1-s2.0-0308016186900670-main

Int. J. Pres. Ves. & Piping 26 (1986) 197-211

A New General Approach for the Fracture of Pressurized Components with an Oblique Flaw and its

Experimental Verification

Li Shijie and Hung Xiaosheng

PWR Research Institute, Department of Applied Mechanics, Southwest Reactor Engineering Research and Design Centre, PO Box 291, Chengdu, Sichuan, People's Republic of China

(Received i May 1986; accepted 14 May 1986)

A BSTRA CT

A key element in the safe use offlawed components is that of developing an accurate method for predicting failure under operational conditions. In this paper a new general approach to the fracture of pressurized components with an oblique flaw is proposed. It can be used for predicting the failure load under operating conditions of a component containing surfaee flaws and/or through-wall oblique flaws, the relevant component being made of ductile structural steel. Experiments on eight pressure vessel models with an oblique through-wall flaw and four with an oblique surface flaw have been performed to support this approach.

The approach proposed is in good agreement not only with the results of the experiments mentioned above but also with tests made at other research units in China. For the specific case of a flaw located in the axial direction, it has been supported by many tests in China and other countries.

INTRODUCTION

In fields such as nuclear power, chemical engineering, boilermaking and shipbuilding, flaws are often found in pressurized components during in-service inspection. Thus, a particular question related to the flaw is whether anything must be done about it immediately or whether

197 Int. J. Pres. Ves. & Piping (26) (1986)-- Elsevier Applied Science Publishers Ltd, England, 1986. Printed in Great Britain

198 Li Shijie, Hung Xiaosheng

it is possible to wait for an occasion when the impact on plant availability is minimal, e.g. until the next refuelling outage. In order to solve such questions, the engineer needs to have at his command some assessment approaches on the size and shape of flaws to determine whether an observed flaw will give rise to failure, and the time required for it to reach the allowable size limit. An attempt is made in this paper to give the engineer a new approach to the assessment of the failure of flawed components by a plastic fracture mechanism under normal operating conditions.

In the course of the last 20 years, very considerable interest has developed in China and other countries in research into the failure of pressurized components with longitudinal and/or circumferential flaws. A vast amount of work concerned with such flaws has been done. 1 -5 But flaws do not always lie exactly in the longitudinal or in the circumferential direction of pressurized components. Many have been found in practice to incline to those axes. To make more simple the application in practice, a relatively straightforward and simple analysis coupled with tests is available to establish the failure law of pressurized components with an oblique flaw. On this basis, we have carried out a considerable variety of theoretical explorations, so that in the end we acquired a new general approach.

In order to verify it, two series of experiments on pressure vessel models with an oblique flaw have been completed and in addition use has been made of test data from the General Machinery Institute and Taiyuan Heavy Machinery Institute in China. 6

BRIEF DESCRIPTION OF EXPERIMENTS

From the viewpoint of engineering mechanics, the same method can be used to analyze the stress in both a cylindrical pressure vessel and a pipe. Because of this, we chose two materials in the form of tubes to be available for our test. The programme contained 12 pressure vessel models in two series, each model approximately 700 mm long. Seven of these tubes were made of ICrl8Ni9Ti stainless steel and five of SUS321TP. The former were divided into two types: five models with an oblique through-wall flaw and the other two with an oblique surface flaw. The five SUS321TP models were also divided into two types: three with an oblique through-wall flaw and two with an oblique surface flaw

Fracture of pressurized components with oblique flaw

TABLE 1 Material Properties and Flaw Types

199

Material Yield Ultimate Oblique flaw type No. of strength strength models (MPa) (MPa)

1Crl8Ni9Ti 224.3 658.2 Through-wall 5 Surface 2

SUS321TP 207.7 618.6 Through-wall 3 Surface 2

(see Tab le 1). All the flaws were located at the mid- length posit ion o f the model . The characterist ic d imensions of the 12 models and their flaws are listed in Table 2.

