Ductile fracture mechanical analyses of large scale thermal shock experiments

Nuclear Engineering and Design 130 (1991) 13-20 North-Holland

13

Ductile fracture mechanical analyses of large scale thermal shock experiments J. Sievers Gesellschaft flit Reaktorsicherheit (GRS) mbH, Schwertnergasse 1, W-5000 KSln 1, Germany Received 15 June 1989, revised version 7 June 1990

Large scale thermal shock tests of Oak Ridge National Laboratory (ORNL), Staatliche Materialpriifungsanstalt Stuttgart (MPA) and Heissdampfreaktor (HDR) have been analysed by pre- and postcalculations with the finite element program ADINA extended by fracture mechanical options based on the J-integral. The results show that temperatures, displacements, strains and stresses can be approximated well. Due to the well-known geometry dependence of specimens' crack resistance in some cases a satisfactory assessment of the crack behaviour can only be obtained by extension of the one-parametric J-integral concept, e.g. with determination of the stress triaxiality in a region in front of the crack tip. Furthermore the influence of residual stresses due to repeated loading of a cracked vessel with plastiflcation at the crack tip seems to be important in fracture assessment.

1. Introduction

cooling combined with pressure transients or axial force has been investigated (fig. 1). A matrix of experiments and analyses performed is presented in fig. 2. Characteristics according to material toughness, geometry of the test vessels, loadings, crack shape and growth are listed. In the frame of our analytical work the applicability of the ductile fracture mechanical J-integral concept on mechanical and thermal loaded structures with flaws is

Emergency cooling through the cold coolant nozzles of a reactor pressure vessel u n d e r o p e r a t i o n conditions is a n example of pressurized thermal shock. In the experiments PTSE-1 a n d 2 p e r f o r m e d at O R N L , NKS-1 to 4 at MPA, Stuttgart a n d T H E L I a n d II at H D R the b e h a v i o u r of cracks in cylinders of materials with different toughness u n d e r axisymmetric or local t h e r m a l shock

,•

portly axial circumf. crack crack.

2960~

D5+7

circumf crack

z:O .

.

J

ORNL

|

HDR

MPA

Fig. 1. Large scale thermal shock experiments.

0029-5493/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved

J. Sievem / Ductile fracture mechanical analyses

14

M a t r i x of t h e r m a l s h o c k e x p e r i m e n t s / a n a l y s i s

material

cyl.geometry

experi- T A us ~OT . ment [°C] [J] (place)

R

t

loading To

AT*) FAx

notch/crack

shape a °

p

[mini [ram]

[°C] [°C] IMN]

[MPa~

Aa

[mm] [mini

NKS-I -5 (MPA-St.)

175

200

200

320

300 75a x i - I00 sym.

0-30

c i r c u m - 50.9 0.8-I.O ferential

NKS-3 60 (MPA-St.)

95

200

200

332

312 100 axi.sym.

30

c i r c u m - 60 ferential

NKS-4 120 65 (MPA-St.) /1 /2

200

200

axi.sym. 310 50 325 55

30

partly cen- 0(t) circumf, ter 30 1.5(r) 31.5 1.6(r)

THEL I (HDR)

330 345

47

70(r) 1480 105+ 310 150(0 7 (cladding)

L~O(injec.) II 60(notch) mixture of water

THEL II 47 (HDR)

70(r) 1480 105+ 310 150(t) 7 (cladding)

260 channel (guided)

PTSE-I (ORNL~ A B C PTSE-2 (ORNL) A B

II0

axi.- sym.

91

343

147.6

2.9-4.6

partly 14.8 O(t) circumf. (center. O(r) branched)

11

14.6

o(0

(center, O(r) branched)

tranaxial sient 280.5 265 3O(max) 12.2 O 293.3 315.3 60(max) 12.2 12.2 291.0 320 95(max) 24.4 16.6 75 60 343 147.6 300 axi.tranaxial sym. sient 11.1(stable) 326 63(max) 14.5 16.8(brittle) 275 301 42.4 3.7(stable) 32.7(brittle) 68.6(unstable) ") temperaturdifference: surface of cylinderwall / cooling fluid r=radial, t=tangential

Fig. 2. Matrix of large scale thermal shock experiments/analyses.

Illl

00 MN

2

O0

1"51

COD (mm)

I crack stop

R 200

~

o

360

l ooo

960

time (s)

~bo

Fig. 3. NKS-3, axisymmetric FE-model, crack mouth opening.

