests was even lower (1 %) lower corresponding stresses can be expected here. Even considering the fact of 2 similar but still different steels the relation
of the strain rate velocity and the corresponding ultimate stress is reasonable. The
conclusion is, that at the lower strain rate the deformation is not a pure plastic one
since plasticity and creep can occur simultaneously.
Finally the multilinear isotropie hardening curve in the code (MISO-option of ANSYS)
has the following structure:
Pure elastic deformation until 0.05 % strain.
- Stress at 0.2 % plastic strain according to true measurement curve.
Highest observed tensile or creep test stress at the true strain where the maximum true stress was observedin the tensile test (cf. inscription in Figure 7).
-
Approximately 2 % higher stress than previous stress at rupture strain of true
strain curve of tensile test (cf. inscription in Figure 7).
This is a reasonable model to take into account prompt plasticity during creep tests
of different geometry, temperature and loading history.
The corresponding figures of the other temperature levels are shown in the appendix
(Figure 20 to Figure 30).
_G_e_n_e_ra_t_io_n_a_n_d_A.....!PwP_Ii_c_at_io_n.:,..o..:..f:.....:a:.:..:...H~ig~h_T.:,..e:..:.m.:..:Jp!:,.e:..:.r.::.:a.::..::tu.:.::.,.re.:...:.:M.::..::a.:.:,te::.;r.:.:ia::..I..=D:.=a:::ta=-=-B.::.as=.,:e=--
21
3. Creep and Damage Modeling in the Transient
Mechanical Calculations
Because of the large spatial and transient temperature and stress changes within the
vessel wall of a 3D-experiment Iike FOREVER, an advanced approach for the numerical creep modeling has been developed. Usually creep is described byanalytical
formulas (creep laws) with a number of free coefficients. The coefficients are used to
adapt the creep laws to creep test results performed at constant load and temperature. However, it is difficult to achieve a satisfying adjustment for a wide range of
temperatures and stresses with only one set of coefficients. Therefore a supplementary tool for the ANSYS® code has been developed, which allows to describe the
creep behavior of a material for different stress and temperature levels independently by means of a creep data base (CDB). The Digital® Fortran Compiler (Rev. 6.5)
was used for programming and for generating the customized ANSYS-executable on
a Windows/NT® platform (/ALT 20001, /WIL 2001/). The creep data base has been
generated based on an analysis of the measured data performed by Ikonen IIKO
1999/. Due to the uncertainties of the creep fracture strains measured in the uniaxial
tests the creep fracture strain 8:'c was set conservatively for each temperature level.
It is ranging from 35% at 600°C to 65% at 1000 °C. The plasticity of the materialis
modeled by using the multilinear isotropie hardening option of ANSYS® IANS2001/.
The plastic fracture strain E ~c is evaluated from the last point of the stress-strain
curve (cf. chapter 2.6).
For the prediction of a failure time it is necessary to calculate a damage criterion.
The material damage due to significant creep and plastic strains is modeJed by a
damage measure D which is incrementally accumulated at the end of a time stepor
substep. D=O means "no damage", which is the initial value for all elements. The
damage includes also the prompt plastic deformation of the structure. The damage
increment is:
,Eq.12
with
E:'c
being the creep fracture strain of the uniaxial creep test at constantstress
and temperature and E ~ being the plastic fracture strainat the corresponding tern..
perature. Both strain components are calculated separately according to the experimentally found material behavior ISA11998/, which is described in the next sections.
R y is a function which considers the damage behavior in dependence on the triaxial..
ity of the stress tensor ILEM 1996/:
~
R" = .(1 + v) +J. (l-2v){
:~
r
where v is the elastic Poisson's ratio,
'ah
Eq.13
is the hydrostatic stress and
G'llqy
is the von"
Mises equivalent stress. The damageincrementis calculated for eachelement
averaging its nodal equivalentcreepstrains. The accumulated damage is:
by
.....:G:.....e:.....n_e_ra_t_io_n.....:a:.....n.....:d_A"'"'""p!....!p'-l.....:ic.:..:a.::..tio.:..:n..:.....:..of:.....a:.:...:...H~ig~h:.....T..:....e.:..:m..:.:.!:.pe..;..r_a_tu_r_e_M_a_t_er_ia_I_D_a_ta
__B_a.....:s_e
ldstep
D= ~>IDi
22
Eq.14
i=l
If the element damage reaches the value of D=1, the element is killed by setting its
death f1ag to 1, Le., this element does no longer contribute to the wall strength. The
implementation of this model is described in IALT 20001.
23
_G_e_n_e_ra_t_io_n_a_n_d_A...:p....:.p_li_ca_t_io_n_o_f--:a_ H_. .:;ig:--h_T_e_m..,.!p!.:,. e:. .:.r. : .at.:.=u:.:. ,;re:. . :.: .M:. .:.a_te:. .:.r.:.=ia:. :. 1.::O..=a.::ta::...;B=-a=.;s::..:e=---
4. The Considered French 16MND5 and German
20MnMoNi55 Steets
In this work 2 nominal types of RPV-steel are considered in different tests: the
French 16MN05 and the German 20MnMoNi55. At first the Creep Oata Base (COB)
is developed fram uniaxial creep tests (/SAI 19981 and IIKO 1999/) of the French
16MN05 RPV-steel and then the comparability of the 2 steels is investigated.
Figure 8 shows the region that is covered by the COB. The arrays 1 to 4 show the
points where uniaxial creep test were performed. The upper bound is not only depended fram the true ultimate stress of the corresponding tensile test, but also fram
the maximum observed theoretical true stress of anycreep test at the corresponding
temperature (cf. chapter 2.6 Plasticity).
