Analysis of initiation and growth of a circumferential crack in the HDR-RPV-cylinder under pressurized thermal shock

Nuclear Engineering and Design 124 (1990) 171-192 North-Holland

171

Analysis of initiation and growth of a circumferential crack in the HDR-RPV-cylinder under pressurized thermal shock H. K o r d i s c h 1, H . T a l j a 2 a n d G . E . N e u b r e c h 3 1 Fh-IWM, Freiburg, Fed. Rep. Germany 2 VTT, Helsinki, Finland 3 KfK/PHDR, Karlsruhe, Fed Rep. Germany Received 2 July 1990

In order to simulate a nuclear emergency cooling situation, longterm cooling tests (pressurized thermal shocks) were carried out under normal operating conditions on the reactor pressure vessel of the HDR (hot steam reactor). Naturally occuring circumferential cracks in the cylindrical part of the RPV, previously induced during cyclic thermal shock tests, were subjected to internal pressure and thermal stresses. The aim of the test was crack initiation and a limited amount of stable crack growth. Analyses, applying fracture mechanical assessment methods, were carried out before and Mter the test and these checked against the experimental results. To this end, comprehensive numerical analyses, investigations into material property characteristics, non-destructive and destructive (fractographical) tests were carried out. Due to the conservative assumptions, the results of the precalculation lay on the safe side; this was intended as these results served, among other aspects, as the basis for the experimental boundary condition. The post calculation which was based on the actual crack geometry, the measured cooling medium temperature and the material properties local to the crack, was in good agreement with the experimental results. Thus a tool is now available which can be successfully applied to the assessment of cracks in reactor components.

1. Objective The nuclear safety aspects require that crack initiation is inconceivable in a reactor pressure vessel (RPV) under normal operating conditions and that an initiated crack is arrested before penetrating 75% of the wall thickness in faulted or emergency conditions. The most severe loading case is the "pressurized thermal shock" (PTS). Axial and circumferential flaws in the vessel cylindrical part and in the nozzle area have to be considered. Due to the toughness requirements and the prevailing temperatures, elastic-plastic fracture mechanics methods seem necessary for a realistic analysis and assessment. The full-size H D R - t e s t facility - a boiling water reactor, now out of service - serves as a test rig for testing simulated realistic and excessive loading conditions. Existing fracture mechanics assessment methods are verified by pre-test and post-test analyses accompanied by nondestructive and destructive crack examination methods [1]. It was found in preceding investigations (TEMB) 0029-5493/90/$03.50

that the actual temperature distribution on the inner wall of the R P V during emergency core cooling is not uniform in the circumferential direction; distinct vertical undercooled strips occur beneath the inlet nozzles due to cooler and therefore denser water entering at the nozzle and sinking to the floor. C o m p a r e d to an axisymmetrical cooling situation, the thermally induced axial stresses are considerably higher in the line of symmetry of the cooled strip; the associated tangential stresses are negligible. Thus circumferential cracks are more dangerous than axial flaws. The largest axial stresses occur when only one inlet nozzle is cooled. As a consequence, the cylindrical part of the H D R pressure vessel (fig. 1), which contains natural circumferential cracks from preceding local thermal fatigue tests was subjected to controlled longterm thermal shock at service conditions (310 * C and 10.6 MPa). The cooling device is shown in fig. 2. Simultaneously a crack in the nozzle area was subjected to thermal shock loadhag; this test is not discussed in this paper. The aims of the PTS experiments, designed for crack

© 1990 - E l s e v i e r S c i e n c e P u b l i s h e r s B.V. ( N o r t h - H o l l a n d )

172

It. Kordisch et al. / Analysis of initiation of a circumferential crack -

nozzleA2

L.

.,,/ l

nozzleF- ~

!.PL

..~L'

i

i

C

~"3 I 1

i

i

linear finite-element programs ( A D I N A T / A D I N A ) [2]. The crack driving parameter J along the crack front is calculated locally using the virtual crack extension method by available program modifications (IWMC R A C K [3]). This also allows a numerical simulation of the local stable crack growth using a node shifting- and releasing technique. Additionally, J-calculations were carried out by the post-processor VTT-VIRT. Correction terms were considered for thermal loading, for pressure loading of the crack surfaces and for mass effects when determining J. A constraint-modified crack growth model, as discussed in [4], can be used to transfer small-scale specimen results to a crack in the real structure. In addition, J was also calculated based on stresses normal to the crack which were derived from the finite element analysis. In order to determine the thermal and thermo-mechanical material parameters as a function of temperature, comprehensive material testing was performed on original cladding and base material taken from drill cores of the H D R pressure vessel (figs. 3 and 4). To evaluate the crack resistance behavior of the base material +at different temperatures and states of stress JR-curves were determined for side-grooved arc-shaped specimens of

Fig. 1. HDR-pressure vessel. initiation and limited amount of stable crack growth, are - Investigation of crack initiation and stable crack growth under the influence of the complex stresses due to internal pressure and realistic thermal shock; - the verification of ductile fracture mechanics analysis and assessment methods, including the transferability of material parameters measured on small-scale specimens to the real component; - the verification of NDT-methods. Extensive numerical analyses and material characterization programs prior to the test were used to define the final test conditions and to ensure safe performanee of the experiment. The test was successfully carried out and has been post-analyzed applying real crack geometry and the real thermal boundary conditions measured during the experiment.

