Stress Corrosion Cracking of the Drip Shield, the Waste Package Outer Barrier, and the Stainless Steel Structural Material Rev 02, ICN 00

ANL-EBS-MD-000005

October 2004

1. PURPOSE 
1.1 PURPOSE AND BACKGROUND 
Stress corrosion cracking is one of the most common corrosion-related causes for premature 
breach of metal structural components. Stress corrosion cracking is the initiation and 
propagation of cracks in structural components due to three factors that must be present 
simultaneously: metallurgical susceptibility, critical environment, and static (or sustained) tensile 
stresses. This report was prepared according to Technical Work Plan for: Regulatory Integration 
Modeling and Analysis of the Waste Form and Waste Package (BSC 2004 [DIRS 171583]). The 
purpose of this report is to provide an evaluation of the potential for stress corrosion cracking of 
the engineered barrier system components (i.e., the drip shield, waste package outer barrier, and 
waste package stainless steel inner structural cylinder) under exposure conditions consistent with 
the repository during the regulatory period of 10,000 years after permanent closure. For the drip 
shield and waste package outer barrier, the critical environment is conservatively taken as any 
aqueous environment contacting the metal surfaces. Appendix B of this report describes the 
development of the SCC-relevant seismic crack density model (SCDM). 
The consequence of a stress corrosion cracking breach of the drip shield, the waste package outer 
barrier, or the stainless steel inner structural cylinder material is the initiation and propagation of 
tight, sometimes branching, cracks that might be induced by the combination of an aggressive 
environment and various tensile stresses that can develop in the drip shields or the waste 
packages. The Stainless Steel Type 316 inner structural cylinder of the waste package is 
excluded from the stress corrosion cracking evaluation because the Total System Performance 
Assessment for License Application (TSPA-LA) does not take credit for the inner cylinder. This 
document provides a detailed description of the process-level models that can be applied to 
assess the performance of Alloy 22 (used for the waste package outer barrier) and Titanium 
Grade 7 (used for the drip shield) that are subjected to the effects of stress corrosion cracking. 
The use of laser peening or other residual stress mitigation techniques is considered as a means 
of mitigating stress corrosion cracking in the waste package final closure lid weld. 
Upstream sources of inputs, DTNs, and cited references that support this report include: 
Plugging of Stress Corrosion Cracks by Precipitates, Aging and Phase Stability of Waste 
Package Outer Barrier, Environment on the Surfaces of the Drip Shield and Waste Package 
Outer Barrier, Drip Shield Structural Response to Rock Fall, General Corrosion and Localized 
Corrosion of the Drip Shield, Structural Calculations of Waste Package Exposed to Vibratory 
Ground Motion, Commercial SNF Waste Package Design Report, 21-PWR Waste Package 
Configuration, and Analysis of Mechanisms for Early Waste Package/Drip Shield Failure. 
This report also provides similar information to General Corrosion and Localized Corrosion of 
the Drip Shield, Hydrogen Induced Cracking of Drip Shield, Screening Analysis of Criticality 
Features, Events, and Processes for License Application, WAPDEG Analysis of Waste Package 
and Drip Shield Degradation, FEPS Screening of Processes and Issues in Drip Shield and Waste 
Package Degradation, and Postclosure Modeling and Analyses Design Parameters. 

1.2 MODEL OVERVIEW 
Stress corrosion cracking is the initiation and propagation of cracks in metal components due to 
three factors occurring simultaneously: material susceptibility, critical environment, and static 
(or sustained) tensile stress. Although Alloy 22, the material used for the waste package outer 
barrier, is highly corrosion resistant, its susceptibility to stress corrosion cracking is addressed 
for the repository environment and the coexisting stress conditions described in Section 6.4. 
Section 6.3.7 provides an analysis that forms the technical basis for screening out stress 
corrosion cracking in the drip shield. A lifetime-modeling approach was developed to assess the 
degradation of the waste package outer barrier due to stress corrosion cracking. Figure 1-1 
shows how the approach considers crack initiation and preexisting manufacturing flaws 
(Section 6.2), stress conditions that drive crack initiation and propagation (Section 6.4), the stress 
threshold that defines crack initiation (Section 6.2.1), threshold stress intensity factor 
(Section 6.3.5) that defines propagation of both initiated incipient cracks and manufacturing 
flaws, and the crack growth model (based on the slip dissolutionfilm rupture theory) that 
determines the crack growth rate (Section 6.3). The stress corrosion cracking modeling approach 
provides the elements (Section 8) necessary to perform a lifetime prediction of the waste package 
outer barrier subjected to the effects of stress corrosion cracking. 
NOTE: When an indicated value of s, KI, or aFinal is less than the indicated parameter value, the corresponding 
crack initiation, crack growth, or breach does not occur. 
Figure 1-1. Flow Diagram of Stress Corrosion Cracking Modeling Approach 
 
2. QUALITY ASSURANCE 
The Office of Civilian Radioactive Waste Management (OCRWM) Quality Assurance (QA) 
program applies to this report. All waste package configurations and drip shields have been 
determined to be important to waste isolation in accordance with AP-2.22Q, Classification 
Analyses and Maintenance of the Q-List and, therefore, are classified as Safety Category (SC) in 
Q-List (BSC 2004 [DIRS 168361], Appendix A; BSC 2004 [DIRS 170992], Section 6.4.2). 
This report has been developed per AP-SIII.10Q, Models, as per Technical Work Plan for: 
Regulatory Integration Modeling and Analysis of the Waste Form and Waste Package 
(BSC 2004 [DIRS 171583]). 
The inputs to this report are documented according to AP-3.15Q, Managing Technical Product 
Inputs. The methods used to control the electronic management of data as required by 
AP-SV.1Q, Control of the Electronic Management of Information, were accomplished in 
accordance with the technical work plan. The process for control of the electronic management 
of information on evaluation of work activities, processes, or process functions outlined in 
Section 5.0 of AP-SV.1Q, is followed to ensure accuracy, completeness, and security of 
information and data used in preparation of this report. Examples of process controls mentioned 
in AP-SV.1Q are: (a) access to the information contained on personal computer is password 
protected; (b) secured backup copies are appropriately labeled and stored before changes are 
made and kept until the changes are confirmed and correct; (c) physical electronic media (tape, 
diskette, CD-ROM, etc.) are appropriately labeled; and (d) for nonphysical electronic media, 
transport mechanisms can be e-mail, TCP/IP, NetBios, etc. and methods of receipt verification 
may include visual inspection, transmission verification settings, check sums, application 
information integrity check, etc. 
Based on these controls, as well as those imposed by the relevant implementing procedures, the 
process-control evaluation performed in accordance with AP-SV.1Q, Control of the Electronic 
Management of Information, states that adequate controls are provided (Attachment I). 
Evaluation of activities in accordance with AP-2.27Q, Planning for Science Activities, reveals 
that each activity is subject to the requirements of Quality Assurance Requirements and 
Description (DOE 2004 [DIRS 171539]. Standard QA controls will apply to the development of 
analyses and models, as well as data qualification efforts. 
Appendix B discusses quality assurance of the seismic crack density model. 

 
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 2-2 
INTENTIONALLY LEFT BLANK 

 
l 
 3-1 
3. USE OF SOFTWARE 
No software or computer codes are used in developing this report or during model validation. 
The computer software-generated data on through-thickness residual stress and stress intensity 
factor profiles at the welds of the middle and outer lids of the waste package design were 
obtained by procurement from a qualified vendor. These data, presented in 
DTN: LL000316205924.142 [DIRS 148895], were developed using computer software 
internally qualified by the vendor (Structural Integrity Associates, Inc., San Jose, CA) in 
compliance with the Structural Integrity Associates Quality Assurance Program, which was 
approved by the YMP Office of Quality Assurance (OQA). 
Microsoft Excel 97 was used to perform support calculations and graphics. Microsoft Excel 97 
is a standardized commercial spreadsheet program designed to assist in routine calculations and 
graphics. The program provides built-in mathematical functions that can be used to automate the 
calculation process. It also includes a graphics package to assist in data presentation. Microsoft 
Excel 97 is a commercial off-the-shelf software program exempt from software qualification in 
accordance with Section 2.1 of LP-SI.11Q-BSC, Software Management. Furthermore, according 
to LP-SI.11Q-BSC, Software Management, Section 2.1, the graphical representation use of Excel 
are exempt, as are the calculations using built-in mathematical functions. When Excel is used 
for calculations (Section 6.3.4), information required for an independent person to reproduce the 
work (including the formula or algorithm used, and listing of inputs or outputs) is provided. The 
calculations using Microsoft Excel 97 can be independently performed on any platform capable 
of running this commercial software program, including Windows 95, 98, 2000, and NT. 
MathCad 2001i is a commercial, off-the-shelf software program used in Section 6.4.5. The 
computations performed in this report using MathCad 2001i use only standard functions and 
produce results independent of the software program used. The program provides built-in 
mathematical functions that can be used to automate the calculation process. It also includes a 
graphics package to assist in data presentation. MathCad 2001i is a commercial off-the-shelf 
software program exempt from software qualification in accordance with Section 2.1 of 
LP-SI.11Q-BSC, Software Management. Furthermore, the graphical representation use of 
MathCad 2001i is exempt per Section 2.1 of LP-SI.11Q-BSC, as are calculations using built-in 
mathematical functions. When MathCad 2001i is used for calculations (Section 6.4.5), 
information required for an independent person to reproduce the work (including formula or 
algorithm used, and listing of inputs or outputs) is provided. The calculations using 
MathCad 2001i can be independently performed on any platform capable of running this 
commercial software program, including Windows 95, 98, 2000, and NT. 
Appendix B discusses the use of software for the seismic crack density model. 

 
l 
 3-2 
INTENTIONALLY LEFT BLANK 

 
l 
 4-1 
4. INPUTS 
Appendix B discusses seismic crack density model inputs. 
4.1 DIRECT INPUT 
The data providing input for the development of parameters or other databases, or both, used in 
the models or analyses documented in this report are identified in Table 4-1. While uncertainty 
in the input data is discussed in Section 6, Tables 4-1 through 4-6, and Figure 4-1 provide: 
 A roadmap to what data are in the DTN, if applicable 
 A description of how the data are used to develop model or analyses input parameters. 
The input data are appropriate for use because they are either qualified acquired or developed 
data. Some of the developed data were obtained from established fact. No developed 
parameters or other input information are used in the model or analyses. To alleviate concerns 
about rounding errors, this report often uses exact rather than significant digits. Also, some 
inputs received in English units are left as is, although all output units in Section 8 are in metric 
units. 
Data used to develop the SDFR model are not used subsequently to validate the model. 
Source: DTN: MO0409GE835924.000 [DIRS 171564], p. 12. 
NOTE: Target test solution composition: 0.27M Na2CO3, 0.35M KCl, 0.41M NaCl, 0.013M NaF, 0.43M NaNO3, 
0.03M Na2SO4, 0.04M Na2SiO3.9H2O (pH = 10.3 at 105C), Table 2-1, DTN: LL021105312251.023 
[DIRS 161253], p 99. This composition represents a concentrated, approximately 15% solution of Basic 
Saturated Water (BSW) whose target composition is given in DTN: LL021105312251.023 [DIRS 161253], 
p 3. sYS (for as-received condition) used in stress ratio for welded specimens. 
Figure 4-1. Applied Stress to Yield Strength Ratio versus Time-to-Failure 

 
l 
 4-2 
Table 4-1. Input Data 
Data Name Data Source DTN Discussion 
Measured crack growth rates in 
mm/s for Alloy 22 specimens 
c153, c144, and c152 tested for 
stress intensity factors of 30 and 
45 MPavm 
Stress corrosion cracking initiation and 
growth measurements in environments 
relevant to high-level nuclear waste 
packages. Submittal date: 01/08/2003 
LL021105312251.023 [DIRS 161253] Input data (Table 4-2) are used in 
Section 6.3.4 for determining the 
repassivation slope 'n' of the slip 
dissolutionfilm rupture model. 
Crack initiation measurements 
for Alloy 22 and Titanium Grade 
7 specimens 
Stress corrosion cracking initiation and 
growth measurements in environments 
relevant to high-level nuclear waste 
packages. Submittal date: 9/02/2004 
MO0409GE835924.000 
[DIRS 171564] 
Input data (Figure 4-1) are used in 
Section 6.2.1 for determining the 
threshold stress for crack initiation for 
Alloy 22 and Titanium Grade 7. 
Coefficients of stress profiles, 
A0, A1, A2, and A3 
Stress corrosion cracking of the drip 
shield, the waste package outer barrier 
and the stainless steel structural 
material. Submittal date: 03/22/2000. 
LL000316205924.142 [DIRS 148895] Input data (Table 4-3) are used in 
Section 6.4.2 for stress profiles in aswelded 
and laser-peened Alloy 22 
closure lids. 
Stress intensity factor profiles Stress corrosion cracking of the drip 
shield, the waste package outer barrier 
and the stainless steel structural 
material. Submittal date: 03/22/2000. 
LL000316205924.142 [DIRS 148895] Input data (Table 4-4) are used in 
Section 6.4.2. 
YS (yield strength) for Alloy 22 Waste package material properties: 
corrosion-resistant materials. 
MO0003RIB00071.000 [DIRS 148850] Input data (Table 4-5) are used in 
Sections 6.2.1 and 6.4.5. 
YS (yield strength) for Titanium 
Grade 7 
Waste package material properties: 
corrosion-resistant materials. 
MO0003RIB00073.000 [DIRS 152926] Input data (Table 4-5) are used in 
Sections 6.2.1 and 6.3.7. 
E (modulus of elasticity) for 
Titanium Grade 7 
Waste package material properties: 
corrosion-resistant materials. 
MO0003RIB00073.000 [DIRS 152926] Input data (Table 4-5) are used in 
Section 6.3.7. 
Vgc, general corrosion rates for 
Alloy 22 
Corrosion rate calculations for Alloy C22 
after 5+ years exposure. 
LL030412512251.057 [DIRS 163712] Input data (Table 4-6) are used in 
Section 6.3.5. 
Initial size of incipient cracks Ford and Andresen 1988 [DIRS 118611] Qualified in Section 6.2.1 per 
AP-SIII.10Q, Section 5.2.1.k 
Input data (0.05 mm incipient flaw 
size) used in Section 6.2.1 
Circumferential variation in weld 
residual stress 
Structural Integrity Associates 
Calculation Files 2004, Calculation 
TRW-06Q-304 
MO0409GGSIACAL.000 
[DIRS 171792] 
Input data (5 ksi about the mean 
stress) used in Section 6.4.5 

 
l 
 4-3 
Table 4-2. Measured Crack Growth Rates for Alloy 22 Specimens 
Specimen 
Tested Stress 
Intensity Factor 
(MPa(vm)) 
Measured Crack 
Growth Rate 
(mm/s)a Source 
c153 30 2.5  10-10 DTN: LL021105312251.023 [DIRS 161253], p. 11 
c153 30 5.0  10-10 DTN: LL021105312251.023 [DIRS 161253], p. 11 
c144 30 b DTN: LL021105312251.023 [DIRS 161253], p. 7 
c152 45 b DTN: LL021105312251.023 [DIRS 161253], p. 10 
c152 45 4.0  10-10 DTN: LL021105312251.023 [DIRS 161253], p. 10 
NOTE: a Growth rates obtained at sustained constant load or at hold times of about 1 to 24 hours. 
b Test results indicated that either cracking appeared to cease or growth rate seemed to arrest, 
indicating growth rates less than 10-11 mm/s, the growth rate detection threshold. 
Table 4-3. Coefficients of Stress Profiles for the Original and Modified CRM21-PWR Design 
Stress Coefficient 
A0 
(ksi) 
A1 
(ksi/in) 
A2 
(ksi/in2) 
A3 
(ksi/in3) Source in DTN 
As-Welded 25-mm 
Lid, Radial Stress Sx 16.871 33.5486 -294.333 264.368 
File Skvrbr1, Sheet 
UnAnneal, Sx, Cells C9 to 
C12 
As-Welded 25-mm 
Lid, Hoop Stress Sz 55.4242 29.8255 -186.269 143.597 
File Skvrbr1, Sheet 
UnAnneal, Sz, Cells C9 to 
C12 
As-Welded 10-mm 
Lid, Sn on Section 1-1 26.34 -427.51 934.32 -596.71 F
ile Thinlid11, Sheet 
UnAnneal,1-1,Sn, Cells 
C9 to C12 
As-Welded 10-mm 
Lid, Sz on Section 2-2 31.90 101.42 -463.23 297.75 F
ile Thinlid11, Sheet 
UnAnneal,2-2, Sz, Cells 
C9 to C12 
Laser-Peened 25-mm 
Lid, Radial Stress Sx -38.5684 383.082 -922.377 603.035 
File Skvrbr1, Sheet 
Peening, Sx, Cells C9 to 
C12 
Laser-Peened 25-mm 
lid, Hoop Stress Sz -42.4391 656.764 -1,322.67 759.752 
File Skvrbr1, Sheet 
Peening, Sz, Cells C9 to 
C12 
Source: DTN: LL000316205924.142 [DIRS 148895]. 

 
l 
 4-4 
Table 4-4. Stress Intensity Factor (SIF) Profiles 
As-Welded Outer Lid, 
CRM21-PWR Design 
As-Welded 10-mm Lid, 
Modified CRM21-PWR Design 
Outer Lid with Laser Peening, 
CRM21-PWR Design 
DTN File Skvrbr1 DTN File Thinlid11 DTN File Skvrbr1 
Sheet 
UnAnneal, Sx 
(Cells A87 to 
A136) 
Sheet 
UnAnneal, Sx 
(Cells C87 to 
C136) 
Sheet 
UnAnneal, Sz 
(Cells C87 to 
C136) 
Sheet 
UnAnneal,1- 
1,Sn (Cells 
A89 to A138) 
Sheet 
UnAnneal,1- 
1,Sn (Cells 
C89 to C138) 
Sheet 
UnAnneal,2-2, 
Sz (Cells C89 
to C138) 
Sheet 
Peening, Sx 
(Cells A87 to 
A136) 
Sheet 
Peening, Sx 
(Cells C87 to 
C136) 
Sheet 
Peening, Sz 
(Cells C87 to 
C136) 
Crack size, 
mm 
SIF for Sx, 
MPa vm 
SIF for Sz, 
MPa vm 
Crack size, 
mm 
SIF for Sn, 
MPa vm 
SIF for Sz, 
MPa vm 
Crack size, 
mm 
SIF for Sx, 
MPa vm 
SIF for Sz, 
MPa vm 
0.3988 4.5146 9.1593 0.2438 4.9033 7.5754 0.3988 -9.1866 -5.6943 
0.8001 6.5821 12.9737 0.4902 6.2685 10.9665 0.8001 -11.7979 -6.4965 
1.1989 8.2395 15.9139 0.7341 6.8580 13.7144 1.1989 -13.0189 -6.1528 
1.6002 9.6422 18.4031 0.9804 6.9761 16.1330 1.6002 -13.4298 -5.1372 
1.9990 10.8381 20.6048 1.2243 6.7631 18.3358 1.9990 -13.2965 -3.6697 
2.4003 11.8425 22.6028 1.4681 6.3044 20.3775 2.4003 -12.7780 -1.8824 
2.7991 12.8589 24.4741 1.7145 5.8250 22.3816 2.7991 -12.2958 0.1212 
3.2004 13.7858 26.2367 1.9583 5.2651 24.3197 3.2004 -11.7214 2.2821 
3.5992 14.5688 27.9039 2.2047 4.6000 26.1726 3.5992 -11.0116 4.5533 
3.9980 15.2083 29.4912 2.4486 3.8615 27.9459 3.9980 -10.2080 6.8939 
4.3993 15.7061 31.0103 2.6924 3.0726 29.6433 4.3993 -9.3437 9.2702 
4.7981 16.0778 32.4703 2.9388 2.2534 31.2668 4.7981 -8.4525 11.6543 
5.1994 16.4072 33.9004 3.1826 1.4282 32.8922 5.1994 -7.6096 14.0165 
5.5982 16.7029 35.3092 3.4290 0.5951 34.5292 5.5982 -6.8298 16.3364 
5.9995 16.8783 36.6797 3.6728 -0.2400 36.1060 5.9995 -6.0675 18.6024 
6.3983 16.9527 38.0157 3.9167 -1.0656 37.6220 6.3983 -5.3416 20.8003 
6.7970 16.9314 39.3202 4.1631 -1.8707 39.0762 6.7970 -4.6612 22.9177 
7.1984 16.8188 40.5961 4.4069 -2.6491 40.4676 7.1984 -4.0331 24.9441 
7.5971 16.7108 41.8581 4.6533 -3.4047 41.8264 7.5971 -3.4507 26.9023 
7.9985 16.7482 43.1357 4.8971 -4.1787 43.2168 7.9985 -2.8535 28.8612 
8.3972 16.7231 44.3927 5.1410 -4.9390 44.5479 8.3972 -2.2745 30.7287 
8.7986 16.6321 45.6302 5.3873 -5.6775 45.8181 8.7986 -1.7170 32.5008 
9.1973 16.4938 46.8495 5.6312 -6.3965 47.0265 9.1973 -1.1860 34.1745 
9.5987 16.3042 48.0515 5.8776 -7.0865 48.1718 9.5987 -0.6829 35.7479 
9.9974 16.0808 49.2372 6.1214 -7.7528 49.2531 9.9974 -0.2101 37.2200 
10.3962 16.0751 50.4839 6.3652 -8.2576 50.3451 10.3962 -0.3513 38.4530 

 
l 
 4-5 
Table 4-4. Stress Intensity Factor (SIF) Profiles (Continued) 
As-Welded Outer Lid, 
CRM21-PWR Design 
As-Welded 10-mm Lid, 
Modified CRM21-PWR Design 
Outer Lid with Laser Peening, 
CRM21-PWR Design 
DTN File Skvrbr1 DTN File Thinlid11 DTN File Skvrbr1 
Sheet 
UnAnneal, Sx 
(Cells A87 to 
A136) 
Sheet 
UnAnneal, Sx 
(Cells C87 to 
C136) 
Sheet 
UnAnneal, Sz 
(Cells C87 to 
C136) 
Sheet 
UnAnneal,1- 
1,Sn (Cells 
A89 to A138) 
Sheet 
UnAnneal,1- 
1,Sn (Cells 
C89 to C138) 
Sheet 
UnAnneal,2-2, 
Sz (Cells C89 
to C138) 
Sheet 
Peening, Sx 
(Cells A87 to 
A136) 
Sheet 
Peening, Sx 
(Cells C87 to 
C136) 
Sheet 
Peening, Sz 
(Cells C87 to 
C136) 
Crack size, 
mm 
SIF for Sx, 
MPa vm 
SIF for Sz, 
MPa vm 
Crack size, 
mm 
SIF for Sn, 
MPa vm 
SIF for Sz, 
MPa vm 
Crack size, 
mm 
SIF for Sx, 
MPa vm 
SIF for Sz, 
MPa vm 
10.7975 15.9957 51.7195 6.6116 -8.7427 51.3729 10.7975 -0.5163 39.5674 
11.1963 15.8601 52.9442 6.8555 -9.2143 52.3351 11.1963 -0.7070 40.5636 
11.5976 15.6646 54.1589 7.1018 -9.6605 53.2313 11.5976 -0.9242 41.4432 
11.9964 15.4259 55.3639 7.3457 -10.0894 54.0602 11.9964 -1.1690 42.2086 
12.3977 15.1398 56.5598 7.5895 -10.4950 54.8214 12.3977 -1.4403 42.8627 
12.7965 15.0982 57.8007 7.8359 -10.9446 55.4811 12.7965 -1.7949 43.4439 
13.1978 15.0836 59.0538 8.0797 -11.4131 56.0586 13.1978 -2.1728 43.9342 
13.5966 15.0159 60.3022 8.3261 -11.8636 56.5637 13.5966 -2.5554 44.3269 
13.9954 14.8966 61.5462 8.5700 -12.3055 56.9965 13.9954 -2.9438 44.6272 
14.3967 14.7274 62.7862 8.8138 -12.7309 57.3567 14.3967 -3.3378 44.8409 
14.7955 14.5229 64.0228 9.0602 -13.1320 57.6444 14.7955 -3.7396 44.9743 
15.1968 14.6570 65.2900 9.3040 -13.7114 57.7587 15.1968 -4.0160 45.0329 
15.5956 15.1057 66.5871 9.5504 -14.4707 57.6946 15.5956 -4.1354 45.0208 
15.9969 15.4787 67.8801 9.7942 -15.2333 57.5522 15.9969 -4.2182 44.9464 
16.3957 15.7929 69.1690 10.0381 -15.9891 57.3322 16.3957 -4.2696 44.8182 
16.7945 16.0516 70.4537 10.2845 -16.7277 57.0353 16.7945 -4.2904 44.6449 
17.1958 16.2578 71.7343 10.5283 -17.4611 56.6626 17.1958 -4.2805 44.4361 
17.5946 16.6700 73.0349 10.7747 -18.4707 56.1419 17.5946 -4.3087 44.2112 
17.9959 17.6878 74.4062 11.0185 -20.3589 55.3276 17.9959 -4.5204 43.9968 
18.3947 18.5558 75.7773 11.2624 -22.2128 54.4422 18.3947 -4.7313 43.7750 
18.7960 19.2803 77.1483 11.5087 -24.0173 53.4878 18.7960 -4.9400 43.5578 
19.1948 19.8861 78.5193 11.7526 -25.7872 54.6294 19.1948 -5.1487 43.3569 
19.5961 20.3775 79.8904 11.9990 -27.4989 56.2191 19.5961 -5.3536 43.1853 
19.9949 20.7777 81.2616 12.2428 -29.1709 57.7865 19.9949 -5.5551 43.0560 
Source: DTN: LL000316205924.142 [DIRS 148895]. 

 
l 
 4-6 
Table 4-5. Input Data for Yield Strength, and Modulus of Elasticity 
Input Data Name 
(Input DTN or Reference) 
Temperature 
K (C) Input Data Value Input Data Unit 
Room Temperature 372 MPa 
366 (93) 338 MPa 
YS (yield strength) for Alloy 22 
(DTN: MO0003RIB00071.000 [DIRS 148850]) 
477 (204) 283 MPa 
Room Temperature 275 to 450 MPa YS (yield strength) for Titanium Grade 7 
(DTN: MO0003RIB00073.000 [DIRS 152926]) 477 (204) 138 to 152 MPa 
294 (21) 106.87 GPa 
366 (93) 103.42 GPa 
E (modulus of elasticity) for Titanium Grade 7 
(DTN: MO0003RIB00073.000 [DIRS 152926]) 
422 (149) 100.66 GPa 
Table 4-6. 5-Year General Corrosion Rates 
Sample 
Rate 
(nm/year) Sample 
Rate 
(nm/year) 
DCA 019 9.40 DCA 175 0.82 
DCA 020 8.22 DCA 176 0.81 
DCA 021 8.63 DCA 177 46.67 
DCA 022 6.36 DCA 178 8.40 
DCA 023 9.75 DCA 179 5.24 
DCA 024 22.52 DCA 180 5.28 
DCA 049 12.04 DCB 019 10.24 
DCA 050 17.29 DCB 020 6.94 
DCA 051 15.75 DCB 022 5.84 
DCA 052 5.76 DCB 023 6.89 
DCA 053 8.30 DCB 049 16.07 
DCA 054 6.40 DCB 050 14.51 
DCA 079 3.06 DCB 052 4.29 
DCA 080 3.10 DCB 053 5.92 
DCA 081 4.19 DCB 079 2.00 
DCA 082 9.52 DCB 080 7.88 
DCA 083 7.23 DCB 082 19.58 
DCA 084 14.71 DCB 083 13.61 
DCA 109 5.81 DCB 109 4.32 
DCA 110 11.60 DCB 110 2.01 
DCA 111 5.77 DCB 112 9.05 
DCA 112 3.11 DCB 113 10.86 
DCA 113 10.56 DCB 139 0.00 
DCA 114 10.91 DCB 140 2.85 
DCA 139 4.71 DCB 142 2.03 
DCA 140 3.54 DCB 143 5.69 
DCA 141 2.74 DCB 175 0.41 
DCA 142 6.27 DCB 176 2.08 
DCA 143 5.89 DCB 178 1.25 
DCA 144 8.27 DCB 179 0.41 
Source: DTN: LL030412512251.057 [DIRS 163712]. 

 
l 
 4-7 
4.2 CRITERIA 
According to Technical Work Plan for: Regulatory Integration Modeling and Analysis of the 
Waste Form and Waste Package (BSC 2004 [DIRS 171583], Table 3-1) the following 
acceptance criteria are applicable to this report: 
1. System Description and Demonstration of Multiple Barriers (NRC 2003 
[DIRS 163274], Section 2.2.1.1.3; PRD-002/T-014, PRD-002/T-016): 
 AC1Identification of Barriers is Adequate 
 AC2Description of the Capability of Identified Barrier is Acceptable 
 AC3Technical Basis for Barrier Capability is Adequately Presented. 
2. Degradation of Engineered Barriers (NRC 2003 [DIRS 163274], Section 2.2.1.3.1.3; 
PRD-002/T-015): 
 AC1System Description and Model Integration are Adequate 
 AC2Data are Sufficient for Model Justification 
 AC3Data Uncertainty is Characterized and Propagated Through the Model 
Abstraction 
 AC4Model Uncertainty is Characterized and Propagated Through the Model 
Abstraction 
 AC5Model Abstraction Output is Supported by Objective Comparisons. 
The criteria as they relate to the waste package and drip shield barriers are addressed in 
Section 8.2, which discusses locations in the report that address individual acceptance criteria 
related to the two primary criteria. 
4.3 CODES AND STANDARDS 
The following codes or standards were used to generate this report: 
 10 CFR 63 [DIRS 156605]. Energy: Disposal of High-Level Radioactive Wastes in a 
Geologic Repository at Yucca Mountain, Nevada 
 ASTM B 575-94 [DIRS 100497]. Standard Specification for Low-Carbon Nickel- 
Molybdenum-Chromium and Low-Carbon Nickel-Chromium-Molybdenum Steel Alloy 
Plate, Sheet, and Strip 
 ASTM G 30-94 [DIRS 137688]. Standard Practice for Making and Using U-Bend 
Stress-Corrosion Test Specimens 
 ASTM E 399-90 [DIRS 117480]. Standard Test Method for Plane-Strain Fracture 
Toughness of Metallic Materials 
 ASTM G 129-00 [DIRS 171563]. Standard Practice for Slow Strain Rate Testing to 
Evaluate the Susceptibility of Metallic Materials to Environmentally Assisted Cracking 
 ASTM G 49-85 [DIRS 171562]. Standard Practice for Preparation and Use of Direct 
Tension Stress-Corrosion Test Specimens. 

 
l 
 4-8 
INTENTIONALLY LEFT BLANK 

 
l 
 5-1 
5. ASSUMPTIONS 
No assumptions were used to perform the model activity. 

 
l 
 5-2 
INTENTIONALLY LEFT BLANK 

 
l 
 6-1 
6. MODEL DISCUSSION 
6.1 INTRODUCTION 
One of the most common corrosion-related causes for premature fracture (breach) of metal 
structural components is stress corrosion cracking. Stress corrosion cracking is the initiation and 
propagation of cracks in structural components due to three factors that must be present 
simultaneously: metallurgical susceptibility, critical environment, and static (or sustained) tensile 
stresses. 
This discussion of stress corrosion cracking is restricted to the waste package outer barrier and 
the drip shield, which are made of Alloy 22 and Titanium Grade 7, respectively. The stainless 
steel waste package inner structural cylinder is not modeled, since the TSPA-LA does not take 
corrosion credit for the stainless steel inner cylinder of the waste package. 
Alloy 22, the material used for the waste package outer barrier, is highly corrosion-resistant, but 
its susceptibility to stress corrosion cracking cannot be ignored for the test conditions that 
simulate the Yucca Mountain environment (Sections 6.2 and 6.3) and the coexisting stress 
conditions induced by welding in the closure welds of the waste package final closure lids 
(Section 6.4). Section 6.3.7 provides an analysis that forms the technical basis for screening out 
stress corrosion cracking in the drip shield. 
A lifetime-modeling approach is developed to assess the degradation of the waste package outer 
barrier due to stress corrosion cracking. As indicated by the flow diagram shown in Figure 1-1, 
the lifetime modeling considers both crack initiation and preexisting manufacturing flaws 
(Section 6.2), the stress conditions that drive the crack initiation and propagation (Section 6.4), 
the stress threshold that defines the crack initiation (Section 6.2.1), the threshold stress intensity 
factor that defines propagation of both initiated incipient cracks and manufacturing flaws 
(Section 6.3.5), and the crack growth model (based on the slip dissolutionfilm rupture theory) 
that determines the crack growth rate (Section 6.3). The stress corrosion cracking model 
provides all the elements (as summarized in Section 8) needed to assess the effects of stress 
corrosion cracking on waste package outer barrier performance. 
Stress corrosion cracking has historically been separated into initiation and propagation 
phases (Jones and Ricker 1987 [DIRS 118672], p. 146). For the purpose of lifetime modeling, it 
is appropriate that initiation is associated with microscopic crack formation at localized corrosion 
or mechanical defect sites. Coalescence of these microscopically small cracks will lead to stress 
corrosion cracking initiation on an otherwise smooth surface. Initial stress corrosion cracking 
can also initiate at surface breaking flaws (or defects) resulting from manufacturing processes 
(such as welding). Crack initiation (including the threshold stress for crack initiation) and 
manufacturing defects are discussed in Section 6.2. 
To account for crack propagation, the slip dissolutionfilm rupture (SDFR) model is adopted as 
the base-case model to provide mathematical formulas for the prediction of crack growth rate. 
The SDFR model relates the advance (or propagation) of cracks, subsequent to crack initiation at 
the bare metal surface, to the metal oxidation that occurs when the protective film at the crack tip 
is ruptured. The SDFR stress corrosion cracking model is described in Section 6.3. A crack, 
however, may reach an arrest state after it enters the propagation phase. A threshold stress 

 
l 
 6-2 
intensity factor (SIF) exists that provides a criterion for determining if an initiated crack or 
preexisting flaw will reach the arrest state. The threshold SIF is based on the theory that below 
a threshold value (KISCC) for the stress intensity factor, KI, no growth occurs for a given crack. 
KISCC is discussed in Section 6.3.5 and the determination of the weld-induced stress and KI 
profiles through the waste package wall are described in Section 6.4. The threshold stress, 
threshold stress intensity factor, and parameters associated with the SDFR crack growth model 
are determined from experimental data developed for environments relevant to the waste 
package and drip shield materials used in the repository. 
An alternative conceptual model, the coupled environmental fracture (CEF) model, was 
developed for the case where the internal and external environments are coupled by the need to 
conserve charge in the system. The CEF model represents an alternative approach to the basecase 
SDFR model for the prediction of the crack growth rate. It is considered only for the 
purpose of validation of the base-case model. The CEF model and the technical basis for 
screening out this model are discussed in Section 6.3.6. 
The base-case SDFR and the alternative CEF models were initially developed to account for 
stress corrosion cracking of sensitized Stainless Steel Type 304 (i.e., stainless steel exposed to 
higher temperatures that make the grain boundaries more susceptible to corrosion). An 
evaluation of other stress corrosion cracking models for sensitized stainless steel indicates a 
weaker theoretical basis for these models (Macdonald and Urquidi-Macdonald 1991 
[DIRS 162702]). Therefore, no additional alternative conceptual models for stress corrosion 
cracking are considered. 
Output parameters associated with the base-case crack growth models developed are used as one 
input to the TSPA-LA. A summary of the various generated outputs is presented in Section 8. 
6.2 CRACK INITIATION AND MANUFACTURING FLAWS 
6.2.1 Threshold Stress for Initiation of Stress Corrosion Cracking 
For a given alloy, metallurgical condition, set of environmental conditions, and in the absence of 
cyclic stresses, initiation of stress corrosion cracking will not occur on a smooth surface 
(without sharp defects such as weld defects that can generate a significant stress intensity factor) 
if the surface stress is below a threshold value defined as the threshold stress (ASM 
International 1987 [DIRS 103753], Vol. 13, p. 276). Stress corrosion cracking crack initiation 
measurements under constant load conditions reported in DTN: MO0409GE835924.000 
[DIRS 171564] are summarized in Figure 4-1. These constant load tests were performed in 
general conformance with ASTM G 49-85 [DIRS 171562], but modified as indicated in 
DTN: LL021105312251.023 ([DIRS 161253]), Section 2.2). The crack initiation stress 
measurements are presented as applied stress ratio (the ratio of applied stress to yield strength) 
versus time-to-failure (or total exposure time without failure) for specimens subjected to 
over 21,000 hours of exposure in hot concentrated and aerated salt solution (pH=10.3 at 105C), 
known as Basic Saturated Water (BSW), (DTN: LL021105312251.023 [DIRS 161253], 
Sections 2.2 and 2.5). As indicated in the note on Figure 4-1, the BSW was diluted to about 15% 
of full concentration to simulate the chemistry of concentrated Yucca Mountain ground water. 
The results shown in Figure 4-1 confirm and extend previously reported test results 
(DTN: LL021105312251.023 [DIRS 161253]) indicating that Alloy 22 exhibits excellent stress 

 
l 
 6-3 
corrosion cracking resistance since failure has not been observed for any of the 120 Alloy 22 
specimens covering a variety of metallurgical conditions (including as-welded). The applied 
stress ratios were up to about 2.1 times the yield strength (YS) of the as-received material and up 
to 2.0 times the yield strength of the welded material. This stress ratio corresponds to an applied 
stress of about 89% to 96% of the measured ultimate tensile strength 
(DTN: LL021105312251.023 [DIRS 161253], Table 2-4). 
These 120 constant load stress corrosion cracking initiation test specimens include both smooth 
surface specimens and notched specimens with the notches located in either weld metal or in the 
weld heat affected zone (DTN: LL021105312251.023 [DIRS 161253], Figures 2-19 
through 2-22 for notch details). They also encompass a range of different microstructures or 
metallurgical conditions, including the annealed condition (solution annealed at a high 
temperature and rapidly cooled); the as-welded condition, including weld metal and heat affected 
zone; the annealed plus thermally aged condition (i.e., heated in a temperature range where 
potentially deleterious precipitates can form) that produces extensive topologically (or 
tetrahedrally) close-packed (TCP) precipitation (700C/175 h), the annealed plus thermally aged 
condition to produce long-range ordering (520C/1,000 hr), and the cold-worked condition 
(20% coldwork) with and without thermal aging (700C/175 hr). The various constant load test 
conditions evaluated were provided in Figure 4-1 and a more detailed description and a series of 
optical and SEM photomicrographs of the various microstructures are presented in 
DTN: LL021105312251.023 [DIRS 161253]. 
Findings summarized in Aging and Phase Stability of Waste Package Outer Barrier (BSC 2004 
[DIRS 171924]) are consistent with the thermal aging conditions evaluated in these constant load 
tests being highly conservative. Aging and Phase Stability of Waste Package Outer Barrier 
(BSC 2004 [DIRS 171924], Section 8) concludes that the formation of TCP or ordered oP6 
phases in Alloy 22 base metal and welds (which are deemed to be similar to base metal) will not 
be a concern for conditions of less than 300C for a period of 500 years followed by temperatures 
less than 200C for a period of 9,500 years, conditions that bound the repository timetemperature 
profiles. To be conservative, the constant load test matrix included the two 
previously described thermal aging conditions to represent TCP and long-range ordering 
conditions. Based on Aging and Phase Stability of Waste Package Outer Barrier (BSC 2004 
[DIRS 171924], Figure 91), the TCP heat treatment of 700C/175 hr results in a grain boundary 
coverage fraction of about 100% and from Table 10 of the same reference (BSC 2004 
[DIRS 171924]) a similar long-range ordering heat treatment at a somewhat higher temperature 
than the 520C used for the test (i.e., 550C/1,000 hr) results in an increase in Alloy 22 
mircohardness from an as-received value of 217 Hv to an as-aged value of 329 Hv. This 
increase in hardness is consistent with the measured increase in yield strength 
(DTN: LL021105312251.023 [DIRS 161253], Table 2-4) noted for this Alloy 22 plate material 
(from 47 ksi (324 MPa) for the as-received Alloy 22 material to 70 ksi (483 MPa) for the longrange 
ordering heat-treated material). 
The high degree of stress corrosion cracking initiation resistance for Alloy 22 determined with 
the constant load tests described above is corroborated by results of high magnification visual 
examination of a number of Alloy 22 U-bend specimens (fabricated and tested per 
ASTM G 30-94, [DIRS 137688]). The specimens were exposed at the Lawrence Livermore 
National Laboratory (LLNL) long-term corrosion test facility to a range of relevant aerated brine 

 
l 
 6-4 
environments at 60C and 90C (Fix et al. 2003 [DIRS 162700], p. 1). No evidence of stress 
corrosion cracking initiation has been observed in these U-bend specimens after five years of 
exposure. According to Fix et al. (2003 [DIRS 162700], p. 3): 
U-bend specimens chosen for laboratory testing contained residual stresses due to 
permanent deformation. The U-bend specimens were machined from sheet stock. 
The specimens were tested in the as-machined condition, which corresponded to a 
root mean square (RMS) roughness of 32 -inch. The specimens were degreased 
in acetone before testing. The U-bend specimens were prepared using -inch 
(~19 mm) wide and 1/16-inch @1.6 mm) thick strips according to ASTM G 30. 
The resulting specimen had a constant nominal separation between both legs, or 
ends, of 0.5 inch (~13 mm) secured by a bolt, which was electrically insulated 
from the specimen through ceramic zirconia washers. The total plastic 
deformation in the external outer fiber of Alloy 22 was approximately 12%. 
Single U-bends were produced using wrought sheets and welded sheets. In the welded 
specimens, the weld was across the apex of the bend. The weld process was gas metal arc 
welding (GMAW) using matching filler metal and the seam had full penetration. Table 6-1 lists 
the chemical composition of the sheet material and the filler metal used for the fabrication of the 
U-bend specimens. 
Table 6-1. Chemical Composition of the Studied Alloy 22 Heats (wt %) 
SINGLE U-BEND WELD FILLER 
METAL 
SSRT 
Element (Heat 2277-0-3264) (Heat 2277-4-3263) (Heat 2277-8-3126) 
C 0.004 0.002 0.004 
Co 1.14 0.89 1.03 
Cr 21.3 21.6 21.70 
Fe 4.4 3.6 3.59 
Mn 0.29 0.32 0.27 
Mo 13.4 13.5 13.26 
Ni ~56 ~56 ~5 
P 0.01 0.009 0.006 
S <0.002 0.003 0.001 
V 0.17 0.15 0.14 
W 2.9 2.9 2.80 
Source: Fix et al. 2003 [DIRS 162700], Table 2. 
Additional corroboration of the very high threshold stress for stress corrosion cracking initiation 
is provided by a series of slow strain rate tensile tests (SSRT) performed in general conformance 
to ASTM G 129-00 [DIRS 171563] and over the range of potentially relevant and accelerated 
environments (Estill et al. 2002 [DIRS 167274]; King et al. 2004 [DIRS 170981]). These slow 
strain rate tests were performed on mill annealed Alloy 22 (alloy heat composition listed in 
Table 6-1) at 22C to 120C, and at a strain rate of 1.66  10-6 per second. Because the SSRT 
specimen is subjected to continuously increasing strain until failure, the test does not generally 
give a direct measure of the threshold stress for stress corrosion cracking initiation. Even though 
stress corrosion cracking may initiate during the test, it is usually not evident at that precise point 

 
l 
 6-5 
in the test. However, the absence of stress corrosion cracking in this test is consistent with the 
material being a stress corrosion cracking resistant material with a high threshold stress. 
These Alloy 22 SSRT results for specimens tested at Ecorr and above (i.e., anodically polarized) 
are summarized in Table 6-2. This table contains a consolidated compilation of results obtained 
from (Estill et al. 2002 [DIRS 167274], Table 6) and (King et al. 2004 [DIRS 170981], Table 2). 
The test data cover a broad range of relevant and potentially accelerated environments, with and 
without lead additions or anodically applied potential. Examination of the tabulated results 
confirm the expected high degree of stress corrosion cracking resistance at open-circuit 
potentials in environments evaluated, including approximately 8.5 M (saturated) CaCl2-type 
brines (pH ~4) at 120C, as well as 1% lead chloride solutions (pH ~4) at 95C. The only two 
evaluated environments in which stress corrosion cracking initiation was or may have been 
observed were 1) simulated concentrated water (SCW) with an applied potential of 200 to 
400 mV versus SSC, which is significantly above the corresponding open-circuit corrosion 
potential of between -76 and -241 mV versus SSC, and 2) 1M NaF at 90C and polarized to 
+400 mV versus SSC versus an Ecorr of 244 mV versus SSC. SCW is a concentrated 
(~1,000-fold) version of J-13 ground water with a pH of ~9-10 and pure 1M NaF with a pH = 7.6 
is an accelerated and not directly relevant environment. Clearly, as described earlier, these 
results, in which the specimens are slowly pulled to the fracture stress, are consistent with the 
very low susceptibility of Alloy 22 to stress corrosion cracking. Even under these highly 
accelerated conditions (SCW at 90C and at the high applied potential of 400 mV versus SSC), 
the stress at which the onset of stress corrosion cracking was first detected, using a sensitive 
acoustic emission monitoring technique, corresponded to an applied stress of 605 MPa, which 
is 156% of the room temperature yield strength for this Alloy 22 plate material (Fix et al. 2003 
[DIRS 162700]). Although this acoustically determined, high stress corrosion cracking onset 
stress (and correspondingly high strain value) does not necessarily measure the initiation stress 
under the highly accelerated conditions, it is consistent with the threshold initiation stress being 
very high for this material. 
With respect to the slow strain rate tests (SSRT), a given strain rate (actually, cross-head motion 
rate) is imposed on these specimens, and once stress corrosion cracking initiates, the crack 
growth rate is partially governed by the imposed strain rate that is much faster than the measured 
growth rates for Alloy 22 using valid compact tension specimens (loaded per ASTM E 399-90 
[DIRS 117480]). Thus, these SSRT data were not used to generate crack growth rates in 
development of the stress corrosion cracking crack growth rate model (Section 6.3.4), as they are 
not representative. However, the SSRT results for the case where lead additions were evaluated 
are discussed in Section 6.3.4. 
To further corroborate the high degree of resistance to stress corrosion cracking initiation 
indicated by the slow strain rate tests (SSRT), two Alloy 22 U-bend specimens (one annealed 
and one as-welded) were exposed for 28 days to 90C SCW while polarized to +400 mV [SSC]. 
At this high potential, incipient stress corrosion cracking was observed under the severe, 
continuous straining condition in the SSRT case (Fix et al. 2003 [DIRS 162700]). 
Stereomicroscopic examination of these U-bend specimens following this exposure revealed no 
evidence of stress corrosion initiation consistent with the high degree of resistance of Alloy 22 to 
stress corrosion cracking. 

