NUREG/CR-6879 

ANL-05/16

Steam Generator Tube Integrity 

Issues: Pressurization Rate 

Effects, Failure Maps, Leak Rate 

Correlation Models, and Leak 

Rates in Restricted Areas 

Office of Nuclear Regulatory Research 
NUREG/CR-6879 

ANL-05/16 

Steam Generator Tube Integrity 

Issues: Pressurization Rate 

Effects, Failure Maps, Leak Rate

Correlation Models, and Leak 

Rates in Restricted Areas 

Manuscript Completed: October 2008 

Date Published: July 2009 

Prepared by 

S. Majumdar, K. Kasza, S. Bakhtiari, J.Y. Park, J. Oras 

J. Franklin, C. Vulyak, and W.J. Shack 

Nuclear Engineering Division 

Argonne National Laboratory 

9700 South Cass Avenue 

Argonne, IL 60439 

M. Stambaugh, NRC Project Manager 

NRC Job Code N6582 

Office of Nuclear Regulatory Research 
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iii 

Abstract 

This report summarizes results obtained under the Third International Steam Generator 

Tube Integrity Program (ISG–TIP–3). Tests were conducted to determine the effect of 

pressurization rate on rupture of flawed tubes. Based on analysis and tests, failure maps were 

developed that delineate ranges of ligament and crack sizes that could be susceptible to ligament 

rupture and/or unstable burst due to pressure drops of PNO (normal operation), PMSLB (main 

steam-line break), 1.4PMSLB, and 3PNO. Tests were conducted to determine the limits of 

applicability with respect to the through wall crack length and crack tightness of the simple orifice 

model for predicting leak rates of cracked tubes. Finally, leak rates were calculated for degraded 

tubes in restricted areas during postulated design-basis and severe accident conditions. 
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Foreword 

This report discusses a study conducted by Argonne National Laboratory (ANL), under 

contract to the U.S. Nuclear Regulatory Commission (NRC), to evaluate four different steam 

generator (SG) tube integrity topics. 

The first topic examines the effect of pressurization rate on steam generator (SG) tube burst 

pressure. Industry tests of pressurization rate suggest that rate has a significant effect. ANL 

noted industry’s use of inconsistent test procedures. Argonne laboratory conducted these tests 

using more consistent test procedures. The results showed that the pressurization rate had a 

small effect which increases as the flaw size decreases. 

In the second section, finite element calculations were used to develop failure maps for 

ligamented flaws. Stress corrosion cracks generally consist of multiple cracks separated by 

ligaments. Although ligament geometries may be complex, this study idealized the ligaments as 

radial, axial, or circumferential. At a SG tube rupture point, partial-throughwall radial cracks 

become throughwall. By contrast, the rupture of axial or circumferential ligaments results in 

longer cracks, which could subsequently rupture under normal or accident conditions. The ANL 

failure maps show the range of ligament and crack sizes that would be susceptible to ligament 

rupture during normal or accident conditions. 

The applicability of an orifice flow model is examined in the third topic of this NUREG. ANL 

conducted tests to establish orifice flow model leak rates. The results show that the orifice flow 

model remains valid when the length of the orifice (i.e., the tube wall thickness) is less than 

approximately five times the hydraulic diameter of the flaw. 

The final section examines the leak rate from flaws located under the tube support plate 

(TSP) during a postulated main steam line break (MSLB) and under severe accident conditions. 

ANL analyzed and predicted the flaw opening area during a postulated MSLB and the expected 

leak rates from cracks located under the TSP. Results indicate that the size of a crack opening 

and leak rate may be affected by SG tube contact with the tube support plate. 

 This research may be used by the NRC in assessment of industry SG tube integrity 

evaluations. The results may be useful to NRC staff during reviews of license amendment requests 

and other licensing actions. Regional inspectors may also find the information valuable when 

verifying proper implementation of licensee steam generator programs. 

Michael J. Case, Director 

Division of Engineering 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 
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vii 

Contents 

Abstract................................................................................................................................ iii

Foreword .............................................................................................................................. v

Executive Summary............................................................................................................ xvii

Acknowledgments ................................................................................................................. xxi

List of Acronyms .................................................................................................................. xxiii

List of Symbols .....................................................................................................................xxv

1 Pressurization Rate Effect on Burst Pressure .................................................................. 1

1.1 Introduction ........................................................................................................... 1

1.2 Factors Influencing Tests to Determine Pressurization Rate Effect .......................... 1

1.2.1 Initial test series....................................................................................... 2

1.3 Test Specimens for the Second Series ..................................................................... 4

1.4 Test Procedure for the Second Series ...................................................................... 5

1.5 Test Results for the Second Series .......................................................................... 5

1.5.1 Tests on 25 mm (1 in.) Long EDM Flaws................................................... 5

1.5.2 Tests on Short EDM Flaws ....................................................................... 7

1.5.3 Tests on Stress Corrosion Cracks ............................................................. 7

1.6 Analysis of Test Results .......................................................................................... 7

1.6.1 Predicted Failure Pressures...................................................................... 7

1.6.2 Post-Test Observations of Specimens ....................................................... 9

1.7 Conclusions............................................................................................................ 9

2 Failure Maps for Complex Multiple Cracks...................................................................... 11

2.1 Introduction ........................................................................................................... 11

2.2 Background Analysis and Tests .............................................................................. 13

2.2.1 Throughwall Axial Cracks......................................................................... 13

2.2.2 Part–Throughwall Axial Cracks................................................................. 15

2.3 Parametric Analyses for Axial Throughwall Cracks ................................................. 16

2.4 Generation of Failure Maps..................................................................................... 22

2.4.1 Failure Maps for Normal Operation (PNO)............................................... 22
viii 

2.4.2 Failure Maps for Main Steam Line Break Pressure (PMSLB) ................... 25

2.4.3 Failure Maps for 1.4xMain Steam Line Break Pressure (1.4PMSLB)........ 28

2.4.4 Failure Maps for 3xNormal Operating Pressure (3PNO)........................... 31

2.5 Discussion and Conclusions................................................................................... 34

3 Leak Rate Studies ........................................................................................................... 37

3.1 Introduction ........................................................................................................... 37

3.2 Test Procedure........................................................................................................ 37

3.3 Test Results............................................................................................................ 38

3.3.1 Stage 1 Room Temperature Test Results................................................... 38

3.3.2 Stage 2 High Temperature Test Results Under MSLB Condition ............... 44

3.4 Leak Rate Model ..................................................................................................... 49

3.5 Conclusions............................................................................................................ 53

4 Leak Rates in Restricted Areas ........................................................................................ 55

4.1 Introduction ........................................................................................................... 55

4.2 Currently Available Leak Rate Data ........................................................................ 55

4.2.1 Westinghouse/EPRI Tube/TSP Data ........................................................ 55

4.2.2 Dampierre-1 Tube/TSP Data.................................................................... 57

4.2.3 Tube/Tube-Sheet Data from a Retired Steam Generator........................... 58

4.3 Analyses of Crack Opening Area and Leak Rate ...................................................... 59

4.3.1 Leak Rate Correlation for MSLB ............................................................... 60

4.3.2 Leak Rate Correlation for Severe Accidents............................................... 60

4.3.3 Material Properties Used in Analysis......................................................... 61

4.4 Results ................................................................................................................... 62

4.4.1 Main Steam-Line Break (MSLB) Conditions .............................................. 62

4.4.2 Severe Accident Conditions ...................................................................... 66

4.5 Effect of Crevice Deposits on Crack Opening and Leak Rate ................................... 69

4.6 Conclusions............................................................................................................ 71

5 References.............................................................................................................. 73
ix 

Figures 

1. Notch depth profile for Type 14 specimen. mp denotes radial ligament stress 

magnification factor. ....................................................................................................... 2

2. Type A: single rectangular notch and Type B: single trapezoidal notch. ........................... 4

3. Type C: 2–colinear notches (axial ligament) and Type D: 2–offset notches 

(circumferential ligament)................................................................................................ 5

4. Predicted vs. observed ligament rupture pressure for quasi–static to 14 MPa /s (2 

ksi/s) tests...................................................................................................................... 8

5. Variation of (a) test ligament rupture pressures and (b) normalized test ligament 

rupture pressures with pressurization rate. .................................................................... 9

6. Typical stress corrosion crack geometry. ......................................................................... 11

7. Idealized single part–throughwall axial crack with a radial ligament................................ 12

8. Two idealized part–throughwall axial cracks each with a radial ligament at the 

through-thickness crack tip and separated from each other by either an axial (Type 

C) or a circumferential (Type D or Type E) ligament......................................................... 12

9. Two-TW axial notches separated by (a) an axial ligament (Type C ) and (b) a 

circumferential ligament (Type D).................................................................................... 13

10. Engineering and true stress–strain curves of Alloy 600 used for finite element 

analysis........................................................................................................................... 14

11. Calculated variation of average inter–notch axial ligament thickness with pressure 

using finite deformation analyses by ANSYS and ABAQUS for two 6–mm (0.25–in.) 

long axial cracks separated by a 0.25–mm (0.01–in.) long axial ligament (Type C). .......... 14

12. Predicted (by FEA, line) vs. observed (symbols) variation of ligament rupture 

pressure with circumferential ligament length for type D specimens having two 6–

and 13–mm long TW notches. ......................................................................................... 15

13. Predicted (line) and observed (symbols) radial through–thickness ligament rupture 

pressures vs. axial or circumferential ligament lengths for two PTW EDM notches (a) 

6–mm (0.25–in.) and (b) 13–mm (0.5–in.) long. ................................................................ 16

14. Specimens with two throughwall axial cracks, separated by (a) an axial ligament 

(Type C) and (b) a circumferential ligament (Type D), analyzed by FEA. ........................... 17

15. Specimens with (a) four and (b) six axial throughwall cracks analyzed by FEA. ............... 17

16. Axial ligament rupture pressure for two throughwall axial cracks separated by an 

axial ligament.................................................................................................................. 17

17. Variation of fitting parameters (a) a1 and (b) a2 with crack length (in mm) for 

specimens with two throughwall axial cracks separated by an axial ligament.................. 18
x 

18. Axial ligament rupture pressure for four throughwall axial cracks separated by 

three equally long axial ligaments. Symbols represent FEA results and lines are 

polynomial fits of the FEA results to Eq. 1....................................................................... 18

19. Variation of fitting parameters (a) a1 and (b) a2 with crack length (in mm) for 

specimens with four throughwall axial cracks separated by three axial ligaments.. ......... 19

20. Axial ligament rupture pressure for six throughwall axial cracks separated by five 

equally wide axial ligaments. Symbols represent FEA results and lines are 

polynomial fits of the FEA results to Eq. 1....................................................................... 19

21. Variation of fitting parameters (a) a1 and (b) a2 with crack length for specimens 

with six throughwall axial cracks separated by five axial ligaments................................. 20

22. Circumferential ligament rupture pressure for two throughwall axial cracks 

separated by a circumferential ligament.......................................................................... 20

23. Variation of fitting parameters M0, M1, and M2 with crack length for specimens 

with two throughwall axial cracks separated by a circumferential ligament..................... 21

24. Effects of axial and circumferential ligament widths on ligament rupture pressure of 

two 12 mm 100%TW axial cracks separated by axial or circumferential ligaments 

(total crack length = 25 mm) ........................................................................................... 21

25. Failure map of a single crack at normal operating pressure PNO................................... 23

26. Failure maps for SG tubes with two 90% deep axial cracks separated by (a) an axial 

ligament (Type C) and (b) a circumferential ligament (Type D) at normal pressure 

(PNO)............................................................................................................................. 24

27. Failure maps for SG tubes with (a) four and (b) six 90% deep axial cracks separated 

by axial ligaments at normal pressure (PNO). "Crack length" denotes the total 

overall length of the individual cracks and ligaments. ..................................................... 25

28. Failure map of a single crack at main steam line break pressure PMSLB. ..................... 25

29. Failure maps for SG tubes with two 90% deep axial cracks separated by (a) an axial 

ligament (Type C) and (b) a circumferential ligament (Type D) at main steam line 

break pressure (PMSLB). "Crack length" denotes the total overall length of the 

individual cracks and ligaments...................................................................................... 26

30. Failure maps for SG tubes with two 80% deep axial cracks separated by (a) an axial 

ligament (Type C) and (b) a circumferential ligament (Type D) at main steam line 

break pressure (PMSLB). "Crack length" denotes the total overall length of the 

individual cracks and ligaments...................................................................................... 26

31. Failure maps for SG tubes with four axial cracks, (a) 90% and (b) 80% deep, 

separated by three axial ligaments (Type C) at main steam line break pressure 

(PMSLB). "Crack length" denotes the total overall length of the individual cracks 

and ligaments ................................................................................................................. 27
xi 

32. Failure maps for SG tubes with six axial cracks, (a) 90% and (b) 80% deep, 

separated by five axial ligaments (Type C) at main steam line break pressure 

(PMSLB). "Crack length" denotes the total overall length of the individual cracks 

and ligaments. ............................................................................................................... 28

33. Failure map of a single crack at 1.4 times main steam line break pressure 

1.4pMSLB. .................................................................................................................... 28

34. Failure maps for SG tubes with two 90% deep axial cracks separated by (a) an axial 

ligament (Type C) and (b) a circumferential ligament (Type D) at 1.4 times main 

steam line break pressure (1.4PMSLB). "Crack length" denotes the total overall 

length of the individual cracks and ligaments.................................................................. 29

35. Failure maps for SG tubes with two 80% deep axial cracks separated by (a) an axial 

ligament (Type C) and (b) a circumferential ligament (Type D) at 1.4 times main 

steam line break pressure (1.4PMSLB). "Crack length" denotes the total overall 

length of the individual cracks and ligaments.................................................................. 30

36. Failure maps for SG tubes with four axial cracks, (a) 90% and (b) 80% deep, 

separated by three axial ligaments (Type C) at 1.4 times main steam line break 

pressure (1.4PMSLB). "Crack length" denotes the total overall length of the 

individual cracks and ligaments...................................................................................... 30

37. Failure maps for SG tubes with six axial cracks, (a) 90% and (b) 80% deep, 

separated by five axial ligaments (Type C) at 1.4 times main steam line break 

pressure (1.4PMSLB). "Crack length" denotes the total overall length of the 

individual cracks and ligaments...................................................................................... 31

38. Failure map of a single crack at 3 times normal operating pressure 3PNO. .................. 31

39. Failure maps for SG tubes with two 90% deep axial cracks separated by (a) an axial 

ligament (Type 2) and (b) a circumferential ligament (Type 4) at 3 times normal 

operating pressure (3PNO). "Crack length" denotes the total overall length of the 

individual cracks and ligaments...................................................................................... 32

40. Failure maps for SG tubes with two 80% deep axial cracks separated by (a) an axial 

ligament (Type C) and (b) a circumferential ligament (Type D) at 3 times normal 

operating pressure (3PNO). "Crack length" denotes the total overall length of the 

individual cracks and ligaments...................................................................................... 33

41. Failure maps for SG tubes with four axial cracks, (a) 90% and (b) 80% deep, 

separated by three axial ligaments (Type C) at 3 times normal operating pressure 

(3PNO). "Crack length" denotes the total overall length of the individual cracks and 

ligaments. ....................................................................................................................... 33

42. Failure maps for SG tubes with six axial cracks, (a) 90% and (b) 80% deep, 

separated by five axial ligaments (Type C) at 3 times normal operating pressure 

(3PNO). "Crack length" denotes the total overall length of the individual cracks and 

ligaments. ....................................................................................................................... 34

43. Stage 1 leak–rate behavior of ODSCC axial Flaw (a) SGL750 and (b) SGL905 under a 

constant pressure of 17.2 MPa (2500 psi) with room–temperature water......................... 39
xii 

44. Stage 1 leak–rate behavior of ODSCC axial flaw (a) SGL904 and (b) SGL911 under 

constant pressure of 17.2 MPa (2500 psi) with room–temperature water......................... 39

45. SCC axial flaw SGL750–OM–3/19/03. ............................................................................ 40

46. SCC axial flaw SGL904–OM–1/15/03. ........................................................................... 40

47. SCC axial flaw SGL905–OM–3/24/03. ............................................................................ 40

48. SCC axial flaw SGL911–OM–2–1/20/03.......................................................................... 41

49. Magnified image of feature sf1 in SCC flaw SGL904–OM, which appears to be an 

intact or possibly torn ligament....................................................................................... 41

50. Image analysis line drawn between the end points of SCC flaw SGL905–OM used to 

calculate flaw length........................................................................................................ 42

51. Image analysis line drawn around the crack perimeter of SCC flaw SGL905–OM by 

the wand method to define the opening........................................................................... 42

52. Crack opening of SCC flaw SGL905–OM highlighted by the threshholding method.......... 42

53. Stage 2 SCC axial flaw SGL750 after the high temperature test....................................... 46

54. Stage 2 SCC axial flaw SGL 904 after the high temperature test...................................... 46

55. Stage 2 SCC axial flaw SGL905–BDTF–4/15/03.............................................................. 46

56. Stage 2 SCC axial flaw SGL911 after the high temperature test....................................... 46

57. Comparison of crack opening areas at the ID and OD for a 12.7 mm (0.5 in.) crack 

at 288°C. Results are shown for finite–element solutions using solid and shell 

elements as well as the analytical solution of Zahoor. ................................................... 48

58. Comparison of crack opening areas at the ID and OD for a 19.0 mm (0.75 in.) crack 

at 288°C. Results are shown for finite–element solutions using solid and shell 

elements as well as the analytical solution of Zahoor....................................................... 48

59. L/D for cracks in SG tubes under normal operating pressures and MSLB 

conditions. The flow length L is taken as the wall thickness and the hydraulic 

diameter D is 2, where  is the average cracking opening............................................... 50

60. Test results from Amos and Schrock8 on flashing as a function of stagnation 

pressure and subcooling for (a) L/D=85 and (b) L/D=135. Numbers next to symbols 

denote location of flashing in cm from entrance (wall thickness=6.35 cm)... .................... 50

61. Flow loss factor as a function of L/D for Amos and Shrock slit tests8 and tests on 

SG tubes......................................................................................................................... 52

62. Gap flow area for a tube with an axial crack inside the TSP............................................. 56

63. Correlation of leak rate data with (a) throughwall crack opening area and (b) limiting 

flow area. ........................................................................................................................ 57
xiii 

64. Optical metallography of a cross-section parallel to the tube axis at the maximum 

EC signals for TS0601 Alloy 600 SG tube specimen R39C43 near the TTS. ..................... 59

65. A throughwall circumferential ODSCC with crack branching in specimen No. 9 just 

below the top of the tube sheet. The crack opening is about 0.04 mm. .......................... 59

66. Finite element model of the tube-to-TSP junction............................................................ 60

67. True stress-plastic strain curves for Alloy 600................................................................. 61

68. Creep rate properties of Alloy 600. .................................................................................. 62

69. Axial variation of radial gap between crack flank and the inner surface of the TSP 

tube hole with pressure for (a) 13 mm (0.5 in.) and (b) 19 mm (0.75 in.) axial cracks 

at 300°C.......................................................................................................................... 63

70. Variation of gap opening area, OD crack opening area, and ID crack opening area 

with pressure for (a) 13 mm ( 0.5 in.) and (b) 19 mm (0.75 in.) axial crack at 300°C........ 63

71. Variation of leak rate with pressure for (a) 13 mm ( 0.5 in.) and (b) 19 mm (0.75 in.) 

axial crack at 300°C........................................................................................................ 64

72. Circumferential variation of radial gap between crack flank and the inner surface of 

the TSP tube hole with pressure for (a) 180° and (b) 240° cracks at 300°C. ..................... 64

73. Radial gap variation between the tube OD surface and the TSP hole/wall for 90, 

180, and 240° circumferential cracks at the postulated MSLB condition......................... 65

74. Variation of gap opening area and ID crack opening area with pressure for (a) 90° 

and (b) 180° circumferential crack at 300°C.................................................................... 65

75. Variation of gap opening area and ID and OD crack opening areas with pressure for 

a 240° circumferential crack. .......................................................................................... 66

76. Variation of leak rate with pressure for 90, 180, and 240° cracks at 300°C. .................... 66

77. Variation of (a) temperature and (b) pressure with time assumed for severe accident 

analysis........................................................................................................................... 67

78. Axial variation of radial gap between crack flank and the inner surface of the TSP 

tube hole with time for (a) 13 mm (0.5 in.) and (b) 19 mm (0.75 in.) axial cracks at a 

pressure of 17 MPa (2.5 ksi)............................................................................................ 67

79. Variation of gap opening area, OD crack opening area, and ID crack opening area 

with time for (a) 13 mm ( 0.5 in.) and (b) 19 mm (0.75 in.) axial crack. ............................ 68

80. Variation of leak rate with time for (a) 13 mm (0.5 in.) and (b) 19 mm (0.75 in.) axial 

crack............................................................................................................................... 68

81. Variation of gap opening area and ID crack opening area with time for (a) 90° and 

(b) 180° circumferential crack. ........................................................................................ 69
xiv 

82. Variation of gap opening area and ID and OD crack opening areas with time for 

240° circumferential crack. ............................................................................................. 69

83. Variation of leak rate with time for 90°, 180°, and 240° circumferential cracks 

during a postulated severe accident. ............................................................................... 69

84. Effect of elastic modulus of sludge on the crack opening displacement of 13 mm 

(0.5 in.) axial crack.......................................................................................................... 70
xv 

Tables 

1. Ligament rupture pressures for < 25 mm (1 in.) long, part–throughwall rectangular 

EDM flaws with and without bladder............................................................................... 3

2. Unstable burst pressures (Stage 2) for < 25 mm (1 in.) long, part–throughwall and 

throughwall rectangular EDM flaws with and without bladder and foil............................ 4

3. EDM flaw ligament rupture pressure (Stage 1) for four flaw types (Types A, B, C, 

and D in Figs. 2–3) and five different pressurization rates. .............................................. 6

4. EDM flaw unstable burst pressure (Stage 2) for four flaw types (Types A, B, C, and 

D in Figs. 2–3) and five different pressurization rates. ..................................................... 6

5. Axial crack lengths and opening areas after the RT tests................................................. 43

6. Variation of gap width along the crack, average gap, flaw length, and area...................... 44

7. Crack opening geometries and flow behavior in tests at 288°C. ....................................... 47

8. Comparison of orifice model predictions and experimental results for the RT tests.......... 49

9. Comparison of orifice model predictions and experimental results for the tests at 

288°C for different back–pressures.................................................................................. 49

10. A summary of leak test data for tube/TS specimens from the retired SG. Note 1000 

psi = 6.895 MPa and 1 gallon = 3.8 L. ............................................................................. 58

 xvii 

Executive Summary 

This report summarizes results on four topics obtained under the Third International Steam 

Generator Tube Integrity Program (ISG–TIP–3). 

A Pressurization rate effects on flawed tube rupture pressure 

The question of whether ligament rupture pressure or unstable burst pressure may vary 

significantly with pressurization rate at room temperature arose from the results of pressure tests 

by Westinghouse on tubes with machined part–throughwall notches. Slow (quasi–static) and fast 

14 MPa/s (2000 psi/s) pressurization rate tests on specimens with nominally the same notch 

geometry appeared to show a significant effect of the rate of pressurization on the unstable burst 

pressure. Unfortunately, the slow and fast loading rate tests were conducted following two 

different test procedures, which could confound the results. The current series of tests were 

conducted on a variety of specimen geometries using a consistent test procedure to better 

establish the effect of pressurization rate. 

