Fracture mechanics analysis on the initiation and propagation of circumferential and longitudinal cracks in straight pipes and pipe bends

Nuclear Engineering and Design 58 (1980) 19- 31 © North-Holland Pubhshing Company

FRACTURE MECHANICS ANALYSIS ON THE INITIATION AND PROPAGATION OF CIRCUMFERENTIAL AND LONGITUDINAL CRACKS IN STRAIGHT PIPES AND PIPE BENDS H.D. SCHULZE and G. TOGLER Rhemtsch.Westfalischer TUV e V., Zentralabtedung Werkstoff- und Bautedverhalten, D-4300 Essen, Federal Repubhc of Germany

E. BODMANN Hoehtemperatur-Reaktorbau GmbH, D-6800 Mannhetm 1, Federal Repubhc of Germany Received 9 July 1979

The safety potentml against pipe fracture of a nuclear piping system is quantified using as an example the fuel circulating system of the THTR 300 MWe. A comparison of the size of cracks expected to occur during operation in the most unfavourable case wath the cnUcal crack sizes from the fracture mechanics aspect is used as a cnterlum for evaluation. A comprehenswe test program was carried out to investigate the dependence of longitudinal and transversal crack sizes upon load (bending and internal pressure), pressure medmm and temperature. The theoretical methods for predicting the crmcal crack sizes were checked by the test results The conclusmn is that pipe rupture does not need to be considered under the condmons investigated

In this analysis, the pipe rupture risk is to be evaluated on the basis of quantitative criteria: Taking into consideration the operating conditions of a specific plant, an evaluation of defective pipes is being carried out based on the fracture mechanics method. A detailed description of the procedure is given in the following sections. In addition it must be ensured that (a) during the operation no material damage will occur, in particular corrosion, which is not covered by the fracture mechamcs considerations, and (b) the material characteristics relevant to the fracture mechanics statements in particular toughness do not deteriorate during operation. This part of the verifications cannot be discussed In more detail within the scope of this analysis, which primarily concentrates on the fracture mechanics aspects. If the fracture mechamcs rules defined in sect:on 3 are met, and if no negative aspects arise from the additional considerations on corrosion and toughness mentioned above, pipe rupture is not assumed and structural measures for pipe rupture control will not

1. Pipe rupture control It has been demonstrated by failure statistics partlcularly In conventional plant operation that failure of pressurized piping is possible, although they were designed to current codes. In this context pipe failure means formation of long and primarily axial ruptures having a rupture surface of more than the inner crosssectional area of the pipes, as well as breaking of a pipe by a circumferential rupture; in the following both effects are classified under the term of pipe rupture. For reasons of plant safety, detaded analyses are carried out during the course of the erection of nuclear power plants on the consequences of a possible pipe rupture, and in certain cases comprehensive hardware measures are Introduced for their control. As an example, the pipe whip restraints are quoted which are restrain facthtles Introduced as a countermeasure against whip effects of ruptured pipes. For analyses and measures of this type the rupture is assumed to occur at the worst possible position in the pipe without quantifying the effective rupture risk of this piplng. 19

20

H.D. Schulze. G Togler, E Bodmann / Fracture mechamcs analysts tn ptpes

be necessary. Thus several negative effects resulting from such measures will be avoided, such as e.g. reduced accessibility of the plant and much increased difficulty of inspection.

do

.........

I!7 l

L=-~

2. Characteristics of the piping system 4 -

The investigation was carried out for the fuel circulating system of the THTR Nuclear Power Plant Within this system the burn-up of the fuel elements discharged from the pebble bed core is measured and according to their burn-up, the spheres are recirculated to different core zones or discharged. The piping system is exposed to the pressure and temperature of the cold side of the primary coolant (helium). The nominal pipe diameter is 65 mm and the wall thicknesses are between 3.2 and 4 mm. A certam part of the pipes are equipped with continuous fins axially arranged on the inner surface for the purpose of guiding the fuel element spheres. The design pressure IS 46 bar and the design temperature 260°(2. The pipe material is 15 Mo 3, a low alloy structural steel. The stress in the pipe due to internal pressure is relatively low, the load on circumferential cracks due to longitudinal pipe stresses primarily results from bending moments. The number of significant operating load fluctuations due to startup and shutdown procedures is 10 000.