 
l 
 6-6 
Table 6-2. Slow Strain Rate Test Results for Annealed Alloy 22 (Strain Rate of 1.66  10-6 Per 
Second) 
Specimen ID 
Test 
Environment 
Temperature 
(C) 
Ecorr 
(mV versus 
SSC) 
EApplied 
(mV versus 
SSC) 
Time to 
Failure of the 
Specimen 
(hours) 
Maximum 
Stress (MPa) 
Reduction in 
Area (%) 
Observation 
012 Air 22 None None 124 786 74 Ductile necking 
040 Air 22 None None 123 813 70 Ductile necking 
098 1M NaCl at pH = 6.9 90 -104 +400 74 b 660 76 No SCC 
123 4M NaCl at pH = 6.2 98 -323 +349 127 762 80 No SCC 
091 1M NaF at pH = 9.2 85 133 Ecorr 112 756 67 No SCC 
130 1M NaF at pH = 7.6 90 -244 +400 112 727 67 Incipient SCC 
004 8.5M CaCl2 at pH ~ 6 120 -140 to -180 Ecorr 127 752 71 No SCC 
013 1% PbCl2 at pH ~ 4 Aerated 95 Ecorr 126 765 72 No SCC 
015 SAW at pH ~ 3 63 -7 to +360 Ecorr 118 758 79 No SCC 
016 SAW at pH ~ 3 + 0.005% Pb(NO3)2 76 -6 to +370 Ecorr 124 772 74 No SCC 
017 SAW at pH ~ 3 + 0.005% Pb(NO3)2 76 0 to +350 Ecorr 125 772 74 No SCC 
003 SAW at pH ~ 3 + 0.005% Pb(NO3)2 95 -90 to +400 Ecorr 118 752 85 No SCC 
127 BSW at pH ~ 13 - [NO3 + SO4] a 98 -240 to -220 Ecorr 123 745 72 No SCC 
124 BSW at pH ~ 13 - [NO3 + SO4] a 105 -330 +100 120 745 78 No SCC 
122 BSW at pH ~ 13 - [NO3 + SO4] a 98 -245 +200 122 752 72 No SCC 
120 BSW at pH ~ 13 105 -323 +400 99 745 74 No SCC 
119 BSW at pH ~ 13 105 -301 +400 118 745 75 No SCC 
115 BSW at pH ~ 13 - [NO3] a 105 -335 +400 115 752 77 No SCC 
129 BSW at pH ~ 13 - [SO4=] a 105 -314 +400 119 731 82 No SCC 
125 SSW at pH ~ 6 100 -154 +400 113 717 71 No SCC 
020 SCW at pH ~ 9 to 10 22 -109 +400 116 800 85 No SCC 
133 SCW at pH ~ 9 to 10 22 -128 +400 124 798 80 No SCC 
032 SCW at pH ~ 9 to 10 50 -129 +400 110 757 75 Incipient SCC 
134 SCW at pH ~ 9 to 10 65 -217 +400 97 684 59 SCC 
112 SCW at pH ~ 9 to 10 73 -93 +400 91 697 71 SCC 
021 SCW at pH ~ 9 to 10 73 -172 +400 90 665 64 SCC 
033 SCW at pH ~ 9 to 10 86 -169 +400 76 642 44 SCC 
113 SCW at pH ~ 9 to 10 75 -200 +317 116 765 63 Incipient SCC 
030 SCW at pH ~ 9 to 10 85 -182 +300 98 725 65 SCC 
020 SCW at pH ~ 9 to 10 22 -109 +291 116 800 85 No SCC 
023 SCW at pH ~ 9 to 10 73 -224 +200 DNB DNB 72 Incipient SCC 
025 SCW at pH ~ 9 to 10 73 -172 +200 116 776 80 Incipient SCC 
029 SCW at pH ~ 9 to 10 89 -144 +200 112 678 73 Incipient SCC 
026 SCW at pH ~ 9 to 10 73 -241 +100 120 764 79 No SCC 
037 SCW at pH ~ 9 to 10 22 -76 Ecorr DNB DNB 32 No SCC 
034 SCW at pH ~ 9 to 10 90 -143 Ecorr 129 712 80 No SCC 
Source: Estill et al. 2002 [DIRS 167274]; King et al. 2004 [DIRS 170981]. 
NOTE: DNB = did not break-equipment stoppage; SAW = simulated acidified water; BSW = basic saturated 
water; SCW = simulated concentrated water; SSW = simulated saturated water; SCC = stress corrosion 
cracking. 
a BSW without the presence of nitrate or sulfate, or both; 
b short time to failure due to crevice corrosion at coating interface 

 
l 
 6-7 
As indicated in Figure 4-1, Titanium Grade 7 was more susceptible to stress corrosion cracking 
initiation as indicated by specimen failures at applied stress ratios of about 1.1 to 1.4 times the 
yield strength in the constant load tests. Some specimens failed relatively early (=168 hours) at 
applied stresses above 110% of yield strength but, at 110% of yield strength, there was a mixture 
of failure and nonfailure runout times from ~200 hours for first failure to at least several 
thousand hours without failure. This is consistent with a runout stress somewhat less than 110% 
of yield strength and is estimated to be at or slightly above the yield strength value. A threshold 
value near or slightly above the yield strength is also consistent with the observation that no 
stress corrosion cracking initiation was detected in a number of fixed deflection Titanium Grade 
7 U-bend test specimens exposed for two years and Titanium Grade 16 (an analogous titanium 
palladium alloy) specimens exposed for five years to a range of relevant environments at 60C 
and 90C (Fix et al. 2004 [DIRS 169321]). These U-bend specimens were bent ~180 degrees 
and then the legs were restrained to give an apex strain (cold-work level) of greater than about 
10% that resulted in sustained stress levels near or somewhat above the yield strength (YS). 
As the above stress corrosion cracking initiation test results are for exposures out to five years, 
an extrapolation scheme is necessary in order to derive a defensible threshold stress value 
associated with the lifetime of waste packages and drip shields from the available experimental 
results. The threshold stress may be derived from the minimum failure stress (or runout stress 
without failure) obtained from the constant load test results described in Figure 4-1 (i.e., 2.0 (YS) 
for Alloy 22 and 1.1 (YS) for Titanium Grade 7) by applying an appropriate safety factor with 
the resulting threshold stress limited to no greater than the yield strength. This approach results 
in threshold stress values of 0.9(YS) for Alloy 22 and 0.5(YS) for Titanium Grade 7 using a 
stress reduction factor (or safety factor) of 2.2. A safety factor of 2.0 has often been used in 
general engineering practice. For example, the American Society of Mechanical Engineers 
(ASME) (ASME 1969 [DIRS 162446], p. 20) uses a reduction factor of 2 on the runout stress 
(endurance limit) for defining fatigue lifetime cycles. The safety factor of 2.2 used for the 
threshold stress is consistent with and somewhat more conservative than the ASME practice. 
The YS values of Alloy 22 and Titanium Grade 7 are listed in Table 4-5. For conservative 
purposes the YS value at the maximum temperature is used. The estimated temperature is 200C 
(with YS approximately 285 MPa) for the waste package (Section 6.3.4) and 140C (with YS 
approximately 221 MPa) for the drip shield (Section 6.3.7). 
As described above, the development of a threshold stress criterion is based primarily on uniaxial 
test data plus results obtained on U-bend specimens under a biaxial stress state. In contrast, 
design calculations that determine the integrity of components under expected loading conditions 
generally result in stress outputs described in terms of multiaxial stress components. The 
application of the multiaxial stress condition (e.g., using a result from a three-dimensional finite 
element model) to assess the potential for crack initiation and through-wall crack propagation in 
a component is consistent with the failure theory used by the ASME, which uses the Tresca 
criteria (maximum shear stress theory) as the failure basis and allows for comparison of 
multiaxial stresses with allowable stresses that were generated from uniaxial test results 
(Bernstein 1988 [DIRS 164860], p. 436). 
For example, the prediction of stress-strain behavior in sophisticated elasticplastic analyses 
(i.e., at high stress and strain values where permanent deformation occurs) typically uses the 
equivalent effective stressstrain approach and uniaxial material stressstrain data to assess 

 
l 
 6-8 
multiaxial stress conditions. In order to apply the uniaxial stress-strain information to multiaxial 
conditions, principal stresses are used. This approach considers that a combination of stresses 
can be equivalent to a uniaxial condition. Even in a uniaxial stressstrain test (where failure 
typically occurs along the 45-degree plane, in pure shear), the cross sections that are not 
perpendicular to the load line are in a multiaxial stress condition that is equivalent to the uniaxial 
condition. These multiaxial stress states can be observed using Mohrs circle (Timoshenko and 
Goodier 1951 [DIRS 122064], p. 14). Thus, the use of uniaxial stress-strain curves for 
multiaxial loading conditions is acceptable when used in combination with principal stresses 
determined from the stress analyses. 
Stress corrosion cracking initiation can be treated as microscopic crack formation due to the 
repetitive process of passive film rupture at slip sites followed by a dissolution transient until 
passivation recurs (Section 6.3). According to Averbach (1968 [DIRS 164859], pp. 449 to 455), 
these microcrack formations are due to the plastic flow in the local state; yielding occurs by slip 
or twin formation; and these slip or twin formations occur in the plane that is subjected (and 
perpendicular) to the maximum stress. 
By analogy to the theories and criteria used in structural type evaluations, initiation test data 
under the uniaxial test condition could be used to determine the initiation threshold under the 
triaxial stress state. The data can be used because the slip and twin formations occur 
perpendicularly to the maximum stress plane. 
Threshold stress intensity factor is another established method of preventing crack propagation. 
In this case, crack propagation will not occur if the applied stress intensity factor remains below 
a threshold value (KISCC) (Section 6.3.5). The stress intensity factor is a direct function of the 
stress perpendicular to the crack plane. Thus, it is a function only of the stress perpendicular to a 
specific plane and similar to looking at uniaxial test data (for the same stress at the specific plane 
location). 
In conclusion, the use of uniaxial test data to predict crack initiation and failure for a multiaxially 
loaded component is consistent with engineering practice. 
Density of Incipient Cracks-In a commercial metal alloy, there is a relatively high density of 
potential incipient surface cracks associated with microscopic discontinuities (e.g., precipitates, 
grain boundaries, passive film rupture sites, etc.). The surface of the waste package is divided 
into many subdivisions, referred to as patches, in the performance assessment. Patch size in 
terms of width and length is determined by the size of the closure weld as well as the stress 
distribution in and near the weld as through-wall cracking can only occur in the closure weld 
region. In any given surface location where the principal tensile stress above the threshold value 
exists, multiple cracks may initiate and grow together, but only one becomes predominant. As 
discussed in Section 6.5.1, the minimum spacing between parallel through-wall radial cracks 
must be greater than the plate thickness for the stress (and resultant stress intensity factor) to be 
sufficient to drive a flaw through-wall. 
Incipient Crack Size-Environmental cracking has historically been separated into initiation 
and propagation phases (Jones and Ricker 1987 [DIRS 118672], p. 146). Although the 
particular crack depth defining the separation of the two phases is arbitrary, when the stress 
exceeds the stress corrosion cracking threshold stress (for the purpose of lifetime modeling), the 

 
l 
 6-9 
initiation crack size (associated with microscopic crack formation at localized corrosion or 
mechanical defect sites) is taken as 0.05 mm as developed by Ford and Andresen (1988 
[DIRS 118611], p. 798; Andresen 1991 [166965], Figures 39 to 41). Thereafter, the crack may 
either reach the arrest state or the propagation phase once the crack tip stress intensity factor 
exceeds the threshold KISCC value. Incipient crack size is one of the intrinsic properties of a 
material related to susceptibility to stress corrosion cracking. Demonstration that the initial size 
(0.05 mm or 50 microns) is suitable for intended use is based on the data evaluation criteria 
specified in the data qualification plan in Appendix A, which requires that one or more of the 
following factors (AP-SIII.10Q, Section 5.2.1.k) be used as is done here using all four factors: 
 Reliability of data sourceThe initial size (0.05 mm) is based on expert observation 
documented in a technical paper (Ford and Andresen 1988 [DIRS 118611]) published in a 
refereed and peer-reviewed publication (i.e., Proceedings of the Third International 
Symposium published by the Metallurgical Society, Warrendale, Pennsylvania). 
 Qualifications of personnel or organizations generating the dataGeneral Electric 
Global Research Center researchers Ford and Andresen (1988 [DIRS 118611]), have 
more than 20 years experience in the field of stress corrosion cracking with international 
reputations. 
 Prior use of the dataIn addition to the data used by Ford and Andresen (1988 
[DIRS 118611]), the initiation flaw size of 0.05 mm (or 50 microns) was also used as the 
upper range of the initiated crack size by Ford (1996 [DIRS 167203], p. 377), another 
technical paper published in a refereed and peer-reviewed publication (i.e., Corrosion, 
published by NACE International, Houston, Texas). 
 Availability of corroborating dataCorroborating data is available in NRC 
NUREG/CR-5864 (Harris et al. 1992 [DIRS 168053], p. 3-8), where the size of 
initiating cracks was measured as 10-3 in. (~0.0254 mm or 25.4 microns). Compared to 
this value, the use of 0.05 mm (or 50 microns) as the crack size for incipient cracks is 
clearly conservative. 
6.2.2 Manufacturing Flaws 
6.2.2.1 Flaw Size and Flaw Density Distribution 
Flaw size and flaw density distributions are addressed in Analysis of Mechanisms for Early 
Waste Package/Drip Shield Failure (BSC 2004 [DIRS 170024], Section 6.2.1). 
The welding process for the waste package final closure weld is a gas tungsten arc welding 
process (CRWMS M&O 1996 [DIRS 124950], p. 5). Selection of this process is fully consistent 
with the recommendations resulting from an expert evaluation of a range of potential closure 
welding processes (Lundin 2002 [DIRS 161780]). This evaluation concluded that the cold wire 
feed gas tungsten arc welding process should be selected for the waste package final closure 
weld process to be implemented in a hot cell. This process was recommended primarily for its 
ability to provide high quality closure weld joints with optimum control of the welding variables. 
The process produces welds that can be readily inspected by automated and remote methods 
(Lundin 2002 [DIRS 161780]). According to Lundin (2002 [DIRS 161780]): 

 
l 
 6-10 
The choice of the GTAW [gas tungsten arc welding] process also naturally limits 
and defines the size and other characteristics of the discontinuities that can be 
induced during welding. Further, the weld face is optimally contoured for ready 
inspection by remote visual methodologies. The discontinuities generated by 
GTAW are well defined and include lack of penetration, lack of fusion, porosity, 
and microfissuring. It is also possible to form defects such as tungsten inclusions, 
caused by the flaking of the tungsten electrode. The extent of any of the 
discontinuities noted above will be related to a single weld pass and do not have a 
tendency to propagate between passes during welding. Thus, they are of a nature, 
which naturally limits their size and orientation within the weld. Since the 
possible generation of discontinuities during welding is limited to the types 
indicated above, they are readily amenable to detection by remote and automated 
inspection using eddy current, ultrasonic and visual methods. With a prior 
knowledge of the type and orientation of any discontinuities, the non-destructive 
examination (NDE) processes most capable for detection and sizing of the 
discontinuities can be defined. 
As the volumetric ultrasonic inspection method is employed as the primary flaw detection 
method for post-weld inspections, there should be no significant undiscovered subsurface defects 
for these welds. Additionally, eddy current or surface wave type ultrasonic inspections are 
planned for evaluating the surface of the weld to detect and repair any surface breaking defects. 
The lack of fusion defect is, by definition, oriented in the direction of the weld bead. The 
tungsten inclusion and porosity defects tend to be smaller rounded defects that have no effective 
directionality. 
Consistent with the above discussion, the expected type, size and orientation of defects that can 
result from the gas tungsten arc welding process are supported by a recent weld defect evaluation 
study in which 16 full-diameter 21-PWR waste package Alloy 22 closure weld mockup ring 
specimens were fabricated using a prototypical gas tungsten arc welding process under 
conditions that simulated hot cell type access restrictions (Smith 2003 [DIRS 163114], Section 
2.3). Weld defects present in these rings were examined by various NDE techniques, including 
liquid penetrant and eddy current surface examinations and volumetric radiographic and 
ultrasonic examinations (Smith 2003 [DIRS 163114], Section 3). These were followed by 
metallographic destructive examination (Smith 2003 [DIRS 163114], Section 4). Information 
gathered from these weld mockup experiments was used to develop a flaw density, orientation, 
and size distribution applicable to the closure welds of the waste package (BSC 2004 [DIRS 
170024], Section 6.2.1). As stated in Analysis of Mechanisms for Early Waste Package/Drip 
Shield Failure (BSC 2004 [DIRS 170024]), the flaw detection and repair-size criterion is 
1/16 inch or 1.6 mm as compared to the somewhat more sensitive 1-mm ultrasonic inspection 
defect detection threshold used for the weld mockup study. The 1-mm ultrasonic inspection 
defect detection threshold was confirmed by metallographic examinations, which verified the 
presence of eight defects (BSC 2004 [DIRS 170024], pp. 19 to 20) detected by ultrasonic and 
confirmed by metallography. The ultrasonic dimensions were consistent with or slightly 
overestimated, the metallographically measured dimensions (BSC 2004 [DIRS 170024], p. 12). 
Imperfections uncovered by metallographic examinations but not detected by ultrasonic 
inspections were gas bubbles, with the majority less than 0.003 inch (approximately 0.08 mm) in 
diameter (BSC 2004 [DIRS 170024], p. 20). Gas bubbles are spherical (BSC 2004 [DIRS 

 
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 6-11 
170024], p. 20) and are not sharp cracks that can propagate due to stress corrosion cracking 
(Andresen and Ford 1985 [DIRS 162528], p. 20). Crack initiation on the bubble surface due to 
stress concentration is ruled out, as weld-induced tensile stress at and near the waste package 
surface is mitigated. All flaws found in the mockup specimens were in the weld metal and root 
of the weld. The flaws were characterized as lack of fusion and were oriented parallel to the 
hoop-stress direction in each case (Smith 2003 [DIRS 163114], Sections 5.1 and 7). Based on 
the results of this 16-weld mockup ring study, the defect size and orientation distributions were 
determined and reported (BSC 2004 [DIRS 170024]). 
The initial weld flaw size distribution is exponentially distributed with an upper-bound 
truncation due to the weld thickness. The size distribution parameter is uncertain and described 
by a gamma distribution (BSC 2004 [DIRS 170024], Section 6.2.1.1.1, Equation 2). Flaws are 
uniformly distributed spatially and their occurrence frequency represented by a Poisson 
distribution. The mean flaw density (Poisson distribution parameter) of the closure weld region 
is uncertain and described by a gamma distribution (BSC 2004 [DIRS 170024], 
Section 6.2.1.1.2, Equation 12). These densities were derived from analysis of the defects 
observed in 16 welded rings subjected to ultrasonic tests. 
These weld flaw characteristics are representative of those to be expected in the noninspected 
weld. An ultrasonic inspection is performed in the shop for fabrication welds and in the site 
closure cell for waste package final closure lid welds to detect and repair the flaws that would 
affect the waste package performance. Consideration of this fact is modeled by use of a 
probability of nondetection curve to derive postinspection flaw size and density distributions 
(BSC 2004 [DIRS 170024], Equations 24 and 28). 
6.2.2.2 Embedded Flaws 
As general corrosion proceeds, embedded flaws can become surface breaking flaws. 
Consideration of preexisting surface breaking flaws only may not be conservative. As an 
alternative conservative approach, the fraction of flaws considered for propagation is increased 
by adding a fraction of the flaws embedded within the entire thickness region of the weld in the 
performance assessment. The fraction of surface breaking flaws is increased by adding the 
fraction of flaws embedded within the one-quarter-thickness region of the weld surface. This is 
conservative as, based on the mean general corrosion rate of 7.23 nm/yr (Section 6.3.5), it will 
take 864,400 years to remove the one-quarter thickness of the surface of the outer lid or 
345,800 years to remove the one-quarter thickness of the surface of the middle lid. 
6.2.2.3 Radial Crack versus Circumferential Crack in Waste Package Closure Welds 
The defect description and orientation distribution obtained from the 16-ring study (BSC 2004 
[DIRS 170024]) is consistent with Shcherbinskii and Myakishev (1970 [DIRS 149953]) who 
describe a statistical treatment of weld flaw orientations based on analysis of a significant data 
set of ultrasonic flaw orientation measurements and concludes that planar type weld defects 
detected ultrasonically tend to be predominately oriented in the direction of the weld center line. 
More than 98% of the defects fall within 16 degrees of the weld center line in the case of steam 
pipe welds (e.g., the tails of the distributions fall to less than 2% probability as the azimuth 
approaches 90 degrees) (Shcherbinskii and Myakishev 1970 [DIRS 149953], Figure 1). A 
similar conclusion, drawn from the data for plate welds (Shcherbinskii and Myakishev 1970 

 
l 
 6-12 
[DIRS 149953], Figure 2), indicates that the statistical distribution of defects with respect to the 
orientation angle approximated by a centered normal distribution with a maximum standard 
deviation of 5 degrees yields a probability of 99% that the defects are located within about 
13 degrees. These data suggest that much less than 1% of these flaws have a potential to 
undergo stress corrosion cracking as radial cracks. There is an obvious typographical error in 
Shcherbinskii and Myakishev (1970 [DIRS 149953]) in Figures 1 and 2 of that reference. This 
reference is an English translation of a Russian publication. The frequencies given as 1.8 and 
2.5 Hz in these figures should read 1.8 and 2.5 MHz, which is typical of those used in ultrasonic 
testing. However, this apparent mistranslation has no effect on the conclusion drawn from this 
paper. 
As discussed above, manufacturing defects, especially those due to welding, would likely be 
oriented along the weld direction. When initiated, the propagation of cracks tends to follow the 
direction perpendicular to the maximum principal stresses, whether the cracks are propagating 
due to fatigue or stress corrosion. In structures where shear stress is not significant (i.e., thin 
wall pipes or plates), the maximum principal stresses are the same as the three directional 
component stresses. Thin wall pipes are usually defined by a radius-to-wall-thickness ratio 
greater than 10. For an axisymmetric structure or model, there is no shear stress in the in-plane 
direction. The hoop (circumferential) stress is usually the most dominant stress component and 
the stress in the through-wall direction (which would drive laminations) is usually the lowest 
among the three stress components. A typical example is a cylindrical shell subjected to internal 
pressure loading. 
Due to the orthogonality effect of stresses, once an oblique-oriented crack (measured with 
respect to the direction of loading) turns into the direction perpendicular to the maximum stress, 
the stresses in the other directions have little effect in turning the crack from that direction. 
Thus, oblique-oriented flaws turning to become perpendicular to the maximum stress cannot be 
ruled out. However, once this occurs, the orientation will not change. Likewise, a radial flaw, 
which is already oriented perpendicular to the maximum (hoop) stress, will remain radially 
oriented. 
In addition, cracks tend to propagate in the direction that offers the least resistance. If a crack 
initiates at the bottom of the weld, near or in the heat affected zone, it tends to propagate in the 
heat affected zone, parallel to the fusion line between the weld and base metal instead of turning 
into the base metal at an oblique angle. Therefore, any crack, initiated and oriented in any 
direction at its very early stage, would adjust its direction and tend to align and propagate in the 
hoop or circumferential orientation, whichever results in the largest stress intensity factor. 
Based on the flaw orientation measurement data provided by Shcherbinskii and Myakshev (1970 
[DIRS 149953]), there is a strong dependence of the flaw orientation on the direction of welding. 
This is consistent with the expected behavior that most defects are associated with the 
application of the weld metal and would tend to be oriented along the interface of deposited 
beads. Although it is unlikely that flaws are observed at significant oblique angles to the 
direction of the weld travel direction, this circumstance cannot be entirely ruled out. Depending 
on the quality of the welds and welding procedures, a more uniform distribution with regards to 
angular orientation may be obtained. However, very tightly controlled ASME/AWS and NDE 
processes will be in place when the waste package closure weld is produced. If flaws were 

 
l 
 6-13 
present that make a significant oblique angle with the direction of the weld placement, it would 
not be surprising to see the flaw direction turn towards the radial direction. 
The potential for flaws turning or not turning towards the radial direction can be studied by 
determining the stress intensity factor for a crack in a plate with an angle, ., to the direction of 
the load, subjected to a constant stress. As an example, for an arbitrary stress and crack length, 
the ratio of the stress intensity factor for a flaw at an angle, ., with the direction of the load to the 
stress intensity factor oriented perpendicular to the stress direction (maximum stress intensity 
factor) can provide some insight to the expected behavior of flaws. Figure 6-1 shows the ratio 
(sin(2.)) with respect to the angle that the flaw makes with the direction of the load. The 
analyses in the figure are based on the solutions presented in The Stress Analysis of Cracks 
Handbook (Tada et al. 2000 [DIRS 167756], p. 127). The results of this calculation demonstrate 
that for a circumferentially oriented flaw in the waste package closure welds subjected to hoop 
stress, the stress intensity factor would be very low. Thus, the ratio of the stress intensity factor 
for a circumferential flaw oriented at a small angle to the load direction subjected to hoop stress 
to that of a radial flaw oriented perpendicular to the load is very low. The ratio is 0.03 and 0.05 
for flaws at 5 and 10 degrees to the load direction, respectively. This demonstrates a very low 
driving force for the crack to change orientation from circumferentially oriented to radially 
oriented. This same circumferential flaw would be oriented close to 90 degrees (perpendicular) 
to the radial stress. Figure 6-1 shows that the ratio of the stress intensity factors is at least 95% 
of a flaw perpendicular to the load direction ( . = 90). Thus, there is a significant driving force 
to keep the flaw in its circumferential direction. Combined with the presence of the heat-affected 
zone, it is unlikely that these flaws would become radial. 
Combining the test results regarding flaw orientation from Shcherbinskii and Myakshev (1970 
[DIRS 149953]) and the stress intensity factor ratio discussed above, it is concluded that the 
probability of an expected circumferentially oriented flaw becoming radial is very small. Only 
flaws that are oriented at angles greater than approximately 45 degrees with the load direction 
may turn in the radial direction and the probability that such flaws exist is very unlikely. 
Essentially all flaws are oriented towards the direction of the welding (circumferentially). An 
investigation of the stress intensity factor for flaws at oblique angles to the load direction 
supports the conclusion that flaws oriented to within approximately 15 degrees of the loading 
direction will not be subjected to sufficient driving force to cause the flaw to turn radial. 
Supporting this conclusion also is the fact that the flaw would need to turn away from the path of 
least resistance, the heat affected zone, to grow into the base or weld metal. If a flaw were to 
occur and be oriented an angle greater than 15 degrees from the load direction, the flaw 
orientation may change such that the flaw will become radially oriented. However, as noted 
earlier, the probability of such flaws occurring is small relative to flaws oriented within 
15 degrees of the welding direction. 
In summary, radially oriented flaws are important to the stress corrosion cracking analysis for 
waste package lifetime calculations as the hoop stress, which drives the radially oriented cracks, 
is the dominant stress component. However, almost all of the flaws are more or less in the 
direction of the weld and only flaws that are oriented at angles greater than about 45 degrees 
with the weld direction may turn in the radial direction. As discussed earlier, about 98% to 99% 
of the flaws are within about 13 to 16 degrees of the weld centerline. Thus, it is conservative 
to recommend that radially oriented flaws (those with a 45-degree or greater angle from the 

 
l 
 6-14 
direction of the weld) comprise approximately 0.5% of the flaws. Note that a slightly more 
conservative value (0.8%) is recommended for this parameter in Analysis of Mechanisms for 
Early Waste Package/Drip Shield Failure (BSC 2004 [DIRS 170024], Table 12). 
Source: Based on solutions presented by Tada et al. (2000 [DIRS 167756], p.127). 
Figure 6-1. Ratio of the Stress Intensity Factor (K( .)) of a Crack Making an Angle ( .) with the Stress 
Direction to the Factor (K(90)) of a Crack Oriented Perpendicular to the Stress Direction 
as a Function of the Angle ( .), for a Crack with an Arbitrary Stress and Crack Length 

 
l 
 6-15 
6.2.2.4 Crack Aspect Ratio 
Crack aspect ratio relates crack length to depth and is an important input for determining crack 
opening area once a crack propagates through-wall. Determination of the crack length for either 
a manufacturing defect or an incipient crack is based on the following considerations: 
Surface flaws are semielliptical with depth a and length 2c. 
The aspect ratio (.) is the ratio of one-half of crack length (c) versus crack depth (a) 
(i.e., . = c/a). A semicircular flaw has an aspect ratio of 1 (. = 1). 
A crack maintains its aspect ratio during its growth until the depth reaches the wall 
thickness. Then, at this point, the shape instantaneously becomes rectangular. 
The crack aspect ratio is 1 for radial cracks in the closure weld. 
The crack aspect ratio is greater than 1 for circumferential cracks with an exponential 
distribution based on one of the formulations provided by Harris et al. (1981 
[DIRS 118624], Equation 2-10, p. 29): 
( ) . - . - = . > . / ) 1 ( e P (Eq. 1) 
where . is the standard deviation of . and has the value of 0.7. From Equation 1, the mean and 
median values (.mean and .50) and the standard deviation (.sd) of . can be obtained by the 
following formulas: 
.mean = 1 + . = 1.7 
.50 = 1 + . ln2 = 1.485 
.sd = . = 0.7 
A gamma or Weibull distribution with a shape factor of one is equivalent to an exponential 
distribution. 
6.3 THE BASE-CASE SLIP DISSOLUTIONFILM RUPTURE MODEL 
6.3.1 Introduction 
A crack propagation rate prediction model can be achieved via a fundamental understanding of 
the cracking mechanism. The formulation of such a fundamentally based model of crack 
propagation requires the choice of a working hypothesis for the cracking mechanism and the 
evaluation of the parameters of importance in the mechanism. For the systems of interest, the 
slip dissolutionfilm rupture (SDFR) mechanism has been chosen. Slip is highly localized, 
microscopic strain that can lead to a surface offset or step where the slip plane intersects the 
surface and, thus, can rupture the passive film present at the surface. This cracking mechanism 
has been successfully applied to model stress corrosion cracking of stainless steel, low-alloy 

 
l 
 6-16 
steel, and nickel-based alloys in light water reactor environments (Ford and Andresen 1988 
[DIRS 118611], pp. 789 to 800; Andresen and Ford 1994 [DIRS 118581], pp. 61 to 70). 
6.3.2 Slip DissolutionFilm Rupture Mechanism 
In accordance with the slip dissolutionfilm rupture theory, crack advance is faradaically related 
to the metal oxidation that occurs when the protective film at the crack tip is ruptured. 
Figure 6-2 (Ford and Andresen 1988 [DIRS 118611], Figure 2; Andresen and Ford 1994 
[DIRS 118581], Figure 1) schematically shows the change in oxidation current and charge 
densities with time following the rupture of a protective film at the crack tip. In Figure 6-2, T V 
is the average crack growth rate at the tip, VS is the crack growth rate at the crack side, M and . 
are atomic weight and density of the crack tip metal, F is Faradays constant, n is the number of 
electrons involved in the oxidation of a metal atom, Qf is the oxidation charge density per film 
rupture, e
ct is the strain rate at the crack tip, and ef is the fracture strain of the film. The initial 
oxidation rate (and, hence, crack advance rate) is rapid, typically controlled by activation or 
diffusion kinetics as the exposed metal rapidly dissolves. Availability of the balancing cathodic 
reduction current is also necessary, but is generally not limiting in hot water environments. 
However, in most (if not all) hot water cracking systems, a protective oxide reforms at the bared 
surface, and the rate of total oxidation (and crack tip advance) slows with time. Thus, crack 
advance can only be maintained if the film rupture process is repetitive. Therefore, for a given 
crack tip environment, corrosion potential, and metallurgical condition, crack growth is 
controlled by the change in oxidation charge density with time and the frequency of film rupture 
at the strained crack tip. The latter parameter is determined by the fracture strain of the film, ef, 
and the strain rate at the crack tip, e
ct. By invoking Faradays law, the average environmental 
crack growth rate, Vt, can be related to the strain rate at the crack tip, e
ct ( e & in Figure 6-2) by the 
following equation (Ford 1996 [DIRS 167203], Equation 1; Ford and Andresen 1988 
[DIRS 118611], Figure 2, p. 790; Andresen and Ford 1994 [DIRS 118581], Figure 1, p. 62): 
 
= ct 
f
f 
t 
Q 
F z
M V e 
e . (Eq. 2) 
where M, . = atomic weight and density of the crack tip metal 
F = Faradays constant 
z = number of electrons involved in the oxidation of a metal atom (n in Figure 6-2) 
Qf = oxidation charge density per film rupture 
ef = fracture strain of the film 
The time, tf, to reach the fracture strain, ef, is: 
 
= ct f f t e e / (Eq. 3) 
Figure 6-3 shows the schematic of oxidation current density versus time following repeated 
oxide rupture events. Repassivation current transients exhibit an initially high bare surface 

 
l 
 6-17 
dissolution current density, io, at an initial short time, to. Thereafter, oxide growth (or 
thickening) leads to a decay in the oxidation current density, which often follows a power law 
relationship: 
n 
o 
o t t
t i i 
- 
.. 
. 
.. 
. 
= 
(Eq. 4) 
Because of this power law relationship, Equation 2 can be reformulated as follows (Andresen 
and Ford 1994 [DIRS 118581], Equation 1, p. 62): 
n 
ct t A V ) ( 
 
= e (Eq. 5) 
where, for a given environment, A and n are material constants that can be measured from the 
repassivation response. The repassivation slope, n, is the slope on a log-log plot of (it/io) versus 
(t/to) from Equation 4. 
If a bare surface condition is maintained at the crack tip (i.e., ef/e
ct < to, or tf < to, hence, it=io), a 
maximum crack growth rate should result. Integration of Equation 4 leads to: 
( ) . . 
.
. 
. . 
.
. 
= = =  . 
ct 
f 
o f o 
t 
t f i t i dt i Q 
f 
e 
e 
0 
(Eq. 6) 
Substitution of Equation 6 into Equation 2 yields the predicted maximum environmental crack 
growth rate: 
o max i 
F z
M V 
. 
= 
(Eq. 7) 

 
l 
 6-18 
Source: Ford and Andresen 1988 [DIRS 118611], Figure 2; Andresen and Ford 1994 [DIRS 118581], Figure 1. 
Figure 6-2. Schematic Oxidation Charge Density versus Time for a Strained Crack Tip and Unstrained 
Crack Sides in the Slip Dissolution Mechanism 

 
l 
 6-19 
Source: Andresen and Ford 1994 [DIRS 118581]. 
Figure 6-3. Schematic of Oxidation Current Density versus Time Following Repeated Oxide Rupture 
Events 
This expression for the maximum environmental crack growth rate is the quantitative basis for 
the early observations relating the maximum oxidation current density on a straining surface to 
the maximum crack growth rate. These early correlations were obtained primarily for alloys in 
concentrated environments (boiling MgCl2, 9M NaOH solutions, etc.) under dynamic straining 
conditions. By comparison, in environments more relevant to conditions at Yucca Mountain, it 
is expected that (a) the passivation rate is high (e.g., in less aggressive chemistries or for lowersusceptibility 
materials) and, thus, n (in Equation 4) will be high; (b) the onset of repassivation 
is rapid, and, thus, to is short; and (c) under constant load or displacement conditions, the 

 
l 
 6-20 
periodicity of oxide rupture, ef/ect, is much greater than to. Consequently, the oxidation charge 
rate, Q, is given by the following equation: 
( ) 
1 
0 1 
-  
.. 
. 
.. 
. - 
= = . n 
ct f 
n 
o o 
t 
t f 
n 
t i dt i Q 
f 
e e 
(Eq. 8) 
Under these circumstances, a bare surface will not be maintained at the crack tip, and the crack 
propagation rate (Ford [167203], Equation 5) is given by the substitution of Equation 8 into 
Equation 2: 
n 
ct nf 
n
n
o t o i 
F z
M 
t V ) ( 
) 1 ( 
 
- 
= e 
e . 
(Eq. 9) 
This is an expanded version of Equation 5 and relates the parameters A and n to the specific 
oxidation rates (Equation 4) and the fracture strain of the oxide at the crack tip: 
n
f 
n
o o 
) n 1 ( 
t i 
F z
M A 
e - . 
= (Eq. 10) 
6.3.3 Model Quantification 
As the repassivation current follows a power law response (Equation 4), the faradaic relationship 
between the oxidation rate following oxide rupture and crack advance increment per time 
(growth rate, Vt), coupled with the relationship between crack tip strain rate, ct e 

, and periodicity 
of oxide rupture, distills to the expression shown in Equation 9. 
Evaluation of the crack advance mechanism leads to the conclusion that the film ruptureslip 
oxidation mechanism represents a justifiable model that is capable of being quantitatively 
evaluated for hot water systems. The mechanism is justifiable because almost all engineering 
alloys depend on the presence of a stable oxide film to act as a kinetic barrier to rapid 
dissolutionoxidation, especially in hot water. It is quantifiable, because predictions result 
directly from measurements of repassivation kinetics, typically obtained by rapidly straining 
wires of base alloy or synthetic (e.g., representative of the grain boundary) composition 
(Figure 6-2). 
According to Andresen and Ford (1994 [DIRS 118581], p. 62), the model can be quantified by 
evaluating the following processes: (1) the steady-state and transient compositions of the 
environment at the crack tip as a function of the conditions in the bulk (external) solution; (2) the 
oxidation rates for the material or environmental system expected at a strained crack tip; and 
(3) the oxide fracture strain and the crack tip strain rate, defined in terms of engineering 
parameters such as the stress intensity factor. For practical application, empirical approaches 
have been used for the model quantification processes. 

 
l 
 6-21 
The initial application of the slip dissolutionfilm rupture model was on the quantitative 
prediction of cracking in austenitic Stainless Steel Types 304 and 316 in 288C high-purity 
BWR water (Ford and Andresen 1988 [DIRS 118611]). The quantification processes for the 
model are summarized as follows: 
Step 1 Measurements of n are obtained from repassivation tests as the repassivation 
current follows a power law response (Equation 4). Those tests typically involve 
rapidly straining wires to increase the anodic passive current density, and 
subsequently measuring the decay of the passive current density with time. 
Step 2 Once n is known, the value of A is determined from Equation 10, which relates 
the parameters A and n to the specific oxidation rates and the fracture strain of 
the oxide at the crack tip. 
An alternative procedure, however, is used to quantify the model parameters. Based on this 
procedure, A is directly determined from n empirically. The empirical determination of A is 
based on stress corrosion cracking crack growth tests that measure the crack growth rate Vt at 
specific crack tip strain rate ct e 

. The value of A is calculated in accordance with Equation 5 
for each set of n, Vt, and ct e 

. Curve fitting is then used to develop the empirical relationship 
between A and n. 
An empirical relationship between A and n (with A in cm-s(n-1) and n being dimensionless) 
of: 
A = 7.8  10-3 n3.6 (Eq. 11) 
was provided by Ford and Andresen (1988 [DIRS 118611], p. 791) for Stainless Steel Type 304 
in 288C water. For Alloy 22 and Titanium Grade 7, independent experimental measurement of 
A and n is preferred but, due to lack of experimental data, the expression above is used for the 
slip dissolution mechanism of Alloy 22 for present purposes. The resulting model is validated 
experimentally as indicated in Section 7. 
Substitution of Equation 11 into Equation 5 leads to: 
Vt = 7.8  10-3 n3.6 (e
ct)n (Eq. 12) 
where Vt is in units of cm/s and ct e 

is in units of s-1. 
For sensitized Stainless Steel Type 304 in 288C water, Figure 6-4 indicates that Equation 12 
with n = 0.54 (i.e., A = 8.5  10-4) is a good prediction model for observed crack growth rate 
versus crack tip strain rate relationships. Further, this slip dissolutionfilm rupture model (using 
the Stainless Steel Type 304 A versus n relationship in 288C water) has been statistically 
validated for the chromium-containing, nickel-based Alloys 600 and 182 over a range of anionic 
impurity concentrations (Ford and Andresen 1988 [DIRS 118611], Figure 10). 

 
l 
 6-22 
Source: Ford and Andresen 1988 [DIRS 118611], Figure 7, p. 791. 
Figure 6-4. Crack Growth Rate (Presented by Observed Data Points and Predicted Curve) versus 
Crack Tip Strain Rate for Sensitized Stainless Steel Type 304 in Oxygenated 288C Water 
The crack tip strain rate, ct e 
 
in Equation 12, is related to the engineering stress parameters (such 
as the stress intensity factor) via formulations by Ford and Andresen (1988 [DIRS 118611], 
Table 1). According to Ford and Andresen (1988 [DIRS 118611], p. 791), the formulations 
provided are semiempirical relationships to normalize the effects of a wide range of stressing 
conditions on the environmentally assisted crack propagation rates. For constant load, the 
relationship is: 
4 14 10 1 . 4 I ct K - 
 
 = e (Eq. 13) 
where the stress intensity factor KI is in MPa (m)1/2. 