Tests conducted on specimens with 25 mm (1 in.) long rectangular or trapezoidal notches 

and specimens with two rectangular notches separated by an axial or circumferential ligament did 

not show a significant effect of pressurization rate effect on the ligament rupture or unstable burst 

pressure. The tests show a small effect of pressurization rate on ligament rupture pressure for 

rates > 7 MPa/s (1000 psi/s) for rectangular notches < 25 mm (1 in.) long with shorter notches 

experiencing slightly greater rate effects than longer ones. However, the observed increases in 

ligament rupture pressure at 14 MPa/s (2000 psi/s), which is the upper limit for most laboratory 

and field pressure tests, are ≤ 10%. This is within the scatter band of the data for quasi–static 

loading. Post–test observation of the 6.35–, 19.05–, and 25.4–mm (1/4–, 3/4–, and 1–in.)–long 

notches indicates large, local, radial bulging deformation around the flaw for all the flaws, but the 

notches < 25–mm (1–in.)–long also experience significant bulk plastic strain away from the flaw 

because the nominal stress in these specimens exceeds the yield strength. The general level of 

plastic deformation diminishes with increasing flaw size, because the larger flaws undergo 

ligament rupture at lower pressures so that the bulk of the tube away from the flaws remains 

elastic. Because strain rate effects on plastic deformation are typically much greater than on 

elastic deformations, the apparent pressurization rate effect observed for the shorter flaws at 

pressurization rates > 7 MPa/s (1000 psi/s) may be the result of the increased overall plastic 

deformation in the tubes. No conclusions can be drawn regarding the effect of pressurization rate 

on unstable burst pressure of initially 100% throughwall notches < 25 mm (1 in.) long because of 

lack of sufficient data. 

Burst pressure results can be affected by pressurization rate, bladder and foil sizes, and 

difference between as-built and nominal geometries of notches. The testing parameters (bladder 

and foil size, lubrication) recommended by the current EPRI guidelines were found to give reliable 

unstable burst pressure and ligament rupture pressure results without any artifact. We found no 

pressurization rate effect on unstable burst pressure or ligament rupture pressure below 1000 

psi/s, which supports the current industry practice of limiting the pressurization rate during insitu testing to 1.4 MPa/s (200 psi/s). In the past, pressurization rates of up to 14 MPa/s (2000 

psi/s) have been used, which may have artificially increased the ligament rupture pressures in 

those tests by up to 10% for flaws less than 25 mm (1 in.) long. 
 xviii 

B Failure maps for complex multiple cracks 

Stress corrosion cracks generally consist of multiple cracks separated by ligaments rather 

than a single, planar crack. Although ligament geometry can be very complex, it can be idealized 

as being either radial (part–throughwall cracks), purely axial (Type C), or purely circumferential 

(Type D). During pressurization, the rupture of radial ligaments results in throughwall cracks and 

the rupture of axial or circumferential ligaments results in a longer crack that may undergo burst 

at pressures corresponding to normal operation (PNO) or design basis accident condition (PMSLB). 

Failure maps have been developed to delineate ranges of crack and ligament sizes that could be 

susceptible to ligament rupture and/or unstable burst due to pressure differences of PNO, 

PMSLB, 1.4PMSLB, or 3PNO. The possibility of the presence of 1, 2, 4 or 6 part–throughwall 

cracks, 80 or 90% deep has been considered. Each map shows the ligament widths and overall 

crack lengths for a number (2, 4, and 6) of axial part–throughwall cracks with a fixed depth that 

result in failure at pressure differentials of PNO, PMSLB, 3PNO, or 1.4PMSLB. The failures could 

occur due to a number of mechanisms. The failure mechanisms that were considered are the 

rupture of radial ligament (following which leakage occurs), crack coalescence (i.e., rupture of axial 

or circumferential ligament), and unstable burst. Each map identifies in terms of crack length and 

ligament width a region for which failure is predicted not to occur. Outside this no-failure region, 

the map delineates in terms of crack length and ligament width the regions of various failure 

mechanisms, e.g., radial ligament rupture, axial/circumferential ligament rupture, and unstable 

burst. 

The maps are based on the ANL radial ligament rupture model for axial part–throughwall 

cracks, and have been validated over the last several years by tests on specimens with a single 

EDM notch or two EDM notches separated by axial or circumferential ligament and the well–

known unstable burst pressure correlation for a single throughwall crack. Finite element analyses 

were then conducted to establish numerical models for predicting the coalescence of two axial 

throughwall cracks separated by axial or circumferential ligament of various widths. The current 

maps have been generated using typical strength properties of 22 mm (0.875 in.) OD, 1.3 mm 

(0.05 in.) wall thickness Alloy 600 tubes at 300°C (570°F), and would have to be modified for tubes 

with different sizes and/or strength properties. 

The failure maps have been generated for idealized and regular geometry of cracks. In 

reality, individual crack lengths and ligament lengths will vary in the same specimen and the 

ligament geometry can be a mixture of the various idealized geometries considered in this report. 

Therefore, to use these maps in an actual application, the user has to exercise judgment in 

determining which map is applicable. Some averaging techniques (e.g., equivalent rectangular 

crack) will be needed to replace the actual crack geometry (as determined by NDE) with one of the 

idealized crack geometries considered in this report. For example, crack lengths and ligament 

lengths could be deliberately chosen to represent an upper or lower bound to the actual case. 

C Leak–rate correlation models 

Leak rates through stress corrosion cracks (SCCs) in steam generator (SG) tubes in the field 

are sometimes calculated assuming that the flow inside the tube wall is choked. However, 

previous tests at ANL have shown that a single–phase orifice discharge model can accurately 

predict leak rates for flaws with gap dimensions as small as 0.18 mm (0.007 in.). Additional tests 

have been performed to better establish the range of validity of the orifice flow model. Tests were 

performed on four stress corrosion cracks (SCCs). Two of the cracks exhibited choked flow, and 
 xix 

two did not. The tightness of the cracks can be described in terms of the length of the flow 

channel L, approximately the wall thickness, and a hydraulic diameter D, which for a crack is 

taken as twice the crack opening displacement. Since all the cracks had L/D values of 2–4, this 

establishes a critical value of L/D for the transition between choked and non–choked flow. This 

value of L/D is strictly valid only for the value of the subcooling used in the tests, which 

corresponds to the cold–leg conditions. The value of L/D required to produce choking for hot–leg 

conditions will be somewhat less. 

These results, together with previous work by Amos and Shrock on flow through slits with 

L/D values from 85–300, have been used to develop a simple leak rate model that accounts for the 

transition between choked and non–choked flow and the effect of friction in tight cracks with 

L/D > 75. The major uncertainty in applying the model is probably the actual crack geometry. The 

crack opening area varies as ~c5.2, where c is the half axial crack length and ~3.5, where is the 

half circumferential crack length. Thus, the presence of ligaments could change the leak rate by 

two orders of magnitude or more. Bounding estimates of crack length will typically grossly 

overestimate the leak rate, more so for axial cracks than for circumferential cracks. 

D Leak rates in restricted areas 

Voltage-based alternate repair criteria have been established with regard to outside-diameter 

stress corrosion cracking of steam generator tubes at tube support plates (TSPs). These criteria 

rely upon an existing database for free span leak rates from cracks to calculate the total leakage 

from tubes with indications remaining in service. The database for free-span leakage is utilized 

because the TSPs could displace laterally during a postulated main steam-line break (MSLB) 

loading and expose the cracks under the TSPs. To justify leaving higher voltage indications in 

service than currently allowed, licensees have minimized the displacement of TSPs during 

transients by expanding a number of tubes above and below the TSPs to effectively lock the TSPs 

to the tubes. Although this procedure does mitigate the potential for burst and reduce leakage for 

cracks in the TSP regions, it will not eliminate the potential for increased leakage during 

postulated MSLBs and severe accidents from such cracks. 

The present study seeks to analytically predict flaw opening areas and leak rate increases 

from a crack, axial or circumferential, under the TSP during postulated MSLB and severe accident 

conditions. The results show that during postulated MSLB and severe accidents, the controlling 

leakage areas are the inner diameter (ID) crack opening area for short cracks [≤ 13 mm (0.5 in.)] 

and the area of the gap between the outer diameter (OD) surface of the tube and the TSP hole/wall 

for longer cracks. These results are in agreement with Westinghouse test results. 

During a postulated MSLB, axial cracks ≤ 13 mm (0.5 in.) in length do not bulge sufficiently 

to contact the TSP hole/wall, which has a nominal radial clearance of 0.2 mm (0.008 in.). This 

length is consistent with the maximum crack length of 14 mm (0.55 in.) reported by Westinghouse 

for a radial clearance of 0.3 mm (0.012 in.) between the tube OD surface and the TSP hole/wall. 

During postulated severe accidents, the bulging is a function of time, and the tube OD surface is 

predicted to make contact with the TSP hole/wall at 12,690 s (t=0 represents start of the accident). 

The contact length increases to 3 mm (0.1 in.) at 13,240 s. 

In contrast to the 13 mm (0.5 in.) crack, a 19 mm (0.75 in.) crack does contact the TSP 

hole/wall over a length of 6 mm (0.25 in.) during postulated MSLB. This result is consistent with 
 xx 

those reported by Westinghouse. During postulated severe accidents the contact length increases 

to 9 mm (0.35 in.) at 13,600 s. 

Circumferential cracks undergo much less radial bulging than axial cracks during postulated 

MSLB. As a result, the minimum crack length at which contact between the tube OD surface and 

the TSP hole/wall occurs is much longer, about 180° (corresponding to a length of 35 mm [1.4 

in.]). The contact length between the tube OD surface and the TSP hole/wall for a 240° crack is 4 

mm (0.15 in.). 

In contrast to axial cracks, the circumferential cracks deform very little by creep during the 

postulated severe accident transient. As a result, the crack opening area and the gap area change 

very little with time during the postulated severe accident. 

At postulated MSLB conditions, the leak rates for 13 and 19 mm (0.5 and 0.75 in.) axial 

cracks under the TSP are predicted to be 8 and 21 L/min (2 and 5.5 gpm), respectively. These 

results are in agreement with experimental results from Westinghouse. The leak rates for 90, 180, 

and 240° circumferential cracks are predicted to be 2, 37, and 78 L/min (0.5, 9.7 and 20.6 gpm), 

respectively. 

At 12,000 s during the postulated severe accident, the leak rates from the 13 and 19 mm 

(0.5 and 0.75 in.) axial cracks under the TSP are predicted to be 7 and 13 kg/min (3 and 5.8 

lb/min). The leak rates from the 90, 180, and 240° circumferential cracks at the same time are 

predicted to be 11, 22, and 44 kg/min (5, 10, and 20 lb/min), respectively, and they decrease 

slightly with time. 

The predicted leak rates reported here are upper bound rates computed assuming that 

crevice deposits are absent. Proprietary tests on tube-to-TSP junctions from an operating reactor 

in France, Dampiere-1, in which deposits were present, showed that leak rates could be reduced 

by as much as a factor of 1000 compared to those without deposits. Studies on deposits carried 

out at Chalk River Laboratories showed that the hardness, crushing strength, and consolidation 

properties of deposits depend strongly on the crevice chemistry. Small changes in crevice 

chemistry can lead to significant changes in these properties. Analytical predictions of leak rates 

that would account for the presence of sludge will require data on the mechanical and physical 

properties of the sludge deposits that are currently not available. 
 xxi 

Acknowledgments 

The authors thank Dr W. J. Shack of Argonne National Laboratory for helpful discussions. 

This work is sponsored by the Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory 

Commission, under Job Code Y–6588; Project Manager E. Reichelt. 
 xxii 

This page is intentionally left blank. 
 xxiii 

List of Acronyms 

ANL 

ARC 

ASME 

CANDU 

COA 

COD 

CTOD 

EdF 

EDM 

EPRI 

FEA 

FWLB 

MA 

MSLB 

NO 

NRC 

OD 

PTW 

RT 

Argonne National Laboratory 

Alternate repair criteria 

American Society of Mechanical Engineers 

Canadian Deuterium Uranium reactor 

Crack opening area 

Crack opening displacement 

Crack tip opening displacement 

Electricitè de France 

Electrodischarge machining 

Electric Power Research Institute 

Finite–element analysis 

Feed water line break 

Mill annealed 

Main steam line break 

Normal operation 

(U.S.) Nuclear Regulatory Commission 

Outer diameter 

Part–throughwall 

Room temperature 

SG 

SLB 

TT 

TTS 

TSP 

TW 

Steam generator 

Steam line break 

Thermally treated 

Top of tubesheet 

Tube support plate 

Throughwall 
 xxiv 

This page is intentionally left blank. 
 xxv 

List of Symbols 

A Cross–sectional area 

a Crack length 

CD Dimensionless orifice discharge coefficient 

D Bending stiffness; in Section 3 and 4 denotes a hydraulic diameter 

 Average opening width of a crack 

E, Eeff Young’s modulus and effective Young’s modulus 

h Wall thickness 

J, J J–integral and range of J–integral 

K, K Stress intensity factor and range of stress intensity factor 

KJ Equivalent stress intensity factor range determined from J 

Kax Axial stiffness 

L Span of beam; in Sections 3 and 4 used to denote the length of a flow channel 

L/D Ratio of channel length to hydraulic diameter 

mp Radial ligament stress magnification factor 

M& Mass flow/unit area through a crack 

N Cycles 

p Pressure drop across the tube wall 

pback Pressure acting on outside surface of tube 

psat Saturation pressure of water at a given temperature 

 fluid density 

R Mean radius of tube 

, eff Poisson’s ratio and effective Poisson’s ratio 
 xxvi 

This page is intentionally left blank. 
 1 

1 Pressurization Rate Effect on Burst Pressure 

1.1 Introduction 

The flow stress of a typical mill annealed (MA) or thermally treated (TT) Alloy 600 or TT Alloy 

690 tube material at temperatures ≤ 300°C is not expected to show a strong dependence on strain 

rate or stress rate. Consequently, the ligament rupture pressure or unstable burst pressure of a 

SG tube with a part–throughwall axial crack is not expected to depend significantly on the rate of 

pressurization at these temperatures. However, Westinghouse conducted a series of room 

temperature (RT) tests with slow (quasi–static) and fast 14 MPa/s (2000 psi/s) pressurization rates 

tests that appeared to show a significant effect of the rate of pressurization on the unstable burst 

pressure. The tests were conducted on tubes with machined part–throughwall notches with a 

complex shape, the so–called Type 14 notch shown in Fig.1.1 These notches were machined 

nominally to the same nominal depth profile (as measured by an eddy current technique) as that 

of a stress corrosion crack in a SG tube in Arkansas Nuclear One, Unit 2 (ANO–2). Slow (quasi–

static) and fast 14 MPa/s (2000 psi/s) pressurization rate tests on these specimens with nominally 

the same notch appeared to show a significant effect of the rate of pressurization on the unstable 

burst pressure. Unfortunately, the two types of tests at the two strain rates were conducted 

following two different test procedures. The slow rate tests were conducted in two steps – first, the 

specimen was pressurized without bladder and foil until ligament rupture occurred (but not 

burst); next, a bladder and foil was inserted and the specimen pressurized until unstable burst. 

The unstable burst pressure during the second step was found to be significantly less than the 

ligament rupture pressure observed during the initial portion of the test, which indicated that the 

specimens would have burst unstably during the initial testing if the pump had sufficient flow 

capacity to maintain pressure after the initial ligament rupture. The fast rate 14 MPa/s (2000 

psi/s) tests were conducted with bladder and foil from the beginning of the tests. The average 

ligament rupture (burst) pressure increased was 30% higher in the tests with a pressurization rate 

14 MPa/s (2000 psi/s) than in the quasi–static case. Subsequent analyses suggested that 

differences in notch profiles between the slow and the fast rate test specimens could account for 

some of the observed “rate effect” but not all of it. 

An earlier series of tests on EDM notch specimens at ANL showed relatively small rate 

effects. A second series of tests was conducted on a variety of specimen geometries to clearly 

determine the effect of pressurization rate on burst pressure. 

1.2 Factors Influencing Tests to Determine Pressurization Rate Effect 

It is known that ligament rupture pressure is more likely to display a pressurization rate 

effect than unstable burst pressure.2 In order to be able to predict ligament rupture pressures 

reliably, we need crack length, the geometry of the crack tip ligament and the flow stress of the 

material. For a given crack geometry, a true pressurization rate effect on ligament rupture 

pressure can occur only if the flow stress of the material is a function of strain rate. Flow stress of 

Alloy 600 (mill-annealed or thermally-treated) at room or normal operating temperature (~300°C) is 

not expected to vary significantly with the range of strain rates that occur in conventional tensile 

testing. However, the effective strain rates in narrow crack tip ligaments at high pressurization 

rates may be significantly higher than what is achievable under conventional tensile testing. The 

effect of pressurization rate can be masked by spurious factors that need to be understood and 
 2 

accounted for before the true pressurization rate effect on ligament rupture pressure can be 

established. Key factors other than the effect of strain rate on the flow stress that could affect the 

pressurization rate effect tests are: 

a) Artificial elevation (or reduction) of ligament rupture and burst pressures due 

to the use of bladder and foil in the test specimens. 

b) Specimen-to-specimen variation in as-fabricated ligament geometry and 

crack length for a given nominal crack geometry. 

Tests were conducted with and without bladder and foil to determine the effect of the bladder 

and foil on the ligament rupture and burst pressure. The typical response time of the pressure 

transducer used in our RT test facility is 5 ms. The rise time to 2500 psi at a rate of 2000 psi/s is 

1.25 s. Because this is much greater than the transducer response time, the response time 

should have negligible effect on the measured pressurization rate. Also, in order to assess the true 

effect of pressurization rate, the variability in the test data due to geometric variation from 

specimen-to-specimen has to be reduced. This was done by first computing the ligament rupture 

pressures of the specimens with the ANL model3 using the as-fabricated flaw geometry and the 

flow stress of the material as determined from conventional tensile tests. If the ligament rupture 

pressures of the tests conducted with various pressurization rates could be predicted within the 

95% confidence limits of the ANL model and showed no systematic bias with respect to the 

predicted values, we concluded that there was no significant effect of pressurization rate on the 

ligament rupture pressure. It is more difficult to directly establish a rate effect for SCCs, because 

the complex SCC flaw geometry varies from specimen to specimen in an arbitrary manner. Thus, 

any conclusion regarding pressurization rate effect in SCC specimens would have to be drawn on a 

statistical basis from a relatively large number of tests. Such a determination has not been made 

under the current study. 

1.2.1 Initial Test Series 

Test results for the initial series of tests on the effect of bladder and foil on ligament rupture 

pressure and unstable burst pressure at different pressurization rates are presented in Tables 1 

-20

0

20

40

60

80

100

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Notch Depth (%)

Axial Location (in.)

Eff. L=0.7 in.

Eff. depth=83%

m

p

=3.52

Figure 1. 

Notch depth profile for Type 14 

specimen. mp denotes radial ligament 

stress magnification factor. 
 3 

and 2, respectively. The tubes were 22 mm (0.875 in.) in diameter with a 1.3 mm (0.050 in.) wall 

thickness and had nominal yield and ultimate tensile strengths of 290 and 630 MPa (42 and 91 

ksi), respectively. The test facility has the capability to maintain a flow rate of 46 L/min (12 gpm) 

at 52 MPa (7500 psi). Because these were standard rectangular EDM notches, the as-fabricated 

geometries of the specimens were close to the nominal values shown in the tables. Table 1 shows 

that at comparable pressurization rates, the ligament rupture pressures for tests using a bladder 

but without any foil are close to those using neither bladder nor foil. The 100% TW, 12.7 mm (0.5 

in.) long notch tests of Table 2 show no significant effect of foil and bladder thickness on burst 

pressures. The 100% TW 6.3 mm (0.25 in.) long notch tests in the same table show no significant 

difference in burst pressures for tests conducted with or without foil and bladder. Similarly, no 

systematic differences were detected in the burst pressures for tests using bladder with a 0.13 mm 

(0.005 in.) brass foil or with bladder but no foil. Although the comparison testing with and without 

bladder and foil has not been exhaustive, Westinghouse has also concluded that the use of 

bladder and foil of the same sizes as used here does not affect the ligament rupture or burst 

pressure significantly.a 

Table 1 Ligament rupture pressures for < 25 mm (1 in.) long, part–throughwall 

rectangular EDM flaws with and without bladder 

Flaw 

 Length Depth 

 mm (in.) (%) 

Foil Bladder Pressurization 

Rate

MPa/s (psi/s) 

Ligament Rupture 

Pressure 

MPa (psi) 

Quasi–static 21.4 (3100) 

19.0 (0.75) 80 No No 13.8 (2000) 24.1 (3500) 

48.3 (7000) 26.2(3800) 

Quasi–static 30.0 (4350) 

6.3 (0.25) 90 No No 5.2 (750) 28.3(4100) 

22.0 (3200) 33.8(4900) 

No 13.8 (2000) 40.7 (5900) 12.7 (0.5) 60 No a 

3/32 in. Tygon 13.8 (2000) 41.4 (6000)a 

6.3 (0.25) 80 No No Quasi–static 37.9 (5500) 

3/32 in. Tygon 20.7 (3000) 43.1 (6250)a

6.3 (0.25) 60 No No 13.8 (2000) 49.60(7200) 

3/32 in. Tygon 20.7 (3000) 47.60(6900)a

a Specimen burst with fishmouth flaw opening 

 

a Private Communication R. Keating of Westinghouse Corp. to S. Majumdar, Argonne National 

Laboratory, 2000. 
 4 

Table 2 Unstable burst pressures (Stage 2) for < 25 mm (1 in.) long, part–throughwall 

and throughwall rectangular EDM flaws with and without bladder and foil. 

Flaw 

 Length Initial Depth 

 mm (in.) (%) 

Foil Bladder Pressurization 

Rate 

MPa/s (psi/s) 

Unstable Burst 

Pressure 

MPa (psi)a

Standard 

0.005 in. 

3/32 in. Tygon 30.3 (4400) 

Standard 

0.005 in. 

1/8 in. Tygon 29.6 (4300) 

Standard 

0.005 in. 

1/8 in. Tygon 30.0 (4350) 

12.7 (0.5) 100 

Oversize 

0.005 in. 

1/8 in. Tygon 

13.8 (2000) 

30.7 (4450) 

No No 22.1 (3200) 44.8 (6500)b 

6.3 (0.25) 90 No 1/8 in. Tygon 4.80(700) 44.8 (6500) 

Standard 

0.005 in. 

1/8 in. Tygon 6.2 (900) 41.4 (6000) 

Quasi–static 42.7 (6200)b

5.2 (750) 44.1 (6400) 6.3 (0.25) 90 No No b

22.0 (3200) 44.8 (6500)b

a Nominal burst pressure of a 13 mm (0.5 in.), 100% throughwall notch is 30 MPa (4400 psi) 

b Specimen did not burst with fishmouth flaw opening 

1.3 Test Specimens for the Second Series 

Four types of EDM notched specimens, shown in Figs 2–3, were fabricated from 0.875 in. (22 

mm-)-diameter MA Alloy 600 tubes for additional pressurization rate effect tests. The tubes had 

nominal yield and ultimate tensile strengths of 290 and 630 MPa (42 and 91 ksi), respectively. The 

total notch length of each specimen was fixed nominally at 1 in. (25 mm). An additional series of 

rectangular EDM notches with shorter notch lengths were tested to determine if pressurization 

rate effects are more pronounced in such specimens. Also, two tests were conducted on 

specimens with SCC. 

1"

0.005"

0.05"

0.01" 0.005"

0.05"

1"

Type A Type B 

Figure 2. Type A: single rectangular notch and Type B: single trapezoidal notch. 
 5 

0.5"

80%TW

0.05"

0.5"

80%TW

0.05"

Type C Type D 

Figure 3. Type C: 2–collinear notches (axial ligament) and Type D: 2–offset notches 

(circumferential ligament) 

1.4 Test Procedure for the Second Series 

Four pressurization rates were used: quasi–static (stepwise pressure increases with 

intermittent hold), 7 MPa/s (1000 psi/s), 14 MPa/s (2000 psi/s), 41 MPa/s (6000 psi/s), and, for 

some tests, >70 MPa/s (>10,000 psi/s). The quasi–static tests were used as controls/references. 

To minimize the effects of bladder and foil on the results, all of the specimens were tested in 

two stages. First, the specimens were pressurized without any bladder or foil at a controlled 

pressurization rate to ligament rupture. Pressurization then was continued until the pump ran 

out of flow or pressure capability. For the specimens that did not undergo unstable burst, a 

bladder and foil was inserted inside the specimens, and the specimens were pressurized at the 

desired rate until unstable burst occurred. Because all the flaws after ligament rupture were 

25.4–mm (1–in.) long, they were expected to exhibit nominally the same burst pressure, and hence 

only a representative number were tested to unstable burst. The bladder used was a hard Tygon 

tubing with a 3.2–mm (1/8–in)–thick wall and a diameter slightly smaller than the specimen ID. 