There are 8 temperature levels in the COB starting from 873 K up to 1573 K in steps
of 100 K. At each temperature level there are 5 equidistant stress levels ranging from
20 % of the yield stress of the next higher temperature level to the ultimate stress
level of the next lower temperature level. I.e. the numerical COß provides also temperature and stress combinations where the stress is higher than the ultimate stress
which is physically unrealistic. However, these areas of the COß are never used because the plasticity model of ANSYS causes a failure after reaching the ultimate
stress (cf. chapter 2.6 Plasticity).
Stress-Temperature-Map
1000
100
f----,f---....p,...~~~t_=""-:::"""-r-;:::--+--t---1
-e-20%-Yield Stress
-tr- Yield Stressor SigO.2%
-e- True Ultimate Stress
--Creep TestArray 1
--Creep Test Array 2
____ Creep Test Array 3
-l-Creep TestArray4
- - Region Covered by COS
--+t-Max. Stress in Creep Test
1
700
800
900
1000
1100
1200
Temperature [K]
1300
1400
1500
Figure 8: Stress-temperature range covered by the 16MN05..based CDB.
1600
Timet[h]
o
20
10
30
50
40
0.7
0.7
0.6
I
I
..:...
i
111
c.
GI
c 0.4
g
GI
~
I
I
..... 0.5
o
• - • - 25MPa ANSYS
- •.• 40MPa ANSYS
• ••. 70MPa ANSYS
• .• - 90MPa ANSYS
--25MPa REVISA
-40MPa REVISA
-70MPa REVISA
90MPa REVISA
i
.
.
~
:
0.3
0.1
o
I
..
1
.
.-
/
..--::;.
-------- ~
V!~
36000
0.6
0.5
/
OA
0.3
./
)/
o
I
.. /
: I
I
i
I
.
I
0.2
T=700·C
0.2
~
_... -...... -
0.1
o
72000
Time t [s]
108000
144000
180000
Figure 9: Comparison of uniaxial creep tests at 700°C.
As an example Figure 9 shows the comparison of the REVISA tests at 700°C with
the calculated results from ANSYS. There are some deviations between the calculated and experimental results, but they are considered as acceptable in view of:
i)
only small conservative deviations of less than 20 % for the short time runs
(like the 90 and 70 MPa-runs) and
ii)
a conservative behavior for long time runs (Iike the 40 MPa-run).
The reason is that the main application of this COßis related to experiments and
prototypic scenarios where a short to medium failure time range is investigated or
expected, Le. typically between 1 and 20 hours. On the other hand it is not known
whether each experimental creep curve is really representative, because there is a
large scatter even for different specimen of the same heat when tested at the same
temperature and stress level.
This can be seen in Figure 10, which shows uniaxial creep tests for the French and
the German steet at 800°C and an engineering stress of 65MPa. There was only 1
test of 16MND5 (CEA), whereas there were 5 tests of 20MnMoNi55 (MPA) with the
fastest and the slowest creep curve shown. The failure occurred after 4,700s in the
stowest test and after 3,800s in the fastest test. This corresponds to a difference of
some 20%, and gives an idea about the scatter that can be expected tor the
16MND5 tests, too. Finally, the red curve shows the calculated ANSYS curve corresponding to the developed 16MND5-based COß.
The comparison ot all REVISA creep tests trom 600°C to 1300°C is shown in the
appendix (Figure 31 to Figure 37).
.....:G:.....:e:...:..n;,.;;e_ra:..:..:t.:..:io..:..;n:.....:a::,:.:.n.:..:d:...::A....:!p!:.!p:..::li:.:;c=at:;,:io:.:n..:-o=-f:...,:a::...:...H:..:.si9:!..:..h:...T.:-:e::::m.:x.:Pe::::r~a:::tu::.re:::..~M~a~te~r..:::ia~I..:::O~a~ta:..:::Ba~s~e~
25
Time t [h]
0.75
1
1.25
1.5
0.8 I - - - - - - - j - - - - - - - t - - - - f - - - - - I - - - - - l - - - - - - - - - + 0.8
o
0.25
0.5
0.6
-..
i 0.5
c
.; 0.4
a
-16MND5 CEA-test
-e-20MnMoNi55 min MPA-test
GI
.g:
1----1
0.5
-ir-20MnMoNi55 max MPA-test
I--+--~-+l---""""""~-+-----+
I) 4
-ANSYS c16m865
•
----+---c----r-------jl--*--"b....=,~~---+-------+
0.3
0.3
I-
.
-,_.~--+~-=----.~F-
0.2
.~-~-
---
------
0.2
·--+0.1
0.1
o~~::::::=:L~~~L~--'--'--'~'--'-'-'-'---'-'-'-'-L~ .............,...L.............,'--'-'-~o
o
900
1800
2700
Time t[$]
3600
4500
5400
Figure 10: Comparison of the creep behavior of 16MNOS and 20MnMoNi5S with the
applied ANSYS COB at 800°C and 65MPa.
Table 1 lists the chemical composition, the thermal treatment, and the mechanical
properties at room temperature of the considered steels. Comparing the chemical
composition it seems that the differences between the two 16MNOS heats are in the
same range as the differences of the 16MN05 steel to the 20MnMoNiS5 steel. Also
the thermal treatment seems to be rather similar. The assumption of similarityis
supported by the resulting bainitic microstructure of aH specimen.
There are some differences in the mechanical properties, buteven the weaker
16MN05 values for the yield and tensile strength would fulfill the regulation values
according to the German KTA 3201.1.
After analyzing these figures it is assumed that an application of the 16MN05-based
COS to creep tests with 20MnMoNiS5-steel is reasonable.
