Int. J. Pres. Ves. & Piping 43 (1990) 301-316

Ductile Crack Growth of Semi-elliptical Surface Flaws in Pressure Vessels

W. Brocks, H. Krafka, G. Kfinecke & K. Wobst

Bundesanstalt ffir Materialforschung und -prfifung (BAM), Unter den Eichen 87, D-1000 Berlin 45, Germany

A BSTRA CT

Experiments on ductile crack growth of some axial surface flaws in a pressure vessel have revealed the well-known canoe shape, i.e. a larger crack extension has occurred in the axial direction than in the wall thickness direction. Two tests have been analyzed by finite element calculations to obtain the variation of the J-integral along the crack front, and the stress and strain state in the vicinity of the crack. The local crack resistance depended on the local stress state. To predict ductile crack extension correctly, JR-Curves have to account for the varying triaxiality of the stress state along the crack front.

INTRODUCTION

Crack initiation and stable crack growth in ductile materials are usually described by J-resistance curves which are obtained from standard specimens. Whereas the initiation value, Ji, is found to be independent of the specimen geometry, J(Aa)-curves may vary with the shape and size of the specimens, 1'2 No criteria exist for applying these curves to surface flaws in components. A leak-before-break analysis requires reliable crack resistance data up to 100% of the remaining ligament, which is beyond any accepted condition of J-control. The analysis also needs a description of how the crack shape will develop during stable growth. It is commonly assumed that the flaw remains geometrically similar, i.e. the aspect ratio a/c is constant while the crack grows. But evidence exists from experiments by Pugh 3 and Milne 4 that the flaw shape may develop quite differently and expand in the longitudinal direction under the surface more than in the wall thickness direction. The consequences for a leak-before-break analysis are evident.

301 Int. J. Pres. Ves. & Piping 0308-0161/90/$03-50 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain

302 W. Brocks, H. Kra[ka G. Kiinecke, K. Wobst

The present contribution reports on experimental investigations by Wobst and Krafka s and elastic-plastic finite element (FE) analyses by Brocks and Kfinecke 6 of test vessels containing an axial surface crack which have been performed for two different materials and crack configurations to analyze the transferability of JR-Curves from specimens to structures. The variation of the J-integral along the crack front as well as the stresses in the vicinity of the crack tip have been evaluated in order to study the dependency of the local crack resistance on the local stress state. Continuing earlier work by Brocks and Noack, 7 the ratio of the hydrostatic to the von Mises effective stress is introduced to characterize the triaxiality of the stress state. By introducing triaxiality-dependent resistance curves, a more realistic assessment of the local ductile crack growth can be given.

TEST MATERIALS

The test materials were two German standard steels of the types 20 MnMoNi 5 5 and StE 460. The chemical composition and the mechanical properties of these steels are given in Table 1. Crack resistance curves of both steels, which were determined on different types of specimen, are shown in Figs 1 and 2.

The JR-Curve of the steel 20 MnMoNi 5 5 in Fig. 1 was obtained from 20% side-grooved compact tension specimens of thickness B -- 25 mm (CT25sg) at a temperature of 22 4-2C according to the standard test procedures of

TABLE I Chemical Compositions (Per Cent Mass) and Mechanical Properties (T-Orientation,

20+TC, f=2 10 4s l) of the lnvestigated Steels

Steel C Mn Mo Ni Si Cr V Cu Al P S N 2

20MnMoNi55 0"19 1"43 0"49 0"56 0"22 0-14 0-07 0'023 0'009 0"009 --- SIE460 0-17 1'52 0"01 0.62 0'28 0"04 0"18 0"03 0"010 0"009 0"009 0"012

20MnMoNi55 StE 460

Sheet Round Sheet Round

Lower yield point Ree (MPa) ~ 459 466 480 490 Ultimate tensile strength Rm (MPa) 604 609 647 647 Elongation Alo (%) 17 16 19 20 Reduction of area Z (%) 63 66 67 64

I MPa = 1 N/ram 2.

/ !

I / /

JR N/ram /

Ji-_ o T-S I c~.~ T-L Io In 1'

. . . j , , . , , /~ ) "c . : .L ~! , , L~.-.

0 i ' ' .6 1.2 1.8 mm 2.4 szw Aa .