3. Crack lengths criteria It lS meamngful for the purpose of this analysis to define certain crack lengths for quantifying the basic safety against pipe rupture' (a) The crack length 2ll is the maximum dimension of an undetected or tolerated crack, i.e., a crack remaining in the material after manufacture of the pipe (initial crack), (b) the quantity 212 is the length of a penetrating crack which can definitely be detected during operation, e.g. by leakage measurement; (c) the quantity 2l 3 is the length of a critical penetrating crack, wluch, in case of minute elongation or load increment, results in pipe rupture by unstable propagation.

@

.

/

10 -6 10 2

.

.

.

I

i ~

J 8

i 10 3

~K [N/ram

3/2]

Fig. 1. Comparison between experimentally determined crack propagation rates and ASME limiting curve A pipe rupture can be excluded, if the condition ll <~12 < 13 is proved to be satisfied (Crack length crlterlum). In addition to the quantitative determination of the three crack lengths l 1/l 2/l 3 a n analysis of the propagation of the initial crack (2ll) as a result of cyclic operating load changes is carried out. This analysis will permit to state whether in the course of plant life the initial crack must be expected to grow to the length of the detectable crack (212). If this is not the case, this statement represents a further safeguard against pipe rupture in addition to the crack length crlterium defined above. If a growth Ofll to l 2 must be expected, the analysis of the fatigue crack propagation will be of special importance with regard to the definition of the intervals of inspections for crack detection (21:) and of the safety margin between 12 and l 3.

4. Manufacturing defects (2/1) A high quality standard is the basic condition for reducing defects occuring in the course of manufac-

H D Schulze, G Togler, E. Bodmann /Fracture mechamcs analysts in ptpes

21

Fig 2. Fatigue crack propagation in the basic material due to alternate bending (circumferential crack). Fig. 2a. lnltml crack dxmenslons(2l × a) 50 mm × 1 mm 30 mm× 1 mm 10 m m × 1 mm. Fig. 2b. Enlargement, mltml crack dimensions 10 mm × 1 mm

ture. Part of the measures ensunng a high quality standard is proved by the technical control and acceptance specifications clalrmng one or several of the following tests for the piping of the fuel circulating system. Ultrasonic tests for longitudinal and transversal cracks in base material and weld seams. Magnetographic tests on finned tubes. Metal-L-check and magnetic particle inspection on pipe bends.

- X-ray tests of finned pipes and seam welds. Gas pressure test and leak tightness test. According to the specifications the cracks remainmg in the piping after manufacture are between 0.2 mm and 1 ram. It must, however, be assumed with a certain probabihty that cracks will remain which are larger than those specified. In a conservative assessment of a maximum remaining crack length a length of 2ll = 10 mm is postulated for further analyses. An assump-

22

H D Schulze, G Togler, E Bodmann /Fracture mechamcs attalysts zn ptpes

tlon on the length of the crack only and not on the depth of the crack IS required, because the length only is of importance to the unstable pipe failure.

leakage rates was carried out by experiments on pipes with fatigue cracks. The results of these experiments cannot be quoted in detail in this context. Two typical results from these experiments are shown below.

5. Detectable cracks (212)

Crack length 21 (mm)

Crack detection in the refuelling system is based on helium loss measurement. For this purpose the correlation between load, crack length, cross-sectional area of the crack, and escaping helium leakage rate must be known. In a first calculation the crack width 2b and the cross-sectional area of the crack A were determined on the basis of the classical hnear fracture mechanics considerations of a crack of 2l in an infinite disk to be 2o'I b-

E

2no*l 2 A-

,

E

where o* IS the circumferential or longitudinal stress in the pipe due to operating load. Since purely elastic deformations are being deternuned in this analysis, it must be assumed and is confirmed by experiments that the effective cross-sectional area of the crack is considerably larger due to additional plastic deformation (fig. 3). Thus the values b and A determined by the formulas quoted above, must be considered as lower hmlts. A separate investigation for determining realistic

Leakage rate :n (kg/s)

30

2 5 X 10 - 2

50

4 0 X 10 - 2

Such leakage rates may be detected wnhout difficulty. The computational prediction provides leakage rates lower by a factor of about 100.

6. Critical crack length (213) Investigations were carried out on the following types of pipes (outside diameter × wall thickness) normal pipe 76.1 mm × 3.6 mm (without fins), 4-fin pipe 75 r a m × 4 mm, 24-fin pipe 75 mm × 4 mm. The choice of these test specimens ensured that the influence of different pipe geometries is taken into account and due to the similar dimensions, the test results will be comparable. The cheinlcal composition determined for the test material and the mechanics parameters are given In table 1. 6 1 Theoretical approach on longitudmal cracks

L

_pjpe bends x normal pipe e n o r m a l ptpe at 2 2 0 °C stro~ht ~jp_e C n o r m a l pipe w i t h t o r s i o n u 4 - f m pipe 04-fro p o e w i t h torsion ~ l L - f i n pipe ot 200°C zx 2/*-fm pipe b ~ 2t,-hn pipe with torston ~00 .