_G_e_n_e_ra_t_io_n_a_n_d_A-:p,-,p_li_c_at_io_n_o_f_a~H:.:.:::ig,-h_T_e_m-.:....pe_r_a_tu_re_M_a_te_r_ia_I_D_a_ta_B_a__
se
Chemical comoosition
[wt.-%]
Source:
C
Si
Mn
P
S
Cr
Ni
Mo
V
Cu
AI
Sn
As
Thermal treatment: Quenching
A.C.: Air Cooled
W.C.: Water Cooled Tempering
F.C.: Furnace Cooled
Simulated Stress
Relieving
Resulting microstructure:
Mechanical
Yield strength
Properties at room
temperature:
Tensile strength
Elonaation
Reduction of area
16MND5
RUPTHER14
IMaN 19991
0.17
0.25
1.44
0.004
0.002
0.2
0.75
0.51
0.004
0.01
0.016
0.001
0.001
877-891 °C_
8.7 hlW.C.
635-652 °C_
9.0h/A.C.
618-625 °C_
6.3 h/F.C.
bainitic
473-488 MPa
620-724 MPa
25%
73%
16MND5
FOREVEREC
IIMA20011
0.105
0.241
1.26
0.0017
0.0006
0.249
0.581
0.568
n/a
0.115
0.0379
n/a
n/a
26
20MnMoNi55
MPA-Meppen
lOBS 19881
0.21
0.24
1.48
0.008
0.005
0.2
0.8
0.52
0.02
0.07
0.015
0.005
0.02
920°C 6.5hlW.C.
655-660 °C_
8.0 h/A.C.
n/a
bainitic
bainitic
567-624 MPa
required: >430 MPa
635-726 MPa
reQ.: 570-710 MPa
22%
64-69 %
Table 1: Comparison of properties and manufacturing data of the investigated
steels.
_G_e_n_e_ra_t_io_n_a_n-:d_A....!.p....!..p_li_ca_t_io_n_o_f_a_H~ig~h.-.,;T:.....:e;..:.;m2P::.....e_rat. ;: u.:. .:re=--M:. :. :. : a: .:te:. .:. rJ:. .:. ·a. :. .'D: . .::.:at.:.:a:....:B::...:a:..:s:.,:;e:...--
27
5. RUPTHER post test calculation
The considered RUPTHER-14-experiment was performed at CEA, France IMON
1999/. Figure 11 shows the principal configuration of this tube failure experiment.
The test pipe of 16MND5 was 270 mm long and 88.9 mmin diameter. The wall
thickness was 2 mm. Due to the centered external heating coil the resulting vertical
temperature profile had its maximum in the vertical center, too. Therefore the maximum displacement and the failure can be expected at the vertical center as shown in
Figure 12.
ANSYS5.7.1
MN
NOOAL SOLUTION
STEP=92
SU8=34
TIME=18960
USUM
RSYS=O
DMX =.012292
SMX =.012292
.0
16
u
~
!
• •001366
•
.002732
•
.004097
•
.005463
.006829
•
.008195
.00956
•
.010926
•
.012292
o
o
V'
Lx
.
\
rx
I
RUPTHER CREEP
Figure 11: Principal configuration of the
RUPTHER-14 experiment
[mm).
Figure 12: Example of resutting
ANSYS deformation at failure
[m}.
-=G:....:e:....:n_e_ra_t_io_n_a_n_d_A-'p~p'-.l_ic_a_tio_n_of_a H;..:..:ig~h__T_e_m_.L.p__
er:..:a:...:.:tu:..:.r..::.e...:..M:..:..a:....:t_e_ria_I-:D:....:a::..:ta=-::B:..:a:..:s..::.e
28
Timet [h]
o
6
8
4
7
2
3
5
30 1 - - - - + - - - - - 1 - - - - + - - - - + - - - 1 - - - - - 1 - - - - - - 1 - - - - - 1 1500
1250
25
g
IGJ
1000 :i
1!GJ
D.
E
750 ~
--···---hH+··---···----ii-·-··--····.. ··-~--··1
5
- Experim. Diameter Increase
- rupto2, T+OK, eps-brk=0.5
- rupt03, T+5K, eps-brk=0.6
-rupt05, T-5K, eps-brk=0.6
-a- Temperature T
__ Pressure p
OJ....-Le...-'--'-~~-'---l.-.L-'--'--'-->---L-'--'~.........J......L--'--'-....c.....J'--'---'--'-'-.L...s.-'--'--'-....i..-'--'--'--'....Jo
o
3600
7200
10800
14400
18000
21600
25200
28800
Timet [sI
Figure 13: Loading history of RUPTHER-14 and comparison of the measured
and calculated diameter increase.
Figure 13 contains the loading history and the central diameter increase of the RUPTHER-14 experiment. After increasing the pressure to 8 bar the temperature was
at the hot spot. This regime was kept until 18,000 s, when the
increased to 1000
pressure was slightly reduced to reach a level of 6 bar after 25,200 s. But the tube
failed earlier: at 22,180 s.
Despite of the application of different boundary conditions and slight temperature
changes it was not possible to get numerical results for the time dependent diameter
increase showing exactly the same behavior as measured. The calculations rupt02
to 05 differ in the slightly changed temperature (+5 K, -5 K respectively) and the assumed rupture strain in rupt02 was reduced to 50 %, while it was normally 60 %. Especially the strong radius increase just after reaching the high temperature level at
1,800 sand the accelerated creep at the pressure reduction stage can not be represented by the code.