Fig. i. JR-curve of the steel 20 MnMoNi 5 5 obtained at a temperature of 22 + 2 C from 20% side grooved CT25 specimens in T-L and T-S orientation (SZW = stretch zone width).

' ' ' I T j ] ) l 'O ' ' I / e L 6

400

e ' , . . . . . . . l . . . . , , , , , i . . . . I [ .5 l 1 .5 mm 2 2.5 SZW A~ . . . . >

Fig. 2.

Symbol

2 31 - . -x 4; - -+ 5 . - -0 61 - -4 . 7; - - - i : l 8~ - - - -0 9" - -qD

10 - - -~

Kind

CT25s 9 CT25 OEC(T)

CC(T)sg

ccO)

Specimen Dimensions In mm

] "o1 ".1 wo oo/Wo Wo-oo 25 191 50 0.5 25 25 - i 40 125 0.8 25

5O0 I oo 20 16 50 0.2 40

0.5 25 0.8 I0

40 125 0.1 112.5 0.5 62.5 0.8 25

JR-Curves of the steel StE 460 obtained at a temperature of 22 + 2~'C from different specimens, CT25sg, CT25, DECT and CCT, in T-L orientation.

304 W. Brocks, H. Kralka G. Kiineeke, K. Wobst

ASTM E 813 s and DVM-Merkblatt. 9 The specimens were cut in the T-L and T-S orientations, corresponding with the definition given in ASTM E 399, t out of that part of the sheet from where the circular inserts for the vessel tests were taken. The analytical blunting lines were calculated from two formulas; those described by ASTM E 8139 and Cornec, Heerens and Schwalbe.I1 The best fits of all the test results are summarized in Table 2. No significant differences have been found between the JR(Aa)-values of the two orientations, thus indicating that the varying stress state along the crack front will cause the crack shape, rather than any anisotropy of the material.

The JR-Curves of the steel StE 460, which were determined on centre- cracked tensile panels (CCT), on double-edge cracked tensile panels (DECT) and on compact tension specimens CT25, are compared in Fig. 2. The blunting line in this figure was also established from an analytical approach by Cornec, Heerens and Schwalbe.11 More details of these tests are given in Ref. 12. The more gradual slopes of the JR-Curves of the CT and DECT specimens are produced by greater constraints in the ligament direction in these specimens than in the CCT specimens. The result that the slopes of the JR-Curves increase in the demonstrated sequence accords with other published results.13-17 The results are summarized in Table 2.

Table 2 shows different J~-values for initiating a stable crack in both steels for differently dimensioned specimens. These J~-values result from JR-Curves

TABLE 2 Fracture Resistance of Various Specimens; Results from JR-Curve Testing

Spec#nen B (B,) W a/W Ji dJ/da (N/mm 2) (ram) (mm) (N/mm)

A~ = 01 1"0 20

Material 20MnMoNi55 CTsg 25 {19j 50 0"5 139 85 83 81 CT 25 50 05 115 143 149 157

Material StE 460 CTsg 25 (19t 50 0"5 117 146 t53 161 CT 25 50 0'5 122 244 171 91 DECT 40 500 0"8 148 147 140 132 DECT 40 125 0"8 123 183 192 203 CCTsg 20 (16t 50 0"2 141 521 296 217 CCTsg 20 (16) 50 0-5 127 544 308 225 CCTsg 20 (16) 50 0"8 130 742 277 194 CCT 40 125 0" 1 94 746 506 239 CCT 40 125 05 149 323 265 201 CCT 40 125 0'8 100 592 541 486

B n = net thickness after side grooving (sg): W = specimen width.

Ductile crack growth Of axial sur/'ace flaws 305

and values for the stretch zone width, SZW, which were determined either as averaged results of several tests or- - in a few cases--ofa single test according to the single specimen method. The scatter of J~ does not imply that the steels show different initiation values depending on the specimen geometry. All that may be concluded is that different J~-values have been determined in single tests because the test conditions were not perfectly reproducible with respect to the material state or loading.

EXPERIMENTAL PRESSURE VESSEL TESTS

Figure 3 shows the dimensions of the test vessel and the location of the outer surface notch. The test flaw was located in a round of 650mm diameter which has been welded into the middle of the cylindrical part of the vessel. The vessel was annealed for stress relief at a temperature of 580 + 20C for 90 min after welding.

