Stress Corrosion Cracking of the Drip Shield, the Waste Package Outer Barrier, and the Stainless Steel Structural Material Rev 01, ICN 00

ANL-EBS-MD-000005

July 2003

1. PURPOSE 
1.1 PURPOSE AND BACKGROUND 
The current revision of this analysis/model report (AMR), ANL-EBS-MD-000005, was prepared 
according to the Technical Work Plan for: Waste Package Materials Data Analysis and 
Modeling, TWP-EBS-MD-000005 REV 05 (BSC 2002 [161132]). As directed by the Technical 
Work Plan, an analysis of the potential degradation by stress corrosion cracking (SCC) of the 
drip shields and waste packages in the engineered barrier system (EBS) of the proposed 
repository at Yucca Mountain is to be conducted. This analysis is conducted by the Performance 
Assessment Projects (PAP) Waste Package Department (WPD) to provide a basis for assessing 
waste package (WP) and drip shield (DS) degradation by SCC under exposure conditions 
anticipated in the proposed repository. This analysis will also provide information useful in 
satisfying requirements of the Yucca Mountain Review Plan (NRC 2002 [158449]). Comments 
by the Waste Package Peer Review Panel (Beavers, et al. 2002 [158781]) as well as Key 
Technical Issue (KTI) Agreements raised by the Nuclear Regulatory Commission (NRC) 
(Reamer 2001 [158380]) were also considered. In the case of the WPOB and DS, the critical 
environment is conservatively taken as any aqueous environment contacting the metal surfaces 
including thin aqueous films as well as dripping water and bulk aqueous electrolytes. Further, for 
any of these environmental cases, SCC can occur over the full expected temperature range for 
both the WPOB and the DS. 
Relevant Features, Events, and Processes (FEPs) considered in this AMR include: FEP 
2.1.03.02.0A, stress corrosion cracking (SCC) of waste packages, and FEP 2.1.03.02.0B, stress 
corrosion cracking (SCC) of drip shields (DTN: MO0301SEPFEPS1.000). This AMR does not 
provide a direct basis for the inclusion of the FEPs in the Total System Performance Assessment 
for License Application (TSPA-LA). Rather, the results of the model/analysis are used by the 
model document, Integrated Waste Package Degradation Model (IWPDM) (ANL-EBS-PA- 
000001), which is currently in preparation, to develop a basis for implementing the FEPs in the 
TSPA-LA. Nevertheless, the technical basis for the inclusion of these FEPs and the process that 
will be utilized to implement the included FEPs are discussed in Section 6.1. 
Technical errors identified in Technical Error Reports TER-02-0024 and TER-02-0051 resulting 
from the Model Validation Status Review conducted by the U.S. Department of Energy (DOE) 
(BSC 2001 [156257], Section 6.10 are addressed in Section 7 (Model Validation) of this AMR. 
The consequence of an SCC failure of the DS, the waste package outer barrier (WPOB), or the 
stainless steel structural material is the initiation and propagation of tight, sometimes branching 
cracks that might be induced by the combination of an aggressive environment and various types 
of tensile stresses that can develop in the DSs or the WPs. For the current design of the DS and 
WP, the Type 316 stainless steel inner structural cylinder of the WP will be excluded from the 
SCC evaluation. The SCC performance assessment will not take credit for the inner cylinder. 
Therefore, 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 WPOB, and titanium grade 7 (Ti-7), 
used for the DS, subjected to the effects of SCC. The possibility of using laser peening or other
residual stress mitigation techniques is considered as a means of mitigating SCC in the WP final 
closure weld. 
Uncertainties (see Sections 6.3.4, 6.3.5, and 6.4.5) and limitations (see Section 6.1) of the 
process level models associated with SCC are also addressed in this AMR. As indicated in 
Section 5, no assumption was used to perform the model activity in this AMR. 
1.2 MODEL OVERVIEW 
SCC is the initiation and propagation of cracks in metal components due to three factors 
presenting simultaneously: material susceptibility, critical environment, and static (or sustained) 
tensile stress. Alloy 22, the material used for WPOB, is highly corrosion resistant but it will be 
shown in this AMR that its susceptibility to SCC cannot be ignored for the Yucca Mountain 
environment and the co-existing stress conditions described in Section 6.4. For the DS, Section 
6.3.7 provides a post-cracking analysis, which forms the technical basis for screening out SCC in 
the DS. A lifetime modeling scheme is developed to assess the degradation of the WPOB due to 
SCC. As indicated by the flow diagram shown below, the lifetime modeling considers both crack 
initiation and pre-existing 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 (Section 6.3.5) that defines propagation of 
both initiated incipient cracks and manufacturing flaws, the crack growth model (based on the 
film rupture/slip dissolution theory) that determines the crack growth rate (Section 3). The SCC 
model provides all the elements (as summarized in Section 8) needed for the performance of a 
lifetime prediction of the WPOB subjected to the effects of SCC. 
Flow Diagram of SCC Model

 9 
2. QUALITY ASSURANCE 
The Office of Civilian Radioactive Waste Management (OCRWM) Quality Assurance (QA) 
program applies to this AMR. The drip shield (DS) was clasiffied (per QAP-2-3) as Quality 
Level-1 in Classification of the MGR Uncanistered Spent Nuclear Fuel Disposal Container 
System (CRWMS M&O 1999 [106190], p. 8). All types of waste packages were classified per 
QAP-2-3 as Quality Level-1 based on the conclusion of Classification of the MGR Uncanistered 
Spent Nuclear Fuel Disposal Container System (CRWMS M&O 1999 [105154], p. 7). This 
classification is still in effect. 
This revision of the AMR has been developed per AP-SIII.10Q [162696] procedure under 
Technical Work Plan for: Waste Package Materials Data Analyses and Modeling (BSC 2002 
[161132]), which, in turn, was developed in accordance with AP-2.27Q [159604], Planning for 
Science Activities. The applicability of Quality Assurance Requirements and Description 
requirements (DOE 2003 [162903]) is documented in the technical work plan (TWP) (BSC 2002 
[161132], Section 8). A process control evaluation was performed in accordance with AP-SV.1Q 
[160533], Control of the Electronic Management of Information., with evaluation results 
documented in Attachment A of the technical work plan (BSC 2002 [161132]). The process for 
control of the electronic management of information on evaluation of work 
activities/processes/process functions, outlined in Section 5.0 of AP-SV.1Q [160533], is 
followed to ensure accuracy, completeness, and security of information and data used in 
preparation of this AMR. Examples of process controls mentioned in AP-SV.1Q [160533] 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 non-physical 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.

 10 
3. COMPUTER SOFTWARE USAGE 
No software or computer codes were used directly in developing this AMR. The computer 
software/code 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 were 
developed using vendor (Structural Integrity Inc., San Jose, CA) internally qualified computer 
software that was accepted by OQA. Accordingly, these data are designated acquired not 
developed for this AMR. 
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 is exempt from software qualification because, in accordance with AP-SI.1Q, Software 
Management [161284], Section 2.1.1, office automation systems such as word processors and 
spreadsheets are not required to be qualified. Furthermore, according to AP-SI.1Q, Software 
Management [161284], the graphical representation use of Excel can be exempted under Section 
2.1.2 and the calculations using built-in mathematical function use can be exempted under 
Section 2.1.6. When Excel is used for calculations (see Section 6.3.4), information required for 
an independent person to reproduce the work (including formula or algorithm used, listing of 
inputs, and listing of outputs) is provided.

 11 
4. INPUTS 
4.1 DATA AND PARAMETERS 
The data providing input for the development of parameters and/or other databases used in the 
models/analyses documented in this AMR are identified in Table 4.1. While uncertainty in the 
input data is discussed in Section 6, this table and the accompanying Tables 4.1-1 through 4.1-5 
and Figure 1 provide 
 A description of the data set(s) used 
 A roadmap to what data are in the DTN, if applicable 
 A description on how the data are used to develop input parameters for the model/analyses. 
The input data are appropriate for using as input to the model/analyses documented in this AMR 
because they are either qualified acquired or accepted data or qualified and verified test data 
developed specifically for this AMR. No developed parameters or other input information are 
used in the model/analyses documented in this AMR. Number of figures used for numerical data 
in this AMR often exceed that of significant figures for concern of round-off errors. 
0.5 
1.0 
1.5 
2.0 
2.5 
0 2000 4000 6000 8000 10000 
Time-to-failure (hrs) 
(smax applied / sYS ) 
C-22 as received 
C-22 creviced 
C-22 HT1 (TCP) 
C-22 HT1 + creviced 
C-22 HT2 (LRO) 
C-22 20% CW 
C-22 20%CW + LRO 
C-22 weld + HAZ 
316NG as received 
316NG creviced 
Ti Gr 7 as received 
Ti Gr 7 creviced 
304SS sensitized 
304SS sens + creviced 
Notched C22 as-rec 
Notched C22 HT1 (TCP) 
Notched C22 weld+HAZ 
Keno Testing (Full Run 2) 
Concentrated Salt Solution 105oC 
Constant Stress; 185 specimens total 
* sYS as rec used in stress ratio for welded specimens 
Pressure increased from 
1000 psi 
to 1500 psi at 168.5 hrs 
Notched C22 
Alloy 22 
316NG 
Ti Gr 7 
ed 
CP) 
AZ 
sUTS/sYS 
Alloy 22 
304SS 
Ti Gr 7 
sUTS/sYS 
C-22 as received 
C-22 creviced 
C-22 HT1 (TCP) 
C-22 HT1 + creviced 
C-22 HT2 (LRO) 
C-22 20% CW 
C-22 20%CW + LRO 
C-22 weld + HAZ 
316NG as received 
316NG creviced 
Ti Gr 7 as received 
Ti Gr 7 creviced 
304SS sensitized 
304SS sens + creviced 
Notched C22 as-rec 
Notched C22 HT1 (TCP) 
Notched C22 weld+HAZ 
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 = 12.4 at room temperature) and p 94. This composition represents an 
approximately 15% solution of Basic Saturated Water (BSW) whose target composition is given in DTN: 
LL021105312251.023, p 3. DTN: LL021105312251.023, Figure 2-1 
Figure 1. Failure stress vs. time-to-failure.