In relat ion to the preparat ion process of the obl ique flaw in each of the pressure vessel models, the main length of obl ique through-wal l flaw was milled with a mil l -cutter 0-3 mm thick and 40mm in diameter; in addit ion, both crack-t ips (approx imate ly 2mm long) were prepared using a 0.1 mm thick steel-saw; the surface flaws were all prepared by mill ing with the same mil l -cutter as ment ioned above.

TABLE 2 Comparison of Predicted and Experimentally Determined Circumferential Stress cr0~ for

Pressure Vessel Models with an Oblique Flaw (headings explained under equations (1) and (3))

exp cal Test on model i [~ t i Ri S Croi ~ro~ (i= 1 . . . . . 12) (deg) (mm) (ram) (mm 2) (MPa) (MPa)

cs8-01 15'00 6"35 36"83 209.3 312.8 283.3 cs8~)2 47-00 6" 10 36.95 233. I 356'4 383"7 cs8-O3 0"00 6"60 36'70 224"4 261 "7 261-1 cs8~)4 42"00 6"25 36.88 404.0 231.4 235'3 cs8~)5 62.00 6.20 36"90 342"5 315'2 357" 1 cs8q)6 42"50 7"60 75.70 561 "7 273.5 288.6 cs8~)7 51.00 7.50 75.75 676.4 262.5 268.0 cs8~)8 30"00 8"15 75.18 838.0 171.9 188.0 cs8~9 ~ 30.00 6.50 36.75 162.0 443.6 415.7 cs8-10 ~ 47.50 6"00 37.00 126.6 538.2 581.7 cs8-11 a 50"00 7"60 75.45 441-7 350.5 389"5 cs8-12" 41'00 7"85 75.33 399.6 320.0 381'0

a Oblique surface-flawed models.


In order to prepare the sharpness of the flaw tips, both for the through-wall flaw and at the front for the surface flaw, so that they were more similar to the practical cases produced in components under operational conditions, models 04, 05, 11 and 12 were not subjected to low-cycle fatigue cycles until the onset of their initial flaws.

A leak-proof device made of 0"2mm thick stainless steel plate and 3 mm thick rubber was used to cover the internal surface of the model at the position of the through-wall flaw, so as to prevent leakage of the liquid pressurization medium from the model with an oblique through- wall flaw under experimental conditions.

The experiments on all the pressure vessel models were carried out with the High Pressure Cycle-Fatigue Device, shown in Fig. 1. The device did not pump machine oil into those filled with water until failure. One of the models after test is shown in Fig. 2.

After the completion of the bursting experiment on all models, the tested objects were photographed, and the deformations of the models

q

Fig. 1. High Pressure Cycle-Fatigue Device. Fig. 2. Fracture area of model.

Fracture of pressurized components with oblique flaw 201

TABLE 3 Measurements of Surface Dimensions of an

Oblique Flaw

((mm) fl(O (ram) f2(~) (mm)

13.80 14.34 14.34 14.30 14.84 13.27 14-80 15.16 12.05 15-30 15.45 10.43 15.80 15.77 9.73 16.34 15.98 9.12 21.00 17.41 10.53 26.00 17.84 11.07 31.00 18.18 11-48 36.00 18.48 ! 1.74 41.00 18.75 11.99 46-00 18.86 12.09 49.38 18.68 12.27 50.13 18.59 12.34 50.33 18.55 16.87 50.53 18.45 17.67 50.72 18.57 18-37

and the sizes of the fractured areas were measured. The fracture area was machined out from the failure region at which the artificial flaw was located, and the surface dimensions of the flaw were measured with a tooling microscope; an example of such measured results is shown in Table 3. Finally, the flaw was studied under the Scanning Electron Microscope.

The results of fractography showed that fracture consisted mainly of the following three parts (see Fig. 3): (a) fatigue-streak, (b) a dimple structure, and (c) a quasi-cleavage structure. The fatigue-streak proves that the fatigue parts of both tips for oblique through-wall flaws and

Fig. 3.

b

Enlargements from fracture surface (original magnification x 4000): (a) fatigue- streak; (b) dimple structure; (c) quasi-cleavage structure.


of the flaw fronts for oblique surface flaws were produced before the bursting of the model. The dimple structure shows that stable crack growth set in more or less before failure. Lastly, the quasi-cleavage structure is typical of unstable crack growth.

