an initial approach to establishing an experimentally proven ‘leak before rupture criterion’ for...

AN INITIAL APPROACH TO ESTABLISHING AN EXPERIMENTALLY PROVEN 'LEAK BEFORE RUPTURE

CRITERION' FOR SNR-300* COMPONENTS

KONRAD DUMM & MANFRED FORTMANN

INTERA TOM, 506 Bensberg, Cologne, West Germany

(Received : 19 September, 1974)

ABSTRACT

Examination of experimental results and fracture mechanics analysis has shown the sudden rupture of one of the SNR-300 main coolant pipes to be impossible. The analysis indicates that, excluding small leaks, the integrity of the sodium filled heat transfer system under normal operating conditions will also be maintained. With regard to small leaks it is considered that i f these are smaller than those which would give a leak rate of less than about 1 kg/h, they can be detected.

INTRODUCTION

Following the example of safety assessments for light water reactors, it was considered desirable to assess the possibility of sudden rupture of a main coolant pipe for the liquid metal fast breeder reactor (LMFBR) SNR-300. The view was taken that, in this case, one should try to maintain and guarantee the integrity of the comparably thin walled components of the heat transfer systems by an experimentally proven 'leak before rupture criterion'. As structural material of the SNR-300, an unstabilised austenitic steel with the German identification number 1.4948, is used.

The general composition of this material is:

* SNR-300 is the prototype of a 300 MWe electrical output sodium cooled fast breeder reactor under construction at Kalkar, Germany.

43 Int. J. Pres. Ves. & Piping (3) (1975)--© Applied Science Publishers Ltd, England, 1975 Printed in Great Britain

44 KONRAD I)UMM, MANFRED FORTMANN

C Cr Mn Ni Si Co

0"04 17'0 I0"0 W e i g h t ~ - - - - 2-0 - - 0.75 0.2

0-08 19.0 max . 12.0 max . max .

Mo P S B Nb Ta

0"4 W e i g h t ~ - - 0.045 '0.030 0.005 0.05 0.005

0 '5 m a x . max . m a x . m a x . m a x .

In spite of intensive quality control it is considered that micro-cracks will always be present in the basic material as well as in connecting welds. These so-called sub-critical cracks may increase in size due to load variations such as vibrations or temperature and pressure changes during operation. They may even penetrate through the whole wall of a component. The possibility of detecting such a leak depends mainly on the behaviour of the leaking sodium. The type of thermal insulation--as well as the composition of the surrounding atmosphere--will influence the possibility of detecting the leak. Moreover, the rate of leakage will depend not only on the size of any crack but also on its shape.

In this analysis, the critical crack size for given geometries was determined. The critical crack size is defined as the crack length (in its most important dimension) at which under design conditions a sudden rupture or fracture would occur.

The difference between this critical crack size (i.e. the size for unstable crack growth) and the detectable crack size will act as a safety margin for the geometry and design in question.

SUB-CRITICAL CRACK G R O W T H

It is argued that, due to very high quality standards being applied to reactor coolant circuits, the probability of undetected defects remaining in the material is extremely low. Nevertheless, for safety reasons, the presence of small initial cracks has to be assumed. Depending on size and load fluctuations during operation, these initial cracks may grow by all of the mechanisms that give sub-critical crack growth. The rate of crack growth by fatigue depends on the fluctuations of the stress intensity factor and the crack growth resistance of the material in question. The direction of a crack growth depends on the direction of the initial flaw, the geometry, types of loading and possibly on inhomogeneities and internal stresses in the material. In a homogeneously stressed pipe the direction of crack growth can usually be predicted. Flaws inside a tube wall will tend to enlarge perpendicularly

EXPERIMENTALLY PROVEN 'LEAK BEFORE RUPTURE CRITERION' 45

---Wall thickness - ~

i i i

I Crack propagation Fig. 1.

to the main stress direction and finally penetrate the wall (see Fig. 1). The crack velocity controlling stress intensity factor K~ can be expressed by :

= +

A surface flaw will grow through the wall thickness much faster than it will grow in crack length. This is due to the more or less plane stress conditions in the tube wall. Figure 2 illustrates schematically the expected behaviour. ~ Some methods of calculating stress intensity factors of surface cracks are listed and discussed in the literature. 2

The application of these more qualitatively orientated considerations shows that a low cycle fatigue crack will penetrate the wall as soon as the crack length has reached a value of two to three times the wall thickness.