 12 
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 
growth and initiation 
measurements in for C-22 and 
Ti-7, General Electric Global 
Research Center (GECRC) 
121202. 
Submittal date: 01/08/2003 
LL021105312251.023 Input data (see Table 4.1-1) are 
used in Section 6.3.4 for 
determining the repassivation 
slope 'n' of the slip 
dissolution/film rupture model. 
Crack initiation measurements 
for Alloy 22 and titanium grade 
7 specimens. 
Stress corrosion cracking 
initiation & growth 
measurements in environments 
relevant to high level nuclear 
waste packages. 
Submittal date: 01/08/2003 
LL021105312251.023 Input data (see Figure 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 Input data (see Table 4.1-2) are 
used in Section 6.4.2 for stress 
profiles in as-welded 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 Input data (see Table 4.1-3) are 
used in Section 6.4.2.

 13 
Table 4.1. Input Data (Contnued) 
Data Name Data Source DTN Discussion 
YS (yield strength) for Alloy 
C22 
Waste package material 
properties: corrosion resistant 
materials. 
MO0003RIB00071.000 Input data (see Table 4.1-4) are 
used in Sections 6.2.1 & 6.4.5. 
YS (yield strength) for titanium 
grade 7 
Waste package material 
properties: corrosion resistant 
materials. 
MO0003RIB00073.000 Input data (see Table 4.1-4) are 
used in Sections 6.2.1 & 6.3.7. 
E (modulus of elasticity) for 
titanium grade 7 
Waste package material 
properties: corrosion resistant 
materials. 
MO0003RIB00073.000 Input data (see Table 4.1-4) are 
used in Section 6.3.7. 
Vgc, general corrosion rates for 
Alloy 22 
Corrosion rate calculations for 
Alloy C22 after 5+ years 
exposure. 
LL030412512251.57 Input data (see Table 4.1-5) are 
used in Section 6.3.5. 
Table 4.1-1. Measured Crack Growth Rates for Alloy 22 Specimens 
Specimen Tested stress intensity 
factor, MPa(m)^.5 
Measured Crack 
Growth Rate, mm/s 
Source (page # of DTN: 
L021105312215.023 
c153 30 2.50E-10 p. 11 
c153 30 5.00E-10 p. 11 
c144 30 See note below p. 7 
c152 45 See note below p. 10 
c152 45 4.00E-10 p. 10 
Note: Test results indicated that either cracking appeared to cease or growth rate seemed to arrest.

 14 
Table 4.1-2. Coefficients of Stress Profiles for the Original and Modified CRM-21 PWR Design from DTN: LL000316205924.142. 
Stress coefficient A0 A1 A2 A3 
Unit ksi ksi/in ksi/in2 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-C12. 
As-welded 25-mm 
lid, hoop stress Sz 55.4242 29.8255 -186.269 143.597 
File Skvrbr1, sheet 
UnAnneal,Sz, cells 
C9-C12. 
As-welded 10-mm 
lid, Sn on Sec. 1-1 26.344 -427.51 934.32 -596.71 
File Thinlid11, 
sheet UnAnneal,1- 
1,Sn, cells C9-C12. 
As-welded 10-mm 
lid, Sz on Sec. 2-2 31.895 101.42 -463.23 297.75 
File Thinlid11, 
sheet UnAnneal,2- 
2,Sz, cells C9-C12. 
Laser peened 25- 
mm lid, radial stress 
Sx 
-38.5684 383.082 -922.377 603.035 
File Skvrbr1, sheet 
Peening,Sx, cells 
C9-C12. 
Laser peened 25- 
mm lid, hoop stress 
Sz 
-42.4391 656.764 -1322.67 759.752 
File Skvrbr1, sheet 
Peening,Sz, cells 
C9-C12.

 15 
Table 4.1-3. Stress Intensity Factor (SIF) Profiles from DTN: LL000316205924.142. 
As-welded outer lid, CRM-21 PWR 
Design 
As-welded 10-mm lid, Modified CRM-21 
PWR Design 
Outer lid with laser peening, CRM-21 
PWR Design 
DTN File Skvrbr1 DTN File Thinlid11 DTN File Skvrbr1 
Sheet 
UnAnnel,Sx 
Cells A87- 
A136 
Sheet 
UnAnnel,Sx 
Cells C87- 
C136 
Sheet 
UnAnnel,Sz 
Cells I87- 
I136 
Sheet 
UnAnnel,1- 
1,Sn Cells 
A89-A138 
Sheet 
UnAnnel,1- 
1,Sn Cells 
C89-C138 
Sheet 
UnAnnel,2- 
2,Sz Cells 
C89-C138 
Sheet 
Peening,Sx 
Cells A87- 
A136 
Sheet 
Peening,Sx 
Cells C87- 
C136 
Sheet 
Peening,Sz 
Cells C87- 
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

 16 
Table 4.1-3. Stress Intensity Factor (SIF) Profiles from DTN: LL000316205924.142. (Continued) 
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 
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

 17 
Table 4.1-4. Input Data for Yield Strength, and Modulus of Elasticity 
Input Data Name 
(Input DTN) 
Temperature 
K (oC) 
Input Data Value Input Data Unit 
YS (yield strength) for 
Alloy C22 
(MO0003RIB00071.000) 
Room Temperature 
366 (93) 
477 (204) 
372 
338 
283 
MPa 
YS (yield strength) for 
titanium grade 7 
(MO0003RIB00073.000) 
Room Temperature 
477 (204) 
275-450 
138-152 
MPa 
E (modulus of elasticity) 
for titanium grade 7 
(MO0003RIB00073.000) 
294 (21) 
366 (93) 
422 (149) 
106.87 
103.42 
100.66 
GPa 
Table 4.1-5. 5-year General Corrosion (GC) Rates (in nanometers/year) from DTN: LL030412512251.057 
Sample GC rate Sample GC rate Sample GC rate Sample GC rate Sample GC rate Sample GC rate 
DCA 019 9.40 DCA 053 8.30 DCA 111 5.77 DCA 175 0.82 DCB 049 16.07 DCB 112 9.05 
DCA 020 8.22 DCA 054 6.40 DCA 112 3.11 DCA 176 0.81 DCB 050 14.51 DCB 113 10.86 
DCA 021 8.63 DCA 079 3.06 DCA 113 10.56 DCA 177 46.67 DCB 052 4.29 DCB 139 0.00 
DCA 022 6.36 DCA 080 3.10 DCA 114 10.91 DCA 178 8.40 DCB 053 5.92 DCB 140 2.85 
DCA 023 9.75 DCA 081 4.19 DCA 139 4.71 DCA 179 5.24 DCB 079 2.00 DCB 142 2.03 
DCA 024 22.52 DCA 082 9.52 DCA 140 3.54 DCA 180 5.28 DCB 080 7.88 DCB 143 5.69 
DCA 049 12.04 DCA 083 7.23 DCA 141 2.74 DCB 019 10.24 DCB 082 19.58 DCB 175 0.41 
DCA 050 17.29 DCA 084 14.71 DCA 142 6.27 DCB 020 6.94 DCB 083 13.61 DCB 176 2.08 
DCA 051 15.75 DCA 109 5.81 DCA 143 5.89 DCB 022 5.84 DCB 109 4.32 DCB 178 1.25 
DCA 052 5.76 DCA 110 11.60 DCA 144 8.27 DCB 023 6.89 DCB 110 2.01 DCB 179 0.41

