Orynyak I.V., Borodii M.V. , Batura A . S .
description
Transcript of Orynyak I.V., Borodii M.V. , Batura A . S .
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
IPS NASUIPS NASU Software “REACTOR”Software “REACTOR”
• 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.
IPS NASUIPS NASU Software advantagesSoftware advantages
• 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 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
Input Data
Table arbitrary sizeTable arbitrary size
a) Axial with weld seama) Axial with weld seam
IPS NASUIPS NASU
Input Data
weld seamheat-affected zonebase materialcladdingcrack
weld seamheat-affected zonebase materialcladdingcrack
base materialcladdingcrack
base materialcladdingcrack
b) circumferentialb) circumferential
3) Crack types3) Crack types
)f(TAKcI
IPS NASUIPS NASU
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,
= 1000, 2000, 2800, 3000, 3160, 3600, 4000 sec - time points
It is given : - stress field, - temperature field,
= 1000, 2000, 2800, 3000, 3160, 3600, 4000 sec - time points
Axial crack. Half-length l - 40 мм., depth a - 50 мм.
Axial crack. Half-length l - 40 мм., depth a - 50 мм.
ii tT
it
ii t
IPS NASUIPS NASU
a) Dependences of the calculated and critical SIF from temperature for time = 3000 sec
a) Dependences of the calculated and critical SIF from temperature for time = 3000 sec
SIF for base material --//-- for welding seam
Critical SIF for base material --//-- for welding seam
--//-- for heat-affected area
SIF for base material --//-- for welding seam
Critical SIF for base material --//-- for welding seam
--//-- for heat-affected area
it
IPS NASUIPS NASU
history for base material --//-- for welding seam critical SIF for base material --//-- for welding seam
--//-- for heat-affected area
history for base material --//-- for welding seam critical SIF for base material --//-- for welding seam
--//-- for heat-affected area
b) History of the dependences calculated SIF from temperature for some points and all times intervals and
critical SIF
b) History of the dependences calculated SIF from temperature for some points and all times intervals and
critical SIF
T
IPS NASUIPS NASU
fields for chosen history pointsminimal marginmargin for time points
fields for chosen history pointsminimal marginmargin for time points
c) Table of the calculated temperature margin
for all points of crack front and time points
c) Table of the calculated temperature margin
for all points of crack front and time points
T
T
calculated temperature marginshift of the temperature by user table
shift of the temperature by analytical model
calculated temperature marginshift of the temperature by user table
shift of the temperature by analytical model
IPS NASUIPS NASUd) Figure of the calculated margind) Figure of the calculated margin
IPS NASUIPS NASU
New geometry for axial crackNew geometry for axial crack
Calculated temperature marginCalculated temperature margin
Half length l - 60мм Depth a - 40 ммHalf length l - 60мм Depth a - 40 мм
Results for other crack geometries
New geometry for axial crackNew geometry for axial crack
Half length l - 40мм Depth a - 60 ммHalf length l - 40мм Depth a - 60 мм
IPS NASUIPS NASU
Calculated temperature marginCalculated temperature margin
Half length l - 60мм Depth a - 30 ммHalf length l - 60мм Depth a - 30 мм
New geometry for circumferential crackNew geometry for circumferential crack
IPS NASUIPS NASU
calculated temperature margincalculated temperature margin
IPS NASUIPS NASU
1. Failure probability calculation for structural element 1. Failure probability calculation for structural element
bIi
f KTK
KK
B
BP i
imin0
min
0exp1
2. Failure probability calculation for crack2. Failure probability calculation for crack
N
iiff PP
1, )1(1
3. Calculation parameters 3. Calculation parameters
))(019,0exp(7731 00 xTTTK
4. In addition4. In addition
Кmin , K0(Т), В0, b - arbitrarily
Pf = 63,2% Кmin = 20 В0 = 25 мм b = 4
Implementation MASTER CURVE Conception
Implementation MASTER CURVE Conception
For time T =0 failure probability equal 1.07*10-05For time T =0 failure probability equal 1.07*10-05
IPS NASUIPS NASU
Time point t4 = 3000 sec - the most dangerous time step
Axial crack half length l - 40 мм., depth a - 50 мм.
Time point t4 = 3000 sec - the most dangerous time step
Axial crack half length l - 40 мм., depth a - 50 мм.
50
60
70
80
90
100
110
0 20 40 60 80 100 120 140 160 180
Angle, degree
K1
SIF dependences on angleSIF dependences on angle
Result for main scenario
Dependences of logarithm probability on TDependences of logarithm probability on T
IPS NASUIPS NASU
ln(Pf) from deltaT
-14
-12
-10
-8
-6
-4
-2
0
0 50 100 150 200
deltaT
ln(P
f)
IPS NASUIPS NASUProbability density for T = 50Probability density for T = 50
IPS NASUIPS NASU CONCLUSIONCONCLUSION
1. Efficient method of stress intensity factor (SIF)calculation is developed.
2. The computer software which reflected all modern requirements for brittle strength analysis of Reactor Pressure Vessel is created.
3. The program application were demonstrated by prediction residual life and temperature margins under modeling of the incident scenario.
1. Efficient method of stress intensity factor (SIF)calculation is developed.
2. The computer software which reflected all modern requirements for brittle strength analysis of Reactor Pressure Vessel is created.
3. The program application were demonstrated by prediction residual life and temperature margins under modeling of the incident scenario.