Brass foils of thickness 0.13 mm (0.005 in.) were used, and they extended 6.35 mm (0.25 in.) 

beyond the flaw extremities. The foil and bladder were sprayed with a lubricant to reduce friction 

between the foil and SG tube. 

1.5 Test Results for the Second Series 

1.5.1 Tests on 25 mm (1 in.) Long EDM Flaws 

Table 3 summarizes the data from the ligament rupture tests on rectangular and nonrectangular flaws 25 mm (1 in.) long. The raw data are somewhat misleading because the as–

received EDM flaws varied somewhat from the specified dimensions which has a significant 

influence on ligament rupture pressure. As noted previously, these results have to be compared 

with predictions of ligament rupture pressures based on the as–fabricated flaw geometry before the 

effect of pressurization rate can be assessed. 

Results from the unstable burst testing are summarized in Table 4. All of the unstable burst 

pressures varied between 14–16 MPa (2000–2300 psi), as expected because all of the notches had 

an overall length of 25 mm (1 in.). Consequently, the rest of the specimens were not tested. 
 6 

Table 3 EDM flaw ligament rupture pressure (Stage 1) for four flaw types (Types A, B, 

C, and D in Figs. 2–3) and five different pressurization rates. 

Pressurization 

Rate, MPa/s 

 Observed Failure Pressures, MPa (psi) [Specimen No.] For Flaw Types 

Indicated in Figs 2–3 

 (psi/s) A B C D 

Stage 1 Testing; Radial Ligament Rupture (no foil or bladder) 

Quasi–steady–

state 

9.1 (1320) 

[OM201] 

13.1 (1900) 

[OM207] 

23.9 (3460) 

[OM214b] 

27.6 (4000) 

[OM219c] 

21.7 (3150) 

[OM223c] 

7 (1000) 12.5 (1815) 

[OM202] 

11.5 (1675) 

[OM204] 

10.6 (1535) 

[OM224] 

24.4 (3540) 

[OM215b] 

22.5 (3264) 

[OM220c] 

14 (2000) 9.1 (1325) 

[OM203] 

12.4 (1800) 

[OM210] 

22.0 (3190) 

[OM216b] 

24.1 (3500) 

[OM222c] 

41 (6000) 11.7 (1690) 

[OM205] 

13.4 (1950) 

[OM211] 

21.6 (3135) 

(OM217b] 

24.3 (3520) 

[OM225c] 

> 69 (>10,000) 13.0 (1885) 

[OM206] 

51.0 (7400) 

[OM209a] 

12.9 (1875) 

[OM212] 

23.7 (3440) 

[OM213b] 

23.1 (3350) 

[OM218b] 

– 

aFlaw much shallower than specified dimensions. 

b Both radial and axial ligaments ruptured. 

c Both radial and circumferential ligaments ruptured. 

Table 4 EDM flaw unstable burst pressure (Stage 2) for four flaw types (Types A, B, C, 

and D in Figs. 2–3) and five different pressurization rates. 

Pressurization 

Rate, MPa/s 

 Observed Failure Pressures, MPa (psi) [Specimen No.] For Flaw Types 

Indicated in Figs 2–3 

 (psi/s) A B C D 

Stage 2 Testing; Unstable Burst (with foil and bladder) 

7 (1000) – – 14.1 (2050) 

[OM215] 

– 

14 (2000) 15.8 (2295) 

[OM203] 

– 14.3 (2075) 

[OM216] 

– 

41 (6000) 14.7 (2130) 

[OM205] 

– 13.9 (2020) 

[OM217] 

– 

> 69 (>10,000) 15.6 (2265) 

[OM206] 

– 15.0 (2175) 

[OM218] 

– 
 7 

1.5.2 Tests on Short EDM Flaws 

Three 6.35–mm– (1/4–in.)–long, 90% TW flaws, OM232, OM234, and OM250, were tested at 

a nominal pressurization rate of 41 MPa/s (6000 psi/s). The observed ligament rupture pressures 

are 40.0, 40.7, and 40.1 MPa (5800, 5900, and 5810 psi), respectively. 

Two 19.05–mm (3/4–in.)–long, 80% TW flaws OM235 and OM236, tested at a nominal rate of 

50.3 MPa/s (7300 psi/s), yielded ligament rupture pressures of 24.8 and 26.8 MPa (3600 and 

3885 psi), respectively. 

1.5.3 Tests on Stress Corrosion Cracks 

Limited tests at various pressurization rates were initiated on 22.2–mm (7/8–in.)–diameter 

tubes containing laboratory–produced ODSCC axial flaws of nominally 12.7– and 19.05–mm (1/2– 

and 3/4–in.) length and ≥80% TW. The two pressure tests conducted on SCC specimens to date 

were inconclusive because, unlike EDM notches, no abrupt ligament rupture event occurred in 

these tests. 

1.6 Analysis of Test Results 

1.6.1 Predicted Failure Pressures 

As noted, to minimize the uncertainties due to specimen-to-specimen variation in flaw 

geometry, the observed ligament rupture pressures should be compared with ligament rupture 

pressures predicted using the as-fabricated geometry. For the tests on the 25 mm (1 in.) flaws, 

this comparison is shown in Fig. 4 where the predicted values are based on a constant rateindependent yield stress=290 MPa (41.6 ksi), a rate-independent constant ultimate tensile 

strength = 630 MPa (91.4 ksi), and a flow stress factor k=0.55. The predicted test ligament 

rupture pressures are within the  95% confidence limits of the test predicted ligament rupture 

pressures and no strong bias about the predicted value is observed. Thus, there is no statistical 

evidence of a systematic pressurization rate effect on the ligament rupture pressure for rates up to 

14 MPa/s (2 ksi/s) for 25 mm (1 in.) long notches. 

 For a 25 mm (1 in.) throughwall crack, the predicted unstable burst pressure is 17 MPa (2.4 

ksi), which is within 10% of all the observed unstable burst pressures. Thus, there is no 

significant pressurization rate effect on the unstable burst pressures for rates up to 14 MPa/s (2 

ksi/s) for 25 mm (1 in.) TW flaws. 
 8 

0

1000

2000

3000

4000

5000

1000 2000 3000 4000 5000 6000

8 12 16 20 24 28 32 36 40

Type A (Quasi-Static)

Type A (1 ksi/s)

Type A (2 ksi/s)

Type B (Quasi-static)

Type B (1 ksi/s)

Type B (2 ksi/s)

Type C (Quasi-static)

Type C (1 ksi/s)

Type C (2 ksi/s)

Type D (Quasi-static)

Type D (1 ksi/s)

Type D (2 ksi/s)

0

4

8

12

16

20

24

28

32

Test Ligament Rupture Pressure (psi)

Predicted Ligament Rupture Pressure (psi)

Lower 95%

confidence limit

Upper 95%

confidence limit

Test Ligament Rupture Pressure (MPa)

Predicted Ligament Rupture Pressure (MPa)

Figure 4. 

Predicted vs. observed ligament rupture 

pressure for quasi–static to 14 MPa /s 

(2 ksi/s) tests. 

The ligament rupture pressure data for flaws < 25 mm (1 in.) are plotted in Figs. 5a as a 

function of pressurization rate. Figs. 5a also includes Type 14 test data from Westinghouse.1 The 

Type 14 data appear to exhibit a larger pressurization rate effect than the ANL tests; 30% increase 

for the Type 14 specimens compared to 10% increase for the ANL tests due to an increase in 

pressurization rate from quasi–static to 13.8 MPa/s (2 ksi/s). 

Much of the variability in the ligament rupture data (particularly the Type 14 data) can be 

traced to the variability in the as–built notch geometry from the nominal geometry.1 As mentioned 

earlier, a better estimate of the true effect of pressurization rate can be obtained by normalizing 

the test results by the predicted ligament rupture pressures using the as–fabricated geometry of 

the notches and the ANL ligament rupture model. The variation of the normalized ligament 

rupture pressures with pressurization rate is shown in Fig. 5b. The scatter band at 138 kPa/s [20 

psi/s (quasi-static)] is estimated from a database on ligament rupture pressure on rectangular 

EDM notches conducted at ANL.2-4 Note that most of the type 14 data fall within the ANL data 

scatter. The plot suggests no significant pressurization rate effect between quasi–static and 7 

MPa/s (1 ksi/s). Beyond 7 MPa/s (1 ksi/s), there is a slight increase in the normalized ligament 

rupture pressure with pressurization rate that varies approximately as pressurization rate raised 

to an exponent 0.129. The shorter notches tend to show a slightly larger rate effect than the 

longer notches. However, if the pressurization rate is limited to 13.8 MPa/s (2 ksi/s), the increase 

in ligament rupture pressure compared to quasi–static is about 10%, which is within the scatter 

band of the quasi–static test data. 
 9 

Figure 5. Variation of (a) test ligament rupture pressures and (b) normalized test ligament 

rupture pressures with pressurization rate. 

1.6.2 Post-Test Observations of Specimens 

Post–test observations of the 6.35–, 19.05–, and 25.4–mm (1/4–, 3/4–, and 1–in.)–long 

notches indicated large radial bulging deformation occurring locally around the flaw for all the 

flaws. However, the < 25–mm (1–in.)–long flaws also experience significant bulk plastic strain 

away from the flaw location because the nominal stress in these specimens exceeded the yield 

strength. The general level of plastic deformation diminishes with increasing flaw size, because 

the larger flaws undergo ligament rupture at lower pressures in a regime where the bulk of the 

tube away from the flaws remains elastic. The observed pressurization rate effect for the shorter 

flaws may be a result of a strain rate effects associated with the more extensive plastic 

deformation. 

1.7 Conclusions 

The 25 mm (1 in.) long rectangular as well as trapezoidal notches and two notches separated 

by axial and circumferential ligament do not show any pressurization rate effect on the ligament 

rupture or unstable burst pressure. Rectangular notches < 25 mm (1 in.) long show a small 

pressurization rate effect on ligament rupture pressure for rates > 7 MPa/s (1000 psi/s), with 

shorter notches experiencing a slightly greater rate effect than longer notches. However the 

increase in ligament rupture pressure at 13.8 MPa/s (2000 psi/s), which is the upper limit for 

most laboratory and field pressure tests5, compared to quasi–static loading is only 10%, which is 

within the scatter of the data for quasi–static loading. Because of lack of sufficient data, no 

conclusions can be drawn regarding the effect of pressurization rate on unstable burst pressure of 

initially 100% throughwall notches < 25 mm (1 in.) long. Burst tests on initially 100% throughwall 

notches < 25 mm (1 in.) long are needed. 

The pressurization rate effect observed in the specimens with shorter part-throughwall flaws 

may be associated with the significant plastic deformation in the bulk of the tubes away from the 

flaws. Plastic deformation is more localized in specimens with longer flaws. 

2

3

4

5

6

7

8

9

10

20

30

40

50

60

0 2 4 6 8 10 12

0.75/80%

0.5"/80%

0.25"/80%

0.25/90%

Type 14

0 10 20 30 40 50 60 70 80

Ligament Rupture Pressure (ksi)

Pressurization Rate (ksi/s)

Ligament Rupture Pressure (MPa)

Pressurization Rate (MPa/s)

0.8

0.9

1

0.01 0.1 1 10

0.75/80%

0.5/80%

0.25"/80%

0.25"/90%

Type 14

0.1 1 10

Normalized Test Ligament Rupture Pressure 1.5

Pressurization Rate (ksi/s)

Scatter band

Pressurization Rate (MPa/s)

p Ý 0.129

(a) (b) 
 10 

The use of tygon bladder ≤ 3 mm (1/8 in.) thick, with or without standard size 0.13-mm 

(0.005 in.) thick brass foils, does not influence the ligament rupture or unstable burst pressures of 

part-throughwall notches. For initially throughwall notches, the change of tygon bladder 

thickness from 2 to 3 mm (3/32 to 1/8 in.) does not affect the unstable burst pressure if it is used 

together with standard size 0.13-mm (0.005 in.) thick brass foils. 

Because of the difficulty of controlling the geometry of actual SCCs, pressurization rate 

effects in SCC specimens would have to be investigated by testing a large number of specimens 

with “similar” SCCs at several pressurization rates and comparing the pressure vs. leak rate data 

on a statistical basis. Such a program is not planned. 

Although the current series of tests have been conducted at RT on MA Alloy 600 tubes, the 

conclusions relative to pressurization rate effect are expected to be applicable to TT tubes at RT as 

well as at operating temperatures (~300°C). The plastic deformation mechanisms and behavior of 

the MA and TT materials are similar and strain rate effects due to thermal creep are not expected 

to be significant at ≤ 300°C. The conclusions should also be applicable to TT Alloy 690 for the 

same reason. The grain boundary carbides associated with TT materials may have significant 

effects on the long–term deformation of grain boundaries, but the failure processes of interest 

involve primarily plastic deformations in the bulk of the grain. 
 11 

2 Failure Maps for Complex Multiple Cracks 

2.1 Introduction 

Stress corrosion cracks generally consist of multiple cracks separated by ligaments (Fig. 6). 

Although ligament geometry can, in general, be very complex, it can be idealized as being either 

radial (part–throughwall cracks, Fig. 7), purely axial (Type C in Fig. 8), or purely circumferential 

(Type D or Type E in Fig. 8). Of all the three types of ligaments, cracks separated by type E 

ligaments show little or no interaction, i.e., they essentially behave as single cracks independent of 

ligament length.2 Therefore, Type E ligament will not be considered separately in this report. 

During pressurization, the rupture of radial ligaments leads to leaking throughwall cracks and the 

rupture of axial (Type C) or circumferential (Type D) ligaments leads to joining of cracks, resulting 

in a longer crack that could undergo burst due to pressure during normal operation (PNO) or 

design basis accident condition (PMSLB). The purpose of this study is to develop failure maps that 

delineate ranges of ligament and crack sizes that could be susceptible to ligament rupture and/or 

unstable burst due to pressure differences of PNO, PMSLB, 1.4PMSLB, and 3PNO. For the 

purpose of this study, we have used PNO = 10 MPa (1.5 ksi) and PMSLB = 18 MPa (2.6 ksi). Such 

failure maps are intended to be used as a tool for identifying cracks that would require more 

detailed investigation during in-service inspection and screening out those for which interactions 

are unimportant. They are also helpful in providing a quantitative understanding of the important 

effect remaining ligaments have on the burst strength of flawed tubes. The maps consider the 

possibility of the presence of 1, 2, 4 and 6 part–throughwall cracks, 80 and 90% deep. Although 

field data show cracks that are generally shallower, for a much shallower crack to fail at any of the 

four critical pressures considered here, the crack would have to be very long. 

Figure 6. 

Typical stress corrosion crack geometry.
 12 

Axial crack

Crack

Radial 

ligament

 

Figure 7. Idealized single part–throughwall axial crack with a radial ligament. 

Radial 

ligaments

Circumferential 

ligament length

th

Ligament

ickness

Circumferential ligament (Type E)

Ligament length

Circumferential ligament (Type D)

Ligament length

Axial ligament length

Type C

 

Figure 8. Two idealized part–throughwall axial cracks each with a radial ligament at the 

through-thickness crack tip and separated from each other by either an axial 

(Type C) or a circumferential (Type D or Type E) ligament. 
 13 

2.2 Background Analysis and Tests 

2.2.1 Throughwall Axial Cracks 

Detailed finite–element analyses (FEA) and tests on specimens containing two notches were 

conducted under ISG–TIP–2 and reported in Ref. 4. Two types of throughwall (TW) notches were 

analyzed. First, in type C specimens (Fig. 9a), two axial notches, 0.19–mm (0.0075–in.) wide, were 

collinear with an axial ligament separating the two. Second, in type D specimens (Fig. 9b), the two 

axial notches, 0.19–mm (0.0075–in.) wide, were offset in the circumferential direction with the 

right tip of the first notch aligning with the left tip of the second notch. Finite element analyses 

were conducted for a type C specimen with two 6–mm (0.25–in.) long TW notches separated by a 

0.25–mm (0.01–in.) long axial ligament at RT. The engineering and true stress–strain curves of the 

as–received material at RT are shown in Fig. 10. The problem was analyzed by ANSYS as well as 

ABAQUS using finite deformation theory (true stress–strain curve). Plots of the average thickness 

vs. pressure (Fig. 11) shows that rapid necking (the last step in the analysis beyond which 

numerical instability develops) in the ligament is predicted to occur at a pressure of 17 MPa 

(2.5 ksi) by ANSYS and 19.5 MPa (2.8 ksi) by ABAQUS, in reasonable agreement with the test 

result. Tests were also conducted on specimens with two TW axial notches (each either 6 or 13–

mm long) in the type D configuration (circumferential ligament). The ligament rupture pressures 

predicted by FEA are compared with the observed ligament rupture pressures in Fig. 12. The two 

dashed lines in Fig. 12 represent the unstable burst pressures corresponding to single TW notches 

(with twice the individual notch length) that result after the coalescence of the two notches 

following circumferential ligament rupture. Specimens whose ligament rupture pressures lie 

above the dashed lines experience unstable burst immediately after ligament rupture, whereas 

those below the corresponding dashed lines remain stable with a single larger notch. 

100%TW

Axial Ligament 

Length

Axial Crack Length

Crack 

Width

Axial Crack 

Length

100%TW

Circumferential 

Ligament Length

(a) (b) 

Figure 9. Two-TW axial notches separated by (a) an axial ligament (Type C ) and (b) a 

circumferential ligament (Type D). 
 14 

0

500

1000

1500

2000

0 0.2 0.4 0.6 0.8 1 1.2

0

40

80

120

160

200

240

280

Stress (MPa)

Strain

True stress-strain curve

Engineering stress-strain curve

Stress (ksi)

Figure 10. 

Engineering and true stress–strain 

curves of Alloy 600 used for finite 

element analysis. 

0

0.02

0.04

0.06

0

0.5

1

1.5

0.1 1

1 10

Average Axial Ligament Thickness (in.)

Pressure (ksi)

Average Ligament Thickness (mm)

Pressure (MPa)

2x0.25x 0.01in. (2x6.35x0.25 mm)

ANSYS

ABAQUS

Finite deformation

Test 

Figure 11. 

Calculated variation of average inter–

notch axial ligament thickness with 

pressure using finite deformation 

analyses by ANSYS and ABAQUS for 

two 6–mm (0.25–in.) long axial cracks 

separated by a 0.25–mm (0.01–in.) long 

axial ligament (Type C). 
 15 

0

1

2

3

4

5

6

0 0.05 0.1 0.15

Test (2x 6 mm)

Test (2x13 mm)

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3 3.5

Circ. Ligament Rupture Pressure (ksi)

Circ. Ligament Length (in.)

2x6 mm

2x13 mm

Burst 

(13 mm TW)

Burst

(25 mm TW)

Circ. Ligament Length (mm)

Circ. Ligament Rupture Pressure (MPa)

Figure 12. 

Predicted (by FEA, line) vs. observed 

(symbols) variation of ligament rupture 

pressure with circumferential ligament 

length for type D specimens having two 

6–and 13–mm long TW notches. 

2.2.2 Part–Throughwall Axial Cracks 

All the tubes considered in this section had a diameter of 22–mm (0.875 in.) and nominal 

yield and ultimate tensile strengths of 300 and 675 MPa (43 and 98 ksi), respectively. We used the 

equivalent rectangular crack method4 to predict the through–thickness (radial) ligament rupture 

for two PTW cracks separated by either an axial (type C) or circumferential (type D) full–thickness 

ligament (see Figs. 7-8 for ligament definitions). The radial ligament rupture pressures for tubes 

with two axial notches, type C (axial ligament) and type D (circumferential ligament), were 

calculated by the equivalent rectangular approach for various notch lengths and inter–notch 

ligament lengths. Tests were conducted in the ANL High Pressure Test Facility on specimens 

without bladders and were interrupted after the through–thickness radial ligament ruptured, as 

evidenced by onset of leakage. The predicted vs. experimental ligament rupture pressures given in 

Figs. 13a–b for two 6– and 13–mm long notches, respectively, indicate that the equivalent 

rectangular crack approach can predict the through–thickness radial ligament rupture pressures 

reasonably well. Unless otherwise noted in the figures, in all of the tests, the axial and 

circumferential ligaments were also ruptured following radial ligament rupture. The rupture/nonrupture of the circumferential ligaments in Figs. 13a–b can be predicted from the circumferential 

ligament rupture pressure data presented in Fig. 12 depending on whether the failure pressures in 

Figs. 13a-b lie above or below the failure pressures for the corresponding crack and ligament 

lengths in Fig. 12. The two dashed lines in Fig. 13b, representing the radial ligament rupture 

pressures of single 13 and 25 mm (0.5 and 1 in.) long, 80%TW notches, provide limits within 

which the radial ligament rupture pressures for the 2 x 13 mm (2 x 0.5 in.) long, 80%TW notches 

must lie. 
 16 

3.5

4

4.5

5

5.5

6

6.5

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

Axial Ligament

Axial Ligament

Circ. Ligament

-2 0 2 4 6 8 10 12 14

25

30

35

40

Radial Ligament Rupture Pressure (ksi)

Axial or Circ. Ligament Length (in.)

2x0.25"x70%

2x0.25"x80%

Circ. lig. not ruptured

Axial or Circ. Ligament Length (mm)

Radial Ligament Rupture Pressure (MPa)

Open symbols-80% deep

Filled symbols-70% deep

2

2.5

3

3.5

4

4.5

5

-0.1 0 0.1 0.2 0.3 0.4

Axial ligament

Circ. ligament

-2 0 2 4 6 8 10

15

20

25

30

Radial Ligament Rupture Pressure (ksi)

Axial or Circ. Ligament Length (in.)

Axial or Circ. Ligament Length (mm)

Radial Ligament Rupture Pressure (MPa)

1x1"x80%

1x0.5"x80%

2x0.5"x80%

Circ. lig. not ruptured

(a) (b) 

Figure 13. Predicted (line) and observed (symbols) radial through–thickness ligament 

rupture pressures vs. axial or circumferential ligament lengths for two PTW 

EDM notches (a) 6–mm (0.25–in.) and (b) 13–mm (0.5–in.) long. 

2.3 Parametric Analyses for Axial Throughwall Cracks 

To generate the failure maps for the various pressure loading, we ran a series of analyses 

with two, four and six axial throughwall cracks (Figs. 14a–b and 15a–b) to develop the pressures 

required for axial and circumferential ligament rupture (i.e., crack coalescence). Note that, in 

contrast to the convention followed so far, the “crack length” is defined as the total tip-to-tip length 

including all of the cracks and ligament lengths. “Ligament length” continues to refer the length of 

an individual ligament between two cracks. For a given overall crack length, individual cracks are 

assumed to all have the same length and individual ligaments are assumed to all have the same 

length. Results from these analyses for four overall crack lengths and ligament lengths are plotted 

(as symbols) in Fig. 16 for the case of two cracks separated by an axial ligament. For interpolation 

and limited extrapolation of the FEA results to different ligament lengths, the ligament rupture 

pressure (lig) for each crack length was fitted by a polynomial function of the ligament lengths (lw) 

of the form: 

 lig  a1lw  a2lw

2 (1) 

The curve fits were constrained to ensure that for a given crack length, as the ligament length 

approached the crack length/the number of ligaments, i.e., as the lengths of the individual cracks 

approached zero, the rupture pressure can not exceed the burst pressure of an unflawed tube. 

The variation of the parameters a1 and a2 with crack length was determined by fitting the results 

for the four crack lengths by power law fits as shown in Figs. 17a–b, respectively. The rupture 

pressure vs. ligament length plot for the case of four axial cracks separated by axial ligaments is 

given in Fig. 18 and plots for the corresponding fitting parameters a1 and a2 are given in Figs. 19a–

b, respectively. The rupture pressure vs. ligament length plot for the case of six axial cracks 

separated by axial ligaments is given in Fig. 20 and plots for the corresponding fitting parameters 

a1 and a2 are given in Figs. 21a–b, respectively. 
 17 

Axial ligament length

Crack Length

Circumferential 

ligament length

Crack length

(a) (b) 

Figure 14. Specimens with two throughwall axial cracks, separated by (a) an axial ligament 

(Type C) and (b) a circumferential ligament (Type D), analyzed by FEA. 