- - W a l l thickness

o u r r a c e c r a c k

Fig. 2.

46 KONRAD DUMM, MANFRED FORTMANN

tube 0 355x10 mm

- - ~ initial -20

, ! - 1 0

~ y i I" 10- 0

L ~t ~ 401 221J -

~]

~ " ~ inside

G measured 6 uniform tube

Fig. 3. Reinforced tube.

With respect to wall penetrating cracks and leak detection when the tube is loaded by internal pressure the most unfavourable initial crack position is given when the discontinuity in the tube wall thickness is on the inner surface (see Fig. 3). The high axial tension stresses on the inner side were assumed to lead to a circumferential crack growth which is much more intensive than in the radial direction. However, the three-dimensional stress conditions in the tube wall, compared with the two-dimensional stress pattern on the inner surface, lead to a reduction of the circumferential crack growth.

On this basis it was decided to use an extremely rigid test specimen (Fig. 3) in order to be able to study crack growth and leak formation at discontinuities. A

~ ring 0 520 x g 355x60mm

I

front 6500 cycles after start of leakage I

of 1-137 bar, 60,5 long start of leakage crack front 22500 cycles after start of leakage of 1-137 bar; 68/53 long; leakage: 20 mg water/min at 10 bar

Fig. 4. Crack growth in a stepwise reinforced tube wall.


tube of 355 mm outer diameter and 10 mm wall thickness was reinforced by a ring of 520 mm outer diameter and 60 mm length. Small initial grooves were milled on the inner surface as shown in Fig. 5 and the tests were performed at room temperature; crack growth from the grooves was excited by oscillations in internal water pressure. Before the tests the specimens were heat treated for 2 h at 900- 950°C and cooled down by 100°C/h. Figure 4 shows the crack growth during cycling by internal pressure, the actual crack length being measured by an ultrasonic detector. The observed crack lengths of four similar initial grooves are depicted in Fig. 5. The shape of these curves, dc to dn, allows the estimation of a form factor M i at the inner tube wall, M i being defined as in eqn. (2):

KI Mi = (2)

~. (~. cp

In the derivation of this form factor the stress intensity factor K~ was assumed to be that reported by James and Schwenk 3 for a similar material. The form factor so derived is used later on for the prediction of actual crack growth.

100

50

0 20

flaw 1 2

103 at 1-137 bar

J + / + •

f I

t

I

I 30 40

~mCm~ ao [mm] 18 2.5 22 3,4 20 2,9 25 3,9

1 3¢ 1.2,4

- / " j start of leakag

50 60 70 80 2c inside [mini

Fig. 5. Start of leakage at a reinforced tube.


K [10 3 N/mm ~1 31 Kcr, min

2

1 l ~ ' - - - I / ~K__K_O__ , .~n~ 10.4 mm/Cycl e

/ ~ ~ KOl , ~ n = 1 0 ~ mm_/Cycle

0 0,5 1,0 1,5 2,0 2,5 3,0 a [mm] • Surface crack depth a in wall thickness t =10 turn:

360°circurnferential; Rm = 295 ram; exposed to 6.a~ = 6'0,2 55o'c = 113N/mm2:,~'=550°C

Fig. 6. Circumferential surface crack.