If the reason for this discrepancy is not the numerical model, one experimental uncertainty might be the temperature. The temperatures might have been higher in the
wall - especially at the beginning of the high temperature level - than the thermocoupies show, because they are mounted on the wall. Additionally a distance change
between the tube and the induction coil can cause a temperature change. This could
be considered for the last stage, when the pressure was dropping, but the creep process accelerated. Another reason can be the scale of the experiment. A wall
thickness of 2 mm is relatively thin and small deviations from the design state - either geometrical or material - have a large influence. The suspension effect of relatively thick components does not apply to this thin tube.
oe
_G_e_n_e_ra_t_io_n_a_n_d_A....!p~·p_li_c_at_io_n_o_f_a_H~i9!.-h_T_e_m_p~e_r:...:..;a...:..;tu;.:,.re-=---M_a_te_r_ia;.:,.I.=.D..::a;,::ta=-B=-a=.s:..:e::....-
29
6. MPA-Meppen post test calculation
The considered MPA-Meppen test was performed at a test site of the German ar:my
in Meppen, Germany lOBS 1988/. Figure 14 shows the principal configuration ofthis
tube failure experiment. The verticaUy positioned test pipe of 20MnMoNi55 was
2,700 mm long and had an internal diameter of 700 mm. The wall thickness was
47 mm. Several external heating coils were placed vertically around the pipe and the
resulting vertical temperature profile had its maximum in the verticaI center with a
measured maximum at the end of the test of 735 oe.
Therefore the maximum displacement and the failure site can be expected at the
vertical centre as shown in Figure 15, which shows the upper half of the deformed
FE-model. The loading history ofthe MPA-Meppen test is given in Figure 16. Starting
with apressure of 120 bar, the pressure was increased to 165 bar and the temperature was increased in three stages to 735 oe at the hot spot. This regime was kept
until failure. Because temperatures around 700 oe were only achieved during the last
1,200 s significant deformation is also only recorded for this period. Figure 17shows
the comparison of the radius development between the test and different calculations
for the last stage. The calculations UR1 to UR3 differ only in their temperature field,
which has been shifted by ß T=5 K up or down.
Suspension
~:
~-="t
~
"
"
ANSYS5.7.1
\
,
Extension Pipe
'"
........... :
0
0
\
......
I
C'I
I
\
\.
--0
"
, __'?5
,
\
\
TestP~
y
47
I
0
I
Material:
20 MnMoNi55
Ap=164 bar
Tmal(=735°C
x
I
,heT°()-"
I
'
.
,
I
,,
0
......
C'I
"
0
,-.
Extension Pipe "
,
"
., 65
I
'.
I
"
&...
!
DM)( =.159562
SMN=.00135
SMX=.159562
.00135
•
.024262
.041175
•
.058087
•
.075
II!I .091912
.108824
.125737
•142649
•
.159562
!!
.,
I
NODAL SOLUTION
STEP=81
SUB =2
TIME=12533
USUM (AVG)
RSYS=O
0
......
C\I
o
o
"
,
,
~
Figure 14: Principal scheme of the
MPA-Meppen test [mm].
MPA-Meppen test
y
Lx
Figure 15: ealculateddisplacementat
failure [m]. (Tma~998K)
Time t [h]
0.5
1
1.5
2.5
2
3.5
3
150
~ 135
B
900
0.120
f
~ 105
11I
f
0..
f
r
90
I
~
E
S 75
a:
-E
:;)
c
'"g
825
i
I
750
I--
675
600
60
45 ~---+---
'ii.
CI>
a
o
o
1800
3600
5400
7200
Timet[s]
9000
10800
12600
Figure 16: Loading history of MPA-Meppen test and comparison of the measured
and calculated radius increase.
3
3.125
3.25 Time t [h] 3.375
3.5
3.625
150
1050
--
--l=--='==F====t-=W--+-~.+---_.
135
1000
120
'E 105
.5.
c:: 90
t----r.-=:J"U~R;n(t)\.e~x;pm;;:;-. --'---I---+---i,L-)-I-·-+t------1 900
-UR2(t) Tmax=993K
~UR1(t) Tmax=998K
.~.~. UR3(t) Tmax=1003K
- - expm ,. Rupture t=12,493s
-Tmax (right axis)
::;)
i
75
~
60
E
~
.Ä.
~
Cl
~._--+-~t--f---jrt-i+----___I850
I-~·----··--·..I---;!-__f__l----ff'-__t-
----1800
=-==-=+=:==:::=:::==t===----J;C--J'---1I-+-+-------1
.~_.=
...gf
ia.
...E
GI
750
GI
45
15
o
- - - t - - - - + - - - - - - - I 600
..................--'-'->...........-L..............................'-'-......L...........-'-"--'-..........--'-L..-............-'-"'--'-.h.....-L."'--'-~'-'-""-'.-....>--l
10900
11250
11700
Timet[s]
12150
12600
550
13050
Figure 17: Comparison of the radius development during the last stage of the
MPA-Meppen test.
_G_e_n_e_ra_t_io_n_a_n_d_A.....,:pc...!.p_li_c_at_io_n_o_t_a_ _
H...;;:ig~h_T_e...:.m..:.:;p!:-e.:...r_a_tu_re_M_a
__te.__r,;.:ia::..'.::..D...;.;a.,;..ta_B_a_s_e
31
A relativelygood agreement between calculation and measurement was achieved.
Again a main uncertainty might be the temperature. It is difficult to readand analyse
the temperatures trom the found literature lOBS 19881 and additionally there might
have been some measurement error. Another reason could be the higher yield stress
of the material applied in Meppen compared to the yield stress in the numerical
model, which is based on 16MND5.
..:G:.:e:.:n.:.:e:.::..:ra=.:t::.:io:..:..n:....:a=n..:.:d:...:A:....:J:..pp!:-:l~ic:..=a=tio,:;.:n:..:....::.o~f
a=...:..H.:..::i9s:!:h~T..:...e,:;.:m:..:...:..cp,:;.:er:....:a:.::.:tU:..:.r..::.e...:.M:.::.:a=.:t:..:.e.:..:.ria=.:I:...:D:..:a::.:t=.a-=B:..::a:..:.s.=.e
32
7. Conclusions
A creep and material data base has been developed from the uniaxial tensile and
creep tests of the REVISA program for the French 16MND5 steel. It is validated that
the code simulates each uniaxial creep test (1 D-problem) conservative and calculates mostly a close to experiment failure time.