The flaw was parallel to the axis of the vessel and to the longitudinal rolling direction of the steels 20 MnMoNi 5 5 and StE 460. In the following, the two vessel tests will be called VT1 and VT2 (Table 3). Lengths and depths of the machined notches, which were 2% = 180-4 mm, ao - 15.0 mm for VT 1 and 2% = 190.7 ram, ao = 20.2 mm for VT2, respectively, were designed so that initiation and stable crack growth could occur from a 5 mm (VT1) and 7.5 mm (VT2) fatigue crack at a pressure lower than the plastic collapse load.

- 3000mm ~1 Fig. 3. Test vessel with axial surface flaw.

TABLE 3 Vessel Tests: Geometry, Material Data and Loading

Vessel test VTI VT2

Pressure vessel Inner radius, r~ (mm) Length of cylindrical part, L (mm) Wall thickness t (mm) t/rl

Surface flaw Length 2c (mm) Depth a (mm) a/(' a/f Folias-faclor mr

Material (round) Yield strength, % (MPa) Ultimate stress, % (MPa) Hardening exponent of

Ramberg-Osgood power law, n Fracture initiation, Ji (N/ram)

Internal pressure at initiation, p~ (MPa) Maximum, Pro., (MPa)

Calculated yield load, py (MPa) Collapse load Pv (MPa)

Pm,,/'PF P>,"PF PmSPv

750 750 3 000 3 000

40 39'8 0"053 0"053

180-4 192 1 21 "6 28"0 0'239 0'292 0"540 0"705 1'156 1352

20MnMoNi55 StE 460 460 490 609 647

7'1 7-4 120 1 l0

22"4 20"0 24'2 22"36

17'5 21"0 21'2 192

1'14 116 0-83 109 1"38 106

~/ . i 97 f i "

Fig. 4. Calibration of the dc potential probe on the vessel: potentials at various pick-ups versus flaw area, S, during the

machining process of the notch (VTI).

I o 4/12 potentiol ~SIm~ v 5/12 p ickups aULuVj ~- 2/lO

L00 o 1/9 ] U X18/24 ] 9.80

}~ I1 /23 ~ ~ .

13.33 200

,~ ----~ 23.81 ~JV ~ --4~ 62.S0

0 0 1000 2000 rnrn 2

S - - - ""

Ductile crack growth o.f axial surface flaws 307

This was done by J-assessments based on the Raju and Newman 1 s formulas and tables including a small-scale yielding correction. 19 The tests were performed at a temperature of about 21C following the single specimen procedure.

The global crack growth, fatigue cracking as well as stable crack growth, was measured by the dc potential drop method. The sensitivity of the potential probe was calibrated before by measurements in the course of the notch machining (Steps 1-4 in Fig. 4) showing that there is a linear relationship between the potential, U, and the area, S, of the flaw; but no local crack extension can be measured by this method. Figure 5 shows the potential pick-up positions on the vessel surface and the positions of the clip gages, which measured the notch opening displacements, V, close to the vessel surface at different points due to the internal pressure, for both test configurations.

Figure 6 is a record of the test conditions during fatigue precracking of VT1 by plotting the potential, U, versus the number of cycles, N. The amplitude of the pulsating pressure, Ap = Pv - PL, was large, i.e. 15.9 MPa, in the beginning to start the fatigue crack from the machined notch. With increasing fatigue crack growth, the lower value, PL, was raised to 7"5 MPa, thus reducing the amplitude to 8"9 MPa.

Potential versus notch opening displacement at the clip gage position 1 (see Fig. 5) during the static test VT1 is recorded in Fig. 7. A change of the slope in the U versus F curve indicates the initiation of stable crack growth and thus renders the corresponding value of the total COD at initiation, Vti. The end of the static test phase is denoted by the subscript 'max'. The pressure versus COD curves for both tests are shown in Fig. 8. The pressure at initiation, Pi, follows from V~i in Fig. 7.