 18 
4.2 CRITERIA 
The Waste Package Technical Work Plan (BSC 2002 [161132], Table C5) has identified the 
following acceptance criteria (AC) based on the requirements mentioned in the Project 
Requirements Document (Canori and Leitner 2003 [161770]) and the Yucca Mountain Review 
Plan (NRC 2003 [162418]): 
1. System Description and Demonstration of Multiple Barriers (NRC 2003 [162418], 
Section 4.2.1.1.3; PRD-002/T-014, PRD-002/T-016) 
2. Scenario Analysis and Event Probability (NRC 2002 [158449], Section 4.2.1.2.1.3; PRD- 
002/T-015) 
3. Degradation of Engineered Barriers (NRC 2002 [158449], Section 4.2.1.3.1.3; PRD- 
002/T-015) 
A closer examination indicates that only Criteria 3 (Degradation of Engineered Barriers) is 
applicable to this AMR. Specific requirements include describing deterioration or degradation of 
engineered barriers and modeling degradation processes using data for performance assessment, 
including total system performance assessment (TSPA). Consideration of uncertainties and 
variabilities in model parameters and alternative conceptual models are also required. To fulfill 
these requirements, the following acceptance criteria are identified in the Waste Package TWP 
(BSC 2002 [161132], Table C5): 
 AC1: System Description and Model Integration are Adequate 
 AC2: Data are Sufficient for Model Justification 
 AC3: Data Uncertainty is Characterized and Propagated Through the Model 
Abstraction 
 AC4: Model Uncertainty is Characterized and Propagated Through the Model 
Abstraction 
 AC5: Model Abstraction Output is Supported by Objective Comparisons 
4.3 CODES AND STANDARDS 
No codes and standards were used to develop the model for this AMR.

 19 
5. ASSUMPTIONS 
No assumption was used to perform the model activity in this AMR.

 20 
6. MODEL DISCUSSION 
6.1 INTRODUCTION 
One of the most common corrosion-related causes for premature fracture of metal structural 
components is stress corrosion cracking (SCC). SCC is the initiation and propagation of cracks 
in structural components due to three factors, which must be present simultaneously: 
metallurgical susceptibility, critical environment, and static (or sustained) tensile stresses. 
The discussion on SCC will be restricted to the waste package outer barrier (WPOB) and the drip 
shield (DS), which are made of Alloy 22 and titanium grade 7, respectively. The stainless steel 
structural material is not modeled. Performance assessment does not take corrosion credit from 
the stainless steel inner barrier of the WP. 
Alloy 22, the material used for WPOB, is highly corrosion resistant but it will be shown in the 
rest of this section that its susceptibility to SCC cannot be ignored for the test conditions that 
simulate the Yucca Mountain environment (Sections 6.2 and 6.3) and the co-existing stress 
conditions induced by welding in the closure welds of the WP lids (Section 6.4). For the DS, 
Section 6.3.7 provides a post-cracking analysis, which forms the technical basis for screening out 
SCC in the DS. 
A lifetime modeling scheme is developed to assess the degradation of the WPOB due to SCC. As 
indicated by the flow diagram shown in Section 1.2, the lifetime modeling considers both crack 
initiation and pre-existing 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 (Section 6.3.5) that defines propagation of 
both initiated incipient cracks and manufacturing flaws, the crack growth model (based on the 
film rupture/slip dissolution theory) that determines the crack growth rate (Section 3). The SCC 
model provides all the elements (as summarized in Section 8) needed for the performance of a 
lifetime prediction of the WPOB subjected to the effects of SCC. 
Stress corrosion cracking has historically been separated into initiation and propagation 
phases (Jones and Ricker 1987, 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. In the area of environmentally assisted cracking (such as SCC), 
coalescence of microscopically small cracks will take place and develop into deeper cracks. Ford 
and Andresen (1988, p. 798) used a crack size of 0.05 mm to start propagating SCC cracks. 
Initial cracks can also be 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 dissolution/film rupture (SDFR) model is adopted in 
this AMR 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 from the bare metal surface, to the metal oxidation that occurs when the 
protective film at the crack tip is ruptured. The SDFR SCC model is described in Section 6.3. A 
crack, however, may reach an arrest state before it enters the "propagation" phase. There exists

 21 
a threshold stress intensity factor (SIF), which provides a criterion for determining if an initiated 
crack or pre-existing 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. The threshold SIF (KISCC) will be discussed in Section 6.3.6 and the determination 
of the weld induced stress and KI profiles through the WP wall will be described in Section 6.4 
of the AMR. 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 Yucca 
Mountain repository. Therefore, there do not appear to be limitations as they are applied to the 
performance assessment of waste packages and drip shields. 
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 will not be used to evaluate the 
total system performance assessment (TSPA) but will be considered in the AMR 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. 
Both the base-case SDFR model and the alternative CEF model were developed to account for 
SCC of sensitized Type 304 stainless steel. An evaluation of other SCC models for sensitized 
Type 304 stainless steel indicates a lack of theoretical basis for these models (Macdonald and 
Urquidi-Macdonald 1991). Therefore, no additional alternative conceptual models for SCC are 
considered in this AMR. 
Output parameters associated with the base-case crack growth models developed in this AMR 
will be used as one input to the total system performance assessment. A summary of the various 
output to be generated by this AMR is presented in Section 8. 
6.2 CRACK INITIATION AND MANUFACTURING FLAWS 
6.2.1 Threshold Stress for SCC Initiation 
For a given alloy, metallurgical condition, set of environmental conditions, and in the absence of 
cyclic stresses, initiation of SCC 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, Vol. 13, p. 276). 
Recently obtained SCC crack initiation measurements under constant load conditions reported in 
DTN: LL021105312251.023 are summarized in Figure 12 (which is Figure 2-15 in DTN: 
LL021105312251.023), where the measurements of crack initiation stress are presented as 
applied stress ratio (the ratio of applied stress to yield strength) vs. time-to-failure (or total 
exposure time without failure) for specimens subjected to 9,600 hours of exposure in hot 
concentrated salt solution (pH=10.3 at 105oC), known as Basic Saturated Water (BSC 2001 
[155640], Section 6.12), designed to simulate the chemistry of concentrated Yucca Mountain 
ground water. The reference indicated that Alloy 22 exhibits excellent SCC resistance since 
failure was not observed for any of the 120 Alloy 22 specimens covering a variety of

 22 
metallurgical conditions (including the as-welded condition). 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 ultimate tensile strength (UTS). The high degree of SCC initiation resistance for 
Alloy 22 is corroborated by results of high magnification visual examination of a number of 
Alloy 22 U-bend specimens exposed to a range of relevant environments at 60 and 90oC (Fix et 
al. 2003). No evidence of SCC initiation has been observed in these U-bend specimens after five 
years of exposure. 
Titanium grade 7 was apparently more susceptible to SCC 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 summarized in Figure 1. Some specimens failed relatively early (=168 hours) at applied 
stresses above 110% of yield stress but, at 110% of yield stress, there was a mixture of failure 
and non-failure runout times from ~200 hours for first failure to greater than 7000 hours without 
failure. This is consistent with a runout stress somewhat less than 110% of yield stress and is 
estimated to be at the yield stress value. A threshold value very near the yield stress is also 
consistent with the observation that no SCC 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 Ti-Pd alloy) specimens exposed for five years to a range of relevant environments 
at 60 and 90oC (Fix et al. 2003). 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% which 
resulted in sustained stress levels at or over yield stress. 
Since the above SCC initiation test results are for exposures out to five years, an extrapolation 
scheme is needed 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 ASME 
Boiler Pressure Vessel code (ASME 1969, p. 80) typically uses a safety factor of 2 on the runout 
stress (endurance limit) for defining fatigue lifetime cycles. Following this precedent, the 
threshold stress value (criterion) may be derived from the minimum failure stress (or runout 
stress without failure) obtained from the constant load tests (i.e., 2.0 (YS) for Alloy 22 and 
1.1(YS) for titanium grade 7) by applying an appropriate safety factor. Based on the criterion 
that the safety factor used should be consistent with or somewhat more conservative than the 
ASME code precedent and the resulting threshold stress should not exceed 0.9(YS), a stress 
reduction factor of 2.2 is applied to the estimated runout stress to obtain a threshold stress value. 
This approach results in threshold stress values of 0.9(YS) for Alloy 22 and 0.5(YS) for titanium 
Grade 7. The YS values or Alloy 22 and titanium grade 7 are listed in Table 4.1-4. For 
conservative purpose, it is recommended that the YS value at the maximum temperature is to be 
used. The estimated temperature is 200oC (with YS approximately 286 MPa) for the waste 
package (see Section 6.3.4) and 140oC (with YS approximately 221 MPa) for the drip shield (see 
Section 6.3.7). 
The development of threshold stress is based on uniaxial test data. However, assessment of the 
integrity of components subjected to a multiaxial stress condition using uniaxial information is 
an acceptable and industry consistent approach. For example, the prediction of stress-strain 
behavior in sophisticated elastic-plastic analyses typically uses the equivalent (von Mises) stressstrain 
approach and uniaxial material stress-strain behavior. The American Society of 
Mechanical Engineers (ASME) Boiler and Pressure Vessel Code uses uniaxial based material