For this analysis a surface flaw of 360 ° circumference having a uniform depth was assumed, even though such a defect was considered to be extremely hypo- thetical. The stress intensity factor for the uniformly loaded pipe region can then be determined according to the PVRC Recommendations. The stress intensity factor of an SNR-300 main sodium pipe at operating conditions has been calculated on the assumption of this complete circumferential flaw being exposed to an extremely high longitudinal stress, including all secondary stresses. The result is shown in Fig. 6. It will be seen that even up to a crack depth of 20 to 3 0 ~ of the wall thickness, the sub-critical crack growth during an expected reactor lifetime of l0 ~ full load cycles is insignificant. Moreover, a fairly large safety margin regarding the critical stress intensity factor Kcr is given.

SUDDEN CRACK PROPAGATION

An increase in crack length and/or load leads to an increase in the stress intensity at the crack tip. If this stress intensity were to reach the critical value the crack would become unstable and enlarge instantaneously. However, in some circumstances where critical crack lengths are large with respect to plate thickness, it can be the case that as crack intensity approaches its critical value the crack gap increases, which with the associated plasticity can lead to increasing leakage of the pressurising fluid.

EXPERIMENTALLY PROVEN ' L E A K BEFORE R U P T U R E CRITERION" 49

The diameter of the SNR-300 main sodium pipes is approximately 600 mm with a wall thickness of 10 ram. The operating temperatures range from 200°C to 550c'C. For the experimental determination of critical crack lengths a tube diameter of 350ram was used; the wall thickness was kept at 10ram, the reduction in diameter was possible as the influence of curvature could be calculated by the geometry factor of Folias.5 On the other hand, it was not considered possible to make any analytical allowance for change in wall thickness under the given plane stress conditions. The tests were performed at room temperature.

The evaluation of the results was made on the basis of Hahn's equations 5 :

Kc = a + . c . l n s e c i . a + ] (3)

with the following nomenclature:

M -- stress magnification factor, = f(,~) for longitudinal cracks 5 for circumferential cracks 6

C 2 ,~2 = - - . 12(1 - v z) (4)

R ' t

a = stress transversely to the crack, but in a crack unaffected region.

a + = flow stress = kl(ao.2 = ant) (5)

The best correlation to experimental data was achieved by using k~ = 0.398. Typical values of 0-2 ~,, yield stress (ao.2), breaking stress (ant) and flow stress

(a +) of the material in question are:

Temperature ao. 2 aB, a + (°C) (N/mm 2) (N/mm 2) (N/mm 2)

20 206 536 295 550 113 368.5 192

For comparably short crack lengths in high toughness material having a nominal hoop stress at failure above 90 ~o of the a0, 2 yield stress, sudden rupture is preceded by large scale yielding or plastic instability. According to Hahn, eqn. (7) has to be applied where the range of validity is limited by eqn. (6).

(Kc/ay) 2 - - > 5 ( 6 )

¢

O -+ o" = - - (7)

M

Figure 7 illustrates the critical stresses and crack lengths for longitudinal cracks and


300

200

100

6"a [N/ram 2]

+

+ test result i

test tube, Rm= 172 ram. ~ =20°C, t = 10 mm ~ N/mm 2 ey = 206 N/ram 2 4565 N/ram 3/2

Rm=295 mm,t=10~'m~.~ . . ~ = maximum stresses for SNR ,~ = 550oC

G + = 192 N/ram 2, Kc= 4565N/ram " ~ ~ G'y= 113 N/ram 2

100 200 300 400 2 C [ m m ]

Fig. 7. Critical stresses for wall penetrat ing longitudinal cracks on SNR-300 material.

Fig. 8 those for circumferential cracks. The evaluation of test results has demon- strated that both types of equation are applicable. Equation (3) is also valid for short crack lengths as is eqn. (7) for cracks up to 200 mm longitudinally and 150 mm circumferentially.