At the end of the stable crack growth in VT1 and VT2, the flawed rounds were cut out and broken by tensile loading at a temperature of - 120C. The crack surfaces are displayed in Fig. 9, showing that the intended extensions of the crack have been realized, both with respect to the mean crack extensions and to the crack shapes. The evaluation of the crack shape of VT2 is restricted to one half, only, as the other one has been reserved to investigate the crack tip opening displacement at different crack front positions by cuts perpendicular to the flaw surface. The maximum crack growth does not occur perpendular to the vessel surface but in the axial direction. The local crack growth, Aa, perpendicular to the fatigue crack front, which has been obtained in both tests at Pmax, can be measured from Fig. 9; it is plotted against the crack front angle, in Fig. 10. is 0 at the deepest point of the crack and + 90 at the penetration points of the crack front at the outer surface of the vessel. The maximum Aa along the crack front is reached at ~-~ 70 for VT1 and ~-~ 80 for VT2. The crack

308 W. Brocks, H. KraJka, G. Kiinecke, K. Wobst

D.C. constant cu

vl v2

cuPrent power eupp ly

~__ BS

gl potential pickups 4 / 12118 / 27

S / 12111 / 23 ca l ib ra t ion : 2 / 10 11 / 28

1 / 9 18 / 24 1 / 1G

veuel Lest' 1 / 18 4 / 12 V 1.2,3 notch crook dieplaoement

(a)

|

f

i

."~MIO I

i ! j

u,n_ r r -h _ . , . '~

.:I! ! IilI.., -~/ i , , -~ ,

I

(b)

Fig. 5. Clip gage positions for the measurement of notch opening displacements, V, and pick-ups for the dc potential measurement at the surface flaw: (a) VTI; (b) VT2.

Ductile crack growth of axial surface flaws 309

450 IJV

U

350

250 0""

i pressure in lUlPo

~ :.~.~-~t~

I " ,io~e

16~.

Y:---" " " utf=zo'c)

I BBBB

N----" Fig. 6. Control diagram for the first fatigue precracking: potential versus number of cycles, upper and lower pressure, Pu and PL, in the course of oscillating loading of the vessel (VTI).

Fig. 7.

l : o / u ~.~f. - -U i &.2

~2o j I I I

Vti 0,6~

~00 . . . . . . . . . . . . . . . ~ ' " ' . . . . . . . . . . . . . . . . . . . . . . 0 0.8 1.6 mm

V 1 ,.

Static loading of the vessel with the first fatigue crack: measured potential versus notch opening displacement (VTI).

,.., 25 0

n

2o .-' / - 15 ,/i' 5

0 0,0

Fig. 8.

exper tment . . . . FE rasu l t s

,.., 25 0

~ 2o cl

5p

pt=20

exper iment

. . . . FE resu l t s l

V l Z V 2

0 i

0,5 1,,0 0 ,0 0,,5 1..0

V [mm] V ['mm]

(a) (b) Static loading of the vessel: internal pressure versus notch opening displacement,

comparison of experimental and numerical results: (a) VT1; (b) VT2.

(a)

stoble cr~]ck -fotigue precrack - notch

/ I

(b) Fig. 9. Crack surfaces of the vessel tests: (a) Alternate phases of fatigue cracking and stable crack growth in VT1 (20 MnMoNi 5 5); (b) fatigue crack and ductile crack in VT2 (StE 460).

E E

o 6

0 -90

I

X VT1. I d> VT2

, )<

-45

I I

0 45 90

r3 Fig. 10 Variation of stable crack growth along the crack front at Pmax-

Ductile crack growth of axial surface flaws 311

propagation in the axial direction is three to four times larger than the crack growth in wall thickness direction at = 0 . This 'canoe' shape of the ductile crack has been observed before by Pugh, 3 Milne, 4 and other investigators, but with no explanation.

NUMERICAL ANALYSIS OF THE TESTS

Materially and geometrically nonlinear FE analyses of the two structures, VT1 and VT2, were realized with Adina 2 based on the incremental theory of plasticity by von Mises, Prandtl and Reuss and allowing for large strain in the vicinity of the crack. The local J-integral was calculated by a post- processor 21 based on the virtual crack extension method of DeLorenzi. 22 No crack growth was simulated in the FE model. Thus, all the calculated values refer to the configuration of the initial fatigue crack, a 0 and c o, only. This appeared to be a severe restriction for the analysis of VT2.

The FE calculations, as well as a limit analysis by means of the Folias factor, showed that the initiation of crack growth occurred near or beyond full yielding of the smallest ligament (see Table 3).