 23 
strength data to assess multi-axial 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 stress-strain 
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 biaxial stress condition that is "equivalent" to 
the uniaxial condition. These biaxial stress states can be observed using Mohr's circle. Thus, the 
use of uniaxial stress-strain curves for multiaxial loading conditions is acceptable when used in 
combination with Von Mises stresses determined from the stress analyses. It is often a good 
simplification to consider only the principal stress component. 
Density of Incipient Cracks-In a commercial metal alloy, there is a relatively high density of 
potential incipient surface cracks associated with microscopic discontinuities such as 
precipitates, grain boundaries, passive film rupture sites, etc. The surface of the WP is divided 
into many subdivisions, referred to as patches, in the performance assessment. Patch size in 
terms of width and length will be determined by the size of the closure weld as well as the stress 
distribution in and near the weld since failure can only occur in the closure weld. 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. Therefore, it appears 
to be sufficient to consider one incipient crack per patch for the WP performance assessment 
(i.e., the number of incipient cracks is the same as the number of patches along the 
circumferential weld). 
Incipient Crack Size-Environmental cracking has historically been separated into initiation 
and propagation phases (Jones and Ricker 1987, p. 146). Although the particular crack depth 
defining the separation of the two phases is arbitrary, for the purpose of lifetime modeling it is 
defined here that the initiation is associated with microscopic crack formation at localized 
corrosion or mechanical defect sites. A crack size of 0.05 mm is developed (Ford and Andresen 
1988, p. 798) if the stress exceeds the threshold stress. 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. 
6.2.2 Manufacturing Flaws 
6.2.2.1 Flaw Size and Flaw Density Distribution 
Flaw size and flaw density distributions are addressed in the Analysis of Mechanisms for Early 
Waste Package/Drip Shield Failure (BSC 2003 [161238], Section 6.2.1). 
The current welding process being considered for the WP final closure weld is one of Gas 
Tungsten Arc Welding (GTAW) processes (CRWMS M&O 1996 [124950], p. 5). This process 
selection is fully consistent with the recommendations resulting from an expert evaluation of a 
range of potential closure welding processes (Lundin 2002). This evaluation concluded that the 
Cold Wire Feed Gas Tungsten Arc Welding (CW-GTAW) process should be selected for the WP 
final closure weld process to be implemented in a hot cell. This process was chosen primarily for 
its ability to provide high quality closure weld joints with optimum control of the welding 
variables. This process produces welds that can be readily inspected by automated and remote 
methods (Lundin 2002). The choice of the GTAW process also naturally limits and defines the

 24 
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 (LOP), lack 
of fusion (LOF), 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 priori 
knowledege 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 
(Lundin 2002). Since the volumetric ultrasonic (UT) inspection method will be 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 
UT 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 GTAW process is supported by a recent weld defect evaluation study in which 
sixteen full diameter 21 PWR container Alloy 22 closure weld mockup ring specimens were 
fabricated using a prototypical cold-wire GTAW process under conditions that simulated hot cell 
type access restrictions (Smith 2003, Sections 1.1 and 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 (UT) examinations (Smith 2003, 
Section 3). These were followed by metallographic destructive examination (Smith 2003, 
Section 4). Information gathered from these weld mockup experiments were used to develop a 
flaw density, orientation and size distribution applicable to the closure welds of the WP (BSC 
2003 [161238], Section 6.2.1). The UT inspection defect detection threshold used was 1 mm and 
this was confirmed by the metallographic examinations that verified the presence of eight defects 
(BSC 2003 [161238], p.12) that were detected by UT and confirmed by metallography. The UT 
dimensions were consistent with or slightly overestimated the metallographically measured 
dimensions (BSC 2003, p.12). Imperfections uncovered by metallographic examinations but not 
detected by UT inspections were gas bubbles, and the majority of them were less than 0.003 inch 
(approximately 0.08 mm) in diameter (BSC 2003 [161238], p. 16). Gas bubbles are spherical in 
shape (BSC 2003 [161238], p. 16) and are not sharp cracks which can propagate due to stress 
corrosion cracking (Andresen and Ford 1985, p. 20). Crack initiation on the bubble surface due 
to stress concentration is ruled out since weld induced tensile stress at and near the WP surface 
will be 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 in each case (Smith 2003, Section 5.1). 
Based on the results of this sixteen weld mockup ring study, the defect size and orientation 
distributions were determined and reported (BSC 2003 [161238]). 
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

 25 
distribution (BSC 2003 [161238], Section 6.2.1.1.1, Equation 2). Flaws are uniformly distributed 
spatially and their frequency of occurrence is 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 2003 [161238], Section 6.2.1.1.2, Equation 12). These 
densities were derived from analysis of the defects observed in sixteen welded rings subjected to 
ultrasonic tests. 
These flaw characteristics are representative of those to be expected in the non-inspected weld. 
An ultrasonic inspection will be performed 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 post inspection flaw size and density distributions (BSC 2003 [161238], 
Section 6.2.1.2, Equations 24 and 28). 
6.2.2.2 Embedded Flaws 
As general corrosion proceeds, embedded flaws can become surface breaking flaws. 
Consideration of pre-existing 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. It is recommended that the fraction of surface breaking flaws is 
increased by adding the fraction of flaws embedded within the 1/4 thickness region of the weld 
surface. This recommendation appears to be conservative since, based on the mean general 
corrosion rate of 7.23 nm/year (Section 6.3.5), it will take 864,400 years to remove the 1/4 
thickness of the surface of the outer lid or 345,800 years to remove the 1/4 thickness of the 
surface of the middle lid. 
6.2.2.3 Radial Crack Versus Circumferential Crack in WP Closure Welds 
The defect description and orientation distribution obtained from the sixteen-ring study (BSC 
2003 [161238]) is consistent with Shcherbinskii and Myakishev (1970) that describes a statistical 
treatment of weld flaw orientations based on analysis of a significant data set of ultrasonic flaw 
orientation measurement 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 & Myakishev, 1970, Fig. 1). A similar conclusion, drawn from the data for plate 
welds (Shcherbinskii & Myakishev 1970, Fig. 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 one percent of these 
flaws have a potential to undergo SCC as radial cracks. (Note: There appears to be an obvious 
typographical error in the figures. This reference is an English translation of a Russian 
publication. The frequencies given as 1.8 and 2.5 Hz should read 1.8 and 2.5 MHz, typical of 
those used in ultrasonic testing.) 
As discussed above, manufacturing defects, especially those due to welding, would would likely 
be oriented along the weld direction. When initiated, the propagation of cracks tend to follow the

 26 
direction perpendicular to the maximum principle 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 principle 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 (circumferencial) 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 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 given in Shcherbinskii and Myakshev (1970), 
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 will be 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, it is expected that a very tightly controlled process will be in place 
when the waste package closure weld is applied. If flaws are 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 2 shows the ratio 
(sin2.) 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 Tada et al. (1973, p. 5.2). 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. The ratio of

 27 
the stress intensity factor for a circumferential flaw oriented at a small angle to the load direction 
subjected to hoop stress to 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. The figure 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 turn radially. 
Combining the test results regarding flaw orientation from Shcherbinskii and Myakshev (1970) 
and the stress intensity factor ratio discussed above, it is concluded that the probability of an 
expected circumferentially oriented flaw turning radially 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 
will be 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 radially. 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. It should be noted that if a flaw were to occur 
and be oriented an angle greater than 15 degrees, 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 orienting within 15 degrees of the welding direction. 
In summary, radially oriented flaws are important to the SCC analysis for waste package lifetime 
calculations since the hoop stress, which drives the radially oriented cracks, is usually 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 center line. In accordance with all the 
discussions given above, it is conservative to recommend that the fraction of flaws that are 
radially oriented (making an angle of 45 degrees or more with respect to the direction of the 
weld) is around 0.5% of the flaws.

 28 
K(.)/K(90) Ratio vs Angle (.) with Direction of Load 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0
0 15 30 45 60 75 90 
Angle (.) with Direction of Load 
. 
Figure 2. 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. 
s 
(Stress)
.