2. M e t h o d s

|

l

|

J

J

i ........t I

and materisl pm~uueters

The analyses of temperature distributions and stresses were performed using three-dimensional, non-

ii Fig. 2. Cooling device.

173

H. Kordisch et al. / Analysis of initiation of a circumferential crack

constant width (B = 12.5 ram) (fig. 5) [5] and for CTspecimens with different thickness at T = 110 ° C (fig. 6) [6]. Fig. 7 shows initiation values of Ji and Jic/Jq in the relevant T - L and T - S directions for the circumferential crack determined according to ASTM-E813-87.

~-60 i

HDR base mate hi

~se

USlJA 22 Lmm~vr 37

4Q

Ii

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|

1'00~

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~. 500 z • . = 400

1.4550

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600

400

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1

--~ ~" 300 uJ 200

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300

400

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600

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1 6O0

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f

¢:

10

~4oo 80

100

200 300 Temperature in'C

400

500

(a) normal to the surface (b) parallel to the surface

Fig. 3. Thermal and thermo-mechanical material parameters.

50'C .......lS0"C --200"C - - 2S0'C - - 300'C

Ddlf core 4 sad 6

Ja~-forOod r ~ l 2~

Material 1,4550 I I 5 10 Strain in %

15

Fig. 4. Thermo-mechanical material parameters.

20

H. Kordisch et aL / Analysis of initiation of a circumferential crack

174 600.0

I

I

I

I

ore-six ~ d spedr ,,en, 8 = t ,,5 mm

6000

I

c E

,•

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4O0.O

CT50(SrS~)

..¢ I

ooc

J

2000

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15

2.0

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~/mm Fig. 6. JR-Curves measured at T = 110 ° C on different CTspecimens.

0.0 -tO

-0.5

5.0

~/mm

Fig. 5. JR-curves measured for different temperatures.

mm respeetively, this representing the cooled strip below the crack under consideration. Fig. 8 gives a general idea of the finite element model with the appropriate boundary conditions. Due to the limited capacity of the

3. Pre-calcubtions 3.1. Numerical model

computer, the temperatures and the linear-elastic a n d

T h e H D R pressure vessel has a n i n n e r radius of R i = 1480 mm. T h e wall thickness is t = 112 m m which includes the austenitio Cladding of 7 mm. F o r reasons of symmetry only' one quarter of the cylinder was modelled; the height of the model was 2500 mm. T h e half width and length of the cooled area is 250 m m a n d 1650

the elastic-plastic stresses had to be calculated using the 180 °-model without crack. The crack is modeUed in a segment with the precalculated displacements on the transition faces with the prescribed boundary conditions (see insert in fig. 8). The 1/r-singularity at the

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26O 240

-

220

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200

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.~

120

-~

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Fig. 7. Crack initiation values ~ in T - L and T - S direction.

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H. Kordisch et al.

/ Analysis of initiation of a circumferential crack

175

ux'°°nst

.--

J Z

/

U = 0

UX= 0

/

",./

y/'J"'

Fig. 8. Finite element model for the pre-calculations.

crack tip is modelled by collapsed volume elements. According to nondestructive examination data, the crack is assumed to be a semi-eUipse of depth a = 28 mm and

length at the surface of 2c = 64 nun, see fig. 9. The finite element mesh of the quarter model consists of 324 twenty noded volumetric elements and 1800 nodal

O .,41"

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- data

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-35

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c [ram] Fig. 9. Assumed crackshapefor thepre-calc~afions.

I

I

25

35

H. Kordisch et al. / Analysis of initiation of a circumferential crack

176

points; the segment has 566 volumetric dements and 3005 nodal points. Initially the temperature distribution due to the cooling transient was calculated using ADINAT. Starting with the operating temperature TO= 310 ° C, (assumed constant in the cylinder wall), the cooling process, (heat convection), was modelled with the medium temperature TM = 5 0 ° C and a heat convection coefficient of h = 5000 W / m 2 K as boundary conditions. The temperature of the medium is assumed constant over the cooled strip. Over the remaining circumference the heat transfer is modelled with TM = 310°C and h = 500 W / m 2 K as boundary conditions. The outer surface is modelled as insulated. Fig. 10 shows time dependent representative temperature distributions through the wall along the line of symmetry. In the second step, the stresses and strains are calculated using the same finite dement mesh using ADINA.