 
l 
 6-23 
For constant load, substituting Equation 13 in Equation 5 leads to the following alternative crack 
growth rate equation: 
( )n 
I K A t V = (Eq. 14) 
where 
( )n x A A 14 10 1 . 4 - = (Eq. 15) 
n 4 n = (Eq. 16) 
6.3.4 Adaptation of Slip Dissolution Model To Alloy 22 
Andresen and Ford (1994 [DIRS 118581], p. 62) indicated that the SDFR model has been 
applied to stainless steels, low-alloy and carbon steels, ductile nickel alloys, and irradiated 
stainless steels. Ford and Andresen (1988 [DIRS 118611], p. 789) also used the SDFR model for 
the Inconel 600 and 182 nickel-based alloys. Further, as indicated in Section 6.3.3, it was 
determined that the SDFR model (using the Stainless Steel Type 304 A versus n relationship 
in 288C water) was statistically valid for these chromium-containing, nickel-based Alloys 600 
and 182 over a range of anionic impurity concentrations (Ford and Andresen 1988 
[DIRS 118611], Figure 10). 
Subsequently, Andresen (1991 [DIRS 166965], Figure 37) used the SDFR model for the higher 
chromium-content nickel-based alloy, Alloy 82 (UNS N06082), and determined that measured 
stress corrosion cracking growth rates agreed reasonably well with predicted rates. Alloy 82 
(UNS N06082) (18% to 22% Cr, UNS NO6082) overlaps Alloy 22 (20% to 22.5% Cr) 
(DTN: MO0003RIB00071.000 [DIRS 148850], p.2) in chromium content. Analyses indicate 
that the inner, protective corrosion films that form in the passive potential range on such 
chromium-containing nickel-based alloys with greater than about 15% chromium contain a very 
thin passive film layer of primarily Cr2O3 (with some nickel content) at the oxidealloy interface 
(Pensado et al. 2002 [DIRS 166944], p. 2-2). Such a thin, passive Cr2O3 film is likely to possess 
similar repassivation kinetics and mechanical properties (e.g., fracture strain) over the range of 
nickelchromium-based alloys of interest. This is consistent with the model having been shown 
to apply or to give reasonable predictive results for a range of nickel base alloys with chromium 
contents spanning the Alloy 22 compositional range. Further, there is general correspondence 
(reasonable statistical agreement) between the observed stress corrosion cracking growth rate 
temperature dependencies for sensitized Stainless Steel Type 304 and nickelchromium-based 
Alloy 600 over the temperature range of most interest (~50C to 200C) when compared under 
comparable stress intensity factor and environmental conditions (Andresen 1993 [DIRS 166966], 
Figures 15 and 16). For example, Figure 6-5 shows that crack growth rates for sensitized 
Stainless Steel Type 304 and Alloy 600 follow the same temperature dependency with 
reasonably similar crack growth rates over a temperature range from about 25C to 275C, which 
is broader than the temperature range of most interest (~50C to 200C) stated above. 
As the SDFR was initially developed for stainless steels and nickel-based alloys Inconel 600 
and 182 under higher temperature (~288C) light water reactor coolant conditions, additional 
confidence in the applicability of this model to Alloy 22 can be gained from observation of the 

 
l 
 6-24 
response of Alloy 22 under similar light water reactor coolant conditions. Test results from 
DTN: MO0402GEA22SCC.000 [DIRS 167911] indicate the crack growth rate response of 
Alloy 22 exposed to 288C relatively pure water (2 ppm O2) is broadly consistent with the crack 
growth rate response of other materials, such as Alloys 600 and 182 (Andresen et al. 2002 
[DIRS 166967]) and austenitic stainless steel (Andresen et al. 2002 [DIRS 167762]) under these 
same conditions. The measured crack growth rates show a similar dependency to parameters 
like corrosion potential and water purity (sulfate). For example, in all test cases, the change in 
corrosion potential from ~ +0.2 VSHE to ~ 0.5 VSHE (due to a change from 2 ppm O2 to 
H2-deaerated water) causes a drop of at least one order of magnitude in the crack growth rate, as 
indicated by Table 6-3. Also, as expected, Alloy 22 shows crack growth rates under 
repository-type oxidizing conditions (i.e., at 0.2VSHE) that are about one order of magnitude 
lower than those of the other materials under identical test conditions, demonstrating its 
superiority as a structural material under conditions where stress corrosion cracking is a concern. 
Source: Andresen 1993 [DIRS 166966], Figure 15. 
Figure 6-5. Temperature-Dependence of Sensitized Stainless Steel Type 304 and Alloy 600 

 
l 
 6-25 
Table 6-3. Measured Crack Growth Rates (mm/s) in 288C, Oxygenated Water Due to Drop in 
Corrosion Potential 
Alloy 
Stress Intensity 
Factor 
MPavm 
Corrosion 
Potential 
+0.2 VSHE 
Corrosion 
Potential 
-0.5 VSHE Reference 
Alloy 22 
27.5 
[25 ksi (vin.)] 
2.3  10-8 4.0  10-9 DTN: MO0402GEA22SCC.000 
[DIRS 167911], Figure 3 
Alloy 182 28.4 3.0  10-7 6.0  10-9 Andresen et al. 2002 
[DIRS 166967], Figure 7 
Alloy 600 30.0 3.3  10-7 3.7  10-8 Andresen et al. 2002 
[DIRS 166967], Figure 8 
Unsensitized Stainless Steel 
Type 316L 
27.5 
[25 ksi (vin.)] 
4.1  10-7 >2.0  10-8 Andresen et al. 2002 
[DIRS 167762], Figure 5 
In addition to the expected similarities in composition and mechanical properties, as indicated 
earlier in this section, for the passive films present on this class of alloys (i.e., austenitic Stainless 
Steel Types 304, 304L, 316, and 316L and nickelchromium-based alloys (Alloys 600 and 22)), 
the expected microdeformation modes of the alloys per se should be comparable, based on 
examination of literature values for stacking fault energies (SFE) (Gordon 2004 [DIRS 167027]). 
A low value of SFE promotes coplanar dislocation arrays (promoting local stress buildups that 
can more easily rupture the passive surface film at slip offsets), whereas high SFE values 
promote dislocation tangles that tend to diffuse local stress buildups. These alloys all possess a 
face-centered cubic-crystallographic lattice structure and have similar relatively low values of 
estimated SFE ranging from about 20 to 30 ergs/cm2 for Stainless Steel Types 304L and 316L to 
about 80 ergs/cm2 for Alloy 600, with the estimated value for Alloy 22 being about 65 ergs/cm2. 
This range is relatively low compared to published values of about 340 ergs/cm2 for pure nickel 
or nickel alloys with much lower chromium contents (Gordon 2004 [DIRS 167027], Table 1). 
Although lower values of SFE can promote micro-stress and resulting micro-strain buildups at 
the surface region that may accelerate stress corrosion cracking initiation, the relatively high 
local deformation at a stressed crack or weld flaw tip is likely to lead to relatively high local 
strains regardless of SFE. Thus, this will tend to overwhelm any effect of SFE on stress 
corrosion cracking propagation. 
Based on the above observations, there is ample reason to conclude that stress corrosion cracking 
of nickel-based Alloy 22 occurs by the same fundamental mechanism characterized by the slip 
dissolution stress corrosion cracking model: 
Vt = A ( ct e 

)n (Eq. 5) 
This model is experimentally benchmarked for Alloy 22 in a range of relevant repository brine 
environments for Yucca Mountain as described in the following equations. 
The relationship between A and n described by Equation 11 (with A in cm-s(n-1) and n 
being dimensionless) becomes the following equation (with A in mm-s(n-1) and n being 
dimensionless): 
A = 7.8  10-2n3.6 (Eq. 17) 

 
l 
 6-26 
For constant load condition, with t V in mm/s and I K in MPa (m)1/2 in Equation 14, Equation 15 
becomes: 
A = 7.8  10-2n3.6(4.1  10-14)n (Eq. 18) 
Substitution of Equations 17 and 18 in Equation 5 leads to: 
Vt = 7.8  10-2n3.6(4.1  10-14)n(KI)4n (Eq. 19) 
For Alloy 22 under constant load condition, the parameter n can be determined from Equation 
19 based on crack growth rates measured at various levels of applied stress intensity factor, KI. 
Stress corrosion cracking crack growth rate measurements from the General Electric Global 
Research Center (GEGRC) (DTN: LL021105312251.023 [DIRS 161253]) are used for the 
quantification of parameters for the SDFR stress corrosion cracking model to be used for 
Alloy 22. The test data were developed from three of the four Alloy 22 specimens (c144, c152, 
c153, and c200) tested at 110C in a concentrated mixed-salt environment know as Basic 
Saturated Water (BSW) with a target composition and solution pH (pH = 13.4 at room 
temperature) listed in DTN: LL021105312251.023 ([DIRS 161253], p. 3 and 6). The compact 
tension specimens (loaded per ASTM E 399-90 [DIRS 117480]) used for the crack growth rate 
measurements were fabricated from Alloy 22 in a range of microstructural conditions. These 
included the solution-annealed condition (Specimens C144 and C152), the 20% cold-worked 
condition (Specimen C-153), and the thermally aged condition (700C for 175 hours, 
Specimen C-200) as described in DTN: LL021105312251.023 [DIRS 161253]. 
The specimens were subjected to cyclic loading in order to initiate crack growth and followed by 
constant loading conditions with various hold times. The set of data from 
DTN: L021105312251.023 [DIRS 161253] used as input for establishing values of n for Alloy 
22 are summarized in Table 6-4 and are based on measured crack growth rates listed in 
Table 4-2. These data were selected based on the following criteria. 
First, the minimum hold time is 24 hours (85,400 seconds) because Equation 19 is applicable 
only to constant loading condition. It is unrealistic to determine the parameters n and A (or A 
and n) in this equation based on test data at relative short hold times. The only exception is the 
data point associated with specimen c144 for which the hold time is relatively short (3,000 
seconds or approximately one hour), but crack growth appeared to cease 
(DTN: LL021105312251.023 ([DIRS 161253], p. 7), consistent with reaching the constant load 
state. 
Secondly, data associated with specimen c200 were not included because this specimen was aged 
at 700C for 175 hours. This aging condition is ultrasevere relative to the expected waste 
package closure weld thermal exposure. According to Aging and Phase Stability of Waste 
Package Outer Barrier (BSC 2004 [DIRS 171924], Section 8), material aging is not a concern 
for the waste package at temperatures less than 300C for up to 500 years and less than 200C 
for the next 9,500 years. It is noted in Table 6-4 that a crack growth rate of 10-11 mm/sec is used 
to represent the test results that indicated cracking appeared to cease propagating (i.e., the growth 
rate seemed to approach zero). The choice of 10-11 mm/sec is judged to be near the lower limit 
of practical growth rate measurement based on the observation that good statistical confidence in 

 
l 
 6-27 
growth rate exists when the crack growth increment is at least 10 times the limiting resolution of 
the technique (Andresen et al. 2002 [DIRS 166967], p. 4). The lower limit of crack growth 
increment cited by Andresen et al. (2002 [DIRS 166967], p. 4) is 1 micron. To gain statistical 
confidence using a 10-micron crack extension, a rate of 10-11 mm/sec would require a test time of 
about 30 years, which is relatively impractical. 
As indicated by Pan et al. (2002 [DIRS 165536], Section 3.1) and described in more detail by 
Barkatt et al. (2000 [DIRS 154496]), stress corrosion cracking was observed in one of several 
Alloy 22 U-bend specimens exposed in 250C concentrated groundwater purposely 
contaminated with 0.5% lead at pH 0.5. Therefore, to evaluate the potential effect of lead under 
more relevant conditions, crack growth rate measurements (DTN: LL021105312251.023 
[DIRS 169321], pp. 10 to 11) were also obtained for Specimen c152 after the addition of 
1,000 ppm of lead (added as Pb(NO3)2) to the autoclave BSW test solution. The lead addition 
was made following 8,670 hours of testing in 110C BSW solution (DTN: LL021105312251.023 
[DIRS 161253], composition p. 3; with solution pH = 13.4 at room temperature, p. 6). Because 
of the relatively high pH of this solution, most of the lead becomes insoluble in the test solution 
because of lead carbonate, lead sulfate, and possibly lead oxide precipitation. Based on a 
detailed comparison of crack growth rates made before and after the lead addition, in all cases 
the growth rate after the lead addition was the same or somewhat slower. The test conditions 
varied over a significant range in loading conditions and growth rates. In addition to these 
higher pH brine stress corrosion cracking crack growth rate results, there are also stress corrosion 
cracking-initiation test results obtained using Slow Strain Rate Tests (SSRT), at 76C to 95C in 
low pH, SAW brine solution (pH ~3) with and without 0.005% lead nitrate additions 
(Section 6.2.1, Table 6-2). These results also show no effect of lead on stress corrosion cracking 
susceptibility; thus, there appears to be no basis for concern that lead will affect stress corrosion 
cracking susceptibility in relevant concentrated brine environments over a broad range of pH 
values. 
To characterize the uncertainty for n, it can be determined from the n values in the last 
column of Table 6-4 that the mean value of n, nMEAN, is 1.304 and the standard deviation (SD), 
nSD, is 0.160, using Excel functions AVERAGE and STDEVP, respectively. Based on these 
mean and standard deviations, a normal distribution for n can be constructed. The n values at 
various percentiles, up to 2(SD), are listed in Table 6-5, where the percentile value is obtained 
by the Excel function NORMDIST for each set of given values of n, nMEAN, and nSD. For 
TSPA-LA applications, n should be sampled from a truncated normal distribution with a mean 
of 1.304, a standard deviation of 0.16, and an upper- and a lower-bound of 1.624 and 0.984, 
which is 2(SD) of the normal distribution, respectively. 

 
l 
 6-28 
Table 6-4. Summary of Source Data for Alloy 22 SDFR Model Quantification 
Specimen 
Hold 
Time 
(hours) 
Tested Stress 
Intensity Factor 
(MPa(m)^.5) 
Measured Crack 
Growth Rate 
(mm/s) Source 
Calculated 
n valueb 
c153 CL 30 2.50E-10 DTN: LL021105312251.023 
[DIRS 161253], p. 11 
1.168 
c153 CL 30 5.00E-10 DTN: LL021105312251.023 
[DIRS 161253], p. 11 
1.119 
c144 1 30 1.00E-11a DTN: LL021105312251.023 
[DIRS 161253], p. 7 
1.391 
c152 24 45 1.00E-11a DTN: LL021105312251.023 
[DIRS 161253], p. 10 
1.563 
c152 24 45 4.00E-10 DTN: LL021105312251.023 
[DIRS 161253], p. 10 
1.281 
NOTES: CL = constant load. 
aCrack growth rate of 1.0E-11 is used to represent test results where cracking appeared to cease propagating 
(i.e., the growth rate seemed to approach zero). 
bCalculated from Equation 19. 
Table 6-5. Distribution of the Parameter n 
n Value Percentile 
0.984 (-2 SD) 2.28 
1.041 5.00 
1.099 10.00 
1.139 15.00 
1.145 (-1 SD) 15.87 
1.170 20.00 
1.221 30.00 
1.264 40.00 
1.304 (Mean) 50.00 
1.345 60.00 
1.388 70.00 
1.439 80.00 
1.464 (+1 SD) 84.13 
1.470 85.00 
1.509 90.00 
1.568 95.00 
1.624 (+2 SD) 97.72 
Source: Generated using Excel function NORMDIST; mean, upperbound, 
lower-bound, standard deviation listed in Output 
DTN: LL030607012251.065. 
The base-case slip dissolutionfilm rupture stress corrosion cracking model developed for 
Alloy 22, represented by Equation 19, is graphically illustrated in Figure 6-6 for n values at 
0.984 (the lower-bound), 1.304 (mean), and 1.624 (the upper-bound), as well as the graphical 
representation of Equation 19 for sensitized Stainless Steel Type 304 (with n=0.54, 
Section 6.3.3). Excellent resistance to stress corrosion cracking for Alloy 22 is illustrated in 
Figure 6-6, where even the higher crack growth rates exhibited by the top curve of Alloy 22 with 

 
l 
 6-29 
n=0.984 are about two orders of magnitude lower than the crack growth rates associated with 
stainless steel curve. 
In summary, the five data points listed in Table 6-4 were used to obtain a mean value and a range 
for the n parameter of the model. Then the model prediction was shown in Figure 6-6 over the 
range of stress intensity factor values (15 to 55 MPavm) and the individual data points were also 
included in Figure 6-6 along with plus and minus 2-sigma limits for the n parameter and not for 
the five data points. 
Source: Plot generated from Equation 19 using Alloy 22 n values from Table 6-5, and Stainless Steel n value from 
Section 6.3.3. Data points for specimens C144, C152, and C153 are from DTN: LL021105312251.023 
[DIRS 161253] and are listed in Table 6-4. 
Figure 6-6. Crack Growth Rate Versus Stress Intensity Factor for Alloy 22 Based on the SDFR Model 
6.3.5 Threshold Stress Intensity Factor 
The threshold stress intensity factor (KISCC) is a critical value of stress intensity factor (KI) such 
that any preexisting crack will not grow or is in an arrest state if KI corresponding to the crack 
size and the applied stress does not exceed KISCC. Preexisting cracks are usually caused by 
manufacturing processes (especially welding) or crack initiation (Section 6.2). 
The concept of threshold stress intensity factor (KISCC) has been commonly used to assess the 
susceptibility of material to stress corrosion cracking. The description of this concept can be 
found in work by Jones and Ricker (1987 [DIRS 118672], pp. 145 to 163) and Sprowls (1987 
[DIRS 118702], pp. 245 to 282). To apply the method, it is necessary to obtain values of 
(1) stress intensity factor KI as a function of crack size correspondent to the stress state at and 
near the crack site, and (2) the threshold stress intensity factor KISCC. The calculations of stress 
intensity factor for the closure welds in the inner and outer lids of the waste package are 
described in Section 6.4. The threshold stress intensity factor is normally determined 
experimentally, but because of the extremely low growth rates observed for Alloy 22, very long 
test times are required. A more conservative approach has been selected. Roy et al. (1998 
[DIRS 118696]) documented an attempt to obtain an experimentally measured K1SCC for 
Alloy 22 at Lawrence Livermore National Laboratory using double cantilever beam-type fracture 

 
l 
 6-30 
mechanics specimens. However, review of these data revealed that the data were invalid as 
described in Dunn (1999 [DIRS 154481], Section 2.2.3, p. 2-5). There were discrepancies 
between the ASTM procedure and the Lawrence Livermore National Laboratory test results 
reported by Roy et al. (1998 [DIRS 118696]). The tests did not comply with the recommended 
test procedure for these double cantilever beam (DCB) specimens. The initial crack length used 
appears to be too short and the specimen crack length to thickness ratio, a/w of 0.31, was below 
the ASTM recommended range of 0.45 to 0.55. Thus, these results are not used as sources for 
threshold stress intensity factor. 
Because of the extremely low stress corrosion cracking growth rates and the need for 
unacceptably long test times, an alternative approach, a more conservative crack-blunting 
criterion is used to define the threshold stress intensity factor. Based on the crack-blunting 
criterion (Andresen and Ford 1994 [DIRS 118581], p. 62), crack blunting occurs when the 
corrosion rate of the crack sides approaches the oxidation rate at the crack tip (i.e., the sharp 
crack will degenerate to a blunt pit). It follows that a stress corrosion cracking crack will not 
grow if the general corrosion rate at the crack sides exceeds the crack tip growth rate. If Vgc is 
the general corrosion rate, the threshold stress intensity factor KISCC can be calculated from the 
SDFR Model as represented by Equation 14, or the following rearrangement of this equation 
with Vt = Vgc: 
KISCC = (Vgc / A ) n / 1 (Eq. 20) 
The mean general corrosion rate, which can be calculated from Table 4-6, is used in Equation 20. 
Observation of Table 4-6 indicates that the general corrosion rate associated with sample 
DCA 177 is an outlier since it is about a factor of six higher than the mean value. If this outlier 
is removed from the data set, the mean general corrosion rate is 7.23 nm/yr. Values for 
n and A can be determined from Equations 16 and 18 for a given value of n. The threshold 
stress intensity factor for Alloy 22, accordingly, can be expressed in Table 6-6, based on the n 
values shown in Table 6-5. 
The threshold stress intensity factor is applied to both incipient flaws (once the threshold stress 
for initiation is exceeded) and for weld flaws. At each time step, the stress intensity factor, KI, at 
a growing crack tip or defect tip is compared with the KISCC value. At the point that the KI value 
drops below KISCC, the crack will arrest. 
For Alloy 22, it is recognized that at the lower stress intensity values (minus two sigma on the 
mean) in Table 6-6, the indicated KISCC may not be realistic. The implication is that the KISCC 
values at the lower limits are highly conservative, considering the high degree of stress corrosion 
cracking initiation and crack growth resistance of Alloy 22 and because the mean value 
(11.38 MPavm) (obtained when the crack growth rate equals the general corrosion rate) is also 
conservatively obtained based on test data from much higher stress intensity values 
(30 and 45 MPavm) at which maintaining crack growth under static loading conditions is 
difficult to accomplish. 

 
l 
 6-31 
Table 6-6. Distribution of the Threshold Stress Intensity Factor, KISCC, for Alloy 22 
n Value KISCC value (MPavm) 
0.984 (-2 SD) 2.65 
1.041 3.65 
1.099 4.90 
1.139 5.90 
1.145 (-1 SD) 6.06 
1.170 6.76 
1.221 8.35 
1.264 9.85 
1.304 (Mean) 11.38 
1.345 13.10 
1.388 15.04 
1.439 17.56 
1.464 (+1 SD) 18.87 
1.470 19.19 
1.509 21.36 
1.568 24.89 
1.624 (+2 SD) 28.50 
Source: Generated using Equation 20; equation listed in Output 
DTN: LL030607012251.065. 
6.3.6 Alternative Model: The Coupled Environment Fracture (CEF) Model 
Alternative conceptual models (ACMs) are based on simplifications that are different from those 
employed, or not used, in the base model. An important reason for considering ACMs is to help 
build confidence that changes in modeling decisions or simplifications will not change 
conclusions regarding subsystem and total system performance. Conceptual model uncertainty 
results from sparse observational data and a lack of available information to corroborate or refute 
plausible alternative interpretations of the subsystem and the processes occurring within the 
subsystem. 
In addition to the base-case slip dissolutionfilm rupture model, which provides formula for 
prediction of the crack growth rate, an alternative conceptual model, the coupled environmental 
fracture (CEF) model (Macdonald and Urquidi-Macdonald 1991 [DIRS 162702]; 
Macdonald et al. 1994 [DIRS 162701]), was developed based on the theory that the internal and 
external environments are coupled by the need to conserve charge in the system. Thus, as 
oxygen reduction on the external surface consumes the positive current emanating from the crack 
mouth, the solution of Laplace's equation for the external environment yields a boundary 
condition for solving Laplace's equation for the internal crack environment. The slip dissolution 
model describes metal dissolution at the crack tip, with the frequency of rupture of the passive 
film being a strong function of the stress intensity factor. The reduction of oxygen on the 
external surfaces is described in terms of a general Butler-Volmer equation that incorporates 
mass transport and charge transport phenomena. In this way, the model incorporates the effects 
of oxygen concentration, flow rate, and the conductivity of the external environment as well as 
accounting for effect of stress on crack growth. The CEF model represents an alternative 

 
l 
 6-32 
approach for the prediction of the crack growth rate. It is considered in this report only to 
corroborate the conservative predictions of the base-case model. 
The CEF model is a physico-electrochemical model developed for intergranular stress corrosion 
cracking in sensitized Stainless Steel Type 304 in simulated light water reactor environments to 
explain and explore the effects of various environmental and mechanical variables on the 
kinetics of crack propagation. The goals are: (1) to derive a physically realistic model that 
unifies the electrochemical, chemical, and mechanical aspects of the propagation of cracks 
through sensitized Stainless Steel Type 304, and (2) to use this model to explore how the rate of 
crack propagation depends on various environmental variables, including oxygen concentration, 
conductivity, and mechanical (stress intensity) parameters. Macdonald and Urquidi-Macdonald 
(1991 [DIRS 162702]) and Macdonald et al. (1994 [DIRS 162701]) discuss the mathematical 
development of the model. 
The slip dissolutionfilm rupture model and the CEF model are similar in several ways. Both 
were developed for intergranular stress corrosion cracking in sensitized Stainless Steel Type 304 
simulated light water reactor environments. Both use Faraday's law to develop the equation for 
the crack growth rate. The departure point starts as the slip dissolutionfilm rupture model takes 
an empirical approach to develop a functional form to express the crack growth rate in terms of, 
explicitly, the crack tip strain rate and a couple of parameters (i.e., A and n) while the CEF 
model stays with an implicit approach. The CEF model is more a theoretical model and the slip 
dissolutionfilm rupture model is a mixed theoretical and empirical model. 
The slip dissolutionfilm rupture model and the CEF model predict the crack growth rate for 
stress corrosion cracking. However, it was discovered that the CEF model has the tendency of 
underestimating the crack growth rate, as compared to the slip dissolutionfilm rupture model 
when both models were applied to predict the crack growth rate for Stainless Steel Type 304 in a 
boiling water reactor (BWR) environment. Figure 6-7 illustrates this nonconservatism. 
Comparison with experimental data summarized by Ford and Andresen (1988 [DIRS 118611], 
Figure 22) for crack propagation rate versus stress intensity factor for sensitized Stainless Steel 
Type 304 in fully aerated, high purity water at elevated temperature indicated that the crack 
growth rate predicted by the CEF model (i.e., 3.2  10-9 cm/s at 20 MPavm) (Macdonald and 
Urquidi-Macdonald 1991 [DIRS 162702], p. 78) tends to be at the lower end of the range cited 
by Ford and Andresen (1988 [DIRS 118611], Figure 22). For this reason, the CEF model was 
not included for further evaluation but used only to corroborate the conservative crack growth 
rate predictions of the base case slip dissolutionfilm rupture model. 

 
l 
 6-33 
Source: Plot generated from data by Ford and Andresen (1988 [DIRS 118611], Figure 22), Macdonald and Urquidi- 
Macdonald (1991 [DIRS 162702], Figure 12), and Macdonald et al. (1994 [DIRS 162701], Figure 5). 
Figure 6-7. Comparison of Predicted Crack Growth Rates for Stainless Steel Type 304 
6.3.7 Stress Corrosion Cracking for the Drip Shield Titanium Grade 7 Material 
The sources of stress that could result in stress corrosion cracking in the Titanium Grade 7 drip 
shield are: (1) weld-induced residual stress, (2) plasticity-induced residual stress caused by 
seismic events, and (3) residual stress produced by rockfalls. Annealing will mitigate 
weld-induced residual stresses. The threshold stress for crack initiation developed in 
Section 6.2.1 is used as the through-wall crack penetration (breach) criterion for both rockfall 
and seismic-induced stress. Seismic stress corrosion cracking is discussed further in 
Appendix B. An analysis of the consequence of residual stress produced by rockfalls is 
presented in this section. 
Stress corrosion cracks in passive alloys such as Titanium Grade 7 tend to be very tight (small 
crack opening displacement) by nature because the slip dissolutionfilm rupture process results 
in a relatively high effective crack tip growth rate as compared to the general corrosion rate of 
the unstressed sides of the crack. As the crack grows through-wall, the tensile stresses normal to 
the crack walls are relieved. The resulting crack faces continue to corrode by general corrosion 
with a median rate of about 0.03 microns per year under the range of environmental conditions 
expected on the drip shield surfaces (BSC 2004 [DIRS 169845], Table 17). 
According to Section 6.2.1, deformation induced residual stress resulting from rockfalls can 
cause stress corrosion cracking crack initiation in the drip shield if the stress exceeds the 
threshold stress for the drip shield material (Titanium Grade 7). Although initiation is assumed 
to occur immediately once the threshold stress is exceeded, it actually takes years to occur as 
indicated by the LTCTF Titanium Grade 16 and Titanium Grade 7 U-bend specimens described 
in Section 6.2.1, which did not experience stress corrosion cracking initiation after up to five 
years exposure at stresses at or somewhat above the yield strength. According to Multiscale 

 
l 
 6-34 
Thermohydrologic Model (BSC 2004 [DIRS 169565], Section 6.3.7), the drip shield can 
potentially reach temperatures over 250C following a low-probability seismic collapsed drift 
and a low rubble thermal conductivity). However, aqueous surface brine films needed for stress 
corrosion cracking are unlikely to form above about 160C and the drip shield is projected to 
spend most of its lifetime below 140C. Therefore, the drip shield wall temperature at which the 
yield strength (YS) value is conservatively selected is 140C. The YS for Titanium Grade 7 
at 140C, using a straight-line interpolation between the room temperature (20C) and 204C 
values from Table 4-5, is 220.7 MPa. Thus, the threshold stress for crack initiation is 0.5 (YS) 
(i.e., 110.4 MPa) (Section 6.2.1). The size (depth) of the initiated crack, based on Section 6.2.1, 
is 0.05 mm. Once initiated, it will take about 40 years for the crack to grow through the 15-mm 
drip shield wall (BSC 2001 [DIRS 156807], Table 5-13) based on an stress corrosion cracking 
crack growth rate of 1.25  10-8 mm/sec estimated by DTN: LL021105312251.023 
([DIRS 161253], Section 1.3, p. 14). 
Once the stress corrosion cracking-initiated crack develops into a through-wall crack, the crack 
length 2c and the crack gap (or width) d, according to Plugging of Stress Corrosion Cracks 
by Precipitation (BSC 2001 [DIRS 156807], Table 5-13) are 130 mm and 157 microns, 
respectively. Thus, the dense passive corrosion oxide film growing normal to each opposing 
crack face would need to grow until it fills the 157-micron gap. This is equivalent to 
~103 microns of metal loss per crack side and results in a total per side oxide thickness of 
~182 microns based on a TiO2 oxide to metal volume ratio of 1.76 (Bradford 1987 
[DIRS 151988], Table 2, p. 64). At a corrosion growth rate of 0.03 microns metal loss per year, 
it will take ~3,400 years for the crack to fill with corrosion product. In the interim, while the 
faces are corroding passively, but before the corrosion film grows to a thickness where it will 
completely fill the crack, there could be a small amount of water transport by surface diffusion 
(film flow) into the crack and through the drip shield. However, the small heat flux present 
across the drip shield wall will result in evaporation of the slowly flowing water and a resultant 
scale deposit (principally calcium carbonate [calcite]) will form over the crack where it intersects 
the upper drip shield surface, as well as within the crack. This formation of calciferous deposits 
is well documented (Cowan et al. 1976 [DIRS 105212], pp. 1 to 39 and 376 to 383) in seawater 
environments and in heat exchangers through which natural brines are forced to flow, such as in 
desalination plants (carrying ~6% NaCl solutions) and in potash plants (carrying >12% brine 
(NaCl/KCl mixtures). In both these cases, titanium surfaces are heat sources at operating 
temperatures of ~100C. Such deposits form rapidly under flowing conditions, and have to be 
regularly removed to avoid loss of heat exchanger efficiency. Other minerals such as amorphous 
silica will also precipitate. 
A detailed calculation of the expected rate of stress corrosion cracking plugging due to calcite 
precipitation resulting from evaporation of a pore water of typical composition dripping onto a 
drip shield at the crack location has been performed (BSC 2001 [DIRS 156807]). The 
calculation conservatively assumes that (BSC 2001 [DIRS 156807], Section 5.3) corrosion 
products generated on the crack faces as well as colloids, particulates, and any precipitated silica 
minerals do not help in plugging the crack opening and that there is a uniform water seepage 
flow in space and time. It was concluded that (BSC 2001 [DIRS 156807], Section 6.3) stress 
corrosion cracking cracks are sealed in a few hundred years at most when water is allowed to 
flow through the cracks at a low film flow rate. When the cracks are bridged by water, the 
sealing process may take thousands of years, but no flow occurs as the water is held by capillary 

 
l 
 6-35 
forces. In a more realistic case of a nonuniform flow onto the drip shield, more precipitation and 
faster plugging will occur. 
Following plugging of such a drip shield crack, any solution flow through the crack would be 
dominated by an efficiency factor determined by the ratio of solution runoff on the drip shield 
surface compared to through crack flow that in turn is determined by scale porosity and 
permeability. Because of the expected high density of the calcite deposits (BSC 2001 
[DIRS 156807]) and lack of a pressure gradient to drive water through the crack, the probability 
of solution flow through the plugged crack would approach zero. However, even if it were 
conservatively assumed that brine transport through any stress corrosion cracking breached areas 
occurs by advective flow, it is highly unlikely that the resultant under drip shield seepage flow 
would align with any through-wall stress corrosion cracking areas on the waste package. Thus, 
this discussion provides a sound technical basis for excluding further consideration of drip shield 
stress corrosion cracking in TSPA-LA. 
Finally, multiple rockfalls on the same spot of the waste package are ruled out because of the 
small probability. Drip shield structural response to rockfalls induced by seismic events is 
addressed in Drip Shield and Waste Package Emplacement Pallet Design Report (BSC 2004 
[DIRS 166879]), where the damaged area of the drip shield is calculated for each of the given 
rock masses. The damaged area is defined as a region of the drip shield where the calculated 
stress exceeds the threshold stress. Seismic stress corrosion cracking is discussed further in 
Appendix B. 
6.4 EVALUATION OF STRESS INTENSITY FACTOR 
6.4.1 Introduction 
The stress intensity factor KI is defined as a function of stress (s) and crack depth size (a): 
KI(a, s) =  s (pa)1/2 (Eq. 21) 
where 
 is a geometry factor dependent on the size and shape of the crack and the configuration 
of the structural component 
s is the tensile stress distribution through the wall thickness of the structural component. 
Closed-form solutions are possible only in some simple cases of uniform tensile stress and 
simple geometry. For example, in considering the classical problem of a single-edge cracked 
plate with thickness h, it has been shown that  can be expressed by the following formula 
(Ewalds and Wanhill 1984 [DIRS 118602], p. 49): 
4 3 2 
h
a 95 . 30 
h
a 72 . 21 
h
a 55 . 10 
h
a 231 . 0 12 . 1  .. 
. 
.. 
. + .. 
. 
.. 
. - .. 
. 
.. 
. + .. 
. 
.. 
. - = 
In most practical cases where stresses are nonuniformly distributed across the thickness, the 
stress intensity factor has to be calculated by some numerical algorithms, such as the finite 

 
l 
 6-36 
element method. Rice (1968 [DIRS 147983], p. 381) has shown that path-independent J-Integral 
taken over an arbitrary contour surrounding the crack tip is proportional to the square of the 
crack tip stress intensity factor KI. According to Chan et al. (1970 [DIRS 147968], p. 8), by 
numerically evaluating the J-Integral for the finite element solution over a path surrounding the 
crack tip, an estimate of the crack tip stress intensity factor can be obtained. 
Although finite element programs can be used to evaluate the stress intensity factor, the effort is 
usually quite time consuming because a series of elaborate finite element analyses must be 
completed for numerous crack sizes starting from 0 through the thickness of the containment 
wall. A simplified solution has been developed by using fracture mechanics to evaluate the 
parameter (KI)PCCRACK, the stress intensity factor (Section 6.4.2.3). Then a geometry correction 
factor, G, which is usually a function of the crack size a, is evaluated from the results of finite 
element analysis. Finally, the true stress intensity factor (KI) is derived from (KI)PCCRACK and G. 
This section summarizes the methodology, calculation procedures, and selected results, which 
are also discussed in detail in Evaluation of the CRM-21 PWR and Viability Availability Waste 
Package (SI 2003 [DIRS 162457]). 
6.4.2 Calculations of Stress Intensity Factors for Waste Package Closure Welds 
6.4.2.1 Introduction 
Only weld-induced residual stress in the final closure welds of the waste package outer barrier 
are considered for performance assessment, based on the following reasons: 
1. Stress corrosion cracking of the drip shield is excluded from the performance 
assessment. According to Section 6.3.7, the sources of stress corrosion cracking in the 
Titanium Grade 7 drip shield are (1) weld-induced residual stress; (2) plastic residual 
stress caused by seismic events; and (3) residual stress produced by rockfalls. The 
weld-induced residual stress is eliminated by annealing. The threshold stress for crack 
initiation developed in Section 6.2.1 is used as the through-wall crack propagation 
criterion for seismic-induced stress corrosion cracking. Seismic stress corrosion 
cracking is discussed further in Appendix B. An analysis of the consequence of 
residual stress produced by rockfalls presented in Section 6.3.7 indicated that stress 
corrosion cracking resulting from rockfall will result in very tight crack openings and 
will not degrade the water diversion function of the drip shield. The Stainless Steel 
Type 316 inner barrier of the waste package will also be excluded from the stress 
corrosion cracking evaluation because the TSPA-LA will not take credit for the inner 
barrier. 
2. Sustained postclosure stresses in the waste package Alloy 22 outer cylinder including 
internal pressure stresses and waste package and pallet contact stresses are limited by 
design and are significantly below 0.9(YS) (BSC 2004 [DIRS 169766], Tables 2, 21, 
22, and 23). Therefore, welds are potentially the regions most susceptible to stress 
corrosion cracking initiation and propagation because (1) welding can produce hightensile 
residual stress in the weld area; (2) preexisting flaws due to fabrication and 
welding have much higher concentration in the weld than in the base metal; and 
(3) welding could result in segregation and nonequilibrium brittle phases, which could 

 
l 
 6-37 
enhance material susceptibility to stress corrosion cracking. All the welds, with the 
exception of the final closure welds, are subjected to solution heat treatment to relieve 
the residual stress when the entire waste package is heat treated before the loading of 
high level wastes. It is recognized that plastic deformation resulting from lower 
probability seismic events has the potential of leading to plastic upsets and resultant 
sustained residual stresses that may initiate cracks and drive them through the wall. 
Breach criteria (crack opening area) governing seismic initiated residual stress have 
been developed for the waste package material (i.e., Alloy 22) and are described in 
Appendix B. The breach criteria are based on a threshold stress, which was discussed 
in Section 6.2.1. Therefore, weld residual stress is the only type of stress of stress 
corrosion cracking concern for the waste package. 
Since by definition, embedded flaws are not exposed to the external waste package aqueous 
surface environment, they will not be subjected to stress corrosion cracking and only outer 
surface-breaking flaws are of concern for performance. 
Based on work by Bokhari (2003 [DIRS 162429], Attachment 1, Figure 1), the initially proposed 
waste package design final closure lid design for the license application (LA) includes the 
following: 
 The inner, stainless steel lid weld is sealed using a spread ring and seal weld. 
 The outer lid mitigation method is laser peening. 
 The middle Alloy 22 lid weld configuration (indicated as inner lid in Attachment 1, 
Figure 1 (Bokhari 2003 [DIRS 162429])) is a fillet-type seal weld and will not be stress 
mitigated. 
 A sketch of the initially recommended LA design of the final closure lid area of the 
waste package (abstracted from Bokhari (2003 [DIRS 162429], Attachment 1, Figure 1) 
is shown in Figure 6-8. The outer closure lid laser peening stress mitigation process 
could be replaced with an alternate controlled plasticity burnishing stress mitigation 
process after further evaluation. Beneficial residual stress profiles resulting from both 
processes are discussed in Sections 6.4.4 and 6.4.5. 

 
l 
 6-38 
Source: Modified from Bokhari 2003 [DIRS 162429], Attachment 1, Figure 1. 
NOTE: Lid thicknesses have been removed. 
Figure 6-8. Sketch of Initially Recommended LA Design for Waste Package Final Closure Weld Region 
For the TSPA-LA of the waste package subjected to stress corrosion cracking, stress and stress 
intensity factor profiles due to weld residual stress in the closure welds are needed for the 25-mm 
Alloy 22 (actually currently 1 in. or 25.4 mm) outer lid subjected to laser peening and the 
as-welded 10-mm Alloy 22 (actually currently 0.5 in. or 12.7 mm) middle lid (BSC 2004 
[DIRS 170710]). These stress and stress intensity factor profiles were provided by a vendor and 
were saved in DTN: LL000316205924.142 [DIRS 148895]). They were calculated prior to the 
current LA design using two different waste package designsone with an equivalent outer lid 
geometry and one with the middle lid weld geometry. These outer and middle lid equivalent 
designs are, respectively, 1) the CRM21-PWR design (which has a single 25-mm Alloy 22 
outer lid), as shown in Figure 6-9, and 2) the modified CRM21-PWR design (which is similar 
to the CRM-21-PRW design but with the outer lid thickness reduced from 25 mm to 10 mm). It 
can be seen that the flat-head outer lid of the currently recommended waste package design is 
similar to the outer lid of the CRM21-PWR design not only in their geometrical configurations 
but also in the welding processes. Section 6.2.2.1 indicates that the current welding process 
being considered for the waste package final closure lid weld is a gas tungsten arc welding 
process. Section 6.4.2.2 shows the heat generation rate used as the input for the thermal analysis 
of the CRM21-PWR design is equivalent to that of a gas tungsten arc welding welding 
procedure. Therefore, calculated stress and stress intensity factor profiles for the 25-mm outer 
Alloy 22 lid of the CRM21-PWR design are used for the as-welded and laser-peened Alloy 22 
waste package outer lid (WPOL) of the current design and calculated stress and stress intensity 
factor profiles for the as-welded 10-mm Alloy 22 lid of the modified CRM21-PWR design are 

 
l 
 6-39 
used for the proposed Alloy 22 waste package middle lid. As discussed earlier, subsequent to the 
proposed waste package closure lid design indicated by Figure 6-8, the middle lid thickness was 
changed to 0.5 in. (12.7 mm) (BSC 2004 [DIRS 170710]). However, as discussed in Section 
6.4.2.4, this small increase in thickness (12.7 mm versus 10 mm) does not have a significant 
effect on calculated through-wall, as-welded residual stress and corresponding stress intensity 
distributions or on the estimated time for through-wall stress corrosion cracking growth. Further, 
the time required to remove the stress mitigated layer at the outer closure lid weld is greater than 
10,000 years after permanent closure, as described in Section 6.4.5. 
Source: SI 2003 [DIRS 162457], Figure 1-4. 
Figure 6-9. Schematic and Dimensions for the CRM21-PWR Waste Package Design 
6.4.2.2 Stress Analysis 
Finite Element Model-Determining the weld residual stress requires a thermal analysis to 
determine the temperature history caused by the welding process and a subsequent weld residual 
stress analysis. This problem has been solved using finite element analysis methods. Although 
the determination of weld residual stress for the waste package welds is a three-dimensional 
problem, it has been found that the use of two-dimensional axisymmetric modeling of the 
problem provides a reasonable estimate of the behavior (Chan et al. 1970 [DIRS 147968], p. 3). 

 
l 
 6-40 
Thus, the waste package closure weld models were treated as being two-dimensionally 
axisymmetric about the waste package axial centerline. 
The finite element model for the CRM21-PWR design of the waste package (Figure 6-9) is 
shown in Figure 6-10. The weld geometry and immediate neighboring material for the outer lid 
are modeled in detail with sufficiently small elements to capture the large thermal and strain 
gradients associated with the weld pass application. The element sizes become larger with 
distance from the weld since the field variable gradients are significantly lower. More on the 
finite element model is discussed in this section under Thermal Analysis. 
Source: SI 2003 [DIRS 162457], Figure 1-2. 
Figure 6-10. Finite Element Model for the CRM21-PWR Waste Package Design 
Figure 6-10 shows the finite element model with all outer lid weld passes deposited. Material 
making up the individual weld passes is added to the model as each weld pass is simulated. This 
process continues until all weld beads (or groups of weld beads) are applied. 
Figure 6-11 includes a close-up view of the outer-lid finite-element model (Figure 6-12) where 
axisymmetrical cross sections selected for stress output are identified. The radial stress in the 
x-direction (Sx) is normal to the section while the hoop stress in the z-direction (Sz) is tangential 
to the section. Similarly, Figure 6-12 is the close-up view of the modified CRM21-PWR design 
that shows the cross sections for stress output. Section 1-1 is selected such that the stress normal 
to the section, Sn, is maximized. The stress component, Sn, is conservatively used as the radial 
stress, Sx, in the weld. Section 2-2, likewise, is selected such that the hoop stress, Sz, is 
maximized and this stress component is conservatively used as the hoop stress in the weld. The 

 
l 
 6-41 
distance (or crack depth) measured from the outer surface of the closure lid on Sections 1-1 
or 2-2 is projected to a vertical cross section that is normal to the plane of the closure lid. 
Source: SI 2003 [DIRS 162457], Figure 2-1. 
Figure 6-11. Selected Cross-Sections for CRM21-PWR Waste Package Design 
Material PropertiesThe material properties are important to the determination of the final 
weld residual stress. The material properties used in this evaluation for Alloy 22 are discussed in 
detail in Evaluation of the CRM-21 PWR and Viability Availability Waste Package (SI 2003 
[DIRS 162457]). For the thermal analysis, the material properties used are thermal conductivity, 
specific heat, and density. For the stress analysis, the material properties used are coefficient of 
thermal expansion, Youngs modulus, Poisson ratio, density, and yield strength. Nonlinear 
properties, such as the elasticplastic behavior and temperature dependency, are also used. 
Thermal AnalysisA thermal analysis of the waste package closure was performed to simulate 
the temperature history caused by each weld pass. Each weld pass will result in a different 
temperature field because as passes are applied, more material is added, residual stress from 
previous passes are being incorporated, and the relative location of the weld heat input is 
changing with respect to the lid thickness. 