Crack length

Axial ligament length

Crack length

Axial ligament length

(a) (b) 

Figure 15. Specimens with (a) four and (b) six axial throughwall cracks analyzed by FEA. 

-10

0

10

20

30

40

50

60

-5 0 5 10 15 20

6 mm

13 mm

25 mm

51 mm

0

2

4

6

8

0 0.2 0.4 0.6

Axial Ligament Rupture Pressure (MPa)

Axial Ligament Length (mm)

2x100% deep cracks

6 mm

(0.25 in.) 13 mm (0.5 in.)

25 mm

(1 in.)

51 mm (2 in.)

Axial Ligament Rupture Pressure (ksi)

Axial Ligament Length (in.)

Figure 16. 

Axial ligament rupture pressure for two 

throughwall axial cracks separated by an 

axial ligament. Symbols represent FEA 

results and lines are polynomial fits of 

the FEA results to Eq. 1. 
 18 

1

10

100

1 10 100

0.1 1

y = 208.05 * x^(-1.2025) R= 0.99791 

a

1

Crack Length (mm)

2x100% cracks

Crack Length (in.)

0.001

0.01

0.1

1

10

1 10 100

0.1 1

y = 181.22 * x^(-2.4311) R= 0.99944 

-a2

Crack Length (mm)

2x100% cracks

Crack Length (in.)

(a) (b) 

Figure 17. Variation of fitting parameters (a) a1 and (b) a2 with crack length (in mm) for 

specimens with two throughwall axial cracks separated by an axial ligament. 

Symbols denote values of fitting parameters for the four crack lengths shown in 

Fig. 16 to Eq. 1 and lines are power-law fits for the fitting parameters as 

functions of crack length. 

-20

0

20

40

60

80

-2

0

2

4

6

8

10

-2 0 2 4 6 8 10

0 0.1 0.2 0.3

6 mm

13 mm

25 mm

51 mm

Axial Ligament Rupture Pressure (MPa)

Axial Ligament Length (mm)

6 mm

(0.25 in.) 13 mm (0.5 in.) 25 mm

(1 in.)

51 mm

(2 in.)

4x100% deep cracks

Axial Ligament Length (in.)

Axial Ligament Rupture Pressure (ksi)

Figure 18. 

Axial ligament rupture pressure for four

throughwall axial cracks separated by

three equally long axial ligaments.

Symbols represent FEA results and lines

are polynomial fits of the FEA results to

Eq. 1. 
 19 

1

10

100

1 10 100

0.1 1

y = 590.33 * x^(-1.1075) R= 0.99922 

a

1

Crack Length (mm)

4x100% cracks

Crack Length (in.)

0.1

1

10

100

1 10 100

0.1 1

y = 1519.5 * x^(-2.253) R= 0.99954 

-a2

Crack Length (mm)

4x100% cracks

Crack Length (in.)

(a) (b) 

Figure 19. Variation of fitting parameters (a) a1 and (b) a2 with crack length (in mm) for 

specimens with four throughwall axial cracks separated by three axial 

ligaments. Symbols denote values of fitting parameters for the four crack 

lengths for the four crack lengths shown in Fig. 18 to Eq. 1 and lines are powerlaw fits for the fitting parameters as functions of crack length. 

-20

0

20

40

60

80

-2

0

2

4

6

8

10

-2 0 2 4 6 8 10

0 0.1 0.2 0.3

6 mm

13 mm

25 mm

51 mm

Axial Ligament Rupture Pressure (MPa)

Axial Ligament Length (mm)

6 mm

(0.25 in.)

13 mm

(0.5 in.)

25 mm

(1 in.)

51 mm

(2 in.)

6x100% deep cracks

Axial Ligament Length (in.)

Axial Ligament Rupture Pressure (ksi)

Figure 20. 

Axial ligament rupture pressure for six

throughwall axial cracks separated by five

equally long axial ligaments. Symbols

represent FEA results and lines are

polynomial fits of the FEA results to Eq. 1.
 20 

10

100

1000

1 10 100

0.1 1

y = 732.86 * x^(-1.0602) R= 0.99644 

a

1

Crack Length (mm)

6x100% cracks

Crack Length (in.)

0.1

1

10

100

1 10 100

0.1 1

y = 2425.8 * x^(-2.1705) R= 0.99949 

-a2

Crack Length (mm)

6x100% cracks

Crack Length (in.)

(a) (b) 

Figure 21. Variation of fitting parameters (a) a1 and (b) a2 with crack length for specimens 

with six throughwall axial cracks separated by five axial ligaments. Symbols 

denote values of fitting parameters for the four crack lengths for the four crack 

lengths shown in Fig. 20 to Eq. 1 and lines are power-law fits for the fitting 

parameters as functions of crack length. 

The rupture pressure curve for the case of two axial cracks separated by a circumferential 

ligament is shown in Fig. 22. In fitting the rupture data, the fit must be constrained to ensure 

that as the ligament length increased, the rupture pressure can not exceed the unstable burst 

pressure of a single crack (i.e., half the crack length). However, a simple polynomial of the type 

used for the case of the axial ligament did not fit the data satisfactorily. A more satisfactory result 

was obtained by expressing log(lig) in terms of a polynomial in log (lw) of the form: 

log( lig )  M0  M1 log(lw )  M2 [log(lw )]2 (2) 

The variation of the parameters M0, M1 and M2 with total crack length is shown in Fig. 23. 

0

10

20

30

40

50

012345678

6 mm

13 mm

25 mm

0

1

2

3

4

5

6

7

0 0.05 0.1 0.15 0.2 0.25 0.3

Circ. Ligament Rupture Pressure (MPa)

Circumferential Ligament Length (mm)

2x100% deep cracks 6 mm (0.25 in.)

13 mm (0.5 in.)

25 mm (1 in.)

Circ. Ligament Rupture Pressure (ksi)

Circumferential Ligament Length (in.)

Figure 22. 

Circumferential ligament rupture pressure

for two throughwall axial cracks separated

by a circumferential ligament. Symbols

represent FEA results and lines are logpolynomial fits of the FEA results to Eq. 2.
 21 

-0.5

0

0.5

1

1.5

5 10 15 20 25 30 35

0.2 0.4 0.6 0.8 1 1.2

M

0

M1

M2

Parameters for Circ Lig, between 2 Cracks

Crack Length (mm)

Crack Length (in.)

Figure 23. 

Variation of fitting parameters M0, M1, and

M2 with total crack length for specimens

with two throughwall axial cracks

separated by a circumferential ligament.

Symbols represent fitting parameters of

the data for the three crack lengths shown

in Fig. 22 to Eq. 2 and lines are linear fits

to the fitting parameters as functions of

crack length. 

A comparison of the effects of axial and circumferential ligament lengths on the ligament 

rupture pressure of 2 x 100% deep cracks of total length 25 mm (1 in.) is shown in Fig. 24. The 

symbols in this figure represent FEA results and the curves are predicted from our fitting 

procedure discussed above. Note that for small ligament lengths, a circumferential ligament 

increases the ligament rupture pressure slightly more than an axial ligament of the same length. 

The asymptotic behavior of the two types of ligaments for large ligament lengths result from the 

fact that for the geometries being considered the total crack length for the axial case includes the 

ligament width whereas the total crack length for the circumferential case is independent of 

ligament width (Figs 14a–b). As a result, the individual crack length in the axial ligament case 

approaches zero as the axial ligament length increases, whereas the individual crack length is 

independent of the circumferential ligament length. The ligament rupture pressure curve for the 

axial ligament case provides a conservative (i.e., upper) bound to the curve for the circumferential 

ligament case at large ligament lengths, whereas the two are comparable for ligament lengths ≤ 3 

mm (0.12 in.). 

-10

0

10

20

30

40

50

60

70

0

2

4

6

8

10

-2 0 2 4 6 8 10

0 0.1 0.2 0.3

Axial ligament (FEA)

Circ. ligament (FEA)

Ligament Rupture Pressure (MPa)

Ligament Length (mm)

Ligament Rupture Pressure (ksi)

Ligament Length (in.)

2x100% cracks

Total crack length = 1 in. (25 mm)

Axial ligament

Circ. ligament

Figure 24. 

Effects of axial and circumferential

ligament widths on ligament rupture

pressure of two 12 mm 100%TW axial

cracks separated by axial or

circumferential ligaments (total crack

length = 25 mm) . Symbols denote the

FEA results and the lines are the fitted

values. 
 22 

2.4 Generation of Failure Maps 

Experience with testing of multiple PTW laser cut and EDM notches has shown that radial 

ligaments at the through-thickness notch tips of individual notches that are > 2.5 mm (0.1 in.) 

long and > 70% deep tend to rupture before the axial or circumferential ligaments of length ≥ 0.25 

mm (0.01 in.).2 Therefore, in generating the failure maps, it was assumed that during 

pressurization, the radial ligaments ruptured first, followed by the rupture of the axial (or 

circumferential) ligaments separating the cracks, and finally unstable burst of the resulting single 

throughwall crack. All the tubes considered in generating the failure maps had a diameter of 22–

mm (0.875 in.). 

Failure maps were developed for 80 and 90% deep cracks at 300°C. An Excel spreadsheet 

was written that computed the radial ligament rupture pressure by the equivalent rectangular 

crack method, the axial (or circumferential) ligament rupture pressure by the correlations 

developed above from FEA, and finally the unstable burst pressure of a single throughwall crack 

by the Erdogan correlation.6 The equivalent area analyses and the burst calculations used: 

Sy = 267 MPa (39 ksi) and Su = 608 MPa (88 ksi) and flow stress parameter k = 0.55 

for the properties at 300°C. 

The failure maps for cracks of a given depth and at a given pressure (e.g., PNO) were generated by 

determining the various combinations of ligament length and crack length that correspond to the 

given pressure. Definitions of the various crack and ligament lengths are given in Figs. 14-15. 

2.4.1 Failure Maps for Normal Operation (PNO) 

Single Crack 

The failure map for a single crack at normal operation is shown in Fig. 25. Any crack of 

length less than 1.7 in. (44 mm), irrespective of depth, is predicted to remain stable (i.e., no 

unstable burst) during normal operation. The map also shows the combination of crack length 

and crack depth where neither radial ligament rupture nor unstable burst is predicted to occur. 

Also shown is the region where radial ligament rupture is predicted to occur without unstable 

burst. 
 23 

0.86

0.88

0.9

0.92

0.94

0.96

0 0.5 1 1.5 2 2.5

0 10 20 30 40 50 60

86

88

90

92

94

96

Crack Depth

Crack Length (in.)

unstable

burst

Radial

ligament

rupture

no burst

No ligament rupture

or burst

PNO=10 MPa (1.5 ksi)

Radial

ligament

rupture and

Crack Length (mm)

Crack Depth (%)

Figure 25. 

Failure map of a single crack at normal 

operating pressure PNO. 

Two Cracks 

Figs 26a–b show failure maps for two–90% deep axial cracks separated by either an axial or a 

circumferential ligament, respectively. As in the case of a single crack, cracks shorter than 1.7 in. 

(44 mm) are predicted to remain stable (no unstable burst) for all ligament widths. Further, if two 

cracks have an axial ligament length greater than 1.4 mm (0.055 in.) or two cracks have a 

circumferential ligament length greater than 1.3 mm (0.050 in.), then cracks with a total length 

longer than 1.7 in. (44 mm) will experience unstable burst only if the ligament length/crack length 

lies in the zone marked “unstable burst”. For shorter ligament lengths, both the radial and axial 

or circumferential ligaments are predicted to rupture provided the crack length/ligament length 

lies in the zones marked “radial/axial lig. rupture” or “radial/circ. lig. rupture” in the figures, but 

the single TW crack that results after the ligament rupture is predicted to remain stable (no 

unstable burst) provided the overall length is less than 1.7 in. (44 mm). The failure maps for the 

axial and circumferential ligament cases are quite similar and the axial ligament case provides a 

conservative bound to the circumferential ligament case, i.e., the non-failure region for the axial 

ligament case is contained within the non-failure region for the circumferential ligament case. The 

failure maps for two–80% deep cracks are not plotted because none of the failure mechanisms 

become active unless cracks are very long and not of practical interest. 

Four Cracks 

Figure 27a shows the failure map for four–90% deep axial cracks separated by three axial 

ligaments. As in the case of a single crack, cracks with a total length shorter than 1.7 in. (44 mm) 

are predicted to remain stable (no unstable burst) for all ligament lengths. Further, if four axial 

cracks have an axial ligament length greater than 0.5 mm (0.02 in.), then cracks longer than 1.7 

in. (44 mm) will experience unstable burst only if the ligament length/crack length lies in the zone 

marked “unstable burst”. For shorter ligament lengths, both the radial and axial ligaments are 

predicted to rupture provided the crack length/ligament length lies in the zone marked “radial and 

axial ligament rupture” in the figure, but the single TW crack that results after ligament rupture is 

predicted to remain stable (no unstable burst) provided the overall length is less than 1.7 in. (44 

mm). 
 24 

0

10

20

30

40

50

60

0

0.5

1

1.5

2

0 0.4 0.8 1.2 1.6 2 2.4 2.8

0 0.02 0.04 0.06 0.08 0.1

Crack Length (mm)

Axial Ligament Length (mm)

Unstable burst

2x90% deep cracks

Crack Length (in.)

pNO=10 MPa (1.5 ksi)

No radial or axial

ligament rupture

Axial Ligament Length (in.)

Radial/axial

lig. rupture

0

10

20

30

40

50

60

0

0.5

1

1.5

2

0 0.4 0.8 1.2 1.6 2 2.4 2.8

0 0.02 0.04 0.06 0.08 0.1

Crack Length (mm)

Circumferential Ligament Length (mm)

Unstable burst

2x90% deep cracks

Crack Length (in.)

pNO=10 MPa (1.5 ksi)

No radial or circ.

ligament rupture

Circumferential Ligament Length (in.)

Radial/circ.

lig. rupture

(a) (b) 

Figure 26. Failure maps for SG tubes with two 90% deep axial cracks separated by (a) an 

axial ligament (Type C) and (b) a circumferential ligament (Type D) at normal 

pressure (PNO). “Crack length” denotes total overall length of the individual 

cracks and ligaments. 

Six Cracks 

Figure 27b shows the failure map for six–90% deep axial cracks separated by five axial 

ligaments. As in the case of a single crack, cracks shorter than 1.7 in. (44 mm) are predicted to 

remain stable (no unstable burst) for all ligament widths. Further, if six axial cracks have an axial 

ligament length greater than 0.3 mm (0.012 in.), then cracks longer than 1.7 in. (44 mm) will 

experience unstable burst only if the ligament length/crack length lies in the zone marked 

“unstable burst”. For narrower ligament widths, both the radial and axial ligaments are predicted 

to rupture provided the crack length/ligament length lie in the zone marked “radial and axial 

ligament rupture” in the figure, but the resulting single crack after ligament rupture is predicted to 

remain stable (no unstable burst) provided the overall crack length is less than 1.7 in. (44 mm). 

10

20

30

40

50

60

0.4

0.8

1.2

1.6

2

0 0.2 0.4 0.6 0.8 1

0 0.01 0.02 0.03

Crack Length (mm)

Axial Ligament Length (mm)

4x90% deep cracks

Crack Length (in.)

No radial or axial

ligament rupture

Unstable burst

Axial Ligament Length (in.)

pNO=10 MPa (1.5 ksi)

Radial and axial

ligament rupture

10

20

30

40

50

60

0.4

0.8

1.2

1.6

2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.005 0.01 0.015 0.02

Crack Length (mm)

Axial Ligament Length (mm)

6x90% deep cracks

Crack Length (in.)

No radial or axial

ligament rupture

Unstable burst

Axial Ligament Length (in.)

pNO=10 MPa (1.5 ksi)

Radial and axial

ligament rupture

(a) (b) 
 25 

Figure 27. Failure maps for SG tubes with (a) four and (b) six 90% deep axial cracks 

separated by axial ligaments at normal pressure (PNO). “Crack length” 

denotes the total overall length of the individual cracks and ligaments. 

2.4.2 Failure Maps for Main Steam Line Break Pressure (PMSLB) 

Single Crack 

The failure map of a single crack at main steam line break pressure is shown in Fig. 28. Any 

crack of length less than 0.85 in. (22 mm), irrespective of depth, is predicted to remain stable (i.e., 

no unstable burst) at main steam line break pressure. The map also shows the combination of 

crack length and crack depth where neither radial ligament rupture nor unstable burst is 

predicted to occur. Also shown is the region where radial ligament rupture is predicted to occur 

without unstable burst. 

0.7

0.75

0.8

0.85

0.9

0.95

1

0 0.5 1 1.5 2 2.5

0 10 20 30 40 50 60

70

75

80

85

90

95

100

Crack Depth

Crack Length (in.)

unstable

burst

Radial

ligament

rupture

no burst

No ligament rupture

or unstable burst

PMSLB=18 MPa (2.6 ksi)

Radial

ligament

rupture and

Crack Length (mm)

Crack Depth (%)

Figure 28. 

Failure map of a single crack at main 

steam line break pressure PMSLB. 

Two Cracks 

Figures 29a–b show the failure maps for two–90% deep axial cracks separated by an axial 

and a circumferential ligament, respectively. As in the case of a single crack, cracks shorter than 

0.85 in. (22 mm) are predicted to remain stable (no unstable burst) for all ligament widths. 

Further, if two Type C cracks have an axial ligament length greater than 2.5 mm (0.1 in.) or two 

type D cracks have a circumferential ligament length greater than 2 mm (0.080 in.), then cracks 

longer than 0.85 in. (22 mm) will experience unstable burst only if the ligament length/crack 

length lies in the zone marked “unstable burst”. For shorter ligament lengths, both the radial and 

axial or circumferential ligaments are predicted to rupture provided the crack length/ligament 

length lies in the zones marked “radial/axial ligament rupture” or “radial/circ. lig. rupture” in the 

figures, but the resulting single TW crack after ligament rupture is predicted to remain stable (no 

unstable burst) provided the overall crack length is less than 0.85 in. (22 mm). Again the failure 

maps for the axial and circumferential ligament cases are quite similar and the axial ligament case 

provides a conservative bound to the circumferential ligament case, i.e., the non-failure regime for 

the axial ligament case is contained within the non-failure regime for the circumferential ligament 

case. 
 26 

The failure maps for two–80% deep axial cracks separated by an axial and a circumferential 

ligament are shown in Figs. 30a–b, respectively. As before, cracks with total lengths less than 

0.85 in. (22 mm) will not burst unstably irrespective of the axial or circumferential ligament 

length. In contrast to the two-90% deep crack case, there is no crack length/ligament length 

regime in which radial/axial (or radial/circumferential) ligament rupture will occur without 

unstable burst. As before, the failure maps for the axial and circumferential ligament cases are 

quite similar and the axial ligament case provides a conservative bound to the circumferential 

ligament case, i.e., the non-failure regime for the axial ligament case is contained within the nonfailure regime for the circumferential ligament case 

0

10

20

30

40

50

0

0.5

1

1.5

012345

0 0.05 0.1 0.15

Crack Length (mm)

Axial Ligament Length (mm)

2x80% deep cracks

Crack Length (in.)

p

MSLB=18 MPa (2.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Unstable burst

Axial Ligament Length (in.)

0

10

20

30

40

50

0

0.5

1

1.5

012345

0 0.05 0.1 0.15

Crack Length (mm)

Circumferential Ligament Length (mm)

2x80% deep cracks

Crack Length (in.)

p

MSLB=18 MPa (2.6 ksi)

No radial or circ.

ligament rupture

or unstable burst

Unstable burst

Circumferential Ligament Length (in.)

(a) (b) 

Figure 30. Failure maps for SG tubes with two 80% deep axial cracks separated by (a) an 

axial ligament (Type C) and (b) a circumferential ligament (Type D) at main 

steam line break pressure (PMSLB). “Crack length” denotes the total overall 

length of the individual cracks and ligaments. 

0

10

20

30

40

50

0

0.4

0.8

1.2

1.6

02468

0 0.05 0.1 0.15 0.2 0.25 0.3

Crack Length (mm)

Axial Ligament Length (mm)

Unstable burst

2x90% deep cracks

Crack Length (in.)

p

MSLB=18 MPa (2.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Radial/axial

ligament 

rupture

no burst

Axial Ligament Length (in.)

0

10

20

30

40

50

0

0.4

0.8

1.2

1.6

02468

0 0.05 0.1 0.15 0.2 0.25 0.3

Crack Length (mm)

Circumferential Ligament Length (mm)

Unstable burst

2x90% deep cracks

Crack Length (in.)

p

MSLB=18 MPa (2.6 ksi)

No radial or circ

ligament rupture

or unstable burst

Radial/circ

ligament 

rupture

no burst

Circumferential Ligament Length (in.)

(a) (b) 

Figure 29. Failure maps for SG tubes with two 90% deep axial cracks separated by (a) an 

axial ligament (Type C) and (b) a circumferential ligament (Type D) at main 

steam line break pressure (PMSLB). “Crack length” denotes the total overall 

length of the individual cracks and ligaments. 
 27 

Four Cracks 

The failure map for four–90% deep axial cracks separated by three axial ligaments is plotted 

in Figure 31a. As in the case of a single crack, cracks with a total length less than 0.85 in. (22 

mm) are predicted to remain stable (no unstable burst) for all ligament widths. Further, if four 

Type C cracks have an axial ligament length greater than 0.75 mm (0.03 in.), then cracks longer 

than 0.85 in. (22 mm) will experience unstable burst only if the ligament length/crack length lies 

in the zone marked “unstable burst”. For shorter ligament lengths, both radial and axial or 

circumferential ligaments are predicted to rupture provided the crack length/ligament length lie in 

the zone marked “radial/axial lig. rupture” in the figure, but the resulting single TW crack after 

ligament rupture is predicted to remain stable (no unstable burst) provided the overall crack 

length is less than 0.85 in. (22 mm). However, in contrast to previous cases, there is a narrow 

region of axial ligament length/crack length in which the cracks will undergo radial ligament 

rupture without experiencing axial ligament rupture or unstable burst. The failure map for four–

80% deep axial cracks separated by three axial ligaments is shown in Figs. 31b. Cracks longer 

than 0.85 in. (22 mm) will not necessarily burst unstably provided the crack length/ligament 

length lie in the region marked as “no radial or axial ligament rupture”. In contrast to the four90% deep crack case, there are no crack length/ligament length regimes in which either radial and 

axial ligaments will rupture or radial but no axial ligament will rupture. 

0

10

20

30

40

0

0.5

1

1.5

0 0.5 1 1.5 2 2.5

0 0.02 0.04 0.06 0.08

Crack Length (mm)

Axial Ligament Length (mm)

4x90% deep cracks

Crack Length (in.)

p

MSLB=18 MPa (2.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Radial/axial

lig. rupture

no burst

Axial Ligament Length (in.)

Unstable burst

no axial 

lig. rupt.

or burst

Radial lig.

rupt.

0

10

20

30

40

50

60

0

0.5

1

1.5

2

0 0.5 1 1.5 2

0 0.02 0.04 0.06

Crack Length (mm)

Axial Ligament Length (mm)

4x80% deep cracks

Crack Length (in.)

p

MSLB=18 MPa (2.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Unstable burst

Axial Ligament Length (in.)

(a) (b) 

Figure 31. Failure maps for SG tubes with four axial cracks, (a) 90% and (b) 80% deep, 

separated by three axial ligaments (Type C) at main steam line break pressure 

(PMSLB). “Crack length” denotes the total overall length of the individual 

cracks and ligaments. 

Six Cracks 

Figures 32a-b show the failure maps for six–90% deep and six-80% deep axial cracks 

separated by five axial ligaments, respectively. The failure maps are similar to the four–90% and 

four-80% deep axial crack cases (Figs. 31a-b), except that the zones where unstable burst occurs 

are more limited. As before, cracks with a total length less than 0.85 in. (22 mm) are predicted to 

remain stable (no unstable burst) for all ligament widths. 
 28 

0

10

20

30

40

50

0

0.4

0.8

1.2

1.6

0 0.5 1 1.5 2

0 0.02 0.04 0.06

Crack Length (mm)

Axial Ligament Length (mm)

6x90% deep cracks

Crack Length (in.)

p

MSLB=18 MPa (2.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Unstable burst

Axial Ligament Length (in.)

no Axial 

lig. rupt.

or burst

Radial lig.

rupt.

