Towards an elastic-plastic fracture mechanics predictive capability for reactor piping

Nuclear Engineering and Design 48 (1978) 117-134 © North-Holland Publishing Company

117

TOWARDS AN ELASTIC-PLASTIC F R A C T U R E MECHANICS PREDICTIVE CAPABILITY FOR REACTOR PIPING * M.F. KANNINEN, D. BROEK, G.T. HAHN, C.W. MARSCHALL, E.F. RYBICKI and G.M. WlLKOWSKI Battelle, Columbus Laboratories, 505 King Avenue, Columbus, Ohio 43201, USA

Received 22 November 1977

Intergranular stress corrosion cracks have been discovered in the recirculation bypass piping and core spray lines of several boiling water reactor (BWR) plants. These cracks initiate in heat-affected zones of girth welds and grow circumferentially by combined stress corrosion and fatigue. Reactor piping is mainly type 304 stainless steel, a material which exhibits high ductility and toughness. A test program described in this paper demonstrates that catastrophic crack growth in these materials is preceded by considerable amounts of stable crack growth accompanied by large plastic deformation. Thus, conventional linear elastic fracture mechanics, which only applies to the initiation of crack growth in materials behaving in a predominantly linear elastic fashion, is inadequate for a failure analysis of reactor piping. This paper is based upon research initiated by a need to develop a realistic failure prediction and a way to delineate leak-before-break conditions for reactor piping. An effective engineering solution for the type of cracks that have been discovered in BWR plants was first developed. This was based upon a simple net section flow stress criterion. Subsequent work to develop an elastic-plastic fracture mechanics methodology has also been pursued. A survey of progress being made is described in this paper. This work is based on the use of fini~ element models together with experimental results to identify criteria appropriate for the onset of crack extension and for stable crack growth. A number of criteria have been evaluated. However, the optimum fracture criterion has not yet been determined, even for conditions which do not include all of the complications involved in reactor piping.

1. Introduction

Intergranular stress corrosion cracks have been discovered in the heat-affected zones of girth welds in type 304 stainless steel recirculation bypass piping and core spray lines o f several boiling water reactor (BWR) plants [1,2]. Figs. 1 and 2 show the prof'fles of cracks in sections o f 100-mm (4-in.) bypass piping removed from the Dresden II and the Quad Cities II BWR plants which illustrate the problem. The cracks typified b y figs. 1 and 2 apparently initiate at the inner surface o f the pipe wall and grow radially and circumferentially by combined stress corrosion and * Expanded version of Invited Paper F8/1" presented at the 4th International Conference on Structural Mechanics in Reactor Technology, San Francisco, California, 15-19 August 1977.

fatigue. Although BWR piping system cracks such as these have been troublesome, there has always been ample time for shutdown and repair. No serious incidents have occurred. Moreover, it is unlikely that failure would occur under normal service loadings. The major concern is an extraordinarily high load which could possibly trigger pipe fracture at the site of a stress corrosion crack. A failure analysis for reactor piping with a flaw in a weld heat-affected zone is difficult because o f the complex state o f stress that exists for cracks in pipe walls. Membrane stresses, bending loads, thermal stresses, and residual stresses can all act simultaneously. Nevertheless, existing data and stress analysis methods, e.g. ref. [1], could probably be used in a design calculation if a fracture prediction criterion was available. However, such a criterion is not now in hand.

118

M.F. Kanninen et al. / Fracture mechanics predictive capability for reactor piping PIPE

PiPE SL; F;', !

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Fig. 1. Profiles of circumferential cracks detected in 100-mm (4-in.) diameter recirculation bypass line of the Dresden-II BWR plant (after Cheng et al. [2]).

The problem addressed in this paper is to determine an appropriate fracture criterion for reactor piping with cracks. Because crack growth instability in tough ductile materials like type 304 stainless steel is always preceded by significant amounts of stable crack growth, linear elastic fracture mechanics (LEFM) is not applicable. In LEFM attention is restricted to the initiation of crack growth in materials that behave in an essentially linear elastic manner. Failure predictions based on these assumptions will give a considerable underestimate of the strength of a ductile material. Because of these complications, a pragmatic approach was taken in the initial phase of this work. The work was limited to type 304 stainless steel pipes of lO0-mm (4-in.) and 710 mm (28-in.) diameter with circumferential cracks located in weld heat-affected zones. As described more completely in ref. [3], an integrated program of theoretical analysis and experiment was conducted towards this goat. The program included both small-scale flat.plate experiments and large-scale pipe experiments. Using these results, a failure analysis was conducted using a simple net-

Fig. 2. Profile of a circumferential crack detected in 100-mm (4-in.) diameter recirculation bypass line (loop B) of the Quad Cities-If BWR (after Cheng et al. [2]).

section flow-stress criterion. As will be shown in the following, this approach gives quite reasonable estimates of the failure loads to be expected. More precise predictions require the development of an elastic-plastic fracture mechanics methodology. As already stated, conventional LEFM techniques are not valid for tough ductile nuclear reactor materials where crack-growth initiation is accompanied by largescale plastic deformation. Crack-opening displacement techniques, usually based on strip-yield crack-tip models, similarly tend to underestimate the strength when crack growth initiation is followed by an extended period of stable growth. While some progress has been madein developing an appropriate criterion for stable crack growth, see refs. [4-16], a generally acceptable approach does not now exist. Further complicating the problem for type 304 stainless steel reactor piping are the very large strains that exist in the vicinity of the crack tip. While not yet offering a complete solution, the basis of a possible approach to an elasticplastic fracture mechanics capability for reactor piping is also given in this paper.