~ o - ' ~ ~ _ ~ _ 1 10 -3

/f

~

~ / ~

1. . 10 -2

.

.

.

.

.

. . 10 I

leak(age cross section oreo/Inner

.

' .

.

.

.

.

.

.

.

.

The results of comprehensive Investigations on the behavlour of pipes with longitudinal cracks subject to internal pressure are available [1], [2]. Most of the investigations were carried out on pipes for long-distant piping systems with diameters above 150 mm. Very little experimental data IS available for pipes with diameters below 150 mm [3]. The common characteristics of all tests carried out on components up to now (a total of more than 200) is the following simple theoretic relation describing the cracking behaviour [4]. The ultimate load IS characterized by the relation

plpe cross sechon oreo

Fig. 3. Interrelation between crack length and leak cross section area (the continuous hne representing the theoretical curve according to [8,9].

o = zr/m.

The Fohas factor m for longitudinal penetrating

(3)

H.D Schulze, G Togler, E. Bodmann / Fracture mechanics analysts in ptpes

23

Table 1 Materml parameters (0 Chenucal composition in weight %

C

S~

Mn

P

S

Mo

Measured values

0.16

0.25

0.69

0.011

0.022

0.31

Values according to DIN 17175

0.120.20

0.150.35

0.50.8

0.04 max.

0.04 max.

0.250 35

(a) Mechanical parameters a Temperature °C

Yield strength N/mm 2

Tensile strength N/mm 2 490 (450-550)

Ultimate elongation m%

Impact b energy J/cm 2

29.7 (22.0)

133

20

335 (290)

100

305

454

29

133

200

293 (260)

534

23 2

134

260

275 (240)

522

12.2

125

a Mean value from 5 specimen. Values In parenthesis represent the guarantee values according to DIN 17 175. b Mean value from 12 specimen.

cracks is I m =

12 /4 ]1/2 1 + 1.255 R--t-- 0.0135 . R 2 t 2 ] .

(4)

For surface cracks, m in eq. (3) must be replaced by rap, where mp is given by mp -

1 - a/tm 1 -- a / t "

(5)

The yield strength g s h o u l d be taken to mean the kink m the stress-strain &agram assuming ideal elasto-plactxc behavlour of the material. Eq. (3) results from a hmit consideration o f the general theoretical approach m [5] ; it is valid for a tough rupture behavlour o f the material. The eqs. (3), (4) and (5) primarily make a statement on the critical load which will increase a surface crack or a penetrating crack already existing m the material. They are, however, also a basis for derwmg a cnterium for the formation of a leak or rupture from surface cracks. Ttus c n t e n u m Is based on the theory that in exceeding the ultimate load determined by eqs. (3), (4) and (5), first the ligament consisting o f

the remaining wall thickness, will fracture, thus turning the surface crack into a penetrating crack o f equal length 2/; if the ultimate load of the surface crack is higher than that of the penetrating crack o f equal length, rupture will arise due to a load greater than critical load on the newly formed penetrating crack. If the ultimate load ts smaller, a subcrltlcal penetrating crack will be formed, i.e., a leak. Hence, the l e a k - r u p t u r e criterlum may be derived equatmg the ultimate loads o f a surface crack and a penetrating crack: a = film = ~/mp.

This means m = rap.

(6)

This relation may be represented as a curve m the crack depth/crack length diagram, which divides the total of the aft combinations into a leak area and a rupture area (cf. e.g. fig. 5). It should be emphasised in this context that relation (6) provades a statement on the formation of leaks during gradual pressure increase. Thus it is only o f interest to the evaluation

24

H D. Schulze, G. Togler, E. Bodmann / Fracture mechamcs analysts m ptpes

of a piping system, if the failure pressures are in the range of the possible operating pressures. Leak formation due to cyclic load changes, which must also be taken into account, follows different inter-relationships, as discussed in section 7. The tests described below carried out on pipes with longitudinal cracks, were for the following purposes: - Determination of the crltlCal crack lengths 213 as a function of the internal pressure. Determination of the influence of addmonal loads such as bending and torsional moments. Determination of the influence of temperature in the range between 20°C and 260°C on the fmlure behavaour. - Venficatmn of the validity of the relatmns (3)-(6).