 
l 
 6-42 
Source: Adapted from Figure 6-11 to show close-up view with cross sections used for stress outputs shown in 
Figure 6-14. 
Figure 6-12. Selected Cross-Sections for the Modified CRM21-PWR Waste Package Design 
The finite element analysis was performed on the CRM21-PWR closure lid design, as the 
detailed LA design configuration and dimensions were not then available. However, that design 
is consistent with the currently described LA design in terms of having a flat, outer final closure 
lid with a thickness of 1 inch. Thus, the analysis on 1-inch-thick welded Alloy 22 was 
representative and expected to yield residual stress results similar to those expected for the 
TSPA-LA waste package. Nominal welding parameters and not the extreme ranges of these 
parameters were used in the analysis and weld heat inputs were not bounded (maximum or 
minimum), although the analysis also added a factor of 15% to account for the heat input 
represented by the filler metal. To provide a basis for expected stress variability due to the range 
of process parameters, a literature search on the expected range of residual stress variability in 
similar thickness weldments provided the basis for the expected uncertainty limits to be used for 
the calculated residual stresses (Section 6.4.5). The heat input used in the finite element 
calculation can be compared with maximum and minimum expected heat inputs once the 
detailed welding process and control limits have been specified. 

 
l 
 6-43 
In the design approach, the closure weld is susceptible to stress corrosion cracking initiation and 
growth and this degradation mode is to be precluded by mitigating the tensile residual stresses by 
implementing a mechanical stress mitigation process, laser peening (with controlled plasticity 
burnishing as an alternative process). A series of design prototype waste packages will be 
fabricated to characterize the closure weld in great detail. 
The effect of each weld pass was simulated through heat generated in the finite elements, which 
represent the weld pass, and then the heat is transferred to the adjoining parts of the waste 
package. The heat generated in the weld pass, represented by the net heat input (Hnet in 
joules/in.) of the welding process can be calculated with Hnet = f1 EI/v (Connor 1991 [148469], 
p. 33, Equation 2.3) for given welding parameters including voltage (E), amperage (I), travel 
velocity of the heat source (v in in./sec) and heat transfer efficiency (f1). Based on a gas tungsten 
arc welding process, the amperage, voltage and average travel speed are, respectively, 330 to 335 
A, 12.1 to 13.0 V and 8.0 in./min (0.133 in./sec) (CRWMS M&O 1998 [DIRS 107722], Table 7- 
1, p. 12). The heat transfer efficiency (f1) for gas tungsten arc welding, according to Connor 
(1991 [148469], Figure 3.1A, p. 69) is 21% to 48%. Using the average values for E (12.55 V), 
I (332.5 A), v (0.133 in./sec), and f1 (0.345) and adding 15% to the final result (to represent heat 
contributed by the filler material), the net heat input is found to be 12,400 joules/in., which is 
close to the heat generation rate (12,268 joules/in.) used in the finite element thermal analysis 
(SI 2003 [DIRS 162457], p. 1-8). 
For the axisymmetric representation of the three-dimensional problem, it is desired to convert the 
nonaxisymmetric heat input into an equivalent axisymmetric heat input, which is representative 
of what a typical point on the circumference of the weld would experience. Since a typical point 
on the circumference would essentially experience an impulse heat input (i.e., a large amount of 
heat input over a short amount of time), the heat input is represented by a triangular-shaped pulse 
for two seconds (ramp up in one second and ramp down in one second) followed by a cooling 
period. The length of cooling period after the deposit of weld beads is determined by the time 
required for the weld torch to travel around the circumference of the closure weld. 
Weld Residual Stress AnalysisThe stress analysis is performed for all individually modeled 
weld passes. For example, if six weld passes are modeled, then six thermal stress analyses are 
performed. The analysis of Weld Pass 1 uses the temperature history for Weld Pass 1 thermal 
analysis. The analysis of Weld Pass 2 uses the Weld Pass 2 thermal analysis and the residual 
stress due to Weld Pass 1 as the initial condition. This process continues until all weld passes are 
analyzed. The final solution (at ambient conditions) is the room temperature weld residual 
stress. 
6.4.2.3 Stress Intensity Factor Calculations 
For the waste package closure welds, the flaw orientations most likely susceptible to crack 
propagation are those of a circumferential flaw (parallel to weld) and a radially oriented flaw 
(perpendicular to weld). Figure 6-13 shows the flaw orientations with respect to the weld. A 
radially oriented flaw would be potentially driven by hoop stress. A circumferentially oriented 
flaw would be driven by radial stress. 

 
l 
 6-44 
Figure 6-13. Flaw Orientation for Lid Welds 
A general form of the stress intensity factor is expressed by Equation 21, i.e.: 
KI =  s (pa)1/2 (Eq. 21) 
As indicated in Section 6.4.1,  is a geometry factor dependent on the size and shape of the crack 
and the configuration of the structural component, and s is the stress distribution through the 
wall thickness of the structural component. Closed-form solutions of Equation 21 are possible 
only in some simple cases of uniform tensile stress and simple geometry. 
Although finite element analyses can be used to evaluate the stress intensity factor 
(Section 6.4.1), the effort is usually quite time consuming because a series of elaborate finite 
element analyses must be completed for numerous crack sizes starting from 0 through the 
thickness of the containment wall. 
A simplified solution procedure was developed by using fracture mechanics to evaluate the 
parameter (KI)PCCRACK for a given stress distribution. Then a geometry correction factor, G, as a 
function of the crack size a, was developed by curve fitting from comparing the simplified 
solutions with the results of finite element analysis for only a limited number of crack sizes. 
Given the geometry correction factor, the true stress intensity factor, KI, for any crack size can be 
derived from (KI)PCCRACK and G, without going through the finite element analysis using the 
following relationship: 
( )PCCRACK I I K G K = (Eq. 22) 
For a circumferential flaw, (KI)PCCRACK was derived from an infinite single edge cracked plate 
(SECP) with an infinitely long flaw. For a radial flaw, (KI)PCCRACK was derived from an 
elliptical surface crack in an infinite plate with a crack aspect ratio of 1 (a semicircular crack). In 

 
l 
 6-45 
either case, the stress distribution was calculated by using a third order polynomial of the type 
represented by the following equation: 
s = A0 + A1x + A2x2 + A3x3 (Eq. 23) 
where x is the distance from the outer surface of the closure lid and A0, A1, A2, and A3 are 
coefficients of the third-order polynomial fit of the through-wall stress distribution (or profile). 
The model of a circular crack in an infinite plate is a better representation of a limited-length 
radial crack in the closure weld rather than an infinite edge crack in an infinite SECP. It is 
judged that a radial crack in the closure weld would not grow into a long semielliptical crack due 
to the rapid decay of hoop stress in the radial distance away from the weld and base metal 
interface, as indicated by examination of Figure 6-14, where 1-1, 2-2, and 3-3 are section 
identifications as indicated in Figure 6-11. 
The stress intensity factor for an infinite SECP with an infinitely long flaw is (Buchalet and 
Bamford 1976 [DIRS 118597], Equation 2, p. 388): 
( ) 
. .
.
. 
. .
.
. 
p 
+ . .
.
. 
. .
.
. 
+ .. 
. 
.. 
. 
p 
+ p = 4 3 
3 
3 2 
2 
2 1 1 0 SECP I F A 
3
a 4 F A 
2 
a F A a 2 F A a ) K ( (Eq. 24) 
where F0, F1, F2, and F3 are magnification factors and A0, A1, A2, and A3 are coefficients of the 
third-order polynomial fit of the through-wall stress distribution (or profile) as indicated in 
Equation 23. 
The magnification factors F0, F1, F2, and F3 are functions of the crack depth (a) versus 
thickness (h) ratio (a/h). They are graphically presented by Buchalet and Bamford (1976 
[DIRS 118597], Figure 6), and used to calculate the stress intensity factor. 
The SECP stress intensity factor is for the ideal geometry and must be modified by the geometry 
correction factor (G) to consider the actual geometry. Figure 6-15 shows, for a circumferential 
flaw, the G-factor distribution in the closure weld of the outer lid of the CRM21-PWR waste 
package as a result of curve fit based on the exact G values calculated at four discrete points 
corresponding to crack-versus-thickness ratios of 0.2, 0.3, 0.4, and 0.6. Figure 6-15 indicates, 
for shallow flaws, the correction factor is near 1. For deeper flaws, the correction becomes 
significant, and using the SECP solution would be very conservative. For a radial flaw, the 
simplified solution obtained from a fracture mechanics crack model that contains a semicircular 
surface flaw in a flat plate and is judged to be close to the final solution. Therefore, the 
geometrical correction factor received a value of unity for the case of radial cracks. 

 
l 
 6-46 
Source: SI 2003 [DIRS 162457], Figure 2-10. 
Figure 6-14. Hoop Stresses in Outer Lid of CRM21-PWR Design 
Source: SI 2003 [DIRS 162457], Figure 3-11. 
Figure 6-15. Outer Lid Circumferential Flaw Geometric Correction Factor 
6.4.2.4 Numerical Results 
According to Section 6.4.2.1, calculated stress and stress intensity factor profiles for the 25-mm 
outer Alloy 22 lid of the CRM21-PWR design are used for the as-welded and laser-peened 
outer Alloy 22 lid of the proposed design and calculated stress and stress intensity factor profiles 

 
l 
 6-47 
for the as-welded 10-mm Alloy 22 lid of the modified CRM21-PWR design are used for the 
middle Alloy 22 lid of the current design. 
The values of the coefficients in Equation 23 for the closure-lid welds of both waste package 
designs are documented in DTN: LL000316205924.142 [DIRS 148895]. For radial and hoop 
stresses in ksi in the 25-mm outer closure-lid weld of the CRM21-PWR design, the coefficients, 
A0, A1, A2, and A3 with stress in ksi and distance, x, in inches are obtained from 
DTN: LL000316205924.142 [DIRS 148895], file name: Skvrbr1, sheet UnAnneal, Sx, cells 
C9 to C12 for radial stress and sheet UnAnneal, Sz, cells C9 to C12 for hoop stress. The 
coefficients are listed in the first and second rows of Table 4-3. Table 6-7 shows the converted 
stress coefficients, A0, A1, A2, and A3, in the metric unit system. The unit conversions used 
are: 1 in. = 25.4 mm; and 1 ksi = 6.8947568 MPa. 
Table 6-7. Stress Coefficients for the As-Welded Waste Package Outer Lid 
Stress Coefficient Unit Radial Stress Hoop Stress 
A0 MPa 116.321 382.136 
A1 MPa/mm 9.107 8.096 
A2 MPa/mm2 -3.146 -1.991 
A3 MPa/mm3 0.111 0.060 
Source: Table 4-3 (first and second rows) with stress coefficients converted to metric units. 
Similarly, for radial and hoop stresses in ksi in the 10-mm lid of the modified CRM21-PWR 
design, the stress coefficients with stress in ksi and distance, x, in inches are obtained from 
DTN: LL000316205924.142 [DIRS 148895], file name: Thinlid11, sheet UnAnneal,1-1.Sn, 
cells C9 to C12 for radial stress and sheet UnAnneal, 2-2, Sz, cells C9 to C12 for hoop stress. 
The coefficients are listed in the third and fourth rows of Table 4-3. Table 6-8 shows the 
converted stress coefficients, A0, A1, A2, and A3, in the metric unit system. 
Table 6-8. Stress Coefficients for the As-Welded Waste Package Middle Lid 
Stress Coefficient Unit Radial Stress Hoop Stress 
A0 MPa 181.636 219.908 
A1 MPa/mm -177.592 56.494 
A2 MPa/mm2 23.385 -20.848 
A3 MPa/mm3 -0.900 1.083 
Source: Table 4-3 (third and fourth rows) with stress coefficients converted to metric units. 
Tables 6-9 and 6-10 show calculated stress profiles (using Equation 23 and the stress coefficients 
in Tables 6-7 and 6-8) and stress intensity profiles (obtained directly from Table 4-4) for the 
outer and middle lids of the waste package design. The x values to be used in Equation 23 to 
calculate the radial and hoop stress profiles are listed in the first column of Table 6-9 or 6-10. 
For the 10-mm middle lid, the projected distance should be used as the value of x in 
Equation 23 to calculate the stress profiles (Section 6.4.2.2 and Figure 6-12). 

 
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Table 6-9. Stress Intensity Factor (SIF) Profiles for As-Welded Waste Package Outer Lid 
Depth 
(mm) 
Radial Stress (Sx) 
(Mpa) 
SIF due to Sx 
(MPavm) 
Hoop Stress (Sz) 
(Mpa) 
SIF due to Sz 
(MPavm) 
0.3988 119.4598 4.5146 385.0522 9.1593 
0.8001 121.6510 6.5821 387.3707 12.9737 
1.1989 122.9098 8.2395 389.0855 15.9139 
1.6002 123.2952 9.6422 390.2419 18.4031 
1.9990 122.8448 10.8381 390.8484 20.6048 
2.4003 121.5958 11.8425 390.9359 22.6028 
2.7991 119.6065 12.8589 390.5265 24.4741 
3.2004 116.8946 13.7858 389.6383 26.2367 
3.5992 113.5369 14.5688 388.3055 27.9039 
3.9980 109.5607 15.2083 386.5472 29.4912 
4.3993 104.9776 15.7061 384.3711 31.0103 
4.7981 99.8883 16.0778 381.8281 32.4703 
5.1994 94.2707 16.4072 378.9090 33.9004 
5.5982 88.2385 16.7029 375.6738 35.3092 
5.9995 81.7579 16.8783 372.1047 36.6797 
6.3983 74.9532 16.9527 368.2700 38.0157 
6.7970 67.8273 16.9314 364.1710 39.3202 
7.1984 60.3743 16.8188 359.8023 40.5961 
7.5971 52.7311 16.7108 355.2424 41.8581 
7.9985 44.8434 16.7482 350.4565 43.1357 
8.3972 36.8535 16.7231 345.5282 44.3927 
8.7986 28.7025 16.6321 340.4181 45.6302 
9.1973 20.5362 16.4938 335.2140 46.8495 
9.5987 12.2935 16.3042 329.8729 48.0515 
9.9974 4.1211 16.0808 324.4855 49.2372 
10.3962 -3.9906 16.0751 319.0413 50.4839 
10.7975 -12.0500 15.9957 313.5283 51.7195 
11.1963 -19.9125 15.8601 308.0395 52.9442 
11.5976 -27.6353 15.6646 302.5282 54.1589 
11.9964 -35.0781 15.4259 297.0873 55.3639 
12.3977 -42.2929 15.1398 291.6709 56.5598 
12.7965 -49.1458 15.0982 286.3704 57.8007 
13.1978 -55.6811 15.0836 281.1418 59.0538 
13.5966 -61.7735 15.0159 276.0744 60.3022 
13.9954 -67.4234 14.8966 271.1577 61.5462 
14.3967 -72.6196 14.7274 266.3850 62.7862 
14.7955 -77.2538 14.5229 261.8399 64.0228 
15.1968 -81.3421 14.6570 257.4879 65.2900 
15.5956 -84.7903 15.1057 253.4070 66.5871 
15.9969 -87.5993 15.4787 249.5687 67.8801 
16.3957 -89.6911 15.7929 246.0446 69.1690 
16.7945 -91.0432 16.0516 242.8325 70.4537 
17.1958 -91.6143 16.2578 239.9383 71.7343 
17.5946 -91.3547 16.6700 237.4217 73.0349 
17.9959 -90.2182 17.6878 235.2739 74.4062 
18.3947 -88.1765 18.5558 233.5452 75.7773 

 
l 
 6-49 
Table 6-9. Stress Intensity Factor (SIF) Profiles for As-Welded Waste Package Outer Lid (Continued) 
Depth 
(mm) 
Radial Stress (Sx) 
(Mpa) 
SIF due to Sx 
(MPavm) 
Hoop Stress (Sz) 
(Mpa) 
SIF due to Sz 
(MPavm) 
18.7960 -85.1608 19.2803 232.2369 77.1483 
19.1948 -81.1667 19.8861 231.3887 78.5193 
19.5961 -76.1004 20.3775 231.0131 79.8904 
19.9949 -69.9834 20.7777 231.1380 81.2616 
Output DTN: LL030607012251.065. 
Source: Table 4-4. 
Table 6-10. Stresses and Stress Intensity Factors for the As-Welded Waste Package Middle Lid 
Depth 
(mm) 
Radial Stress (Sx) 
(MPa) 
SIF due to Sx 
(MPavm) 
Hoop Stress (Sz) 
(MPa) 
SIF due to Sz 
(MPavm) 
0.1593 153.9288 4.9033 228.3849 7.5754 
0.3203 127.1172 6.2685 235.9015 10.9665 
0.4797 101.7315 6.8580 242.3296 13.7144 
0.6407 77.2206 6.9761 247.8300 16.1330 
0.8000 54.0676 6.7631 252.3158 18.3358 
0.9593 31.9924 6.3044 255.8750 20.3775 
1.1203 10.7596 5.8250 258.5570 22.3816 
1.2797 -9.2150 5.2651 260.3330 24.3197 
1.4407 -28.3699 4.6000 261.2667 26.1726 
1.6000 -46.3322 3.8615 261.3655 27.9459 
1.7593 -63.3265 3.0726 260.6697 29.6433 
1.9203 -79.5368 2.2534 259.1863 31.2668 
2.0797 -94.6509 1.4282 256.9724 32.8922 
2.2407 -109.0061 0.5951 254.0088 34.5292 
2.4000 -122.3284 -0.2400 250.3830 36.1060 
2.5593 -134.7922 -1.0656 246.0945 37.6220 
2.7203 -146.5363 -1.8707 241.1150 39.0762 
2.8797 -157.3405 -2.6491 235.5736 40.4676 
3.0407 -167.4522 -3.4047 229.3818 41.8264 
3.2000 -176.6850 -4.1787 222.6938 43.2168 
3.3593 -185.1690 -4.9390 215.4749 44.5479 
3.5203 -193.0032 -5.6775 207.6685 45.8181 
3.6797 -200.0480 -6.3965 199.4620 47.0265 
3.8407 -206.4725 -7.0865 190.7114 48.1718 
4.0000 -212.1664 -7.7528 181.6234 49.2531 
4.1593 -217.2211 -8.2576 172.1366 50.3451 
4.3203 -221.7016 -8.7427 162.1726 51.3729 
4.4797 -225.5376 -9.2143 151.9633 52.3351 
4.6407 -228.8312 -9.6605 141.3230 53.2313 
4.8000 -231.5367 -10.0894 130.4975 54.0602 
4.9593 -233.7127 -10.4950 119.4050 54.8214 
5.1203 -235.3959 -10.9446 107.9526 55.4811 
5.2797 -236.5735 -11.4131 96.4029 56.0586 
5.4407 -237.2926 -11.8636 84.5422 56.5637 
5.6000 -237.5602 -12.3055 72.6415 56.9965 

 
l 
 6-50 
Table 6-10. Stresses and Stress Intensity Factors for the As-Welded Waste Package Middle Lid 
(Continued) 
Depth 
(mm) 
Radial Stress (Sx) 
(MPa) 
SIF due to Sx 
(MPavm) 
Hoop Stress (Sz) 
(MPa) 
SIF due to Sz 
(MPavm) 
5.7593 -237.4080 -12.7309 60.6057 57.3567 
5.9203 -236.8501 -13.1320 48.3342 57.6444 
6.0797 -235.9201 -13.7114 36.1065 57.7587 
6.2407 -234.6208 -14.4707 23.6946 57.6946 
6.4000 -233.0011 -15.2333 11.3811 57.5522 
6.5593 -231.0713 -15.9891 -0.9356 57.3322 
6.7203 -228.8287 -16.7277 -13.3570 57.0353 
6.8797 -226.3414 -17.4611 -25.6005 56.6626 
7.0407 -223.5802 -18.4707 -37.8942 56.1419 
7.2000 -220.6238 -20.3589 -49.9583 55.3276 
7.3593 -217.4669 -22.2128 -61.8935 54.4422 
7.5203 -214.0957 -24.0173 -73.7955 53.4878 
7.6797 -210.6019 -25.7872 -85.3924 54.6294 
7.8407 -206.9348 -27.4989 -96.8987 56.2191 
8.0000 -203.1923 -29.1709 -108.0509 57.7865 
Output DTN: LL030607012251.065 
Source: Table 4-4. 
A comparison of the near-outer-surface as-welded hoop stresses for the 25-mm-thick outer lid 
(Table 6-9) and the 10-mm-thick middle lid (Table 6-10) indicates that for both cases, the tensile 
stresses in about the outer 1 mm of the lids exceeds the stress corrosion cracking stress initiation 
criteria of 0.9 YS (YS listed in Section 6.2.1 as 285 MPa) or 257 MPa although only slightly for 
the 10-mm middle lid. 
6.4.3 Impact of Corrosion 
The results presented in Section 6.4.2.3 were performed for the as-built condition. Thus, the full 
thickness for all the waste package components was used. In order to simulate the effect of wall 
thinning caused by general corrosion, a layer of elements from the outside surface of the outer lid 
was removed. The thickness of this layer is 0.125 inch (about 3.18 mm), which is equivalent to 
the removal of 12.7% of the wall of the outer lid. The general corrosion rates are very low for 
the Alloy 22 material. Based on the mean general corrosion rate of 7.23 nm/yr (Section 6.3.5), 
the 0.125-inch removal is the amount of material that will corrode in 439,140 years. Removal of 
these elements causes a redistribution of the stress pattern. 
Figure 6-16 shows the row of elements removed to simulate the general corrosion of the outer lid 
surface. Figures 6-17 and 6-18 show, respectively, the through-wall radial stress profiles (with 
and without corrosion effects) and hoop-stress profiles at Section 1-1 in Figure 6-16. These 
results demonstrate the redistribution of the residual stress. In general, the stress distribution 
appears to be not very sensitive to the effects of corrosion. 
Figures 6-19 and 6-20 show the stress intensity factor distribution for Section 1-1 in Figure 6-16 
for circumferential and radial cracks. These figures show the stress intensity factor as a function 
of distance from the outside surface and normalized distance from the outside surface. These 
figures also demonstrate that the overall effect of general corrosion is small. 

 
l 
 6-51 
Source: SI 2003 [DIRS 162457], Figure 4-1. 
NOTES: (a) Finite element model. 
(b) Sections for stress profile. 
Figure 6-16. Finite Element Model Used for Study of Corrosion 

 
l 
 6-52 
Source: SI 2003 [DIRS 162457], Figure 4-2. 
Figure 6-17. Effect of Corrosion on Radial Stress in Outer Lid 
Source: SI 2003 [DIRS 162457], Figure 4-4. 
Figure 6-18. Effect of Corrosion on Hoop Stress in Outer Lid 

 
l 
 6-53 
Source: SI 2003 [DIRS 162457], Figure 4-6. 
NOTES (a) X-axis is crack depth in inches. 
(b) X-axis is shown as the ratio of crack depth (a) versus thickness (t). 
Figure 6-19. Stress Intensity Factor for Full-Circumference Flaw in Outer Lid 

 
l 
 6-54 
Source: SI 2003 [DIRS 162457], Figure 4-7. 
NOTES: (a) X-axis is crack depth in inches. 
(b) X-axis is shown as the ratio of crack depth (a) versus thickness (t). 
Figure 6-20. Stress Intensity Factor for Radial Elliptical Crack in Outer Lid 

 
l 
 6-55 
6.4.4 Mitigation of Weld Residual Stress 
Stress is one of the three basic factors that cause initiation and propagation of cracks in structural 
components due to stress corrosion cracking. The other two factors are metallurgical 
susceptibility and environment. Stress corrosion cracking can be reduced to a manageable state 
if the weld residual stress in the waste package can be effectively mitigated. 
Weld residual stress can be mitigated by optimizing the waste package design geometrical 
configuration. Residual stress can also be mitigated through specially designed weld processes, 
such as narrow-groove and other low heat input welding processes, as well as spray cooling of 
final weld passes to produce compressive outer surface stress. 
For the final closure welds of the waste package, according to Bokhari (2003 [DIRS 162429], 
Attachment 1), a nonthermal stress-mitigation process (laser peening or low-plasticity 
burnishing) was selected to replace the prior local induction-annealing residual stress-mitigation 
process, as this results in less possibility of harming Alloy 22 characteristics through heat 
treatment (local induction annealing), thus reducing performance uncertainty. For the purpose of 
license application (LA), Bokhari (2003 [DIRS 162429], Attachment 1, Figure 1) indicates that 
laser peening is the nonthermal mitigation method selected. The laser peening treatment, which 
is used for the 25-mm outer lid of the outer barrier to evaluate stress mitigation, involves use of 
the laser peening process, where a high-powered laser beam introduces shock pulses on the 
material surface. Laser peening is similar to the traditional shot-peening procedure, but is better 
adapted to waste package closure cell remote application. For laser peening, the intense stream 
of tiny metal or ceramic balls used in the traditional shot peening is replaced by high-energy 
lasers with pulse lengths in the tens of nanoseconds, short enough to generate a rapid, yet 
energetic shock. This process can produce a uniform layer of highly shocked and compressed 
material that is extremely resistant to cracks and corrosion. 
According to measured data reported by Hornbach (1999 [DIRS 147757], Figures 18 to 21), 
laser peening is capable of producing a compressive surface layer of about 60 mils (1.5 mm) 
with compressive stress in the range of 20 to 60 ksi for a one-inch-thick welded Alloy 22 plate. 
A typical example for is shown in Figure 6-21 (DTN: LL000320005924.145) for measured 
stress profiles at the weld centerline for stress component 1 (S1, parallel to the weld center line) 
and stress component 3 (S3, perpendicular to the weld center line) before and after laser peening. 
It is evident from this figure that compressive stresses on the order of 40 ksi persist to a depth of 
at least 0.06 in. (1.5 mm). 
Therefore, to demonstrate the effect of laser peening on the stress intensity factor, the 
weld-induced residual stress in the 25-mm outer lid of the CRM21-PWR design was reduced 
from tensile stress to 40 ksi compressive stress for a depth of 0.06 in. (1.5 mm) at the outside 
surface (Figure 6-22). Using a depth of compressive stress of 0.06 in. (1.5 mm) is conservative, 
as measured results from more recently processed, multipass laser peened 1-inch welded 
Alloy 22 plate, (Figure 6-32), as well as an assessment based on measured laser-peened depth of 
compression versus plate thickness (Chen et al. 2002 [DIRS 165441], Figure 20) indicates a 
compressive stress depth significantly greater than 0.06 in. (1.5 mm) is readily obtainable for a 
25-mm-thick Alloy 22 weldment. However, assuming a compressive depth of 0.06 in. (1.5 mm), 
the residual stress is then varied linearly from 0.06 in. (1.5 mm) to 0.12 in. (3.0 mm) below the 

 
l 
 6-56 
surface. From this point on, the stress remains undisturbed (i.e., uses the as-welded stress 
distribution). The stress intensity factor was calculated for the reduced stress profile and 
compared to the stress intensity factor previously calculated for the original stress profile as 
shown in Figure 6-23 (i.e., graphical presentations of (a) Column 3 and (b) Column 5 of 
Tables 6-9 and 6-12). It is evident that for the laser-peened outer lid, the radial through-wall 
stress intensity factor is less than zero indicating circumferential cracks will not propagate 
entirely through the wall thickness. 
For radial and hoop stresses in ksi in the laser-peened 25-mm outer lid of the waste package 
design, the stress coefficients with stress in ksi and distance x in inches are obtained from 
DTN: LL000316205924.142 [DIRS 148895], file name: Skvrbr1, sheet Peening, Sx, cells C9 
to C12 for radial stress and sheet Peening, Sz, cells C9 to C12 for hoop stress. The coefficients 
are listed in the fifth and sixth rows of Table 4-3. Table 6-11 shows the converted stress 
coefficients, A0, A1, A2, and A3, in the metric unit system. Table 6-12 shows the calculated 
stress and stress intensity profiles for the outer waste package lid subjected to laser peening. 
Based on the hoop-stress profile and yield stress of 285 MPa for Alloy 22, examination of 
Table 6-12 indicates the depth to which the outer weld stress is in compression is about 1.92 mm, 
and the depth to which it is less than 90% of yield stress is about 4.6 mm. 
Any thermally induced stress relaxation of the through-wall stress distribution is expected to be 
small at waste package temperatures below about 300C. A small amount of stress relaxation 
was potentially observed based on measured leg springback in 5-year exposed U-bend specimens 
tested at 90C and removed from the LLNL Long Term Corrosion Test Facility and 
disassembled (Fix et al. 2003 [DIRS 162700], p. 5). However, stress relaxation reduces 
subsurface tensile stresses, as well as the beneficial outer surface compressive stresses, and it is 
unlikely that relaxation of stresses in a surface stress mitigated layer would significantly change 
the depth to reach stresses below the threshold stress value for stress corrosion cracking initiation 
discussed in Section 6.2.1. Even the full removal (by corrosion) of the outer ~3mm of mitigated 
surface layer did not significantly change the through-wall stress distribution as described in 
Section 6.4.3. 
Table 6-11. Stress Coefficients for the Laser-Peened Waste Package Outer Lid 
Stress Coefficient Unit Radial Stress Hoop Stress 
A0 MPa -265.920 -292.607 
A1 MPa/mm 103.987 178.277 
A2 MPa/mm2 -9.857 -14.135 
A3 MPa/mm3 0.254 0.320 
Source: Table 4-3, (fifth and sixth rows) with units converted to metric system; Output DTN: LL030607012251.065, 
Table 8-1. 

 
l 
 6-57 
Source: DTN: LL000320005924.145 [DIRS 148482]. 
Figure 6-21. Mitigation of Weld Stress in Alloy 22 with Laser Peening 
Table 6-12. Stresses and Stress Intensity Factors for Laser-Peened Waste Package Outer Lid 
Depth 
(mm) 
Radial Stress 
(Sx) (MPa) 
SIF due to Sx 
(MPavm) 
Hoop Stress (Sz) 
(MPa) 
SIF due to Sz 
(MPavm) 
0.3988 -226.0035 -9.1866 -223.7417 -5.6943 
0.8001 -188.9005 -11.7979 -158.8532 -6.4965 
1.1989 -154.9833 -13.0189 -98.6408 -6.1528 
1.6002 -123.7220 -13.4298 -42.2143 -5.1372 
1.9990 -95.4153 -13.2965 9.8344 -3.6697 
2.4003 -69.6047 -12.7780 58.2916 -1.8824 
2.7991 -46.5198 -12.2958 102.6663 0.1212 
3.2004 -25.7687 -11.7214 143.6471 2.2821 
3.5992 -7.5170 -11.0116 180.8374 4.5533 
3.9980 8.4709 -10.2080 214.6297 6.8939 
4.3993 22.3728 -9.3437 245.3299 9.2702 
4.7981 34.1098 -8.4525 272.6715 11.6543 
5.1994 43.9293 -7.6096 297.1262 14.0165 
5.5982 51.8041 -6.8298 318.5068 16.3364 
5.9995 57.9323 -6.0675 337.2088 18.6024 
6.3983 62.3334 -5.3416 353.1178 20.8003 
6.7970 65.1483 -4.6612 366.4827 22.9177 
7.1984 66.4775 -4.0331 377.4871 24.9441 
7.5971 66.4012 -3.4507 386.1141 26.9023 
7.9985 65.0162 -2.8535 392.5969 28.8612 

 
l 
 6-58 
Table 6-12. Stresses and Stress Intensity Factors for Laser-Peened Waste Package Outer Lid 
(Continued) 
Depth 
(mm) 
Radial Stress 
(Sx) (MPa) 
SIF due to Sx 
(MPavm) 
Hoop Stress (Sz) 
(MPa) 
SIF due to Sz 
(MPavm) 
8.3972 62.4372 -2.2745 396.9757 30.7287 
8.7986 58.7292 -1.7170 399.4297 32.5008 
9.1973 54.0361 -1.1860 400.0499 34.1745 
9.5987 48.3961 -0.6829 398.9677 35.7479 
9.9974 41.9777 -0.2101 396.3190 37.2200 
10.3962 34.8443 -0.3513 392.2239 38.4530 
10.7975 27.0415 -0.5163 386.7654 39.5674 
11.1963 18.7651 -0.7070 380.1350 40.5636 
11.5976 10.0075 -0.9242 372.3715 41.4432 
11.9964 0.9766 -1.1690 363.6954 42.2086 
12.3977 -8.3447 -1.4403 354.1195 42.8627 
12.7965 -17.7414 -1.7949 343.8874 43.4439 
13.1978 -27.2353 -2.1728 332.9919 43.9342 
13.5966 -36.6092 -2.5554 321.6934 44.3269 
13.9954 -45.8267 -2.9438 310.0462 44.6272 
14.3967 -54.8472 -3.3378 298.0958 44.8409 
14.7955 -63.4595 -3.7396 286.1158 44.9743 
15.1968 -71.6755 -4.0160 274.0769 45.0329 
15.5956 -79.2941 -4.1354 262.2538 45.0208 
15.9969 -86.3145 -4.2182 250.6192 44.9464 
16.3957 -92.5507 -4.2696 239.4426 44.8182 
16.7945 -97.9528 -4.2904 228.7710 44.6449 
17.1958 -102.4495 -4.2805 218.6644 44.4361 
17.5946 -105.8869 -4.3087 209.3730 44.2112 
17.9959 -108.2109 -4.5204 200.9017 43.9968 
18.3947 -109.2950 -4.7313 193.4801 43.7750 
18.7960 -109.0551 -4.9400 187.1369 43.5578 
19.1948 -107.3973 -5.1487 182.0747 43.3569 
19.5961 -104.2024 -5.3536 178.3522 43.1853 
19.9949 -99.4140 -5.5551 176.1390 43.0560 
Source: Table 4-4. 
Output DTN: LL030607012251.065. 

 
l 
 6-59 
Source: DTN: LL000316205924.142 [DIRS 148895], File dgzRs1R11, Sheets 1-1 Sx and 1-1 Sz. 
NOTE: (a) Radial Stress, Sx, and (b) Hoop Stress, Sz. 
Figure 6-22. Stress in Outer Lid With and Without Laser Peening 

 
l 
 6-60 
Source: Graphical presentations of (a) Column 3 and (b) Col. 5 of Tables 6-9 and 6-12. 
Figure 6-23. Stress Intensity Factors due to (a) Radial Stress and (b) Hoop Stress With and Without 
Laser Peening 

 
l 
 6-61 
6.4.5 Uncertainty and Variability of Residual Stress and Stress Intensity Factor in Waste 
Package 
Section 6.4.2.2 states that, although the determination of weld residual stress for the waste 
package welds is a three-dimensional problem, a two-dimensional axisymmetric modeling 
approach has been used for the finite element analyses of the weld residual stresses. The result is 
that the stress distribution is axisymmetrical about the waste package axial centerline 
(i.e., constant along the circumference). An assessment of circumferential residual stress 
variation in stainless steel piping welds (DTN: MO0409GGSIACAL.000 [DIRS 171792], 
Calculation TRW-06Q-304) indicated that the residual stress shows a sinusoidal distribution 
around the circumference with a range of about 5 ksi about the mean stress. Based on this 
conclusion, the variability of the mean stress along the circumference (.S) is represented by the 
following equation: 
S.(x)= S0(x)  .S(1  cos(.)) (Eq. 25a) 
where 
. is the angle measured in degrees from a reference location (. = 0) on the 
circumference 
S.(x) is the weld residual stress profiles at an angle . 
S0(x) is calculated weld residual stress profile at . = 0 
.S is taken to be 2.5 ksi or 17.236893 MPa. 
Variability in stress intensity factor is treated similarly to that for stress because stress intensity 
factor is a linear function of stress: 
K.(x)= K0(x) (S.(h) / S0(h)) (Eq. 25b) 
where h is the thickness of the closure lid. 
The uncertainty of the weld residual stress calculated by the simplified finite element analysis 
can be adequately represented by a normal distribution with the calculated residual stress as the 
mean (S.(x)) and a 3-sigma bound to be defined. 
Mohr (1996 [DIRS 147981], p. 39) indicated that the uncertainty range of the residual stress is a 
function of the yield strength of the material and varies about the mean by 35% of the yield 
strength. The high degree of uncertainty (or variability) associated with Mohrs data was related 
to the large scatter in measured residual stress data resulting from use of a large number of 
different carbon steel welded pipes covering a range of thicknesses, welding processes, weld 
joint configurations, weld heat inputs, yield strengths, etc. In the case of the final closure welds 
of the dual-lid improved waste package design, the various parameters contributing to residual 
stress variation are closely controlled. This includes close, automated control on the welding 
process parameters, the use of a single alloy for the base material and for the weld wire, close 
control of the weld joint configuration and spacing, etc. 
In contrast to the high degree of scatter noted by Mohr (1996 [DIRS 147981]), data available on 
shot-peened (analogous to laser-peened) nickel alloy Incoloy 908 (Pasupathi 2000 

 
l 
 6-62 
[DIRS 149968]) indicate a narrow residual stress scatter range for as-welded and as-welded plus 
shot-peened nickel alloy material with one-sigma value of 3% of the measured stress value for 
shot-peened surfaces (Pasupathi 2000 [DIRS 149968], Tables II and VI) or an uncertainty range 
of about 9% at the 3-sigma level. In comparison, the residual stresses measured on a peened 
surface by the X-ray diffraction technique (Lu 1996 [DIRS 149957], Table 5-4, p. 103) showed 
an average measurement uncertainty of about 15 MPa, which is about 5% of the Alloy 22 
yield strength. Values of yield strength, YS, of Alloy 22 are listed in Table 4-5. For 
conservative purpose, the higher YS value at the room temperature may be used. 
The data listed by Pasupathi (2000 [DIRS 149968]) are for both welded and nonwelded samples 
(peened and unpeened), many of which also contain some cold work due to tube-reduction 
drawing. Thus, they represent a range of metallurgical and process variables that the waste 
package closure-lid weld regions also contain (cold-work, as-annealed, and as-welded conditions 
for peened and unpeened material). Further, in the case of the final closure welds of the dual-lid 
waste package design, good process control plus periodic quality control measurements will be 
used in the site closure cell on the final, postprocessed Alloy 22 material. The quality control 
measurement process(es) to be used will depend on the finally selected stress mitigation process. 
For the laser peening process, the so-called Almen strips, which are commonly used to control 
shot-peening processing and laser-peening processing, may be used. Almen strips are thin 
rectangular strips that, when peened from one side, deflect with the deflection related to the 
depth of applied residual compressive stress resulting from the process. If stresses are found to 
deviate from the specified range, the weld can be reprocessed, repaired, or scrapped. 
Thus, based on the above discussion, a 3-sigma stress uncertainty range of 15% of the material 
mean yield strength appears to be a conservative representation of the realistic case that is 
achievable through appropriate levels of process controls. 
The minimum and maximum stresses at the 3-sigma level, ( )min x S . and ( )max x S . in the weld 
can be obtained from the mean stress, ( ) x S . , by the following equations: 
( ) ( ) ( )
( ) . .. 
. 
. .. 
. . - = 
h S 
S h S x S x S 
. 
. 
. . min (Eq. 26a) 
( ) ( ) ( )
( ) . .. 
. 
. .. 
. . + = 
h S 
S h S x S x S 
. 
. 
. . max (Eq. 26b) 
where ( ) h S . is the mean residual stress on inside surface (x=h, where h is the thickness of the 
closure lid) and .S is the amplitude of variation between the maximum and minimum stresses at 
the inner surface of the waste package lid. The stress intensity factor calculated from the mean 
stress as described in Section 6.4.2.2 is the mean stress intensity factor ( ) x K . . The minimum 
and maximum stress intensity factors are calculated similarly to those for stress because stress 
intensity factor is a linear function of stress. 

 
l 
 6-63 
( ) ( ) ( )
( ) . .. 
. 
. .. 
. . - = 
h S 
S h S x K x K 
. 
. 
. . min Eq. 26c) 
( ) ( ) ( )
( ) . .. 
. 
. .. 
. . + = 
h S 
S h S x K x K 
. 
. 
. . max (Eq. 26d) 
where . is the angle measured from a reference location (. = 0) on the circumference and 
.S = 0.15 YS (YS is the mean yield strength given in Table 4-5). 
As described in Section 6.2.2, the hoop stress, which promotes radially oriented crack growth, is 
the dominant component of stress in the waste package outer barrier final closure lid weld 
regions and, thus, only the hoop stress profiles are considered in calculating the expected range 
of stress and stress intensity factor through-wall variation. The stress and stress intensity factor 
profiles in the waste package outer barrier closure weld regions are variable and uncertain. 
Variability (angular variation) in the hoop stress ( s in MPa) as a function of depth (x in mm) in 
the closure weld regions of the Alloy 22 waste package outer barrier is given by a third order 
polynomial equation (Equation 23), repeated here, where the values of the coefficients are given 
in Section 6.4.4, Table 6-11 and are listed in metric units in Section 8.3, Table 8-1. 
3 
3 
2 
2 1 0 ) 0 , ( x A x A x A A x + + + = s (Eq. 23) 
The second argument in the stress function is used to represent angular variation (. = 0, 
arbitrarily chosen) around the circumference of the Alloy 22 waste package outer and middle 
closure-lid welds. The angular variation is included using the following functional form, based 
on Equation 25a: 
( ) ( ) ( ) ( )) cos 1 ( 17.236893 0 , , . s . s -  - = x x (Eq. 25a') 
Defined in Equation 25a', s(x, 0) uses the stress coefficients (Ai) defined in Equation 23 with x in 
units of mm and the stress variability term defined in Equation 25a and listed in Table 8-1. 
Using Equation 25a', Figure 6-24 shows the median (not accounting for uncertainty, which is 
discussed below) stress variation with angle for the waste package outer barrier outer closure lid 
weld region and Figure 6-25 shows the median stress variation with angle for the waste package 
outer barrier middle closure lid weld region. Also included on the graphs is the stress threshold 
for nucleation of incipient flaws. The depth on these graphs does not start at zero thickness, nor 
extend to the full lid thickness. For consistency, stress values were calculated at the same depth 
values as for the corresponding stress intensity factor profiles that were calculated using 
Equation 25b and are shown plotted with angle for the outer and middle closure lid weld regions 
in Figures 6-26 and 6-27, respectively. 
Uncertainty for the outer and middle closure lid weld regions (with relevant parameter values 
listed in Table 8-1) were calculated for the residual stress distributions based on Equations 26a 
and 26b and are shown plotted in Figures 6-28 and 6-29, respectively at . = 0. Similarly, 
uncertainty for the outer and middle closure lid weld regions (with relevant parameter values 

 
l 
 6-64 
listed in Table 8-1) were calculated for the stress intensity factor distributions based on 
Equations 26c and 26d and are shown plotted in Figures 6-30 and 6-31, respectively. 
As can be seen from Figure 6-28, the analysis results predict that the threshold stress (90% of 
yield strength) for the laser peened outer closure lid will be reached at a depth of about 4.6 mm, 
based on mean values. More conservatively, the analysis predicts the threshold stress will be 
reached at a depth of about 3.8 mm, based upon the upper bound of uncertainty. Corroborative 
measurements of the through-wall residual stress have been made on Alloy 22 gas tungsten arc 
weldments (1-inch thick) processed with a several pass laser-shock peening process and with an 
alternate controlled plasticity-burnishing stress mitigation process. These measurements shown 
in Figure 6-32 and Figure 6-33, respectively, show that the predicted values shown in 
Figure 6-24 are very conservative estimates of the depth of compression that can be achieved 
through stress mitigation. These experimental measurements were obtained using the 1-inch 
ring-core technique and are reported in DTN: MO0301SPAXRA52.001 [DIRS 165147]. Note 
the stresses parallel to the weld centerline are referred to as being in the parallel direction. 
The time-to-breach due to stress corrosion cracking at the stress-mitigated closure weld will be 
determined primarily by the time required to corrode through the material to a level where the 
stress exceeds 90% of the yield strength. Added to this is the time required for the initiated crack 
to propagate through the remaining lid thickness. Any relaxation of the residual-stress gradient 
tends to reduce the compressive surface-stress magnitude and the subsurface tensile-stress 
magnitude and thus, may increase the depth to reach 90% of the yield strength. Further, as the 
outer compressive surface layer is slowly removed by general corrosion, the neutral axis shifts 
inward. 
The scenario for removal of the compressive layer by corrosion is relatively easy to assess. 
Because of very low general corrosion rates of the waste package outer barrier for the conditions 
expected in the repository, waste package performance is not limited by general corrosion during 
the regulatory time period. As a bounding and conservative analysis, for a constant waste 
package surface temperature of 150C, the median penetration depth by general corrosion over 
10,000 years, using the median general corrosion rate of 51.8 nm/yr (BSC 2004 [DIRS 169984], 
Section 8.1) is about 518 m, which is about 11% of the mean depth of the stress mitigated layer 
(about 4.6 mm, Figure 6-28). Using an upper-bound value of the general corrosion rate of 
256 nm/yr (99.99th percentile rate at 150C (BSC 2004 [DIRS 169984], Section 8.1)) the total 
penetration depth by general corrosion is about 2,560 m, which is about 56% of the about 
4.6-mm mean depth of the stress-mitigated layer and about 67% of the total maximum 
uncertainty (minimum depth) of the stress-mitigated layer (about 3.8 mm, Figure 6-28). This 
bounding analysis demonstrates that the final closure lid weld stress-mitigated layer is deep 
enough to extend the lifetime of the waste package well beyond 10,000 years after permanent 
closure using conservative values of mitigated layer depth. 