M.F. Kanninen et aL / Fracture mechanics predictive capability for reactor piping

2. Mechanical fracture predictions for sensitized stainless steel piping with circumferential cracks 2.1. Small-scale flat-plate experiments

Tensile tests were conducted on flat-plate specimens, both with and without cracks, machined from commercially produced type 304 stainless steel plate. The stress-strain characteristics were obtained from smooth-bar tension tests on 8-ram thick plate specimens. Curves of load-versus-strain recorded at test temperatures of 25 and 205°C are shown in fig. 3. Similar curves were also obtained for sensitized and as-welded material. Little difference was found between the various conditions. Crack-growth behavior was obtained from two types of precracked specimens: a center-cracked tension (CCT) panel 8-mm thick by 305-ram wide, to simulate 100-mm (4-in.) diameter piping and a single-edgenotched (SEN) panel 25-mm thick by 125-mm wide, to simulate 710-mm (28-in.) diameter piping. The SEN geometry chosen for the thicker plate was such as not to exceed the available capacity of the testing machine. Details of the panel geometries for the CCT

and SEN configurations are shown in figs. 4 and 5, respectively. Details of the crack shapes used in the experiments are shown in fig. 6. Photographs of actual center cracked panels before testing and after the onset of failure, are presented in figs. 7(a) and (b). In most of the notched-specimen tests, records were obtained of crack length, crack-tip opening angle, displacement across the crack line at several locations, and the cross-head displacement; each as a function of applied load. Details of the twelve center cracked-test (CCT) panels and the two singleedge-notch (SEN) configurations are summarized in table 1. Cracks in reactor bypass pipes occur in sensitized regions of the heat-affected zones (HAZ) of butt welds. Accordingly, some center-cracked specimens were prepared by butt welding. The crack was located parallel to the weld line in the sensitized region. For comparison, other specimens were prepared from (a) as-received material (annealed) without welding, and (b) material that was purposely sensitized to a high level by heating to 620°C for 24 hr. Based on the observed similarity in smooth-bar properties between the as-received material and the pur-

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~tes Fig. 5. Single-edge-notch tension specimen. Notes: 1, notch was prepared in two steps: (a) saw cut, and (b) EDM the final 8 mm (5/16 in.) to produce a very small notch radius and notch angle; 2, carbon steel end plates were attached to the type 304 stainless steel test section by a full-penetration butt weld; 3, arrow denotes principal rolling direction.

M.F. Kanninen et al. I Fracture mechanics predictive capability for reactor piping

121

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Fig. 6. Crack shapes used in the center-cracked flat-plate experiments. posely sensitized material, it appeared unlikely that crack propagation in the HAZ of a weld would differ greatly from that in as-received material. This proved to be true. Hence, most of the subsequent specimens were prepared without butt welding. Both through-thickness cracks and part-through cracks (depth equal to two-thirds thickness) were investigated. All had sharp tips to simulate a natural crack. They were prepared by electrical discharge machining. A single specimen, CCT-2, was fatigue precracked for comparison. This specimen exhibited a large opening displacement at the fatigue crack tip prior to stable crack growth. The blunting prior to stable crack growth suggested that sharp machined notches could be used to model the behavior of natural cracks. Again, the initial test results confirmed this. Most specimens therefore were tested with sharpended machined cracks. The yield strength and ultimate strength of the annealed 8-mm thick plates were found to be about 265 and 630 MN/m 2, respectively, at room temperature. Nearly identical values were obtained on plate specimens that had been deliberately sensitized.

Fig. 7. Photographs of center-crackedpanel. (a) Sensitized specimen prior to load. (b) Welded specimen after test.

122

M.b2 Kanninen et al. / Fracture mechanics predictive capability for reactor piping

Table 1 Summary of flat-plate experimental results Specimen number

Material condition

Crack tip condition

Crack length (cm)

Test temperature (°C)

Net section stress at crack growth initiation (MPa)

Maximulll net-section stress (MPa)

30-cm wide panels, 8-mm thickness, with through-wall center cracks 7.6 7.6 7.6 7.6 13.3 13.3 7.6 7.6

25 25 25 25 25 205 205 205

395 375 415 385 410 310 290 325

490 475 495 475 455 350 400 380

wall center cracks 335 275 290 315

440 455 375 395

CCT-1 CCT-2 CCT-3 CCT-4 CCT-5 CCT-6 CCT-7 CCT-8

as-received a sensitized b as-welded sensitized as-received as-received as-received as-welded

saw cut (EDM) fatigue saw cut (EDM) saw cut saw cut (EDM) saw cut (EDM) saw cut (EDM) saw cut (EDM)

CCT-9 CCT-10 CCT-11 CCT-12

as-welded as-received as-received as-received

30-cm wide panels, 8-mm thickness, with part-through EDM 7.6 205 EDM 13.3 205 EDM 13.3 205 EDM 13.3 c 205

SEN-1 SEN-2

as-received as-received

12.5-cm wide panels, 2.5-cm thickness, with through-wall edge cracks saw cut (EDM) 5.54 205 295 saw cut (EDM) 3.18 205 270

360 400

a Annealed. b 24 hr at 620°C inert gas. c Total length of two coplanar cracks including 0.53 mm separation.