Figure 8 shows a comparison of the pressure versus notch opening displacement curves obtained in the vessel tests and in the FE analysis, respectively. The curves indicate a slightly higher plastic limit load in the experiment than in the FE calculation but they coincide at the initiation pressure, p~. As no crack growth was simulated, the numerical results will necessarily deviate from the experimental data beyond initiation. Consequently, the calculated J-integral will deviate from the 'real' J-values with increasing pressure. This deviation can be eliminated by remembering that J is related to the work of external forces; the latter may be calculated from the area, A, under the load versus load line displacement curve

; fo A = ~m(V) d V = ri o t p (V)dV (1) Evaluating eqn (1) for both experimental and numerical data, a 'revised' J is obtained by

JIA~(*) = JIFEI(O) x (Aexp/AFO (2)

and plotted in Fig. 11 versus the crack front angle for the three pressure values Pi, Py, Pmax" This revised J according to eqn (2) will be used for the crack growth analysis. It shows a maximum at = 0 as in linear elastic fracture mechanics but, with increasing plastification, two additional local maxima develop at = 55 and = ___ 65 for VT1 and VT2, respectively. The dashed lines denote the initiation values, J~, obtained from compact

312 IV. Brocks, H. Kralka, G. Kiinecke, K. Wobst

E E 600 m P i \ O Pl Z & Pie= L-=

Y J i

400

200

0 -90

_ " - 'e , -~6, . . "

-45 0 45 90 ~ [o3

soo 'k u 0 PL

rtl Pu

400 Y Jl

200 ~

0 . . . . . . . . . . . . . ' ' ' ' ' ' . . . . . . . . -9O -/.5 0 45 90

~ [3

(a) (b)

Fig. I1. Variation of J-integral along the crack front from FE calculation, corrected by experimental p versus V data according to eqn (2): (a) VTI ; (b) VT2.

specimens for the respective materials. According to these results, some amount of stable crack extension has apparently occurred before the potential curve of Fig. 7 indicated initiation. The variation of CTOD, 6,, along the crack front is quite similar to that of J (see Fig. 12). This variation of J and CTOD along the crack front does not accord with the variation of stable crack extension, Aa, in Fig. 10.

An attempt to explain the canoe-shape phenomenon has been made by Brocks and Ktinecke 6 for VT1 by introducing the local ratio oftriaxiality of the stress state

ak(r, O, O) o=o Z(O) = maxr ~o(r, 0, O) (3)

where a h and a e are the hydrostatic and the von Mises effective stress, r is the distance to the crack tip, and 0 is the angle to the ligament in a local polar coordinate system. This ratio has proved to be a parameter characterizing

~COo3 - t \ ~o .3

-St ,,~....._ ~ -.,,,~ . _ . . .~ o.1 0,0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 .0

-90 -45 0 45 90 -90 ~ [o3

(a)

Fig. 12.

, ,

i;L PU -45 0 45 90

C ]

(b)

Variation of CTOD along the crack front: (a) VT1; (b) VT2.

Ductile crack growth o/" axial surface.flaws 313

x o~2.5

@ 1o \

t-

"o 2 .0

I . .5

1o0 -90

X VT1.. ]

VT2

. . . . . . . . . . . , , , ,"r . . . . . . . . . . . . . . . .

-45 0 45 90 [o]

Fig. 13. Variation of the triaxiality of the stress state along the crack front, eqn (3).

the stress state in various specimen geometries 23 and has also been proposed by Kordisch and Sommer. 24 Its physical significance for void growth in elastic-plastic materials is well known from the investigations of McClintock, 25 and Rice and Tracey. 26 The variations of the triaxiality according to eqn (3) along the crack front (Fig. 13) reveal that the maxima of crack growth occur close to the maxima of triaxiality. Another measure of local crack tip constraint, i.e. the ratio J/(6t~y), has been proposed by Steenkamp. 2~ Figure 14 shows that these curves have similar shapes to those of g(~). Thus, both quantities seem to be suited to describe the local triaxiality or crack tip constraint that appears to influence the local resistance against ductile crack growth.

In the present paper, the z-parameter will be used to describe the dependency of the local R-curves on the triaxiality of the stress state. For simplicity, and as no other information about the progress of Aa(~) under

2.5 ...J

or"

2.0

1,5

Fig. 14.

I X VT1 r VT2

1.o 0 . . . . . . . . . . . . . . i . . . . . . . . . . . . . .

-90 -45 0 45 90 [o]

Variation of crack tip constraint along the crack front.