 
l 
 6-65 
Source: Figure 6-24 generated for this report using Equation 25a and data reside in Output 
DTN: LL030607012251.065 and plotted graph in Output DTN: MO0310MWDWAPAN.002. 
Figure 6-24. Variation of Hoop Stress Versus Depth for Waste Package Outer Closure Lid 
Source: Figure 6-24 generated for this report using Equation 25a and data reside in Output 
DTN: LL030607012251.065 and plotted graph in Output DTN: MO0310MWDWAPAN.002. 
Figure 6-25. Variation of Hoop Stress Versus Depth for Waste Package Middle Closure Lid 

 
l 
 6-66 
Source: Figure 6-26 generated for this report using Equation 25b and data reside in Output 
DTN: LL030607012251.065 and plotted graph in Output DTN: MO0310MWDWAPAN.002. 
Figure 6-26. Variation of Stress Intensity Factor Versus Depth for Waste Package Outer Closure Lid. 
Source: Figure 6-27 generated for this report using Equation 25b and data reside in Output 
DTN: LL030607012251.065 and plotted graph in Output DTN: MO0310MWDWAPAN.002. 
Figure 6-27. Variation of Stress Intensity Factor Versus Depth for Waste Package Middle Closure Lid 

 
l 
 6-67 
Source: Figure 6-28 generated for this report using Equation 26a and data reside in Output 
DTN: LL030607012251.065 and plotted graph in Output DTN: MO0310MWDWAPAN.002. 
Figure 6-28. Variation of Hoop Stress (. = 0) Versus Depth for Waste Package Outer Closure Lid 
Source: Figure 6-29 generated for this report using Equation 26b and data reside in Output 
DTN: LL030607012251.065 and plotted graph in Output DTN: MO0310MWDWAPAN.002. 
Figure 6-29. Variation of Hoop Stress (. = 0) Versus Depth for Waste Package Middle Closure Lid 

 
l 
 6-68 
Source: Figure 6-30 generated for this report using Equation 26c and data reside in Output 
DTN: LL030607012251.065 and plotted graph in Output DTN: MO0310MWDWAPAN.002. 
Figure 6-30. Variation of Stress Intensity Factor (. = 0) Versus Depth for Waste Package Outer Closure 
Lid 
Source: Figure 6-31 generated for this report using Equation 26d and data reside in Output 
DTN: LL030607012251.065 and plotted graph in Output DTN: MO0310MWDWAPAN.002. 
Figure 6-31. Variation of Stress Intensity Factor (. = 0) Versus Depth for Waste Package Middle 
Closure Lid 

 
l 
 6-69 
Source: DTN: MO0301SPAXRA52.001 [DIRS 165147], Figure 4. 
Figure 6-32. Measured Stress (Using 1-Inch Ring Core Method) Versus Depth for Alloy 22 Laser- 
Peened 1-Inch-Thick Gas Tungsten Arc Welding Welded Plate 

 
l 
 6-70 
Source: DTN: MO0301SPAXRA52.001 [DIRS 165147], Figure 7. 
Figure 6-33. Measured Stress (Using 1-Inch Ring-Core Method) Versus Depth for Alloy 22 Controlled 
Plasticity Burnished 1-Inch-Thick Welded Plate 
6.5 ESTIMATE OF LENGTH AND INTERCRACK SPACING OF RADIAL 
THROUGH-WALL CRACKING AND CRACK OPENING 
The information provided in Section 6.5 is not used directly in the SDFR model. Rather, it is 
provided as information that can be used for performance assessment in calculating radionuclide 
release rates through stress corrosion cracks. 
6.5.1 Estimated Length and Intercrack Spacing of Radial Through-Wall Cracking 
As discussed in Section 6.2.2.3, radially oriented flaws are important to stress corrosion cracking 
of waste packages since the hoop stress, which drives the radially oriented cracks, is usually the 
dominant stress component. The stress intensity factor resulting from the through-wall hoop 
stress gradient (or profile) can result in propagation of through-wall stress corrosion cracking for 
cracks in the radial direction. Based on stress distributions shown in Figure 6-14, rapid-weld 
residual stress decay is observed with increasing distance normal to the weldmetal interface 
(i.e., in the radial direction). As the tensile stress decays, the driving force for crack extension in 
the radial direction also decreases rapidly and appears to fully attenuate at distances from the 
weld center line on the order of the welded plate thickness. Thus, the expected maximum length 
of these radial cracks is approximately two times the plate thickness. 

 
l 
 6-71 
With respect to the expected minimum spacing between parallel through-wall radial cracks, 
detailed analysis (Structural Integrity Associates 2002 [DIRS 161933]) indicated, because of 
stress field interactions between closely spaced parallel cracks that for a one-inch-thick plate, the 
distance between two neighboring through-wall cracks would need to be greater than the plate 
thickness for the stress (and resultant stress intensity factor) to be sufficient to drive a flaw 
through-wall. 
6.5.2 Estimate of Crack Opening 
Leak through a crack can occur if the crack grows into a through-thickness crack. Leak rate 
depends on the size of crack opening, among other factors. A simplified crack opening 
calculation approach is described below. 
1. A crack is either circumferential (perpendicular to the radial stress) or radial 
(perpendicular to the hoop stress) in the outer surface of the closure weld of the waste 
package. 
2. A circumferential crack is treated as a semielliptical crack with depth, a, and length, 
2c. The aspect ratio c/a for a radial crack is 1 (i.e., a semicircular crack (c = a)). 
3. The crack length 2c of a circumferential crack remains unchanged but the final 
length of a through-wall crack is at least twice the wall thickness. Consequently, most 
cracks will grow in both directions of the minor (depth a) and major (length 2c) 
axes and become semicircular (i.e., a = c) when they become through-wall cracks. 
According to fracture mechanics (Ewalds and Wanhill 1984 [DIRS 118602], 
Section 2.5, p. 43), a tends to grow faster than c because the stress intensity factor 
tends to have a maximum value at the end of the minor axis and a minimum value at 
the end of the major axis. Eventually, a semielliptical crack will become a 
semicircular crack. The crack length 2c will remain unchanged only for very long 
cracks with initial crack length greater than twice the wall thickness. For such long 
cracks, the occurrence rate is usually very low. The length of a semicircular crack will 
always be equal to twice the crack depth. 
4. The crack opening has an elliptical shape with length 2c and a gap d. 
Tada et al. (2000 [DIRS 167756], p. 125), showed that the opening of a crack, d, with length, 2c, 
in an infinite sheet is given for plane stress condition as: 
( ) 
E
c s d 4 = (Eq. 28) 
where 
s = stress 
E = Youngs Modulus 

 
l 
 6-72 
The opening area, Acr, for an elliptical crack, therefore, can be estimated by: 
( ) ( ) 
E
c c Acr 
s p d p 2 2 2 4 = = (Eq. 29) 
When Equations 28 and 29 are used to estimate the crack opening and opening area, s is the 
maximum stress across the thickness of either the radial stress (for a circumferential crack) or the 
hoop stress (for a radial crack). 
6.6 FEATURES, EVENTS AND PROCESSES 
The development of a comprehensive list of features, events, and processes (FEPs) potentially 
relevant to postclosure performance of the repository is an ongoing, iterative process based on 
site-specific information, design, and regulations. To support TSPA-LA, the FEP list was 
reevaluated in accordance with The Enhanced Plan for Features, Events, and Processes (FEPs) 
at Yucca Mountain (BSC 2002 [DIRS 158966], Section 3.2). Table 6-13 provides a list of FEPs 
included in this report and provides specific references to within this report where the FEPs are 
discussed. A description of these FEPs can be found in DTN: MO0407SEPFEPLA.000 
[DIRS 170760], while a complete list of all FEPs related to waste package and drip shield 
degradation can be found in FEPs Screening of Processes and Issues in Drip Shield and Waste 
Package Degradation (BSC 2004 [DIRS 169997]). 
Table 6-13. Included FEPs 
FEP No. FEP Name Section Where Disposition is Described 
2.1.03.02.0A Stress corrosion cracking (SCC) of waste packages Section 6.1 
This report does not provide a direct basis for the inclusion of FEP 2.1.03.02.0A in the Total 
System Performance Assessment for License Application (TSPA-LA). Rather, its results are 
used by WAPDEG Analysis of Waste Package and Drip Shield Degradation to develop a basis 
for implementing or excluding these FEPs in the TSPA-LA. 

 
l 
 7-1 
7. MODEL VALIDATION 
Model validation activities for the SDFR model are described below. Validation activities for 
the seismic crack density model are discussed in Appendix B in Section B7. 
7.1. INTENDED PURPOSE OF THE MODEL 
Stress corrosion cracking is a potential corrosion mode that can result in penetration of the drip 
shield, waste package outer barrier ls. The purpose of 
this report is to provide the evaluation of the potential for stress corrosion cracking of the drip 
shield, the waste package outer barrier, and waste package stainless steel inner structural cylinder 
under exposure conditions consistent with the repository during the regulatory period of 10,000 
years after permanent closure. As no lifetime credit is taken for the stainless steel structural 
material, it is not modeled. For the drip shield and waste package outer barrier, the critical 
environment is conservatively taken as any aqueous environment contacting the metal surfaces. 
The output models feed outputs to FEPs Screening of Processes and Issues in Drip Shield and 
Waste Package Degradation and is included in abstracted form in WAPDEG Analysis of Waste 
Package and Drip Shield Degradation. 
This stress corrosion cracking model directly supports the following TSPA components: 
 Drip Shield Stress Corrosion Cracking and Other Corrosion Modes 
 Waste Package Stress Corrosion Cracking and Other Corrosion Modes. 
Thus, this report supports TSPA-LA. 
7.1.1 Confidence-Building During Model Development to Establish Scientific Basis and 
Accuracy for Intended Use 
Section 2.2.1 of Technical Work Plan for: Regulatory Integration Modeling and Analyses of the 
Waste Form and Waste Package (BSC 2004 [DIRS 171583]) specifies the following steps for 
confidence building during model development: 
 The model will contain documentation of decisions and activities implemented during 
the model development process to build confidence and verify a reasonable and credible 
technical approach using scientific and engineering principles. 
 The development of the model should be documented in accordance with the 
requirements of Section 5.3.2(b) of AP-SIII.10Q. 
The development of the SDFR SCC crack growth rate model was conducted according to the 
following criteria: 
(1) Selection of input parameters and/or input data, and a discussion of how the 
selection process builds confidence in the model (AP-SIII.10Q 5.3.2(b)(1); 
AP-2.27Q, Attachment 3, Level I (a)). 

 
l 
 7-2 
The bases for selecting the input data listed in Section 4.1 and used to determine and develop the 
SDFR model for application to the waste package are documented in Section 6.3.4. Detailed 
discussion about model concepts can be found in Section 6. Thus, this requirement can be 
considered satisfied. 
(2) Description of calibration activities, and/or initial boundary condition runs, 
and/or run convergences, and a discussion of how the activity or activities build 
confidence in the model. Inclusion of a discussion of impacts of any nonconvergence 
runs. (AP-SIII.10Q 5.3.2(b)(2)). 
Not applicable. 
(3) Discussion of the impacts of uncertainties to the model results including how 
the model results represent the range of possible outcomes consistent with 
important uncertainties. (AP-SIII.10Q 5.3.2(b)(3); AP-2.27Q, Attachment 3, 
Level 1 (d) and (f)). 
Uncertainties associated with the model analysis are discussed in Section 6.3.4 for the n model 
parameter and in Section 6.4.5 for the through-wall stress and stress intensity factor model 
parameter. Thus, this requirement can be considered satisfied. 
(4) Formulation of defensible assumptions and simplifications. (AP-2.27Q, 
Attachment 3, Level I (b)). 
No assumptions were used for model development. A discussion of simplifications and their 
rationale are provided in Section 6. Thus, this requirement can be considered satisfied. 
(5) Consistency with physical principles, such as conservation of mass, energy, 
and momentum. (AP-2.27Q, Attachment 3, Level I (c)). 
Discussion of relevant physical phenomena and processes are discussed in Section 6.3.2 for the 
waste package and in Section 6.3.7 for the drip shield. 
(6) Description of simulation conditions set up to span the range of intended use 
and avoid inconsistent outputs. (AP-2.27Q, Attachment 3, Level I (e)). 
Stress corrosion crack growth rate data were obtained over a range of chemical conditions, and 
applied stress intensity factor levels Sections 6.3.4 and 7.4.2.3. Experimental tests were 
conducted in a range of concentrated J-13-type brines or other similar composition solutions, 
Sections 6.3.4 and 7.4.2.3, as well as accelerated test temperatures. Sets of test specimens were 
exposed over a range of pH values, test temperatures as well as the presence of potential 
deleterious impurity elements such as lead. Thus, this requirement can also be considered 
satisfied. 

 
l 
 7-3 
7.1.2 Confidence-Building After Model Development To Support The Scientific Basis Of 
The Model 
Postmodel development validation is required by AP-2.27Q for Level I, Level II, and Level III 
models. For confidence building after model development, Table 2-1 of Technical Work Plan 
for: Regulatory Integration Modeling and Analysis of the Waste Form and Waste Package 
(BSC 2004 [DIRS 171583]) specifies this model as Level III with two validation activities for 
the SDFR model and an independent technical review for the seismic crack density model that 
also includes two additional validation activities. The validation criterion for the SDFR model is 
that corroborating data must match qualitatively. Validation is described in the following 
subsections. Corroborating or supporting data and information used to develop and validate the 
SDFR model parameters are listed in Table 7-1. 
Table 7-1. Supporting (Corroborating) Information Used to Validate the SDFR Model 
Criterion 
Supporting (Corroborating) Information 
Source Data/Information 
1 Andresen and Ford (1994 [DIRS 118581]) Corroborative information regarding application of the 
SDFR Model to a range of alloy systems 
1 Ford and Andresen (1988 [DIRS 118611], 
p. 789) 
Corroborative data supporting use of the SDFR model for 
other Nickel Alloys, Inconel 600/182 
1 
Andresen (1991 [DIRS 166965], Figure 37) Corroborative data supporting use of the SDFR model for 
a Nickel Alloy (Alloy 82 (UNS N06082)) with chromium 
content similar to Alloy 22 
3 Ford and Andresen (1988 [DIRS 118611], p 
791) 
Model parameter n and A = f(n) for stainless steels 
3 Ford and Andresen (1988 [DIRS 118611], 
Figure 10) 
Model parameter n and n = f(A) for stainless steels are 
applicable for nickel alloys 600/182 
3 Mohr (1996 [DIRS 147981]) Weld residual stress uncertainty range of +/- 35% 
3 Pasupathi (2000 [DIRS 149968] Uncertainty in shot peened residual stress in nickel alloy 
5 Ford and Andresen (1988 [DIRS 118611]) Faradays Law used to relate SCC crack advance to 
metal oxidation charge density per film rupture. 
5 Bradford (1987 [DIRS 151988] Titanium oxide to metal volume ratio used for crack 
plugging analysis 
6 LLNL (DTN : LL030300612251.035 
[DIRS 166971]) 
Alloy 22 experimental crack growth rates in a range of 
relevant test environments used to validate SDFR model 
7.2. DETERMINATION OF THE LEVEL OF CONFIDENCE REQUIRED 
Laboratory test results indicate that the waste package outer barrier material, Alloy 22, is highly 
resistant to stress corrosion cracking initiation and propagation on smooth surfaces and at defects 
such as those that might exist in the region of the closure welds. Thus, although stress corrosion 
cracking is unlikely to initiate or propagate, or both, under waste package highly static loading 
conditions where the only significant tensile stresses are final closure lid welding-related 
stresses, the stress corrosion cracking potential will be mitigated by a residual stress reversal 
process (laser peening or potentially controlled plasticity burnishing) that results in a 
compressive layer over the outer waste package closure lid weld region surfaces. Under 
compression, stress corrosion cracking does not initiate or grow. However, once the surface 
compressive layers are removed by general corrosion, current predictions indicate that stress 

 
l 
 7-4 
corrosion cracking will initiate and can grow in the through-thickness direction. The time 
required for corrosion to remove the compressive layers is calculated to be greater than the 
regulatory period. Further, if stress corrosion cracking were to initiate and grow through-wall, 
the cracks would be extremely tight and very limited in length (Section 6.3.7). Consequently, 
any water transport through the waste package or the drip shield (in the absence of oxide 
plugging) and any radionuclide egress through these tight waste package outer barrier cracks 
would be restricted to diffusive flow and, thus, would be very limited. In establishing the 
required level of confidence for the stress corrosion cracking model, the following criteria were 
considered: 
Is the model extrapolated over large distances, spaces, or time frames? 
Yes. The stress corrosion cracking model is extrapolated over the entire repository footprint 
and over the entire regulatory compliance period. 
Does the model have large uncertainties? 
No. While there is uncertainty in the parameters used in the stress corrosion cracking model, 
these uncertainties are not large. 
Will the model be used to demonstrate compliance or licensing positions? 
Yes. The stress corrosion cracking model is used as an input to WAPDEG, which provides 
realistic waste package and drip shield stress corrosion cracking degradation estimates as 
a function of time under the exposure conditions anticipated in the potential repository. 
The stress corrosion cracking model inputs to IWPD support several primary factors and 
TSPA-LA components. 
Will the output of the model have impacts (positive or negative) on TSPA-LA dose calculation 
results? 
Yes. Although the effect of stress corrosion cracking penetrations in the drip shield and waste 
package outer barrier are estimated to have relatively small impacts on TSPA-LA dose 
calculations, the stress corrosion cracking model is used as an input to WAPDEG that is 
used to provide realistic waste package and drip shield degradation estimates as a 
function of time under the exposure conditions anticipated in the repository. The 
WAPDEG model supports several primary factors and TSPA-LA components. 
Consistent with the above and as per Technical Work Plan for: Regulatory Integration Modeling 
and Analysis of the Waste Form and Waste Package (BSC 2004 [DIRS 171583], Section 2.2), 
waste package models must obtain Level III validation, which requires that the model must meet 
at least two of the validation activities listed in Section 5.3.2c of AP-SIII.10Q, Models. This 
requirement is met for the Alloy 22 waste package outer barrier material. 
However, as described in more detail in Section 6.3.7, for the drip shield, even if stress corrosion 
cracking propagates through-wall, the seepage diversion function of the drip shield will remain 
intact. On this basis, stress corrosion of the drip shield is categorized as an excluded 

 
l 
 7-5 
FEP (2.1.03.02.0B) and thus is not considered further with respect to the SDFR crack growth 
model validation activities (Section 7.4). 
Furthermore, although the threshold stress intensity factor and the threshold stress for SCC 
initiation are not models per se, rather they are parameters or criteria that are coupled to the 
SDFR Model, it is important to demonstrate a defensible technical basis for each parameter. 
Consequently, a non-validation related activity (Activity Four) is included for each of these 
parameters for both Titanium Grade 7 and Alloy 22 materials. 
7.3. VALIDATION ACTIVITIES AND ASSOCIATED CRITERION USED TO 
DETERMINE THAT THE REQUIRED LEVEL OF CONFIDENCE HAS BEEN 
OBTAINED 
The stress corrosion cracking model involves the slip dissolutionfilm rupture (SDFR) crack 
growth model, the threshold stress intensity factor (KISCC) for crack growth, and the threshold 
stress for crack initiation, all of which are described in peer-reviewed scientific journals. As 
described in Section 7.2, the threshold stress intensity factor and the threshold stress for SCC 
initiation are not models per se, but rather are parameters or criteria that are coupled to the SDFR 
model. However, while validation of these parameters is not required per AP-SIII.10Q, it is 
important to demonstrate a defensible technical basis for each parameter. 
With respect to the SDFR SCC crack growth rate model, validation is done through the use of 
the validation activities defined in AP-SIII.10Q, Section 5.3.2c. Two validation activities (VA) 
were selected, which are consistent with Technical Work Plan for: Regulatory Integration 
Modeling and Analysis of the Waste Form and Waste Package (BSC 2004 [DIRS 171583], 
Table 2-1). They are in summary, 1) quantitative comparisons of crack growth rate model 
predictions to observed rates available in the peer-reviewed published literature (AP-SIII.10Q, 
Section 5.3.2.c.3), and 2) demonstration of consistency of crack growth rate model predictions to 
Q data generated by the Project (AP-SIII.10Q, Section 5.3.2.c.1). In addition, a third SDFR 
validation activity, corroboration of results with an alternative mathematical model, 
(AP-SIII.10Q, Section 5.3.2.c.2) is implemented. This activity is in addition to the two identified 
in Technical Work Plan for: Regulatory Integration Modeling and Analysis of the Waste Form 
and Waste Package (BSC 2004 [DIRS 171583]). These three SDFR model-related validation 
activities are listed below and are consistent with those identified in AP-SIII.10Q, 
Section 5.3.2.c. 
In addition, Activity Four demonstrates the appropriateness of the parameters for the threshold 
stress intensity factor and the threshold stress for SCC initiation. 
These various activities, listed below, will be compared with the criterion listed in Table 2-1 of 
Technical Work Plan for: Regulatory Integration Modeling and Analysis of the Waste Form and 
Waste Package (BSC 2004 [DIRS 171583]) (i.e., the Corroborating data must match 
qualitatively). 
Activity One: Demonstrate that the crack growth rates, predicted by the film rupture 
repassivation crack growth model, are consistent with observed rates published in the peerreviewed 
literature (AP-SIII.10Q, Section 5.3.2.c.3). 

 
l 
 7-6 
Activity Two: Demonstrate that the crack growth rates, predicted for Alloy 22 and Titanium 
Grade 7 by the film rupturerepassivation crack growth model, are consistent with experimental 
rates obtained from data not used to develop the model (AP-SIII.10Q, Section 5.3.2.c.1). 
Activity Three: Demonstrate that the crack growth rates, predicted by the film rupture 
repassivation crack growth model, are consistent with growth rates predicted by an alternative 
mathematical model (AP-SIII.10Q, Section 5.3.2.c.2). 
Activity Four: Demonstrate that the establishment of the threshold stress intensity factor (KISCC) 
and threshold stress represent an acceptable approach for Alloy 22 and Titanium Grade 7 under 
environmental conditions relevant to the waste package and drip shield, respectively. 
This latter activity (Activity Four) is applicable to both the threshold stress intensity factor 
parameter (KISCC) and the threshold stress criterion for SCC initiation on a smooth surface 
(i.e., in the absence of fabrication defects such as weld flaws). While the technical work plan 
states VA = NA, this report provides a defensible basis consistent with VA 1 (AP-SIII.10Q, 
Section 5.3.2.c.1, compare with laboratory results). Since there is no relevant theoretical basis in 
the literature to describe these parameters, they are each selected based on a conservative 
empirical approach. Therefore, they do not require validation and the technical work plan 
(Table 2-1) activity listed does not cite an AP.SIII.10Q, Section 5.3.2.c specific model validation 
activity. However, a description of the defensible and conservative basis for selection of the 
values for each of these parameters is described in Section 7.4 to provide additional confidence. 
To meet the model validation acceptance criterion (corroborating data must match qualitatively) 
for the SDFR model, it is informative to consider what is the indicated range of scatter and, 
based on this, what is a reasonable match between experimentally generated crack growth rate 
results and model predictions. Examination of the literature dealing with measured versus 
predicted stress corrosion cracking growth rates, indicates that in general, crack growth rates 
within two or three orders of magnitude may be considered to be within reasonable agreement. 
For example, see work by Andresen (1991 [DIRS 166965], Figures 2, 37, and 38) and Andresen 
(2002 [DIRS 166967], Figure 1) for the nickel alloys (Alloys 600, 82, and 182), exposed to 
288C water environments where it is evident that scatter of this magnitude occurs. The issue of 
reasonable agreement is discussed further in Section 7.4.1. However, considering the spread in 
measured versus predicted rates observed in the literature, terms such as consistent and 
reasonable are used in the model validation section to define a qualitative match. 
7.4 COMPARISON OF ACTIVITIES PERFORMED TO GENERATE CONFIDENCE 
IN THE MODEL WITH MODEL VALIDATION CRITERION 
According to Technical Work Plan for: Regulatory Integration Modeling and Analysis of the 
Waste Form and Waste Package (BSC 2004 [DIRS 171583], Section 2.2.5), the developed 
model is to be validated in accordance with the activities described in the previous section with 
specific activities to be performed to generate the desired confidence in the model or model 
parameter (i.e., to meet the criterion listed in the technical work plan). All activities are 
applicable to Alloy 22, whereas only Activity Two (comparison of experimental crack growth 
rates with model predictions) and Activity Four (related to an acceptable approach for 
establishment of a threshold stress and threshold stress intensity factor) are applicable to the drip 

 
l 
 7-7 
shield (Titanium Grade 7). However, as described in Section 6.3.7, the only stress corrosion 
cracking breach criterion for the Titanium Grade 7 drip shield is the threshold stress (for stress 
corrosion cracking initiation). Thus, whether from rockfall or from direct seismic-related 
residual stresses as described in Appendix B, if the resultant stresses exceed the threshold stress 
criteria, the crack growth rate is such that breach (i.e., through-wall stress corrosion cracking) 
occurs essentially instantaneously, consistent with a threshold stress intensity factor value of 
zero. Further, as described in more detail in Section 6.3.7, even if stress corrosion cracking 
propagates through-wall, the seepage diversion function of the drip shield will remain intact. On 
this basis, stress corrosion of the drip shield is categorized as an excluded FEP (2.1.03.02.0B and 
is not considered further in this SDFR model validation (Section 7.4), except with respect to 
establishment of a threshold stress as described in Activity Four (confidence building, not 
validation). This section shows that the required confidence level for the waste package related 
SDFR model (Level III) has been achieved because all activities specified in the technical work 
plan are fully (or very conservatively) complied with to generate confidence in the model and the 
validation criterion listed in Table 2-1 (Corroborating data must match qualitatively) has been 
successfully met. 
7.4.1 Activities Performed for Validating the SDFR Model Using Peer-Reviewed 
Literature 
The applicable Activity relating to validation of the SDFR model is Activity One listed in 
Section 7.3: 
Demonstrate that the crack growth rates, predicted by the film rupture 
repassivation crack growth model, are consistent with observed rates 
published in the peer-reviewed literature. 
The film rupturerepassivation crack growth model terminology is often used when referring to 
the slip dissolutionfilm rupture (SDFR) model and the two are equivalent. The input parameter 
(exponent n) of this crack growth rate prediction model (Equation 19), used to compare model 
predicted rates with corresponding literature values, is that obtained for stainless steel as 
documented in Section 6.3.3. The model predictions are compared to results, already published 
in peer-reviewed literature, that were calculated using the same input parameters. This ensures 
that the model details and calculation methods described in the earlier version or in Section 6 
yield results fully consistent with the peer-reviewed journal-published values. The activities 
performed to satisfy Activity One and to achieve the desired confidence in the model are 
discussed. 
As documented in Section 6.3.3, input parameter (exponent n) obtained for sensitized Stainless 
Steel Type 304 is 0.54. Figure 6-4 indicates that crack growth rates predicted by the slip 
dissolutionfilm rupture crack growth model are in reasonable agreement with observed rates 
published in the peer-reviewed literature for stainless steel. Figure 7-1 indicates that the range of 
the prediction error (i.e., the ratio of the difference of the predicted and the observed values 
divided by the observed value) for the majority of results is 3 to +3 and, if including the 
extreme results, is 5 to +7 with positive ratio indicating overprediction and negative ratio, 
underprediction. It is, therefore, concluded that the prediction error, as discussed in the previous 
statement, is well within 2 orders of magnitude and, thus, within the required accuracy 

 
l 
 7-8 
prescribed in Section 7.3. This has ensured that the model details and calculational methods 
yield results fully consistent with the peer-reviewed journal-published values and are, therefore, 
qualitatively corroborated. 
Source: Ford and Andresen 1988 [DIRS 118611], Figure 8. 
Figure 7-1. Frequency Distributions of the Ratio of the Calculated to Observed Crack Growth Rates for 
Stainless Steel Type 304 
7.4.2 Activity Performed for Validating the SDFR Model Applicable to Alloy 22 using 
Independently Obtained Experimental Data 
The applicable activity is Activity Two, Section 7.3: 
Demonstrate that the crack growth rates, predicted for Alloy 22 and Titanium 
Grade 7 by the SDFR crack growth model, are consistent with experimental 
rates. 

 
l 
 7-9 
Having established the validity of the model predictions of crack growth rate versus stress 
intensity for stainless steel, the model is then utilized to predict selected crack growth rates as a 
function of stress intensity for Alloy 22 utilizing model input parameters developed specifically 
for Alloy 22 using qualified experimental data generated under an approved test program at the 
General Electric Global Research Center. 
Validity and predictive capacity of the model developed for Alloy 22 is then established if crack 
growth rates predicted for this material by the SDFR crack growth model are in reasonable 
agreement (qualitatively consistent) with growth rates determined independently under an 
approved test program at Lawrence Livermore National Laboratory. The activities performed to 
satisfy Activity Two listed in Section 7.3 and to achieve the desired confidence in the model, in 
accordance with Section 2.2.2 of the technical work plan (BSC 2004 [DIRS 171583]), are 
discussed below. 
7.4.2.1 Stress Corrosion Cracking Behavior of Nickel-Chromium Base Alloys at 
Temperatures Relevant to the Waste Package 
In addition to stainless steels, the model has been shown to apply to several nickel-based alloys, 
including Alloy 600, a nickel-based alloy with lower chromium-content than Alloy 22. 
Table 7-2 lists nominal composition for Alloys 600, 182 and 82 and specified composition for 
Alloy 22. 
Table 7-2. Nominal Chemical Composition of Several Ni-Cr Base Alloys (wt %) 
Alloy 
Composition 
Alloy 22 
(ASTM B 575-94 
[DIRS 100497]) 
Alloy 600 
(UNS N06600)* 
Alloy 182 (AWS 
ERNICRFE-3)* 
Alloy 82 (AWS 
ERNICR-3)* 
Element 
C 0.015 max. 0.07 0.04 0.02 
Co 2.5 max. - - - 
Cr 20-22.5 16.1 14.0 19.6 
Fe 2.0-6.0 9.4 6.9 1.2 
Mn 0.50 max. 0.2 7.9 2.9 
Mo 12.5-14.5 0.2 - - 
Ni Balance 73.7 ~68.5 73.1 
P 0.02 max. 0.01 0.013 0.003 
S 0.02 max 0.002 0.003 0.001 
V 0.35 max 0.03 - - 
W 2.5-3.5 - - - 
NOTE: *Heat compositions from (Andresen 1991 [DIRS 166965], Table I). 
To apply this model to Alloy 22 under relevant conditions, the following discussion shows that 
(1) results demonstrating that the observation of similar stress corrosion cracking growth 
behavior of stainless steel and Alloy 600 also applies over the range of temperatures relevant to 
the waste package (~50C to 200C); and (2) results are consistent with the model for other 
nickelchromium alloys with higher chromium content than Alloy 600 (similar to Alloy 22). 
Demonstration of the applicability of the model to these other nickelchromium alloys supports 
the applicability of the SDFR model to Alloy 22 with respect to chromium, which is the alloy 

 
l 
 7-10 
addition responsible for formation of the protective Cr2O3-passive film for stainless steels and 
chromium-containing nickel-based corrosion-resistant passive alloys including Alloy 22 
(DTN: LL021105312251.023 [DIRS 161253], Section 3.3). Specifically, in addition to stainless 
steel (i.e., activities performed to meet Activity One), the SDFR model has been validated for a 
range of alloys, including irradiated stainless steels; Inconel 600 and 182 nickel-chromium base 
alloys; and, subsequently, the higher chromium content nickelchromium-base alloy, Alloy 82 
(UNS N06082) (Section 6.3.4), where extensive observations are presented to indicate that there 
is ample reason to conclude that stress corrosion cracking of nickel-chromium-molybdenum base 
Alloy 22 occurs by the same fundamental mechanism characterized by the SDFR stress 
corrosion cracking model, but with alloy specific values for the A and n parameters. 
Andresen and Ford (1994 [DIRS 118581], p. 62) indicated that the SDFR model has been 
applied to stainless steels, low alloy and carbon steels, ductile nickel alloys, and irradiated 
stainless steels. Ford and Andresen (1988 [DIRS 118611], p. 789) also used the SDFR model for 
the nickel-chromium based alloys Inconel 600/182. Further, as indicated in Section 6.3.3, it was 
determined that the SDFR model (using the Stainless Steel Type 304 A versus n relationship 
in 288C water) was statistically valid for the chromium-containing, nickel-based Alloys 600 and 
182 over a range of anionic impurity concentrations (Ford and Andresen 1988 [DIRS 118611], 
Figure 10). Subsequently, Andresen (1991 [DIRS 166965], Figure 37), used the SDFR model 
for comparison of crack growth rate predicted versus measured values with reasonable 
agreement for the higher chromium content-nickel-based alloy, Alloy 82 (UNS N06082). 
Alloy 82 (18% to 22% Cr, UNS N06082) overlaps Alloy 22 (20% to 22.5% Cr) 
(DTN: MO0003RIB00071.000 [DIRS 148850], p. 2) in chromium content. Analyses indicate 
that the inner, protective corrosion films that form in the passive potential range on such nickelbased, 
chromium-containing alloys with greater than about 15% chromium contain a very thin 
passive film layer of primarily Cr2O3 (with some nickel content) at the oxidealloy interface 
(Pensado et al. 2002 [DIRS 166944], p. 2-2). Such a thin, passive Cr2O3 film possesses similar 
repassivation kinetics (depending on actual chromium content) and mechanical properties 
(e.g., fracture strain) over the range of nickelchromium-based alloys of interest. This is 
consistent with the model having been shown to apply or to give reasonable predictive results for 
a range of nickel-based alloys with chromium contents spanning the Alloy 22 compositional 
range. 
Further, there is general correspondence (reasonable statistical agreement) between the observed 
stress corrosion cracking growth rate temperature dependencies for sensitized Stainless Steel 
Type 304 and Alloy 600 over the temperature range of most interest (~50C to 200C) when 
compared under comparable stress intensity factor and environmental conditions (Andresen 1993 
[DIRS 166966], Figures 15 and 16). For example, from examination of Figure 6-5 in 
Section 6.3.4 (Andresen 1993 [DIRS 166966], Figure 15), it is seen that crack growth rates for 
sensitized Stainless Steel Type 304 and Alloy 600 follow the same temperature dependency with 
reasonably similar crack growth rates over a temperature range from about 25C to 275C, which 
is broader than the temperature range of most interest (~50C to 200C) stated above. 
In addition to the similarities in composition and mechanical properties, as indicated earlier in 
this section, for the passive films present on this class of face-centered cubic crystal structure 
austenitic alloys, (i.e., austenitic stainless steels and nickelchromium-based alloys such as 
Alloys 600, 82, and 22), the expected microdeformation modes of the alloys are also comparable, 

 
l 
 7-11 
based on examination of literature values for stacking fault energies (SFE) (Gordon 2004 
[DIRS 167027]). A low value of SFE tends to promote coplanar dislocation arrays (promoting 
local stress buildups that can more easily rupture the passive surface film at slip offsets) whereas 
high SFE values promote dislocation tangles that tend to diffuse local stress buildups. These 
alloys possess a face-centered cubic-crystallographic lattice structure and have similar relatively 
low values of estimated SFE ranging from about 20 to 30 ergs/cm2 for Stainless Steel 
Types 304L and 316L to about 80 ergs/cm2 for Alloy 600 with the estimated value for Alloy 22 
being about 65 ergs/cm2. This range is relatively low compared to published values of about 
340 ergs/cm2 for pure nickel or nickel alloys with much lower chromium contents (Gordon 2004 
[DIRS 167027], Table 1). Although lower values of SFE can promote microstress and strain 
buildups that may accelerate stress corrosion cracking initiation, the relatively high local 
deformation at a stressed crack or weld flaw tip is likely to lead to relatively high local strains 
and to overwhelm the effect of SFE on micro stress or strain buildups with respect to stress 
corrosion cracking propagation. 
7.4.2.2 Stress Corrosion Cracking Behavior of Alloy 22 at Higher Temperatures 
(~288C) 
Other General Electric Global Research Center results are described for Alloy 22 tested at higher 
temperatures (~288C) illustrating that Alloy 22 follows similar behavior to Stainless Steel 
Types 304 or 316 and Alloy 600 at similar temperatures (~288C), further supporting the 
argument that the initial application of the model to BWR coolant temperatures of ~288C is 
consistent with the application at lower waste package temperatures. The results were discussed 
in Section 6.3.4 and are summarized below. 
As the SDFR was initially developed for stainless steels and nickel-based alloys Inconel 600 
and 182 under higher temperature (~288C) light water reactor coolant conditions, additional 
confidence in the applicability of this model to Alloy 22 can be gained from observation of the 
response of Alloy 22 under similar conditions. Test results from DTN: MO0402GEA22SCC.000 
[DIRS 167911] indicate the crack growth rate response of Alloy 22 exposed to 288C relatively 
pure water (2 ppm O2) is broadly consistent with other materials, such as Alloys 600 and 182 
(Andresen et al. 2002 [DIRS 166967]) and unsensitized austenitic stainless steel (Andresen et 
al. 2002 [DIRS 167762]) under these same conditions. The measured crack growth rates show a 
similar dependency to parameters like corrosion potential and water purity (sulfate). For 
example, in all test cases, the change in corrosion potential from ~ +0.2 VSHE to ~ 0.5 VSHE (due 
to a change from 2 ppm O2 to H2-deaerated water) causes a drop of at least one order of 
magnitude in the crack growth rate, as indicated by Table 6-3 in Section 6.3.4. Also, as 
expected, Alloy 22 shows crack growth rates under repository type oxidizing conditions (i.e., at 
0.2VSHE), which are about one order of magnitude lower than those of the other materials under 
identical test conditions, consistent with the higher n parameter values obtained for Alloy 22 
using Project-sponsored testing, Section 6.3.4, and demonstrating its superiority as a structural 
material under conditions where stress corrosion cracking is a concern. 

 
l 
 7-12 
7.4.2.3 Stress Corrosion Cracking Behavior of Alloy 22 in Other Relevant 
Environments 
Whereas the initial Alloy 22 crack growth rate data obtained at GE Global Research were 
generated in the pH ~13, BSW brine environment at 110C, the discussion that follows 
demonstrates that stress corrosion cracking growth rate results obtained at LLNL in other 
relevant environments, SAW (pH ~ 2.8]) and SCW (pH ~ 9 to 10) at about 95C as well as in 
BSW (pH ~13) at 100C, fall within the model uncertainty bands predicted by the SDFR model, 
providing further qualitative corroboration of the model applicability to Alloy 22 over the range 
of repository-relevant environments consistent with the stress corrosion cracking model 
validation criterion (corroborating data must match qualitatively) cited in Section 7.3. Citing all 
of these results strongly supports the use of the SDFR model for Alloy 22. 
The good crack growth rate predictive capability of Equation 19, benchmarked with the 
experimental results presented in Table 6-4, determined by direct measurements under an 
accepted Q test program at General Electric Global Research Center (GEGRC) 
(DTN: LL021105312251.023 [DIRS 161253]), has been validated with a separate set of 
measured crack growth rates (Table 7-3). These separate results are plotted in Figure 7-2 along 
with the initial GE crack growth rate measurements. This separate set of measured crack growth 
rates were collected using the reversing direct current crack growth measurement technique with 
compact tension type fracture mechanics specimens (loaded per ASTM E 399-90 
[DIRS 117480]) tested at LLNL (DTN: LL030300612251.035 [DIRS 166971]). As can be seen 
from Figure 7-2, there is good agreement between the LLNL data and the predictive curves and 
statistical limits based on the GE crack growth rate results (i.e., five data points summarized in 
Table 6-4). Table 7-4 shows that the prediction error ratio is in the range of -0.93 to 54.87. 
While the prediction error ratio is generally within the expected two orders of magnitude, the 
prediction model has a tendency of overprediction (with positive error ratio) (i.e., on the 
conservative side), rather than underprediction (with negative error ratio). Also, for specimen 
DCT-22, the measured growth rate is below the crack growth detection limit and, thus, the 
comparison between measured and predicted rates is not directly relevant. Furthermore, it can be 
seen from Figure 7-2 that measured data fall nicely between the two bounds representing two 
standard deviations of the mean value. The agreement between the prediction and measured data 
shown in Figure 7-2 provides important input to the validation of the SDFR model for Alloy 22, 
corroborating the excellent qualitative match between model predictions and independently 
measured Alloy 22 crack growth rates over a range of environments and pH values. 

 
l 
 7-13 
Table 7-3. Summary of LLNL Crack Growth Rates in Compact Tension Specimens 
Specimen 
ID 
Test 
Solution 
Nominal Test 
Temperature (C) 
Average 
Stress Intensity 
MPavm 
Crack Growth 
Rate (mm/sec) 
DCT-13 BSW-13 100 45.13 2.12E-09 
DCT-14 BSW-13 100 44.88 4.23E-09 
DCT-16 BSW-13 100 46.38 1.41E-09 
DCT-18 SAW 94 45.07 2.12E-10 
DCT-19 SAW 94 45.08 1.41E-11 
DCT-20 SCW 95 45.11 4.23E-10 
DCT-21 SCW 95 44.68 2.82E-11 
DCT-22 SCW 95 44.37 4.94E-12 
Source: DTN: LL030300612251.035 [DIRS 166971], Figure 6. 
Source: Plot from Figure 6-6 with initial test data for C144, C152, and C153 from DTN: LL021105312251.023 
[DIRS 161253] and LLNL test data from DTN: LL030300612251.035 [DIRS 166971]. 
Figure 7-2. Comparison of the SDFR Prediction Model and Measured Data for Alloy 22 