In order to obtain the engineering strength indices of the materials in the form of tubes, a standard tension specimen with cross-section in the form of a circular arc was prepared according to the relevant Chinese standard, as Fig. 4 shows. Six specimen pieces of 1Crl8Ni9Ti and six

Fig. 4. Standard tension specimen.

of SUS321TP in the form of tubes were prepared and tensioned with the Type IS-10T test machine under room temperature conditions. The average values of their engineering strength indices are shown in Table 1.

NEW GENERAL APPROACH

By test observations and metallography of fracture planes, we concluded that there occurred first a crack initiation, then a slow stable crack growth and finally a fast unstable crack propagation in cracked components made of ductile structural steel with work-hardening under internal pressure load-controlled conditions; and that these conditions were completely controlled by the overall plastic behaviour in a crack region. The plastic response of the crack region to applied loads must be related to the characteristic dimensions of the component, to the characteristic dimensions of the flaw, and to the material engineering strength indices. The relation can be shown by an expression which will predict a limit-load capacity of the cracked component or a limiting size of the crack that will cause the component to fail. The expression can be determined if in the plastic limit-load analysis it is assumed that the average stress in the zone near the flaw will increase to a steady value when the cracked component fails. This assumption is equivalent to acknowledging that a critical number of dislocations are emitted into the structural material in the vicinity of flaw regions during fracture of the cracked component on the basis of dislocation theory.

After completion of a simplified plastic limit-load analysis, we derived

Fracture of pressuriged components with oblique flaw 203

B o

Fig. 5. Initial-cracked surface.

the following new general approach to predetermine the ultimate failure loading of an oblique-flawed component.

[ayj + (auj -- try j)~(1 + 1.151a2~i/Riti)'47](1 + sin 2 fig) a i - [1 + 1.636(1 + 7"640cosfli)aEp~/Rgtg] 235 (1)

where ao~ denotes fracture-nominal circumferential stress for component i, try i and trui the yield and the ultimate strength for structural material j, respectively, fli is the angle of an oblique flaw with respect to the axial direction of component i, R~ and t~ mean the average radius and the wall thickness of component i, respectively, and ap~ is defined as follows:

ap, = ~ [f,(() - f2(()] d( (2)

The functions fl(~) and f2(~) express respectively the upper and lower boundary lines of an initially cracked plane, that is, a cracked plane before the onset of the stable crack growth under bursting conditions. These are shown in Fig. 5.

Based on differential-integral calculus, the right-hand side of eqn (2) can be approximated by the trapezium expression. Hence, it can be converted as follows:

o)-~k ap, = S/t, = 2nt, {[f,((o) -f2((o)] + 2[f,(,) -f2((,)]

+"" + [f ,(( . - ,) - f2( . - ,)] + [1]((.) -f2((.)]} (3)

where S is initial flaw area.

204 Li Sho'ie, Hung Xiaosheng

When fli = 0, eqn (1) is simplified to

ayj + (auj - try j)/(1 + 1.151a2i/Rit i) '47 ~ri = [1 + 14"135a2oi/Riti] 235 (4)

When fli = 90, eqn (1) takes its simplest form and can be applied to a circumferentially cracked component under internal pressure in the range of values of aZojRit~ from 6 to 16.

If internal pressure P~ and external bending moment Mx~ are applied to component i with a circumferential flaw, another equation can give a satisfactory outcome, as follows:

~(1 + l '636aZoJRit~)235ao~ + [cos 0 i + sin 0~/(rc - O~)]mxi /

R2iti[rt - 0 i - sin 20 i - (2 sin 2 0)/(re - Oi) ]

= ayj + (truj - Cry~)/(1 + 1.151a2oi/Rit i) '47 (5)

where 0~ is the half-angle of a circumferential flaw for the above component i, in radians.