The numerical creep and plasticity model has been applied to 2 tube-failure (2Dproblem) experiments at different scales and of nomiinal different steels. The RUPTHER-14 and the "MPA-Meppen"-experiment. The comparison shows that not all
effects can be represented by the numerical model, but the reason might not be the
different kinds of steels rather than temperature effects in the experiments or different heats of the same steel. This assumption has to be investigated further.
An application of the numerical model to the 3D-experiment EC-FOREVER-2 has
been performed, but will be improved. Also an extension to other 3D-problems is
planed.
,~-
_
-------- -----
_G_e_n_e_ra_ti...::.o~n...::.a:.:..;:n.::.d.:..AIP..!:.p:..::..:lic:.:a.:..::.:ti.::.on:...:....:..of.:..a::....:....H:..:.5ig:!.:.h:...T:....:e:.:.m:..:Jpc:..::e:.:.r=at:::u.:.;re::....:M:..:.=at=e::.:ri=al:...:D:.:a~t::::.a-=B:.:::a::::.se::::.-..
33
8. References
IALT 20001
IANS 20011
ICHU 19991
IIKO 19991
ILEM 19961
IMON 19991
lOBS 19881
IREM 19931
ISAI19981
ISEH19991
ITHF 19971
IWIL 20011
E. Altstadt, Th. Moessner. Extension of the ANSYS® creep and damage simulation capabilities. Report, FZR-296, Forschungszentrum
Rossendorf, Dresden, Germany, 2000.
ANSYS®, Programmer's Manual, ANSYS®, Inc., 2001.
T.V. Chu, M.M. Pilch, J.H. Bentz, J.S. Ludwigsen, W.Y. Lu, L.L.
Humphries: Lower Head Failure Experiments and Analyses. Report,
NUREG/CR-5582, SAND98-2047, Sandia National Laboratories, AIM. Kadner, Prüfbericht
buquerque, NM, USA, 1999.11MA 20011
Nr. A 191/1, Chemical Analysis of a steel specimen, Dresden, 2001.
Ikonen, K., Creep Model Fitting Derived from REVISA Creep, Tensile
and Relaxation Measurements, Technical Report MOSES-4/99, VTTEnergy, Espoo, Finland, 1999.
J. Lemaitre, A Course on Damage Mechanics, ISBN 3-540-60980-6,
2nd edition Springer-Verlag Berlin, Heidelberg, New York, 1996.
Ph. Mongabure, M. Desmet, RUPTHER Test#14 - Rupture test at
1000°C and variable pressure 8 then 6 bars, Report
SEMT/LISN/RT/99-003/A, CEA, France, 1999.
V.-D. Obst, A. Klenk, P. Juliseh, K. Maile, Versuche zum Versagen
einer Hauptkühlmittelleitung infolge Kriechbruch unter hohem Systemdruck, (Tests about the failure of a main feed line due to creep
under high system pressure) Report MPA 1500 771, Stuttgart, Germany, 1988.
J.L. Rempe, S.A. Chavez, G.L Thinnes, C.M. Allison, G.E. Korth,R.J.
Witt, J.J. Sienicki, S.K. Wang, LA. Stickler, C.H. Heath, S.O. Snow:
Light Water Reactor Lower Head Failure Analysis. Report NUREG/CR-5642, Idaho Falls, 1993.
C. Sainte Catherine, Tensile and creep tests material characterization
of pressure vessel steel (16MND5) at high temperatures (20 up (o
1300°C), Rapport SEMT/LISN/RT/98-009/A, CEA, France, (experimental data files), 1998.
Sehgal, B.R., Nourgaliev, RR., Dinh, T.N., Karbojian, A, FOREVER
experimental program on reactor pressure vessel creep behaviour
and core debris retention, Proceedings of the 15-th International Conference on Structural Mechanics in Reactor Technology (SMiRT..15),
Seoul, Korea, August 15-20, 1999.
T.G. Theofanous, C. Liu, S. Additon, S. AngeHni, O. Kymäläinen, T.
Salmassi. In-vessel coolability and retention of a core melt NucJ.Eng.
Des. 169 1-48 1997
H.-G. Willschütz, E. Altstadt, B.R Sehgal, and F.-P Weiss: Coupled
thermal structural analysis of LWR vessel creep (ai/ure experiments,
NUCLEAR ENGINEERING AND DESIGN, vol 208, pp 265-282, 2001.
9. Acknowledgement
This work has been funded by the German Ministry of Economics BMWi under Contract No. 1501254.
The FOREVER experiments are performed under the sponsorship of the ARVI Project of the 5th-Framework Programme of the EU and the APRI Project jointly supported by SKI, Swedish and Finish Power Companies, USNRC, and HSK.
This work is supported by the ARTHUR UND AENNE FEINDT-STIFTUNG, Hamburg.
_G_e_n_e_ra_t1_·o_n_a..:...n:..::;d..:...Ä2p::..!:p:..:.:li..:...ca..:...t....:io:..:..n:......;o:..:f:..:a:...;H:...:.3
ig~h--:T:..:e:..:.;m:.:!p:.:e::.ra:::.:t:::u~re~M~a.::.:te::.ri:=:::a.:...;1D~at~a~B~a~s~e:--
35
10. Appendix
700
--
~ ----
600
'iii' 500
~..... ~~
~
c..
!.
.~ 400
------
V
111
III
GI
.b
eil
I:ll
C
300
--.J
(
-
'e
GI
GI
.5 200
l:ll
-20·C
200·C
- - 400·C
-500·C
--550·C
-600·C
-650·C
-700·C
-SOO·C
-950·C
--1000·C
--1100·C
-1200·C
1300·C
~~
~
-~
~
1\.
C
w
/"
100
r-0
15
10
Engineering Strain eps r't.]