6.2. Tests on longitudinal cracks zn straight pipes

The tests were carried out on all types of pipes, Le., normal pipes, 4-fin pipes and 24-fin pipes. A water-gas-mixture was apphed as pressurizing medium. The pressure was increased up to the point of pipe rupture. On four tubes, a torsional moment of 3 kNm was apphed in addmon to the internal pressure. Tests were carried out on pipes w~th cracks penetrating the wall and with surface cracks. Penetratmg cracks were sealed by a tubular liner in the pape with a reinforcement In the crack area. The crack length 2l varied between 17 mm and 125 mm. Table 2 gives a survey of all results obtained from the tests on the three types of pipes. An ultimate stress-crack-length diagram in fig. 4 shows a plot of the results. This diagram gwes also the theoretically determined failure curves for cracks completely penetratmg the wall and for surface cracks having a depth of 80% of the wall thickness, based on a yield strength of 650 N/mm 2. The experimental results are in very good agreement with the theoretical predictions. In the diagram the primary membrane stress resulting from Increased pressure under emergency conditions is also plotted. As can be seen, the critical crack length 213 is greater than 200 mm. This can be seen also in fig. 5, which gives a comparison between the experimental results with respect to the type o f failure (leakage or rupture) and the theory. Here we have

also a good agreement between experiment and theor)' The results on the mechanical behavlour ot straxght pipes wath longitudinal cracks can be summarized as follows - The experimental results correlate well with the theoretical predictions. - In the case of a torsional moment of 3 kNm applied in addition to the internal pressure, an influence on the mechamcal behaviour cannot be established, the same apphes to the Influence of temperature. - The critical crack length 213 is greater than 200 mm. 6. 3. Tests on longitudinal cracks m pipe betuds

For the investigation of the mechamcal behavlour of detbctwe pipe bends the following pipe geometries were selected: - 24-fin pipe / radms of curvature 220 mm/angle 180 ° - normal pipe / radms o f curvature 95 mm/angle 90 °. Tests were camed out with penetrating cracks and surface cracks. The cracks were located in the outer fibre of the bend m longitudinal direction The pipe bends were subject to an internal pressure employing water or gas as pressurizing media. The pressure was increased until failure in the pipe bend occured. In the case o f three pipe bends a constant bending moment of 3 kNm was applied in addltaon to internal pressure. In addition to the tests at 20°C, further tests were carried out at 220°C and 240°C. A total of 16 tests were carried out; the crack lengths under investigation were between 20 mm and 140 ram. Table 3 gives a complete survey of the test results. In addition to crack dimensions and pressure, at which failure occurred, the table indicates the type of fadure (rupture or leakage) and, m case of leakage, also the leak cross-sectional area related to the Inner pipe cross-sectional area. Fig. 6 shows a plotting of the test results. The failure lines for penetrating cracks and surface cracks to a depth of 85% of the wall thickness were calculated using eq. (3) with a yield strength o f 614 N/mm 2. There is a good agreement between experimental results and theory, here as well as in the following fig. 7. This figure shows a comparison of the experimental results for the different types of failure (rup-

H.D Schulze, G. Togler, E. Bodmann / Fracture mechanics analysis m pipes

25

Table 2 Test results on straight pipes with longitudinal cracks Specimen no.

Type of pipe

Wall thickness (mm)

Crack size length (mm)

depth (mm)

Crack length after test (mm)

Pressure (bar)

Type of failure

Cross section

Faalure of seal Pipe 1.4 crack welded, 100 m/s rupture speed

normal pipe

3.2

17

3.2

-

343

(1.4)

normal pipe

3.2

17

17

118

380

rupture

20

1.3 1.2 1.1

normal pipe normal pipe normal pipe

3.3 3.4 3.2

50 100 200

3.3 3.4 3.2

165 250 205

252 122 61

rupture rupture -

20 20 20

2.4 2.3 2 2 2.1

normal normal normal normal

3.8 3.2 3.4 3.45

17 45 65 115

32 2.4 2.8 2.6

14 a 36 a 65 115

353 196 173 153

leakage leakage leakage leakage

20 20 20 20

0.0013 0.012 0.075 0 165

3.1 3.2 3.3 3.4

normal pipe normal pipe 4 - f i n pipe 2 4 - fin pipe

3.4 3.4 3.8 4.0

115 65 65 65

2.3 2.6 3.1 3.1

115 65 65 65

157 194 203 236

leakage leakage leakage leakage

20 20 20 20

018 0.075 0.035 0.066

4 3 42 4.3 5.3 5.2 5.1

4 - f i n pipe 4 - f r o pipe 4 - f i n pipe 2 4 - f i n pipe 2 4 - f i n pipe

4.0 3.9 3.9 4 4 4

45 65 115 45 65 115

3.1 31 3.1 3.1 3.4 3.4

32 65 115 36 55 110

a a a

261 207 157 260 189 175

leakage leakage leakage leakage leakage leakage

20 20 20 20 20 20

003 0.06 0.1 0.02 0.03 0.09

6.2 6.1

4-fro pipe 4-f'm pipe

3.8 3.9

80 125

3.0 2.9

76 a 115 a

163 141

leakage leakage

200 200

0.09 0.13

a

Comments

area normalazed

1.4

pipe pipe pipe pipe

-

Test temp. (°C)