To simulate a long cylinder the nodal points at the upper end of the cylinder were allowed to move axially but restrained to remain on a plane. The mechanical loading due to internal pressure of Pi 10.6 MPa is superimposed on the thermal loading. The axial stress due to internal pressure was applied at the end of the cylinder. Crack surfaces are loaded with the internal pressure. Temperature dependent material parameters are defined according to the data in figs. 3 and 4. A bilinear approximation is used for the stress-strain curves. To be on the conservative side, the analysis was based on the thermal coefficients of expansion a of the H D R nozzle cladding material. The stress-free reference temperature is assumed to be TRef = 310 o C which is the normal operating temperature of the HDR. The thermal expansion coeffficient a, defined for room temperature, is therefore corrected for ?'Ref. =

3.2. Results of the pre-calculations Tk=50"C . h=5000 W/m2 K

it

I

411

k

7o~

o

~ 0

20

40

WoL l

a)

thickness

8{)

100

[mm3

Fig. 10. Temperature distribution through the wall.

120

Linear-elastic and elastic-plastic stresses were calculated for the quarter model without crack. The axial stress components through the wall in the line of symmetry serve as input for analytical calculations of J when assessing hypothetical crack geometries for a preliminary study. Fig. 11 shows a comparison of analytical J-values and finite element results of the crack tip at its deepest point (apex) for the circumferential crack under consideration. The overall agreement is satisfactory. The elastic and elastic-plastic stresses are associated with the upper and lower bounds respectively. Because the plastic deformation limits the absolute stresses, the analytical J as calculated in [7] is lower on the basis of the elastic-plastic stresses. The elastic-plastic J-values along the crack front resulting from the combined mechanical and thermal loading are shown for different times in fig. 12. Due to the temperature gradient through the wall J is lower at the apex of the crack than at the surface. The highest value appears at the interface between base material and cladding. For an assessment of the initiation behavior of the crack, the temperature and J-distributions as function of time are plotted for the apex of the crack and at the interface in figs. 13 and 14 respectively. It has to be pointed out, that the J-values increase steadily up to 1800 s. In addition to the applied J, initiation values Ji (see fig. 7) are plotted as a function of the local temperature at the crack tip. It can clearly be seen from figs. 13 and 14 that crack initiation is expected for all differently defined initiation values but at different times. For a safety assessment it is important to know whether the subsequent crack growth is stable or unsta-

177

H. Kordisch et aL / Analysis of hlitkztion of a circumferential crack

+ Janal.( ~ fin.-elast.)

~I

0

JFE

Janal. ( ~ elast.-plast.)

o

i

0

!

!

~0

!

!

40o

!

!

eO0

i

i

eO0

!

i

!

t000

Time t

i

1~o

!

!

1400

i

!

leO0

i

!

1800

i

2O0O

[sec]

Fig. 11. J-distribution at the apex position of the crack vs. time (analytical and numerical results).

ble. The safety margins of the test were determined in a conservative estimation carried out by the MPA in Stuttgart. A maximum of 0.8 mm stable crack growth and a minimum temperature of 80 ° C at the crack tip ensures upper shelf behavior. These conditions will be met up to a cooling time of 900 s. The test facilities have to guarantee by on-line monitoring, with NDTmethods and temperature measurements in the wall, that the transient can be discontinued immediately when these specified values are reached.

4. Additional investigations Additional investigations have been carried out in order to improve the accuracy of fracture mechanics assessments: a 2D-parameter study on the influence of different assumptions on a finite element analysis and an intermediate test with a 4-point-bending specimen to obtain a supplementary link in the chain of transferability of small-scale specimen results to large components. 4.1. 2D-parameter study

Even for a fixed geometry the results obtained by a finite element analysis depend strongly on the numeri-

cal model. Particularly in the case of pressurized thermal shock with superposed mechanical and time-dependent thermal loading, different assumptions in the input data can lead to unexpectedly large differences between the calculated results and the experimental values, [1]. In order to obtain an idea of this effect, an elastic-plastic parameter study of an axisymmetric model of the HDR-cylinder with a 30 mm deep circumferential crack was carried out. The finite dement mesh is shown in fig. 15. The results are discussed in terms of CMOD and J, which are plotted in figs. 16 and 17. CMOD and J reach a maximum after approx. 180 s and decrease when the cylinder wall is cooled down over the whole circumference which is in contrast to the local strip cooling. An upper and a lower bound solution results from different assumptions: - upper bound solution: initial temperature TO and TRef ffi 310°C, bilinear 8-c-curves, conservatively large values of the coefficient of thermal expansion, a, measured in the H D R nozzle area, singular dements at the crack tip, internal pressure on the crack. - l o w e r bound solution: starting temperature TO= 305 o C and TRer ----50 o C, multilinear 8-c-curves, coefficient of thermal expansion, u, of the reference cladding material 1.4550, rectangular elements at the

H. Kordisch et aL / Analysis of initiation of a circumferential crack

178

Thus the influence in the 3D-analysis might be even higher.

B: Thermal stress-free reference temperature TRef A reference temperature TRee= 310 ° C compared to TRef = 50 ° C leads to higher CMOD- and J-values. In defining TRef = 50 ° C, crack closure effects must be considered.