VERIF ICATIONS AND APPLICATIONS

As mentioned above, the results of our experiments on the two series of oblique-flawed pressure vessel models under internal pressure load conditions are listed in Table 2. Using the above-measured data, the surface areas of the initial flaws were calculated by means of eqn (3) and are also listed in Table 2.

Figures 6 and 7 compare the experimental results with the predictions of eqns (1) and (3) respectively. The maximum percentage difference between a predicted value and its corresponding test value is . -19% and most such differences are below +_ 10%. From these results it is considered that the new general approach is validated, and that it can be used as a new prediction method to be applied to the assessment of the limiting sizes for oblique flaws which will cause components to fail by a ductile fracture mechanism under internal pressure operating conditions.

We would now like to give several examples to illustrate the application of this new general approach, as follows:

(1) In the first example, we take account of the experiments given in Ref. 6. In this paper, it is reported that a group of 18MnMoNb


60(

301

Fig. 6. and

exper iments

a~i I Ri t i : 0.501

o ,, 0 .550

. . . . 1.161

A 1,193

', 1 '619

O ,, 3 .334

. . . . ~.532

, i 1 I 0 30 60 90

~i (degree)

Comparison between prediction test--circumferential stresses for

models 014)5, 09 and 10.

exper iments

A a~i I Rit i =1.095

" 1.473

0 2. 373

3' 579

4.314

500

m a.

300 '

\ 2.373 3.5:,9

4"314 I l I

0 30 60 90 ~i (degree)

Fig. 7. Comparison of prediction and test---circumferential stresses for models

06-08, 11 and 12.

alloy steel vessels with slant cracks located at a longitudinal weld seam have been investigated experimentally. One of the vessels is shown in Fig. 8. The conditions of their heat treatments are classified into two classes, i.e. quench-tempered and normalized. Their chemical composition, the mechanical properties of the base material and weld seam, and the experimental results for the slant-cracked model vessels are extracted in Tables 4, 5 and 6 respectively. The circumferential stresses predicted from eqn

u, ~,.~L, v-=,,,= V welding

Fig. 8. Simulated cylinder.

206 Li Sho'ie, Hung Xiaosheng

TABLE 4 Chemical Composition (wt%) of 18MnMoNb Vessels

Investigated in Ref. 6

Material C Si Mn Mo P S Nb

Weld seam 0.14 0.28 1.40 0.50 0.017 0.014 0.026 Base 0.21 0 1-50 0.51 0.01 0 0.041

TABLE 5 Mechanical Properties of 18MnMoNb Vessels Investi-

gated in Ref. 6

Condition of heat treatment a yj ~roj (MPa) (MPa)

Quench-tempered base material 601.5 719.1 Quench-tempered electroslag

weld seam 640.7 738.7 Quench-tempered manual

weld seam 642.3 760.0 Normalized base material 449.5 598.2 Normalized electroslag

weld seam 428.3 616.2

(1) and found by experiment are compared in Fig. 9. They are in good agreement.

(2) Equation (4) has been successfully used in such areas as nuclear engineering, boiler building and others. 7 2o One such example is given in Fig. 10.

(3) The third example relates to two test results for circumferentially through-wall flawed pipes which were subjected simultaneously to internal pressure and external momentum. The relevant results are extracted from the paper 21 in Tables 7 and 8. The predictions of eqn (5) are in accord with the experiments within a percentage deviation range of + 19%.

(4) The fourth example relates to work by Julisch et al. 22 who have performed experiments on circumferentially cracked pipes of various materials and dimensions under conditions similar to the operational conditions in nuclear power plants. Except that values of a~oi/Rit i for components 1, 2 and 3 were beyond the applicable range of eqn (5) and another (No. 11) was not


600

-~ 400 n

:E , - :

200

Y ( - &

e&

200 400 0 'exp (MPa)

ei

I 0 600

Fig. 9. Comparison between predicted and tested results: l , normalized electroslag weld seam; Q, Q-T electroslag weld seam; A, normalized base material; /k, Q-T base

material.