Radial/axial

lig. rupture

no burst

0

10

20

30

40

50

0

0.4

0.8

1.2

1.6

0 0.2 0.4 0.6 0.8 1

0 0.01 0.02 0.03

Crack Length (mm)

Axial Ligament Length (mm)

6x80% deep cracks

Crack Length (in.)

p

MSLB=18 MPa (2.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Unstable burst

Axial Ligament Length (in.)

(a) (b) 

Figure 32. Failure maps for SG tubes with six axial cracks, (a) 90% and (b) 80% deep, 

separated by five axial ligaments (Type C) at main steam line break pressure 

(PMSLB). “Crack length” denotes the total overall length of the individual 

cracks and ligaments. 

2.4.3 Failure Maps for 1.4xMain Steam Line Break Pressure (1.4PMSLB) 

Since a safety factor of 1.4 is used for accident analysis, the failure maps for 1.4PMSLB are 

of interest. 

Single Crack 

The failure map of a single crack at 1.4 times main steam line break pressure, shown in Fig. 

33, is similar to that at main steam line break pressure (Fig. 28) except that the maximum crack 

length below which no unstable burst is predicted is reduced to 0.59 in. (15 mm). 

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2

0 10 20 30 40 50

50

60

70

80

90

100

Crack Depth

Crack Length (in.)

unstable

burst

Radial

ligament

rupture

no burst

No radial ligament rupture

or unstable burst

Radial

ligament

rupture and

Crack Length (mm)

Crack Depth (%)

1.4 PMSLB=25 MPa (3.6 ksi)

Figure 33. 

Failure map of a single crack at 1.4 times

main steam line break pressure

1.4pMSLB. 
 29 

Two Cracks 

Figures 34a–b show the failure maps for two–90% deep axial cracks separated by an axial 

and a circumferential ligament, respectively. The maps are similar to those for the postulated 

MSLB case (Figs. 29a-b), except cracks with a total length shorter than 0.59 in. (15 mm) are 

predicted to remain stable (no unstable burst) for all ligament lengths. Again the failure maps for 

the axial and circumferential ligament cases are quite similar, and the axial ligament case provides 

a conservative bound to the circumferential ligament case, i.e., the non-failure regime for the axial 

ligament case is contained within the non-failure regime for the circumferential ligament case. 

0

10

20

30

40

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 2 4 6 8 10

0 0.1 0.2 0.3

Crack Length (mm)

Axial Ligament Length (mm)

Unstable burst

2x90% deep cracks

Crack Length (in.)

1.4pMSLB=25 MPa (3.6 ksi)

No radial or axial

ligament rupture

or burst

Axial Ligament Length (in.)

Radial/axial

lig. rupture

no burst

0

10

20

30

40

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 2 4 6 8 10

0 0.1 0.2 0.3

Crack Length (mm)

Circumferential Ligament Length (mm)

Unstable burst

2x90% deep cracks

Crack Length (in.)

1.4pMSLB=25 MPa (3.6 ksi)

No radial or circ.

ligament rupture

or unstable burst

Circumferential Ligament Length (in.)

Radial/circ.

lig. rupture

no burst

(a) (b) 

Figure 34. Failure maps for SG tubes with two 90% deep axial cracks separated by (a) an 

axial ligament (Type C) and (b) a circumferential ligament (Type D) at 1.4 times 

main steam line break pressure (1.4PMSLB). “Crack length” denotes the total 

overall length of the individual cracks and ligaments. 

The failure maps for two–80% deep axial cracks separated by an axial and a circumferential 

ligament are shown in Figs. 35a–b, respectively. The maps are similar to those for the postulated 

MSLB case (Figs. 29a-b), except cracks shorter than 0.59 in. (15 mm) are predicted to remain 

stable (no unstable burst) for all ligament lengths and there is a small zone of crack 

length/ligament length where radial and axial (or circumferential) ligaments are predicted to 

rupture without burst. 

Four Cracks 

The failure map for four–90% deep axial cracks separated by three axial ligaments is plotted 

in Figure 36a. The map is similar to the map for the postulated MSLB case (Fig. 31a), except that 

cracks shorter than with a total length 0.59 in. (15 mm) are predicted to remain stable (no 

unstable burst) for all ligament widths. The failure map for four–80% deep axial cracks separated 

by three axial ligaments is shown in Figs. 36b. Because of the higher pressure, two additional 

failure zones, which were absent in the postulated MSLB case (Fig. 31b), appear in the 1.4pMSLB

case (Fig. 36b). 
 30 

0

10

20

30

40

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 2 4 6 8 10

0 0.08 0.16 0.24 0.32

Crack Length (mm)

Axial Ligament Length (mm)

Unstable burst

2x80% deep cracks

Crack Length (in.)

1.4pMSLB=25 MPa (3.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Axial Ligament Length (in.)

Radial/axial

lig. rupture

no burst

0

10

20

30

40

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 2 4 6 8 10

0 0.08 0.16 0.24 0.32

Crack Length (mm)

Circumferential Ligament Length (mm)

Unstable burst

2x80% deep cracks

Crack Length (in.)

1.4pMSLB=25 MPa (3.6 ksi)

No radial or circ.

ligament rupture

or unstable burst

Circumferential Ligament Length (in.)

Radial/circ.

lig. rupture

no burst

(a) (b) 

Figure 35. Failure maps for SG tubes with two 80% deep axial cracks separated by (a) an 

axial ligament (Type C) and (b) a circumferential ligament (Type D) at 1.4 times 

main steam line break pressure (1.4PMSLB). “Crack length” denotes the total 

overall length of the individual cracks and ligaments. 

0

10

20

30

40

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5 3

0 0.05 0.1

Crack Length (mm)

Axial Ligament Length (mm)

Unstable burst

4x90% deep cracks

Crack Length (in.)

1.4pMSLB=25 MPa (3.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Axial Ligament Length (in.)

Radial/axial

lig. rupture

no burst

no Axial 

lig. rupt.

or burst

Radial lig.

rupt.

0

10

20

30

40

50

0

0.4

0.8

1.2

1.6

0123

0 0.02 0.04 0.06 0.08 0.1

Crack Length (mm)

Axial Ligament Length (mm)

Unstable burst

4x80% deep cracks

Crack Length (in.)

1.4pMSLB=25 MPa (3.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Axial Ligament Length (in.)

Radial/axial

lig. rupture

no burst

no Axial 

lig. rupt.

or burst

Radial lig.

rupt.

(a) (b) 

Figure 36. Failure maps for SG tubes with four axial cracks, (a) 90% and (b) 80% deep, 

separated by three axial ligaments (Type C) at 1.4 times main steam line break 

pressure (1.4PMSLB). “Crack length” denotes the total overall length of the 

individual cracks and ligaments. 

Six Cracks 

Figure 37a-b show the failure maps for six–90% and six-80% deep axial cracks separated by 

five axial ligaments, respectively. The maps are similar to those for the postulated MSLB case 

(Figs. 32a-b), except cracks with a total length shorter than 0.59 in. (15 mm) are predicted to

remain stable (no unstable burst) for all ligament widths. Also, because of the higher pressure, an 
 31 

additional failure zone, which was absent in the postulated MSLB case (Fig. 32b), appears in the 

1.4pMSLB case (Fig. 37b). 

5

10

15

20

25

30

35

40

45

0.5

1

1.5

0 0.5 1 1.5 2

0 0.02 0.04 0.06

Crack Length (mm)

Axial Ligament Length (mm)

6x90% deep cracks

Crack Length (in.)

1.4 p

MSLB=25 MPa (3.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Unstable burst

Axial Ligament Length (in.)

no Axial 

lig. rupt.

or burst

Radial lig.

rupt.

Radial/axial

lig. rupture

no burst

5

10

15

20

25

30

35

40

45

0.5

1

1.5

0 0.5 1 1.5 2

0 0.02 0.04 0.06

Crack Length (mm)

Axial Ligament Length (mm)

6x80% deep cracks

Crack Length (in.)

1.4 p

MSLB=25 MPa (3.6 ksi)

No radial or axial

ligament rupture

or unstable burst

Unstable burst

Axial Ligament Length (in.)

Radial/axial

lig. rupture

no burst

(a) (b) 

Figure 37. Failure maps for SG tubes with six axial cracks, (a) 90% and (b) 80% deep, 

separated by five axial ligaments (Type C) at 1.4 times main steam line break 

pressure (1.4PMSLB). “Crack length” denotes the total overall length of the 

individual cracks and ligaments. 

2.4.4 Failure Maps for 3xNormal Operating Pressure (3PNO) 

Since a safety factor of 3 is used in design, the failure maps for 3PNO are of interest. 

Single Crack 

The failure map of a single crack at 3 times normal operating pressure (3PNO) is shown in 

Fig. 38. The map is similar to the 1.4PMSLB case (Fig. 33), except that any crack of length less 

than 0.44 in. (11 mm), irrespective of depth, is predicted to remain stable (no unstable burst) at 3 

times normal operating pressure. 

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

0 5 10 15 20 25

50

60

70

80

90

100

Crack Depth

Crack Length (in.)

unstable

burst

Radial

ligament

rupture

no burst

No radial ligament rupture

or unstable burst

Radial

ligament

rupture and

Crack Length (mm)

Crack Depth (%)

3PNO=30 MPa (4.4 ksi)

Figure 38. 

Failure map of a single crack at 3 times 

normal operating pressure 3PNO. 
 32 

Two Cracks 

Figures 39a–b show the failure maps for two–90% deep axial cracks separated by an axial 

and a circumferential ligament, respectively. The maps are similar to the 1.4PMSLB case (Figs. 34

a-b), except cracks with a total length shorter than 0.44 in. (11 mm) are predicted to remain stable 

for all ligament widths. As before, the failure maps for the axial and circumferential ligament 

cases are quite similar, and the axial ligament case provides a conservative bound to the 

circumferential ligament case, i.e., the non-failure regime for the axial ligament case is contained 

within the non-failure regime for the circumferential ligament case. 

0

5

10

15

20

25

30

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12

0 0.1 0.2 0.3 0.4

Crack Length (mm)

Axial Ligament Length (mm)

Unstable burst

2x90% deep cracks

Crack Length (in.)

3pNO=30 MPa (4.4 ksi)

No radial or axial

ligament rupture

or burst

Axial Ligament Length (in.)

no Axial 

lig. rupt.

or burst

Radial lig.

rupt.

Radial/axial

lig. rupture

no burst

0

5

10

15

20

25

30

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12

0 0.1 0.2 0.3 0.4

Crack Length (mm)

Circumferential Ligament Length (mm)

Unstable burst

2x90% deep cracks

Crack Length (in.)

3pNO=30 MPa (4.4 ksi)

No radial or circ.

ligament rupture

or unstable burst

Circumferential Ligament Length (in.)

Radial/circ.

lig. rupture

no burst

(a) (b) 

Figure 39. Failure maps for SG tubes with two 90% deep axial cracks separated by (a) an 

axial ligament (Type 2) and (b) a circumferential ligament (Type 4) at 3 times 

normal operating pressure (3PNO). “Crack length” denotes the total overall 

length of the individual cracks and ligaments. 

The failure maps for two–80% deep axial cracks separated by an axial and a circumferential 

ligament are shown in Figs. 40a–b, respectively. The maps are similar to the 1.4PMSLB case (Figs. 

35a-b). As before, the axial ligament case provides a conservative bound to the circumferential 

ligament case, i.e., the non-failure regime for the axial ligament case is contained within the nonfailure regime for the circumferential ligament case. 

Four Cracks 

The failure maps for four–90% and four-80% deep axial cracks separated by three axial 

ligaments are plotted in Figure 41a-b, respectively. The maps are similar to the 1.4PMSLB case 

(Figs. 36a-b), except cracks with a total length shorter than 0.44 in. (11 mm) are predicted to

remain stable (no unstable burst) for all ligament widths. 
 33 

0

10

20

30

40

0

0.4

0.8

1.2

0 2 4 6 8 10

0 0.1 0.2 0.3

Crack Length (mm)

Axial Ligament Length (mm)

2x80% deep cracks

Crack Length (in.)

No radial or axial

ligament rupture

or burst

Unstable burst

Axial Ligament Length (in.)

3pNO=30 MPa (4.4 ksi)

Radial and axial

ligament rupture

no burst 0

10

20

30

40

0

0.4

0.8

1.2

0 2 4 6 8 10

0 0.1 0.2 0.3

Crack Length (mm)

Circumferential Ligament Length (mm)

Unstable burst

2x80% deep cracks

Crack Length (in.)

3pNO=30 MPa (4.4 ksi)

No radial or circ.

ligament rupture

or burst

Circumferential Ligament Length (in.)

Radial/circ.

lig. rupture

no burst

(a) (b) 

Figure 40. Failure maps for SG tubes with two 80% deep axial cracks separated by (a) an axial 

ligament (Type C) and (b) a circumferential ligament (Type D) at 3 times normal operating 

pressure (3PNO). “Crack length” denotes the total overall length of the individual cracks 

and ligaments. 

Six Cracks 

Figure 42a-b show the failure maps for six–90% and six-80% deep axial cracks, respectively, 

separated by five axial ligaments. The maps are similar to the 1.4PMSLB case (Figs. 37a-b), except 

cracks shorter than 0.44 in. (11 mm) are predicted to remain stable for all ligament widths. Also, 

because of the higher pressure, an additional failure zone, which was absent in the 1.4PMSLB

case (Fig. 37b), appears in the 3PNO case (Fig. 42b). 

0

10

20

30

40

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3 3.5

0 0.05 0.1

Crack Length (mm)

Axial Ligament Length (mm)

4x90% deep cracks

Crack Length (in.)

No radial or axial

ligament rupture

or burst

Unstable burst

Axial Ligament Length (in.)

Rad. lig. rupt.

No ax. lig. rupt.

or burst

3pNO=30 MPa (4.4 ksi)

Radial and axial

ligament rupture

no burst

0

10

20

30

40

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3 3.5

0 0.05 0.1

Crack Length (mm)

Axial Ligament Length (mm)

4x80% deep cracks

Crack Length (in.)

3pNO=30 MPa (4.4 ksi)

No radial or axial

ligament rupture

or unstable burst Radial and axial

ligament rupture

no burst

Axial Ligament Length (in.)

Unstable burst

Rad. lig. rupt.

No ax. lig. rupt.

or burst

(a) (b) 

Figure 41. Failure maps for SG tubes with four axial cracks, (a) 90% and (b) 80% deep, separated 

by three axial ligaments (Type C) at 3 times normal operating pressure (3PNO). “Crack 

length” denotes the total overall length of the individual cracks and ligaments. 
 34 

0

10

20

30

40

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5

0 0.02 0.04 0.06 0.08

Crack Length (mm)

Axial Ligament Length (mm)

6x90% deep cracks

Crack Length (in.)

No radial or axial

ligament rupture

or unstable burst

Unstable burst

Axial Ligament Length (in.)

Rad. lig. rupt.

No ax. lig. rupt.

or burst

3pNO=30 MPa (4.4 ksi)

Radial and axial

ligament rupture

no burst

0

5

10

15

20

25

30

35

40

0

0.5

1

1.5

0 0.5 1 1.5 2 2.5

0 0.02 0.04 0.06 0.08

Crack Length (mm)

Axial Ligament Length (mm)

6x80% deep cracks

Crack Length (in.)

No radial or axial

ligament rupture

or unstable burst

Unstable burst

Axial Ligament Length (in.)

Rad. lig. rupt.

No ax. lig. rupt.

or burst

3pNO=30 MPa (4.4 ksi)

Radial and axial

ligament rupture

no burst

(a) (b) 

Figure 42. Failure maps for SG tubes with six axial cracks, (a) 90% and (b) 80% deep, 

separated by five axial ligaments (Type C) at 3 times normal operating pressure 

(3PNO). “Crack length” denotes the total overall length of the individual cracks 

and ligaments. 

2.5 Discussion and Conclusions 

The ANL radial ligament rupture model for axial part–throughwall cracks have been validated 

over the last several years by tests on specimens with a single EDM notch or two EDM notches 

separated by axial or circumferential ligaments. At the same time, finite element analyses have 

been conducted to establish numerical models for predicting the coalescence of two axial 

throughwall cracks separated by axial or circumferential ligament of various widths. All of these 

models together with the well–known unstable burst pressure correlation for a single throughwall 

crack were used to generate a series of failure maps. Each map, plotted with ligament length and 

overall crack length as coordinates, is based on the ligament lengths and crack lengths for a fixed 

number (2, 4, and 6) of axial part–throughwall cracks with a fixed depth that are predicted to fail 

by various mechanisms at pressure differences of PNO, PMSLB, 3PNO, or 1.4PMSLB. The failure 

mechanisms that are considered are the rupture of radial ligament (following which leakage 

occurs), crack coalescence (i.e., rupture of axial or circumferential ligament), and unstable burst. 

Each map delineates the regions of various failure mechanisms from each other and identifies 

regions (i.e., combinations of crack length and ligament length) for which failure (or non-failure) of 

one of the following types is predicted: 

(a) No radial or axial (or circumferential) ligament rupture and no unstable burst. 

(b) Radial ligament rupture but no axial (or circumferential) ligament rupture or unstable 

burst. 

(c) Radial and axial (or circumferential) ligament rupture but no unstable burst. 

(d) Unstable burst. 

These maps illustrate the importance of ligament and crack sizes in structural and leakage 

integrity evaluations and may be useful for identifying flaws that require more detailed evaluation 

during in-service inspection. They have been generated using the typical strength properties of 22 
 35 

mm (0.875 in.) OD, 1.3 mm (0.05 in.) wall thickness Alloy 600 tubes at 300°C (570°F). If 

necessary, the maps can be modified for tubes of a different size and/or strength properties. 

However, because the failure pressures corresponding to all the failure mechanisms depend 

linearly on the flow stress and the maps are plotted in terms of the crack and ligament lengths, 

they should be invariant provided the ratio between the relevant pressure difference (PNO or 

PMSLB) and the flow stress remains approximately constant. 

The failure maps have been generated for idealized and regular geometry of cracks. In 

reality, individual crack lengths and ligament lengths will vary in the same specimen and the 

ligament geometry can be a mixture of the various idealized geometries considered in this report. 

Therefore, to use these maps in an actual application, the user has to exercise judgment in 

determining which map is applicable. Some averaging techniques (e.g., equivalent rectangular 

crack) will be needed to replace the actual crack geometry (as determined by NDE) with one of the 

idealized crack geometries considered in this report. For example, crack lengths and ligament 

lengths could be deliberately chosen to represent an upper or lower bound to the actual case. If 

NDE is unable to resolve the ligaments, the predicted failure pressure based on the total crack 

length will in all cases be conservative. Real stress corrosion cracks have highly complex 

geometries, and although we have made some progress in the understanding of the various failure 

mechanisms involved by analyzing and testing a limited number of idealized geometries, the 

prediction of failure pressures of complex stress corrosion cracks is still evolving. 

 37 

3 Leak Rate Studies 

3.1 Introduction 

The primary water in the steam generator tubes must be maintained at high pressure to 

remain liquid. If a leak occurs in the tube, when the water from the primary side enters the lower 

pressure secondary side, it will flash to steam. For incompressible flows, the leak rate is 

proportional to p1/2 and the flow rate for a given condition on the primary side will monotonically 

increase as the secondary side pressure is decreased. For compressible fluids a phenomenon 

called choking can occur in which for secondary pressures lower than a certain critical value the 

flow no longer continues to increase as the secondary pressure is decreased. Most 

phenomenological models of leaks from cracks in steam generator tubes in main steam line break 

accidents assume that the flow through a crack is choked. However, earlier studies at ANL have 

shown for a range of crack geometries choking does not occur. For such geometries, the flow 

through the crack can be described by the flow of an incompressible fluid through an orifice with 

an area equal to that of the flaw. This model has yielded excellent predictions over a wide range of 

pressures and temperatures for flaw opening dimensions as small as 0.18 mm (0.007 in.). 

However, it is clear that for some geometries choking may occur and that for short cracks, 

frictional losses, which are not accounted for in a simple orifice model, will become significant. A 

series of tests has been performed to try to better determine the range of geometries for which the 

simple, single–phase orifice model is applicable. 

3.2 Test Procedure 

The tests were performed in two stages. The first stage was carried out in the room–

temperature, high–pressure test facility. The target pressure for the overall leak testing was 17.2 

MPa (2500 psi), which is approximately the postulated MSLB pressure. However, if a flaw leaked 

at 7.6 MPa (1100 psi), which corresponds to normal SG operating pressure, it was then tested at 

this lower pressure. The leak rate was measured at several values of the pressure up to the target 

pressure and then re–measured at several values of the pressure as the pressure was decreased. 

After a tube was tested at RT, the flaw opening was characterized, and then the tube was 

tested in the High–Temperature Blowdown Test Facility (Stage 2 testing). In the Stage 2 tests, the 

flaws were first tested at RT to provide a check on results from the initial RT tests. They were then 

tested at 282°C (540°F) with zero back–pressure. The elevated–temperature test was then 

continued at the same primary pressure but with increasing levels of back–pressure. A decrease 

in flow rate with increasing back–pressure beyond that expected from the change in crack opening 

area due to a decrease in the elastic deformation indicates that the flow through the flaw is not 

choked. 

Digital photography was used to characterize the flaw length and the OD opening along the 

flaw length. The photographs were taken with a Fujifilm Digital FinePix S1 Pro camera with an 

image file size of 3,040 x 2,016 pixels. The camera is fitted with a long range microscope Infinity 

K2 lens which can yield optical magnifications up to about 100x with add–on front objective 

lenses. The photographic system also includes fixtures to position the tube while focusing 

critically on the cracks and lighting to improve uniformity of flaw illumination and reduce glare. 
 38 

The high–resolution flaw images produced by the hardware were analyzed using the ImageJ 

image analysis software, a public domain program based on the NIH Image software. The image 

analyses provided direct experimental measurements of crack opening displacement and crack 

opening area. Using digital magnification of the flaw images at highest resolution, the image can 

be magnified more than 400x without significantly degrading the image. 

3.3 Test Results 

3.3.1 Stage 1 Room Temperature Test Results 

Four 22.2–mm (7/8–in.)–diameter Alloy 600 tubes containing laboratory–produced 

throughwall flaws were tested. These specimens are identified as SGL904, SGL905, SGL911, and 

SGL750, respectively. 

The leak behavior of these flaws may be summarized as follows: 

(1) In the 280 kPa (40 psi) air–pressurization test with the tube submerged in a water 

bath, all the flaws leaked air. Very small bubbles were emitted from one or two sites 

along the flaw length. When pressurized with water, none of the flaws showed any 

visual signs of leakage until much higher pressures. Specimen SGL904 leaked at a 

pressure of 13.8 MPa (2000 psi), SGL905 at 15.2 MPa (2200 psi), SGL911 at 9.7 MPa 

(1400 psi), and SGL750 leaked at 10.3 MPa (1500 psi) internal pressure, In all cases, 

the initial leak was in the form of individual droplets forming every 5–10 s, and none 

of the flaws leaked in the form of a continuous jet of liquid until the pressure was 

increased by a few MPa. 

(2) Leak rate vs. pressure data were obtained at discrete intervals from flow collection and 

stop–watch measurements for pressures up to 17.2 MPa (2500 psi). In addition, the 

leak rate for each flaw was monitored vs. time at a constant pressure of 17.2 MPa 

(2500 psi) over time periods of 2–5 h to evaluate how stable the flaws were under 

constant pressure conditions. 

(3) The leak rates increased with time at the constant test pressure of 17.2 MPa (2500 

psi). Figures 43 and 44 show the leak rate as a function of time at 17.2 MPa (2500 

psi) for Specimens SGL750, SGL905, SGL904, and SGL911, respectively. The leak 

rate for SGL904 started out at 0.90 kg/min (1.98 lbs/min) and, after somewhat more 

than five hours under constant pressure, the leak rate increased to 9.03 kg/min (19.9 

lbs/min), a ten–fold increase. The other specimens exhibited similar behavior. At the 

end of the test period none of the flaws showed any evidence that the rate of increase 

in the leak rate was diminishing or approaching a stable, constant leak rate. The final 

leak rates were used with the observed crack opening areas for comparisons with the 

orifice model. 
 39 

(a) (b) 

Figure 43. Stage 1 leak–rate behavior of ODSCC axial Flaw (a) SGL750 and (b) SGL905 

under a constant pressure of 17.2 MPa (2500 psi) with room–temperature 

water. 