 29 
6.2.2.4 Crack Aspect Ratio 
Crack size is normally characterized by crack depth but crack length is needed in determination 
of the crack opening area as the crack becomes a through-wall crack. Determination of the crack 
length for either a manufacturing crack or an incipient crack is based on the following 
considerations: 
(1) Surface flaws are semi-elliptical in shape with depth a and length 2c. 
(2) The aspect ratio (.) is the ratio of one-half of crack length (c) vs. crack depth (a), i.e., . = 
c/a. A semi-circular flaw has an aspect ratio of 1 (. = 1). 
(3) A crack maintains its aspect ratio during its growth until the depth reaches the wall thickness. 
Then, at this point, the shape instantaneously turns into a rectangular one. 
(4) The crack aspect ratio is 1 for radial cracks in the closure weld. 
(5) The crack aspect ratio is greater than 1 for circumferential cracks with an exponential 
distribution based on one of the formulations given in Harris et al. (1981, 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 
It is noted that a gamma or Weibull distribution with a shape factor of one is equivalent to an 
exponential distribution.

 30 
6.3 THE BASE-CASE SLIP DISSOLUTION/FILM RUPTURE (SDFR) MODEL 
6.3.1 Introduction 
Environmental cracking has historically been separated into initiation and propagation 
phases (Jones and Ricker 1987, p. 146). For the purpose of lifetime modeling it is appropriate to 
assume that initiation is associated with microscopic crack formation at localized corrosion or 
mechanical defect sites. In the area of environmentally assisted cracking (such as SCC), 
coalescence of microscopically small cracks will take place and develop into deeper cracks. 
Thereafter, the crack may either reach an "arrest" state or a "propagation" phase. Ford and 
Andresen (1988, p. 798) assumed that cracks start propagating from a size of about 0.05 mm. A 
lifetime crack propagation 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 
dissolution/film rupture mechanism has been chosen. This cracking mechanism has been 
successfully applied to model SCC of stainless steel, low-alloy steel, and nickel-based alloys in 
light water reactor environments (Ford and Andresen 1988, pp. 798-800; Andresen and Ford 
1994, pp. 61-70). 
6.3.2 Slip Dissolution/Film Rupture Mechanism 
In accordance with the slip dissolution/film rupture theory, crack advance is Faradaically related 
to the metal oxidation that occurs when the protective film at the crack tip is ruptured. Figure 3 
(Ford and Andresen 1988, Figure 2; Andresen and Ford 1994, 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 3, 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) will be 
rapid, typically controlled by activation or diffusion kinetics as the exposed metal rapidly 
dissolves. Availability of the balancing cathodic reduction current is also clearly 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 will be 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 3) by the following equation (Ford and Andresen 
1988, Figure 2, p. 790; Andresen and Ford 1994, Figure 1, p. 62):

 31 
 
= 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 3) 
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 4 show the schematic of oxidation current density vs. time following repeated oxide 
rupture events. Repassivation current transients exhibit an initially high bare surface 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, Equation 1, p. 62): 
n 
ct t A V ) ( 
 
= e (Eq. 5) 
where, for a given environment, A and n are material constants, which can be measured 
from the repassivation response. The repassivation slope, n, is the slope on a log-log plot of (it/io) 
vs (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)

 32 
Figure 3. Schematic Oxidation Charge Density Versus Time for a 
Strained Crack Tip and Unstrained Crack Sides in the Slip 
Dissolution Mechanism

 33 
Figure 4. Schematic of Oxidation Current Density Versus Time 
Following Repeated Oxide Rupture Events

 34 
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. However, these early correlations were obtained primarily for 
alloys in concentrated environments (boiling MgCl2, 9M NaOH solutions, etc.) under dynamic 
straining conditions. By comparison, in relatively dilute environments it is expected that (a) the 
passivation rate will be high (e.g., in unaggressive chemistries or for lower-susceptibility 
materials) and thus n (in Equation 4) will be high; (b) the onset of repassivation is rapid, and 
thus to will be short; and (c) under constant load or displacement conditions, the periodicity of 
oxide rupture, ef/e
ct, will be 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 will be 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 (e.g., 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 
Since the repassivation current follows a power law response (i.e., 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 rupture/slip 
oxidation mechanism represents a justifiable model for hot water systems that is capable of being 
quantitatively evaluated. 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 
dissolution/oxidation, 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 (see 
Figure 4).

 35 
In accordance with Andresen and Ford (1994, 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/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. 
The initial application of the slip dissolution/film rupture model was on the quantitative 
prediction of cracking in austenitic type 304/316 stainless steels in 288oC high-purity BWR 
water (Ford and Andresen 1988). The model quantification processes can be summarized by the 
following steps: 
Step 1 - Measurements of n can be 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 can be 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 can be directly determined from n empirically. The empirical determination of 
A is based on SCC 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), 
A = 7.8 x 10-3 n3.6 (Eq. 11) 
has been given by Ford and Andresen (1988, p. 791) for 304 stainless steel in 288oC water. For 
Alloy 22 and Ti-7, independent experimental measurement of A and n is preferred but, due to 
lack of experimental data, the expression above will be 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 x 10-3 n3.6 (e
ct)n (Eq. 12) 
where Vt has the unit of cm/s and ct e 

has the unit of s-1.

 36 
For 304 stainless steel in 288oC water, Figure 5 (Ford and Andresen. 1988, Figure 7, p. 791) 
indicates that Equation 12 with n = 0.54 (i.e., A = 8.5 x 10-4) is a good prediction model for 
observed crack growth rate versus crack tip strain rate relationships. Further, this slip 
dissolution/film rupture model (using the 304 stainless steel A vs n relationship in 288 oC water) 
has been statistically validated for the chromium containing, nickel base Alloys 600 and 182 
over a range of anionic impurity concentrations (Ford and Andresen 1988, Figure 10). 
The crack tip strain rate, ct e 
 
in Equation 12 is related to the engineering stress parameters (such 
as the stress intensity factor) via the formulations in Table 1 of Ford and Andresen (1988). 
According to Ford and Andresen (1988), p. 791, the formulations given in the table 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. 
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 14 10 x 1 . 4 A A - = (Eq. 15) 
n 4 n = (Eq. 16)

 37 
Figure 5. Crack Growth Rate (Presented by Observed Data Points and Predicted Curve) vs. Crack Tip 
Strain Rate for Sensitized Type 304 Stainless Steel in Oxygenated 288C Water

 38 
6.3.4 Adaptation of Slip Dissolution Model To Alloy 22 
Andresen and Ford (1994), 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, p. 789), also used the SDFR model for, in addition to 304/316L stainless steel, 
A533B/A508 low alloy steel and Inconel 600/182 nickel-based alloys. Therefore, there is ample 
reason to hypothesize that SCC of nickel-based Alloy 22 occurs by the same fundamental 
mechanism characterized by the slip dissolution SCC model, i.e., Equation 5: 
Vt = A ( ct e 

)n (Eq. 5) 
The model quantification process is also used for Alloy 22. The resulting model is validated 
experimentally using data generated by the Yucca Mountain Program. 
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): 
6 . 3 2 n 10 x 8 . 7 A - = (Eq. 17) 
For constant load condition, with t V in mm/s and I K in MPa (m)1/2 in Equation 14, Equation 15 
becomes: 
( )n 14 6 . 3 2 10 x 1 . 4 n 10 x 8 . 7 A - - = (Eq. 18) 
Substitution of Equations 17 and 18 in Equation 5 leads to: 
( ) n I K n x n x t V 4 14 10 1 . 4 6 . 3 2 10 8 . 7 .. .
.. .
- - = (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. 
Recent SCC crack growth rate measurements from the General Electric Global Research Center 
(GEGRC) (DTN: LL021105312251.023) have been made available for the quantification of 
parameters for the SDFR SCC model to be used for Alloy 22. The test data were developed from 
four Alloy 22 specimens (c144. c152, c153, and c200) tested at 110oC 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, p 3, 6. The 
specimens were subjected to cyclic loading in order to initiate crack growth and then followed by 
constant loading conditions with various hold times. The set of data from DTN: 
LL021105312251.023 to be used as input for establishing value of n for Alloy 22 are 
summarized in Table 6-1 of which the measured crack growth rates are derived from Table 4.1- 
1. These data were selected based on the following criteria. Firstly, the minimum hold time is 24 
hours (or 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