5
0
25
20
Figure 18: Engineering stress-strain curves of 16MND5 (REVISA-tests).
100
-;p
/'
600
500
'iii'
c..
r!.
400
l:ll
'jjj
~
'tI
~
:::.-L---r
111
300
GI
~
-- ~
---- ~ '\
Ir
----.,
~
"\~
~
200
100
r
r.r-
~,
~,
.~-
-
o
o
-20·C
-200·C
-400·C
-500°C
-550°C
-600°C
-650·C
_700°C
-SOO°C
-,-950"C
-1000·C
_. 1100"C
-1200·C
-·1300"C
~
I'
III
1:eil
-
5
15
10
TrueStrain ep$l%]
20
Figure 19: True stress-straincurves of 16MND5 (REVISA..tests).
25
...:G:..:e:..:.n.:..:e...:..ra::..;t:..:io...:..n:....:a=n.:..:d::...:A:....:p!:...!p~l.:..:ic...:..a...:.tio:..:n...:....::...of:..:a:::...:...H:.:.:ig:!.-h_T_e_m_~pe_.r_a_tu_re_M_a_t_er_ia_I...:.D:....:a.:..:ta.:.-=:B...::.a:..:.s..::...e
700
~
600
/
500
:!
'-'"
~
.--
-~
~
--
I~
~
1
'iii'
Q.
~
-- --
I
i,
I'
400
36
I
1
lCll
'ijj
III
III
G)
300
.tI
VI
200
--REVISA 20°C Eng. StrainJStress
--REVISA 20°C True StrainJStress
- ... ANSYS MISO 20°C
100
o
o
10
5
15
20
25
Strain eps rk]
Figure 20: Measured and modeled Stress-strain relations at 20°C.
700
500
'iii'
Q.
~ 400
t
-
/- -....
600
~--
-:::....-
-
----... ~
~I\
J
I
,~
..
...
g
--11
111
300
VI
200
- - REVISA 200°C Eng. StrainJStress
-REVISA 200°C True StrainJStress
100
o
o
5
10
15
20
Strain eps rk]
25
_G_e_n_e_ra_t_io_n-.:.a.:.:..n:....::d...:..A..;!:p:...!;p:.:.:li.:.,ca.:.:..t::..;io:.:..n:...:o::.:f...:a:...:H:"":3:!ig~h....:T:..;e:.:.:m:..:Jp:.:e:.:.r.::.at=u::..:re::...:.:.M:::::a::::te:.:.r.:..:ia:=-1.:::::D~a~ta~B~a~s~e:.-
37
700
600
ß
500
I'~
';'
a.
l;5. 400
I:')
.......
Cl)
-.......
~
~
~,
J
J
'jii
1Il
1Il
0
~----
300
r.n
200
)
-.-REVISA 400°C Eng. StrainlStress
--REVISA 400°C True StrainlStress
100
I
o
o
10
5
15
25
20
Strain eps 1%]
600
500
';'
.~
r;
l!.
J
400
a.
I:')
'jii
..-r.:=-
I
300
-
--=:::: ,
~
1Il
1Il
Cl)
J:I
r.n
200
~
'\
--REVISA 500°C Eng. StrainlStress
-REVISA 50QOC True StrainlStress
- ... ANSYS MISO 50QoC
100
o
D
5
10
15
Strain epS [Ok]
25
400
350
-~
""'Ir
300
-......J
J
'I
.--
';;' 250
Q.
~
Cl
ii
------ ---
.-- -----
... J_
-
-
~
------ -------"""
~
------ ~
200
~
~
rn
rn
....e
t/)
I-
150
\ "
100
REVlSA 600°C Eng. StrainfSlress
REVlSA 600°C True SlrainlStress
- . ANSYS MISO 600°C
- - REVlSA 248MPa Creep Test True StrainfSlress
50 I - -
""
\
o
o
5
10
15
25
20
35
30
straln eps [%]
180
,
160
140
120
';j'
~
~ 100
1:1)
..,..... ..---"i""
J
tf=: ~
I
J
l,...--
';
=
=
~
80
l»
,J:l
'""
---
~
~
~ [>< i'..
""-...
........
r-.-.. ~
~
(I)
--
~
60
~
~
'""-
~~
~
40
~ "'\ "r"\. ~ .......
--REVISA 700°C Eng. StrainJStress
REVISA 700°C True StrainJStress
REVISA 90MPa Creep Test True StrainlStress
20
'\
..........
o
o
5
10
15
20
25
30
35
40
45
50
55
Straineps [%1
"
60
I'-
65
70
_G_e_n_e_ra_ti_o_n_a_n_d_A....!,p...!.p...;.li_ca_t_io..,;.n;.,..o::...::f-:a::....;H:...:.:.s!ig~h......:T-:e:..:..:m:.:!p:.:e:.:.:ra=t=u.:.:re::...:M::.:::a.::te:.:.:ri=a.:....:1D:::.a~t~a:.....::B~a::::s~e:...-
39
60
fo-.
50
/
/
•
40
J'~-
';'
c.
il!.
al
'jjj
30
t?
!--
lI)
lI)
~
(/)
20
".-
-------
--
V
-------- ---~
><:
l..---""
--- V- ',...-~
~
"\
--- ----
""-
V
\
--1"",,-
T
I
I
35 40 45
Strain eps rlo]
50
55
I
I
o
5
10
15
20
25
30
I
---- -
\
--REVISA 950°C Eng. Strain/Stress
-.--REVISA 950°C True Strain/Stress
- .. ANSYS MISO 950°C
-·-REVISA 1000°C 26MPa Creep Test True Strain/Stress
10
o
/
-
1--11
-
/
\
60
65
70
75
60
50
I-
-
-
/
/
/
al
.1
30
I/)
I/)
~
(/)
~
I.
)
W ~ ~ rr- , ~ ~
-,
c.