(a) (b) 

Figure 44. Stage 1 leak–rate behavior of ODSCC axial flaw (a) SGL904 and (b) SGL911 

under constant pressure of 17.2 MPa (2500 psi) with room–temperature water. 

Based on dye penetrant results, the nominal pretest lengths on the outer surface of the flaws 

ranged from 5.8–7.9 mm (0.23 to 0.31 in.). Figures 45–48 show high–resolution images of flaws 

SGL750, SGL904, SGL905, and SGL911 after being tested at 17.2 MPa (2500 psi) in Stage 1 at RT. 

In all cases, there is an apparent increase in length during the testing. Superimposed on each 

image are 9 reference points (g1 – g9) equally spaced along the length of each flaw. These points 

are locations at which the flaw opening has been measured. These points, together with special 

feature numbers (sf1, sf2, etc.), serve as points of reference in the magnified images. Each flaw 

image contains a ruler with 0.40–mm (1/64–in.) divisions. The ruler image permits one to relate a 

specific number of image pixels to the known distance and thereby define the scale for the image 

analysis. 
 40 

Figure 45. SCC axial flaw SGL750–OM–3/19/03. 

Figure 46. SCC axial flaw SGL904–OM–1/15/03. 

Figure 47. SCC axial flaw SGL905–OM–3/24/03. 
 41 

Figure 48. SCC axial flaw SGL911–OM–2–1/20/03. 

Figure 49 shows a magnified image of the feature sf1 identified in Fig. 46 on flaw SGL904–

OM. The feature appears to be an intact or possibly torn ligament. This is one of two ligaments 

evident in this flaw at the end of Stage 1 testing. 

Figure 49. Magnified image of feature sf1 in SCC flaw SGL904–OM, which appears to be 

an intact or possibly torn ligament. 

Several approaches were used to determine the flaw opening area. If the perimeter of the 

opening could be identified, image analysis software was used to calculate the enclosed area. The 

perimeters were highlighted either by drawing a line around the crack perimeter (the “wand” 

method) or using contrast to set the opening to white and everything else to black (the 

“threshholding” method). Fig. 51 shows a line drawn around the crack perimeter by the wand 

method. Figure 52 shows the crack opening for SGL905–OM highlighted by the threshholding 

method. 
 42 

Figure 50. Image analysis line drawn between the end points of SCC flaw SGL905–OM used 

to calculate flaw length 

Figure 51. Image analysis line drawn around the crack perimeter of SCC flaw SGL905–OM 

by the wand method to define the opening 

Figure 52. Crack opening of SCC flaw SGL905–OM highlighted by the threshholding 

method 

Table 5 shows the lengths and areas of the flaws as determined by post–test image analysis 

as well as the pretest lengths determined by eddy current NDE and dye–penetrant exam. The eddy 

current estimates are based on conventional PlusPoint analysis. In most cases the wand and the 

threshholding methods gave similar results, but in some cases the differences were significant. 

For flaw SGL905–OM, the crack length is 10.7 mm (0.42 in.). The crack opening area was 

determined to be 1.44 mm2 (0.00223 in.2) by the wand method and 1.01 mm2 (0.00156 in.2) by 

the threshholding method. The wand method gave the most consistent agreement with the room–

temperature, single–phase flow measurements when used with the orifice model . 
 43 

The opening width of the cracks as a function of distance along the crack was measured from 

the images, and the values are given in Table 6. The widths at G1 and G9, which are the end 

points of the flaws, are zero and are not shown. The average opening width reported in Table 6 

was calculated by averaging the values at locations G2 through G8. The measured widths can be 

used to compute an alternative estimate of flaw opening area, which is reported in the last column 

of Table 6. A comparison of these approximate areas with those presented obtained by image 

analysis shows reasonable agreement, but the areas determined by image analysis using the wand

method are taken as the most accurate representation of the OD area of the crack. 

Table 5 Axial crack lengths and opening areas after the RT tests 

Length, mm (in.) Post–test Area, mm2 (in.2) 

Flaw ID 

Eddy 

Current 

(Pretest) 

Dye 

Penetrant 

(Pretest) 

Image 

Analysis 

(Post–test) 

Wand 

Traced 

B&W 

Thresh– 

Holding 

SGL750–OM–

3/19/03 

 7.6 

 (0.3) 

 7.9 

 (0.31) 

 10.2 

 (0.40) 

 1.26 

 (0.00196) 

 1.39 

 (0.00215) 

SGL904–OM–

1/15/03 

 12.7 

 (0.5) 

 7.9 

 (0.31) 

 10.7 

 (0.42) 

 1.16 

 (0.00180) 

* 

SGL905–OM–

3/24/03 

 10.2 

 (0.4) 

 5.8 

 (0.230 

 10.7 

 (0.42) 

 1.44 

 (0.00223) 

 1.01 

 (0.00156) 

SGL911–OM–2–

1/20/03 

8.0 

(0.3) 

 7.6 

 (0.30) 

 10.4 

 (0.41) 

 1.23 

 (0.00191) 

* 

*Thresholding difficult because the digital photos lacked sharp focus and the lighting caused 

glare from crack walls. 

The disagreement between the pretest measurements of crack length by dye penetrant and 

the post–test measurements is not surprising. SCC cracks are typically very tight and it can be 

difficult to get the penetrant to penetrate the crack. However, the time dependent behavior of the 

leak rate shown in Figs. 43 and 44 indicates the situation is more complicated than simply the 

opening of a tight crack under load. At least for flaw SGL904 there is a visual indication of a 

ligament across the crack opening (Fig. 49). Thus part of the increase in leak could be associated 

with time–dependent failure of ligaments on the crack faces. The mechanical behavior of SG tubes 

at RT or at operating temperature is usually described in terms of time–independent plastic 

behavior. However, some short–term plastic behavior would not be unexpected, although steady 

state creep rates at these temperatures are very low. Even time–dependent failure of the ligaments 

and some time–dependent opening of the crack does not seem to completely explain the observed 

behavior, since these would be expected to lead to some stable, steady–state condition. Instead 

the leak rates in all cases seem to be increasing with time. Later tests have shown that it is 

possible to have crack growth driven by the dynamics of the leak jet, but in these tests no 

intermediate crack lengths were measured so it is not possible to distinguish clearly between the 

increase in leak rates associated with time dependent crack opening, ligament failure, and jet–

driven crack growth. 
 44 

3.3.2 Stage 2 High Temperature Test Results Under Postulated MSLB Condition 

Circular Orifice 

A 1.59–mm (1/16–in.)–diameter EDM circular orifice was tested as a reference case. This 

orifice leaks at about the same rate as the SCC flaws tested in this series. At RT with 17.2 MPa 

(2500 psi) internal pressure and zero back–pressure, the observed leak rate was 12.6 kg/min (27.7 

lbs/min). A value of 13.1 kg/min (28.8 lbs./min) was obtained in Stage 1 testing in the High–

Pressure Facility. At 288°C (550°F) with 17.2 MPa (2500 psi) internal pressure and zero back–

pressure, the leak rate was 11.3 kg/min (24.9 lbs./min). The mass flow rate ratio for the room–to–

elevated–temperature is 12.6/11.3 = 1.11, which is close to the value of 1.15 predicted by the 

orifice model due to the change in density of the fluid. 

For the same elevated temperature and internal pressure but with a back–pressure of 1.85 

MPa (269 psi), the leak rate was 10.6 kg/min (23.3 lbs./min). The reduction in leak rate with an 

increase in back–pressure below the saturation pressure indicates that the flow was not choked. 

The orifice model for the circular hole predicted flow rates of 13.2, 11.4, and 10.8 kg/min (29.2, 

25.1, and 23.8 lbs./min) for the room–temperature test, the elevated–temperature test with zero 

back–pressure, and the elevated–temperature test with a back–pressure of 1.85 MPa (269 psi), 

respectively. Hence the flow model gives good predictions under this non–choked condition. 

Stress Corrosion Cracks 

Flaws SGL750, SGL904, SGL905, and SGL911 were tested first at a 17.2 MPa (2500 psi) 

internal pressure level and zero back–pressure at RT. The elevated–temperature cases were then 

tested for the same internal pressure with increasing levels of back–pressure to determine if 

choked flow occurs. 

Table 6 Variation of the opening width along the crack, average crack opening width, flaw 

length, and area. 

 Width at Locations g1, g2,... along the Flaw, mm (in.) 

Flaw 

ID g2 g3 g4 g5 g6 g7 g8 

Ave. 

width 

mm 

(in.) 

Flaw 

length,

mm 

(in.) 

Flaw 

area, 

mm2

(in.2) 

SGL 

750 

0.10 

(0.00413) 

0.16 

(0.00642) 

0.15 

(0.00587) 

0.15 

(0.00587)

0.06 

(0.00241)

0.10 

(0.00409)

0.10 

(0.00413)

0.12 

(0.004700 

10.1 

(0.398) 

1.21 

(0.00187)

SGL 

904 

0.08 

(0.00299) 

0.05 

(0.00192) 

0.07 

(0.00278) 

0.08 

(0.00320)

0.07 

(0.00256)

0.14 

(0.00533)

0.06 

(0.00235)

0.08 

(0.00302) 

10.8 

(0.425) 

0.83 

(0.00128)

SGL 

905 

0.09 

(0.00349) 

0.09 

(0.00349) 

0.15 

(0.00581) 

0.09 

(0.00349)

0.12 

(0.00465)

0.12 

(0.00465)

0.09 

(0.00349)

0.11 

(0.00415) 

10.6 

(0.416) 

1.12 

(0.00173)

SGL 

911 

0.11 

(0.00439) 

0.11 

(0.00443) 

0.11 

(0.00439) 

0.10 

(0.00376)

0.11 

(0.00443)

0.11 

(0.00439)

0.11 

(0.00443)

0.11 

(0.00432) 

10.4 

(0.409) 

1.14 

(0.00177)
 45 

SGL905 had a flow rate of 7.6 kg/min (16.8 lbs./min) at room–temperature with 17.2 MPa 

(2500 psi) internal pressure and zero backpressure. This is reasonably close to the Stage 1 leak–

rate value of 8.0 kg/min (17.6 lbs./min). At the 288°C (550°F) test with 17.2 MPA (2500 psi) 

internal pressure and zero back–pressure, the flaw leaked at a rate of 14.0 kg/min (30.8 lbs./min). 

The back–pressure was then raised to 2.34 MPa (340 psi) back–pressure, yielding a flow rate 

of 13.9 kg/min (30.6 lbs/min). Comparison of the zero and non–zero back–pressure cases reveals 

essentially identical flow rates, indicating a choked flow condition. At a back–pressure of 8.83 

MPa (1280 psi), the flow rate was 10.98 kg/min (24.21 lb/min), which indicates the flow was not 

choked, and that the back–pressure was too high for choking to occur. The pressure ratio of 

downstream to upstream was 0.512, which is below the critical value of 0.528 for choked flow of 

gas through a converging nozzle. 

SGL904 yielded a flow rate of 7.5 kg/min (16.6 lbs./min) at room–temperature with 17.2 

MPa (2500 psi) internal pressure and zero backpressure. This compared favorably to the Stage 1 

leak–rate value of 9.0 kg/min (19.9 lbs./min). For the 288°C (550°F) test at 17.2 MPa (2500 psi) 

internal pressure with zero back–pressure, the flaw leaked 15.0 kg/min (33.1 lbs./min). The mass 

flow rate ratio for the room–to–elevated–temperature testing is 16.6/33.1 = 0.50. Assuming a 

crack length of 11.2 mm (0.44 in.), a reduction in yield stress with temperature of 15%, and the 

orifice flow model, a ratio of 0.61 is expected. 

At 288°C (550°F) test at the 17.2 MPa (2500 psi) internal pressure, Flaw SGL904 was then 

tested with 4.08 MPa (593 psi) back–pressure, yielding a flow rate of 15.0 kg/min (33.0 lbs/min). 

Comparison of the zero and non–zero back–pressure cases reveals essentially identical flow rates, 

indicating a choked flow condition. At a back–pressure of 5.90 MPa (855 psi), the flow rate was 

13.0 kg/min (28.7 lb/min), which indicates the flow was not choked. After elevated–temperature 

testing with 17.2 MPa (2500 psi) internal pressure and zero backpressure, SGL904 yielded a flow 

rate of 19.2 kg/min (42.2 lbs./min) under room–temperature testing. This is much larger than 

would be expected simply from the increased plastic deformation that occurred due to decrease in 

yield stress during testing at 288°C. Comparison of Figs. 46 and 54 suggests that ligaments were 

present after that RT test that failed during the high temperature test. 

SGL750 was tested with 17.2 MPa (2500 psi) internal pressure and at 288°C (550°F) with no 

back–pressure and a back–pressure of 3.84 MPa (557 psi) yielding flow rates of 12.8 and 12.3 

kg/min (28.1 lb/min and 27.0 lb/min), respectively. In contrast to SGL905 and SGL904, SGL750, 

which is nominally about the same length as the other two flaws, exhibited a reduction in leak rate 

with an increase in back–pressure indicating the flow was not choked. 

SGL911 was tested with 17.2 MPa (2500 psi) internal pressure and at 288°C (550°F) with no 

back–pressure and a back–pressure of 5.12 MPa (742 psi), yielding flow rates of 9.6 and 9.0 

kg/min (21.2 lb/min and 19.9 lb/min), respectively. Hence, this SCC flaw, like flaw SGL750, 

exhibited a reduction in leak rate with an increase in back–pressure; indicating the flow was not 

choked. 

Thus, for the four SCC flaws tested at 17.2 MPa (2500 psi) and 288°C (550°F), SGL904 and 

SGL905 appear to exhibit choking, and SGL750 and SGL911 do not. 

Figs. 53–56 show images of flaws SGL750, SGL904, SGL905 and SGL911 after Stage 2 

testing. The reference points (g1– g9) again denote the locations at which the flaw opening was 
 46 

measured and sf1, sf2, etc. again denote special features of note. Comparison of the post–test 

Stage 1 and Stage 2 flaw areas shows that each flaw area has increased between 100 to 275% 

from the end of Stage 1 testing to the end of Stage 2 testing. 

Figure 53. Stage 2 SCC axial flaw SGL750 after the high temperature test. 

Figure 54. Stage 2 SCC axial flaw SGL 904 after the high temperature test. 

Figure 55. Stage 2 SCC axial flaw SGL905–BDTF–4/15/03. 

Figure 56. Stage 2 SCC axial flaw SGL911 after the high temperature test. 

The geometry of the crack openings after the high temperature tests are summarized in Table 

7. A hydraulic diameter, D, was defined as 4A/P where A is the area of the flaw and P is the 
 47 

perimeter. For cracks, D is 2 where  is the opening width. For the 1.59 mm (1/16–in.)–diameter 

EDM circular hole flaw the hydraulic diameter is equal to the geometric diameter. The ratio of the 

wall thickness to hydraulic diameter gives the effective L/D for the flaw. For the flaws tested, L/D 

ranges from 1.7 to 3.2. Larger L/D ratios would be associated with larger frictional flow losses and 

would tend to lead to choked flow. Because two of the flaws had choked flow and two did not, this 

suggests that the transition to choked flow will occur for L/D ratios in the range of 2–4, i.e., for 

cracks of the order of 12 mm (0.5 in.) for postulated MSLB pressures and a temperature of 288°C 

(550°F). The critical value would be expected to depend on the degree of subcooling. In the tests 

summarized in Table 7, the subcooling is representative of that expected in the cold leg. In the hot 

leg, where the subcooling is less, choking would be expected to occur with smaller frictional losses, 

i.e., for smaller L/D ratios (i.e., larger flaws). Thus using a value of L/D of 5–10 to describe the 

onset of choking would be conservative for leaks in both the hot and cold leg. 

Table 7 Crack opening geometries and flow behavior in tests at 288°C. 

Flaw SGL905 SGL904 SGL750 SGL911 

1/16–in 

Orifice 

Choked Yes Yes No No No 

Flaw Area 

mm2 (in.2) 

2.97 

(0.00461)

4.32 

(0.00671)

3.10 

(0.00481)

2.36 

(0.00366)

1.97 

(0.00306)

Flaw Length, 

mm (in) 

11.2 

(0.442) 

11.9 

(0.470) 

11.3 

(0.446) 

12.0 

(0.471) 

1.5875 

(0.0625) 

Ave. Width, mm 

(in) 

0.265 

(0.01043)

0.365 

(0.01438)

0.274 

(0.01078)

0.197 

(0.00777)

1.5875 

(0.0625) 

L/D 2.4 1.7 2.3 3.2 0.8 

The crack opening areas on the OD and ID surfaces can be significantly different. To 

estimate this difference, finite element calculations were performed. The calculations were done 

with five layers of solid elements through the thickness. The results shown in Fig. 57 for 288°C 

suggest that the difference of about a factor of 1.4 between the OD and ID areas for a 12 mm 

(0.5–in) crack. The effect is smaller at low–temperature because of the higher yield strength. 

Shell–element solutions appear to give good approximations to the OD opening area, but 

overestimate the ID area. The closed form solution of Zahoor7 gives reasonable to conservative 

solutions for the OD area when the yield stress is used to characterize the material. 
 48 

0

0.001

0.002

0.003

0 0.5 1 1.5 2 2.5 3

IDCOA (Solid)

ODCOA (Solid)

COA (Shell)

0

0.4

0.8

1.2

1.6

0 5 10 15 20

Crack Opening Area (in2

)

p (ksi)

Crack Opening Area (mm2

)

p (MPa)

0.5 in. crack

Zahoor (using yield stress)

Zahoor (using flow stress)

Figure 57. 

Comparison of crack opening areas at 

the ID and OD for a 12.7 mm (0.5 in.) 

crack at 288°C. Results are shown for 

finite–element solutions using solid and 

shell elements as well as the analytical 

solution of Zahoor. 

0

0.01

0.02

0.03

0.04

0 0.5 1 1.5 2 2.5 3

IDCOA (Solid)

ODCOA (Solid)

COA (Shell)

0

5

10

15

20

25

0 5 10 15 20

Crack Opening Area (in2

)

p (ksi)

Crack Opening Area (mm2

)

p (MPa)

0.75 in. crack

Zahoor (using yield stress)

Zahoor (using flow stress)

Figure 58. 

Comparison of crack opening areas at 

the ID and OD for a 19.0 mm (0.75 in.) 

crack at 288°C. Results are shown for 

finite–element solutions using solid and 

shell elements as well as the analytical 

solution of Zahoor. 

The flaw opening areas from image analysis of the flaws after the test together with computed 

corrections for the elastic contribution and the differences between the OD and ID opening areas 

were used to estimate the flow area. For the RT tests, the observed flows and the flows predicted 

using the estimated flow areas and an orifice coefficient of 0.6 are summarized in Table 8. The 

agreement between the observed and predicted flows is good and indicates that the orifice model 

has not been invalidated by flow path frictional losses for these flaws. 

Similar results for the tests at 288°C are shown in Table 9. The predicted flows were again 

obtained from the orifice model using a coefficient of 0.6. The differences between the ID and OD 

areas are larger than in the RT case and both areas were used to compute predicted flows. For 

flaws SGL905, SGL904, which appeared to have choked flow, an estimate of the choked flow based 

on the assumption that for back–pressures less than the saturation pressure, psat, the effective 

pressure difference is p – psat. 
 49 

In Table 9, the observed and predicted flows for the tests at 288°C with different back–

pressures are given. In addition to the actual predicted flows, normalized values that are scaled to 

agree with the observed flow rates for zero back–pressure were also computed. This reduces the 

effect of uncertainties in the flow area and orifice coefficient and provides a better estimate of the 

dependence on the pressure difference. The assumption that the effective pressure difference is 

p – psat in the choked flow regime seems to be slightly conservative. 

Table 9 Comparison of orifice model predictions and experimental results for the 

tests at 288°C for different back–pressures 

Flaw Back–

pressure MPa 

Observed Q,

kg/min 

Predicted Q 

Choked Flow 

kg/min 

Predicted Q 

Non–choked 

kg/min 

Normalized Q 

Choked Flow 

kg/min 

Normalized Q 

Non–choked 

kg/min 

SGL904 0 15.0 14.3 19.0 15.0 15.0 

SGL904 4.08 15.0 14.3 16.6 15.0 13.1 

SGL904 5.9 13.0 14.3 15.4 15.0 12.2 

SGL905 0 14.0 9.8 13.1 14.0 14.0 

SGL905 2.34 13.9 9.8 12.2 14.0 13.0 

SGL905 8.83 11.0 9.1 9.1 12.9 9.8 

SGL750 0 12.8 10.3 13.6 12.8 12.8 

SGL750 3.84 12.3 10.3 12.0 12.8 11.3 

SGL911 0 9.6 7.8 10.4 9.6 9.6 

SGL911 5.12 9.0 7.8 8.7 9.6 8.0 

3.4 Leak Rate Model 

The tests reported here and previous results3,4 show that the orifice model works well for 

flaws with L/D ≤ 3–4. As shown in Fig. 59, this corresponds to cracks about 10–12 mm (0.43–in) 

under postulated MSLB pressures and to cracks about 25 mm (1–in) long under normal operating 

conditions. For shorter cracks where L/D can be much larger, frictional losses in the channels 

could be significant and lead to significant reduction in the flow rates predicted by the orifice 

model. Amos and Schrock8 have conducted a series of tests on two–phase critical flow on 

rectangular slits in a plate of thickness 2.5 in. (6.35 cm) with the slit opening varying between 

Table 8. Comparison of orifice model predictions and experimental results for the RT 

tests. 

Flaw 

Image Analysis

Flaw Area, mm2

Observed Q, 

kg/min 

Predicted 

Q kg/min 

SGL750 1.26 8.5 8.4 

SGL904 1.16 9.0 7.7 

SGL905 1.43 8.0 9.5 

SGL911 1.23 6.4 8.2 
 50 

0.007 and 0.03 in. which gives L/D values of 85–300. Their results can be used to get insight into 

the effect of larger L/D values on the flow rate. 

In the Amos and Schrock tests, the channels were instrumented so that it could be 

determined whether flashing was occurring within the channel or at the exit. Their results on 

flashing are shown in Figs. 60a–b. The dashed lines provides estimates of the minimum 

subcooling necessary to ensure that flashing does not occur inside the wall as a function of 

stagnation pressure, i.e., the pressure in the reservoir feeding the flaw, for values of L/D of 85 and 

135. An L/D of 135 would correspond to about a 3 mm (0.12-in) crack in a steam generator tube 

under postulated MSLB conditions or about a 6 mm (0.24-in) crack under normal operating 

conditions (Fig. 59). The data show that the minimum subcooling initially increases with 

Figure 59. 

L/D for cracks in SG tubes under normal

operating pressures and postulated MSLB

conditions. The flow length L is taken as

the wall thickness and the hydraulic

diameter D is 2, where  is the average

cracking opening. 

-10

0

10

20

30

40

50

60

70

2 4 6 8 10 12 14 16 18

Flashing at Exit

Flashing in Wall

0.5 1 1.5 2 2.5

Subcooling (°C)

Stagnation Pressure (MPa)

L/D=85

Stagnation Pressure (ksi)

2.72

4.45 6.15

0.13

5.21

0.29

-10

0

10

20

30

40

50

60

70

2 4 6 8 10 12 14 16 18

Flashing at Exit

Flashing in Wall

0.5 1 1.5 2 2.5

Subcooling (°C)

Stagnation Pressure (MPa)

L/D=135

Stagnation Pressure (ksi)

5.9

6.34 6.18

4.9

4.69

3.37 2.33 0.6 1.0

(a) (b)

Figure 60. Test results from Amos and Schrock8 on flashing as a function of stagnation pressure and 

subcooling for (a) L/D=85 and (b) L/D=135. Numbers next to symbols denote location of 

flashing in cm from entrance (wall thickness=6.35 cm). 
 51 

stagnation pressure, but reaches a peak beyond which it either drops slightly (L/D=85) or drops 

substantially (L/D=135). The maximum value of subcooling needed to prevent flashing inside the 

wall increases from 20°C (stagnation pressure=1 ksi) to 26°C (stagnation pressure=1.7 ksi) when 

L/D is increased from 85 to 135 (i.e., when the crack becomes smaller). The pressures in the 

Amos and Schrock tests are lower than those of interest in PWRs, but the results suggest that for 

cracks with L/D ≤ 135 (i.e., for crack lengths > 3 mm (0.12-in) for postulated MSLB conditions), 

flashing within the wall of the steam generator tube would not occur in either the cold leg or the 

hot leg. 