Although weld-lnetal properties were not determined directly, it was inferred from tests on welded specimens that the yield strength of the weld metal was in the range of about 345--415 MN/m 2. At 205°C, both the strength and the ductility were reduced. The yield strength at this temperature was 180 MN/m 2 while the ultimate strength was 460 MN/m 2. Tests on precracked-plate specimens were characterized by a high degree of ductility. Typically, the initial sharp crack tip underwent extensive blunting. Simultaneously, the region immediately ahead of the crack experienced extensive plastic deformation before crack growth began. The net-section stress at the onset of crack extension was well in excess of the tensile-yield strength. Tests on specimens with part-through cracks revealed that these cracks initially propagate through the thickness before extending in the width direction. Crack break-through was accompanied by a drop in load. The amount of load drop depended on the part-

through crack geometry. In the experiment in which the crack front was a circular arc (CCT-9) a load drop was barely discernible. In the experiments with fiatbottomed cracks (CCT-10, 11, 12), the load dropped substantially in a short period of time. The reason is that breakthrough occurred over much of the notch length simultaneously in the latter cases. No detrimental effects of welding on resistance to crack growth were observed in this investigation. The net-section stress and the crack tip opening displacement (CTOD) measured at the onset of crack extension were approximately the same for the welded specimens as for the nonwelded specimens. Nor was the effect of sharpening the crack by fatigue significant.

2.2. Full-scale pipe experiments Two full-scale experiments were performed on 100-mm (4-in.) nominal diameter schedule 80 type

M.F. Kanninen et aL /Fracture mechanics predictive capability for reactor piping

123

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N Return internal pressure

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dead weight pressure gage, and pressure transducer

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304 stainless steel pipe with circumferential throughwall cracks located in the heat-affected zone of the girth welds. The girth welds were made by manual gas tungsten-arc welding (GTAW) and manual shielded

metal -arc welding (SMAW) with 308L stainless steel weld rod according to recommended welding procedures. Pressurization was with a water-methanol mixture in the first experiment and water with gaseous

Fig. 9. Pipe specimen in bending frame - experiment 2.

124

M.F. Kanninen et al. / Fracture mechanics predictive capabiliO, for reactor piping

l:ig. 10. Pipe specimen after unstable fracture arrested -- experiment 2. nitrogen in the second experiment. The crack length in the first experiment was 133 ram; in the second, 76 ram. The pressure was held by a 1.6 nun thick stainless steel patch cemented to the inner wall of the pipe in both cases. The experiments were conducted by first pressurizing the pipe specimen to the service pressure of 7.23 MPa (1050 psi). Then, a bending load was applied by four-point loading until failure occurred. The bending force was supplied by two hydraulic rams at the inside locations of the four-point bending frame. Fig. 8 illustrates the pipe test experimental layout. Figs. 9 and 10 show the actual test set up for the second experiment, prior to and following unstable crack propagation, respectively. The pipe specimen for the first experiment contained a circumferential through-wall 135 ° flaw. The flaw was 6 mm from the edge of the girth weld. It was made by a saw cut with the tips being sharpened by a jeweler's saw having 0.07-0.10 mm radius. The temperature of the pipe during the experiment was 3°C. The maximum bending moment achieved during the experiment was 9435 Nm. The center crack-opening displacement at crack-growth initiation was 0.10 mm. The crack grew 3.81 cm on each end of the initial crack tips. This

left 15.0 cm or 41% of the circumference unbroken. The pipe specimen for the second experiment contained a circumferential through-wall flaw with a length equal to 75.8 ° around the circumference of the pipe. The flaw was located 0.25 cm from the edge of the girth weld. The flaw tips were sharpened with a jeweler's saw as in the first experiment. The temperature of the pipe during the experiment was 4°C. As in the first experiment, the specimen was first pressurized to 7.23 MPa. The bending loads were then applied and increased until the capacity of the hydraulic rams was reached, i.e at 13 800 Nm. The bending moment was held constant for several minutes at the maximum capacity of the test apparatus. Because the strain-gage readings indicated that the flaw was remaining stable, it was decided to fail the pipe by increasing the internal pressure. The internal pressure was accordingly increased to 17.2 MPa, the maximum pressure available from the nitrogen cylinders used to pressurize the specimen. This pressure was held for about one minute at which time failure occurred. Fig. 11 is the top view of the pipe after the crack arrested with the specimen still under load. This photograph shows the large displacements and plastic-

M.F. Kanninen et al. / Fracture mechanics predictive capability for reactor piping

125

Fig. 11. Top view of fractured pipe specimen with final bending load - experiment 2. ity in the cracked region. The opening at the center of the crack was 2.87 cm. Fig. 12 is a drawing of the crack profde after the load was removed. The crack-opening angle with the load removed was 1 4 . 5 - 1 7 ° and was 15.5-18.0 ° with the final load on. The crack-tip clip-gage displacements at initiation were 4.17 and 3.56 mm for clip gages that were 10.2 and 5.08 mm above the outer pipe surface, respectively. With these data, linear extrapolation back to the outer surface gave a displacement of 2.95 mm across the crack tip at initiation of crack growth.

