bay zoltán foundation for applied research institute for logistics and production systems bay-logi...

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


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)


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


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


• 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


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


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


FEM results – process zone

Von Mises stress Eq. plastic strain


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


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


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


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


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


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


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


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


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



• 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


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


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



• 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


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


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


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


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


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


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

bay zoltán foundation for applied research institute for logistics and production systems bay-logi...

Documents

bay zoltn foundation

applied research institute

exponent slide

c slide

mpa slide

plastic strain slide

exponent variation slide

v i bereminmodell slide