~5;o

1800

15

J. Sievers / Ductilefracture mechanical analyses J I N/mm /

3OO

investigated. For the fracture mechanical pre-and postanalyses of experiments a version of the finite element program ADINA [1] extended by J-integral calculation model based on the method of virtual crack extension [2] and a crack growth model with node shift and release according to a crack resistance curve is used [3].

~

2OO

o

i

2 3 4 6 7 8 g q [averaged on about 10% of the ligament)

2. Analyses of pressurized thermal shock experiments

NKS-3

°iI

J-R curve (22 NiMoCr 37, T = 220°C) J (N/rnm)

5 ~

, lexP;l calc',

,

4

1 mm 0

3 2 crack growth

~

2.1. NKS-experiments, MPA-Stuttgart

d.integral versus time J (N/mm)

ol 0

, 300

i,crack,stop ,

,

600 900 1200 time

s 1800

In NKS-1 and NKS-3 a circumferential crack was loaded by axisymmetric cooling, internal pressure and additional axial force. The crack loading (CMOD, J-integral) is rather similar in both experiments but the crack grew due to different material toughness, which is related to the crack resistance, about 0.9 and 3.6 mm respectively. Temperature distribution and deformation have been approximated by analyses well (fig. 3, [4]).

I

Fig. 4. NKS-3, fracture assessment due to J-integral concept with consideration of stress triaxiality.

/~.5 /"

/

~IICM

,14.7..y

~".~%3. J

CM=material in crack region BM=base material

T/°C/ 350 300

LEGEND O

250

t=110s

Z& t = 200

4-

so~ r e

112s

[MPa]

t =140s

4- Experiment

150

X 100 50 i.

~

t=

O

Experiment

V

t --

0 0

tip

40

60

80

100

120

wall thickness / mm /

t=190s

O

300s

400

i 140

,

time [sl 160

Fig. 5. PTSE-2A, finite element model, temperature distribution in the wall and pressure transient.

16

J. Sievers / Ductile fracture mechanical analyses 140 -

J / N/mm LEGEND

120 -

O a = 1".5 mm

.>< plane strain

100 -

0 plane stress 8060402000

1 2 3 4 5 6 q (averaged on about 10% of

7 the

8 9 [igement}

10

PTSE - 2A

300

,oo

200

20C

PTSE-2: Crack resistance curves

J-Integral versus Time

J INImml

INImm] 600

600

LEGEND 500'

o ADINA a-14,5 mm =, ADINA 1=19.6

400

I*Cl

100(pre}

1751pre) 1751post) 250(pre) 2501post)

100 0 100 150

200

250

300

350

400

450

500

550

600

Time/s/

I~ 0 r O0

~ ~I 2.5

exl:~rimen! iI : 5.0 7,5 &a[rnm]

i 10.0

12~5

15D

PTSE-2A

Fig. 6. PTSE-2A, fracture assessment due to J-integral concept with consideration of stress triaxiality.

In fracture assessment stress triaxiality ]) has been evaluated to prove, whether CT-25 specimen approximate the crack resistance of the NKS-cylinder. During the crack growth takes place fig. 4 shows that plane strain conditions approximate the stress state best and crack growth can be determined with good coincidence between experiment and analysis based on the JR-Curves given. 2.2. PTS-experiments, ORNL

In PTSE-1 and PTSE-2 an axial surface flaw was loaded by axisymmetric cooling and different pressure transients and showed cleavage fracture (crack jumps), arrest and in PTSE-2 also phases of stable crack growth 1)

q=

Oxx q-

Oyy q- Ozz

with ov effective stress due to v. Mises.

interrupted by a warm prestressing (WPS) phase and crack jumps up to a leak due to instable crack growth [5]. Fig. 5 shows the finite element model (2d plane strain) and the calculated temperature distribution of PTSE-2A compared with experimental data. Sensitivity analyses show that the crack mouth openhag is strongly dependent on the correct approximation of the crack growth, which is about 5.1 nun during the first 190 s and of the temperature dependence of the material data, which is not sufficiently known. Therefore the best estimate analysis underestimates CMOD by about 15% which influences the fracture assessment strongly. During the first 190 s the J-integral (fig. 6) shows a typical increase due to axisymmetric cooling and 5.1 mm stable crack growth takes place, followed by a warm prestressing phase, further 2.9 mm stable crack growth and a crack jump of 16.8 mm, mainly controlled