Fig. 13 shows that the data points for crack-growth initiation and for the maximum load can both be cor-

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2. 3. Analysis o f results Top ,,H [;:I

Values for the applied stress at crack-growth initiation and at failure for the 8-mm plate tests at room temperature show that the behavior of as-received material, sensitized material, and welded material is essentially the same. The acuity of the notch is also of no significance. The crack tip blunts to such a degree that, once crack growth starts, all cracks in type 304 stainless steel have about the same acuity and the effect of the original notch vanishes completely. Results for the tests on plates with throughwall cracks at room temperature are shown in fig. 13.

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126

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Fig. 14. Residual strength of 8-mm plates with both throughwall and part-through-wall cracks at 205°C as a function of crack area.

related very well with single stress values. This suggests that a criterion for both crack growth initiation and for fracture is a critical net-section stress. This is confirmed by examination of the complete record of crack size as a function of the applied stress. Furthermore, when the part-through crack results are plotted on the basis of cracked area, it is found that crack initiation (break-through) is still governed by the same net-section stress as for the through-wall cracks. The results for the 205°C tests confirming this are shown in fig. 14. The tests for the 25-mm SEN specimens were also conducted at 205°C. It was found that, not only is a net-section stress criterion satisfied, the values for initiation and fracture are very nearly the same as for the 8-ram plate. As a result of these observations a relatively simple method for predicting the failure

load for pipes with circumferential cracks is apparent. This method is based on the net-section collapse principle. Owing to the large amount of plasticity, the stress distribution in the cracked section is almost uniform. The fiat-plate results show that, for practical purposes, the uniform stress distribution is a good approximation. Crack growth and fracture are both dictated by this uniform stress reaching a critical value (i.e. the flow stress af). Collapse o f the pipe under internal pressure and bending can be dealt with in the same way by assuming a uniform bending-stress distribution. Collapse takes place at the same flow-stress values as in the plate. This approach requires temperature-dependent flow-stress values to be determined for the onset of stable crack growth and for the onset of unstable crack propagation. The particular values determined

Table 2 Critical flow-stress values for type 304 strainless steel at two temperatures for use in a net-section col/apse failure criterion Temperature (°C)

Critical flow stress corresponding to the initiation of stable crack growth (MPa)

Critical flow stress corresponding to the maximum applied load (MPa)

24 205

403 276

438 348

M.F. Kanninen et aL/ Fracture mechanics predictive capability for reactor piping ~

for type 304 stainless steeel in this program are given in table 2. Note again that these values appear to be independent of crack size and shape and, to the limited extend to which it was examined in this program, of the pipe-wall thickness.

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2.4. Application o f the net-section collapse criterion to cracked pipes The load levels for the onset of stable growth and the maximum load levels achieved in the small-scale fiat-plate tests are the basis for the critical flow stress values given in table 2. These data were obtained for both through-wall and part-through-wall cracks of various shapes and sizes on plates of width equal to the pipe circumference and of the same thickness. On the basis of the fiat-plate test results, predictions of the two full-scale tests were made. Table 3 shows the comparison of the failure loads predicted by the net-section collapse criterion using the fiat-plate data, i.e. the critical flow stress values at room temperature given in table 2, with those actually measured. These results are also shown in fig. 15. It can be seen that the predictions are in quite reasonable agreement with the pipe test results. The net-section collapse-failure criterion can be extended to determine the conditions under which a leak-before-break failure would be expected for a given part-through crack in the pipe wall. This is done by assuming that the unbroken ligament for the part-through crack fails during the stable crack-growth process. Hence, the applied load,_'ngrequired to experience a leak condition is that giving a net-section collapse using the flow stress corresponding to the onset of stable growth. The maximum load calculation is based on the part-through crack becoming a throughwall crack of length equal to the greatest circumferen-

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tial dimension of the original part-through crack. The net-section collapse using the flow stress associated with instability is then calculated. Some illustrative calculations based on rectangularshaped cracks in 100-mm (4-in) pipes are given in table 4 and for 710-mm (28-in.) pipes in table 5. In these calculations M B denotes the applied bending moment required for complete rupture of the pipe - the 'break' condition - while ML denotes the applied bending moment for rupture of the ligament - the 'leak' condition. The parameter x denotes the ratio of the initial crack depth to the pipe wall thickness. The conditions assumed in the calculations presented in table 4 encompass the typical BWR recirculation bypass line cracks shown in figs. 1 and 2. Consequently, these results can provide a rough guide for

Table 3 Comparison of predicted bending moments at failure based on net-section collapse criterion in 100-mm diameter circumferentially cracked pipes with results obtained from full-scale tests at ambient temperature Full-scale pipe test number

Initial crack length (cm)

Internal pressure at failure (MPa)

Bending moment at failure Experimental (Nm)

Predicted (Nm)

Percent difference

1 2

13.3 7.6

7.23 17.2

9435 13 800

8600 15 100

-9.8 +9.4

128

M..F. Kanninen et al. / Fracture mechanics predictive capability for reactor piping

Table 4 Calculated results on 100-ram (4-in.) diameter pipes with circumferential part-through cracks 2~ (degrees)

MB (in.-lbs.)