[sec]

%

i

•~

1800

x

900

+ 420

C: Coefficients of thermal expansion The individual coefficients of thermal expansion measured for the base material (reference steel 22NiMoCr 3 7 and the original HDR-material) and for the cladding material in particular (taken from the cylinder with lower a-values or from the nozzle area with higher a-values) differ significantly (see fig. 3). The input of higher a-values leads to higher CMOD- and J-values. It has to be kept in mind, that the a-distributions must be corrected according to the definition of TRef.

f

0

i

l

l

u

i

o 15

l

u

i

25 D i s t o n c e f r o m opex

I

5O [mm]

Fig. 12. J-distribution vs. the curvilinear distance from the apex along the crack front (dotted curves: J-values calculated directly at the crack front).

crack tip, without internal pressure on the crack. For these two enveloping solutions the following parameters were varied successively.

A: Bilinear and multilinear approximation of the stressstrain curves In some finite element codes a temperature dependent multilinear formulation for the ~-c-curves is not available. Thus the user has to confine himself to an individual bilinear approximation in order to match the expected degree of plastic deformation in the structure under consideration. In the axisymmetric case the influence is relatively small. It has to be pointed out, that the maximal total strain here is (t = 25, whereas in the local strip cooling situation, (t = 55 to 65 with full plastic deformation of the ligament through the wall.

D: Numerical model of the crack tip (fig. 15) The crack tip area can be modelled by small rectangular elements. The 1/r-singularity at the crack tip is achieved by using collapsed elements. The internal pressure on the crack surfaces can be considered, which requires an appropriate correction term in the J-calculation. A more realistic modelling of the crack tip area leads to higher CMOD- and J-values, whereby the influence is more pronounced for the J-calculation. R: Remaining influences The remaining differences are dependent on slight differences in the assumed service temperatures (TO-305 ° C and TO= 310 ° C, respectively) and different multilinear approximations of the 8-(-curves. The latter is decisive for the J-calculation. Further parameters such as the order of integration, iteration parameters or distinct (incremental) time steps which can be of influence are not investigated in this study. The influences on the maximum values of CMOD and J are compared for the different solutions and are summarized in table 1. An examination of the 2D-parameter study results shows that different assumptions lead to differences of up to 605 for the CMOD and up to 475 for J. There might be good reasons for choosing individual input data: e.g. conservative calculation, complex material laws which the FE-Code cannot adequately simulate or different assumptions for the residual stresses under service conditions etc. For the PTS-test post calculations all input data should be chosen to agree with the experimental results, thus being realistic without being too conservative.

H. Kordisch etaL/Analys~ofinitiationofa circumferentialcrack

179

Aoex

o

Jappl JIc(ASTM

e

87)

+ Jio K

Temp.

Jiu

o-I--0

2OO

~00

600

800 1000 rimo t [soc.!

1200

11,00

1600

1800

2000

Fig. 13. Assessment of initiation at the apex position.

4.2. Intermediate test (4-point bending specimen) A realistic assessment of the behawor of the surface flaw in a ductile material is necessary for the PTS-test. The transferability of experimental results from smallscale test specimens to actual components, however, has not yet proved for several reasons: - J and accordingly the response varies greatly along the crack front. Thus three-dimensional elastic-plastic calculations are necessary to obtain good results. Even in homogeneous materials, the resistance to crack growth varies along the crack front. This results from differences in the triaxiality of the stress state, defined as the constraint effect. Due to this constraint effect the JR-curves obtained from smooth and side-grooved CT-specimens or from specimens with different geometries and dimensions differ. - The crack growth resistance curves are determined on test specimens subject to mechanical loads at elevated, but constant temperatures. Up to now the influence of a temperature gradient on JR-curves

with time-dependent material behavior has not been investigated. The actual loading situation and material resistance can be very complex as in the case of the temperature gradient due to emergency cooling of a reactor pressure vessel. A method has recently been developed at Fh-IWM to account for the constraint dependence of the resistance along the crack front in the numerical simulation of stable crack growth [4]. The degree of triaxiality of the stress state is described by a constraint factor h = 8h/8 v, which is the quotient of the mean stress 8 h to the equivalent stress 8v. In order to describe the geometry effect, the average h m value of the CT-specimen as calculated in advance of the crack front, is correlated to the measured JR-curve. This is consistent with the fact that a JR-curve essentially represents the dependence between average J-integral and average crack growth. Initially a linear relationship between h m and the slope d J / d a is established which is used to simulate the local crack growth. In order to verify the method and to obtain a further

180

H. Kordisch et aL / Analysis of initiation of a circumferential crack I nterfnce bose mnt./c[odding

Jappl

0 ~4

Jic (ASTM 87)

8 Temp. 0

o

1

!

200

0

!

!

~

!

600

!

!

i

800

I

I

1000

Time t

I

I

1200

i

!

