Orynyak I.V., Borodii M.V., Batura A.S. IPS NASU Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine SOFTWARE FOR ASSESSMENT OF BRITTLE FRACTURE OF THE NPP REACTOR PRESSURE VESSEL USING THE FRACTURE MECHANICS METHODOLOGY
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Orynyak I.V., Borodii M.V., Batura A.S. IPS NASU Pisarenko’ Institute for Problems of Strength, Kyiv, Ukraine National Academy of Sciences of Ukraine Pisarenko’
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Orynyak I.V., Borodii M.V., Batura A.S.
Orynyak I.V., Borodii M.V., Batura A.S.
IPS NASUIPS NASU
Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine
Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine
SOFTWARE FOR ASSESSMENT OF BRITTLE FRACTURE OF THE NPP REACTOR PRESSURE VESSEL USING THE FRACTURE MECHANICS METHODOLOGY
SOFTWARE FOR ASSESSMENT OF BRITTLE FRACTURE OF THE NPP REACTOR PRESSURE VESSEL USING THE FRACTURE MECHANICS METHODOLOGY
• Residual life is calculated Residual life is calculated deterministically and deterministically and probabilistically (MASTER probabilistically (MASTER CURVE approach) for CURVE approach) for various points of crack frontvarious points of crack front
• Residual life is calculated Residual life is calculated deterministically and deterministically and probabilistically (MASTER probabilistically (MASTER CURVE approach) for CURVE approach) for various points of crack frontvarious points of crack front
• This program is intended This program is intended for calculation of reactor for calculation of reactor pressure vessel residual life pressure vessel residual life and safety margin with and safety margin with respect to brittle fracturerespect to brittle fracture.
• This program is intended This program is intended for calculation of reactor for calculation of reactor pressure vessel residual life pressure vessel residual life and safety margin with and safety margin with respect to brittle fracturerespect to brittle fracture.
• The sizes of stress and temperature fields' aren't bounded• Number of time moments is bounded only by the
computer memory size • Cladding is taken into account • Welding seam and heat-affected area are taken into
account • Deterioration is taken into account not only as shift of
the material fracture toughness function but also as its inclination
• Original feature of the software is using of the author variant of the weight function method. It allows to set loading on the crack surface in the form of table.
• The sizes of stress and temperature fields' aren't bounded• Number of time moments is bounded only by the
computer memory size • Cladding is taken into account • Welding seam and heat-affected area are taken into
account • Deterioration is taken into account not only as shift of
the material fracture toughness function but also as its inclination
• Original feature of the software is using of the author variant of the weight function method. It allows to set loading on the crack surface in the form of table.
IPS NASUIPS NASU Report sectionsReport sections
Theoretical background and verification of the SIF calculation methods.
Kinetics of the crack growth by fatigue or stress-corrosion mechanism.
Software description and residual life calculation of the NPP pressure vessel using fracture mechanics methods
Theoretical background and verification of the SIF calculation methods.
Kinetics of the crack growth by fatigue or stress-corrosion mechanism.
Software description and residual life calculation of the NPP pressure vessel using fracture mechanics methods
IPS NASUIPS NASU1. SIF calculation by Point Weight
Function Method1. SIF calculation by Point Weight
Function Method
Q’- point on the front; - value SIF; -weight function;
- loading; - crack surface; Q – load application point
Q’- point on the front; - value SIF; -weight function;
- loading; - crack surface; Q – load application point
'QK
)(' QW
QQ
)(Qq S
)(
'' )()(S
QQQ dSQqQWK
Q’
x
!!! The contribution in SIF 1/800 area nearby Q’ point correspondent to 1/4 value of SIF
We search weight function in the form
- asymptotic WF (elliptic crack in infinite body)
- correction coefficient, basic solution is used
We search weight function in the form
- asymptotic WF (elliptic crack in infinite body)
- correction coefficient, basic solution is used
Rr
DWW AQQQQ
1)(1''
'QQW
AQQ
W '
)(D
1
2'
2'
21
2
24
1
')(
)(1)(2
QQQQ
AQQ
l
dl
R
raW
IPS NASUIPS NASU
IPS NASUIPS NASUUsing our Point Weight Function Method
in engineering applications Using our Point Weight Function Method
in engineering applications 1. Software for fracture design of the complex turbine engine
component (Southwest Research Institute, San Antonio, USA, 2004)
1. Software for fracture design of the complex turbine engine component (Southwest Research Institute, San Antonio, USA, 2004)