The flow in the channel wall is then single phase for L/D ≤ 135. The mass flow rate per unit 

area M. for a single–phase flow though a long channel with friction is 

M

2p  f L

D





 





0.5

 (3) 

where f is a friction factor (function of Reynolds number and surface roughness). For flow through 

an orifice 

M

2p  CD (4) 

where CD is the orifice discharge coefficient, which has a value of 0.6. 

For the channel, the flow rate depends on L/D; for the orifice, it is independent of L/D. The 

loss factors computed from the tests of Amos and Schrock8 on slits with opening varying from 

0.007 to 0.03–in. at subcooling temperatures of 54–60°C and the steam generator flaw tests at 

ANL are shown as a function of L/D in Fig. 61. 

A value of L/D ≈ 75 marks the transition between channel flow (dependent on L/D) and 

orifice flow (independent of L/D). L/D ≈ 3-4 marks the transition between a choked orifice and an 

unchoked orifice. For L/D > 4 the flow is always choked. Flashing will occur outside the wall for 

L/D < 135, but the flow will behave as though it is choked. For L/D > 75 in addition to the losses 

due to choking, frictional losses within the wall become important. 

For L/D > 75 a fit to the Amos and Schrock8 data gives 

M

2p  13.44 L

D





 





0.72

 (5) 

The observed dependence on L/D is reasonably close to that expected for single–phase flow. The 

data shown in Fig. 61 suggest that the orifice model should be valid for L/D < 75. This 

corresponds to cracks with an unligamented length > 5mm (0.2–in) for postulated MSLB pressures 

and > 8 mm (0.3–in) for normal operating pressures. For larger values of L/D the frictional losses 

in the channel dominate the expansion loss associated with the orifice. For L/D > 135 flashing 

could occur within the wall. This would result in an additional reduction in flow beyond that 

predicted by Eq (5). 
 52 

Eqs (4) and (5) give the mass flow rate per unit area. To estimate the actual leak rate, an 

expression is needed for the crack opening area. The Zahoor model7 for the crack opening area: 

A  2ce

2Vo / E  Vo (2ce )(ce / E) (6) 

where Vo is a geometry factor, ce is the effective crack half length.  is the hoop stress = pR / h , R 

and h = mean radius and thickness of tube, E is Young’s modulus, Sy is the yield strength, 

ce  c 1 F

2



Sy













2 















, F  1 1.302  2.69x1024  5.35x104 6 ,

2  c2 / Rh , 

Vo  1 0.65e

2  8.97x103e4  1.34x104 e6 , e2  ce2 / Rh

and c is the half length of the crack, has been found by comparison with finite–element analyses 

and experiment to give good estimates of the crack opening area until the pressure begins to 

approach that for unstable burst. The average crack opening displacement is 

 = A/2c. 

Although flashing did not occur within the channel for L/D < 135 in the Amos and Shrock 

tests, in the current tests on steam generator flaws, choked flow was observed to occur for 

L/D ≈ 3–4. This result and the results shown in Fig. 61 are strictly valid only for the case where 

the subcooling is 50–60°C, i.e., cold leg conditions. Amos and Schrock8 attribute the departure 

from the expected choked behavior when flashing occurs to the kinetics of the flashing process. 

The fluid passes through the narrow steam generator wall so quickly that there is not enough time 

for it to flash and thus it acts and behaves more like a single phase liquid. For the lower values of 

subcooling in the hot leg, the flow would be expected to flash more readily than under cold leg 

conditions, and would be expected to be choked at lower values of L/D than measured in our 

current tests. Because choking will result in lower flow rates, the current model will thus tend to 

overpredict leak rates in the hot leg for a range of L/D values between those assumed to produce 

Figure 61. 

Flow loss factor, M 2p , as a function 

of L/D for Amos and Shrock slit tests8 and 

tests on SG tubes. 
 53 

choking here (3–4) and the somewhat lower values of L/D that actually characterize choking in 

the hot leg. 

The flow rate equations and their expected regions of validity are summarized as follows: 

M

2p  0.6 L/D ≤ 75 (7) 

M

2p  13.44 L

D





 





0.72

 L/D > 75 

where for cracks L is the wall thickness and the hydraulic diameter D is twice the crack opening 

displacement. For very tight cracks, the effective length can be even longer than wall thickness 

because of crack meandering, but taking L as the wall thickness should give conservative 

estimates. The effective p is:

p = p–pback L/D ≤ 5 

p = p–pback L/D > 5 and pback ≥ psat 

p = p–psat L/D > 5 and pback < psat

where pback is the secondary side back–pressure and psat is the saturation pressure. The value of 

L/D for the onset of choked flow has been taken as 5, since the tests indicated a transition value 

ranging from 2–4. The results are based on tests with 50–60°C of subcooling (cold leg conditions). 

The model should tend to overpredict leak rates for hot leg conditions for a range of L/D < 5. Eq 

(7) is similar to that proposed in Ref. 9, but in that case the flow was always assumed to be choked 

and no limits were proposed for L/D. 

The uncertainties in prediction of leak rates through cracks will usually be dominated by 

uncertainties associated with crack geometry. The Zahoor model, Eq (6), gives a dependence of the 

crack opening area on the crack length approximately proportional to c5.2. Thus, the presence of 

ligaments could change the leak rate by two orders of magnitude or more. Bounding estimates of 

crack length will typically grossly overestimate the leak rate. 

3.5 Conclusions 

Previous tests at ANL have shown that a single–phase orifice discharge model can accurately 

predict leak rates for flaws with widths as small as 0.18 mm (0.007 in.). Additional tests have 

been performed to better establish the range of validity of the orifice flow model. The tightness of 

cracks can be described in terms of the length of the flow channel L, approximately the wall 

thickness, and a hydraulic diameter D, which for a crack is taken as twice the crack opening 

displacement. The test results suggest that the critical value of L/D for the transition between 

choked and non–choked flow is on the order of 3–4. This value of L/D is strictly valid only for the 

value of the subcooling used in the tests, which corresponds to the cold–leg conditions. However, 

these values should give conservative estimates of the critical value of L/D for hot–leg conditions. 

These results together with previous work by Amos and Shrock on flow through slits have 

been used to develop a simple leak rate model. A value of L/D ≈ 75 (7 mm, operating p; 4 mm, 
 54 

MSLB) marks the transition between channel flow (dependent on L/D) and orifice flow 

(independent of L/D). L/D ≈ 3-4 (19 mm, operating p; 11 mm, MSLB) marks the transition 

between a choked orifice and an unchoked orifice. For L/D > 4 the flow is always choked. 

Flashing will occur outside the wall for L/D < 135 (5 mm, operating p; 3 mm, MSLB), but the flow 

will behave as though it is choked. For L/D > 75 in addition to the losses due to choking, 

frictional losses within the wall become important. For L/D > 135 flashing could occur within the 

wall. This would result in an additional reduction in flow beyond that predicted by the model. 

The major uncertainty in applying the model is probably the actual crack geometry. 

Remaining ligaments could greatly reduce the actual crack opening area, which is usually 

estimated based on a simple, rectangular or elliptical crack shape. 
 55 

4 Leak Rates in Restricted Areas 

4.1 Introduction 

Voltage-based alternate repair criteria have been established with regard to axial outsidediameter stress corrosion cracking (ODSCC) of steam generator (SG) tubes at tube support plates 

(TSPs). These criteria rely on an existing database for free-span leak rates from cracks to calculate 

the total leakage from tubes with indications remaining in service. The database for free-span 

leakage is utilized because the TSPs could displace laterally during postulated main steam-line 

break (MSLB) loading exposing the cracks under the TSPs. To justify leaving higher voltage 

indications in service, a few licensees have minimized the displacements of TSPs during transients 

by expanding a number of tubes above and below the TSPs to effectively lock the TSPs to the 

tubes. Although this procedure does mitigate the potential for burst and reduce leakage for cracks 

in the TSP regions, it will not eliminate the potential for leakage during postulated MSLB and 

severe accidents from such cracks.

The objective of the present study is to analytically predict flaw opening area at postulated 

MSLB pressure and expected leak rate from a crack, axial or circumferential, under the TSP. A 

second objective is to calculate the flaw opening and leak rates from similarly situated cracks as a 

function of time during postulated severe accidents. 

4.2 Currently Available Leak Rate Data 

4.2.1 Westinghouse/EPRI Tube/TSP Data 

Under Electric Power Research Institute (EPRI) sponsorship, Westinghouse carried out a test 

program to develop a database for leakage from indications restricted from burst (IRB) for a wide 

range of crack sizes. An IRB is defined as a crack inside the TSP that would burst if located in 

the free-span region. The principal objective of the test program was to define a bounding leak 

rate for a limiting IRB in an unpacked crevice. Most of the tests were performed in a high-energy 

steam facility with flow capability up to 30 L/min (8 gpm). The steam-line break (SLB) conditions 

were taken as a primary coolant temperature of 324°C (615°F) and a pressure differential of 18 

MPa (2.56 ksi). The high-temperature tests were augmented by tests in a room–temperature, 

high–pressure test facility. 

Two types of tests were run. First, testing was done with the crack completely contained 

within the TSP and with one end of the crack aligned with the edge of the TSP. Second, testing 

was done with one tip of the crack positioned (offset) outside the TSP. 

The test consisted of internal pressurization of the tube and measurement of the leak rate 

through the crack. To prevent leakage a bladder was inserted in the tube, and the crack was 

opened by pressurizing the tube to the predicted free-span burst pressure with the tube 

constrained within the TSP. After removing the bladder, leak rate tests were then conducted on 

these specimens. Fifteen tube specimens (Alloy 600 MA) were tested in this way. Specimens were 

prepared by (1) accelerated corrosion, (2) accelerated corrosion followed by fatigue cycling, and (3) 

laser cutting. The laser-cut specimens were rejected because they did not simulate the leakage 
 56 

behavior of stress corrosion cracks. Eight of the specimens were 22 mm (0.875 in.) in diameter, 

and the rest 19 mm (0.75 in.) in diameter. 

Cracks with lengths of 6 to 20 mm (0.24 to 0.809 in.) were tested. The TSP thickness of 19 

mm (0.75 in.) implies that the longest axial crack that can be under the TSP is 19 mm (0.75 in.). 

The critical throughwall crack length in 19-mm (0.75-in.) diameter tubing with lower tolerance 

limit material under these pressure and temperature conditions always happens to be ≈19 mm 

(0.75 in.). To be conservative, the diametral clearance between the tube OD and the tube hole in 

the TSP was set at 0.6 mm (0.025 in.), which is significantly greater than the nominal 0.4 mm 

(0.016 in.) clearance in the Model 51 SG. 

The bounding leak rate (21 L/min [5.5 gpm] at 18 MPa [2.56 ksi]) was determined from a 

single test with a crack length of 19 mm (0.76 in.) and supported by two other tests with long 

cracks. Tests with short cracks (< 10 mm [0.4 in.]) showed no interaction with the TSP because of 

the small opening at postulated MSLB pressure. Cracks with throughwall lengths ≥ 14 mm (0.55 

in.) and a tube/TSP gap of 0.6 mm (0.025 in.) interacted with the TSP prior to reaching the 

postulated MSLB pressure. For these cracks, increasing p after this point did not cause further 

increases in leak rate. Initially, the limiting flow area is the crack opening area (COA), but as the 

crack is pressurized it becomes the gap flow area, which is twice the area between the TSP wall 

and the tube OD (Fig. 62) on the radial plane through the crack: 

Gap flow area = 2 crack (gap) dx (8) 

where dx denotes integration along the tube axial direction. 

TSP Hole

Tube

TSP

0.008"

gap

Crack

Figure 62. Gap flow area for a tube 

with an axial crack inside the TSP. 

For such cracks, at some point increases in pressure increase the bulging and cause 

physical interaction between the crack flanks and the TSP, reducing the available flow area. 

Finally, further increases in pressure may cause the crack flanks to buckle toward the centerline 

of the tube, resulting in the tube being pressed tight against the TSP because of radial deformation 

due to elastic unloading of the crack flanks. 

Except the data for the offset cracks, the leak rate data on specimens pre-deformed by 

pressurization with a bladder are plotted against the crack opening area and the gap flow area in 

Fig. 63. From the solid lines, it is evident that, except for a couple of tests with very small crack 
 57 

opening area (and hence limited bulging), the correlation is better with gap flow area than with 

crack opening area. [Note that these data are for crevices that are unpacked with a diametral 

clearance between the tube OD and the TSP hole/wall of 0.6 mm (0.025 in.).] 

1

10

4

5

6

7

8

9

10

20

30

0.001 0.01

1 10

Throughwall Crack Area (in. 2

)

Max. 

p Leak rate (gpm)

Max. 

p Leak rate (L/min)

Throughwall Crack Area (mm2)

1

10

4

5

6

7

8

9

10

20

30

0.001 0.01

0.8 1 3 5 7 9

Limiting Flow Area (in.2

)

Max. 

p Leak rate (gpm)

Max. 

p Leak rate (L/min)

Limiting Flow Area (mm2)

(a) (b) 

Figure 63. Correlation of leak rate data with (a) crack opening area and (b) gap flow area. 

4.2.2 Dampierre-1 Tube/TSP Data 

Intact tube/TSP junctions were removed from the French reactor Dampierre-1. Dampierre-1 

commenced operation in 1980 and the SGs were replaced in 1990. All-volatile-treatment (AVT) 

water chemistry was used throughout the operation, and pH was controlled by ammonia addition 

until 1984 (8.8<pH<9.2) and morpholine after 1984 (9.1<pH<9.3). The assemblies included the 

tube, the surrounding TSP, and the crevice deposits, which held the tube in the TSP during 

removal. The crevice deposits were examined and were considered by Electricité de France (EdF) 

to be typical of SGs with drilled carbon-steel support plates. The removed assemblies were used to 

assess leak rates in the presence of crevice deposits and leak rates as a function of TSP 

displacement relative to the tube. The tests were run on crevices with and without chemical 

cleaning. 

The leak tests were conducted at room temperature. A 0.5 mm (0.02 in.) hole was drilled 

through the middle of the TSP and through the deposits and the tube. The hole in the TSP was 

then plugged so that the leakage path from the 0.5 mm (0.02 in.) hole in the tube was through the 

crevice deposits. Without crevice deposits, the expected leak rate from a 0.5 mm (0.02 in.) hole at 

p=17.2 MPa (2.5 ksi) is 90 L/h (0.4 gpm). The measured leak rates through the deposit were < 

0.1 L/h (4 x 10-4 gpm), which represents a reduction in leak rate of about a factor of 1000 due to 

the crevice deposits. The reduction factors from the drilled hole tests were considered to be 

conservative because they only include the flow resistance due to the presence of the deposits 

whereas the leakage from cracks within a packed crevice will also be reduced by the reduction in 

crack opening area due to presence of hard deposits in the crevice. 
 58 

4.2.3 Tube/Tube-Sheet Data from a Retired Steam Generator 

Several tube/tube-sheet (TS) junctions removed from a retired SG, including the crevice 

deposits, were leak tested at the ANL room-temperature, high-pressure test facility. The 

circumferential cracks in the specimens were very close to the top of the TS; therefore, the results 

are relevant to leakage under the TSP. The test data are summarized in Table 10. 

The eddy-current (EC) measurements for specimen No. 6 indicated a circumferential ODSCC, 

with a maximum depth of 60% throughwall (TW) and 41 mm (250°) in length. Room-temperature 

pressure tests showed the beginning of a water leak at about 35.2 MPa (5100 psi) with a rate of 

0.57 L/min (0.15 gpm). Specimen No. 6 was sectioned parallel to the tube axis, and the cross 

section was examined. Figure 64 is an optical metallograph of the cross section at the NDE 

indication of the maximum penetration. A circumferential crack initiating in the tube wall 

penetrates into the crevice deposit at the secondary side of the tube just above the top of the tube 

sheet (TTS). 

Specimen No. 9 did not have any measurable leak rate up to a pressure of 52 MPa (7.5 ksi). 

However, post-test sectioning revealed the presence of a throughwall circumferential crack that is 

0.04 mm (0.002 in.) wide (Figs. 65a-b). In contrast to specimen No. 6, the dense deposits in the TS 

crevice apparently prevented any leakage in this case even though the crack opening was relatively 

wide. 

Tests on specimens 6 and 9 demonstrated that the leakage behavior of circumferential 

throughwall cracks at the top of tube-to-TS junctions in the presence of deposits can be widely 

different even in the same SG. 

Table 10 A summary of leak test data for tube/TS specimens from a retired SG. Note 

1000 psi = 6.895 MPa and 1 gallon = 3.8 L. 

Tube Number 

Plus Point Volts 

 1997 2002 

Pressure when leak 

rate was measurable 

(psi) Leak rate 

(gpm) 

6 1.54 2.95 5100 0.15 

7 0.76 0.78 7300* 0.08 

8 Not available 2.5 No leak to 7500 psi No leak 

9 2.36 24.85 No leak to 7500 psi No leak 

* Detected initiation of flaw weeping but no measurable leak rate at 6600 psi. 
 59 

Figure 64. Optical metallography of a 

cross-section parallel to the tube axis at 

the maximum EC signals for TS0601 Alloy

600 SG tube specimen R39C43 near the 

TTS. 

(a) (b) 

Figure 65. A throughwall circumferential ODSCC with crack branching in specimen No. 9 

just below the top of the tube sheet. The crack opening is about 0.04 mm. 

4.3 Analyses of Crack Opening Area and Leak Rate 

Finite element analyses (FEAs) were conducted for throughwall axial cracks, 13 mm (0.25 in.) 

and 19 mm (0.75 in.) long, and throughwall circumferential cracks, 90, 180, and 240° long. All of 

the tubes [22 mm (0.875 in.) OD and 1.3 mm (0.05 in.) wall thickness] were located symmetrically 

inside the TSP hole/wall with a 0.4 mm (0.016 in.) diametral clearance (Fig. 66). The 

circumferential cracks were located at the central plane of symmetry in all cases. No offsets of 

cracks or unsymmetrical positioning of the tube with respect to the TSP hole/wall were modeled. 

The TSP thickness was taken as 19 mm (0.75 in.). Most of the analyses ignored the effect of 

crevice deposits. A limited number of analyses were conducted to explore the effects of such 

deposits on crack opening area. 
 60 

The limiting flow area for the leakage calculation was assumed to be the least of the following 

three quantities: the gap area (Eq. 1), the ID crack opening area, or the OD crack opening area. If 

there was a length of the crack flanks over which the radial gap between the tube OD surface and 

the TSP hole/wall was calculated to be fully closed, contributions from this portion of the crack to 

the gap area and the OD crack opening area were ignored. Because of the rotation of the tube wall 

associated with the bulging of the cracked section of the tube, the crack opening area was 

generally less on the ID than on the OD. Since the mechanical properties of the deposits are 

unavailable, leak rates were calculated assuming that the TSP crevices are free of deposits. 

4.3.1 Leak Rate Correlation for a Postulated MSLB 

An orifice discharge model has been found to be reasonably accurate for flow through cracks 

of length ≥ 11 mm (0.43 in.) for postulated MSLB conditions (see Section 3.4): 

qm = 0.6(2p)1/2 (9) 

where qm = mass flow rate per unit area, p = pressure difference across the tube, and  = density 

of water. In metric units (qm in kg/m2-s, p in MPa, and  in kg/m3), Eq. 9 becomes 

qm = 848.3(p)1/2 (10) 

(a) (b) 

Figure 66. Finite element model of the tube-to-TSP junction. 

4.3.2 Leak Rate Correlation for Postulated Severe Accidents 

Since the secondary side is at atmospheric pressure, it is reasonable to assume that the flow 

exiting the crack for a postulated severe accident is choked. Under these conditions, the exit 

velocity, pressure, and mass flow can be calculated with the additional assumption that the 

superheated steam can be treated as an ideal gas. The exit velocity is given by 

V *  2

 1

RT (11) 
 61 

where  = ratio of specific heats at constant pressure and constant volume (1.4), R is the gas 

constant for steam (456 N-m/kg-K), and T is gas temperature in K. The mass flow per unit area (in 

kg/m2-s) is given by 

qm  2

 1













1

 1 2

 1

p2

RT (12) 

where p = upstream gas pressure in Pa. 

4.3.3 Material Properties Used in Analysis 

Elastic Properties 

The effective elastic constants for a TSP weakened by tube holes and flow holes were 

obtained from Westinghouse Electric Corporation data. The elastic modulus of Alloy 600 was 

assumed to be 193 GPa (28,000 ksi) with Poisson’s ratio = 0.3. 

Plastic Properties 

The true stress-strain properties of Alloy 600, as reported in Ref. 10, are reproduced in Fig. 

67. Because of the low stresses, the TSP was considered to behave elastically. 

0

50

100

150

0

200

400

600

800

1000

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

-5 0 5 10 15 20 25 30

True Stress (ksi)

True Plastic Strain

25°C

527°C

627°C

727°C

827°C

True Stress (MPa)

True Plastic Strain (%)

Figure 67. True stress-plastic strain 

curves for Alloy 600. 

Creep Properties 

The creep rate data of Alloy 600, as reported in Ref. 10, are reproduced in Fig. 68. The data 

can be fitted by the following equation: 



c  2.086x1024 

E













4.8038

exp  65000

RT











 (13) 
 62 

where  = stress, E = Young’s modulus, R = 1.987 cal/mol-K, and T = temperature in K. Because 

of the low stresses in the TSP, its creep deformation was ignored. 

105

106

107

108

109

1010

1011

1012

10-4 10-3

732°C

871°C

982°C

1093°C

/E(T)

y=2.086x1024x4.8038

Creep Rate in 1/s

Alloy 600

Figure 68. Creep rate properties of 

Alloy 600. 

4.4 Results 

4.4.1 Postulated Main Steam-Line Break (MSLB) Conditions 

The internal pressure in the SG tube during a postulated MSLB accident was taken as a 

constant 17 MPa (2.5 ksi ), with a constant temperature of 300°C. 

Axial Crack 

Two lengths of axial crack were studied: 13 and 19 mm (0.5 and 0.75 in.). The axial 

variation of the radial gaps between the crack flanks and the TSP tube hole/wall are shown as a 

function of pressure in Figs. 69a and b, respectively. The crack flanks of the 13 mm (0.5 in.) crack 

do not contact the TSP tube hole up to a pressure of 17 MPa (2.5 ksi). However, the flanks of the 

19 mm (0.75 in.) crack make first contact with the TSP tube hole at a pressure of 12 MPa (1.8 ksi), 

and the radial gap is fully closed over a central length of 6 mm (0.25 in.) at 17 MPa (2.5 ksi). 

The variation of the crack opening areas and the gap areas with pressure for 13 and 19 mm 

(0.5 and 0.75 in.) cracks is shown in Figs 70a and 70b, respectively. 

In the calculation of the gap area, the contribution of the central portion of the crack, where 

the flanks make contact with the TSP hole/wall, to the integral in Eq. 8 is assumed to be 

negligible. In the calculation of the crack opening area for leakage, the contribution of the central 

portion of the crack opening area where the OD surface is in contact with the TSP is again taken 

as negligible. The limiting flow area for leakage, which is the least of the gap area, OD crack 

opening area, or ID crack opening area, can be taken as the lower bound of the curves shown in 

Figs 70a-b. For the shorter crack, the ID COA is always the limiting area. For the longer crack, 

the ID COA is limiting at operating pressure, but the gap area is limiting at postulated MSLB 

conditions. 
 63 

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.1

0.15

0.2

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

-2 0 2 4 6 8 10 12 14

Gap Opening (in.)

Distance Along Crack (in.)

1 ksi

1.5 ksi

2 ksi

2.5 ksi

Gap Opening (mm)

Distance Along Crack (mm)

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-0.2 0 0.2 0.4 0.6 0.8

-5 0 5 10 15 20

0 ksi

1.8 ksi

0.875 ksi

2.5 ksi

Gap Opening (in.)