 39 
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, 
according to DTN: LL021105312251.023, p. 7, cracking appeared to cease, i.e., reaching the 
constant load state. Secondly, data associated with specimen c200 were not included because this 
specimen was aged at 700oC for 175 hours. This aging condition is ultra-severe relative to the 
expected WP closure weld thermal exposure. According to the conclusion of BSC (2001) 
[151550]), material aging does not appear to be a problem for the waste package at temperature 
below about 260oC. It is noted in Table 6-1 that a crack growth rate of 10-11 mm/s is used to 
represent the test results that indicated either cracking appeared to cease or the growth rate 
seemed to arrest. The choice of 10-11 mm/s is judged to be the limit of measurement base on the 
observation that the lowest growth rate measured in the test program appeared to be 1.4x10-10 
mm/s. (DTN: LL021105312251.023, p. 9) 
Crack growth rate measurements reported in DTN: LL021105312251.023, p 10-11, were also 
obtained for Specimen c152 after the addition of 1000 ppm of Pb added as PbNO3 was made to 
the autoclave BSW test solution. The Pb addition was made following 8670 hours of testing in 
just the 110oC BSW solution (composition given in DTN: LL021105312251.023, p 3 and 
solution pH, p 6 (pH = 13.4 at room temperature)). Because of the relatively high pH of this 
solution, most of the Pb 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 Pb addition, in all cases, the growth rate after the Pb 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 SCC crack growth rate results, 
there are also SCC initiation test results obtained using Slow Strain Rate Tests (SSRT), at 76- 
95oC in low pH, SAW brine solution (pH ~3) with and without 0.005% lead nitrate additions 
DTN:LL020603612251.015. These results also show no effect of Pb on SCC susceptibility, 
Thus, there appears to be no basis for concern that Pb will affect SCC susceptibility in these 
relevant concentrated brine environments over a broad range of pH values. 
Table 6-1. 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 (page # 
of DTN: 
LL0211053122 
51.023 
Calculated 
"n" value 
(see Note 3) 
c153 CLNote 1 30 2.50E-10 p. 11 1.168 
c153 CLNote 1 30 5.00E-10 p. 11 1.119 
c144 1 30 1.00E-11 Note 2 p. 7 1.391 
c152 24 45 1.00E-11 Note 2 p. 10 1.563 
c152 24 45 4.00E-10 p. 10 1.281 
Notes: 
1. CL = Constant Load 
2. Crack growth rate of 1.0E-11 is used to represent test results where either cracking 
appeared to cease or the growth rate seemed to arrest. 
3. Each of the values in the column "Calculated "n" value" is calculated from Equation 19.

 40 
To characterize the uncertainty for n, it can be determined from the n values in the last column of 
Table 6-1 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 deviation, a normal distribution for "n" can be constructed. The n values at various 
percentiles, up to 2(SD), are listed in Table 6-2, where the percentile value is obtained by the 
Excel function NORMDIST for each set of given values of n, nMEAN, and nSD. For TSPA 
applications, it is recommended that n is to be sampled from a truncated normal distribution 
with a mean of 1.304, a standard deviation of 0.16, and an upper bound and a lower bound of 
1.624 and 0.984, the 2(SD) of the normal distribution, respectively. 
The base case slip dissolution/film rupture SCC model developed for Alloy 22, represented by 
Equation 19, is graphically illustrated in Figure 6 for n values at 0.984 (the lower bound), 1.304 
(mean), and 1.624 (the upper bound), along with test data presented in Table 6-1, as well as the 
graphical representation of Equation 19 for stainless steel (with n=0.54). Excellent resistance to 
SCC for Alloy 22 is clearly illustrated in Figure 6 where even the higher crack growth rates 
exhibited by the top curve of Alloy 22 with n=0.984 are about 2 orders of magnitude lower than 
the crack growth rates associated with stainless steel curve. 
Table 6-2. 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

 41 
Crack growth rate for Alloy 22 
1.E-13 
1.E-12 
1.E-11 
1.E-10 
1.E-09 
1.E-08 
1.E-07 
1.E-06 
1.E-05 
1.E-04 
1.E-03 
1.E-02 
15 20 25 30 35 40 45 50 55 
Stress intensity factor, MPa (m)^0.5 
Crack growth rate, mm/s 
Stainless steel, n=0.54 
Test data C144 @ 30 MPa(m)^.5 
Test data C152 @ 45 MPa(m)^.5 
Test data C153 @ 30 MPa(m)^.5, 20% cold work 
Model prediction, n=0.984 (-2 standard deviation) 
Model prediction, n=1.304 (mean) 
Model prediction, n=1.624 (+2 standard deviation) 
Figure 6. Crack growth rate vs. 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 pre-existing 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. Pre-existing cracks are usually caused by 
manufacturing processes (especially welding) or crack initiation (see Section 6.2). 
The concept of threshold stress intensity factor (KISCC) has been commonly used to assess the 
susceptibility of material to SCC. The description of this concept can be found in Jones and 
Ricker (1987, pp. 145-163) and Sprowls (1987, pp. 245-292). 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 WP are described in Section 6.4. The threshold stress intensity factor is normally 
determined experimentally. Such experiments, which require very long test times and extremely 
high measurement accuracy, are impractical for Yucca Mountain Project applications. As an 
alternative approach, a crack blunting criterion is used to define the threshold stress intensity 
factor. Based on the crack blunting criterion (Andresen and Ford 1994, 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 an SCC 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 (GC) rate, the threshold stress intensity factor KISCC can be calculated from 
Equation 19, or the following equation: 
KISCC = (Vgc / A ) n / 1 (Eq. 20)

 42 
The mean general corrosion rate, which can be calculated from Table 4.1-5, will be used in 
Equation 20. Observation of Table 4.1-5 indicated that the GC rate associated with sample DCA 
177 appears to be an outlier. The mean GC rate is 7.23 nm/y if this outlier is removed from the 
data set. Values for n and A can be determined from Equations 18 and 16 for a given value of 'n'. 
The threshold stress intensity factor for Alloy 22, accordingly, can be expressed in Table 6-3, 
based on the "n" values shown in Table 6-2. 
The threshold stress intensity factor will be 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 will be compared with the KISCC value. At the point that 
the KI value drops below KISCC, the crack will arrest. 
Table 6-3. 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

 43 
6.3.6 Alternative Model: The Coupled Environment Fracture (CEF) Model 
Alternative conceptual models (ACMs) are based on assumptions and 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 assumptions 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 dissolution/film 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, Macdonald et al. 1994), was 
developed on the basic assumption that the internal and external environments are coupled by the 
need to conserve charge in the system. Thus the solution of Laplace's equation for the external 
environment, as oxygen reduction on the external surface consumes the positive current 
emanating from the crack mouth, yields a boundary condition for solving Laplace's equation for 
the internal crack environment. Metal dissolution at the crack tip is described by the slip 
dissolution model, 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 approach for the prediction of the crack 
growth rate. It will be considered in the AMR only for the purpose of validation of the base-case 
model. 
The CEF model is a physico-electrochemical model developed for intergranular stress corrosion 
cracking in sensitized Type 304 stainless steel 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 were: (1) to derive a physically realistic model that 
unifies the electrochemical, chemical and mechanical aspects of the propagation of cracks 
through sensitized Type 304 SS in pure water under BWR recirculation piping conditions, 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. The mathematical development of the model can be found in Macdonald 
and Urquidi-Macdonald (1991) and Macdonald et al. (1994). 
The slip dissolution/film rupture model and the CEF model are similar in several ways. Both 
were developed for intergranular stress corrosion cracking in sensitized Type 304 stainless steel 
in 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 dissolution/film 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

 44 
model stays with an implicit approach. It can be said that the CEF model is more a theoretical 
model and the slip dissolution/film rupture model is a mixed theoretical and empirical model. 
Both the slip dissolution/film rupture model and the CEF model are capable of predicting the 
crack growth rate for stress corrosion cracking. However, it was discovered that the CEF model 
appears to have the tendency of underestimating the crack growth rate as compared to the slip 
dissolution/film rupture model when both models were applied to predict the crack growth rate 
for Type 304 stainless steel in the light boiling water reactor (BWR) environment. This 
nonconservatism is evidenced by Figure 7. Comparison with experimental data summarized by 
Ford and Andresen (1988), Figure 22, for crack propagation rate versus stress intensity factor for 
sensitized Type 304 stainless steel in fully aerated, high purity water at elevated temperature 
indicated that the crack growth rate predicted by the CEF model (i.e., 3.2x10-9 cm/s at 20 MPa 
m0.5) (Macdonald and Urquidi-Macdonald 1991, p. 78) tends to be at the lower end of the range 
cited by Andresen and Ford (1988). For this reason, the CEF model was not included for further 
evaluation but only used to validate the base case slip dissolution/film rupture model. 
1.E-10 
1.E-09 
1.E-08 
1.E-07 
1.E-06 
1.E-05 
5 10 15 20 25 30 35 40 
Stress intensity factor, M Pa (m)^0.5 
Crack growth rate, cm/s 
Slip d issolution mode (n=0.54)l 
CEFM (Macdonal & U rquidi-Macdonald 1991, F ig. 12) 
CEFM (Macdonal et al. 1994, F ig. 5 ) 
Figure 7. Comparison of predicted crack growth rates for 304 stainless steel.