 
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 7-14 
Table 7-4. Comparison of Predicted and Measured Crack Growth Rates for Alloy 22 
Specimen 
ID 
Test 
Solution 
Nominal Test 
Temperature 
(C) 
Average 
Stress 
Intensity 
MPavm 
Measured 
Crack Growth 
Rate (mm/s) 
Predicted 
Crack Growth 
Rate (mm/s) 
Prediction 
Error Ratio 
DCT-13 BSW-13 100 45.13 2.12E-09 3.02E-10 -0.86 
DCT-14 BSW-13 100 44.88 4.23E-09 2.93E-10 -0.93 
DCT-16 BSW-13 100 46.38 1.41E-09 3.48E-10 -0.75 
DCT-18 SAW 94 45.07 2.12E-10 3.00E-10 0.42 
DCT-19 SAW 94 45.08 1.41E-11 3.00E-10 20.28 
DCT-20 SCW 95 45.11 4.23E-10 3.01E-10 -0.29 
DCT-21 SCW 95 44.68 2.82E-11 2.87E-10 9.18 
DCT-22 SCW 95 44.37 4.94E-12 2.76E-10 54.87 
NOTES: 1. Columns 1 through 5 are obtained from Table 7-3. 
2. Values in Column 6 are obtained from Equation 19 (in Section 6.3.4) with n = 1.304. 
3. Prediction error ratio (Col. 7) = (Col. 5  Col. 6) / Col. 5 
7.4.3 Corroboration of SDFR Model with Available Alternative Conceptual Models 
Although not a required model validation activity per the technical work plan (BSC 2004 
[DIRS 171583], Table 2-1), corroboration with available alternative conceptual models (ACMs) 
such as the coupled environment model, a mathematical model used to predict stress corrosion 
crack growth rates, can be used to validate the developed model. The alternative conceptual 
model is summarized, discussed, and contrasted with the base-case model. The developed basecase 
model should be comparable or more conservative than the alternative conceptual models. 
More details about alternative conceptual models are provided in Section 6.3.6. 
Corroboration with available alternative conceptual models, such as the coupled environment 
fracture model for stress corrosion cracking, was considered for the validation of the base-case 
model. Section 6.3.6 concludes that the slip dissolutionfilm rupture and the CEF models are 
capable of predicting the crack growth rate for stress corrosion cracking. However, the CEF 
model has a tendency of underestimating the crack growth rate as compared to the slip 
dissolutionfilm rupture model when both models were applied to predict the crack growth rate 
for Stainless Steel Type 304 in the boiling water reactor (BWR) environment (Figure 6-7). 
Comparison with experimental data summarized by Ford and Andresen (1988 [DIRS 118611], 
Figure 22) for crack propagation rate versus stress intensity factor for sensitized Stainless Steel 
Type 304 in fully aerated, high-purity water at elevated temperature indicated that the crack 
growth rate predicted by the CEF model (i.e., 3.2  10-9 cm/sec at 20 MPavm) is at the lower end 
of the range cited by Ford and Andresen (1988 [DIRS 118611]) and (Macdonald and Urquidi- 
Macdonald 1991 [DIRS 162702]). For this reason, the CEF model was not included for 
evaluation but only used to further validate the base case slip dissolutionfilm rupture model. 

 
l 
 7-15 
7.4.4 Activities Performed to Demonstrate the Technical Basis for the Selection of the 
Threshold Stress Intensity Factor and the Threshold Stress Parameter for SCC 
Initiation 
As indicated in Table 2-1 of Technical Work Plan For: Regulatory Integration Modeling and 
Analysis of the Waste Form and Waste Package (BSC 2004 [DIRS 171583]), these activities 
(listed as Activity Four) are not for model validation but rather are for demonstration of the 
establishment of an acceptable approach for determining KISCC and the threshold stress for SCC 
initiation under environmental conditions relevant to the waste package and drip shield. Thus, to 
provide additional confidence, a defensible technical basis for selection of each of these 
parameters is described in the following subsections. 
7.4.4.1 Activities Performed to Demonstrate the Technical Basis for the Threshold 
Stress Intensity Factor (KISCC) for Alloy 22 
As described earlier in Section 7.4, consideration of KISCC in the Titanium Grade 7 drip shield is 
not relevant since the value is effectively zero (i.e., once SCC is initiated in the drip shield as a 
result of rockfall or seismic damage, it is conservatively assumed to propagate through-wall 
instantly regardless of the through-wall KISCC values). 
In general, stress corrosion crack growth can occur at a rate, such as that predicted by the slip 
dissolutionfilm rupture (SDFR) model, only if the calculated stress intensity at any flaw of 
given dimensions of length and depth exceeds a threshold value known as KISCC. Since there is 
no accepted theoretical basis for deterministic calculation of KISCC, this parameter is 
conservatively determined by selecting a KI value corresponding to a conservative lower limit 
value for the crack growth rate, Vt. To accomplish this, the general form of the previously 
validated SDFR model (see Activities One, Two, and Three) (i.e., Equation 14 is used to 
calculate the stress intensity factor value corresponding to a crack growth rate equal to the 
general corrosion rate, Vgc, in Section 6.3.5). This calculated value is defined as KISCC. 
The theoretical basis for this approach is that if the crack growth rate equals the rate at which the 
surface recedes due to general corrosion, then it is not possible to maintain a sharp crack (the 
crack tip will blunt) and stress corrosion cracking will effectively arrest. Based on this crack 
blunting theory (Andresen and Ford 1994 [DIRS 118581], p. 62), it follows that any existing 
stress corrosion crack will not continue to grow (i.e., will arrest, if the crack growth rate is equal 
to or less than the general corrosion rate). If Vgc is the mean general corrosion rate, the threshold 
stress intensity factor KISCC can be calculated from Equation 20 (a rearrangement of 
Equation 14) of Section 6.3.5, which represents the SDFR model for the case of constant 
(noncyclic) stress (i.e., for the waste package sustained loading conditions): 
KISCC = (Vgc / A ) n / 1 (Eq. 20) 
The mean general corrosion rate, Vgc, based on Section 6.3.5, is 7.23 nm/yr. The threshold stress 
intensity factor for Alloy 22, accordingly, can be calculated and its distribution is listed in 
Table 6-6, based on the n value distribution shown in Table 6-5. In conclusion, Activity Four 
is satisfied since an acceptable, conservative KISCC value was obtained by setting the crack 

 
l 
 7-16 
growth rate in the validated SDFR model to a value equal to the mean general corrosion rate at 
the alloy surface. 
7.4.4.2 Activities Performed to Demonstrate the Technical Basis for the Threshold 
Stress for Alloy 22 and Titanium Grade 7 
Similar to the previously described establishment of a KISCC value, the purpose of this activity is 
to demonstrate a defensible technical basis for selecting a threshold-stress parameter for SCC 
initiation. Thus, Activity Four specifies the demonstration of an acceptable approach for the 
establishment of a threshold stress for SCC initiation for Alloy 22 and Titanium Grade 7 under 
environmental conditions relevant to the waste package and drip shield, respectively. 
Although the threshold stress concept is described in peer-reviewed journal papers, there is no 
firm accepted basis for calculating a threshold stress value for a given material or environment 
combination. The threshold stress is that value below which stress corrosion cracking will not 
initiate on a smooth metal surface. Therefore, as described in Section 6.2.1, a conservative, 
empirical approach is implemented to develop a defensible threshold-stress parameter. For the 
purpose of lifetime modeling, a smooth surface is one that contains microscopic defects 
associated with incipient environmental crack formation, or metallurgical or mechanical defect 
sites. The initial defect depth is taken as 0.05 mm, a value qualified for use in Section 6.2.1 
using AP-SIII.10Q, Section 5.2.1.k. Thus, when the metal surface stress exceeds the stress 
corrosion cracking threshold stress, SCC is initiated at these smooth surface microdefects. 
Once initiated, the crack may either reach the arrest state or the propagation phase, once the 
crack tip stress intensity factor exceeds the threshold KISCC value described above. Since it is 
necessary to experimentally establish the threshold stress values, a conservative approach is 
taken based on qualified experimental data. 
As addressed in Section 6.2.1, long-term SCC initiation stress measurement results have been 
obtained under constant active applied loading conditions using uniaxial tensile specimens 
covering a range of metallurgical conditions (Figure 4-1). These experimental measurements of 
crack initiation stress are presented in Figure 4-1 as the ratio of applied stress-to-yield strength 
(YS) versus time-on-test for specimens exposed in hot concentrated salt solution (pH = 10.3 
at 105C) designed to simulate the chemistry of concentrated Yucca Mountain ground water. 
Specimens have been on test for over 21,000 hours. It is indicated in Section 6.2.1 that Alloy 22 
exhibits excellent stress corrosion cracking resistance since failure was not observed for any of 
the 120 Alloy 22 specimens under applied stress ratios of about 2.0 (YS) for annealed material 
and 2.1(YS) for welded material. These stress ratios correspond to about 89% to 96% of the 
ultimate tensile strength. Alloy 22 was also found to be highly resistant to stress corrosion 
cracking initiation in slow strain rate tests and U-bend tests covering a broad range of 
environments. Titanium Grade 7, although still fairly resistant to stress corrosion cracking, 
experienced stress corrosion cracking failures at applied stress ratios at and above 1.1 (YS) in the 
constant load tests. However, it (and its analog, Titanium Grade 16) did not exhibit stress 
corrosion cracking in two- to five-year exposed U-bend specimen tests covering a range of test 
environments. Thus, it is evident that the threshold stress for Alloy 22 in relevant environments 
is significantly above the yield stress level whereas the value for Titanium Grade 7 is likely at or 
slightly above the yield strength value. 

 
l 
 7-17 
As described in Section 6.2.1, these high SCC-initiation threshold stress values are 
independently corroborated for both Alloy 22 and Titanium Grade 7 based on examination of a 
series of U-bend SCC-initiation specimens stressed at or above yield strength levels. These 
specimens were exposed in the LLNL Long Term Corrosion Test Facility in a range of relevant 
brine environments for times out to five years. In all cases, high magnification examination of 
the highest stressed portions of these specimens indicated no SCC initiation consistent with the 
constant load test results and with a threshold stress above the yield strength. 
In establishing a defensible safety factor, it is appropriate to consider other accepted precedents 
based on threshold or runout stress measurements used in general engineering practice. For 
example, the ASME code (ASME 1969 [DIRS 162446], p. 20) utilizes a reduction factor of 2 on 
stress when dealing with high cycle fatigue (i.e., the code-allowable threshold value is set at half 
the experimentally measured runout threshold value known as the endurance limit, which is the 
maximum stress below which a material can presumably endure an infinite number of stress 
cycles). In dealing with stress corrosion cracking rather than fatigue, it is considered appropriate 
to also use a conservative safety factor on the measured threshold values. Consequently, 
threshold stress values to be used are based on applying a conservative reduction factor of at 
least 2 on the measured threshold or runout stress ratio values obtained from the constant load 
tests described above. In addition, it is prudent to select a threshold stress value below the 
materials yield strength. Applying this philosophy and a reduction factor of 2.2, the threshold 
stress values selected are 0.9 (YS) for Alloy 22 and 0.5 (YS) for Titanium Grade 7. Based on the 
foregoing discussion, Activity Four, the demonstration of a defensible technical basis for the 
selection of the threshold stress for SCC initiation for Alloy 22 and Titanium Grade 7 has been 
satisfied. 

 
l 
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INTENTIONALLY LEFT BLANK 

 
l 
 8-1 
8. CONCLUSIONS 
In this section, output of the base-case stress corrosion cracking model is discussed. Output of 
the seismic crack density model is discussed in Appendix B, Section B8. 
8.1 CONCLUSION 
This document provides a detailed description of the process-level models and the associated 
outputs developed for use in the performance assessment of the Alloy 22 waste package outer 
barrier subjected to stress corrosion cracking due to weld-induced stress in the final closure lid 
welds. All the welds with the exception of the final closure lid welds are subjected to solution 
heat treatment to relieve the residual tensile stresses when the entire waste package is heat 
treated before the loading of spent fuel elements. It is recognized that dynamic loads resulting 
from unlikely seismic events have the potential of leading to plastic upsets and resultant 
sustained residual tensile stresses that may initiate cracks and drive them through the wall. 
Stress corrosion cracking through-wall propagation criteria governing seismic initiated stress 
corrosion cracking have been developed for the waste package material (i.e., Alloy 22). The 
breach criteria are based on a stress threshold as discussed in Section 6.2.1. Seismic stress 
corrosion cracking is discussed further in Appendix B. 
The drip shield is excluded from the stress corrosion cracking evaluation because the drip shield 
is annealed to relieve the weld residual stress and stress corrosion cracking resulting from 
rockfall will result in very tight crack openings that will become plugged with oxide and thus 
will not degrade the water diversion function of the drip shield (Section 6.3.7). The only 
remaining issue of concern for stress corrosion cracking associated with the drip shield is the 
potential for crack initiation due to plastic deformation induced residual stress caused by unlikely 
seismic events. Through-wall crack penetration criteria governing seismic initiated residual 
stress for the drip shield material (i.e., Titanium Grade 7) are based on a stress threshold, which 
is discussed in Section 6.2.1. Once initiated, stress corrosion cracking is treated as being 
through-wall. The Stainless Steel Type 316 inner barrier of the waste package is excluded from 
the stress corrosion cracking evaluation because the TSPA-LA does not take credit for the inner 
barrier. 
The base-case slip dissolutionfilm rupture model relates stress corrosion cracking initiation and 
subsequent crack advance to the metal oxidation that occurs when the protective film at the crack 
tip is ruptured. The slip dissolutionfilm rupture model can be applied to assess the breach (or 
the lack of it) of the waste package due to the stress corrosion cracking crack propagation for 
given manufacturing cracks (e.g., weld flaws) or cracks initiated by the combined effects of 
stress and environment, or both. The threshold stress intensity factor (SIF) is based on the theory 
that there exists a threshold value (KISCC) for the stress intensity factor such that there is no 
growth of a preexisting crack or flaw having a stress intensity factor less than the threshold 
value. The threshold SIF provides a criterion for determining if a stress corrosion cracking crack 
will reach an arrest state or enter a propagation phase. 
The model validation is accomplished by comparing experimental measurements of key model 
parameters to data measurements and corroborative data available from the open scientific 

 
l 
 8-2 
literature and by comparing with another alternative conceptual model. Uncertainty and 
variability associated with model parameters are assessed. 
The application of the stress corrosion cracking models to the waste package and drip shield also 
requires input of weld residual stress profiles and stress intensity factor profiles along with 
uncertainty and variability. These input data have been developed for the 25-mm outer lid 
(subjected to laser peening) and the as-welded 10-mm middle lid (which has a through-wall 
stress distribution similar to the currently proposed 12.7 mm (1/2 in.) middle lid thickness) and 
are reported in this section as output data. This report also provides other outputs needed as 
input for a complete TSPA-LA for the degradation of the waste package due to stress corrosion 
cracking effects in the following areas: threshold stress for crack initiation and an estimate of 
crack opening size. In addition, a summary of size, density, and orientation distributions for 
manufacturing flaws or defects, which are technical product output of the calculation Analysis of 
Mechanisms for Early Waste Package/Drip Shield Failure (BSC 2004 [DIRS 170024]), is 
provided in Section 6.2.2, but is not part of the technical product output. 
8.2 COMPLIANCE WITH YMP ACCEPTANCE CRITERIA 
Yucca Mountain Review Plan, Final Report (NRC 2003 [DIRS 163274]) contains Acceptance 
Criteria (AC) intended to establish the basis for the review of the material contained in the 
License Application. As this report serves, in part, as the basis for the License Application, it is 
important the information contained herein conforms to those same Acceptance Criteria. 
This report addresses the degradation of two components of the engineered barriers, the waste 
package and drip shield. Based on the engineered barrier role of the waste package and the drip 
shield, the processes involved with their degradation, and the potential impact of their 
degradation, the YMRP Acceptance Criteria applicable to this report are identified in Technical 
Work Plan for Regulatory Integration Modeling and Analysis of the Waste Form and Waste 
Package (BSC 2004 [DIRS 171583], Table 3-1) and are delineated below in italics. 
A discussion of how this report addresses appropriate criteria follows each Acceptance Criterion, 
coupled with an indication of where within the report the appropriate information can be found. 
8.2.1 System Description and Demonstration of Multiple Barriers 
The waste package and the drip shield meet the definition of a barrier in 10 CFR 63.2 
[DIRS 156605]. The following acceptance criteria can be found in Section 2.2.1.1.3 of Yucca 
Mountain Review Plan, Final Report (NRC 2003 [DIRS 163274]). 
Acceptance Criterion 1  Identification of Barriers is Adequate 
Barriers relied upon to achieve compliance with 10 CFR 63.113(b), as 
demonstrated in the total system performance assessment, are adequately 
identified and clearly linked to their capability. 
This report addresses the system known as the engineered barrier system (EBS) and the barriers 
created by the waste package (WP) and the drip shield (DS). The engineered barrier system 
components are identified in Section 1.1. The drip shield barrier is to contribute to waste 
isolation by keeping seepage waters and dropping rocks away from the waste package for its 

 
l 
 8-3 
lifetime and, when breached by stress corrosion cracking, by reducing the contact of water with 
the waste package. The waste package barrier is to contribute to waste isolation by keeping 
water away from the waste for its lifetime and, when breached, by reducing the contact of water 
with the waste and radionuclide release rate from the waste. 
Acceptance Criterion 2  Description of Barrier Capability Is Acceptable 
The capability of the identified barriers to prevent or substantially reduce the 
movement of water or radionuclides from the Yucca Mountain repository to the 
accessible environment or prevent the release or substantially reduce the release 
rate of radionuclides from the waste is adequately identified and described: 
(1) The information on the time period over which each barrier performs its 
intended function, including any changes during the compliance period, is 
provided; 
(2) The uncertainty associated with barrier capabilities is adequately described; 
(3) The described capabilities are consistent with the results from the total system 
performance assessment; 
(4) The described capabilities are consistent with the definition of a barrier at 10 
CFR 63.2. 
The drip shield barrier contributes to waste isolation by keeping seepage waters and dropping 
rocks away from the waste package for its lifetime and, when breached by stress corrosion 
cracking, by reducing the contact of water with the waste package. The waste package barrier 
contributes to waste isolation by keeping water away from the waste for its lifetime and, when 
breached, by reducing the contact of water with the waste and radionuclide release rate from the 
waste. The drip shield barrier capability is addressed in this report principally in Section 6.3.7. 
The waste package barrier function of isolating the waste from water is addressed throughout this 
report and more specifically in Sections 6.4.2.1, 6.4.5, and 8.3. Although SCC can lead to waste 
package barrier breach at the outer closure lid weld, stress mitigation of this weld (Section 6.4.5) 
is calculated to extend the barrier lifetime beyond the regulatory period. 
Acceptance Criterion 3  Technical Basis for Barrier Capability is Adequately Presented. 
The technical bases are consistent with the technical basis for the performance 
assessment. The technical basis for assertions of barrier capability is 
commensurate with the importance of each barriers capability and the 
associated uncertainties. 
As the Acceptance Criteria delineated above address the overall description and capability of the 
engineered barriers as a unit, compliance with these criteria are addressed partially in this report 
and more fully in other reports. The technical basis for the drip shield barrier capability is 
documented in Sections 6.3.7, 7.3, and 7.4 and for the waste package barrier capability in 
Sections 7.3, 7.4, and Appendix B, Section B7. 

 
l 
 8-4 
8.2.2 Degradation of Engineered Barriers 
The following acceptance criteria can be found in Section 2.2.1.3.1.3 of Yucca Mountain Review 
Plan, Final Report (NRC 2003 [DIRS 163274]). 
Acceptance Criterion 1  System Description and Model Integration are Adequate 
(1) TSPA adequately incorporates important design features, physical phenomena 
and couplings and uses consistent assumptions throughout the degradation of 
engineered barriers abstraction process; 
The models and analyses addressed in this report accurately reflect the relevant waste package 
design features as discussed in Sections 6.3.4, 6.4.2, and 6.4.3 of the main body of the report and 
Appendix B in Sections B1, B6, B.6.1, B.6.2, and B.6.4, and the drip shield in Sections 1.1 
and 6.3.7. 
(2) Abstraction uses assumptions, technical bases, data and models that are 
appropriate and consistent with [those used] in other abstractions. 
Not applicable. 
(3) The descriptions of the engineered barriers, design features, degradation 
processes, physical phenomena, and couplings that may affect the degradation of 
the engineered barriers are adequate. 
Throughout this report, detailed descriptions of the relevant design features (waste package in 
Section 6.4 and drip shield in Section 6.3.7), degradation processes (waste package and drip 
shield in Sections 1.1, 6.2, and 6.3), physical phenomena (Section 6.3.2 for the waste package 
and Section 6.3.7 for the drip shield), and couplings (Sections 1.1 and 6.3.7) that may affect the 
degradation of the engineered barriers are provided. These descriptions are consistent with the 
information delineated elsewhere in other reports and are adequate for their intended purposes 
(i.e., to enable the modelers to develop and implement appropriate models and to enable the 
reviewer to understand the bases for the analytical activities performed by the applicant and the 
results thereof.). 
(4) Initial and boundary conditions are propagated consistently throughout the 
abstraction process. 
Throughout this report, relevant initial and boundary conditions for the performed analyses (i.e., 
waste package closure configuration, welding process, heat treatments, anticipated temperature, 
pressure) are used in a manner that is consistent with the data received from other abstractions 
and models. Examples can be found in Sections 6.3 and 6.4. 
One FEP was identified related to the potential degradation of the waste package and drip shield. 
Section 6.6 indicates the waste package stress corrosion cracking FEP was included. Table 6-13 
provides the location where an explanation related to these decisions is discussed. 

 
l 
 8-5 
(6) Guidance in NUREG 1297 and NUREG 1298 [re: Expert Elicitation] are 
followed. 
Not applicable. 
Acceptance Criterion 2  Data Are Sufficient for Model Justification 
(1) Parameters used to evaluate the SCC degradation of EBS are adequately 
justified; 
The input data and parameters used for the performance of the waste package and drip shield 
stress corrosion cracking degradation models and model related parameters came, primarily, 
from four sources: 
 Other analysis models performed for the Yucca Mountain Project 
 Laboratory experiments and tests performed for the project 
 Industry reviewed and accepted technical or scientific reports and papers 
 Industry handbooks. 
Justification for the use of specific parameters is typically provided in the section in which the 
parameter is initially discussed (Section 4.1), used (Sections 6.2 and 6.3) or in the source 
document for the specific parameter. As a result, the parameters used for the analysis have been 
adequately justified. 
(2) Sufficient data have been collected to establish initial and boundary 
conditions; 
Extensive scientific investigations and experiments have been performed to develop the data 
necessary to support the analyses provided in this report. In those instances where insufficient 
data was available for the specific materials used for the waste package or drip shield stress 
corrosion cracking degradation, data on alloys known to be analogous to those anticipated in the 
waste package were used with conservative assumptions to provide the basis for the performed 
analyses. Initial and boundary conditions have been adequately and appropriately established 
and justified. 
(3) Data on the degradation of the engineered barriers (predominately stress 
corrosion cracking and to a lesser extent general corrosion and phase stability) 
are based on laboratory measurements, industrial and/or natural analogs and 
tests designed to replicate anticipated conditions. As appropriate, sensitivity or 
uncertainty analyses are provided and are shown to be adequate. 
Data related to the various potential drip shield and waste package degradation modes (in 
particular for stress corrosion cracking and to a lesser extent for general corrosion and phase 
stability) are discussed in various subsections throughout this report. Specifically, the data 
associated with the drip shield is discussed in Sections 6.2.1 and 6.3.7 and with the waste 
package in Sections 6.2.1, 6.3.4, and Appendix B. 

 
l 
 8-6 
(4) Degradation models and related parameters for the applicable processes are 
adequate. For example, the SCC propagation model (SDFR Model), the 
threshold SCC initiation stress parameter and the threshold stress intensity factor 
parameter are described in significant detail. The SDFR Model is applied 
specifically to the waste package outer barrier material and the threshold SCC 
initiation stress criterion to both the waste package and the drip shield. Effects of 
general corrosion and phase stability on SCC are given appropriate 
consideration and treatment relative to their effect on SCC susceptibility. 
The various stress corrosion cracking models (i.e., the SDFR model and the alternative CEF 
model) related to potential waste package stress corrosion cracking crack propagation are 
discussed in Section 6.3 and waste package and drip shield stress corrosion cracking crack 
initiation parameters are discussed in detail in various sections throughout this report. 
Specifically, the SCC approach associated with breaching of the drip shield is discussed in 
Sections 6.2.1 and 6.3.7, and the modeling of the waste package outer barrier stress corrosion 
cracking is discussed in Sections 6.2 and 6.3. 
Acceptance Criterion 3  Data Uncertainty is Characterized and Propagated Through The 
Model Abstraction 
(1) Models use parameter values, assumed ranges, probability distributions 
and/or bounding assumptions that are technically defensible, reasonably account 
for uncertainties and variabilities, and do not result in under-representation of 
the risk estimate. 
Each of the models and related SCC initiation and crack arrest criteria developed in this report 
uses parameter values, assumed ranges, probability distributions or bounding assumptions, or 
both, that are technically defensible, reasonably account for uncertainties and variabilities, and 
do not result in under-representation of the risk estimate. In each situation, discussion and 
consideration of the uncertainties associated with specific data are addressed in detail. Examples 
include the discussion of the range of expected residual stress variation, associated data and data 
uncertainty in Section 6.4.5, the development of the threshold stress intensity factor, associated 
data and data uncertainty is discussed in Section 6.3.5, and the modeling of the Alloy 22 stress 
corrosion cracking growth rate, associated data, and data uncertainty are addressed in 
Section 6.3.4. 
(2) Appropriate parameters, based on techniques that may include laboratory 
experiments, field measurements, and industrial analogs are used. 
The SDFR model, and related SCC initiation and crack arrest criteria addressed in this report use 
data and parameters that have been developed based on a variety of techniques including 
laboratory experiments, and industrial analogs. Examples of each category include: 
 The use of iron and nickelchromium-based industrial alloy crack growth rate data 
experimentally developed or compiled from the literature for the study of stress 
corrosion cracking propagation rates in water containing oxygen as a function of 
temperature in Section 6.3.4 

 
l 
 8-7 
 Review of the stress corrosion cracking crack patterns (morphology) in actual industrial 
equipment (i.e., light water reactors) (Appendix B, Section B.6.3) 
 Experimental measurement of stress corrosion cracking initiation stress using constant 
load specimens, U-bend specimens and SSRT specimens in a range of brine 
environments (Section 6.2.1) 
 Use of experimentally measured residual stress distributions resulting from laser peening 
stress mitigation process to benchmark calculated through-wall residual stress 
distribution conservatively expected in final closure lid weld region (Sections 6.4.4 
and 6.4.5). 
(3) Assumed range of values and probability distributions for parameters used in 
conceptual and process-level models are not likely to underestimate the actual 
degradation and failure of engineered barriers. 
In those instances where uncertainties exist regarding the range of values and probability 
distributions, modelers were careful to choose values that were anticipated to either provide 
conservative results or to provide a distribution that bounds the expected range of values. 
Results of such calculated values were compared with values predicted by an alternative model 
or laboratory experiments, or both, to demonstrate the inherent conservatisms in the analyses. 
Examples include the comparison of the crack propagation SDFR model-predicted rates with 
experimentally independently measured rates (Section 7.4.2.3 and Table 7-4). 
(4) Appropriate methods of NDE of fabricated-engineered barriers are used to 
assess the type, size and location of fabrication defects that may lead to 
premature failure of engineered barriers. 
NDE performed to characterize welding flaws on waste package closure lid weld mockups were 
verified by destructive metallography and were used to assess the expected type, size and 
orientation of welding related fabrication defects that could lead to premature stress corrosion 
cracking related failure of the outer Alloy 22 waste package barrier (Section 6.2.2). 
(5) Where sufficient data do not exist, the definition of parameter values and 
conceptual models is based on appropriate use of other sources, such as expert 
elicitation. 
In most instances where sufficient data for the exact materials to be used in the repository and 
processes addressed in this section were not found to be available, data from analogous materials 
was either found to be or was made available. As a result, the use of expert elicitation in the 
development and implementation of the stress corrosion cracking related models was extremely 
limited as it was determined that the data and information that was available was adequate to 
support the required analyses. However, an independent technical review that involved expert 
elicitation was performed to verify the applicability and conservative nature of the seismic crack 
density model in Appendix B (Section B7.3). 

 
l 
 8-8 
Acceptance Criterion 4  Model Uncertainty is Characterized and Propagated Through the 
Model Abstraction 
(1) Alternative modeling approaches are considered and are consistent with 
available data and current scientific understanding. 
An alternative modeling approach for the SDFR model that is consistent with available data and 
current scientific understanding was considered and evaluated. 
The use of the Coupled Environmental Fracture (CEF) stress corrosion cracking propagation rate 
model was considered and model predictions were compared with available literature 
experimental data for stainless steel. The SDFR model selected was found to be conservative 
relative to CEF model (Sections 6.3.6 and 7.4.2.4). 
A conservative threshold stress intensity factor parameter approach was developed for use since 
experimental measurement of this parameter was not feasible because of the high resistance of 
Alloy 22 to stress corrosion cracking propagation (Section 6.3.5). 
An alternative seismic crack density model was evaluated for its prediction of stress corrosion 
cracking crack area density and found to be reasonably consistent with the base-case model in 
Appendix B (Sections B6.4.3 and B7.3). 
(2) Consideration of conceptual model uncertainty is consistent with available 
site characterization data, laboratory experiments, and the treatment of 
uncertainty does not result in under-estimation of the risk estimate. 
Consideration of uncertainties in the models used in this report is an integral part of the 
performed analyses. Conceptual model uncertainty is consistent with the information that has 
been developed from laboratory experiments. Care has been taken to ensure that the treatment of 
uncertainty does not result in under-estimation of the risk estimate. Examples of the treatment of 
such uncertainties are as follows: 
 Treatment of residual stress and stress intensity factor uncertainty is described in 
Section 6.4.5. 
 A conservative approach was used to determine the threshold stress for stress corrosion 
cracking initiation parameter for both Alloy 22 waste package outer barrier and the 
Titanium Grade 7 drip shield as described in Section 6.2.1. 
 Treatment of uncertainty in the threshold stress intensity factor parameter is described in 
Section 6.3.5 and the range of values is listed in Table 6-6. 
(3) Alternative modeling approaches, consistent with available data and current 
scientific understanding, are used and the modeling results are evaluated using 
tests that are sensitive to the processes modeled. 
Wherever it was deemed appropriate (and accepted alternative models were known to exist), 
alternative modeling approaches, consistent with available data and current scientific 

 
l 
 8-9 
understanding, were considered. In all instances, it was determined that the base-case model 
provided a similar but more conservative result than would be achieved through the use of the 
alternative models. Thus, although due consideration was given to the use of alternative 
modeling approaches, no alternative models were used. 
Acceptance Criterion 5  Model Abstraction Output Is Supported By Objective 
Comparisons 
(1) Models implemented in this report for input to total system performance 
assessment abstraction (provide results consistent with output from detailed 
process-level models and or empirical observations (laboratory and field testing, 
and/or natural analogs). 
The results of model abstractions developed in this report are for use as input to WAPDEG and 
thus direct input for use in the total system performance assessment abstraction. Thus, AC 5-1 is 
not applicable. 
(2) Numerical corrosion models used to calculate the lifetime of the engineered 
barriers are adequate representations, considering the associated uncertainties in 
long term behavior, range of conditions (including residual stresses) and the 
variability in fabrication processes. 
The numerical stress corrosion models used to calculate the lifetime of the waste package are 
based on appropriate design considerations and are validated against laboratory results to ensure 
that they are adequate representations of the involved processes, considering the associated 
uncertainties in long term behavior, range of conditions (including residual stresses) and the 
variability in fabrication processes (Sections 6.2.2, 6.4.2.1, and 6.4.2.2). 
(3) Evidence is sufficient to show that models will not underestimate the actual 
degradation and failure of engineered barriers. 
In those instances where there was doubt about the appropriateness or accuracy of the models, 
related parameters or data, modelers were careful to select a conservative approach or 
conservative data that would result in an overestimation of risk rather than an underestimation 
(Sections 6.2.1, 6.3.5, 7.4.3, and 7.4.4). The results of analyses were compared against results 
obtained from laboratory tests or industrial experience to demonstrate the conservatism of the 
analytical methods. Examples of such instances are provided in Section 7.4.2.3. 
(4) Mathematical degradation models are based on the same environmental 
parameters, material factors, assumptions and approximations shown to be 
appropriate for closely analogous applications. 
Mathematical degradation models presented in this report are based on environmental 
parameters, material factors, assumptions and approximations that have been demonstrated to be 
appropriate for closely analogous applications. In those instances where it was determined that 
adequate data did not exist to support the modeling effort, data from testing of analogous 
materials was used. Examples of such instances can be found in Section 6.3.4. 

 
l 
 8-10 
(5) Accepted and well documented procedures are used to construct and test the 
numerical models that simulate the EB chemical environment and degradation of 
EBS; 
The development and testing of the numerical models and related parameters used to simulate 
the repository environment and analyze the potential degradation of the engineered barrier 
components, including the drip shield and waste package, were performed in accordance with 
previously established well-documented Yucca Mountain project procedures that are based on 
industry established norms. These procedures also established the appropriate quality assurance 
requirements for such activities and appropriate checking, auditing and other activities were 
performed to ensure the adequacy and appropriateness of the models and data. Examples of such 
QA requirements and associated procedures can be found in Sections 2, 9.2, and Appendix B, 
Section B2, respectively. 
(6) Sensitivity analyses or bounding analyses are provided to support the 
abstraction of the degradation of engineered barriers. 
Bounding analyses associated with the abstraction of the stress and stress intensity factor 
through-wall gradients driving the stress corrosion cracking degradation of the waste package 
engineered barrier were performed and are documented herein. Examples of such activities can 
be found in Section 6.4.5. 
In addition to the above, Acceptance Criterion 5 (Model Output is Supported by Objective 
Comparisons) is addressed in Tables 8-1, 8-2, and 8-3. Objective comparisons with 
experimental data and relevant literature are described for predicted-versus-measured Alloy 22 
crack growth rates in Sections 6.3.5, 7.4.2.2, and 7.4.2.3. 
The above Acceptance Criteria (3, 4, and 5) are also addressed by the waste package degradation 
analysis, which describes the abstracted stress corrosion cracking models and related parameters 
and the propagation of uncertainties in those models and parameters for the case of nonseismic 
related stress corrosion cracking. Acceptance Criteria 3 through 5 will also be addressed in the 
seismic consequence abstraction model report, which describes the abstracted stress corrosion 
cracking models and the propagation of uncertainties in those models for the case of seismic 
stress corrosion cracking. 
8.3 SUMMARY OF OUTPUT 
Output from Appendix B for the seismically induced crack area density distribution is provided 
in DTN: MO0403SPASCRKD.000. 
Tables 8-1, 8-2, and 8-3 summarize stress corrosion cracking model report output data listed in 
DTN: LL030607012251.065 and associated output stress and stress intensity factor distribution 
plots are given in DTN: MO0310MWDWAPAN.002. These can be used as input for the 
WAPDEG with no restrictions if the waste package design, material, and environment are 
consistent with those considered in the reported modeling activities. The model uses 25-mm and 
10-mm measurements (Section 6.4.2.1 and Table 8-1) for the outer and middle lids of the waste 
packages potentially subject to stress corrosion cracking. The current proposed increase in 
middle closure lid thickness to 12.7 mm has no significant effect on model predictions of the 

 
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 8-11 
time for stress corrosion cracking to initiate and propagate through the combination of both lids. 
The annealing process will eliminate weld-induced residual tensile stresses in the as-fabricated 
waste package Alloy 22 outer cylinder thus precluding stress corrosion cracking for this region 
of the waste package. 
Stress profiles for radial stress and hoop stress versus depth are presented in look-up Table 8.2 
and Table 8.3. For the laser-peened waste package outer lid, it is clear from Table 8-3 that the 
hoop stress and corresponding stress intensity factors (SIF) are the predominant stress and SIF 
components. As described in Section 6.4.4, the modeled depth of laser-peened compressive 
stress (-40 ksi) is conservatively taken as 1.5 mm. However, based on the hoop stress profile, 
Figure 6-28, the estimated depth to which the outer weld stress is below the threshold stress 
depth (depth to which it is less than 90% of yield strength (i.e., 257 MPa)) is about 4.6 mm for 
the mean value and about 3.8 mm for the upper uncertainy bound value. Thus over 10,000 years, 
using the conservative 150C median general corrosion rate of 51.8 nm/yr (BSC 2004 
[DIRS 169984], Section 8.1), the depth of metal removal is about 518 m, which is about 11% 
of the mean depth of the stress mitigated layer. Using an upper-bound value of the general 
corrosion rate of 256 nm/yr (99.99th percentile rate at 150C, (BSC 2004 [DIRS 169984], 
Section 8.1) the total penetration depth by general corrosion is about 2,560 m, which is about 
67% of the estimated maximum uncertainty-level depth of the stress mitigated layer. This 
bounding analysis demonstrates that the final closure lid weld stress mitigated layer is deep 
enough to extend the lifetime of the waste package well beyond 10,000 years. 
Table 8-1. Summary of Output 
Output Name Output Value or Equation Unit Note 
Yield strength (YS) for 
Alloy 22 from Table 4-5 
372 at room temperature 
338 at 366K 
283 at 477 K 
MPa Linear between 
temperatures 
(Section 6.2.1) 
Yield strength (YS) for 
Titanium Grade 7 from 
Table 4-5 
275 to 450 at room temperature 
138 to 152 at 477K 
MPa Same as above and use 
average at temperature 
Threshold stress 
(Alloy 22) 
0.9 (YS) 
(Section 6.2.1) 
MPa YS at 200C (473K) for 
waste package 
Threshold stress (Titanium 
Grade 7) 
0.5 (YS) 
(Section 6.2.1) 
MPa YS at 140C (413K) for 
drip shield 
Initial size of incipient cracks 0.05 
(Section 6.2.1) 
mm 
Depth of plate to be included 
for embedded flaws 
0.25 
(Section 6.2.2.2) 
Fraction of the 
plate thickness 
Oblique flaws to be added to 
radial flaws 
0.005 a) 
(Section 6.2.2.3) 
Fraction of the 
total flaws 
Mean of repassivation slope, 
Alloy 22 SDFR model 
1.304 
(Section 6.3.4) 
Dimensionless 
Standard deviation of 
repassivation slope, Alloy 22 
SDFR model 
0.16 
(Section 6.3.4) 
Dimensionless 