Our approach is used
completely
IPS NASUIPS NASUUsing our Point Weight Function Method
in engineering applications Using our Point Weight Function Method
in engineering applications 2. Modeling of elliptical crack in a infinite body and in a
pressured cylinder by a hybrid weight function approach (France, Int. J. Pressure Vessel and Piping. 2005)
2. Modeling of elliptical crack in a infinite body and in a pressured cylinder by a hybrid weight function approach (France, Int. J. Pressure Vessel and Piping. 2005)
Our approach to take for a
basis
SIF along crack front (angle), homogeneous loadingSIF along crack front (angle), homogeneous loading
IPS NASUIPS NASUCheck of the PWFM accuracy for
semi-elliptic cracks
Check of the PWFM accuracy for semi-elliptic cracks
a/l=0.2 (a/t=0.8)
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
2
0 20 40 60 80 100
Angle, degree
Tension by the PWFM Tension by Raju-Newman
Bending by the PWFM Banding by Raju-Newman
a/l=0.4 (a/t=0.8)
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
0 20 40 60 80 100
Angle, degree
Tension by the PWFM Tension by Raju-Newman
Bending by the PWFM Bending by Raju-Newman
0
90
IPS NASUIPS NASU
a/l=0.6 (a/t=0.8)
0
0,2
0,4
0,6
0,8
1
1,2
1,4
0 20 40 60 80 100
Angle, degree
Tension by the PWFM Tension by Raju-Newman
Bending by the PWFM Bending by Raju-Newman
a/l=1.0 (a/t=0.8)
-0,2
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
0 20 40 60 80 100
Angle, degree
Tension by the PWFM Tension by Raju-Newmen
Bending by the PWFM Bending by Raju-Newman
a/l=2.0 (a/t=0.8)
-0,2
0
0,2
0,4
0,6
0,8
1
0 20 40 60 80 100
Angle, degree
Tension by the PWFM Tension by Raju-Newman
Bending by the PWFM Bending by Raju-Newman
IPS NASUIPS NASU
IPS NASUIPS NASU
Homogeneous loading
1
1,2
1,4
1,6
1,8
2
0 0,2 0,4 0,6 0,8 1 1,2
a/l
90 degree by the PWFM 90 degree by Murakami
0 degree by the PWFM 0 degree by Murakami
Linear loading
0,2
0,4
0,6
0,8
1
1,2
1,4
0 0,2 0,4 0,6 0,8 1 1,2
a/l
90 degree by the PWFM 90 degree by Murakami
0 degree by the PWFM 0 degree by Murakami
Dependence SIF from ratio a/lDependence SIF from ratio a/l
IPS NASUIPS NASU
Quadratic loading
0
0,2
0,4
0,6
0,8
1
1,2
0 0,2 0,4 0,6 0,8 1 1,2
a/l
90 degree by the PWFM 90 degree by Murakami
0 degree by the PWFM 0 degree by Murakami
Cubic loading
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 0,2 0,4 0,6 0,8 1 1,2
a/l
90 degree by the PWFM 90 degree by Murakami
0 degree by the PWFM 0 degree by Murakami
Dependence SIF from ratio a/lDependence SIF from ratio a/l
),( RKfdN
dlI
1),( CRKfdN
daI )/()(
if ,
if ,
)(
32
2
12
1
2
HafKfdt
da
KKv
KC
KKv
Kfdt
dl
I
upTHI
n
lowTHI
I
1. Fatigue
2. Stress-corrosion
IPS NASUIPS NASU2. Kinetics of the crack growth by fatigue or
stress-corrosion mechanism2. Kinetics of the crack growth by fatigue or
stress-corrosion mechanism
upTH
lowTH KK ,
IPS NASUIPS NASU
TdaTkdaaaa CFCF
TdlTkdllll CFCF
where C1, C2 , v1 , v2 , - material constants
t, - time, N – loading cycles, H – wall thicknessT – unit time, k – number of cycles in unit of time
where C1, C2 , v1 , v2 , - material constants
t, - time, N – loading cycles, H – wall thicknessT – unit time, k – number of cycles in unit of time
Complex damageComplex damage
IPS NASUIPS NASUUsing stable form crack growthUsing stable form crack growth
nIKAl
af
dl
da
fc
fc
dldldl
dadada
0 2 4 6 8 10 12 14 16 0.0
0.5
1.0
1.5
2.0
00 / la
2
0.666
0.2
0.1
Stable form
a/L,
a, мм
Input Data
1) Stress field for time1) Stress field for time it
Table arbitrary sizeTable arbitrary size
IPS NASUIPS NASU3. Residual Life calculation of the NPP
pressure vessel using fracture mechanics methods
3. Residual Life calculation of the NPP pressure vessel using fracture mechanics
methods
IPS NASUIPS NASU
2) Temperature field for time2) Temperature field for time0t it
4) The basic material characteristics4) The basic material characteristics
1. Arctangents 1. Arctangents 0arctan2 TTBAK
cI
2. Exponent2. Exponent
0exp TTBAKcI
Common shape of the crack growth resistance function is
for user function A takes from coordinates of first point
Common shape of the crack growth resistance function is
for user function A takes from coordinates of first point
3. User (pointed) function3. User (pointed) function
IPS NASUIPS NASU
1. Shift1. Shift
TTAKcI
f
2. Shift + Inclination2. Shift + Inclination
TT
TTTAK
cI
1
1f
A
ICK
T
T
A
ICK
T
T
5) Shift and inclination conceptions 5) Shift and inclination conceptions
nn
FF YTF
ffAAT
exp
0
00
IPS NASUIPS NASU
a)Analytical forma)Analytical form
b)Table formb)Table form
6) Dependence of shift on radiation6) Dependence of shift on radiation
IPS NASUIPS NASU Results
Scenario – Break of the Steam Generator Collector WWER-1000 operated at full powerScenario – Break of the Steam Generator Collector WWER-1000 operated at full power
It is given : - stress field, - temperature field,