J. Sievers / Ductile fracture mechanical analyses

In the second thermal shock phase (PTSE-2B) with a monotonic increasing pressure transient (fig. 7) stable crack growth of about 4 m m followed by two crack jumps of 32.7 nun in total and finally instable crack growth to a leak was observed. Due to strong plastification of the crack region at the end of transient A it is necessary to consider the loading history in the analysis of transient B. Therefore a residual stress state with a pressure stress region of about 20 mm in front of the crack tip has been calculated as result of loading the PTSE-2B model (crack depth a = 42.4 mm) with transient A before starting transient B. The effective stress distribution in front of the crack tip as well as the J-integral show much lower values during the first minutes due to consideration of the residual stress state (fig. 7).

by the pressure transient. The analysis of crack growth is strongly dependent on the correct approximation of the crack resistance by specimen JR-curves, which are dependent on temperature, specimen geometry and pre/posttest condition. In the fracture assessment of the first period with stable crack growth (fig. 6) consideration of the stress triaxiality (q) on the ligament has been included. The q-variation during the loading in PTSE-2A looks similar to that shown in NKS-3. The best estimate analysis with crack depth including the observed crack growth (a = 19.6) compared with CT-25-JR-curves of crack tip temperature after 190 s (about 135°C) confirms only about 2.5 mm crack growth but there is still an underestimation of crack loading as mentioned before in CMOD.

700

17

von-Mises/MPa/ LEGENDE

600

[ ] t=200 s, with RS .[.]. . .t'=200 . . . . . . . . s, . . .without . . . . . RS 0 t=300 s, with RS

500 400 300

~.

..E). t .=.3.90 .s.,..w.fl..ho.ut" RS

II "'"'--

<> ,-5oo s.w,,hRS

,, ,..

200-

, , ~

, ~ .......

100 0 20

40

60

80

100

120

Ligament/mm/ PTSE-2B

RS = residual stresses

/ N/ram /

250 -

too

MPa

start of thermal shock t = 155s

80

200 ~ 150 I

100 J

60

U% U} (:D t..

5040

0-

(3.

crack-

-50 /

O w i t h RS

-I00-

%

~0o

,oo

time

soo S

soo

-150150 200

250

300

350 time

400 / s /

450

500

550

Fig. 7. PTSE-2B, stress distribution on the ligament, pressure transient and calculated J-integral.

600

J. Sievers / Ductile fracture mechanical analyses

18

Again the fracture assessment of the crack behaviour is strongly dependent on the correct approximation of the crack resistance in the vessel, which may change during the transients due to the crack tip blunting and changes of stress triaxiality near the tip. It is well known that a crack which has already seen a transient with a certain amount of plastification has a higher crack resistance with increased initiation value [6]. Therefore the stable crack growth could not be determined satisfactorily with the available crack resistance curves based on fatigue precracking. 2.3. THEL-experiments,

ation conditions is cooled in an artificial axial canal between an upper and a lower nozzle [7]. In that case the axial stress, which is much higher than the circumferential component, loads the crack. The unsymmetric cooling process effects an ovalization of the cylinder with strong plastification in the wall behind the cooling canal (fig. 8). During the loading phase the J-integral and the degree of triaxiality in front of the crack is determined (fig. 9). The q-values shown are representative for the region in front of the crack except the part near the surface where the plane stress state is to be approximated by a q-value of two. Fracture assessment of the precalculation shows about 0.5-l mm crack growth after 20 min, dependent on the modelled crack depth and the crack shape which

HDR

In THEL II the reactor pressure vessel of the HDR with a partly circumferential notch under normal oper-

vonMises

stress

tip

3 in

-

I

0

2b

4b

60

wallthickness

sb

60

120

mm

Fig. 8. THEL II, finite element model of precalculation with assumed crack geometry due to non destructive testing including safety factors. effective stresses in the wall.

J. Sievers / Ductilefracture mechanical analyses 200 -

19

J / N/ram - - LEGEND

I

O THEL- II

150 -

/l

planestress

+ planestruin

100 -

50

o~ O

1

3

4

5

6

7

8

9

10

q (averaged on about 10% of the ligament} THEL-II

S51St.with J(TS 10) 1 H best eslimate S21S3withJ(TL 2) J

i

3O0

N/mm

J

;5

t : ...... t = -.- t : --- t =

'-. "-.'~i..\ bose material

.

.

.

.

.

.

.

500

.

.

i

.

1000

.

.

.

.

.

.

1500

.