ML/M B (Nm)

x = 0.4

x = 0.6

x = 0.8

x = 0.9

Case I: T= 75°F (24°C),p = 1050 psig (7.23 MPa) 30 285 000 (17 500) 1.02 60 232 000 (14 300) 1.17 90 180 000 (1 l 100) 1.42 120 131 000 (8050) 1.85 150 87 000 (5300) 2.65 180 50 000 (3100) 4.45

0.99 1.09 1.26 1.56 2.12 3.39

0.95 1.01 1.09 1.25 1.54 2.20

0.94 0.96 1.01 1.08 1.23 1.56

Case II: T = 400°F (205°C), p = 1050 psig (7.23 MPa) 30 225 000 (13 800) 0.87 60 183 000 (11 200) 1.01 90 141 000 (8700) 1.23 120 101 000 (6200) 1.61 150 66 000 (4100) 2.36 180 36 000 (2200) 4.17

0.85 0.94 1.09 1.35 1.86 3.12

0.82 0.86 0.93 1.06 1.32 1.95

0.80 0.82 0,85 0.91 1.03 1.33

Case III: T = 500°F (260°C),p = 1050 psig (7.23 MPa) 30 206 000 (12 700) 0.81 60 168 000 (10 300) 0.94 90 129 000 (7900) 1.15 120 92 000 (5700) 1.51 150 59 000 (3600) 2.23 180 31 000 (1900) 4.04

0.79 0.86 1.01 1.26 1.75 2.99

0.76 0.80 0.86 0.98 1.22 1.83

0.74 0.76 0.80 0.84 0.94 1.21

Case IV: T = 400°F (205°C),p = 0 30 230 000 (14 100) 60 191 000 (11 700) 90 152 000 (9300) 120 115 000 (7100) 150 83 000 (5100) 180 55 000 (3400)

0.86 0.99 1.18 1.47 1.97 2.87

0.84 0.93 1.06 1.26 1.62 2.26

0.82 0.86 0.93 1.04 1.22 1.56

0.81 0.83 0.86 0.92 1,01 1.19

Case V: T = 400°F (205°C),p = 2100 psig (14.5 MPa) 30 218 000 (13 400) 0.88 60 172 000 (10 600) 1.03 90 127 000 (7800) 1.29 120 85 000 (5200) 1.80 150 47 000 (2900) 3.07 180 14 000 (860) 9.42

0.84 0.94 1.12 1.46 2.31 6.59

0.81 0.85 0.93 1.09 1.49 3.48

0.79 0.81 0.84 0.90 1.06 1.84

a wide range o f service flaws. The critical flow stress values used in the calculations are based on a linear e x t r a p o l a t i o n o f the data given in table 2. The results shown in tables 4 and 5 indicate that a leak-before-break c o n d i t i o n (i.e. M L / M B < 1) can always be e x p e c t e d if the crack is fairly deep. As the circumferential dimension increases f r o m zero, the depth required to p r o d u c e the leak-before-break

c o n d i t i o n steadily increases to the p o i n t where the ligament thickness for leak-before-break b e c o m e s vanishingly small for crack lengths in excess o f 180 °. N o t e that the results given in table 4 do not corresp o n d to those in table 3 because the temperatures are different and because the special circumstances o f the full-scale pipe tests required a s o m e w h a t differ. ent calculational approach.

M.F. Kanninen et al. / Fracture mechanics predictive capability for reactor piping

129

Table 5 Calculated results on 71-cm (28-in.) diameter pipes with circumferential part-through cracks 2~

MB

ML/M B

(degrees) 106 in.-lb.

(MNm)

x = 0.4

T= 400°F (205°C) andp = 1050 psig (7.23 MPa) 30 31.9 (1.96) 0.87 60 25.0 (1.54) 1.03 90 18.2 (1.12) 1.31 120 11.8 (0.72) 1.88 150 6.0 (0.37) 3.44 180 1.1 (0.068) 17.36

3. Status of a plastic fracture methodology for nuclear components The successful applications of fracture mechanics to date have been mostly based upon the concepts and methodology of linear elastic fracture mechanics (LEFM). However, there are situations where LEFMbased predictions are so conservative that the structure is inordinately penalized. One of these is the application of interest here: the assessment of the margin of safety of flawed nuclear pressure vessels and piping near and beyond general yielding conditions. Rice [13] has provided a starting point for this work. The results described here are primarily based on recent work by Hahn et al. [4] which has proceeded from this basic work. The discussion also reflects the results of parallel programs conducted in this general area by Shill et al. [14] and by Norris et al. [15]. The ongoing research of Hahn et al. [4] encompasses three main stages. First, center cracked panels of a 'toughness-scaled' material are tested to obtain data on crack growth initiation and stable growth. The toughness-scaled materials selected for these experiments exhibit essentially the yield/crack growth character of full thickness A533B pressure vessels but in reduced thicknesses. This device greatly simplifies the testing requirements and thereby allows a much wider range of conditions to be examined than would otherwise be possible. The second stage involves 'generation-phase' analyses. In these calculations the experimentally observed applied stress/stable crack growth behavior is reproduced in a finite element model. Each of a number