In order to apply the test results to the normal operating temperature the critical stress intensity factor was assumed to be the same as that in the test vessel on the basis that the real wall thickness of the tubes is equal to that of the test specimen. The flow stress has been developed by using eqn. (5). The nominal hoop stress at failure has been calculated by eqn. (3) although the range of validity for eqn. (7) is still given. For this reason the results can be regarded as pessimistic. Under these

16a[Nmm-2]

I ~ j Duniform tube I \ 1 ~ I I X~ 3) reinforced t u ~ I

test tube 2ooi ~ F I ~ I ~ Rm=172mm; t=lOmm;~=20°C I " ~ ~ 16 + = 295 N/mm2o,,~ I

I I / Rm=295mmlt=10mm; '~'=550°C

0 100 200 300 400 _-- crack length

2c[rnm]

Fig. 8. Critical stresses for wall penetrat ing circumferential cracks on SNR-300 tubes.


circumstances the critical crack lengths for the SNR-300 main sodium pipe are calculated to be: 200 mm for longitudinal through-wall flaws and 400 mm for circumferential through-wall flaws, this value being 20 to 40 times the wall thickness. These results can be taken to imply that a ' leak-before-break' situation is likely on the basis that a critical crack size greater than the wall thickness (a through-wall crack) will lead to leakage. This statement is valid even for a circumferential crack in a reinforced region (see Figs. 5 and 8). More details on the detectability of such leaks are given in the next section.

Calculations for predicting the safety margin between leak occurrence and sudden rupture can only be made when accepting comparably large errors. This is due to the fact that, for instance, values describing t he influence of sodium on crack growth are not available. Therefore only a rough estimate is possible by applying the following equat ion:

2 c)"-- ~ (8) N = (n - 2). C . [(Tz) ~ • M . Aa]" " 2)/2 Ce(n--

with : N = Number of cycles.

dc - crack growth/cycle -- C . AK" (9)

d ,

according to the literature 3 for 550°C and AISI 304, however without sodium influence,

C = 5949. 10 -1 l n = 2343

~6a[Nlmm o o,21 ' \

'°° i

50

SNR 300 Rm = 295; ~ = 550 ° C z ~le= ~k =el mm

SNR 300 conservativ n&number of load changes which Cleakenlarges to Cleak+Ccr

50 100 150 n [103]

Fig. 9. Leaks before rupture at reinforced tube.


are used where the crack growth, c, is given in mm and the AK is N / m m - 3/2

M = form factor, evaluated by eqn. (2) from crack growth measurements at room temperature.

M . . . . = 1'23 for cm~ X

2% = crack length at start of leakage = 61 mm 2ce = ca + ccr, crack length at which, after start of leakage, 50 ~, of the critical

crack length 2% is reached. The result given in Fig. 9 shows the large safety margin in spite of the incomplete

knowledge of the effect of the high temperature sodium environment.

LEAK BEHAVIOUR

The rate of leakage through a defect penetrating a tube wall is controlled by the separation and nature of the crack faces. Under unloaded conditions they may even seal the leak. Tension stresses applied to a cracked tube or component lead to the enlargement of crack gaps. The sodium penetrates the crack and becomes detectable. Assuming extremely small cracks, the sodium in such cracks may form reaction products, such as sodium oxide, which are able to plug the crack at times. Load changes induce pumping effects on the cracks, whereby these reaction products are swept away so that the leak becomes detectable.

In order to obtain an impression of the leak rates at different crack configurations, the crack gaps were continuously measured during the rupture tests previously mentioned. In the case of comparatively low stresses accompanied by insignificant plastic deformations, the crack opening can be described by6:

~r.c V~ 2Vj = 2 . . . . (10)

E C a

where V1/C1 is a geometrical factor as given by Erdogan and Ratwrani 6 and 2 V1 is defined as being the maximum gap of the crack at a given internal pressure.