Distance Along Crack (in.)

Gap Opening (mm)

Distance Along Crack (mm)

0.75 in. crack

(a) (b) 

Figure 69. Axial variation of radial gap between crack flank and the inner surface of the 

TSP tube hole with pressure for (a) 13 mm (0.5 in.) and (b) 19 mm (0.75 in.) 

axial cracks at 300°C. 

-0.002

0

0.002

0.004

0.006

0.008

0.01

-0.5 0 0.5 1 1.5 2 2.5 3

GapOpening Area

IDCOA

ODCOA

-1

0

1

2

3

4

5

6

0 4 8 12 16 20

Gap or Crack Opening Area (in2

)

p (ksi)

Gap or Crack Opening Area (mm2

)

p (MPa)

0.5 in. crack

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

-0.5 0 0.5 1 1.5 2 2.5 3 3.5

Gap Area

IDCOA

ODCOA 0

2

4

6

0 5 10 15 20

Gap or Crack Opening Area (in2

)

p (ksi)

Gap or Crack Opening Area (mm2

)

p (MPa)

0.75 in. crack

(a) (b) 

Figure 70. . Variation of gap opening area, OD crack opening area, and ID crack 

opening area with pressure for (a) 13 mm ( 0.5 in.) and (b) 19 mm (0.75 in.) 

axial crack at 300°C. 

The calculated leak rates as a function of pressure for 13 and 19 mm (0.5 and 0.75 in.) 

cracks are shown in Figs 71a and 71b, respectively. The leak rate for the 13 mm (0.5 in.) crack 

under the TSP is predicted to be the same as a free-span crack of the same length, because the 

tube OD surface at the crack section under the TSP does not contact the TSP hole/wall up to a 

pressure of 17 MPa (2.5 ksi), and the crack opening area at the ID surface controls the leakage in 

both cases (Fig. 71a). On the other hand, the tube OD with a 19 mm (0.75 in.) crack makes 

contact with the TSP hole/wall at a pressure of 12 MPa (1.8 ksi), as shown in Fig. 69b. 

Consequently, the leak rate curve diverges from that for the free span at pressures > 12 MPa (1.8 

ksi), as shown in Fig. 71b, and at 17 MPa (2.5 ksi) the leak rate under the TSP is more than a 

factor of five less than the leak rate from the same size crack in the free-span region (Fig. 71b). At 

the postulated MSLB conditions, the leak rates for the 13 and 19 mm (0.5 and 0.75) cracks under 

the TSP are predicted to be 8 and 21 L/min (2 and 5.5 gpm), respectively. The results for the 19 

mm crack are consistent with the Westinghouse/EPRI test data. 
 64 

-0.5

0

0.5

1

1.5

2

2.5

-0.5 0 0.5 1 1.5 2 2.5 3

-2

0

2

4

6

8

10

12

14

0 4 8 12 16 20

Leak Rate (gpm)

p (ksi)

300°C

13 mm (0.5 in.) crack

Leak Rate (lb/min)

p (MPa)

Under TSP

Free Span

-10

0

10

20

30

40

-0.5 0 0.5 1 1.5 2 2.5 3

-40

0

40

80

120

160

200

0 4 8 12 16 20

Leak Rate (gpm)

p (ksi)

300°C

19 mm (0.75 in.) crack

Leak Rate (lb/min)

p (MPa)

Under TSP

Free Span

(a) (b) 

Figure 71. Variation of leak rate with pressure for (a) 13 mm ( 0.5 in.) and (b) 19 mm (0.75 

in.) axial crack at 300°C. 

Circumferential Cracks 

In comparison to axial cracks, circumferential cracks undergo much less radial bulging. As 

a result, the minimum crack extent for which contact between the tube OD surface and the TSP 

hole/wall occurs is about 180° at the postulated MSLB conditions of 17 MPa (2.5 ksi) and 300°C. 

The circumferential variations of the radial gap between the crack flanks and the TSP tube hole 

with pressure for 180 and 240° cracks are shown in Figs. 72a and 72b, respectively. Note that the 

contact length between the tube OD surface and the TSP hole/wall for a 240° crack at 7 MPa (1 

ksi) is 4 mm (0.15 in.), which increases to 6 mm (0.25 in.) at a pressure of 17 MPa (2.5 ksi). The 

relative gap openings for 90, 180, and 240° cracks at the postulated MSLB pressure of 17 MPa (2.5 

ksi) are compared in Fig. 73. 

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0 5 10 15

Gap Opening (in.)

Distance Along Crack (in.)

Gap Opening (mm)

Distance Along Crack (mm)

180° crack

0.5 ksi

1 ksi

2.5 ksi

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-0.2 0 0.2 0.4 0.6 0.8 1

-5 0 5 10 15 20 25

Gap Opening (in.)

Distance Along Crack (in.)

Gap Opening (mm)

Distance Along Crack (mm)

240° crack

2.5 ksi

1 ksi

0.5 ksi

(a) (b) 

Figure 72. Circumferential variation of radial gap between crack flank and the inner surface 

of the TSP tube hole with pressure for (a) 180° and (b) 240° cracks at 300°C. 
 65 

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-0.2 0 0.2 0.4 0.6 0.8 1

-5 0 5 10 15 20 25

Gap Opening (in.)

Distance Along Crack (in.)

Gap Opening (mm)

Distance Along Crack (mm)

240° crack

180° crack

90° crack

300°C

2.5 ksi Figure 73. Radial gap variation 

between the tube OD surface and the 

TSP hole/wall for 90, 180, and 240° 

circumferential cracks at the postulated 

MSLB condition. 

The variation of the ID crack opening area and the gap area with pressure for 90 and 180° 

cracks is shown in Figs 74a and 74b, respectively. The crack opening area is greater on the OD 

than the ID. The leakage-controlling area for both cases thus corresponds to the ID crack opening 

area. 

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

-0.5 0 0.5 1 1.5 2 2.5 3

0

2

4

6

0 4 8 12 16 20

Gap or Crack Opening Area (in2

)

p (ksi)

Gap or Crack Opening Area (mm2

)

p (MPa)

90° crack

Gap opening

ID Crack opening

-0.005

0

0.005

0.01

0.015

0.02

0.025

-0.5 0 0.5 1 1.5 2 2.5 3

0

4

8

12

16

0 4 8 12 16 20

Gap or Crack Opening Area (in2

)

p (ksi)

Gap or Crack Opening Area (mm2

)

p (MPa)

180° crack

Gap opening

ID Crack opening

(a) (b) 

Figure 74. Variation of gap opening area and ID crack opening area with pressure for (a) 

90° and (b) 180° circumferential crack at 300°C. 

Since contact between the tube OD surface and the TSP hole/wall for a 240° crack occurs 

over a more extended region than the 180° crack, the leakage-controlling area changes with 

increasing pressure from initially the ID crack opening area, to the OD crack opening area, and 

finally to the gap area at 17 MPa (2.5 ksi), as shown in Fig. 75. 
 66 

-0.02

0

0.02

0.04

0.06

0.08

-0.5 0 0.5 1 1.5 2 2.5 3

-8

0

8

16

24

32

40

48

0 4 8 12 16 20

Gap or Crack Opening Area (in2

)

p (ksi)

Gap or Crack Opening Area (mm2

)

p (MPa)

240° crack

Gap opening

ID Crack opening

OD Crack opening

Figure 75. Variation of gap opening area 

and ID and OD crack opening areas with 

pressure for a 240° circumferential crack.

In Fig. 76, calculated leak rates are plotted against pressure for 90, 180, and 240° cracks. At 

the postulated MSLB condition, the leak rates for these cracks are predicted to be 2, 37, and 78 

L/min (0.5, 9.7, and 20.6 gpm), respectively. Although very large circumferential cracks can result 

in high leak rates, the leakage for cracks in the TSP region is likely to be dominated by that due to 

axial cracks because circumferential cracks are not allowed to remain in service with the voltagebased alternate repair criteria. 

0.1

1

10

1 10

1

10

100

4 6 8 10 30 50

Leak Rate (gpm)

p (ksi)

300°C

Leak Rate (lb/min)

p (MPa)

90°

180°

240°

Figure 76. Variation of leak rate with 

pressure for 90, 180, and 240° cracks at 

300°C. 

4.4.2 Postulated Severe Accident Conditions 

Representative temperature and pressure histories during the high temperature portion of 

the postulated severe accident transient are shown in Figs. 77a and 77b, respectively.11 The 

maximum time is taken as 14,000 s because the surge line and hot leg are predicted to fail long 

before this time. Also, to be conservative, we assumed a constant pressure equal to 17 MPa (2.5 

ksi). 
 67 

200

400

600

800

1000

1200

1400

1600

9000 10000 11000 12000 13000 14000 15000

Temperature (°C)

 t (s)

Steam

Tube

0

0.5

1

1.5

2

2.5

3

9000 10000 11000 12000 13000 14000 15000

0

5

10

15

20

p (ksi)

 t (s)

p (MPa)

(a) (b) 

Figure 77. Variation of (a) temperature and (b) pressure with time assumed for postulated 

severe accident analysis. 

Axial Crack 

The axial variations of the radial gap between the crack flanks and the TSP tube hole with 

time for 13 and 19 mm (0.5 and 0.75 in.) cracks are shown in Figs. 78a and 78b, respectively. 

Although initially at 17 MPa (2.5 ksi) pressure and low temperatures, the OD surface with a 13 

mm (0.5 in.) crack does not contact the TSP hole/wall (Fig 69a). The first contact between the 

tube OD surface and the TSP hole/wall occurs at 12,690 s (Fig. 78a) during the transient. In the 

case of the 19 mm (0.75 in.) crack, the OD surface of the tube contacts the TSP hole/wall over a 

length of 6 mm (0.25 in.) at low temperature (Fig. 69b). At the end of 13,600 s, the contact length 

increases to 9 mm (0.35 in.), as shown in Fig. 78b. 

-0.002

0

0.002

0.004

0.006

0.008

0.01

-0.05

0

0.05

0.1

0.15

0.2

0.25

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

-2 0 2 4 6 8 10 12 14

Gap Opening (in.)

Distance Along Crack (in.)

11800 s

12690 s

13240 s

13960 s

Gap Opening (mm)

Distance Along Crack (mm)

0.5 in. Crack

-0.005

0

0.005

0.01

0.015

0.02

-0.1

0

0.1

0.2

0.3

0.4

0.5

-0.2 0 0.2 0.4 0.6 0.8

-5 0 5 10 15 20

10,000 s

11,800 s

13,600 s

Gap Opening (in.)

Distance Along Crack (in.)

Gap Opening (mm)

Distance Along Crack (mm)

0.75 in. crack

(a) (b) 

Figure 78. Axial variation of radial gap between crack flank and the inner surface of the 

TSP tube hole with time for (a) 13 mm (0.5 in.) and (b) 19 mm (0.75 in.) axial 

cracks at a pressure of 17 MPa (2.5 ksi). 

The crack opening area and the gap area vs. time for 13 and 19 mm (0.5 and 0.75 in.) cracks 

are plotted in Figs 79a and 79b, respectively. Because the first contact between the OD surface of 

the tube with a 13 mm (0.5 in.) crack and the TSP hole/wall occurs at time 12,600 s during the 
 68 

postulated severe accident transient, and the contact length increases progressively with time, the 

controlling area for leakage changes from the ID crack opening area to the gap area at 12,600 s 

(Fig. 79a). For the 19 mm (0.75 in.) crack, the controlling area is the gap area at all times (Fig. 79

b). 

The calculated leak rates as function of time for the 13 and 19 mm (0.5 and 0.75 in.) cracks 

are shown in Fig. 80. 

0

0.001

0.002

0.003

0.004

0.005

9000 10000 11000 12000 13000 14000 15000

GapOpening Area

IDCOA

ODCOA

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

Gap or Crack Opening Area (in2

)

t (s)

Gap or Crack Opening Area (mm2

)

0.5 in. crack

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

9000 10000 11000 12000 13000 14000 15000

Gap Area

IDCOA

ODCOA

2

4

6

8

10

12

Gap or Crack Opening Area (in2

)

t (s)

Gap or Crack Opening Area (mm2

)

0.75 in. crack

(a) (b) 

Figure 79. Variation of gap opening area, OD crack opening area, and ID crack opening 

area with time for (a) 13 mm ( 0.5 in.) and (b) 19 mm (0.75 in.) axial crack. 

1

2

3

4

5

6

7

0.5

1

1.5

2

2.5

3

9000 10000 11000 12000 13000 14000

Leak Rate (lb/min)

t (s)

Leak Rate (kg/min)

0.75 in.

0.5 in.

Figure 80. Variation of leak rate with 

time for (a) 13 mm (0.5 in.) and (b) 19 mm 

(0.75 in.) axial crack. 

Circumferential Cracks 

In contrast to axial cracks, the circumferential cracks deform little by creep during the 

postulated severe accident transient. As a result, the crack opening areas and gap area change 

very little with time, as shown in Fig. 81a-b for the 90° and 180° cracks and in Fig. 82 for the 240° 

crack. As in the postulated MSLB case (Figs. 74a-b and 75), the leakage-controlling area during 

the postulated severe accident for the 90 and 180° cracks is the ID crack opening area, and that 

for the 240° crack is the gap area. The leakage rates plotted in Fig. 83 show a slight reduction 

with time. 
 69 

0

0.002

0.004

0.006

0.008

0.01

9000 10000 11000 12000 13000 14000 15000

0

1

2

3

4

5

6

Gap or Crack Opening Area (in2

)

t (s)

Gap or Crack Opening Area (mm2

)

90° crack

Gap area

IDCOA

0.006

0.0065

0.007

0.0075

0.008

0.0085

0.009

0.0095

0.01

9000 10000 11000 12000 13000 14000 15000

4

4.5

5

5.5

6

Gap or Crack Opening Area (in2

)

t (s)

Gap or Crack Opening Area (mm2

)

180° crack

Gap area

IDCOA

(a) (b) 

Figure 81. Variation of gap opening area and ID crack opening area with time for (a) 90° 

and (b) 180° circumferential crack. 

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

10

20

30

40

50

9000 1 104 1.1 104 1.2 104 1.3 104 1.4 104

Crack Opening Area (in2

)

t (s)

Crack Opening Area (mm2

)

240° crack

Gap opening

ID Crack opening

OD Crack opening

Figure 82. Variation of gap opening area 

and ID and OD crack opening areas with 

time for 240° circumferential crack. 

0.1

1

10

100

0.1

1

10

9000 10000 11000 12000 13000 14000

Leak Rate (lb/min)

t (s)

Leak Rate (kg/min)

240°

180°

90°

Figure 83. Variation of leak rate with 

time for 90°, 180°, and 240° 

circumferential cracks during a postulated 

severe accident. 

4.5 Effect of Crevice Deposits on Crack Opening and Leak Rate 

The leak rate results presented so far assume that there are no crevice deposits, so that the 

tube OD surface is free to bulge radially outwards up to 0.2 mm (0.008 in.) before making contact 
 70 

with the TSP hole/wall. However, if deposits are present, they will affect the leak rate by two 

mechanisms. First, they will resist the radial growth of the tube and reduce the amount of crack 

opening area through which leakage occurs. Second, the leak rate itself will be reduced, 

depending on the porosity of the deposits. 

The tests on the Dampierre-1 tubes, discussed earlier, showed that the reduction due to the 

flow resistance of the deposits alone may be as much as a factor of 1000. As reported earlier, two 

tests on the tube-to-TS junction specimens from the retired steam generator conducted at ANL 

showed different behavior. One leaked at a rate of 0.57 L/min (0.15 gpm) after the circumferential 

crack became throughwall at a pressure of 35.2 MPa (5.1 ksi). The other did not have any 

measurable leak rate up to a pressure of 52 MPa (7.5 ksi), even though post-test sectioning 

revealed a 0.04-mm (0.002-in.) wide throughwall circumferential crack. Thus, the effect of 

deposits on the leak rate varies widely. 

The resistance provided by the deposits on the tube deformation will depend on its stiffness. 

Figure 84 shows the effect of the elastic modulus of the deposits on the crack opening 

displacement of a 13 mm (0.5 in.) axial crack under the TSP. Depending on the effective modulus 

of the deposits, the maximum COD may be reduced by almost a factor of 5 or perhaps more. 

-0.001

0

0.001

0.002

0.003

0.004

0.005

0.006

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

-2 0 2 4 6 8 10 12 14

Crack Opening Displacement (in.)

Axial Location (in.)

0.5 in. Crack

2.5 ksi

Axial Location (mm)

Crack Opening Displacement (mm)

w/o Deposit

E=0.1x10 6 psi

E=106

 psi

Figure 84. Effect of elastic modulus of 

deposits on the crack opening 

displacement of a 13 mm (0.5 in.) axial 

crack. 

The mechanical properties of the crevice deposits are not well characterized. Although the 

elastic bulk modulus of pure crystalline magnetite is known,12 it is not relevant for our purposes. 

More detailed information is available on deposits, which have some similarity to crevice deposits. 

The physical and chemical composition of deposits is complex. Turner et al. at Chalk River 

Laboratory13 conducted a detailed study on the effect of chemistry on the hardness of deposits. 

The deposits are formed from corrosion products from the feed train, which are continuously fed 

into the steam generator during normal operation. Copper and iron species are the main corrosion 

products together with impurities such as silica, carbonate, sodium, magnesium, calcium, 

chloride, and sulfate. These chemicals are introduced to the feed train by the make-up water and 

condenser leakage and form a hard, consolidated deposits in the SG. The investigation at Chalk 

River13 determined the effects of both physical and chemical processes on the consolidation and 

hardness of the deposits, which are a result of the elimination of porosity within the deposits in 

much the same way as sintering of ceramics. Tests were conducted in both isothermal and heat 

transfer conditions after corrosion products were added. Hardness of the deposits was measured 

by both the Vickers hardness number and crushing strength. Depending on the impurities, the 

deposits can be either soft or hard. A relatively small amount of chemical reaction or precipitation 

significantly increased hardness. All samples with added phosphates were harder than those 

without added phosphates and had significantly higher crushing strength. For example, the 

crushing strength of deposits made from a mixture of iron and cupric oxides increased from about 
 71 

2 MPa with zero phosphate to a maximum 20 MPa with 3 mol % of phosphates. Similarly, 1 mol % 

addition of zinc silicate caused a maximum increase of the hardness of the deposits. Further 

increases of concentration of phosphates or zinc silicates actually reduced the hardness. 

Precipitation of soluble impurities, such as calcium sulfate, within the pores of the deposits was 

identified as an effective mechanism for deposits consolidation. 

The parametric studies that have been performed show that the presence of deposits in the 

crevice is likely to have a significant impact on the effective leak area. However, to develop an FEA 

model for leak rate through cracks under TSPs with deposits, we will need better data on the 

mechanical properties of deposits as well as other physical properties, such as porosity and 

permeability, neither of which are currently available. Because of their strong dependence on 

chemistry, the physical and mechanical properties of the deposits may vary from plant to plant 

and maybe even from TSP to TSP in the same plant. 

4.6 Conclusions 

Finite element analysis of the SG tube with axial cracks under the TSP showed that the 

controlling leakage area during postulated MSLB and severe accidents is the ID crack opening 

area for short cracks [≤ 13 mm (0.5 in.)] and the gap area between the OD surface and the TSP 

hole/wall for longer cracks. This observation is in agreement with that reported by Westinghouse 

test results. 

During a postulated MSLB, axial cracks ≤ 13 mm (0.5 in.) do not contact the TSP hole/wall 

with a radial clearance of 0.2 mm (0.008 in.), assuming there are no deposits in the crevice. This 

length is consistent with the maximum crack length of 14 mm (0.55 in.) reported by Westinghouse 

for a radial clearance of 0.3 mm (0.012 in.) between the tube OD surface and the TSP hole/wall. 

During postulated severe accidents, the tube OD surface makes contact with the TSP hole/wall at 

12,690 s, and the contact length increases to 3 mm (0.1 in.) at 13,240 s. 

In contrast to the 13 mm (0.5 in.) crack, the 19 mm (0.75 in.) crack does contact the TSP 

hole/wall over a length of 6 mm (0.25 in.) during MSLB. This observation is also consistent with 

that made by Westinghouse. During postulated severe accidents the contact length increases to 9 

mm (0.35 in.) at 13,600 s. 

In comparison to the axial cracks, the circumferential cracks undergo much less radial 

bulging during a postulated MSLB. As a result, the minimum crack length at which contact 

between the tube OD surface and the TSP hole/wall occurs is about 180° (corresponding to a 

length of 35 mm [1.4 in.]). The contact length between the tube OD surface and the TSP hole/wall 

for a 240° crack is 4 mm (0.15 in.). 

In contrast to axial cracks, the circumferential cracks deform very little by creep during the 

postulated severe accident transient. As a result, the crack opening areas and gap area change 

very little with time during the postulated severe accident. 

At the postulated MSLB conditions, the leak rates for 13 and 19 mm (0.5 and 0.75) axial 

cracks under the TSP are predicted to be 8 and 21 L/min (2 and 5.5 gpm), respectively. The leak 

rates for the 90, 180, and 240° circumferential cracks are predicted to be 2, 37, and 78 L/min 

(0.5, 9.7, and 20.6 gpm), respectively. 
 72 

At 12,000 s during the postulated severe accident, the leak rates in the 13 and 19 mm (0.5 

and 0.75) axial cracks under the TSP are predicted to be 1.4 and 2.6 kg/min (3 and 5.8 lb/min). 

The leak rates in the 90, 180, and 240° circumferential cracks at the same time are predicted to be 

2.3, 4.5, and 9 kg/min (5, 10, and 20 lb/min), respectively, and they decrease slightly with time. 

The calculated leak rates reported here assume that crevice deposits are absent. Tests on 

Dampiere-1 tube-to-TSP junctions, including deposits, showed that leak rates could be reduced by 

as much as a factor of 1000 compared to those without deposits. Studies on deposits carried out 

at Chalk River showed that the hardness, crushing strength, and consolidation properties of 

deposits depend strongly on the crevice chemistry. Small changes in crevice chemistry can lead to 

significant changes in these properties. 
 73 

5 References 

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TR–1006252, EPRI, Palo Alto, September 2001. 

2. K. Kasza, S. Majumdar, J. Park, and J. Franklin, “Results from Pressure and Leak Rate 

Testing of Laboratory-Degraded Steam Generator Tubes,” NUREG/CR-6789, Argonne 

National Laboratory, 2002. 

3. S. Majumdar, K. Kasza, and J. Franklin, Pressure and Leak–Rate Tests and Models for 

Predicting Failure of Steam Generator Tubes, NUREG/CR–6664, Argonne National 

Laboratory, 2000. 

4. S. Majumdar, S. Bakhtiari, K. Kasza, and J. Y. Park, Validation on Failure and Leak–Rate 

Correlations for Stress Corrosion Cracks in Steam Generator Tubes, NUREG/CR–6774, 

Argonne National Laboratory, 2002. 

5. Steam Generator Tubing Burst Testing and Leak Rate Testing Guidelines, Report TR1006783, EPRI, Palo Alto, December 2002. 

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Engineering, Vol. 88, pp. 261–274, 1984 

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for steam generator tubes”, SMIRT–9, Vol. D, Lausanne, 1987. 

10. J. L. Rempe, S. A. Chavez, G. L. Thinnes, C. M. Allison, G. E. Korth, R. J. Witt, J. J. 

Sienicki, S. K. Wang, L. A. Stickler, C. H. Heath, and S. D. Snow, “Light Water Reactor 

Lower Head Failure Analysis,” NUREG/CR-5642, Idaho National Engineering Laboratory, 

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11. C. D. Fletcher, R. W. Shumway, and D. L. Barber, “Revised SCDAP/RELAP5 Base Case 

Calculation for Zion TMLB’ Station Blackout Event”, ISL-NSAD-TR-03-18, Information 

Systems Laboratories, Inc., Idaho Falls, ID, October 2003. 

12. C. Haavik, S. Stolen, H. Fjellvag, M. Hanfland, and D. Hausermann, “Equation of State of 

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Pressure,” American Mineralogist, Volume 85, pages 514–523, 2000. 

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