Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Temperature dependence of Beremin-modell parameters
for RPV steel
Gyöngyvér B. LenkeyRóbert BeleznaiSzabolcs Szávai
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Objectives
• Parameter study on the effect of material properties (Ry, n)
• To determine the temperature dependence of Beremin-modell parameters
(PERFECT EU Integrated project: Prediction of Irradiation Damage Effects in Reactor Components)
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Stress-strain curve for JRQ reference RPV material
• ASTM A533 grade B class 1• D=6 mm cylindrical specimens • with strain measurement on the specimen• -70 °C
Average stress-strain curve for JRQ material at -70 °C
0
100
200
300
400
500
600
700
800
900
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain, -
Str
es
s, M
Pa
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Fracture toughness results and master curve data provided by KFKI AEKI
• JRQ reference RPV material (pre-cracked Charpy specimens): at –60, -70, -90, -110 °C
Me as ure d fracture toughne s s data - JRQ mate rial
0
20
40
60
80
100
120
140
160
180
-120 -110 -100 -90 -80 -70 -60 -50 -40
T, °C
Jc,
kJ/
m^
2
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
• Failure probability - Weibull distribution:
• Weibull-stress:
– where - major principal stress in Vi
PRW
u
m
1 exp
Beremin-modell
Wi
i
m im
VV
10
1i
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Weibull-parameter calculation
• Fixed m: m=10 (temperature independent)
• u was determined from the master curve:
– at Jmed the probability of failure is Pf=0.5:
m
Wf
u
P 0.5 1 exp
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
FEM model
• 2D plain strain• Different models for different crack length
values of the specimens• Refined mesh size at the crack tip: 10 m• Blunted crack tip: 2.5 m
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
FEM results – process zone
Von Mises stress Eq. plastic strain
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Performed analysis
• Sensitivity analyses: – Three different values of yield strength
(Ry measured ±25 MPa)
– Three different values of strain hardening exponent.
• Further analyses:– Temperature dependence of u
(from –110 to –60 °C) – using artificially generated stress-strain curve based on measured yield strength values
– Effect of strain hardening exponent
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Yield strength variation
0
100
200
300
400
500
600
700
800
900
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
Plastic strain
Str
ess,
MP
a +25 MPa
Average measured -70 °C
-25 MPa
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Effect of yield strength variation
m=10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2500 2700 2900 3100 3300 3500 3700
Weibull stress, MPa
Pf
Ry=527
Ry=552
Ry=577
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Effect of yield strength
• 10 % variation in yield strength causes 5% change in u.• appr. linear relationship.
m=10
2800
2900
3000
3100
3200
3300
3400
3500
520 530 540 550 560 570 580
Ry, MPa
u, M
Pa
u, M
Pa
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Hardening exponent variation
0
100
200
300
400
500
600
700
800
900
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Plastic strain
Str
ess,
MP
a n=0,1
n=0.1748-average measured
n=0,25
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Effect of hardening exponent variation
m=10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2500 3000 3500 4000 4500
Weibull stress, MPa
Pf
n=0,1
n=0,1748
n=0,25
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Effect of hardening exponent
• not linear relationship.• larger effect for the higher n value.
m=10
2600
2800
3000
3200
3400
3600
3800
4000
0 0.05 0.1 0.15 0.2 0.25 0.3
n
u, M
Pa
u, M
Pa
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Determine the temperature dependence of u
• Master curve describe the T dependence of Kmed
Jmed
• From FEM calculation: u(Jmed) u(T) formal relationship – for a given material law
• From the calculation: u(Jmed) u(T) formal relationship for different material law (Ry variation, n variaton)
• Knowing the T dependence of Ry u(T) can be determined
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
0
50
100
150
200
250
300
-120 -100 -80 -60 -40 -20 0
T, °C
K,
MP
a.m
^0.
5
KJc-1T
KJc-Charpy
To=-76.6 °C
0
20
40
60
80
100
120
-120 -110 -100 -90 -80 -70 -60 -50 -40
T, °C
J-m
ed, k
N/m
).(019.0exp.7030 01 TTK T
25.0
11 )20(20
Charpy
TTCharpy B
BKK
EKJ medmed /)1( 22
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Determine the temperature dependence of u
• Master curve describe the T dependence of Kmed (T) Jmed(T)
• From FEM calculation: u(Jmed) u(T) – for a given material law
• From the calculation: u(Jmed) u(T) for different material law (Ry variation, n variation!)
• Knowing the T dependence of Ry u(T) can be determined
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Yield strength effect
y = 1751.2x0.1466
y = 1660.8x0.154
y = 1814.6x0.1459
y = 1714.2x0.1508
y = 1928x0.1339
y = 2019.1x0.1326
2000
2200
2400
2600
2800
3000
3200
3400
3600
3800
4000
0 20 40 60 80 100 120 140 160 180
J, kN/m
u, M
Pa
Ry-25 MPa
T=-70 °C
Ry+25 MPa
T=-60°C
T=-90°C
T=-110°CRy - increasing
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Strain hardening effect, T=-90 °C
y = 1956.9x0.1122
y = 1928x0.1339
y = 1766.2x0.1799
y = 1914.8x0.1332
2000
2200
2400
2600
2800
3000
3200
3400
3600
3800
4000
0 20 40 60 80 100 120
J, kN/m
u, M
Pa
T=-90°C; n=0.25
T=-90°C; n=0.175
T=-90°C; n=0.1
T=-90°C; n=0.05
n - increasing
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Determine the temperature dependence of u
• Master curve describe the T dependence of Kmed Jmed
• From FEM calculation: u(Jmed) u(T) – for a given material law
• From the calculation: u(Jmed) u(T) for different material law (Ry variation)
• From the T dependence of Ry u(T) can be determined
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Temperature dependence of the yield strength
JRQ, unirradiated
y = -1.5998x + 453.74
400
425
450
475
500
525
550
575
600
625
650
-120 -100 -80 -60 -40
T, °C
Ry,
MP
a
Measured earlier
Measured recently by BZF
Slope: 16 MPa/10 °C
Material law was generatedbased on measured Ry
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
To=-76.6 °C
2500
3000
3500
4000
4500
-150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0
T, °C
u, M
Pa
m=10; Ry-25 MPa
m=10; T=-70 °C
m=10; Ry+25 MPa
m=10,T=-60°C
m=10,T=-90°C
m=10,T=-110°C
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
n effrect - To=-76.6 °C
1500
2000
2500
3000
3500
4000
4500
5000
-150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0
T, °C
u, M
Pa
T=-90°C; n=0.25
T=-90°C; n=0.175
T=-90°C; n=0.1
T=-90°C; n=0.05
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Temperature dependence of u for JRQ reference RPV material
2900
3000
3100
3200
3300
3400
3500
3600
-120 -100 -80 -60 -40 -20
T, °C
u,
MP
a
To=-76,6 °C
Determined from the yield s trengthvariation
n effect - To=-76.6
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
n e ffe ct - T=-90 °C
2900
3000
3100
3200
3300
3400
3500
3600
0 0.1 0.2 0.3
n
u,
MP
a
Bay Zoltán Foundation for Applied ResearchInstitute for Logistics and Production Systems BAY-LOGI
Conclusions
• Both Ry and n have significant effect on the Beremin-modell parameter (u) with fix m value
• If the master curve describes well the material behaviour, it is possible to formulate the temperature dependence of u - based on fracture toughness values measured at one temperature and the temperature dependence of the stress-strain curve