I

1600

1800

i

1400

CsecJ

Fig. 14. Assessment of initiation at the interface base material/cladding.

°'8,x •.

~

-Co~st.ralnts 200

/

U I fl I II I II I I

/

/

II II

Jl ,i

]1 II H II II II

I I I I I I I

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I

V

III

I

lJ] II

/ 112 PL

1480

1592

Fig. 15. Finite element meshes for the axisymmetric parameter study.

!

2000

H. Kordisch et al. / Analysis of initiation of a circumferential crack

181

influence of A@: bilinear ~ multilinear c-c-curves B@: TRef=50°C ~ 305°C C~: thermal expansion coefficient i

0 p.

A

A

Ill

/ . . ~ .

•

-

cladding:

cylinder ~ nozzle

base mat.: ref. data ~ orig. mat. D@: numerical model

--_ --.- .... - ~

rectangular el./without Pi on crack/ no J-correction ~ singular el./ Pi on crack/J-correction R@: -

"i

TO=305/310Oc

- different appr. of ~-e-curves

d

0v ' -

dI

I

0

I

100

I

I

I

I

200

I

30O

Time t

I

I

4~0

I

I

SO0

60O

[sec] Fig. 16. 2D~parameter study: C M O D

9

vs. time.

influence of A@: blllnear ~ m u l t l l l n e a r c-e-curves TRef-50°C 4 305°C C@: thermal expansion c o e f f i c i e n t a Be:

8

/.--~ =:-:"-,7.~_,

/ ,,

-

cladding:

-

base mat.:

cylinder ~ nozzle ref. data 4 orig. mat.

D~: numerical model

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rectangular el./without Pi on crack/

"~-.~.~ --..'-%.. ~--.\-......-,.. " ~

no J - c o r r e c t i o n ~ singular el./ Pi on crack/J-correction R~:- To=305/3100C - different appr. of c-c-curves

"3

0 ,4"

TRe f = 50"C

o~ 0

100

20O

300

Time t

400

500

600

Esec3 Fig. 17. 2D-parameter study: J-intelralws.time.

H. Kordisch et aL / Analysis of initiation of a circumferential crack

182

link in the chain of transferability, a large flawed plate made of RPV-steel 22 NiMoCr 3 7 was tested under four point bending at T = 70 o C [8]. The depth of the surface crack was 35% of the wall thickness with a c/a-ratio of 2.5. JR-curves for the material were measured from side-grooved and smooth CT-specimens with different dimensions. Three-dimensional elastic-plastic finite element

CT40/80

analyses simulating the initiation and stable crack growth were carried out. The results for the CT-specimens and for the bending test are plotted in figs. 18 and 19 respectively. The crack growth was substantially overestimated in the vicinity of the free surfaces, when the lower bound JR-curve measured from a side-grooved specimen was used to control crack growth over the whole front. The agreement between calculation and

20~ SK

/ j/

?

....

Exp.

(D J-R=const. I

I

-20

I

I

I

I

-4

-12

I

I

12

4

20

Oistonce from centre (ram) O~ 5K

CT40/BO

? •t . . ,

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.... oJ I

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-20

i

i

-12

I

-4

J

I

4

I

i

12

I

20

Distance From centre (ram)

Fig. 18. Numerical simulation of the local stable crack growth in different CT-specimens.

H. Kordisch et aL / Analysis of initiation of a circumferential crack CT12.S/S0

183

0X .~<

~O

,4"

/?\ Od ¸

O

. . . . Od I

Exp.

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"T I

-10

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-6

I

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[

I

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6

2

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Oistonce from centre (mm~ Fig. 18 (continued).

experiment clearly improved when "constraint-modified" JR-Curves were taken into account.

5. E v a l u a t i o n o f t h e P T S - e x p e r i m e n t

The experiment was successfully concluded in September 1988. Temperatures and strains at distinct points of the RPV were measured and recorded during the test.

The test was discontinued after approximately 19 minutes of cooling, because the safety limit of T = 80 o C at the crack tip had been reached. A drill core was extracted from the cracked area after the test and subsequently examined using fractographical methods. The comparison of calculated and measured temperatures shows satisfactory agreement. The CMOD-values 8

Table 1 Influence of different parameters ~n the maximum values of CMOD and J Inflmmce of

CMODm~ (~)

A : bilinear --, multilinear 8-ecurves - 1.7 B : Tad = 5 0 ° C --* 305(310)°C +21.0 C : thermal expansion coefficient a - cladding: cylinder ~ nozzle - basematl.: ref.data ---~orig.matl. +13.2 D : numerical model rectangular eL/without Pi on crack/no J-correction --. singular e l . / p i on crack~J-correction + 7.0 R : - To=305/310°C - different appr. of 8 - e-curves + 7.2 Maximal (lower to upper bound solution) + 60.0

Jmax (~) -4.0 +7.1

+4.4

• t/I O

+ Experiment

VJ.

O o J - R = const.