x = 0.6 0.84 0.94 1.13 1.50 2.54 11.83

x = 0.8

x = 0.9

0.81 0.85 0.93 1.10 1.57 5.80

0.79 0.80 0.83 0.89 1.07 2.62

of candidate crack initiation and stable growth criteria are evaluated for the material tested. In the third stage, 'application-phase' finite element analyses are performed using one of the candidate criteria to determine applied stress/crack growth behavior for a given geometry. The feasibility and accuracy of the application phase calculations then offers a basis for appraising the various candidate fracture criteria. T_,he fracture criteria examined include the J integral, the crack opening angle, and the conventional LEFM R curve together with a new candidate, the generalized energy release rate ~. The latter corresponds with the energy flowing into a computational process (CP) zone surrounding the tip of the extending crack with c-~ being the critical CP zone energy for crack extension. With the possible exception of the LEFM R curve, each of the candidate criteria evaluated by Hahn et al. is attractive in one way or another. Hence, the task of selecting the best criterion for application to nuclear pressure vessels is not an easy one. In fact, at the time of writing no clear choice has yet emerged. A primary source of the difficulty in selecting a criterion for a plastic fracture methodology is that the basis upon which the choice must be made is not now definitely established. To advance the selection process, some trial selection criteria have been postulated. A current appraisal of the leading approaches - those involving the J integral, the crack opening angle, the generalized energy release rate and the LEFM R curve is given in table 6. The concepts involved in table 6, together with a discussion of the results that the appraisal is based upon, are discussed in what follows.

130

M.F. Kanninen et al. / Fracture mechanics predictive capability for reactor piping

Table 6 Preliminary appraisal of candidate fracture criteria for the basis of a plastic fracture mechanics methodology Possible fracture criteria * Basis of evaluation

CTOA = (CTOA) c

~ =c~

Appraisal of crack driving force parameter yes yes yes

no

yes

Exhibits computational efficiency

yes

yes

yes

yes

no

Has physical significance

no

yes

no

yes

yes

Appraisalof materialresistance parameter no no no

yes

yes

Independent of initial crack length

yes

yes

yes

yes

yes

Possibility of direct measurement

no

no

yes

yes

no

good

good

Computer model independence

Constant during stable growth in same mode

G=R

J = Jc

COA = (COA)c

Overall appraisal of potential for wide-spread use poor good poor * Criteria notation is as follows: G = LEFM-based strain energy release rate (R = critical values of G), J = J integral, COA = average crack opening angle, CTOA = crack tip opening angle, ~= generalized energy release rate (c~ = critical value of ~ ). First o f all, it is important to recognize that the appraisal given in table 6 is based upon a limited set o f experiments and calculations. As described more fully in a recent paper by Hahn et al. [16], experimental data have been obtained and analyzed only on center cracked panels of two toughness-scaled materials: aluminum 2219-T87 and 7075-T73. Generation-phase calculations were performed for three different initial crack lengths. While these results have sufficed to delineate many of the characteristics of the candidate criteria, additional work must still be performed. In particular, it has not yet been possible to determine whether values determined in one type of fracture specimen will be the same as those determined in another. Clearly, geometry independence is a crucial test o f the acceptability o f a plastic fracture criterion. With these qualifications, some conclusions can be

drawn from the progress made so far. First, the J integral is generally acceptable as a criterion for crack growth initiation and for a limited amount of stable crack growth. It has been used for rough estimates in various situations by Paris et al. [12] (actually, Paris et al. focus on dJ/da) which do not involve extensive stable growth. A J integral-based approach might be expected to be unable to cope with large amounts o f stable crack growth attended by large-scale plasticity. The reason is that it is based upon deformation plasticity which requires small plastic strains and precludes material unloading. Nevertheless, it appears that either a J integral, a crack opening angle, or an energy release rate methodology can cope with large amounts o f stable growth. However, in turn, each o f these has some definite shortcomings which partly offset this advantage. The crack opening angle may seem to be appeal-

M.F. Kanninen et al. / Fracture mechanics predictive capability for reactor piping Two-dimensional continuum region /Two-dimensional continuum [// plasticit, region

elosticlty

__ ~

,/ /

nonlinear deformation region

Fig. 16. Illustration of geometry-dependent and geometryindependent energy dissipation involved in stable crack growth. ing because of its readily grasped physical significance and the opportunity that if offers for direct measurement. However, these may be illusory. First, it should be recognized that there are two different definitions of the crack opening angle. As defined by de Koning [ 11 ], a crack tip value that reflects the actual slopes of the crack faces can be used. This is denoted here as CTOA. Alternatively, as defined by Green and Knott [17], an average value based on the original crack tip position can be used. This is denoted by. COA. While the critical value of the COA can be measured, it is difficult to see how its value has any direct connection with the fracture process. Conversely, while the critical value of the CTOA can likely be associated with the fracture process, it presents a formidable measurement task. In addition, there are clearly