20

Failure of seal before reachmg rupture pressure

Test with superimposed torsional moments T = 3000 Nm

Test w~th superheated water as pressure medium AUtests were carried out with a watergas mixture

a The penetrating crack m the notch root did not reach the full length of the machined notch.

ture or leakage) w i t h t h e t h e o r e t i c a l s t a t e m e n t s m a d i a g r a m o f n o r m a l i z e d crack l e n g t h s against n o r m a l lzed c r a c k d e p t h . T h e d i f f e r e n t failure b e h a v i o u r m case o f r u p t u r e a n d leakage, respectively, is clearly s h o w n in t h e p h o t o g r a p h s o f test s p e c i m e n s in fig. 8. As can b e seen f r o m t h e figs. 6 a n d 7, t h e c n t i c a l c r a c k l e n g t h 213 for pipe b e n d s , t a k i n g i n t o considera-

t i o n t h e stress in case o f a n a c c i d e n t , is g r e a t e r t h a n 2 0 0 m m . This is close to t h e value for defective straight pipes. T h e results f r o m t h e tests o n t h e crack b e h a v a o u r o f defective pipe b e n d s m a y b e s u m m a r i z e d as follows: - The m e c h a n i c a l b e h a v i o u r o f defective pipe b e n d s c a n b e d e s c r i b e d b y t h e r e l a t i o n given in eq. (3), if

H.D Schulze, G. Togler, E Bodmann / Fracture mechantcs analysts m tripes

26

normal pipe

o penetrating crock e surface crack 4~ surface crock with superimposed torsional momentof 3KNm 4- fin PJIZe_~

stress

iN/mm2]

700

rupture leakage

crock depth / wcdl thickness

Ic~akooe

failure curve for

' oi. . . . . .

~

,

~

.....

~

surface crack

-~-surface crack with torsional moment 3KNm ~ surface crack at 200°C 24- fin p_lpe & surface crock ~- surface crock,superimposed

600 \

/\ 500

~I\

400

/~k \e\

crY,ok penetrating the wail ~ors~onal m o m e n t ,\ \ N o at crack depth/wall thickness

08-

r4pture

0 04

\- ~

300 200

rface crock ~

100 ~- = 0,8 accident pressure. . . . . . . . . . .

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

20

4'0

6'0

8b

11~'0 1:~0 1/~0

(o)

tim]

160 11~02docrack length 21

02

20

Z,O

I

2

60

80 3

100 crack length[ram} t,

5

I

Fig 7 Longitudinal c r a c k s i n pipe lends comparison between theory and experiment on the formation of leak or rupture

Ftg. 4. Longitudinal cracks In stralght pipes, comparison between theory and experiment on failure stress.

• fadure due to leakage o fodure due to rupture crack depth / wall thlckrless 0.8

e

failure curve for occident pressure

°

e

~

t

leakage

u

r

e

0,5

crack position and pipe geometry are taken rata consideration m determining the effective stresses Ttus also apphes to the type of failure (leakage or rupture). - Any influence of an addlUonat bending moment of 3 kNm on the mechanical behavlour cannot be established. Neither does the temperature exert an influence m the range examined m the tests. - The critical crack length 213 is greater than 200 ram.

0.4. 0,2

I

,2 2'0

4'0

? 6'0

÷ 8'0

5

,6

,7

160 120 1/~0

~,

If)0

~vE

180 200crack length 21 [mm]

Fig. 5. Longitudinal cracks in straight pipes: comparxson between theory and experiment on the formation of leak or rupture.

2L,-hn_P.tpe bends o penetrohng the wall -o-penetrahng the wail.superimposed bendmg moment 3KNm , Ifodure of seal

stress

INlmm~

surface crack

600

normal ~tpe_ bends

500

il surface crack ~. s urface crack,increased test

\ \

400

temperotur

~ol

300200 '

100

~crack depth/wall thickness t

~ i@'crack / penetrohnge / ~ the wall

~ =0,85 .