Lr

+ 8.4 0

+ 16.5 + 47.0

20

40

60

80

100

Distance from surface [mm]

Fig. 19. Numerical simulation of the local stable crack growth for the 4-point bending specimen.

184

H. Kordisch et al. / Analysis of initiation of a circumferential crack -40

-20

I

i

I

0 I

I

20 i

RPV loller I I f l c e

I

i

Notch 2

i

hoewever, differ by a factor of more than 2 when comparing pre-calculation and measurement (see the upper curve in fig. 25 and the experimental data). The reason is apparent from fig. 20: the real crack depth, found in the drill core, was a factor 2 smaller than the depth predicted prior to the test by NDT-methods. The pre-calculation thus greatly overestimated the crack size. The calculated axial and hoop strains at the outside surface of the RPV are higher than the measured strains (see fig. 28), which indicates that the temperature difference AT = 310-50 ° C = 260 o C, assumed in the analysis, is not realistic. Fig. 21a shows the deployment of thermocouples on the inside surface of the wall in the cooled region. An examination of the measured temperatures in the circumferential direction near the crack area shows that the fluid temperature is not constant over the cooling strip (fig. 22). The temperature is 50 o C along the vertical axis of symmetry increasing to 150 ° C

40 I

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F~. 20. Crack contours.

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RPV - wall

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Fig. 21a. Instrumentation plan (RPV-wall, inside surface). Fig. 21b. Instrumentation plan (RPV-waU, cross section).

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H. Kordisch et ai.

/ Analysis of initiation of a circumferential crack

185

IN

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Cooling area [mm] Fig. 22. Temperature of the fluid in circumferential direction in the cooling device.

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Fig. 23. Finite dement mesh for the post-calculations.

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H. Kordisch et aL / Analysis of initiation of a circumferential crack

186

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#4

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• 1iii••ii•ii•i!i•i•i•i•i•i!i!i•iiii•i•i••iiiiiiii!i•iiii•i•i•!i!i!i••iii•i•i•i•iiii•[ii••iii,!i•iil•i•!i• I iii!•i•i!i•i•i!i•i•!i•i•i•i•i•i•i•!i•i!i•i•i•!i•!•i1•i!i•!i•!i!i!i!i•i!i•i•!i•!•!••!i•!••i!i!i!i•i1iI•!•i,,1 L

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Fig. 24. Details of crack area, definition of crack front positions.

device guide plate deforming. These two characteristic time periods are shown shaded in fig. 22. Because of the significant differences between the test requirements used for the pre-calculations and the

at the outer edges. Also, the flow pattern of the cold fluid on the left and right circumferential region of the cooling strip is not the same. This difference increasing significantly after 450 s is probably due to the cooling

influence of A

: crack size

B

: material

C

: thermal

i

parameters boundary cond.

J

B

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i

i

200

400

i

i

600

I

i

800

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i

1000

i

[

i

1200

[sec.7

Fig. 25.3D-parameter study: CMOD vs. time.

I

1400

i

I

1600

i

1800

187

H. Kordisch et al. / Analysis of initiation of a circumferential crack

6.2. 3D-parameter study

reality, it was decided to carry out best-estimate postcalculations with the actual crack geometry and the actual thermal boundary conditions.

Complementary to the 2D-parameter study, three calculations with different parameters were carried out with the three-dimensional model. Again the main results are discussed in terms of CMOD (fig. 25) and J at the apex of the crack (fig. 26):

6. Post-calculations

A. Influence of crack size

6.1. Numerical model

An analysis was performed with the real crack size but with the same thermal and thermo-mechanical material parameters for comparision with the pre-calculations with a larger crack. As expected, the CMODand J-values are significantly smaller. They converge rapidly to almost constant values associated with plastic deformations occurring at the crack tip region. The J-distribution at the apex of the shallow crack is higher than for the deeper crack during the first 400 s of the cooling time because the temperature transient reaches the crack tip area of the former earlier.

For the post-test calculations a new finite element mesh was generated by VTT which is shown in fig. 23. The length of the cylinder and the cooling area is 1600 mm and 800 mm respectively, the latter representing the upper part of the cooling strip in the test. The mechanical boundary conditions are the same as in the precalculations. The real flaw is idealised as a 14.8 ram deep and 64 mm long circumferential crack, which penetrates the cladding at an angle of 90 degrees to the circumference and is semi-elliptical in the base material (fig. 24). The 7 mm thick cladding is modelled with two element layers. The mesh contains 841 twenty noded volumetric elements and 4470 nodal points.

B: Influence of material parameters The second analysis was carried out still applying a constant fluid temperature of T = 50 o C, but multilin-

J (opex)

i I influenceof B: aatarial paraneters A : crack

C : thermal

alze

boundary

cond.

b

~ /./-_

0

200

...............................................................

400

600

800 Time t

1000

1200

1400

£secJ

Fig. 26. 3D-paxametcr study: J-integral vs. time.