 45 
6.3.7 Stress Corrosion Cracking for the Drip Shield Material Titanium Grade 7 
The sources of stress corrosion cracking in the titanium grade 7 DS are (1) weld induced residual 
stress; (2) plasticity induced residual stress caused by seismic events; and (3) residual stress 
produced by rock falls. The weld induced residual stress will be mitigated by annealing. The 
threshold stress for crack initiation developed in Section 6.2.1 will be used as the failure criterion 
for seismic induced stress and, if the seismic induced residual stress exceeds the threshold, the 
affected areas of the waste package or drip shield are conservatively defined as having failed as a 
barrier to flow and transport. An analysis of the consequence of residual stress produced by rock 
falls is presented in this section. 
Stress corrosion cracks in passive alloys such as Ti Grade 7 tend to be very tight (small crack 
opening displacement) by nature because the crack tip stress induced passive film rupture, 
repassivation and re-rupture repetitive process (or the analogous crack tip hydride precipitation, 
hydride fracture and reprecipitation of crack tip hydrides repetitive process) results in a relatively 
high effective crack tip corrosion rate as compared to the unstressed sides of the crack. As the 
crack grows through-wall, the tensile stresses normal to the crack walls are relieved, and the 
resulting crack faces continue to corrode by general corrosion at the very low passive corrosion 
rate with a median value of 0.03 microns/year (CRWMS M&O 2000 [144971], Section 6.5.4). 
According to Section 6.2.1, residual stress resulting from rock falls can cause SCC crack 
initiation in the drip shield if the stress exceeds the threshold stress for the DS material (titanium 
grade 7). The maximum temperature in the drip shield wall, according to CRWMS M&O 2001 
[154594], Figure 48, is 140oC. The average yield strength (YS) for titanium grade 7 at 140oC, 
using a straight-line interpolation between the room temperature (20oC) and 204oC from Table 
4.1-4, is 220.7 MPa. The threshold stress for crack initiation, according to Section 6.2.1, is 
0.5(YS), i.e., 110.4 MPa. The size (depth) of the initiated crack, based on Section 6.2.1, is 
0.05mm. It will take about 40 years for the crack to grow through the 15-mm DS wall (BSC 
2001 [156807], Table 5-13) based on an SCC crack growth rate of 1.25 x 10-8 mm/s estimated by 
DTN: LL021105312251.023, Section 1.3, p. 13. 
Once the SCC initiated crack develops into a through-wall crack, the crack length "2c" and the 
crack gap (or width) "d", according to BSC 2001 [156807], Plugging of Stress Corrosion Cracks 
by Precipitation, 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/crack side and results 
in a total per side oxide thickness of ~182 microns based on a TiO2 oxide/metal volume ratio of 
1.76 (Bradford 1987, Table 2, p. 64). At a passive growth rate of .03 microns metal loss/year it 
will take ~3400 years for the crack to fill with corrosion product. In the interim, while the crack 
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 
intersect the upper drip shield surface as well as within the crack. This formation of calciferous 
deposits is well documented in seawater environments and in heat exchangers through which 
natural brines are forced to flow; e.g. in desalination plants (carrying ~6% NaCl solutions) and in

 46 
potash plants (carrying >12% brine (NaCl/KCl mixtures)). In both these cases, Ti surfaces are 
heat sources at operating temperatures of ~100oC. Such deposits form rapidly under flowing 
conditions, and have to be regularly removed to avoid loss of heat exchanger efficiency. In the 
case of concentrating pore water or J-13 water, calcite precipitation is the first stage of the 
concentration process (BSC 2001 [155640], Section 6.7.1). Other minerals such as amorphous 
silica will also precipitate. 
A detailed calculation of the expected rate of SCC 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 [156807]). The calculation conservatively assumes 
(BSC 2001 [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 [156807], Section 6.3) SCC cracks are sealed in a few hundred years at most when 
water is allowed to flow through the cracks at the expected very low film flow rate. When the 
cracks are bridged by water, the sealing process may take thousands of years, but no flow occurs 
since the water is held by capillary forces. In a more realistic case of a non-uniform 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 run-off on the drip shield 
surface compared to through crack flow which in turn is determined by scale 
porosity/permeability. Because of the expected high density of the calcite deposits BSC 2001 
[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. 
Finally, multiple rock falls on the same spot of the waste package is ruled out because of the 
small probability. Drip shield structural response to rock falls induced by seismic events is 
addressed in BSC 2003 [162598], 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 effects are being treated in the Seismic 
Consequences Abstraction AMR, MDL-WIS-PA-000003 REV 00.

 47 
6.4 EVALUATION OF STRESS INTENSITY FACTOR 
6.4.1 Introduction 
The stress intensity factor KI is usually 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 approximate 
formula (Ewalds and Wanhill 1984, 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 non-uniformly distributed across the thickness, the 
stress intensity factor has to be calculated by some numerical algorithms, such as the finite 
element method. Rice (1968, 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. In accordance with Chan et al. (1970, 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 (more detail in 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 of the AMR summarizes the methodology, calculation procedures, and selected results, 
which are discussed is detailed in SI (2003). 
6.4.2 Calculations of Stress Intensity Factors for Waste Package Closure Welds 
6.4.2.1 Introduction

 48 
Only weld induced residual stress in the final closure welds of the waste package outer barrier 
will be considered for performance assessment, based on the following reasons: 
1. SCC of the DS will be excluded from the performance assessment. According to Section 
6.3.7, the sources of stress corrosion cracking in the titanium grade 7 DS are (1) weld 
induced residual stress; (2) plastic residual stress caused by seismic events; and (3) residual 
stress produced by rock falls. The weld induced residual stress will be eliminated by 
annealing. The threshold stress for crack initiation developed in Section 6.2.1 will be used as 
the failure criterion for seismic induced stress and, if the seismic induced residual stress 
exceeds the threshold, the effected area of the waste package or drip shield are assumed to 
have failed as a barrier to flow and transport. An analysis of the consequence of residual 
stress produced by rock falls presented in Section 6.3.7 indicated that SCC resulting from 
rock fall will result in very tight crack openings and will not degrade the water diversion or 
function of the DS. The Type 316 stainless steel inner barrier of the WP will also be excluded 
from the SCC evaluation because the performance assessment will not take credit from the 
inner barrier. 
2. Welds are the most susceptible to SCC because (1) welding can produce high tensile residual 
stress in the weld; (2) pre-existing 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 non-equilibrium brittle phases, which could enhance material susceptibility to SCC. All 
the welds with the exception of the final closure welds will be subjected to heat treatment to 
relieve the residual stress when the entire WP is heat treated before the loading of spent fuel 
elements. 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. Failure criteria governing seismic 
initiated residual stress will be developed for the WP material, i.e., Alloy 22. The failure 
criteria are based on a threshold stress which was discussed in Section 6.2.1 of this AMR. 
Therefore, weld residual stress is the only type of stress of SCC 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 SCC and only outer surface-breaking flaws 
are of concern for performance. 
According to Arthur (2003), Attachment 1, Figure 1, the currently recommended waste package 
design for the license application (LA) consists of the following changes from the Site 
Recommendation (SR) design: 
(a) replacing the full penetration stainless steel lid weld with a spread ring and seal weld; 
(b) eliminating the outer lid extension; 
(c) changing the outer lid mitigation method from induction annealing to laser peening; 
(d) changing the inner lid weld configuration from a full penetration weld to a seal weld; and 
(e) eliminating laser peening of the inner lid.

 49 
Sketches of the Site Recommendation design and the current recommended LA design of the 
waste package are shown in Figure 8 (Arthur 2003, Attachment 1, Figure 1). 
Figure 8. Site Recommendation Design and Recommended LA Design of Waste Package 
For the performance assessment 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 outer lid subjected to laser peening and the as-welded 10-mm 
Alloy 22 middle lid. Calculated stress and stress intensity factor profiles due to weld residual 
stresses for the currently recommended waste package design are not available. However, stress 
and stress intensity factor profiles have been calculated and saved in DTN: 
LL000316205924.142 for two different WP designs: the CRM-21 PWR design (which has a 
single 25-mm Alloy 22 outer lid), as shown in Figure 9 (SI 2003, Figure 1-4), and the modified 
CRM-21 PWR design (which is similar to the CRM-21 PRW design but the thickness of the 
outer lid is reduced from 25 mm to 10 mm). It can be seen that the flat-head outer lid of the 
currently recommended WP design is similar to the outer lid of the CRM-21 PWR design not 
only in their geometrical configurations but also in the welding processes. It is indicated in 
Section 6.2.2.1 that the current welding process being considered for the WP final weld is a 
GTAW process. It will be shown in Section 6.4.2.2 that the heat generation rate used as the input

 50 
for the thermal analysis of the CRM-21 PWR design is equivalent to that of a GTAW welding 
procedure. Therefore, it is recommended that calculated stress and stress intensity factor profiles 
for the 25-mm outer Alloy 22 lid of the CRM-21 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 
CRM-21 PWR design are used for the Alloy 22 waste package middle lid (WPML) of the current 
design. 
Figure 9. Schematic and Dimensions for the CRM-21 PWR WP Design

 51 
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 WP 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, p. 3). Thus, the WP closure weld models 
were assumed to be two-dimensionally axisymmetric about the WP axial centerline. 
The finite element model for the CRM-21 PWR design of the WP (Figure 9) is shown in Figure 
10. The weld geometry and immediate neighboring material 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. 
Figure 10 shows the finite element model with all weld passes deposited and both lids in place. 
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. 
DTN: LL000319805924.143 
Figure 10. Finite Element Model for the CRM-21 PWR WP Design