.

.

.

20

a acc~dent pressure-~- . . . . . . . . . . . . . . .

.

4'0

{50

80

160 120 1/,0

160 180 crack Ler~gthtim]

Fig. 6. Longitudinal cracks in pipe bends: comparison between theory and experiment on failure stress.

6. 4. Theoretical approach on the determmatton oJ the ctrcumferennal cracks

In contrast to the mechamcal behavlour of pipes with longitudinal cracks there are no simple methods avadable in literature for a theoretical descnpuon of the mechamcal behawour o f ptpes having ctrcumferentlal cracks. Hence, m the following an approach will be gwen for an analytical descripUon of the fadure behaviour of pipes subject to internal pressure and bending moments. The geometry of surface cracks and penetrating cracks is defined by the values ~0c or ~0c and ts, respectively (cf. fig. 9). The test results suggest that surface cracks and penetrating cracks become unstable, when the remaining cross secUon becomes fully.plastic. Assummg the material is 1deal elasto-plastic, the critical load of the remaining cross section is determined by taking rata account that the longitudinal force from the pressure acting in the pipe axis creates an additional bending moment with reference to the neutral axas of the residual cross section. In a simplification the neutral

2.2 2.1 1.2 1.1

3.6 3.5

1.3.1 1.3.2

normal pipe rad. o f curva- < 3.3 ture. 95 m m 3.5 3.6 3.5

"3.6

1.3

20 50 103

4 4 4

69 115 70 113

36 39

36

25 65 110

51 100

20

length (mm)

C r a c k s~ze

4 4

"4 4

Wall tluckness (mm)

4 4 4

2 4 - f i n pipe rad. of curvature: 220 m m

Type o f pipe

4.3 4.2 4.3

4.4

Specimen no.

Table 3 Test results on pipe bends with longitudinal cracks

3.0 3.0 3.0 3.0

3.2 3.0

3.2

2.6 3.0 3.2

4 4 4

4 4

4

depth (mm)

24 105 60 102

27 29

117 165 150

140 165

145 160

Crack size after test (mm)

gas gas gas gas

water water

gas

water water water

water water water

water water

water water

Pressure medmm

82 67 115 75

239 216

140

455 256 186

468 294 165

265 168

480 580

Pressure (bar)

leakage leakage leakage leakage

leakage leakage

leakage

rupture rupture rupture

rupture rupture

rupture rupture

Type of failure

20 20 250 220

20 20

260

20 20 20

20 20 20

20 20

20 20

area

(°c)

0.008 0.06 0.05 0.09

0.001 ) 0.005

normahzed

Leakage cross section

Test of temp.

leakage cross section area n o r m a h z e d to inner pipe cross section area

(speclm f r o m pipe 1 3)

no failure

Failure of seal additional bending m o m e n t of 3 k N m

Failure of seal pipe 4.4 w t h welded crack

Comments

e~

H D Schulze, G Togler, E Bodmann / Fracture mechamcs analysts m pipes

28

ts

fiber penetrating

surface

crack

c' ,:,:~

loads acting on cross section c o n ta{nlng the crack

a }'0 c m

general d l s t n b u h o n of Iongdudmat stresses

Fig. 9 D e f i m t l o n of s y m b o l s for a c t r c u m f e r e n t m l c r a c k

lated from a consideration of equdlbrlum surface crack = --

~On 4 g R t

+-1~0

2 c

Rt O

+ lrr

(7)

'

penetrating crack

~°n

F

SOc+rr

= --+---4~Rt

2

(8)

'

where F = ¼rr(2R - 02 " p ,

b

Fig. 8. Crack pattern xn pipe bends. Fig. 8a. Rupture of 24-fro pipe bends originating from surface cracks, pressure medmm water. Fig. 8b. Leak m normal pipe bends, pressure medium gas.

whmh Is the longitudinal force resulting from the internal pressure. The ultimate moments M of the remaining cross section will then be surface crack M = 2o~R2t(2 sm ~On- s m ~Oc)+ 2~R2sts sm ~Oc •

(9)

penetrating crack M = 2~-R2t(2 sin ~0n - sin ~0c) •

(10)

6.5. Tests o n c i r c u m f e r e n t i a l cracks

hne is replaced by two radial lines cutting the pipe axis, which are inclined to the vertical by an angle of ~0n. Above these lines there are tensile stresses in the surroundings of the crack of the magnitude of ~, below the lines there are pressure stresses of this magnitude. The angular p o m i o n of the neutral fiber ts calcu-

The investigations on the behavmur of pipes with circumferential cracks in the joint welds were camed out on 4-fin pipes only. The invesUgatlons were carned out on pipes with penetrating cracks and surface cracks with various cracks lengths of artificially applied cracks and fatigue cracks between 15 mm and 135 mm.