800

oo I b 400 , - 0

200

0

Fig. 10.

A,

a R.W. Derby 7 0 R.H. Bryan et al. 8 A H. Larsson et al. 9 R.J. Eiber et al. 10

I I I I ~oo .,oo 600 800

o';';" ( .Pa)

ca= and tested ex~ 7-1o Comparison between predicted aol aoi.


TABLE 6 Tested and Predicted Results for 18MnMoNb Vessels

Investigated in Ref. 6

Model fli aai Ri ti aex" a'al no. (deg) (ram) (rnrn) (mm) (MPa) (MPa)

C401 a 90.0 40.60 41.40 3.60 501.9 522.1 C402 a 75.0 31.00 41.30 3.50 468.7 424.1 C403 a 61.7 21.80 41.50 3.43 460.3 426.5 C404 45.0 14.50 41.33 3,54 467.1 427.4 C708 a 0.0 9.50 41.44 3.53 435.1 336.6 CM3 b 0.0 10.00 41-34 3.62 475.9 324.6 T508 c 75-0 33.00 41.38 3.65 578.1 561.7 T509 c 60-5 33.00 41.41 3.55 494.2 455-3 T510 c 45.0 22.60 41.32 3.48 468.1 437-4 T512 c 30.0 17.00 41.42 3.60 445.7 408.5 TI01 c 0.0 13.75 41.45 3.50 456.4 339.6 TM3 d 0.0 13.50 41.34 3.52 458.4 361.6

a Flaw located at h Flaw located at c Flaw located at seam. d Flaw located at

the normalized electroslag weld seam. the normalized base material. the quench-tempered electroslag weld

the quench-tempered base material.

TABLE 7 Material Properties and External Load for Pipes Investi-

gated in Ref. 21

Tesl ayj auj P Mxi (Nmm -2) (Nmm -2) (Nmm -2) (Nmm)

15 310 633 17'2 13"8 10 6 16 310 633 7'23 9'4 10 6

TABLE 8 Predicted Results for Pipes Investigated in Ref. 21

Test Ri li Oi Pical MxC~l (mm) (ram) (deg) (Nmm- 2) (Nmm)

15 53.4 8.56 38"0 17.20 15.5 10 6 16 53.4 8'56 67.5 7-23 7-8 10 6


accompanied by a full description of its engineering strength indices, generally speaking, in relation to this whole series of tests, the predictions of eqn (5) are in good agreement with the tests.

DISCUSSION

The method proposed in Ref. 6, which is used to calculate the failure load of pressure vessels with an oblique through-wall flaw, contains the following formulae:

Pi = (2tiao/Mpi)/(R[(1 + cs2 fli) 2 "t'- (COS fli sin fli)2] 1/2) (6) a o = %j + ~auj - tTyj)tTuj/ay j (7)

where Mai is the coefficient of bulge effect in the region of an oblique flaw.

If we compare the present paper's approach with that of Ref. 6, we at once find that the former has some advantages over the latter. First, the former can be applied to more materials than the latter because the latter involves the so-called flow stress ao-

In accordance with the idea of flow stress, eqn (7) is usable only for materials having performance of yield strength-to-ultimate strength ratio >0-5. For materials such as stainless steel with cryj/aui


CONCLUSIONS

A new general approach has been theoretically derived and its predictions have been compared with various experiments. The important conclusions emerging from the preceding section are as follows:

(1) The validity of the new general approach has been verified by the experiments. Its accuracy proved to be very good.

(2) The specific form of this approach, i.e. the use of eqn (4) for calculating the failure load of a longitudinally cracked component, has been confirmed by many experiments, including not only models but also prototypes carried out in China and other countries.

(3) The application of the approach covers an extensive range of importance in engineering practice.

(4) Another equation, i.e. eqn (5), has also been supported by some experiments.

ACKNOWLEDGEM ENTS

The authors wish to thank the Heads of the PWR Research Institute and its Department of Applied Mechanics for their permission to allow the publication of the present paper. They also thank Mr Zhang Yong for typing it.