1600

1800

I-I. Kordisch et aL / Analysis of initiation of a circumferential crack

188

I

THEL

Curves 1-4: Post - calculation Curves 5-0: Measurement

310 270230" 190"

~.150(0

20mm

1107030

0

1()0

2()0

3()0

4()0

500 600 Time In s

7()0

800

900

10~)

1100

Fig. 27. Temperature distribution at different positions in the wall vs. time.

ear stress-strain curves and the thermal coefficients of expansion of the original H D R base material and cladding material of the cylindrical part of the RPV with lowers a-values. This resulted in a reduction of the CMOD of approx. 27% and of J of 13%. C: Influence of the real thermal boundary conditions As shown in fig. 22 the fluid temperature is not uniform over the cooled inner wall area in the circumferential direction. A symmetrical model can only describe one half of the cooling strip with appropriate thermal boundary conditions. The left hand side was chosen because strain gauges were attached directly to the back of the wall on the left hand side outer surface. Thus an opportunity to compare the local numerical strains with the measurement was provided. The influence of the actual thermal boundary conditions is relatively small with a reduction of 7% in the CMOD and a reduction of about 14% in J. The calculated CMOD-values agree very well with the experimental findings (see fig. 25). 6.3. Comparison experiment/post-calculations During the test the temperatures were measured with thermocouples attached in the wall at a cross section near the crack. Fig. 21b shows the instrumentation plan. The thermocouple BI 1008 at the inner surface was

embedded in gold which was hammered into an 1 ram deep keyway. (A thermocouple embedded in gold measures the surface temperature very accurately for the following reasons: (a) its accuracy is not affected by the fluid temperature, (b) as the thermal diffusivity a = ~,/(p- Cp) of gold is 26.7 times higher than that of the austenitic cladding, the resulting temperature gradient in gold between the surface and the tip of the thermocouple is negligible.) The measured temperatures therefore represent the real response of the structure and correspond to the numerical results. The measured and calculated temperature distributions at different locations through the wall are plotted as a function of time in fig. 27. The agreement is very good up to a depth of 40 nun. The calculated temperatures at the outside of the cylinder were overestimated throughout. In conclusion, it must be mentioned that the numerical model does not consider heat transfer through the outer surface, as it should do in the case of the initial steady state in order to improve the starting situation for the thermal shock load. Fig. 25 shows the good agreement between the calculated and measured CMOD-values. The pre-calculation overestimated the strains at the outer surface because the fluid temperature was assumed constant. The post-calculated and measured strains are in good agreement (fig. 28), even to the

H. Kora~sch et a£

/ Analysis of initiation of a circumferential crack

Outside RPV Surface: Curves1,3,5: Axial Strain Curves 2,4,6: Hoop Strain

2

189

I

I THEL

1,0"

/.2-

J

Post - Calculation

,

~.8J

- 44

~

Measurement

~'--........~~_~_~St - Calculation

'

t

-,0

0

i

i

i

e

i

|

,

,

,

0

100

200

300

400

500

600

700

800

900

?

i

1000 1100

Time in e Fig. 28. Strain distribution at the outside RP'/surface.

.,

~

0

ot=

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+ t=

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~

X t= 420 s

~

~ t= 480 s

u

o

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t=1200 s

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8

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10

20

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T

30

D/stance From apex

!

I

40

I

50

[mm]

Fig. 29. J-distribution vs. the curvilinear distance from the apex along the crack front.

H. Kordisch et aL / Analysis of initiation of a circumferential crack

190

Apex (pQth o8)

804,

Jlc

(ASTN

87)

"b Temp.

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j[ _ _

.

~

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__

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Jiu ,0

0

I

I

200

I

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I

400

i

600

i

i

i

800

I

I

1000

Time t

I

i

1200

i

1400

I

i

1600

i

i

1800

I

2O00

(see2

Fig. 30. Assessment of initiation at the apex position.

extent of considering the change of slope after approx. 480 s, resulting from the increasing fluid temperatures at the left hand side of the cooled strip. The local response of the vessel at the outer surface is very sensitive to differences in the local cooling on the inner surface.

direction, respectively. The crack should only have initiated at the apex at a toughness corresponding to the lower limit Jiu.

6. 4. Assessment of the behavior of the crack

The described three-dimensional calculation prior to the PTS-test on the HDR-RPV cylinder was aimed at solving two problems with contrasting requirements. On the one hand, predicting the intended stable crack growth as accurately as possible. On the other hand serving as a basis for assessing the safety of the PTS-test such as establishing the critical point for breaking off the test. In case of doubt, the assumptions must necessarily be on the safe side. As an example, the thermal coefficient of expansion of the cladding was only measured for material from the manually cladded nozzle. This differed significantly from the value of the machine-made cladding on the cylindrical wall which was examined after the PTS-test (see fig. 3). The two-dlmensional and the subsequent three-di-

In fig. 29 the J-values are plotted along the crack front for different times. During the period of increasing thermal load the highest J appears in the cladding. This was also seen in the pre-caleulations with the deeper crack (see fig. 12). When the thermal load decreases, the J-values drop near the surface whilst they remain relatively constant at the apex position. To enable the initiation of the crack to be assessed the temperature and J-distributions as a function of time were plotted in fig. 30 for the apex position and in fig. 31 at the interface of base material/cladding, together with the temperature-dependent scatter bands of initiation values Ji for the T - S direction and the T - L

7. Conclusion

191

H. Kordisch et al. / Analysis of initiation of a circumferential crack InterfQce bose mot./ctoddin(j (pnth o3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0 ,4F O~

i

~8

/

. . . . . .