H D Schulze, G. Togler. E Bodmann /Fracture mechamcs analysts ,n ptpes

29

Table 4 Tests on pipes wath ctrcumferential surface cracks, crack depth 75% of wall thickness, test temperature equal to room temperature, pressure. 46 bar Mean crack length

Bending moments

(degrees)

(m,-n)

Me

MI (kNm)

15 21 33

10 13 20

7 7

77 8.8

33 33 40 40 40 40 40 40 60 60 90 113 165 214

20 20 25 25 25 25 25 25 38 38 56 71 108 134

7 6.9 76 74 7.3 69 7.6 7.4 6.7 7.0 6.0 6.1 78 53

8.5 84 8.6 8.6 8 1 82 85a 85a 7.4 7.9 6.2 6.7 7.8 5.3

Comments Mm

10.6 9.2 9.4 8.7 9 1 8.6 8.7 7.5 8.0 6.2 6 7 78 5.3

1100°C/6h/water Deflection stopped at leakage Leak area 5 mm 2

Pressure 0 bar Pressure 100 bar lhpes heated to 900°C and quenched m ice water

(5 7) b

(5.0) (4.3) 1100°C/6h/water ( 1.9)

M e Bending moment at the end of elastic range. M 1 . Bending moment at leakage. Mm: Maximum tolerable bendmg moment. a After exceeding M m. b In the event of leakage spontaneous crack opening occurs. Bending.moment is reduced to the values quoted in parentheses.

Table 5 Tests on pipes with circumferential penetrating cracks, test temperature equal to room temperature, pressure: 46 bar Mean crack length (degrees)

(mm)

0

0

20 38 41 63

12.5 24 26 40

71 72 96 151

Crack shape

45 45 60 95

Bending moments (kNm) Me Mm

Rectangular notch w~dth 0.8 mm

Fatigue crack

7.3

11.0

7.0 7.7 7.7 6.3

9.1 9.2 9.3 7.5

6.1 6.0 4.6 3.3

6.9 6.6 5.7 3.8

T h e pipes were subject t o a d e f o r m a t i o n - c o n t r o l l e d b e n d i n g l o a d to failure. A n i n t e r n a l pressure o f 4 6 bar was generally a p p h e d . Tests, h o w e v e r , were carried o u t w i t h o u t a n y i n t e r n a l pressure as well as at a pressure o f 100 bar. Tables 4 a n d 5 gwe a survey o f all test results. The results are p l o t t e d in fig. 10. This d i a g r a m c o n t a i n s t h e t h e o r e t i c a l failure curves d e t e r m i n e d a c c o r d i n g t o eqs. (8) a n d (9), giving a g o o d c o r r e l a t i o n w i t h t h e e x p e r i m e n t a l results. T h e c a l c u l a t i o n was carried o u t b a s e d o n a yield s t r e n g t h o f 5 0 0 N / m m 2. In a d d i t i o n , t h e figure s h o w s t h e m a x a m u m b e n d m g m o m e n t m t h e p i p i n g s y s t e m due t o e x t e r n a l loads i n c l u d i n g e a r t h q u a k e effects. T h i s results in a critical c r a c k l e n g t h 213 o f 110 m m , w h i c h corres p o n d s t o h a l f t h e pipe c i r c u m f e r e n c e . T h e test results m a y b e s u m m a r i z e d in t h e following s t a t e m e n t s :

30

H D Schulze, G. Togler, E Bodmann

I Z 1| ulhmafe bending moment o [10~Nm]

\ 8

x

1%

A "~.,o\\

a

O\\~\" \\ 6

2

penetrating crack -

\

×

~

o

x

"\\

\/

surface crack a '

".