'jjj
.
,
rn''''''i
_....LIoi
';'
!.
.1 •
-,
40
r:-
~
~
J
r
~
(lC
~
1[""Ti'f
~
-----
11"" ~
~
T~
~ ..
,
\
o
-REVISA 1000°C Eng.StrainlStress
-REVISA 1000°C True StrainlStress
- .. ANSYS MISQ 1000°C
-REVISA 1000°C 26MPacreep Test True StrainlStress
o
5
10
15
20
25
-
....
20
10
.--..- ~
30
35 40 45
Strain epsrk]
50
,
N
5560
~
65
Figure 27: .Measured and modeled Stress-strainrelations at 1000°C.
70
75
_G_e_n_e_ra_t_io_n_a_n....,:d_A_p!....!pc.....l_ic_a_tio_n__
of.:..-a.:.:...:.-H.:..:::ig~h.:.:.T.:...e.:...m----Lp..:..er:...:a=tu=r..:.e~M:....a_t_e:..:.ria:..:.:I-=D:.....:a:.:.:ta.::.-=B:...:a=s..:.e
.-
30
j
25
l'
~ ~
~
) ~
20
l
'iii'
c.
r!
l:Il
'in 15
Ul
Ul
~
I- _ -
--
-- -- -- --
I--
~~
I.--J,o Ir""
1
1
lLi
1' ~
V
/
~ ~l. ~
I
1
J:l
CI)
10
~~~\
- - REVISA 11 OO°C Eng. StrainJStress
--REVISA 1100°C True StrainlStress
--REVISA 16MPa Creep Test True StrainJStress
o
o
5
10
•
--",V
l»
5
1---
40
15
20
25
30
~
35 40
45
Strain eps [010]
~
• ~~
I
~
50
1
I
f"i~
,j
55
60
~
65
'" l..
70
75
Figure 28: Measured and modeled Stress-strain relatiions at 11 oooe.
18
16
--
---- ----
14
12
'iii'
c.
:!. 10
'.
l:Il
al
Ul
~
CI)
8
6
4
--REVISA 1200°C Eng. StrainlStress
2 I---H---REVISA 1200°C True StrainlStress
-REVISA 9MPa Creep Test True StrainlStress
0
5
10 15
20
25
30
35 40
45
0
Strain eps [010]
50
55
60
65
Figure 29: Measured and modeled Stress-strain relations at 1200o e.
70
75
_G_e_n_e_ra_t_io_n-:a...:..n:....:.d:...:.A",,:!p:..rp:.:;li:..:.c.::.at::..;io:....:.n.:.-o:..:;f-.:;a:...:...:H3;ig!.:..:h:-:T:..:e:::.m:..:.Jpt:..:e::..:.r.::.at~u::re~M::::a:::te::..:.r.:::ia::..1~D~a~ta~B~a~s~e~
41
12
--REVISA 1300·C Eng. StrainlStress
--REVISA 1300·C True StrainlStress
- . ANSYS MISO 1300·C
--REVISA 4MPa Creep Test True StrainlStress
10
....
8
';'
Q.
~
Cl
'iii
6
Ul
III
~
rA
4
2a_-I---+--/---\----+--J+---IJ!..J--.J.+L----Jf..-I....
O*-'-'--'-'-L....................l--'-'-.......J.~.........L'_'_'_.....L.....L...L..o,...L,.....................L.....c'_'_'_L.................JL......Jf..........l............
o
5
10
15
20
25
30
35
40
45
50
55
60
65
70
Strain eps [Ok]
Figure 30: Measured and modeled 8tress-strain relations at 1300°C.
Time t[h)
o
30
20
10
40
50
0.5 ,--..,..--.,----,,--..,..--..-----.,-...-...,-----.,-...--.---y--.---.--,.-,.---.-------,...--.---, 0.5
T=600·C
0.45
E------j------t------t--;::====:::::l:::======:::::::;-.-:J 0.45
I
.- •• 115MPa ANSYS
0.4 ~--:---I-__I_-----+------1-__I" - . 150MPaANSYS ---.,.; 0.4
•••• 190MPa ANSYS
0.35 ~-..!-----l-__I_----+--+------1-+__I- - .. 248MPa ANSYS ---.,.; 0.35
I
Z
~
0.3
'"
J.:
~ 0.25
~
0.2
0.15
0.1
-115MPaREVISA
1+---'----+-+---.;.--+-------1-1j-I--150MPa REVlSAI---O.3
;
I
--190MPaREVISA
-248MPa REVISAI-- 0.25
1+--_-'--/+---+------i:'-----l----/--j4------+-----1
0.2
: J-----J'---::-~••----t/--::..,.,e-----t-----+.-:.:-=:-,........;:..:.;...._---l M
~-';'~-f/
" /
~/
-~
.
D.15
o
____::::::::::?:': _.' _•• • •
•
~·~f/~~.~.--t··~~~~~~=:·:-=-:·
"3:-:~"~.-~.~':-:'t==:J---"'"ot
0.05
05
'-.'/ ~ .,.
i:-:~~-'
o
36000
72000
Timet(s}
108000
144000
Figure 31: Comparison of uniaxialereep tests andcalculation at 600"0,
'0
180000
75
Timet[h]
o
10
20
40
30
50
0.7
0.1
T=800·C
0.6
·
,·
·
.,·
0.5
:
:::::
III
i'
0.4
c
!
Cl>
...e
0.6
I
0.3
/
,//
'
~
/
~----
-
o
/
..
I
o
~.j
/
.
0.1
/)
/
1
0.2
I
11
:
- - -. 18MPaANSYS
- • - • 25MPa ANSYS
•••• 43MPa ANSYS
... - 65MPa ANSYS
--18MPaREVJSA
-25MPaREVISA
--43MPa REVISA
65MPa REVISA
............. -.- --'
.