314 W. Brooks, H. Kra[ka, G. Kiinecke, K. Wobst

increasing J(tl)) was available for the surface flaws, these R-curves have been approximated by straight lines. Ji is assumed to be a material constant not depending on geometry or stress state. Assuming furthermore that upper and lower limits of the slopes of the R-curves exist that correspond to the limiting cases of plane strain and plane stress, respectively, an approxi- mation function is: 6'28

AJ D - - Z A-~ (Z) = A + B tanh ~ (4)

The resulting Aa(~) predictions, by both the conventional method of using JR-curves of compact specimens and an extended J-concept of z-dependent local resistance curves, are plotted in Fig. 15.

The conventional concept of a unique characteristic J(Aa) overestimates the real crack growth for VT1 at = 0 in the wall thickness direction up to four times and is not able to predict the maximum crack growth for VT1 and VT2 at = 70 and 80 , respectively. Commonly, an overestimation of a critical event is supposed to give a conservative prediction. But this is different with respect to a leak-before-break assessment as the real crack may become unstable due to its axial extension before it penetrates through the vessel wall. Thus, a J(Aa) analysis may yield non-conservative estimates. The improved concept of local JR-Curves depending on the triaxiality of stresses gives a much better qualitative and quantitative explanation of the ductile crack growth for VT1. It also gives a qualitatively better prediction of Aa(O) for VT2, i.e. it reflects the ratio Aam~ x :Aami n obtained in the experiment as well as the approximate position of Aamax. The quantitative results for VT2 are still poor, which might be due to the restriction of the FE analysis which did not account for the geometry changes from the large amount of crack growth.

4 E

I

o -90

/ \ / \

/ k

~, :1. [& experiment ] \ \

& / ; - I | - - - d J /do ,CTL _ Y

/__'. I -!-, " - - -o

. . . . . . . I . . . . . . . I . . . . . . . . . . . . . . . .

-~5 0 45 90

C ]

,-, 8 E E

0 G- ..:3

0 -90

J -45

I...Jr,No, ] :': - - - d J /da ,CT " ' - - d J /do( X ) 4~

' ~k

A h,

. . . . . . . . . . . . . , I . . . . . .

0 45 90

(a) (b) Fig. 15. Variation of stable crack growth along the crack front at Pmax; test results

compared with conventional and improved J-based predictions: (a) VT1; (b) VT2.

Ductile crack growth of axial surface flaws 315

ACKNOWLEDGEMENT

The results reported here have been obtained in the course of investigations supported by the Bundesminister fiJr Forschung und Technologie of the Federal Republic of Germany under Contract Number 1500 490.

REFERENCES

1. McCabe, D. E., Landes, J. D. & Ernst, H. A., Prediction of heavy section performance of nuclear vessel steels from surveillance size specimens. Trans. 7th SMiRT Conf., Vol. G, 1983, paper G2/4.

2. Julisch, P. & Stadtmiiller, W., Valuation of a ductile vessel rupture by R-curve analysis with CT specimens and wide plate tests. Trans. 8th SMiRT Conf., Vol. G, 1985, paper G 3/1.

3. Pugh, C. E., HSST program quarterly report for Jan. to March 1983. NUREG/CR-3334, Vol. l, ORNL/TM-8787/V1, NRC Fin. No. B 80119.

4. Milne, I., Notes for EGF task group I exercise in predicting ductile instability: Phase III. Report RL/IM/PL, CEGB, Leatherhead, UK, 1984.

5. Wobst, K. & Krafka, H., Experimental investigation of stable crack growth of an axial surface flaw in a pressure vessel. In Proc. 14th MPA-Seminar, Stuttgart, 1988, Vol. 2, paper 41.

6. Brocks, W. & Kiinecke, G., Elastic-plastic fracture mechanics analysis of a pressure vessel with an axial outer surface flaw. In Proc. 14th MPA-Seminar, Stuttgart, 1988, Vol. 2, paper 42.

7. Brocks, W. & Noack, H. D., J-integral and stresses at an inner surface flaw in a pressure vessel. Int. J. Pres. Ves. & Piping, 31 (1987) 187-203.

8. ASTM E 813-8 l, Standard test method for J~c, a measure of fracture toughness. In Annual Book of ASTM Standards. American Society for Testing and Materials, Philadelphia, PA, 1981.