~-:0,75

o penetrohng crack -x surface crack \ ~, z~ surface crack, heat treat ~ max "~ ment 1100 ° C / 6 h / w a t e r loading m o - ~ a surface crack, heat treatment ment g 0 0 ° C / w a t e r • surface crock, pressure 0 bar

/Fracture m~chantcs

attalysts m ptl)e~

ASME-Code section X1 ( da/dN over AA) r epresent~ ,~ conservatwe description of the experlmentai result,~ (cf. fig 1 ) Computational as well as expermlental lnvestiganons have shown that a ~ignIficant propaganon of the initial cracks (2li) due lo the operating load fluctnatmns must not be expected Further attention was directed to the character at fatigue crack propagation It could be demonstrated that surface cracks - which are the only type o~" cracks which may remain m the pipes after mmal pressure test preferably tend t~) propagate mtu the depth o f the material. Fig 2 shows the fatigue crack propaganon a o also on the example of a crack of 10 mm length (corresponding to 2ll). The result is m good agreement with other lnvestlganons [6], [7]

8. E v a l u a t i o n o f r e s u l t s

20 20 do 8o

40 40

crack length --~angle 2 ~°c [el Fig. 10. Circumferential crack, compaxlson between t h e o r y

and experiment on ultimate bending moment.

The test results correlate well with the theoretical methods. - An influence o f pressure m the range up to 100 bar investigated has not been established. - The mechanical behaviour is not influenced by the geometry of the crack (fatigue crack or machined crack, notch of 0.8 mm width). - The critical crack length 213 is 110 mm thus corresponding to half the pipe circumference. -

7. F a t i g u e c r a c k p r o p a g a t i o n

Computational and experimental analyses were carried out on the problem of crack propagation due to fatigue. Pipes contaimng deliberately induced circumferential cracks o f different lengths were exposed to a pulsating load by a bending moment of 5 kNm - which is a pessimistic value compared to operating loads. Crack propagatmn was measured. The computatxonal verification of the experiments has shown that the limiting curve for crack propaganon gwen in

The concept for a quantitative evaluation of pipe rupture risk in piping systems compnses a comparison of the initial cracks present in the material after manufacture with the detectable cracks during operation, as well as a comparison of the detectable cracks with the critical cracks resulting in unstable failure. In this testing program these three crack values were analysed for the piping system of the THTR fuel circulating system. It has been shown, that, due to the quahty control measures used, the cracks remamlng after manufacture are considerably smaller than those detectable with confidence by hehum leakage. It was further shown that considering the mechanisms of damage in the fuel circulating system, crack propagation can occur only to a very lirmted extent. The greater part of the investigation was dtrected to the experimental determination of the crltxcal crack length. In this context the different crack positions, pipe geometnes and types of stress as well as the comparison with the theoretical methods were the essential items of investigation. The tests carried out under conditions specific to the fuel circulating system have shown that the distances between cracks arising dunng manufacture or cracks occurring during operation are sufficiently large compared to the critical crack dimensions even m the event of a reactor incident.

H D Schulze, G Togler. E Bodmann / Fracture mechantcs analysts m ptpes

Hence the installation o f pipe whip restraints will not be necessary for the plplng o f the fuel circulating system.

E Kc zSK N

= = = =

31

Youngs modulus Fracture toughness Range o f stress intensity factor N u m b e r o f load cycles

Nomenclature R = Mean pipe radius R s = Mean radms o f the remaining wall (circumferential crack) t = Pipe wall thickness ts = Remaining wall thickness (circumferential crack) l = Half crack length a = Crack d e p t h b = Half crack width A = Crack cross section area m = Fohas-factor for penetrating longitudinal crack mp = Fohas-factor for surface longitudinal crack ¢c = Angle o f circumferential crack Cn = Angular position o f neutral fiber o = Circumferential stress in non-&sturbed-plpe at failure O- = Yield strength p = Pressure F = Pipe longitudinal force f r o m pressure M = Critical m o m e n t o f the residual cross section (circumferential crack)

References [1] W.A. Maxey, J F. Klefner, R.J. Elber and A.R. Duffy, IGU/C 34-73, 12th World Gas Conference, Nice, 1973. [2] M.B. Reynolds, Quartely Progress 20, GEAP-11069 (1970). [3] K. Welhnger and D. Sturm, Fortschr Bencht VDI-Z Relhe 5, Nr 13 (1971). [4] B.A. Bllby, A.H Cottrell, F R.S and K H. Swmden, Proc. Roy Soc.,A272(1963) 304 314 [5] W.A. Maxey, Conf Proceedings American Gas Association, Texas, 1974. [6] R.H. Bryan, J G. Merkle, M.N Raftenberg, G.C. Robinson, J.E. Smith, ORNL-5059, NRC-1, NRC-5 (1975) [7] Combustion Engineering, CENPD-168, Revision 1, (1976). [8] D J. Ayres, Session 1~7-1, SM1RT-4, San Francxsco, 1977. [9] E Theuer and D J Ayres, Session F7-7, SM1RT-4, San Francisco, 1977 [10] R.J Elbert et al, Task 17, Final Report BMI 1908 (1971)