 
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Table 8-1. Summary of Output (Continued) 
Output Name Output Value or Equation Unit Note 
Lower bound of 
repassivation slope, Alloy 22 
SDFR model 
0.984 
(Section 6.3.4) 
Dimensionless 
Upper bound of 
repassivation slope, Alloy 22 
SDFR model 
1.624 
(Section 6.3.4) 
Dimensionless 
Crack growth rate, Vt ( )( )n 
I 
n 
t K n V 4 14 6 . 3 2 10 1 . 4 10 8 . 7 - -   = 
(Section 6.3.4, Equation 19), where KI 
is the SIF in MPavm 
mm/s n is the repassivation 
slope 
Mean general corrosion rate, 
Vgc, Alloy 22 
7.23 
(Section 6.3.5) 
nm/y 
Threshold stress intensity 
factor, KISCC KISCC = (Vgc / A ) n / 1 (Section 6.3.5, 
Equation 20), where 
( )n n A 14 6 . 3 2 10 1 . 4 10 8 . 7 - -   = 
(Section 6.3.4, Equation 18) and 
n 4 n = (Section 6.3.3, Equation 16) 
MPavm n is the repassivation 
slope 
Vgc in mm/s 
Radial stress coefficient A0, 
WPML, as-welded 
181.636 
(Section 6.4.2.4, Table 6-8) 
MPa 
Radial stress coefficient A1, 
WPML, as-welded 
-177.592 
(Section 6.4.2.4, Table 6-8) 
MPa/mm 
Radial stress coefficient A2, 
WPML, as-welded 
23.385 
(Section 6.4.2.4, Table 6-8) 
MPa/mm2 
Radial stress coefficient A3, 
WPML, as-welded 
-0.900 
(Section 6.4.2.4, Table 6-8) 
MPa/mm3 
Hoop stress coefficient A0, 
WPML, as-welded 
219.908 
(Section 6.4.2.4, Table 6-8) 
MPa 
Hoop stress coefficient A1, 
WPML, as-welded 
56.494 
(Section 6.4.2.4, Table 6-8) 
MPa/mm 
Hoop stress coefficient A2, 
WPML, as-welded 
-20.848 
(Section 6.4.2.4, Table 6-8) 
MPa/mm2 
Hoop stress coefficient A3, 
WPML, as-welded 
1.083 
(Section 6.4.2.4, Table 6-8) 
MPa/mm3 
Radial stress coefficient A0, 
WPOL, laser-peened 
-265.920 
(Section 6.4.4, Table 6-11) 
MPa 
Radial stress coefficient A1, 
WPOL, laser-peened 
103.987 
(Section 6.4.4, Table 6-11) 
MPa/mm 
Radial stress coefficient A2, 
WPOL, laser-peened 
-9.857 
(Section 6.4.4, Table 6-11) 
MPa/m2 
Radial stress coefficient A3, 
WPOL, laser-peened 
0.254 
(Section 6.4.4, Table 6-11) 
MPa/mm3 
Hoop stress coefficient A0, 
WPOL, laser-peened 
-292.607 
(Section 6.4.4, Table 6-11) 
MPa 
Hoop stress coefficient A1, 
WPOL, laser-peened 
178.277 
(Section 6.4.4, Table 6-11) 
MPa/mm 

 
l 
 8-13 
Table 8-1. Summary of Output (Continued) 
Output Name Output Value or Equation Unit Note 
Hoop stress coefficient A2, 
WPOL, laser-peened 
-14.135 
(Section 6.4.4, Table 6-11) 
MPa/mm2 
Hoop stress coefficient A3, 
WPOL, laser-peened 
0.320 
(Section 6.4.4, Table 6-11) 
MPa/mm3 
Mean stress profile at .=0, 
S0(x) 
S0(x) = A0 + A1x + A2x2 + A3x3 
(Section 6.4.2.3, Equation 23) 
MPa x (in mm) is crack depth 
S0(x), radial stress, WPML, 
as-welded 
Table 8-2, 2nd column MPa Calculated from 
Equation 23 
S0(x), hoop stress, WPML, 
as-welded 
Table 8-2, 4th column MPa Calculated from 
Equation 23 
SIF, K0(x), radial stress, 
WPML, as-welded 
Table 8-2, 3rd column MPavm 
SIF, K0(x), hoop stress, 
WPML, as-welded 
Table 8-2, 5th column MPavm 
S0(x), radial stress, WPOL, 
laser-peened 
Table 8-3, 2nd column MPa Calculated from 
Equation 23 
S0(x), hoop stress, WPOL, 
laser-peened 
Table 8-3, 4th column MPa Calculated from 
Equation 23 
SIF, K0(x), radial stress, 
WPOL, laser-peened 
Table 8-3, 3rd column MPavm 
SIF, K0(x), hoop stress, 
WPOL, laser-peened 
Table 8-3, 5th column MPavm 
WPOL thickness (h) 25 
(Section 6.4.2.1, Figure 6-8) 
mm 
WPML thickness (h) 10 
(Section 6.4.2.1, Figure 6-8) 
mm 
Stress variability, .S 17.236893 
(Section 6.4.5) 
MPa 
Stress profile, S.(x), at angle 
. from S0(x) 
S.(x)= S0(x)  .S(1  cos(.)) 
(Section 6.4.5, Equation 25a) 
MPa 
SIF profile, K.(x), at angle . 
from K0(x) 
K.(x)= K0(x) (S.(h) / S0(h)) 
(Section 6.4.5, Equation 25b) 
MPavm 
Variation amplitude of S0(x), 
S . 
0.15 (YS) 
(Section 6.4.5; use YS value at the 
room temperature) 
MPa Uncertainty for S . is 
represented by a normal 
distribution truncated at 
3-sigma (15% YS). 
Lower bound of stress 
variation ( ) ( ) ( )
( ) . .. 
. 
. .. 
. . - = 
h S 
S h S x S x S 
. 
. 
. . min 
(Section 6.4.5, Equation 26a) 
MPa 
Upper bound of stress 
variation ( ) ( ) ( )
( ) . .. 
. 
. .. 
. . + = 
h S 
S h S x S x S 
. 
. 
. . max 
(Section 6.4.5, Equation 26b) 
MPa 

 
l 
 8-14 
Table 8-1. Summary of Output (Continued) 
Output Name Output Value or Equation Unit Note 
Lower bound of SIF variation 
( ) ( ) ( )
( ) . .. 
. 
. .. 
. . - = 
h S 
S h S x K x K 
. 
. 
. . min 
(Section 6.4.5, Equation 26c) 
MPavm 
Upper bound of SIF variation 
( ) ( ) ( )
( ) . .. 
. 
. .. 
. . + = 
h S 
S h S x K x K 
. 
. 
. . max 
(Section 6.4.5, Equation 26d) 
MPavm 
Output DTN: LL030607012251.065. 
NOTE: a Note that a slightly more conservative value (0.8%) is recommended for this parameter in the Analysis of 
Mechanisms for Early Waste Package/Drip Shield Failure (BSC 2004 [DIRS 170024], Table 12). 
Table 8-2. Stresses and Stress Intensity Factors for the As-Welded Waste Package Middle Lid 
Depth 
(mm) 
Radial stress (Sx) 
(MPa) 
SIF due to Sx 
(MPavm) 
Hoop stress (Sz) 
(MPa) 
SIF due to Sz 
(MPavm) 
0.1593 153.9288 4.9033 228.3849 7.5754 
0.3203 127.1172 6.2685 235.9015 10.9665 
0.4797 101.7315 6.8580 242.3296 13.7144 
0.6407 77.2206 6.9761 247.8300 16.1330 
0.8000 54.0676 6.7631 252.3158 18.3358 
0.9593 31.9924 6.3044 255.8750 20.3775 
1.1203 10.7596 5.8250 258.5570 22.3816 
1.2797 -9.2150 5.2651 260.3330 24.3197 
1.4407 -28.3699 4.6000 261.2667 26.1726 
1.6000 -46.3322 3.8615 261.3655 27.9459 
1.7593 -63.3265 3.0726 260.6697 29.6433 
1.9203 -79.5368 2.2534 259.1863 31.2668 
2.0797 -94.6509 1.4282 256.9724 32.8922 
2.2407 -109.0061 0.5951 254.0088 34.5292 
2.4000 -122.3284 -0.2400 250.3830 36.1060 
2.5593 -134.7922 -1.0656 246.0945 37.6220 
2.7203 -146.5363 -1.8707 241.1150 39.0762 
2.8797 -157.3405 -2.6491 235.5736 40.4676 
3.0407 -167.4522 -3.4047 229.3818 41.8264 
3.2000 -176.6850 -4.1787 222.6938 43.2168 
3.3593 -185.1690 -4.9390 215.4749 44.5479 
3.5203 -193.0032 -5.6775 207.6685 45.8181 
3.6797 -200.0480 -6.3965 199.4620 47.0265 
3.8407 -206.4725 -7.0865 190.7114 48.1718 
4.0000 -212.1664 -7.7528 181.6234 49.2531 
4.1593 -217.2211 -8.2576 172.1366 50.3451 
4.3203 -221.7016 -8.7427 162.1726 51.3729 
4.4797 -225.5376 -9.2143 151.9633 52.3351 

 
l 
 8-15 
Table 8-2. Stresses and Stress Intensity Factors for the As-Welded Waste Package Middle Lid 
(Continued) 
Depth 
(mm) 
Radial stress (Sx) 
(MPa) 
SIF due to Sx 
(MPavm) 
Hoop stress (Sz) 
(MPa) 
SIF due to Sz 
(MPavm) 
4.6407 -228.8312 -9.6605 141.3230 53.2313 
4.8000 -231.5367 -10.0894 130.4975 54.0602 
4.9593 -233.7127 -10.4950 119.4050 54.8214 
5.1203 -235.3959 -10.9446 107.9526 55.4811 
5.2797 -236.5735 -11.4131 96.4029 56.0586 
5.4407 -237.2926 -11.8636 84.5422 56.5637 
5.6000 -237.5602 -12.3055 72.6415 56.9965 
5.7593 -237.4080 -12.7309 60.6057 57.3567 
5.9203 -236.8501 -13.1320 48.3342 57.6444 
6.0797 -235.9201 -13.7114 36.1065 57.7587 
6.2407 -234.6208 -14.4707 23.6946 57.6946 
6.4000 -233.0011 -15.2333 11.3811 57.5522 
6.5593 -231.0713 -15.9891 -0.9356 57.3322 
6.7203 -228.8287 -16.7277 -13.3570 57.0353 
6.8797 -226.3414 -17.4611 -25.6005 56.6626 
7.0407 -223.5802 -18.4707 -37.8942 56.1419 
7.2000 -220.6238 -20.3589 -49.9583 55.3276 
7.3593 -217.4669 -22.2128 -61.8935 54.4422 
7.5203 -214.0957 -24.0173 -73.7955 53.4878 
7.6797 -210.6019 -25.7872 -85.3924 54.6294 
7.8407 -206.9348 -27.4989 -96.8987 56.2191 
8.0000 -203.1923 -29.1709 -108.0509 57.7865 
Output DTN: LL030607012251.065; Section 6.4.2.4, Table 6-10. 
Table 8-3. Stresses and Stress Intensity Factors for Laser-Peened Waste Package Outer Lid 
Depth 
(mm) 
Radial stress (Sx) 
(MPa) 
SIF due to Sx 
(MPavm) 
Hoop stress (Sz) 
(MPa) 
SIF due to Sz 
(MPavm) 
0.3988 -226.0035 -9.1866 -223.7417 -5.6943 
0.8001 -188.9005 -11.7979 -158.8532 -6.4965 
1.1989 -154.9833 -13.0189 -98.6408 -6.1528 
1.6002 -123.7220 -13.4298 -42.2143 -5.1372 
1.9990 -95.4153 -13.2965 9.8344 -3.6697 
2.4003 -69.6047 -12.7780 58.2916 -1.8824 
2.7991 -46.5198 -12.2958 102.6663 0.1212 
3.2004 -25.7687 -11.7214 143.6471 2.2821 
3.5992 -7.5170 -11.0116 180.8374 4.5533 
3.9980 8.4709 -10.2080 214.6297 6.8939 
4.3993 22.3728 -9.3437 245.3299 9.2702 
4.7981 34.1098 -8.4525 272.6715 11.6543 
5.1994 43.9293 -7.6096 297.1262 14.0165 
5.5982 51.8041 -6.8298 318.5068 16.3364 

 
l 
 8-16 
Table 8-3. Stresses and Stress Intensity Factors for Laser-Peened Waste Package Outer Lid 
(Continued) 
Depth 
(mm) 
Radial stress (Sx) 
(MPa) 
SIF due to Sx 
(MPavm) 
Hoop stress (Sz) 
(MPa) 
SIF due to Sz 
(MPavm) 
5.9995 57.9323 -6.0675 337.2088 18.6024 
6.3983 62.3334 -5.3416 353.1178 20.8003 
6.7970 65.1483 -4.6612 366.4827 22.9177 
7.1984 66.4775 -4.0331 377.4871 24.9441 
7.5971 66.4012 -3.4507 386.1141 26.9023 
7.9985 65.0162 -2.8535 392.5969 28.8612 
8.3972 62.4372 -2.2745 396.9757 30.7287 
8.7986 58.7292 -1.7170 399.4297 32.5008 
9.1973 54.0361 -1.1860 400.0499 34.1745 
9.5987 48.3961 -0.6829 398.9677 35.7479 
9.9974 41.9777 -0.2101 396.3190 37.2200 
10.3962 34.8443 -0.3513 392.2239 38.4530 
10.7975 27.0415 -0.5163 386.7654 39.5674 
11.1963 18.7651 -0.7070 380.1350 40.5636 
11.5976 10.0075 -0.9242 372.3715 41.4432 
11.9964 0.9766 -1.1690 363.6954 42.2086 
12.3977 -8.3447 -1.4403 354.1195 42.8627 
12.7965 -17.7414 -1.7949 343.8874 43.4439 
13.1978 -27.2353 -2.1728 332.9919 43.9342 
13.5966 -36.6092 -2.5554 321.6934 44.3269 
13.9954 -45.8267 -2.9438 310.0462 44.6272 
14.3967 -54.8472 -3.3378 298.0958 44.8409 
14.7955 -63.4595 -3.7396 286.1158 44.9743 
15.1968 -71.6755 -4.0160 274.0769 45.0329 
15.5956 -79.2941 -4.1354 262.2538 45.0208 
15.9969 -86.3145 -4.2182 250.6192 44.9464 
16.3957 -92.5507 -4.2696 239.4426 44.8182 
16.7945 -97.9528 -4.2904 228.7710 44.6449 
17.1958 -102.4495 -4.2805 218.6644 44.4361 
17.5946 -105.8869 -4.3087 209.3730 44.2112 
17.9959 -108.2109 -4.5204 200.9017 43.9968 
18.3947 -109.2950 -4.7313 193.4801 43.7750 
18.7960 -109.0551 -4.9400 187.1369 43.5578 
19.1948 -107.3973 -5.1487 182.0747 43.3569 
19.5961 -104.2024 -5.3536 178.3522 43.1853 
19.9949 -99.4140 -5.5551 176.1390 43.0560 
Output DTN: LL030607012251.065; Section 6.4.4, Table 6-12. 

 
l 
 9-1 
9. INPUTS AND REFERENCES 
9.1 DOCUMENTS CITED 
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Beach, Florida, November 17-22, 1985. Rungta, R., ed. PVP-Vol. 99. Pages 17- 
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118581 Andresen, P.L. and Ford, F.P. 1994. Fundamental Modeling of Environment 
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Corrosion Crack Growth Rate Behavior of Ni alloys 182 and 600 in High 
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l 
 9-2 
164859 Averbach, B.L. 1968. Microcrack Formation. Section III of Chapter 7 of Fracture, 
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000-00B. Las Vegas, Nevada: Bechtel SAIC Company. ACC: ENG.20040709.0001 
166879 BSC 2004. Drip Shield and Waste Package Emplacement Pallet Design Report. 000- 
00C-SSE0-00100-000-00A. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: ENG.20040225.0016. 

 
l 
 9-3 
169997 BSC (Bechtel SAIC Company) 2004. FEPs Screening of Processes and Issues in 
Drip Shield and Waste Package Degradation. ANL-EBS-PA-000002, Rev. 03. Las 
Vegas, Nevada: Bechtel SAIC Company. ACC: DOC.20041012.0004. 
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l 
 9-4 
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of Alloy 22 in Simulated Concentrated Ground Waters. Corrosion/2004, 59th 
Annual Conference & Exposition, March 28-April 1, 2004, New Orleans. Paper No. 
04548. Houston, Texas: NACE International. TIC: 255943. 
149957 Lu, J., ed. 1996. Handbook of Measurement of Residual Stresses. Lilburn, Georgia: 
Fairmont Press. TIC: 247903. 
161780 Lundin, C.D. 2002. Re: Welding Process Considerations for Waste Package 
Fabrication. Letter from C.D. Lundin to J.A. Cogar (BSC), September 11, 2002, 
with attachment. ACC: MOL.20021015.0209. 
162702 Macdonald, D.D. and Urquidi-Macdonald, M. 1991. A Coupled Environment 
Model for Stress Corrosion Cracking in Sensitized Type 304 Stainless Steel in LWR 
Environments. Corrosion Science, 32, (1), 51-81. New York, New York: Pergamon 
Press. TIC: 254386. 
162701 Macdonald, D.D.; Urquidi-Macdonald, M.; and Lu, Pai-Chuan 1994. The Coupled 
Environmental Fractural Model - A Deterministic Method for Calculating Crack 
Growth Rates. Corrosion 94. Paper No. 246, Houston, Texas: NACE International. 
TIC: 254388. 

 
l 
 9-6 
147981 Mohr, W.C. 1996. Internal Surface Residual Stresses in Girth Butt-Welded Steel 
Pipes. Residual Stresses in Design, Fabrication, Assessment and Repair, PVP-Vol. 
321, 37-44. New York, New York: American Society of Mechanical Engineers. 
TIC: 247502. 
163274 NRC (U.S. Nuclear Regulatory Commission) 2003. Yucca Mountain Review Plan, 
Final Report. NUREG-1804, Rev. 2. Washington, D.C.: U.S. Nuclear Regulatory 
Commission, Office of Nuclear Material Safety and Safeguards. TIC: 254568. 
165536 Pan, Y.-M.; Brossia, C.S.; Cragnolino, G.A.; Dunn, D.S.; Gute, G.D.; and Yang, L. 
2002. Stress Corrosion Cracking and Hydrogen Embrittlement of Container and Drip 
Shield Materials. CNWRA 2003-02. San Antonio, Texas: Center for Nuclear Waste 
Regulatory Analyses. TIC: 254055 
149968 Pasupathi, V. 2000. Documentation of Literature on Residual Stress 
Measurements. Interoffice correspondence from V. Pasupathi (CRWMS M&O) to 
G.M. Gordon, May 19, 2000, LV.WP.VP.05/00-070, with enclosures. 
ACC: MOL.20000522.0146. 
166944 Pensado, O.; Dunn, D.S.; Cragnolino, G.A.; and Jain, V. 2002. Passive Dissolution 
of Container MaterialsModeling and Experiments. CNWRA 2003-01. San 
Antonio, Texas: Center for Nuclear Waste Regulatory Analyses. TIC: 254056. 
147983 Rice, J.R. 1968. A Path Independent Integral and the Approximate Analysis of 
Strain Concentration by Notches and Cracks. Journal of Applied Mechanics, 
Transactions of the SME, 35, 379-386. New York, New York: American Society of 
Mechanical Engineers. TIC: 247487. 
118696 Roy, A.K.; Fleming, D.L.; Freeman, D.C.; and Lum, B.Y. 1998. Stress Corrosion 
Cracking of Alloy C-22 and Ti GR-12 Using Double-Cantilever-Beam Technique. 
UCRL-JC-132145. Livermore, California: Lawrence Livermore National 
Laboratory. ACC: MOL.19990420.0114. 
149953 Shcherbinskii, V.G. and Myakishev, V.M. 1970. Statistical Distribution of Welding 
Defects with Respect to Azimuth. Central Scientific-Research Institute of Technical 
Engineering. Translated from Defektoskopiya, No. 4., UDC 620.179.16,143-144. 
New York, New York: Plenum Publishing Corporation. TIC: 247890. 
162457 SI (Structural Integrity Associates), Inc. 2003. Evaluation of the CRM-21 PWR and 
Viability Availability Waste Package. Report No. SIR-99-094. Revision 1. Prepared 
for Bechtel SAIC Company, Las Vegas, Nevada, by Structural Integrity Associates, 
Inc., San Jose, California. March 2003. ACC: MOL.20030327.0004. 
163114 Smith, D. 2003. Weld Flaw Evaluation and Nondestructive Examination Process 
Comparison Results for High-Level Radioactive Waste Disposal Container 
Manufacturing Program. TDR-EBS-ND-000007 REV 01. Las Vegas, Nevada: 
Bechtel SAIC Company. ACC: ENG.20030515.0003. 

 
l 
 9-7 
118702 Sprowls, D.O. 1987. Evaluation of Stress-Corrosion Cracking. Metals Handbook 
Ninth Edition. Volume 13. Corrosion. 245-282. Metals Park, Ohio: ASM 
International. TIC: 209807. 
161933 Structural Integrity Associates. 2002. Structural Integrity Associates Support of 
Waste Package Design for Year 2001. SIR-02-073. San Jose, California: Structural 
Integrity associates. ACC: MOL.20020709.0389. 
167756 Tada, H.; Paris, P.C.; and Irwin, G.R. 2000. The Stress Analysis of Cracks 
Handbook. 3rd. New York, New York: American Society of Mechanical Engineers. 
TIC: 255547. 
122064 Timoshenko, S. and Goodier, J.N. 1951. Theory of Elasticity. 2nd Edition. New 
York, New York: McGraw-Hill. TIC: 224221. 
9.2 CODES, STANDARDS, REGULATIONS, AND PROCEDURES 
100497 ASTM B 575-94. 1994. Standard Specification for Low-Carbon Nickel-Molybdenum- 
Chromium and Low-Carbon Nickel-Chromium-Molybdenum Steel Alloy Plate, Sheet, 
and Strip. Philadelphia, Pennsylvania: American Society for Testing and Materials. 
TIC: 237683. 
137688 ASTM G 30-94. 1994. Standard Practice for Making and Using U-Bend Stress- 
Corrosion Test Specimens. Philadelphia, Pennsylvania: American Society for Testing 
and Materials. TIC: 246890. 
117480 ASTM E 399-90 (Reapproved 1997). 1991. Standard Test Method for Plane-Strain 
Fracture Toughness of Metallic Materials. West Conshohocken, Pennsylvania: 
American Society for Testing and Materials. TIC: 246299. 
171563 ASTM G 129-00. 2000. Standard Practice for Slow Strain Rate Testing to Evaluate 
the Susceptibility of Metallic Materials to Environmentally Assisted Cracking. West 
Conshohocken, Pennsylvania: American Society for Testing and Materials. 
TIC: 256501. 
171562 ASTM G 49-85 (Reapproved 2000). 2000. Standard Practice for Preparation and 
Use of Direct Tension Stress-Corrosion Test Specimens. West Conshohocken, 
Pennsylvania: American Society for Testing and Materials. TIC: 249897. 
156605 10 CFR 63. Energy: Disposal of High-Level Radioactive Wastes in a Geologic 
Repository at Yucca Mountain, Nevada. Readily available. 
AP-2.22Q, Rev. 1, ICN 1. Classification Analyses and Maintenance of the Q-List. 
Washington, D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste 
Management. ACC: DOC.20040714.0002. 

 
l 
 9-8 
AP-2.27Q, Rev. 1, ICN 4. Planning for Science Activities. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20040610.0006. 
AP-3.15Q, Rev. 4, ICN 5. Managing Technical Product Inputs. Washington, D.C.: 
U.S. Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20040812.0004. 
AP-SIII.10Q, Rev. 2, ICN 7. Models. Washington, D.C.: U.S. Department of Energy, 
Office of Civilian Radioactive Waste Management. ACC: DOC.20040920.0002. 
AP-SV.1Q, Rev. 1, ICN 1. Control of the Electronic Management of Information. 
Washington, D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste 
Management. ACC: DOC.20040308.0001. 
LP-SI.11Q-BSC, Rev. 0, ICN 1. Software Management. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20041005.0008. 
9.3 SOURCE DATA, LISTED BY DATA TRACKING NUMBER 
148895 LL000316205924.142. Stress Corrosion Cracking of the Drip Shield, the Waste 
Package Outer Barrier l. Submittal date: 
03/22/2000. 
148482 LL000320005924.145. Corrosion Cracking of the Drip Shield, the Waste Package 
Outer Barrier l. Submittal date: 
03/22/2000. 
161253 LL021105312251.023. Stress Corrosion Crack Growth and Initiation Measurements 
for C-22 and Ti-7, General Electric Global Research Center (GEGRC) 121202. 
Submittal date: 01/08/2003. 
166971 LL030300612251.035. Reversing DC Test Generated Fatigue Crack Growth Data. 
Submittal Date: 07/09/2003. 
163712 LL030412512251.057. LTCTF Corrosion Rate Calculations for Five-Year Exposed 
Alloy C22 Specimens Cleaned Under TIP-CM-51. Submittal date: 05/28/2003. 
148850 MO0003RIB00071.000. Physical and Chemical Characteristics of Alloy 22. 
Submittal date: 03/13/2000. 
152926 MO0003RIB00073.000. Physical and Chemical Characteristics of Ti Grades 7 and 
16. Submittal date: 03/13/2000. 
165147 MO0301SPAXRA52.001. X-Ray Diffraction and Ring Core Determination of the 
Subsurface Residual Stress Distributions in Two Alloy 22 Welded Plates. Submittal 
date: 01/30/2003. 

 
l 
 9-9 
167911 MO0402GEA22SCC.000. Alloy 22 Stress Corrosion Crack Growth Rate Data in 
288C Water. Submittal Date: 02/25/2004. 
170760 MO0407SEPFEPLA.000. LA FEP List. Submittal date: 07/20/2004 
171564 MO0409GE835924.000. Stress Corrosion Crack Initiation & Growth Measurements 
for C-22 and Ti-7 in Environments Relevant to High Level Nuclear Waste Packages. 
Submittal date: 09/09/2004. 
171792 MO0409GGSIACAL.000. Structural Integrity Associates Calculation Files 2004. 
Submittal date: 09/22/2004 
9.4 OUTPUT DATA, LISTED BY DATA TRACKING NUMBER 
LL030607012251.065. Output of Stress Corrosion Cracking AMR ANL-EBS-MD- 
000005 REV. 01 ICN 00. Submittal date: 06/20/2003. 
MO0310MWDWAPAN.002. WAPDEG Analysis of Waste Package and Drip Shield 
Degradation. Submittal date: 10/16/2003. 
MO0403SPASCRKD.000. Seismic Crack Density Model Outputs For LA. Submittal 
date: 03/09/2004. 

 
l 
 9-10 
INTENTIONALLY LEFT BLANK 

 
l 
 A-1 
A. DATA QUALIFICATION PLAN 

 
l 
 A-2 
INTENTIONALLY LEFT BLANK 

 
l 
 B-1 
B. SEISMIC CRACK DENSITY MODEL 
B1. PURPOSE 
As directed by the technical work plan (BSC 2004 [DIRS 171583]), an abstraction model 
(the seismic crack density model (SCDM)) for the crack area density (crack area per unit 
seismically damaged area) of waste packages subjected to seismic activity has been developed. 
This activity was conducted by the Performance Assessment/Confirmation Project (PACP) 
Waste Package Modeling Department (WPMD). This activity provided the PACP with 
estimates of crack area density (crack area per unit seismically damaged area). This abstraction 
model provides information to address requirements of Yucca Mountain Review Plan, Final 
Report (NRC 2003 [DIRS 163274]). 
Seismic activity can lead the waste packages to impact other components in the drift including 
the emplacment pallets, drip shields, and other waste packages. If the seismically induced 
impacts are of sufficient magnitude, the impacts could physically dent the waste package outer 
barrier and potentially the waste package inner vessel. These deformations could cause cold 
work of the waste package barrier and vessel materials, producing a cold-worked gradient 
typically highest on the outer surface and smallest on the inner surface. Impacts could also 
create complex through-wall residual stress profiles. These stress profiles and cold-work 
gradients may lead to stress corrosion cracking in the seismically affected area of the waste 
packages. 
Similar damage can be expected for drip shields under seismic loadings. However, as in the 
treatment of stress corrosion cracking due to rockfalls discussed in the main body of this report 
(Section 6.3.7), stress corrosion cracks in the drip shields are expected to be tight and plugged 
with corrosion products or mineral deposits, or both, leading to negligible water flow through 
these openings. However, even if advective or diffusive flow-through stress corrosion cracking 
were to occur, any resulting under drip shield seepage would be unlikely to align with any 
through-wall stress corrosion cracking present in the waste package Alloy 22 barrier. 
This Appendix B evaluation addresses the potential for stress corrosion cracking that could occur 
in the waste package as a result of stresses and cold work generated by an unlikely seismic event. 
After initiation of stress corrosion cracking, it may provide a path for subsequent radionuclide 
release from the waste package but, similar to the drip shield case, aqueous transport and 
radionuclide release through stress corrosion cracking induced crack areas in the waste package 
is likely to be negligible due to plugging by corrosion products or mineral deposits, or both. 
However, conservatively, no credit is taken in TSPA-LA for the crack-plugging phenomenon in 
the waste package case. 
The crack area density (crack area per unit seismically damaged area) determined in this 
Appendix is used as a scaling factor applied to the total seismic damaged area (determined in 
Seismic Consequence Abstraction (BSC 2004 [DIRS 169183])) to obtain the total area of the 
crack network through which radionuclide transport could occur. It is expected that the crack 
area density will serve as input to Seismic Consequence Abstraction (BSC 2004 [DIRS 169183]). 
This model should be used only as input to Seismic Consequence Abstraction (BSC 2004 

 
l 
 B-2 
[DIRS 169183]), and not for generic analyses of stress corrosion crack densities or morphologies 
under other loadings or for other applications. 
B2. QUALITY ASSURANCE 
The quality assurance (QA) program applies to the development of this technical product. 
Technical Work Plan for: Regulatory Integration Modeling and Analysis of the Waste Form and 
Waste Package (BSC 2004 [DIRS 171583]) determined that this activity is subject to Quality 
Assurance Requirements and Description (DOE 2004 [DIRS 171539]) requirements. All waste 
package configurations have been determined to be important to waste isolation in accordance 
with AP-2.22Q, Classification Analyses and Maintenance of the Q-List and, therefore, are 
classified as safety category (SC) in Q-List (BSC 2004 [DIRS 168361], Appendix A; BSC 2004 
[DIRS 170992], Section 6.4.2). The drip shields have been determined to be important to waste 
isolation in accordance with AP-2.22Q and, therefore, are classified as safety category (SC) in 
Q-List (BSC 2004 [DIRS 168361], Appendix A). 
The inputs to this report are documented according to AP-3.15Q, Managing Technical Product 
Inputs. The methods used to control the electronic management of data as required by 
AP-SV.1Q, Control of the Electronic Management of Information, were accomplished in 
accordance with the technical work plan. The process for control of the electronic management 
of information on evaluation of work activities, processes, or process functions, outlined in 
Section 5.0 of AP-SV.1Q, is followed to ensure accuracy, completeness, and security of 
information and data used in preparation of this report. Examples of process controls mentioned 
in AP-SV.1Q are (a) access to the information contained on personal computer is password 
protected; (b) secured backup copies are appropriately labeled and stored before changes are 
made and kept until the changes are confirmed and correct; (c) physical electronic media (tape, 
diskette, CD-ROM, etc.) are appropriately labeled; and (d) for nonphysical electronic media, 
transport mechanisms can be e-mail, TCP/IP, NetBios, etc. and methods of receipt verification 
may include visual inspection, transmission verification settings, check sums, application 
information integrity check, etc. 
This document is prepared in accordance with AP-SIII.10Q, Models, and reviewed in accordance 
with AP-2.14Q, Document Review. 
B3. USE OF SOFTWARE 
B3.1 EXCEL 97 SR-2 
Excel 97 SR-2 is a commercial off-the-shelf software program used in this report. The 
computations performed in this report using Excel use only standard functions and are 
documented in sufficient detail to allow an independent technical reviewer to reproduce or verify 
the results by visual inspection or hand calculation without recourse to the originator. The 
formulas or algorithms used and a listing of inputs to and outputs from the formulas or 
algorithms are sufficiently documented to allow results to be reproduced. Therefore this 
software is exempt from LP-SI.11Q-BSC, Software Management, Section 2.1. Excel 97 SR-2 is 
appropriate for its intended use because it offers the mathematical functionality necessary to 
perform and document the numerical manipulations used in this report. Excel 97 SR-2 was 

 
l 
 B-3 
executed on a Optiplex GX260 Workstation (CRWMS M&O tag 152849, located in the 
Summerlin Offices, Las Vegas, Nevada) equipped with the Windows 2000 operating system. 
B4. INPUTS 
B4.1 DIRECT INPUT 
Data used to develop the SCDM are not used subsequently to validate the model. 
Table B-1. Summary of Seismic Crack Density Model Direct Inputs 
Input Name Input Source DTN Input Value or Equation 
Alloy 22 Yield Strength Waste package material 
properties: corrosionresistant 
materials. 
MO0003RIB00071.000 
[DIRS 148850] 
372 MPa at room temperature 
338 MPa at 366 K 
283 MPa at 477 K 
Alloy 22 Youngs Modulus Waste package material 
properties: corrosionresistant 
materials. 
MO0003RIB00071.000 
[DIRS 148850] 
206 GPa at room temperature 
203 GPa at 366 K 
196 GPa at 477 K 
Crack Mouth Opening, ( d) 
of a Single Crack for Plane 
Stress Conditions in an 
infinite plate 
Tada et al. 2000 
[DIRS 167756], p. 125 
E
c s d ) 4 ( = 
where d is crack mouth 
opening, 2c is the crack length, 
s is the value of plane stress, 
and E is the modulus of 
elasticity. 
Section B6.4.2, Eq. B-2 
Solution for Radial and 
Tangential Stress in a 
Hollow Cylinder Under 
Internal Pressure Under 
Plane Stress Conditions 
Timoshenko and Goodier 
(1970 [DIRS 121096], 
pp. 68 to 71) 
( ) 
( ) 
2 2 
2 2 
2 2 2 
2 2 
2 2 
2 2 
2 2 2 
2 2 
1 
1 
a b 
b p a p 
r a b 
p p b a 
a b 
b p a p 
r a b 
p p b a 
o i i o 
o i i o 
r 
-
- 
+ 
- 
- 
- = 
-
- 
+ 
- 
- 
= 
. s
s 
where sr 
is radial stress 
component, s. is tangential 
stress component, pI is 
internal pressure, po is external 
pressure, r is radius, a is 
inner radius and b is external 
radius 
Section B6.4.3, Equation B-15 
These inputs are appropriate for their intended use because they are qualified developed data, 
some of which have established fact as their source. They provide reasonable and appropriate 
measures of the mechanical properties of the Alloy 22 material used in construction of the waste 
package outer barrier. 
B4.2 CRITERIA 
The technical work plan (BSC 2004 [DIRS 171583], Table 3-1) identified the Acceptance 
Criteria applicable to the seismic crack density model as part of the Acceptance Criteria 
identified for this report. 

 
l 
 B-4 
B4.3 CODES AND STANDARDS 
No codes and standards were used to develop the model for this report. 
B5. ASSUMPTIONS 
No assumptions were used, in the absence of direct confirming data or evidence, to perform this 
model activity. 
B6. MODEL DISCUSSION 
Seismic activity can lead waste packages to impact other components in the drift including the 
emplacment pallets, drip shields, and other waste packages. If the seismically induced impacts 
are severe enough, the impacts can physically deform the waste package outer barrier and 
potentially the waste package inner vessel. These deformations could cause cold work of the 
waste package barrier and vessel materials, producing a cold-worked gradient typically highest 
on the outer surface and smallest on the inner surface. Impacts could also create complex 
through-wall residual stress profiles. These residual stress profiles and cold-work gradients 
could lead to stress corrosion cracking in the seismically affected areas. The conservative 
modeling assumption is made that, regardless of the actual chemical environment on the waste 
package surface, the environment is sufficiently severe to support stress corrosion cracking 
processes. Thus the requisite concurrent conditions for stress corrosion cracking are present, 
namely residual tensile stress, an environment that supports corrosion, and a material that is 
susceptible (cold worked Alloy 22). 
Similar seismic damage can be expected for drip shields under seismic loadings; however, as in 
the treatment of stress corrosion cracking due to rockfalls discussed in this Section 6.3.7, stress 
corrosion cracks in the drip shields are expected to be tight and plugged with corrosion products 
or mineral deposits, or both, leading to negligible water flow through these openings. Therefore, 
since the primary role of the drip shield is to keep water from contacting the waste package, 
stress corrosion cracking of the drip shield does not compromise its intended design purpose. On 
this basis, stress corrosion cracking of the drip shield due to seismic activity is not considered 
further and does not need to be modeled in TSPA-LA. 
This evaluation addresses the potential for stress corrosion cracking that could occur as a result 
of stresses and cold work generated by seismic activity. The stress corrosion cracks could 
provide a path for subsequent radionuclide release from the waste package. 
The crack area density (crack area per unit seismically damaged area) determined in this 
Appendix is used as a scaling factor applied to the total seismic damaged area (determined in 
Seismic Consequence Abstraction (BSC 2004 [DIRS 169183]) to obtain the total area of the 
crack network through which radionuclide transport could occur. It is expected that the crack 
area density will serve as input to Seismic Consequence Abstraction (BSC 2004 [DIRS 169183]). 
This model should only be used as input to Seismic Consequence Abstraction (BSC 2004 
[DIRS 169183]) and not for generic analyses of stress corrosion crack densities or morphologies 
under other loadings or for other applications. 

 
l 
 B-5 
B6.1 STRESS CORROSION CRACKING MORPHOLOGY 
The purpose of this section is to present observations of stress corrosion crack morphology 
relevant to Alloy 22 (the waste package outer barrier material). It is known that Alloy 22 is 
potentially susceptible to stress corrosion cracking under repository-relevant environmental 
conditions. The morphology of stress corrosion cracking is expected to be transgranular and not 
intergranular, which is commonly observed (e.g., in high-tensile, Light Water Reactor (LWR) 
environments) (Andresen et al. 2001 [DIRS 167840]; Herrera 2004 [DIRS 168133], Section 2.0). 
Figures B-1 and B-2 present typical examples of transgranular stress corrosion cracking and 
intergranular stress corrosion cracking, respectively. 
Depending on the stress distribution, cracking may initiate and propagate through-wall. If 
several cracks were to initiate in the same general area and coalesce and propagate through-wall 
and remain straight (i.e., perpendicular to the surface) and maintain smooth crack faces, a 
sizeable section of material could fall out leading to a larger area for release than would an 
array of separated stress corrosion cracks (Herrera 2004 [DIRS 168133], Section 2.0). However, 
the occurrence of all of these events in conjunction is improbable; therefore, only tight and 
relatively separate through-wall cracks are expected (Herrera 2004 [DIRS 168133], Section 2.0). 
Stress corrosion cracks would greatly impede radionuclide transport because of their tightness, 
the tortuous nature of the crack path, and the possibility (similar to cracks in drip shields) of 
being plugged with corrosion products or mineral deposits, or both, leading to negligible water 
flow through these openings (Section 6.3.7). Unlike cracks in the drip shield, cracks in the waste 
package could lead to release of radionuclides to the environment. For this reason, cracks in the 
waste package must be considered in TSPA-LA. 

 
l 
 B-6 
Source: Herrera 2004 [DIRS 168133], Figure 2-1. 
Figure B-1. Typical Example of Transgranular Stress Corrosion Cracking in Stainless Steel 

 
l 
 B-7 
Source: Herrera 2004 [DIRS 168133], Figure 2-2. 
Figure B-2. Typical Example of Intergranular Stress Corrosion Cracking in Stainless Steel 
B6.2 NATURE OF SEISMIC DEFORMATION AND CRACK GROWTH 
The nature of most seismically induced deformations in cylindrical vessels is such that it is very 
unlikely that a residual stress profile would be created that would allow an initiated stress 
corrosion crack to propagate through-wall and circumscribing the deformed area (Herrera 2004 
[DIRS 168133], Section 3.0). Any through-wall residual stress fields resulting from impact 
loads would be a secondary-type stress (displacement controlled). There is no significant stress 
from other sources (e.g., due to internal pressure) since sustained, postclosure primary stresses in 
the waste package Alloy 22 outer cylinder including internal pressure stresses and waste 
packagepallet contact stresses are limited by design and are significantly below 0.9 (YS) 
(BSC 2004 [DIRS 169766], Tables 2, 21, 22, and 23). Further, for such outer surface-induced 
residual stress gradients, stresses and strains are of higher magnitude at the outer surface and 
tend to decrease through the thickness (Herrera 2004 [DIRS 168133], Section 3.0). Thus any 
stress corrosion cracking that initiates and propagates under such a driving stress intensity factor 

 
l 
 B-8 
may arrest before penetrating the full thickness (Herrera 2004 [DIRS 168133], Section 3.0). 
Therefore, seismically induced deformation-generated stresses are highly unlikely to lead to a 
residual stress profile that results in a sufficiently positive stress intensity factor as the crack 
grows to result in cracking through-wall and around the entire deformed area. Similarly, the 
stress intensity factor (KI) will tend to decrease as the crack propagates due to stress relaxation 
associated with crack growth that relieves stresses normal to the crack faces. 
Herrera (2004 [DIRS 168133], Section 4.0) concluded that cracks that are in close proximity can 
reduce the overall driving force for crack growth because the stress intensity factor (KI) for 
parallel cracks is actually less than that for a single flaw. Similarly, as discussed in 
Section 6.5.1, detailed analysis presented in Structural Integrity Associates Support of Waste 
Package Design for 2001 (Structural Integrity Associates 2002 [DIRS 161933]), indicates that 
the distance between two neighboring through-wall cracks would need to be greater than the wall 
thickness for the stress (and resultant stress intensity) to be sufficient to drive a flaw throughwall. 
In addition, neighboring cracks will also reduce the crack driving force by decreasing the 
overall residual stress state. In the case of a single crack embedded in a secondary stress field 
(e.g., residual stress), as the crack grows, the through-wall residual stress field will redistribute 
and can significantly change from the original distribution. As experience in boiling water 
reactors (BWRs) has shown (Herrera 2004 [DIRS 168133], Section 5 and Appendix A), cracks 
can actually initiate, grow partly through-wall, and arrest before penetration. The crack arrest is 
due to the redistribution of the weld residual stress such that the stress intensity factor drops 
below the threshold value for crack growth. 
If two cracks are in close proximity in a residual stress field, this relaxing effect is amplified to 
the point that one of the cracks may grow significantly deeper than the second crack as the 
growth of one of the cracks significantly reduces the driving force on the second crack 
(Herrera 2004 [DIRS 168133], Section 4.0). This has been the experience in many light water 
reactor (LWR) cases (field experience and mockup testing of austenitic stainless steels and 
nickel-based alloys (Alloy 22 is also a nickel-based alloy)) (Herrera 2004 [DIRS 168133], 
Section 4.0) (Section B6.3). Through-wall growth of neighboring cracks has not been observed 
and it is expected that the stress-relieving effect of neighboring cracks is the cause for this 
behavior. 
Even if through-wall stress corrosion cracking occurs such that it circumscribes the deformed 
area, the nature of stress corrosion cracking (crack face roughness) on this scale will preclude the 
deformed area from falling out (Herrera 2004 [DIRS 168133], Section 3.0). Stress corrosion 
cracking in Alloy 22 is expected to be transgranular, but whether transgranular or intergranular, 
the crack path is complex, with some local areas of branching, and all areas exhibiting a 
roughness and tortuosity that make it essentially impossible for separation of the inner plug to 
disengage from the rest of the material in the absence of superimposed primary load 
(e.g., significant internal pressure) (Herrera 2004 [DIRS 168133], Section 3.0). Any small 
internal pressure that develops from heat up of the waste package or corrosion due to the small 
amount of internal water vapor, or both, would not be sufficient to force the deformed area from 
the wall. 

 
l 
 B-9 
B6.3 LIGHT WATER REACTOR CASE HISTORIES 
The previous section concluded that multiple surface cracks will not grow to through-wall cracks 
when they are in close proximity to each other. Herrera (2004 [DIRS 168133], Appendix A) 
summarizes several case histories of stress corrosion cracking for light water reactors (LWRs) 
(i.e., boiling water reactor (BWR) and pressurized water reactor (PWR) components). Some of 
the most significant incidences of cracking discussed included the presence of crevices and did 
not always occur in areas subjected to the full primary system pressure (i.e., cracking in regions 
subjected to low differential pressures such as the BWR core shrouds) top guides and steam 
dryers and in PWR tube sheet and tube support plate creviced regions and at tube bend areas. 
Cracking often occurred in regions removed from welds and appeared to be driven by cold work 
related residual stresses. In describing the total extent of cracking (i.e., length and depth), it is 
important to distinguish between cracking driven by a combination of residual stress plus 
primary pressure stress-induced loads, and that due solely to residual stresses. The seismically 
loaded waste package is similar to cases when cracking is caused solely by residual stress (in the 
absence of differential pressure). 
Herrera (2004 [DIRS 168133], Appendix A) also reviewed a number of incidents of stress 
corrosion cracking observed in LWRs, involving austenitic stainless steels and nickel-based 
alloys (Alloy 22 is also a nickel-based alloy). In many of these cases, the cracking has been 
extensive, sometimes becoming fully circumferential on the component as driven by weld 
residual tensile stress plus pressure induced primary stresses. Even under these severe stress 
conditions, there has never been a documented case where any section of material dropped out as 
a result of the observed cracking. Observations in the BWR and PWR industry are consistent 
with the behavior of cracks that are located in close proximity. For example, the very few 
SCC-related steam generator tube ruptures observed occurred only under full-system differential 
pressure. Certainly, no material representing a continuous, through-wall circle has occurred that 
would give rise to a through-thickness piece being removed. 
Therefore, based on the analyses presented in Sections B6.1 to B6.3, seismic activity will not 
result in large areas separating from the waste package outer barrier. Instead, a network of stress 
corrosion cracks is expected to form in the waste package outer barrier due to residual stresses 
induced by seismic activity. The remainder of this document is devoted to modeling the 
characteristics of such a network of stress corrosion cracks. 
B6.4 ESTIMATION OF CRACK AREA DENSITY DUE TO SEISMIC ACTIVITY 
This section outlines the overall approach to obtain an estimate of the crack opening area on a 
waste package damaged by a seismic event. The cracks within the damaged area are assumed to 
be caused as a result of stresses induced by a seismic event. In order to assess the damage 
scenario that these individual cracks would not lead to significant radionuclide release due to a 
collectively large opening of these cracks, it is necessary to assess the possible number of cracks 
in the damaged area and the opening areas of these cracks. The total crack opening area within 
the seismic damaged area can be used in an assessment for the waste package subjected to 
various seismic events. 

 
l 
 B-10 
This section provides the basis for the selection of the effective crack opening area for use in the 
waste package performance assessment. The previous discussion presented the justification that 
deformation of areas during seismic events will not result in areas falling out from the waste 
package wall. The expected behavior of flaws that are in close proximity, consideration of the 
stressstrain fields due to the deformation, and LWR field experience provides the basis for the 
conclusion that areas will not fall out of the waste package wall. Previous analytical work, 
supported by field experience, has demonstrated that through-wall flaws will not grow when they 
are in close proximity. Results of prior analyses indicate that through-wall flaws would not be 
present if the spacing were less than the thickness of the component (Section 6.5.1). Using this 
information, the following section provides an estimate of the crack density and crack opening 
area for use in the performance assessment of the waste packages. 
B6.4.1 Technical Approach 
Based on the previous discussions, it is considered unrealistic that the deformed area would fall 
out of the waste package wall. The most likely limiting case is that the damaged areas on the 
waste package are penetrated by a network of tight cracks. This network of cracks will allow 
diffusive transport, but prevent advective flow and advective transport because of the small 
effective crack opening area of individual cracks. 
The seismic scenario requires three inputs to represent the effective area of a network of cracks: 
(1) the total damaged area on the waste package 
(2) the crack density in the damaged area on the surface of the barrier 
(3) the crack opening area of an individual crack. 
The damage abstractions for the seismic scenario will define the total damaged area on the 
barrier. The total area of the crack network, ASCC, NET, is then the product of the seismically 
damaged area, AD; the crack density, .SCC (# cracks per unit area); and the crack opening area of 
an individual crack, ASCC (area/crack), expressed as (Herrera 2004 [DIRS 168133], Section 6.1): 
ASCC, NET = AD ( .SCC ASCC) (Eq. B-1) 
The factor ( .SCC ASCC) (the crack area density or crack area per unit seismically damaged area 
(i.e., the fraction of the seismically damaged area, AD) through which radionuclides can be 
released) can be viewed as a scaling factor applied to the seismically damaged area to obtain the 
total area of the crack network, ASCC, NET. Section B6.4.2 provides estimates of the crack area 
density through analysis of networks of cracks arranged in a hexagonal geometry. 
Section B6.4.3 provides an alternative model for the crack area density by analysis of a damaged 
area with a circular geometry circumscribed by a single through-wall crack. Because the 
hexagonal array represents a high effective density (close spacing) of individual cracks, this 
hexagonal case, with crack center spacings set at the plate thickness, t, (Section B6.4.2) is 
considered a conservative representation. Section B6.4.3 provides an alternative model for the 
crack area density by analysis of a damaged area with a circular geometry circumscribed by a 
single through-wall crack. This is considered a limiting realistic case. 