9. DVM-Merkblatt Nr. 2, Ermittlung yon Rissinitiierungswerten und Risswider- standskurven bei Andwendung des J-Integrals. Deutscher Verband fiir Materialpriifung, Berlin, 1987.

10. ASTM E 399-81. Standard test method for plane-strain fracture toughness of metallic materials. In Annual Book of ASTM Standards. American Society for Testing and Materials, Philadelphia, PA, 1981.

I I. Cornec, A., Heerens, J. & Schwalbe, K.-H., Bestimmung der Rissaufweitung CTOD und Rissabstumpfung SZW aus dem J-Integral. Berichtsband der 18. Sitzung des DVM-Arbeitskreises Bruchvorgfinge, Deutscher Verband fiir Materialpriifung, Berlin, 1987, pp. 265-79.

12. Aurich, D., Wobst, K. & Krafka, H., JR-curves of wide plates and CT25 specimens--comparison of the results of a pressure vessel. Nucl. Engineering & Design, l l2 (1989) 319-28.

13. Garwood, S. J., Effect of specimen geometry on crack growth resistance. ASTM STP 677, American Society for Testing and Materials, Philadelphia, PA, 1979, pp. 511-32.

316 W. Brocks, H. Krafica, G. Kiinecke, K. Wobst

14. Garwood, S. J., Measurement of crack growth resistance of A533B wide plate tests. Fracture Mechanics, ASTM STP 700, American Society for Testing and Materials, Philadelphia, PA, 1980, pp. 271 95.

15. Simpson, L. A., Effect of specimen geometry on elastic-plastic R-curves for Zr-2.5% Nb. Advances in Fracture Research, Proc. 5th Int. Conf. Fracture. Vol. 2, Cannes, 1981, pp. 833-41.

16. Shih, C. F., German, D. & Kumar, V., An engineering approach for examining crack growth and stability in flawed structures. Int. J. Pres. Ves. & Piping, 9 (1981) 159-96.

17. Roos, E., Eisele, U. & Silcher, H., A procedure for the experimental assess- ment of the J-integral by means of specimens of different geometries. Int. J. Pres. Ves. & Piping, 9 (1986) 81-93.

18. Raju, I. S. & Newman, C. J., Stress intensity factors for internal and external surface cracks in cylindrical vessels. Trans. ASME, J. Pressure Vessel Technology, 104 (1982) 293-6.

19. Brocks, W. & Noack, H.-D., Elastic-plastic J-analysis of an inner surface flaw in a pressure vessel. In Proc. 1986 SEM Fall Conference on Experimental Mechanics, Keystone, Experimental Mechanics, June 1988, pp. 205-9.

20. Bathe, K. J., ADINA, a finite element program for automatic dynamic incremental nonlinear analysis. Report AE84-1, ADINA Engineering Inc., Watertown, 1984.

21. Matzkows, J., Boddenberg, R. & Kaiser, F., Programm JINFEM, Post- prozessor ffir das Programm ADINA. Report Hb-18-030, IWiS GmbH, Berlin, 1985.

22. de Lorenzi, H. G., On the energy release rate and the J-integral for 3D crack configurations. J. Fracture, 19 (1982) 183-93.

23. Brocks, W., KiJnecke, G., Noack, H. D. & Veith, H., On the transferability of fracture mechanics parameters to structures using FEM. In Proc. 13th MPA- Seminar, Stuttgart, 1987, Vol. 1, paper 3.

24. Kordisch, H. & Sommer, E., 3D-effects affecting the precision of lifetime predictions. 19th Nat. Syrup. on Fracture Mechanics. San Antonio, 1986. ASTM STP 969, 1988, pp. 73-87.

25. McClintock, F. A., A criterion for ductile fracture by growth of holes. J. Appl. Mechanics, 35 (1986) 363-71.

26. Rice, J. R. & Tracey, D. M., On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids, 17 (1969) 201 17.

27. Steenkamp, P. A. J. M., Investigation into the validity of J-based methods for the prediction of ductile tearing and fracture. PhD-thesis, Technical University Delft, 1986.

28. Brocks, W., Veith, H. & Wobst, K., Experimental and numerical investigations of stable crack growth of an axial surface flaw in a pressure vessel. IAEA Specialists' Meeting, Stuttgart, FRG, 1988.