5IC(ASTM

87)

"b

Temp. m

" ~ -

-'-'~"~-

~

~"

~"

~'

Jappl

&

~"

o

0

I

I

200

I

44)0

I

I

600

I

I

I

800

I

I

1000

Time t

I

1200

I

I

1600

I

I

1600

I

i

1800

1

2O0O

[soc2

Fig. 31. Assessment of initiation at the interface base material/cladding.

mensional parameter study demonstrated that the precalculation was clearly conservative because of the "safe" assumptions mentioned above. The 2D-parameter study was also used to investigate the influence of additional model variations. The numerical simulation of the local stable crack growth in different CT-specimens and in a large-scale 4-point-bending specimen showed excellent agreement between the calculated and the experimental results thus complementing the PTS calculation. In contrast to the pre-test calculation the mechanical loading, the initial crack geometry, and all material properties, were well defmed for the calculations of the specimens. The intended cooling conditions supposed in the pre-calculation were not matched exactly during the PTS-test. Above all the destructive testing of the crack after the ITS-test revealed a grave overestimation of the initial crack depth indicated by the nondestructive exam/nation performed prior to the test. The pre-calculation results for CMOD or strains on

the outside surface of the RPV deviated considerably from the test results. The three-dimensional parameter study together with the post-calculation showed that" the inaccurate N D T description of the crack and the difference between designed and real cooling conditions were the main reasons for these deviations. The calculation' after the PTS-test was based on the real crack size, on the measured cooling water temperatures and on the actual thermal coefficient of expansion determined a f t e r , t h e test. The post-calculation yielded an excellent agreement between calculation and measurement for the wall temperatures, CMOD or strains on the outside surface of the RPV. The three-dimensional calcination containing a constraint-modified crack growth model was thus verified for mechanical loadings leading to stable crack growth in specimens. In the case of the PTS-test, the calculation was verified up to the point of crack initiation. For the post-calculation, the crack tip loading only just reached the limit of crack initiation. The full verification of the

192

H. Kordisch et aL / Analysis of initiation of a circumferential crack

calculation of stable crack growth during a PTS on a RPV requires an additional PTS-test with a deeper crack.

Nomenclature

CMOD E h h J

Ji Pi Rpo.2 Rm

ro rM TRef Ct

co O'h Ov

crack mouth opening displacement, Young's modulus, heat convection coefficient, and oh/o v -- constraint factor, crack driving parameter J-integral, initiation value, internal pressure, yield stress, tensile strength, operating temperature, medium temperature, stress-free reference temperature, thermal coefficient of expansion, heat capacity, thermal conductivity, mean stress, equivalent stress after v. Mises.

References [1] K. Kussmaul, E. Roos, H. Diem, G. Katzenmeier, M. Klein, G.E. Neubrech, L. Wolf, Cyclic and transient thermal loading of the HDR reactor pressure vessel with respect to crack initiation and crack growth, 10th SMiRT Post Conference Seminar No. 2, August 1989, Monterey, California, USA. [2] K.H. Bathe, ADINA, a finite element program for Automatic Dynamic Incremental Nonlinear Analysis, Report 82 448-1, MIT, Cambridge, Mass., USA (1980). [3] IWM-CRACK, a subroutine package for crack problems, Fraunhofer-Institut fiir Werkstoffmechanik, Freiburg, FRG. [4] H. Kordisch, E. Sommer and W. Sehmitt, The influence of triaxiality on stable crack growth, Nucl. Engrg. Des. 112 (1989) 27-35. [5] B. Voss, JR-Kurven f'~ HDR-RDB-Werkstoff, Report V38/87 of the Fraunhofer-Institut ftir Werkstoffmecbanik (1987). [6] Ermitflung yon JR-Kurven fiir den HDR-RDB-Werkstoff und erganzende Werkstoffuntersuchungen im Rahmen der Prfifungen der Bohrkerne 7 und 8, Report 815 710/1 of the MPA Stuttgart (1989). [7] E. Keim, Siemens/KWU (private communication, 1987). [8] H. Talja, L. Hodulak, H. Kordiscli, B. Voss and N. Knee, Durchftihnmg und Analyse eines Laborversuches zur numerischen Simulation des stabilen Risswachstams, Report V40/88 of the Fraunhofer-Institut f ~ Werkstoffmechanik (1988).