 
l 
 B-11 
B6.4.2 Primary Conceptual Model for Crack Area Density: Hexagonal Geometry 
This section estimates the crack area density for a network of cracks arranged in a hexagonal 
geometry. Two crack arrangements are considered (Herrera 2004 [DIRS 168133], Section 6.2): 
Case 1The centers of elliptical cracks form a hexagonal array with major axis of length, 
3 
2t , where t is the wall thickness, with crack centers separated by 
3 
2t (Figure B-3). For 
this case, the hexagon side length is 
3 
2t , and the perpendicular bisector (the distance 
from the hexagon center to the midpoint of one of the hexagon sides) is the wall 
thickness, t. 
Case 2The centers of elliptical cracks form a hexagonal array with major axis of length 
2t, where t is the wall thickness, with crack centers separated by t (Figure B-5). For this 
case, the hexagon side length is t and the perpendicular bisector is 
2
3t . In this case, 
significant crack overlap is allowed to occur. 
As discussed in Section 6.5.1, detailed analysis presented in Structural Integrity Associates 
Support of Waste Package Design for 2001 (Structural Integrity Associates 2002 
[DIRS 161933]), indicates that the distance between two neighboring through-wall cracks would 
need to be greater than the wall thickness for the stress (and resultant stress intensity) to be 
sufficient to drive a flaw through-wall. This conclusion is based on stress field interactions 
between closely spaced parallel cracks. Case 1 uses the crack arrangement such that the 
perpendicular bisector is the wall thickness, t, while Case 2 uses the crack arrangement such that 
the distance between crack centers is equal to the wall thickness. 
The results from either of these conceptual models of crack arrangement are considered to be 
conservative because the crack centers are arranged in a densely packed closely spaced array, 
which allows for neighboring in-plane stress fields to overlap. 
Both conceptual models use the recommendations in Section 6.5 regarding the estimated length, 
intercrack spacing, and intercrack opening for the weld regions in the waste package lid. While 
the seismically induced damage to the waste package can occur at any location on the surface of 
these structures, the generic recommendations provide reasonable guidance for estimating the 
crack density and crack area in the seismic scenario. 
It was shown in Sections 6.5.1 and 6.5.2 that: 
1. The minimum distance between two neighboring parallel through-wall cracks is equal 
to the plate thickness 
2. The crack opening area is elliptical 

 
l 
 B-12 
3. The crack width of a single crack, d, for plane stress conditions in an infinite plate is 
given as (Tada et al. 2000 [DIRS 167756], p. 125): 
E
c s d ) 4 ( = (Eq. B-2) 
where 2c is the crack length, s is the value of plane stress, and E is the modulus of 
elasticity. The crack width corresponds to the minor axis of the elliptical cross-section 
of the crack. The crack opening area, ASCC, is equal to the area of the elliptical 
cross section: 
E
c c 
E
c c ASCC 
s p s p d p ) 2 ( ) 2 ( 
2 
2 
2 
2 
= .. 
. 
.. 
. = .. 
. 
.. 
. 
.. 
. 
.. 
. = (Eq. B-3) 
B.6.4.2.1 Case 1: Hexagonal Array with Side Length and Crack Length of 2t/v3 
Consider a hexagonal array with side length 
3 
2t , where t is the plate thickness (Figure B-3). 
Each point of the hexagonal array is the center of a crack with length 
3 
2t . This length allows 
for cracks, if they lie in the same plane, to just touch without overlapping as shown in 
Figure B-3. This crack length is smaller than that used for the waste package closure weld 
region as discussed in Section 6.5.1 of the main body of this report, in which it was concluded 
that the crack length was equal to twice the thickness. However, that conclusion was based on 
stress interaction between parallel cracks and, in this case, overlap between neighboring cracks is 
avoided (this is not true of the next case shown in Figure B-5). 
The crack density, .SCC is the average number of cracks in a hexagon of the array divided by the 
area of the hexagon. The number of cracks in each hexagonal unit cell is 3 regardless of crack 
orientation. This is easy to see for Figure B-3 in which the cracks are aligned in parallel. The 
crack at the center of the array in Figure B-3 provides a full crack. The cracks at each of the six 
corners of the hexagon are shared by two other hexagons, effectively contributing an average of 
one-third of a crack per corner, regardless of actual crack orientation (in Figure B-3, the cracks 
directly adjacent to the center contribute almost one-half of a crack and the other four edge 
cracks closer to (but not exactly) one-fourth of a crack). One should consider that the same 
shape is placed on each of the six corners of the hexagon and each corner is shared by three 
hexagons. Figure B-4 shows the cracks in random orientation to aid in visualization. Thus, each 
hexagon contains three full cracks. The area of the unit hexagon is calculated as the area of six 
equilateral triangles with side, , 
3 
2t as: 
3 
6 ) ( 
3 
2 
2
1 6 
2 t t t = . .. 
. 
. .. 
. 
.. 
. 
.. 
. (Eq. B-4) 

 
l 
 B-13 
It follows that the crack density, .SCC, is given by: 
2 2 2 
3 
3 
6
3 
t t 
.SCC = 
. .. 
. 
. .. 
. 
= (Eq. B-5) 
Then, using Equations B-3 and B-5 with 2c = 
3 
2t (the crack length), the crack area density 
(crack area per unit seismically damaged area) can be expressed as: 
E
s 
E 
s p 
E 
s t p 
t 
A . SCC SCC 81 . 1 
3 3 
) 2 ( 
2 
3 2 
2 . = = (Eq. B-6) 
NOTE: Not to scale. 
Figure B-3. Parallel Rows of Parallel Cracks Whose Centers are Arranged in a Hexagonal Array (with 
Row Spacing Equal to the Wall Thickness, t) 

 
l 
 B-14 
NOTE: Not to scale. 
Figure B-4. Parallel Rows of Randomly Oriented Cracks Whose Centers are Arranged in a Hexagonal 
Array (with Row Spacing Equal to Wall Thickness, t) 
B.6.4.2.2 Case 2: Hexagonal Array with Side Length, t, and Crack Length, 2t 
Consider a hexagonal array with side length t, where t is the plate thickness (Figure B-5). Each 
point of the hexagonal array is the center of a crack with length 2t. This crack length is the same 
as used for the waste package closure weld region as discussed in Section 6.2.2, in which it was 
concluded that the crack length was equal to twice the thickness. This geometry allows for 
cracks, if they lie in the same plane, to overlap significantly (each crack overlaps about half of 
each of its neighboring cracks) as shown in Figure B-5. The maximum overlap occurs when the 
cracks are exactly in line. The overlap will decrease if the crack orientation has some offset from 
the in-line direction. Conservatively, in calculating the total crack opening area, crack overlap is 
not considered (i.e., overlapped areas are counted twice) in order to provide an upper bound on 
the crack area density. 
The crack density, .SCC, is the average number of cracks in a hexagon of the array divided by the 
area of the hexagon. As in the previous case, the number of cracks in each hexagonal unit cell is 
three regardless of crack orientation. The area of the unit hexagon is calculated as the area of six 
equilateral triangles with side t as: 
2
3 3 ) ( 
4
3 6 
2 
2 t t = . .
.
. 
. .
.
. 
(Eq. B-7) 
It follows that the crack density, .SCC, is given by: 
2 2 3
2 
2
3 3 
3 # 
t t hexagon unit of area 
cracks of .SCC = 
. .
.
. 
. .
.
. 
= = (Eq. B-8) 

 
l 
 B-15 
Then, using Equations B-3 and B-8 with 2c = 2t, the total crack opening area per unit damage 
area can be expressed as: 
E
s 
E
s p 
E 
s t p 
t 
A . SCC SCC 26 . 7 
3 
4 ) 2 ( 
3
2 2 
2 . = = (Eq. B-9) 
NOTE: Not to scale. 
Figure B-5. Parallel Rows of Parallel Flaws (with Row Spacing Equal to (v3/2) Wall Thickness) 
B6.4.2.3 Summary of Primary Conceptual Model for Crack Area Density 
The crack area density for Case 1 (where cracks can barely touch) is 
E 3
s p , and that for Case 2 
(where significant crack overlap is allowed) is 
E 3 
4 s p . The crack area density is shown to be 
proportional to the applied stress, essentially residual stress due to seismic activity, and inversely 
proportional to the Youngs Modulus. It does not depend on the wall thickness. Therefore, the 
crack area density is recommended to be represented as a uniform distribution between 
E 3
s p 
and 
E 3 
4 s p , i.e.: 
E 
C 
3 
Density Area Crack ps = (Eq. B-10) 
where C = epistemic uncertainty factor given by a uniform distribution between 1 and 4. 
The use of a uniform distribution is reasonable since it accurately reflects the lack of knowledge 
of the exact value of the crack area density. In general, a uniform distribution is appropriate for 
uncertain quantities where the range can be established by physical arguments or expert 
knowledge  but not much else is known about the relative likelihood of values within the range 
(Mishra 2002 [DIRS 163603], Section 2.3). The use of a distribution ranging up to the very 

 
l 
 B-16 
conservative upper bound allows for uncertainties, such as the potential for crack overlap and 
deviations from a regular array of identically shaped cracks, to be appropriately accounted for. 
The yield strength of the material should be used as a very conservative estimate for the stress 
component in the crack area density calculation. The yield strength is considered conservative 
because the process of crack initiation and through-wall crack propagation will result in 
significant reduction in the residual stress. The use of material yield strength will give a 
conservative estimate of the crack area density appropriate for probabilistic evaluation. Values 
of the Alloy 22 yield strength and Youngs Modulus at room temperature and at 150C 
(the temperature at which the structural calculations of the waste package exposed to ground 
motion were conducted (BSC 2004 [DIRS 167083], Section 3)) are shown in the second and 
third columns of Table B-2. The value of the Alloy 22 yield strength at 150C (~423 K) was 
determined by linear interpolation between the values for the Alloy 22 yield strength at 366 K 
and 477 K (Table B-1): 
( ) MPa 310 MPa 338 MPa 283 
K 366 - K 477 
K 423 - K 477 - MPa 283 K 423 @ . -  . .. 
. 
. .. 
. 
= Strength Yield (Eq. B-11) 
The value of the Alloy 22 Youngs Modulus at 150C (~423 K) was determined by linear 
interpolation between the values for the Alloy 22 Youngs Moduli at 366 K and 477 K 
(Table B-1): 
( ) GPa 199 GPa 203 GPa 196 
K 366 - K 477 
K 423 - K 477 - GPa 196 K 423 @ ' . -  . .. 
. 
. .. 
. 
= Modulus s Young (Eq. B-12) 
In Table B-2, calculations of the crack length (hexagon side length), crack density, crack width, 
crack opening area, and crack area density are shown for various barrier thicknesses for both 
hexagonal cases are presented. Table B-2 shows that the range of the crack area density (crack 
area per unit seismically damaged area) ranges from 3.28  10-3 to 1.31  10-2 at room 
temperature, and 2.83  10-3 to 1.13  10-2 at 150C. It is recommended that the room 
temperature range of crack area density be used for performance assessment as this choice yields 
higher (more conservative) crack area densities. 

 
l 
 B-17 
Table B-2. Crack Characteristics for Hexagonal Geometry 
Temperature 
(C) 
Yield 
Stress 
(MPa) 
Youngs 
Modulus 
(GPa) Case 
Barrier 
Thickness1 
(mm) 
Crack 
Length2 
(mm) 
Crack 
Density3 
(/mm2) 
Crack 
Width4 
(mm) 
Crack 
Opening 
Area5 
(mm2) 
Crack 
Area 
Density6 
18.0 20.8 2.67  10-3 7.51  10-2 1.23 3.28  10-3 
20.0 23.1 2.17  10-3 8.34  10-2 1.51 3.28  10-3 
23.0 26.6 1.64  10-3 9.59  10-2 2.00 3.28  10-3 1 
25.0 28.9 1.39  10-3 1.04  10-1 2.36 3.28  10-3 
18.0 36.0 3.56  10-3 1.30  10-1 3.68 1.31  10-2 
20.0 40.0 2.89  10-3 1.44  10-1 4.54 1.31  10-2 
23.0 46.0 2.18  10-3 1.66  10-1 6.00 1.31  10-2 
Room 372 206 
2 
25.0 50.0 1.85  10-3 1.81  10-1 7.09 1.31  10-2 
18.0 20.8 2.67  10-3 6.48  10-2 1.06 2.83  10-3 
20.0 23.1 2.17  10-3 7.20  10-2 1.31 2.83  10-3 
23.0 26.6 1.64  10-3 8.27  10-2 1.73 2.83  10-3 1 
25.0 28.9 1.39  10-3 8.99  10-2 2.04 2.83  10-3 
18.0 36.0 3.56  10-3 1.12  10-1 3.17 1.13  10-2 
20.0 40.0 2.89  10-3 1.25  10-1 3.92 1.13  10-2 
23.0 46.0 2.18  10-3 1.43  10-1 5.18 1.13  10-2 
150C 310 199 
2 
25.0 50.0 1.85  10-3 1.56  10-1 6.12 1.13  10-2 
Output DTN:MO0403SPASCRKD.000. 
NOTES: 1. The values of the barrier thickness are for illustration purposes only. 
2. The crack length equals 
3 
2t for Case 1 and 2t for Case 2. 
3. The crack density equals 
2 2 
3 
t 
for Case 1 and 
2 3
2
t 
for Case 2. 
4. The crack width of a single crack is given by Equation B-2 for the given thickness for each case. 
5. The crack opening is calculated from Equation B-3 for the two cases. 
6. The crack area density is calculated from Equation B-6 for Case 1 and Equation B-9 for Case 2. 
B6.4.3 Alternative Conceptual Model for Crack Area Density: Circular Geometry 
This section considers a conceptual model of a through-wall crack circumscribing a circular 
damaged area. The main purpose of this model is to provide an alternative mathematical model 
for crack area density, which can be used in validation of the primary crack area density model. 
Even though this model leads to a fully circumscribed area, the inner area material would not fall 
out due to the roughness of crack surfaces. It should be emphasized that this calculation and 
associated postulated crack morphology are strictly for calculating an alternative crack opening 
area. It is not meant to imply that this of crack morphology is observed. 
Timoshenko and Goodier (1970 [DIRS 121096], pp. 68 to 71) present the solution to a hollow 
cylinder under internal pressure (pi) and external pressure (po) of inner radius (a) and external 
radius (b) (Figure B-6) under plane stress conditions. This solution can be easily adapted to 
determining the displacement about a hole in a two-dimensional infinite body subjected to a 
radial stress, S. The surface of the hole can be considered to be the crack surface for the 

 
l 
 B-18 
purposes of this analysis. For this radially symmetric problem (Timoshenko and Goodier 1970 
[DIRS 121096], p. 70): 
r
u = . e (Eq. B-13) 
Further, Hookes Law can be written for an isotropic material for plane stress as: 
r E .s s e . . - = (Eq. B-14) 
where 
u = the radial displacement 
r = distance from the origin in a polar coordinate system 
E = Youngs modulus and 
. = Poissons ratio. 
Figure B-6. Hollow Cylinder of Inner Radius a and Outer Radius b Subject to Internal Pressure pi and 
External Pressure po 
The following are expressions for the radial and tangential stress components (Timoshenko and 
Goodier 1970 [DIRS 121096], p. 70): 
( ) 
( ) 
2 2 
2 2 
2 2 2 
2 2 
2 2 
2 2 
2 2 2 
2 2 
1 
1 
a b 
b p a p 
r a b 
p p b a 
a b 
b p a p 
r a b 
p p b a 
o i i o 
o i i o 
r 
-
- 
+ 
- 
- 
- = 
-
- 
+ 
- 
- 
= 
. s
s 
(Eq. B-15) 

 
l 
 B-19 
For the purposes of this analysis, b approaches infinity (infinite plate), po = -S, and we are 
interested in the radial displacements at r = a (the surface of the hole). With these conditions, at 
r = a, sr = 0 and s. = 2S. Using Equations B-13 and B-14, the radial displacement, u, at r = a is: 
E
aS u 2 = (Eq. B-16) 
More generally, it has been shown by the above analysis that the radial displacement (u) at the 
surface of the hole of radius, r, under the action of a radial stress, s, could be written as: 
E
s r u 2 = (Eq. B-17) 
where r = radius of hole (i.e., radius of damaged area) 
s = applied stress. 
The radial displacement (u) in Equation B-17 can be considered the crack opening for a crack 
circumscribing a damaged area with a radius of r. This is equivalent to the conservative case 
where the inner material is detached (i.e., cracked through-wall around the entire circumference) 
and not subjected to any stress (i.e., not decreasing the displacement particularly by pulling on 
the outer material). The crack opening area of this crack can be expressed as: 
E 
s r p 
E
s r r p ru p ASCC 
2 4 2 2 2 = = = (Eq. B-18) 
The damaged area is pr2. Therefore the crack area density, realizing that there is one circular 
crack in each circular area of radius r, can be expressed as: 
E
s 
E 
s r p 
r p 
A . SCC SCC 4 4 1 2 
2 = . .. 
. 
. .. . 
.. 
. 
.. 
. = (Eq. B-19) 
The crack area density (.SCC ASCC) depends only on the stress state and the Youngs modulus. 
Values of the Alloy 22 yield strength and Youngs modulus at room temperature and at 150C 
are shown in the second and third columns of Table B-3. In Table B-3, calculations of the crack 
length, crack density, crack opening area, and crack area density are shown for various radii of 
the damaged area are presented. The crack area density calculated using values of the Alloy 22 
yield strength and Youngs Modulus at room temperature is about 7.22  10-3, while the crack 
area density calculated at 150C is about 6.23  10-3. 

 
l 
 B-20 
Table B-3. Crack Characteristics for Circular Geometry 
Temperature 
(C) 
Yield 
Stress 
(MPa) 
Youngs 
Modulus 
(GPa) 
Radius1 
(mm) 
Crack 
Length2 
(mm) 
Crack 
Density3 
(/mm2) 
Crack 
Width4 
(mm) 
Crack 
Opening 
Area5 
(mm2) 
Crack Area 
Density6 
18.0 113 9.82E-04 6.50E-02 7.35 7.22E-03 
20.0 126 7.96E-04 7.22E-02 9.08 7.22E-03 
23.0 145 6.02E-04 8.31E-02 12.0 7.22E-03 
Room 372 206 
25.0 157 5.09E-04 9.03E-02 14.2 7.22E-03 
18.0 113 9.82E-04 5.61E-02 6.34 6.23E-03 
20.0 126 7.96E-04 6.23E-02 7.83 6.23E-03 
23.0 145 6.02E-04 7.17E-02 10.4 6.23E-03 
150C 310 199 
25.0 157 5.09E-04 7.79E-02 12.2 6.23E-03 
Output DTN: MO0403SPASCRKD.000. 
NOTES: 1Values of the barrier thickness are for illustration purposes only. 
2Crack length equals 2pr. 
3Crack density equals 1/pr2 from Equation B-13. 
4Crack width is given by Equation B-17. 
5Crack opening is calculated from 2pru from Equation B-18. 
6Crack area density is calculated from Equation B-19. 
B7. VALIDATION 
The seismic crack density model is an abstraction model whose primary purpose is to provide 
input to Seismic Consequence Abstraction (BSC 2004 [DIRS 169183]). The developed crack 
area density is used as a scaling factor applied to the total seismic damaged area to obtain the 
total area of the crack network through which radionuclide transport could occur. 
This model was validated using the approach described in the technical work plan governing this 
activity (BSC 2004 [DIRS 171583]) and is consistent with AP-SIII.10Q, Models. This procedure 
calls for the determination of the level of confidence required for the model and identifies criteria 
that can be utilized to show that the level of confidence has been achieved. These criteria 
include performing an independent technical review. In addition, confidence building has been 
incorporated into this section. 
B.7.1 DETERMINATION OF LEVEL OF CONFIDENCE REQUIRED 
The current technical work plan for this report (BSC 2004 [DIRS 171583], Section 2.2.2) states 
that the seismic crack density model (SCDM) warrants a high level of confidence (Level III). 
This conclusion was based on the answers to several questions related to the characteristics of 
the SCDM. These questions and answers are repeated below: 
Is the model extrapolated over large distances, spaces, or time frames? 
Yes. The Seismic Crack Density Model is extrapolated over the entire repository footprint and 
over the entire regulatory compliance period. 

 
l 
 B-21 
Does the model have large uncertainties? 
Yes. There is uncertainty in the parameters used in the Seismic Crack Density Model, these 
uncertainties can be large. 
Will the model be used to demonstrate compliance or licensing positions? 
Yes. The SCDM is used as an input to the seismic consequence report, which provides the 
estimates of the crack opening area for ingress of water into the waste package. 
Will the output of the model have impacts (positive or negative) on TSPA dose calculation 
results? 
Yes. Although the effect of nonseismic stress corrosion cracking penetrations in the drip shield 
and waste package outer barrier are estimated to have relatively small impacts on TSPA 
dose calculations, the SCDM is used as an input to Seismic Consequence Abstraction 
(BSC 2004 [DIRS 169183]) and the impacts of the model on dose calculations are 
expected to be large. 
Based on the above, it is reasonable to assign the level of confidence needed for the SCDM to be 
high (Level III). This is consistent with the technical work plan (BSC 2004 [DIRS 171583], 
Table 2-1) that lists several postdevelopment model validation methods described in 
Section 5.3.2.c of AP-SIII.10Q, Models. 
B7.2 IDENTIFICATION AND DOCUMENTATION OF VALIDATION ACTIVITIES 
AND ASSOCIATED CRITERION TO BE USED TO DETERMINE THAT THE 
REQUIRED LEVEL OF CONFIDENCE HAS BEEN OBTAINED 
The technical work plan (BSC 2004 [DIRS 171583], Table 2-1) for this report identified the 
following criteria and associated activities to be used to determine that the required level of 
confidence has been obtained for the seismic crack density model (SCDM). 
Criterion One: Corroborating data must match qualitatively 
Activity One: Demonstrate corroborating data match qualitatively 
Activity Two: Demonstrate the model results for crack patterns in the damaged areas are 
consistent with the results of an alternative conceptual model 
Criterion Two: Independent technical review to demonstrate: 
Corroborating data or alternative models selected by the technical reviewer must match 
qualitatively (corroboration will be considered successful if deemed defendable by the reviewer). 
Activity One: Conduct an independent technical review for the crack density model (only), and 
the review will answer the following questions: 

 
l 
 B-22 
- Subactivity One: Are the representations of the damaged area in the form of a crack 
network instead of a hole consistent with observation in literature? This activity deals 
with the validity of the crack density representations in the seismically damaged areas. 
- Subactivity Two: Are the model results for crack patterns in the damaged areas 
consistent with the results of an alternative conceptual model? 
The activities and associated criteria are primarily related to confidence building during model 
development although they do provide additional confidence in the SCDM results. In particular, 
the criteria and related activity cited in Table 2-1 of the technical work plan (BSC 2004 [DIRS 
171583]) are consistent with Section 5.3.2.c of AP-SIII.10Q, Models. 
B7.3 DOCUMENTATION OF ACTIVITIES TO BE PERFORMED TO GENERATE 
CONFIDENCE IN THE MODEL DURING MODEL DEVELOPMENT 
The criteria and related activities to be used to determine that the required level of confidence 
has been obtained for the seismic crack density model (SCDM) were listed in Section B7.2. 
Criterion One, Activity One is satisfied by the discussions throughout this appendix but 
particularly those of Sections B6.2 and B6.3 in which the nature of stress corrosion cracking and 
analysis of BWR and LWR stress corrosion cracking case histories are discussed. 
Among the observations made in Section B6.2: 
 It is unlikely that the residual stress profile, which would be created by seismic loading, 
would allow an initiated stress corrosion crack to propagate both through-wall and 
circumscribing the deformed area 
 The through-wall residual stress fields resulting from impact loads would be a secondary 
type stress (displacement controlled) and there is no source of significant internal 
pressure 
 Stress fields would be expected to be maximum at the outer surface and decrease with 
depth 
 The magnitude of the stress state will decrease as the crack propagates 
 Stress field interactions between adjacent cracks would tend to decrease the driving 
force for crack growth 
 The nature of stress corrosion cracks (crack face roughness, branching, and tortuosity) is 
such that large sections of material will not fall out of the cracked structure. 
The primary observation made in Section B6.3 was, even under the severe stress conditions 
experienced in LWRs, there are no documented cases where any section of material dropped out 
as a result of cracking. 

 
l 
 B-23 
On the basis of these observations, a reasonable level of confidence has been obtained that 
representations of the damaged area in the form of crack network instead of a hole is consistent 
with observations in the literature and is the expected morphology of waste package throughwall 
stress corrosion cracking due to seismic loading. 
Criterion One, Activity Two is satisfied by Section B6.4.3, in which an alternative mathematical 
model for stress corrosion crack morphology and damaged area shape is presented. The primary 
model for crack area density was summarized in Section B6.4.2. The crack area density based 
on hexagonal crack arrays was found to be given by a uniform distribution between 
E 3
s p and 
E 3 
4 s p (~1.81 
E
s and ~7.26 
E
s). For the alternative model (Section B6.4.3), the crack area density 
based on a circular seismically damaged area with a single circumferential crack was found to be 
4 
E
s. The crack area density from the alternative mathematical model lies between the bounds of 
the crack area density resulting from the primary mathematical model. Therefore, the results of 
the alternative mathematical model corroborate the results of the primary mathematical model. 
This model validation methodology is consistent with Section 5.3.2.c.2 of AP-SIII.10Q, Models. 
To satisfy validation criterion two, a technical review, planned in the technical work plan for this 
activity (BSC 2004 [DIRS 171583], Section 2.2.3.2), was conducted by reviewers independent 
of the development, checking, and interdisciplinary review of the model documentation. The 
results of this technical review also serve to satisfy the model validation requirements of 
AP-SIII.10Q, Models, Section 5.3.2.c.5. 
Technical reviewers were asked to address the following criteria (Pasupathi 2004 
[DIRS 168350]): 
1. Is the representation of the failure in the form of cracks in the damaged area 
technically appropriate? 
2. Does the model consider a variety of crack patterns and distributions? 
3. Are the crack networks considered in the model appropriate and reasonable? 
4. Does the crack network representations considered in the model represent optimum 
crack density (i.e., number, size, shape and distribution of cracks) such that the largest 
possible crack opening area is included? 
5. Do alternative models exist for crack geometry morphology? 
6. Has uncertainty in the parameters used to describe the model been adequately 
characterized? If not, what additional uncertainties should be added? 
7. Are there alternate crack patterns that are more defensible from a technical standpoint? 

 
l 
 B-24 
The responses to each of these independent technical review criteria are considered throughout 
the remainder of this section. 
(1) Is the representation of the failure in the form of cracks in the damaged area 
technically appropriate? 
Generally, the technical reviewers felt that the analysis has done a good job of looking at various 
crack geometries in the damaged area (Jones 2004 [DIRS 168353]). The representation of the 
failure in the form of cracks in the damaged area was found to be technically appropriate 
(Payer 2004 [DIRS 168352]). One technical reviewer (Beavers 2004 [DIRS 168354]) agreed 
that the damaged area likely failed by SCC clusters (arrays of cracks) rather than by the 
formation of large holes; however, the technical reviewer felt that the report sent for his review 
did not effectively prove this was the case. This technical reviewer (Beavers 2004 
[DIRS 168354]) recommended that additional analysis and discussion be provided. The report in 
question was revised (Herrera 2004 [DIRS 168133]) in response to these comments and the 
revision forms the basis for the model documented in this appendix. 
Conclusion/Response: On this basis, it is concluded that the technical reviewers agreed that the 
representation of the failure in the form of cracks in the damaged area is technically appropriate. 
(2) Does the model consider a variety of crack patterns and distributions? 
(3) Are the crack networks considered in the model appropriate and reasonable? 
The technical reviewers generally provided their answers to both of these review criteria 
together. Therefore, their responses are treated together in this summary. 
A variety of crack patterns and distributions are considered (Payer 2004 [DIRS 168352]). The 
technical reviewers felt that the crack networks considered in the model were appropriate and 
reasonable (Payer 2004 [DIRS 168352]; Jones 2004 [DIRS 168353]). The technical reviewers 
expressed concerns that a more relevant geometry might be cracks constrained to an annulus 
around the deformed area and not cracks distributed throughout the deformed area (Jones 2004 
[DIRS 168353]; Beavers 2004 [DIRS 168354]). Additional analysis was recommended for this 
damaged area geometry (Jones 2004 [DIRS 168353]; Beavers 2004 [DIRS 168354]). One 
reviewer (Beavers 2004 [DIRS 168354]) suggested that a circular crack circumscribing the 
damaged area was also a reasonable geometry to consider. 
Conclusion/Response: The area damaged by seismic activity is not assigned a specific shape, 
only an area, AD. The hexagonal crack density is applied to whatever area is seismically 
damaged regardless of its specific shape. A circular crack circumscribing the damaged area was 
considered as an alternative conceptual model in this report. Given the preceding observations, it 
is concluded, overall, the report considers a variety of crack patterns and distributions and the 
crack networks considered in the model are appropriate and reasonable. 

 
l 
 B-25 
(4) Does the crack network representations considered in the model represent 
optimum crack density i.e. number, size, shape and distribution of cracks, such 
that the largest possible crack opening area is included? 
In the context of this review, the wording the largest possible crack opening area should be 
restated as an appropriate representation of crack area. The technical reviewers generally 
agreed that the hexagonal array of cracks was the optimum crack density or geometry for 
analysis, however, additional justification should be provided for the intercrack spacing (t, the 
wall thickness) (Beavers 2004 [DIRS 168354]; Jones 2004 [DIRS 168353]). 
Conclusion/Response: The technical reviewers did not evaluate the documented basis for the 
intercrack spacing used, Structural Integrity Associates Support of Waste Package Design 
for 2001 (Structural Integrity Associates 2002 [DIRS 161933]; Section 6.5.1). If the technical 
reviewers reviewed this detailed minimum crack spacing analysis, they would be more confident 
in the choice made for intercrack spacing. 
On this basis, the crack network representations considered in the model represent the optimum 
crack density (i.e., the number, size, shape and distribution of cracks), such that an appropriate 
representation of crack area is included. 
(5) Do alternative models exist for crack geometry morphology? 
Two of the reviewers (Jones and Payer) were aware of alternative models for crack geometry, 
although only one (Jones) could specify what he thought was the most relevant geometry. The 
third reviewer (Beavers) was unaware of any alternative models for crack geometry (Payer 2004 
[DIRS 168352]; Jones 2004 [DIRS 168353]; Beavers 2004 [DIRS 168354]). 
Conclusion/Response: The area damaged by seismic activity is not assigned a specific shape, 
only an area, AD. The hexagonal crack density is applied to whatever area is seismically 
damaged regardless of its specific shape. A circular crack circumscribing the damaged area was 
considered as an alternative conceptual model in this report. Given the preceding observations, 
overall, the technical reviewers were satisfied that alternative models for crack geometry or 
morphology were considered. 
(6) Has uncertainty in the parameters used to describe the model been adequately 
characterized? If not, what additional uncertainties should be added. 
One technical reviewer (Payer 2004 [DIRS 168352]) had no response. One reviewer 
(Beavers 2004 [DIRS 168354]) did not think the report, as supplied for review, adequately 
addressed uncertainty. Another reviewer (Jones 2004 [DIRS 168353]) pointed out several 
conservatisms in the analysis: 
a) The analysis did not consider the decrease in residual stress as the crack propagates. 
There is a possibility of crack arrest, although no credit is taken for this process. Also 
decreased stress states would lead to narrower crack openings. 

 
l 
 B-26 
b) The analysis uses the crack mouth opening to represent the crack opening. The crack 
tip opening is less than the crack mouth opening. The reviewer supplied a crack 
mouth opening equation, which is less conservative than the one used in the analysis. 
c) The use of the yield stress as the stress load on the cracks is conservative (the residual 
stress at penetration should be lower). 
and pointed out some possible nonconservatisms: 
d) The Tada analysis used to determine the crack opening is based on an infinite plate, 
how much difference would there be for a finite cylinder? 
e) Deformation beyond the yield strength could result in work hardening and a higher 
value of yield strength. 
Conclusion/Response: The crack opening results presented in this Appendix are based upon 
plane stress conditions in an infinite plate. The actual structure for the Alloy 22 waste package 
outer barrier consists of a cylindrical shell of finite length. It would be expected that crack 
openings in an infinite plate under plane stress would be different than in a finite cylindrical shell 
in that the membrane stresses and flexural stresses for given loadings in combination with other 
loads would be different. The analysis is used to determine a crack area density (crack area per 
unit seismically damaged area) given a seismically damaged area determined elsewhere 
(BSC 2004 [DIRS 167083]). That is, the spatial stress state is determined elsewhere and 
determined based upon consideration of a cylindrical shell of finite length. Structural 
Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 
[DIRS 167083], Section 3) uses a residual stress threshold, which is uniformly distributed 
between 80% and 90% of the yield strength of Alloy 22 at 150C. This calculation uses a stress 
state that is equal to the yield strength at room temperature (i.e., the temperature and stress state 
used are conservative). Detailed comparisons between crack openings in infinite plates and 
finite cylinders were not undertaken in this analysis, however, the results of analyses such as 
those in Structural Integrity Associates Support of Waste Package Design for 2001 (Structural 
Integrity Associates 2002 [DIRS 161933]) indicate that the presence of multiple cracks will tend 
to decrease the residual stress state to values well below the yield strength. This would result in 
crack openings that are smaller than those calculated. Coupling this result to the listed 
conservatisms outlined in this section (decreasing stress states as the crack propagates, 
conservative crack opening equations, the use of the yield strength at room temperature), it can 
be concluded that the current model will provide a reasonably conservative representation of the 
total crack opening area. On the basis of the discussion in this ection, it is concluded that 
uncertainty in the parameters used to describe the model been adequately characterized at least to 
the extent that the total crack opening area will not be underestimated using the current model. 
(7) Are there alternate crack patterns that are more defensible from a technical 
standpoint? 
This criterion is similar to criteria 2 through 5. As stated in the discussion of criterion 2, the 
technical reviewers did express concerns that a more relevant geometry might be cracks 
constrained to an annulus around the deformed area and not cracks distributed throughout the 

 
l 
 B-27 
deformed area (Jones 2004 [DIRS 168353]; Beavers 2004 [DIRS 168354]). One reviewer 
(Beavers 2004 [DIRS 168354]) indicated that while the hexagon pattern is a reasonable, 
defensible crack pattern for the deformed area of the waste package . . . a combination of this 
pattern with the circumferential pattern to produce a series of circular cracks around the dents is 
the most reasonable pattern. Further conversation with this technical reviewer (Pasupathi 2004 
[DIRS 168351]) led to the conclusion that what was meant by circumferential pattern of cracks 
to produce a series of circular cracks was actually cracks constrained to an annulus around the 
deformed area and not cracks distributed throughout the deformed area. 
Conclusion/Response: The area damaged by seismic activity is not assigned a specific shape, 
only an area, AD. The hexagonal crack density is applied to whatever area is seismically 
damaged regardless of its specific shape. A circular crack circumscribing the damaged area was 
considered as an alternative conceptual model in this report. Given the preceding observations, it 
is concluded that, overall, the technical reviewers were satisfied that alternative models for crack 
geometry or morphology were considered and the crack patterns analyzed were sufficient from a 
technical standpoint. 
On this basis, the validation criteria from AP-SIII.10Q, Models, related to corroboration and 
those listed in the technical work plan governing this report (BSC 2004 [DIRS 171583], 
Section 2.2.5) have been satisfied and the SCDM is valid for use in TSPA-LA. 
B8. CONCLUSIONS 
Seismic activity can lead the waste packages to impact other components in the drift including 
the emplacement pallets, drip shields, and other waste packages. If the seismically induced 
impacts are of sufficient magnitude, the impacts may physically deform the waste package outer 
barrier and potentially the waste package inner vessel. These deformations could cause cold 
work of the waste package barrier and vessel materials, producing a cold-worked gradient 
typically highest on the outer surface and smallest on the inner surface. Impacts could also 
create complex through-wall residual stress profiles. These stress profiles and cold-work 
gradients could lead to stress corrosion cracking in the seismically affected area of the waste 
packages. 
Similar damage can be expected for drip shields under seismic loadings, however, as in the 
treatment of stress corrosion cracking due to rockfalls discussed in Section 6.3.7, stress corrosion 
cracks in the drip shields are expected to be tight and plugged with corrosion products or mineral 
deposits, or both, leading to negligible water flow through these openings. Therefore, since the 
primary role of the drip shield is to keep water from contacting the waste package, stress 
corrosion cracking of the drip shield does not compromise its intended design purpose. 
A number of incidents of stress corrosion cracking have been observed in LWRs involving both 
austenitic stainless steels and nickel-based alloys. In many of these cases, the cracking has been 
extensive, sometimes becoming fully circumferential on the component as driven by weld 
residual tensile stress plus pressure induced primary stresses. Even under these severe stress 
conditions, there has never been a documented case where has any section of material dropped 
out as a result of the observed cracking. Observations in the BWR and PWR industry are 
consistent with the expected behavior of flaws that are located in close proximity. For example, 

 
l 
 B-28 
the very few stress corrosion cracking related steam generator tube ruptures observed occurred 
only under full system differential pressure. Certainly, no material representing a continuous, 
through-wall circle has occurred that would give rise to a through thickness piece being 
removed. 
On the basis of these results, it is concluded that seismic activity will not result in large areas 
separating from the waste package outer barrier. Instead a network of stress corrosion cracks is 
expected to form in the waste package outer barrier due to residual stresses induced by seismic 
activity. An uncertain distribution for the crack area density (crack area per unit seismically 
damaged area) was developed and is discussed in the next section. 
B8.1 DEVELOPED OUTPUTS 
For the Alloy 22 waste package outer barrier, the crack area density is given by (Section B6.4.2): 
E 
C 
3 
Density Area Crack ps = (Eq. B-20) 
where C = epistemic uncertainty factor given by a uniform distribution between 1 and 4. 
It is recommended that the room temperature Alloy 22 yield strength (372 MPa) and Youngs 
modulus (206 GPa) be used (Table B-1). These values lead to the crack area density being 
uniformly distributed between 3.28  10-3 and 1.31  10-2 (Table B-2). These results are 
summarized below in Table B-4. 
Table B-4. Crack Area Density Parameters and Their Sources 
Parameter Name Parameter Source (for TSPA) Parameter Value Units 
Crack Area Density DTN: MO0403SPASCRKD.000 Uniform distribution between 
3.28  10-3 and 1.31  10-2 N/A 
B8.2 TREATMENT OF ACCEPTANCE CRITERIA 
The acceptance criteria identified in Section B4.2 are discussed in Section 8.2. 
B.9 INPUTS AND REFERENCES 
This document may be affected by technical product input information that requires 
confirmation. Any changes to the document that may occur, as a result of completing the 
confirmation activities, are reflected in subsequent revisions. The status of the input information 
quality may be confirmed by review of the Document Input Reference System database. 
B9.1 DOCUMENTS CITED 
167840 Andresen, P.L.; Emigh, P.W.; Young, L.M.; and Gordon, G.M. 2001. Stress 
Corrosion Cracking of Annealed and Cold Worked Titanium Grade 7 and Alloy 22 in 
110C Concentrated Salt Environments. Corrosion/2001, [56th Annual Conference 

 
l 
 B-29 
& Exposition, March 11-16, 2001, Houston, Texas, USA]. Paper No. 01130, 
Houston, Texas: NACE International. TIC: 255671. 
168354 Beavers, J. 2004. Report Review. E-mail to P. Pasupathi. 02/24/2004. 
ACC: MOL2004.0311.0147. 
169766 BSC (Bechtel SAIC Company) 2004. Commercial SNF Waste Package Design 
Report. 000-00C-DSU0-02800-000-00B. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: ENG.20040709.0001 
170992 BSC 2004. Safety Classification of SSCs and Barriers. 000-00C-MGR0-01000-000- 
00A. Las Vegas, Nevada: Bechtel SAIC Company. ACC: ENG.20040721.0005. 
168361 BSC 2004. Q-List. 000-30R-MGR0-00500-000-000 REV 00. Las Vegas, Nevada: 
Bechtel SAIC Company. ACC: ENG.20040721.0007. 
169183 BSC 2004. Seismic Consequence Abstraction. MDL-WIS-PA-000003, Rev. 01. Las 
Vegas, Nevada: Bechtel SAIC Company. 
167083 BSC 2004. Structural Calculations of Waste Package Exposed to Vibratory Ground 
Motion. 000-00C-WIS0-01400-000-00A. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: ENG.20040217.0008. 
171583 BSC 2004. Technical Work Plan For: Regulatory Integration Modeling and Analysis 
of the Waste Form and Waste Package. TWP-WIS-MD-000009 REV 00 ICN 01. Las 
Vegas, Nevada: Bechtel SAIC Company. ACC: DOC.20040910.0001. 
168133 Herrera, M.L. 2004. Evaluation of the Potential Impact of Seismic Induced 
Deformation on the Stress Corrosion Cracking of the YMP Waste Packages. SIR-04- 
015 Revision No. 1. San Jose, California: Structural Integrity Associates, Inc. 
ACC: MOL.20040311.0149. 
168353 Jones, R.H. 2004. "RE: Independent Technical Review of the Seismic Crack Density 
Model." E-mail from R.H. Jones to J. Payer, J. Beavers, and P. Pasupathi, February 
20, 2004, with attachment. ACC: MOL.20040311.0145. 
163603 Mishra, S. 2002. Assigning Probability Distributions to Input Parameters of 
Performance Assessment Models. SKB TR-02-11. Stockholm, Sweden: Svensk 
Krnbrnslefrsrjning A.B. TIC: 252794. 
163274 NRC (U.S. Nuclear Regulatory Commission) 2003. Yucca Mountain Review Plan, 
Final Report. NUREG-1804, Rev. 2. Washington, D.C.: U.S. Nuclear Regulatory 
Commission, Office of Nuclear Material Safety and Safeguards. TIC: 254568. 
168350 Pasupathi, P. 2004. Independent Technical Review of the Seismic Crack Density 
Mode. Las Vegas, Nevada: Bechtel SAIC Company. ACC: MOL.20040311.0141. 

 
l 
 B-30 
168351 Pasupathi, P. 2004. Additional Clarification Provided by the Independent Technical 
Reviewer on the Seismic Crack Density. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: MOL.20040311.0148. 
168352 Payer, J.H. 2004. "Independent Technical Reviews." E-mail from J.H. Payer to P. 
Pasupathi, February 29, 2004, with attachment. ACC: MOL.20040311.0143. 
161933 Structural Integrity Associates. 2002. Structural Integrity Associates Support of 
Waste Package Design for Year 2001. SIR-02-073. San Jose, California: Structural 
Integrity Associates. ACC: MOL.20020709.0389. 
167756 Tada, H.; Paris, P.C.; and Irwin, G.R. 2000. The Stress Analysis of Cracks 
Handbook. 3rd. New York, New York: American Society of Mechanical Engineers. 
TIC: 255547. 
121096 Timoshenko, S.P. and Goodier, J.N. 1970. Theory of Elasticity. 3rd Edition. New 
York, New York: McGraw-Hill. TIC: 245469. 
B9.2 CODES, STANDARDS, REGULATIONS, AND PROCEDURES 
AP-2.22Q, Rev. 1, ICN 1. Classification Analyses and Maintenance of the Q-List. 
Washington, D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste 
Management. ACC: DOC.20040714.0002. 
AP-2.27Q, Rev. 1, ICN 4. Planning for Science Activities. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20040610.0006. 
AP-3.15Q, Rev. 4, ICN 5. Managing Technical Product Inputs. Washington, D.C.: 
U.S. Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20040812.0004. 
AP-SIII.10Q, Rev. 2, ICN 7. Models. Washington, D.C.: U.S. Department of Energy, 
Office of Civilian Radioactive Waste Management. ACC: DOC.20040920.0002. 
AP-SV.1Q, Rev. 1, ICN 1. Control of the Electronic Management of Information. 
Washington, D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste 
Management. ACC: DOC.20040308.0001. 
LP-SI.11Q-BSC, Rev. 0, ICN 1. Software Management. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20041005.0008. 
B9.3 SOURCE DATA LISTED BY DATA TRACKING NUMBER 
148850 MO0003RIB00071.000. Physical and Chemical Characteristics of Alloy 22. 
Submittal date: 03/13/2000.