2000

\\ L \ \ - .\ \ ~

x

~:

cladding 0

0 min 10 rain 20 min 30rain

--

$1\:'/D 33.5

m m

'/

D

-time s

Fig. 9. THEL II, fracture assessment of crack growth due to J-integral concept with consideration of stress triaxiality (precalculation).

were assumed due to the non-destructive tests results before the experiment. Postcalculations of THEL II [8] with the real initial crack depth (maximum 15.5 mm) and the loading conditions of the experiment show good coincidence in strains and crack mouth opening. The calculated fracture mechanics results confirm the experimental result that no crack growth happened for that crack depth.

3. Conclusions

In the frame of our analytical work the fracture mechanical behaviour of experimentally investigated precracked vessels loaded by thermal shock, internal pressure a n d / o r axial force has been analysed with the program A D I N A extended by fracture mechanical op-

tions based on the J-integral concept. The large scale thermal shock tests PTSE-2, NKS-3 and THEL II performed at ORNL, MPA Stuttgart and H D R have been analysed by pre- and postcalculations and discussed, respectively. Within the analyses the temperature distribution, the structure mechanical behaviour of the vessels and the fracture mechanical behaviour of the crack have been determined and compared with experimental results. From the analytical point of view the overall review of the results concludes that temperatures, displacements, strains, stresses and crack loading can be approximated well. Due to the well-known geometry dependence of crack resistance curves from specimens a satisfactory description of the crack behaviour can only be obtained by extension of the one-parametric J-integral concept, e.g. with determination of the stress

20

.i.. Sieoers / Ductile fracture mechanical analyses

triaxiality in a region in front of the crack tip. A comparision of this triaxiality with the correspondent value of fracture mechanical specimens might lead to the approximation of the crack resistance of the investigated cracked component, i.e. the appropriate crack resistance curve(s) to estimate the crack growth. Furthermore the temperature dependence of the crack resistance can be described by the crack tip temperature sufficiently. Concerning the correlation between crack resistance and triaxiality the physical-numerical relations should be investigated in more detail. The influence of residual stresses due to repeated loading of a cracked vessel with plastification at the crack tip seems to be important in fracture assessment of crack behaviour and should be investigated experimentally and analytically in more detail. Concerning the transferability of the analysis and test results of the thermal shock experiments to nuclear power plants it should be noted that for some pressure vessels with longitudinal welds the assumption of an axial crack at core mid-height is obvious which sees the highest values of neutron embrittlement. In German PWR-plants, however, only circumferential welds beo tween forged cylinder rings exist. Therefore a circumferential crack may be of greater interest in this case, especially if local cooling of the pressure vessel wall has to be considered.

Acknowledgement We thank the German Minister for Research and Technology (BMFT) who sponsored our work and also the Projekt HDR of Kernforschungszentrum Karlsruhe, the Materialprufungsanstalt Stuttgart and the Oak Ridge

National Laboratory for supplying the experimental data.

References [1] ADINA, A Finite Element Program for Automatic Dynamic Incremental Nonlinear Analysis, ADINA Engineering, Inc. Report AE 84-1 (1984). ADINAT, A Finite Element Program for Automatic Dynamic Incremental Nonlinear Analysis of Temperatures, ADINA Engineering, Inc. Report AE 84-2 (1984). [2] H.G. DeLorenzi, Energy release rate calculations by the finite element method, Engng. Fract. Mech. 21, No. 1 (1985) 129-143. [3] H.G. DeLorenzi, J-integral and crack growth calculations with ADINA, EPRI contract RP 601-2 (1978). [4] J. Sievers, Ductile fracture mechanical analyses of thermal shock experiments, Transactions of the 9th SMIRT-Conf. Vol. G (Balkema, 1987) pp. 361-367. [5] R.H. Bryan et al., Pressurized-thermal-shock test of 6-in.thick pressure vessels, PTSE-2: Investigation of low tearing resistance and warm prestressing, NUREG/CR-4888 (1987). [6] K. Kussmaul et al., Some conclusions with regard to the safety assessment of cracked components drawn from the research program integrity of components (FKS II) at the Present State, 12. MPA-Seminar, paper 25 (1986). [7] G.E. Neubrech et al., Experimental and analytical thermal shock investigations on the reactor pressure vessel of the HDR power plant, IAEA Specialists Meeting on Large Scale Testing, paper 22 (Stuttgart, 1988). [8] J. Sievers, H. Schulz, H. Kordisch und H. Talja, Z~thbruchmechanische Analysen zum Verhalten der Zylinderwand des Druckbeh~ilters mit Teilumfangsriss unter Thermoschockbelastung infolge Streifenkiihlung, 13. Statusbericht PHDR (Karlsruhe, 1989).