. --,
.-- ,-- -. -
- -- --
--. ---·
---
0.5
0.4
0.3
----.- -
-
0.2
0.1
o
36000
12000
Time t [s]
144000
108000
180000
Figure 32: Comparison of uniaxial creep tests and calculation at 800°C.
Timet[h]
o
10
20
40
30
50
0.8
0.8
T=900·C
0.7
.
0.6
::::: 0.5
III
Co
GI
gc 0.4
t.n
~ 0.3
...
s
I
f
0.2
o
V
I
,,
,
·
:
··
. :/
U!
l
0.1
I
.
..
•
,..
.,"
. ~/
.Y
~
o
)
I
I
---
36000
/v
-
0.7
- - -. 13MPa ANSYS
• • - • 20MPa ANSYS
· • - • 28MPa ANSYS
• - - . 38MPa ANSYS
13MPa REVISA
-20MPa REVJSA
-28MPa REVISA
-38MPa REVISA
/
0.6
0.5
0.4
-
~
.
,
.-
-.----::: ~
'"
-~
0.3
0.2
0.1
o
72000
Time t [s]
108000
144000
Figura 33: Comparison of uniaxial creep tests and calculation at 90QoC.
180000
_G_e_n_e_ra_t_io_n_a_n_d_A.....!p'-!.p:...;.li:...;.c_at_io_n_o~f:....::a::...:....:H:.:.si9:!.:..h:.-T:...;.e:.:.m.:.:.p!:.,.e::.;:li..=a:.:.:tu::.re:::...:.:M.::a:.:te::..:r:..::ia::..I..=D::a:.::.:ta::..::::::B,::a:::.:se:::..
43
Time t [h]
o
10
20
30
50
40
0.1
0.1
• . - - 9.5MPa ANSYS
• - - - 15.1MPa ANSYS
• - - - 17.1MPa ANSYS
- - - - 26MPa ANSYS
-9.5MPa REVISA
15.1MPa REVISA
-17.1MPaREVISA
--26MPa REVISA
0.6
I (:
0.5
,
"i'"
.-
1
III
,/,.: .: /
c
g
lI)
GI
0.3
0.2
o
/
/
'
!I
.. -~
~
o
~
36000
-~
........
~
..
.
.
...
.
.. .
.
.
.
0.6
.
..
.
..
0.5
0.4
~ - -------.
7/
2
I-
0.1
J!
. .
tO.4
T=1000·C
0.3
0.2
0.1
o
72000
108000
144000
Timet [5]
180000
Timet[h]
o
0.1
10
40
30
20
50
,..--..,---n-,..----r--r-r---r----,--...----.---.--r----r--r-,...--r----r-.---,,----'"J
0.7
I
- - - • 4.0MPa ANSYS
I r - - - ; - / - - - f - - - - - j - . -. 5.5MPaANSYS H-_---.+-__f-TJ...:'=::.J,1l..1.1WLnnc.k-I'"_-I 0.6
0.6
9.0MPa ANSYS
----16MPaANSYS
:
1
0.5 I ! I - - - ,~--+----...,--4.0MPa REVISA
- 4 - - - - - 1 - - - - - - - 1 0.5
!
I
--.-
1-1--/-4-
:;::
t 0.4'
c '
~
." 0 3
- - 5.5MPa REVISA
• /
- - 9.0MPa REVISA I-f--.L-+.----+-------l 0.4
--16MPa REVISA
.:
V
~I
14--+--+------+---..,-::y~=--------l_-----l0.3
ß'
j ':tl----.J.,I----I-------f-=...;;-o::.----t------+-------;
.J
,y"
. 1/
02
~V
.~
0.1~. ...------- . --". ------o
-_ ... _. .. -* ....
0.1
o
~
o
0.2
36000
12000
Timet [5]
108000
144000
Figure 35: Comparison of uniaxial creep tests andcalculationat 1100~C.
180000
Timet[h]
o
10
20
30
50
40
0.7
0.7
T=1200·C
0.6 'I
.
1
"\
0.5
I
::!::
JI
1Il
~
0.4
~
0.3
l»
~
I
0.2
/
.1
.
.
I~l'
/. .. ---
0.1
I
.
I
//
.5
CI)
..
i
.I
. .. . .-
. . - . . .-
~-_
..
..
. . . --
.
...
0.6
- ••• 2.4MPa ANSYS
• .•• 3.0MPa ANSYS
• .•. 4.5MPa ANSYS
• .•. 9.0MPa ANSYS
2.4MPa REVISA
3.0MPa REVISA
-4.5MPa REVISA
-9.0MPa REVISA
f---
0.5
I---
0.4
0.3
#
.
~
- .' - .- --;::..::-- -
~--
-
-~
0.2
0.1
o
o
o
36000
72000
108000
144000
180000
Timet[s]
Timet[h]
o
10
20
40
30
50
0.7
0.6
0.5
Il
: DA
T=1300·C
!·
!
··
·· .
·· •
I
I
VI
l»
0.3
I-
0.2
e
0.1
g
.•!
.
.
.
·, . I
/
·· Ji" / .~~./
··
v
/
,
Q
t
YII./ -_._--_
~
1 .'
_._
o ~
o
• • - . O.8MPa ANSYS
- - •• 1.5MPa ANSYS
• • - . 2.4MPa ANSYS
· ••. 4.0MPa ANSYS
-O.8MPa REVISA
-1.5MPa REVISA
-2.4MPa REVISA
-4.0MPa REVISA
J
t
,
t
c
'g
0.7
........
~
_.-~.
0.6
f---
0.5
f--
004
0.3
-- .
.. - -:.;:...--.-. -..,:;.:.: --
0.2
0.1
o
36000
72000
108000
144000
Timet(s]
180000

V - HZDR

Transcription

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