A comparison of calculated and measured crack gaps is given in Fig. 10. The conformity is completely satisfactory. An estimate of sodium flow rates has been made based on these results. Due to crack size, laminar or turbulent flow conditions have to be considered where the Reynolds Number is the controlling factor. Figure 11 shows the calculated sodium flow rate versus the relative critical pressure for one of the test tubes employed. The calculated and measured values corre- spond satisfactorily up to 60 ~ of the critical pressure. Under these circumstances the leak flow rates can be calculated for different crack conditions on SNR-300 main coolant pipes. The result shown in Fig. 12 demonstrates that early detection is possible when adequate leak detection systems are available. The curves show that even under a pressure of 0"1 bar, cracks of comparatively short lengths are

EXPERIMENTALLY PROVEN %EAK BEFORE RUPTURE CRITERION' 53

Fig. 10.

1 0 0 ¸

10

/ + o teat results

teat tubes la = 355 mm

. 20oc - ---]

curves calculated acc.to. (6) [ L

100 200 300 400 500 600 2 c [ m m ]

Elastic behaviour of crack flanks under internal pressure.

10,5

10 4

5

2

lO 3

10:

10

V'[crn3/s]

+ calculated by measured c r a ~ J

~elaatic crack ~lap / calculated acc. to t6)

0 0,5

turbulent/laminar

/

longitudinal ;rack 2c -191.7 mr Da-358 mrr

t =10,25 m

P / P c r i

Fig. I 1, Sodium leak rate through cracks opened by internal pressure.


Fig. 12.

10 3

lO 2

lO-

1

lo -1

0

l'[cm3/s] , 10 bar

I,

ba, G=8

i

100 200 300 400 500 2 c [ m m ]

Calculated sodium leak rates on SNR-300 main coolant pipes (without plastic deformation).

detectable. A leak rate of 1 kg/h was postulated as a sufficient detection sensitivity. This requirement is fulfilled by the use of an electrical detection system consisting of an arrangement of double nickel wires inserted in perforated ceramic pearls. These pearl-insulated wires are attached to the components which have to be controlled. Signals occur when either one of the wires become electrically short- circuited to the component wall or to the second wire by the leaking sodium. Moreover, an interruption of one of the wires due to corrosion from sodium reaction products also is arranged to give a leak signal. These arrangements have been thoroughly and extensively tested.

The influence of the surrounding atmosphere on the leak behaviour of the sodium was also taken into consideration during those tests. For instance: the atmosphere in the primary system contains only 0-7 vol ~ of oxygen while the secondary systems are exposed to normal atmospheric conditions. The ability of the system to detect small leaks is also influenced by the type of thermal insulation of the components. The possibility of leaking sodium being absorbed by the insulation instead of trickling to the detection wires should be avoided. This means that the inner side of such an insulation has to be completely lined with sheet material.

FINAL REMARKS

The test results discussed in this paper, their conformity with theoretical considerations provided by fracture mechanics, the examination of the rates of sodium


leakage through cracks and the use of a sensitive and reliable leak detection system allow the 'leak before rupture criterion' to be applied to the safety assumed of the SNR-300 reactor compared. On the other hand, the results gained so far should be considered only as a first approach. Effort still has to be made with respect to observations at operating temperatures, including questions on high temperature embrittlement and irradiation.

REFERENCES

1. SOMMER, E. Risse in Konstruktionsteilen, Umschau 72 (1972) Heft 16. 2. MERKLE, J. G. A review of some of the existing stress intensity factor solutions for part-through

surface cracks, ORNL-TM-3983. 3. JAMES, LEE A. ,~ SCHWENK, EARL B., JR. Fatigue-crack propagation behaviour of type 304

stainless steel at elevated temperatures, Metallurgical Transactions, 2 (February, 1971) p. 491. 4. PVRC Recommendations on Toughness Requirements for Ferritic Materials, 175/August

1972. 5. EIBER, ROBERT J., MAXEY, WILLARD A., DUFFY, ARTHUR R. & ATTERBURY, THOMAS J. Review

of through-wall critical crack formulations for piping and cylindrical vessels, BMI 1883. 6. ERDOGAN, F. & RATWRANI, i . Fracture of cylindrical and spherical shells containing a crack,

Technical Report NASA-TR-71-3, July, 1971.

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