REFERENCES

1. Ye Gang Da, Assessments of the safety and the life of oxygen or hydrogen storage vessel with a defect, J. New Metal Material (China), No. 11-12, 1975,

2. Sun Xun Fang, Fracture mechanics analysis of cracked pressure vessel, Experimental Mechanics (Sichuan, China), 1980.

3. Duffy, A. R., Studies of hydrostatic test levels and defect behavior, Symposium on Line Pipe Research, American Gas Association, New York. 1965.

4. Hahn, G. T. et al., Criteria for crack extension in cylindrical pressure vessels, Int. J. Fract. Mech., 5(3) September (1969).

5. Folias, E. S., On the prediction of failure in pressurized vessel, Proc. 1st Int. Con[i on Pressure Vessel Technology, Delft, The Netherlands, 29 September- 2 October 1969.


6. Li Zezhen, Chen Shuyi and Zhou Zegong, Application of the equivalent displacement of crack tip to pressure vessel with slant crack, Proc. ICF Int. Symp. on Fracture.Mechanics, Beijing, China, 22-25 November 1983.

7. Derby, R. W., Fracture studies of model pressure vessels made of nuclear grade steel, Proc. 1st SMiRT Conf., Berlin, 1971, paper G6/6.

8. Bryan, R. H. et al., Heavy-section steel technology program, intermediate- scale pressure vessel tests, Proc. 4th SMiRT Conf., San Francisco, 1977, paper G 1 / l *.

9. Larsson, H. and Bernard, J., Fracture of longitudinally cracked ductile tube, Int. J. Pres. Ves. & Piping, 6 (1978), pp. 223-43.

10. Eiber, R. J. et al., Investigation of the initiation and extension of ductile pipe rupture, AEC BMI-1908, 1971.

I I. Eiber, R. J. et al., Review of through-wall critical crack formulations for piping and cylindrical vessel, BMI- ! 883, May 1970.

12. Carlsson, A. J., Fracture criterion for surface flaws and weld defects in structures of ductile material, Proc. 2nd Int. Conf. on Pressure Vessel Technology, San Antonio, Texas, !-4 October 1973.

13. Krenk, S. Influence of transverse shear on plasticity around an axial crack in a cylindrical shell, Proc. 4th SMiRT Conf., San Francisco, 1977, paper G5/3.

14. Derby, R. W. et al., Test of 6-in-thick pressure vessels, Series 1: Intermediate Test Vessels V-1 and V-2, ORNL-4895, February 1974.

15. Bryan, R. H. et al., Test of 6-in-thick pressure vessels, Series 2." Intermediate Test Vessels V-3, V-4 and V-6, ORNL-5059, November 1975.

16. Henry, B., Application of fracture mechanics to the prediction of rupture behaviour of thin cylindrical structures, Proc. 3rd SMiRT Conf., London, 1975, paper L7/5.

17. General Machinery Institute, Study on application of fracture mechanics in pressure vessels, J. Chemical and General Machinery, No. 3, 1975.

18. Merkle, J. G. et al., An evaluation of the HSST Program intermediate pressure vessel tests in terms of light-water-reactor pressure vessel safety, ORNL-TM-5090, November 1975.

19. Merkle, J. G. et al., Test of 6-in-thick pressure vessels, Series 4." Intermediate Test Vessels V-5 and V-9 with inside nozzle corner cracks, ORNL/NUREG- 7, August 1977.

20. Eiber, R. J. et al., Investigation of the initiation and extent of ductile pipe rupture, Phase 1. Final Report Test 17, BMI-1866, July 1969.

21. Kastner, W. et al., Critical crack sizes in ductile piping, Int. J. Pres. Ves. & Piping, 9 (1981), pp. 197-219.

22. Julisch, P. et al., Exclusion of rupture for safety-relevant piping systems by component tests and a simple calculation, Proc. 8th SMiRT Conf., Brussels, 1985, paper G3/8.

1-s2.0-0308016186900670-main

Documents

Transcript of 1-s2.0-0308016186900670-main