some difficulties in making either value apply to mixed character shear/flat crack growth. The ~ =c~ criterion suffers from the fact that, like its LEFM counterpart, a direct measurement of c;~ is not possible. However, c;~ appears to be a physically meaningful local toughness parameter that is independent of the details of the numerical analysis method used; e.g. a finite element grid size. As pointed out originally by Rice [18], there is a theoretical basis for expecting a dependence of an energy release rate parameter based only on the work of separating the crack faces. This is apparently compensated by the CP zone energy dissipation rate, however. The advantages of the J integral are its virtual independence of finite element type and size and the computational ease involved in evaluating it. Its disadvantage is that it cannot be a true measure of the fracture energy. This is reflected by the fact that Jc continually increases with stable crack growth. Yet, as the alternative parameters make clear, the energy required to continue the fracture process does not increase. The inescapable conclusion is that Jc also includes the energy dissipated in plastic deformation remote from the crack tip. This may well be geometry dependent. Paris et al. [12] have suggested that (dJ/da)c may not suffer from this shortcoming, but conclusive proof is currently lacking. A proper stable crack growth criterion must delinate between the energy dissipated in direct fracture-related process near the crack tip and energy dissipated in geometry-dependent plastic deformation remote from the crack tip. Fig. 16 illustrates this

Table 7 Representative elastic-plastic fracture mechanics analyses based on an energy balance concept Ref.

Investigators

Concept

[4] [5 ]

generalized energy release rate crack-tip work rate

AR/As

separation energy rate

GA

[ 7]

Hahn et al. (USA) de Koning (The Netherlands) Kfouri and Miller (England) Hellan (Norway)

specific crack extension work

C

[ 8]

Carlsson (Sweden)

net energy-release rate

G*

[9]

Cotterell and Reddel (Australia) Andrews and Billington

specific essential work

we

apparent energy-releaserate

-dE/dA

[6]

[ 10]

(England)

131

Crack driving force symbols

M.F. Kanninen et al. / Fracture mechanics predictive capability for reactor piping

132

demarcation. In addition to Hahn et al. [4], a number of other investigators have opted for a generalization of the LEFM energy release rate as the basic plastic fracture methodology parameter to achieve this. Table 7 indicates the variety of names and symbols that have been attached to essentially the same concept pursued independently by these investigators. The inherent difficulty caused by the dependence on the computational model has not yet been resolved. But, as argued by Kfouri and Rice [19], for example, this can be circumvented by appealing to micromechanical considerations. At the same time CTOA and J based approaches also remain viable possibilities. First, the measurement difficulties for CTOA may have been overcome. Some success has been achieved in extending infiltration techniques for replicating crack profiles to the tip of a stably growing crack. Secondly, while it is possible to obtain closed-form solutions for stable crack growth - for examples, see Shih and Hutchinson [20] and Amazigo and Hutchinson [21] -

.....

iiii

ooobs

iii-P

~

1 5 1 , 0 0 0 ~bs

P = ~60,000

tbs

P : 175,000 Ini~lOtlOtt

Ibs

4. Discussion and conclusions

P ~ { 8 2 , 0 0 0 Ibs Maximum Lood

~

P = 168,000

Ibs

P = 124,000

P = 83,000

these will be limited to highly idealized conditions for some time to come and, consequently, finite element computations will provide the only practical way of addressing nuclear pressure vessel and piping problems of concern. Because of their inherent computational efficiency, CTOA and J based approaches are therefore highly attractive. It is also conceivable that future work may not need to focus on an explicit parameter at all. Both and (COA)c may be related to a measure of the resistance of the material to the initiation of growth, e.g. Jxc- If this proves to be correct, the most useful parameter will be one that will serve only an operational function in the calculations. It will not need to be measured (or even specified) externally. Consequently, computational model dependence and other deficiencies may prove to be a moot point. Further work is in progress to develop this possibility. The results will be reported subsequently [22]. Finally, it must be recognized that the problem of immediate concern in this paper - the failure of type 304 stainless steel piping - offers additional complications beyond those presently being addressed. In addition to the effect of the pipe geometry, stable crack growth in type 304 stainless steel is accompanied by very large plastic deformation. This is illustrated in fig. 17 which shows the crack shape at varying stages in the flat-plate experiment CCT-1. Clearly, more involved analyses are required to treat these materials than have so far been used.

Ibs

Ibs

Ru p t u re

Fig. 17. Development of crack growth in flat-plate experiment CCT-1.

Work aimed specifically at developing a fracture criterion for ductile materials such as BWR piping requires an integrated program of theoretical analysis and experiment. Such a program will involve smallscale laboratory experiments, finite-element computations, and full-scale component testing. By using the experiments and finite-element computations in combination, criteria governing the onset of growth and the stable crack-growth regime may be determined. However, in BWR piping a simpler alternative procedure was made possible by the finding that the onset of crack growth and fracture for a wide range of crack sizes in type 304 stainless steel could be correlated with temperature-dependent net-section flowstress values. These values can be used to obtain a

M.F. Kanninen et al. / Fracture mechanics predictive capability for reactor piping

simple, but accurate way of estimating the margin of safety in reactor piping containing circumferential cracks. The possibility of a leak-before-break condition can also be examined using these data. Other significant facts about the failure process emanating from a circumferential crack in a weld heat-affected zone in Type 304 stainless steel were found in this program: (1) Because of the substantial crack tip blunting that precedes crack growth, the applied stress at failure is virtually independent of the sharpness of the initial flaw. (2) The presence of the weld and the sensitization of the material surrounding the flaw do not significantly affect the applied stress at failure. (3) The exact shape of the flaw is o f considerably less importance than the area of the flaw (or of the net flaw area when multiple flaws exist) in determining the applied stress at failure. It was also found that a critical value o f the 'cracktip stretch' parameter - defined as the elongation of a material element immediately ahead of the crack tip - of about 2.5 mm could be used as a fracture parameter in a fracture mechanics approach to the problem. Current work aimed at the development of an elastic-plastic fracture methodology for reactor grade steels is examining a wide range of crack-tip fracture criteria. Of these, the most prominent are the crack-opening angle, the J integral, and a generalized energy-release parameter. Values of these parameters are computed by forcing a finite element model to match the applied load-crack lengths observed in center-cracked flat-plate specimens pulled to failure. Critical values of the crack-growth criterion can thereby be inferred from the calculations. These critical values could be used in a finite-element model for a cracked pipe or other structure to calculate the failure load that terminates the stable crack-growth period. Guided by current results, the paper appraises the various candidates for a fracture criterion applicable to reactor materials and concludes that, while several have definite merit, no one clearly superior parameter has yet been identified.

133

Acknowledgement This paper is based upon work performed for the Electric Power Research Institute, Palo Alto, California through project numbers RP585-1 and RP601-1. The authors would like to express their appreciation to T. Marston, R. Smith, T. Oldberg, and K. Stahlkopf of EPRI for their support of this work.

References [1] H.H. Kelpfer et al., Report No. NEDO-21000-1, 75 NED 35, The General Electric Co., San Jose, CA, July (1975). [2] C.F. Cheng, W.A. Ellingson and J.Y. Park, Corrosion]76, Houston, "IX March, 1976). [3] M.F. Kanninen, D. Broek, C.W. Marschall, E.F. Rybicki, S.G. Sampath,F.A. Simonen and G.M. Wilkowski, EPRI NP-192, Battelle's Columbus Laboratories Report to the Electric Power Research Institute, Sept. (1976). [4] G.T. Hahn et al,, Methodology for Plastic Fracture, BatteUe's Columbus Laboratories Reports to the Electric Power Research Institute (1976-1977). [5] A.U. de Koning, 14th IUTAM Congress, Delft, The Netherlands, 30 Aug. - 4 Sept. (1976). [6] A.P. Kfouri and K.J. Miller, Proc. Inst. Mech. Eng. 190 (1976) 571. [7] K. Helian, Eng. Fracture Mech. 8 (1976) 501. [8] A.J. Carlsson, 14th IUTAM Congress, Delft, The Netherlads, 30 Aug.-4 Sept. (1976). [9] B. CottereU and J.K. Reddel, Int. J. Fracture 13 (1977) 267. [10] E.H. Andrews and E.W. Billington, J. Mater. Sci. 11 (1976) 1354. [11] K.B. Broberg, J. Mech. Phys. Solids 23 (1975) 215. [12] P.C. Paris et al., Washington University Report to the Nuclear Regulatory Commission, NUREG-0311 (1977). [13] J.R. Rice, in: The Mechanics of Fracture, F. Erdogan, ed. ASME Publication AMD, vol. 19 (1976) p. 23. [14] C.F. Shih et aL, Methodology for Plastic Fracture, General Electric Company (Corporate Research and Development) Reports to the Electric Power Research Institute (1976-1977). [15] D.M. Norris, Jr. et al., Fundamental Study of Crack Initiation and Propagation, Lawrence Livermore Laboratories Reports to the Electric Power Research Institute (1976-1977). [16] G.T. Hahn, D. Brock, C.W. Marschall, A.R. Rosenfeld, E.F. Rybicki, D.W. Schmueser, R.B. Stonesifer and M.F. Kanninen, Conference on Tolerance of Flaws in Pressurized Components, London, 16-18 May (1978). [17] G. Green and J.F. Knott, J. Mech. Phys. Solids 23 (1975) 167. [18] J.R. Rice, Proc. 1st Int. Conf. on Fracture, vol. 1

134

M.b: Kanninen et al. / Fracture mechanics predictive capability for reactor piping

(Japanese Society for Strength and Fracture, Tokyo, 1966) p. 309. [19] A.P. Kfouri and J.R. Rice, Proc. 4th Int. Conf. on Fracture, vol. 1 (Univ. Waterloo Press, 1977) p. 43. [20] C.F. Shih and J.W. Hutchinson, J. Eng. Mater. Technol. 98 (1976) 289.

[21] J.C. Amazigo and J.W. Hutchinson, J. Mech. Phys. Solids 25 (1977) 81. [22] M.F. Kanninen, E.F. Rybicki, R.B. Stonesifer, D. Broek, A.R. Rosenfield, C.W. Marschall and G.T. Hahn, ASTM Symposium on Elastic-Plastic Fracture, Atlanta, GA, 16-18 Nov. (1977).