 52 
Figure 11 shows a close-up view of the finite element model (Figure 10) where axisymmetrical 
cross sections selected for stress output are identified. The radial stress, Sx, in the x-direction, is 
normal to the section while the hoop stress, Sz, in the z-direction, is tangential to the section. 
Similarly, Figure 12 is the close-up view of the modified CRM-21 PWR design which shows the 
cross sections for stress output. Section 1-1 is selected such that the stress Sn normal to the 
section is maximized. The stress component Sn will be conservatively used as the radial stress, 
Sx, in the weld. Section 2-2, likewise, is selected such that the stress Sz, the hoop stress, is 
maximized and this stress component will be conservatively used as the hoop stress in the weld. 
The distance (or crack depth) measured from the outer surface of the closure lid on section 1-1 or 
2-2 will be projected to a vertical cross section which is normal to the plane of the closure lid. 
DTN: LL000319805924.143 
Figure 11. Selected Cross-Sections for CRM-21 PWR WP Design

 53 
DTN: LL000319805924.143 
Figure 12. Selected Cross-Sections for the Modified CRM-21 PWR WP Design 
Material Properties-The 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 SI (2003). 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. 
Non-linear properties, such as the elastic-plastic behavior, and temperature dependency are 
properly considered. 
Thermal Analysis-A thermal analysis of the WP closure was performed to simulate the 
temperature history caused by each weld pass. Each weld pass will result in a different 
temperature field since as passes are applied, more material is added, residual stress from

 54 
previous passes are being incorporated, and the relative location of the weld heat input is 
changing with respect to the lid thickness. 
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 WP. The 
heat generated in the weld pass, represented by the net heat input (Hnet in joules/in.) of the 
welding process can be calculated according to Equation (2.3), p. 33, of DTN: 
LL000312705924.132, Hnet = f1 EI/v, for given welding parameters including voltage (E), 
amperage (I) and travel velocity of the heat source (v in in./sec.) and heat transfer efficiency (f1). 
Based on a Gas Tungsten Arc Welding (GTAW) process, the amperage, voltage and average 
travel speed are, respectively, 330-335 A, 12.1-13.0 V and 8.0 in./min. (0.133 in./sec.) (CRWMS 
M&O 1998, Table 7-1, p. 12). The heat transfer efficiency (f1) for gas tungsten arc welding, 
according to DTN: LL000312705924.132, Figure 3.1A, p. 69, is 21-48%. 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 very close to the heat generation rate 12268 Joules/in used in the finite 
element thermal analysis (SI 2003, p. 1-8). 
For the axisymmetric representation of the three-dimensional problem, it is desired to convert the 
non-axisymmetric heat input into an equivalent axisymmetric heat input, which would be 
representative of what a typical point on the circumference of the weld would experience. Since 
a typical point on the circumference would experience essentially 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 over a two-second time interval (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 Analysis-The stress analysis is performed for all individually modeled 
weld passes. For example, if six weld passes are being 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 WP 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 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.

 55 
Top View of 
Lid 
Circumferential 
Flaw (Parallel to Weld) 
Radial Stress is Driving 
Force. 
Radial Flaw (Perpendicular to 
Weld) Hoop Stress is Driving 
Force. 
Weld 
Figure 13. Flaw Orientation for Lid Welds 
A general form of the stress intensity factor can be expressed by Equation 21, i.e., 
KI =  s (pa)1/2 
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 (see Section 
6.4.1.1), 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

 56 
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 0.5 (a semi-circular crack). In 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, 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 radial crack in the 
closure weld 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 semi-elliptical crack due to the rapid decay of hoop 
stress in the radial distance away from the weld and base metal interface (Figure 14, where "1-1", 
"2-2", etc. are section identifications as indicated in Figure 11). 
Initial WP, Outer Lid, 125C 
-10
0 
10 
20 
30 
40 
50 
60
0 0.5 1 1.5 2 2.5 3 
Distance From Inside Surface (in) 
1-1 
2-2 
3-3 
4-4 
DTN: LL000316205924.144 
Figure 14. Hoop Stresses in Outer Lid of CRM-21 PWR Design

 57 
The stress intensity factor for an infinite SECP with an infinitely long flaw is (Buchalet and 
Bamford 1976, 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, 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) and are graphically presented in Buchalet and Bamford (1976), 
Figure 6, which are 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 15 shows, for a circumferential flaw, 
the G factor distribution in the closure weld of the outer lid of the CRM-21 PWR WP as a result 
of curve fit based on the exact G values calculated at four discrete points corresponding to crackversus-
thickness ratios of 0.2, 0.3, 0.4 and 0.6. Figure 15 indicates that, 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 which contains a semi-circular surface flaw in a flat plate 
and is judged to be close to the final solution. Therefore, the geometrical correction factor is 
assumed to be equal to unity for the case of radial cracks. 
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 CRM-21 PWR design will be used for the as-welded and laser peened 
outer Alloy 22 lid of the current design and calculated stress and stress intensity factor profiles 
for the as-welded 10-mm Alloy 22 lid of the modified CRM-21 PWR design will be 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 WP designs are 
documented in DTN: LL000316205924.142. For radial and hoop stresses in ksi in the 25-mm 
outer closure-lid weld of the CRM-21 PWR design, the coefficients, A0, A1, A2, and A3 with 
stress in ksi and distance x in inches are obtained from DTN: LL000316205924.142, file name: 
Skvrbr1, sheet "UnAnneal, Sx", cells C9 - C12 for radial stress and sheet "UnAnneal, Sz", cells 
C9-C12 for hoop stress. The coefficients are listed in the third and fourth rows of Table 4.1-2. 
Table 6-4 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. 
Similarly, for radial and hoop stresses in ksi in the 10-mm lid of the modified CRM-21 PWR 
design, the stress coefficients with stress in ksi and distance x in inches are obtained from DTN: 
LL000316205924.142, file name: Thinlid11, sheet "UnAnneal,1-1.Sn", cells C9 - C12 for radial 
stress and sheet "UnAnneal,2-2,Sz", cells C9-C12 for hoop stress. The coefficients are listed in

 58 
the fifth and sixth rows of Table 4.1-2. Table 6-5 shows the converted stress coefficients, A0, A1, 
A2, and A3, in the metric unit system. 
Tables 6-6 and 6-7 show calculated stress profiles (using Equation 23 and the stress coefficients 
in Tables 6-4 and 6-5) and stress intensity profiles (obtained directly from Table 4.1-3) for the 
outer and middle lids of the WP design. The values of x's to be used in Equation 23 to calculate 
the radial and hoop stress profiles are listed in the first column of Table 6-6 or Table 6-7. Note 
that, 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 (see Section 6.4.2.2 and Figure 12). 
Table 6-4. Stress coefficients for the As-Welded WP 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 
Table 6-5. Stress coefficients for the As-Welded WP 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 

 59 
Table 6-6. Stress Intensity Factor (SIF) Profiles for As-Welded WP Outer Lid 
Depth, 
mm 
Radial stress (Sx), 
MPa 
SIF due to Sx, 
MPa-m0.5 
Hoop stress (Sz), 
MPa 
SIF due to Sz, 
MPa-m0.5 
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 
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 

 60 
Table 6-7. Stresses and Stress Intensity Factors for the As-Welded WP Middle Lid 
(Output DTN: LL030607012251.065) 
Depth, 
mm 
Radial stress (Sx), 
MPa 
SIF due to Sx, 
MPa-m0.5 
Hoop stress (Sz), 
MPa 
SIF due to Sz, 
MPa-m0.5 
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 
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 

 61 
DTN: LL000319905924.144 
Figure 15. Outer Lid Circumferential Flaw Geometric Correction Factor 
DTN: LL000319905924.144 
Figure 16. Stress Intensity Factors for Circumferential Flaw in Outer Lid

 62 
DTN: LL000319905924.144 
Figure 17. Stress Intensity Factor for Radial Flaw in Outer 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, 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/year (Section 6.3.5), the 0.125- 
inch removal is the amount of material subject to general corrosion in 439,140 years. Removal of 
these elements causes a redistribution of the stress pattern. 
Figure 18 shows the row of elements removed to simulate the general corrosion of the outer lid 
surface. Figures 19 and 20 show, respectively, the through-wall radial stress profiles (with and 
without corrosion effects) and hoop stress profiles at Section 1-1 in Figure 18. These results 
demonstrate the redistribution of the residual stress. In general, stress appears to be not very 
sensitive to the effects of corrosion. 
Figures 21 and 22 show the stress intensity factor distribution for Section 1-1 in Figure 18 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 demonstrate that the overall effect of general corrosion is small.

 63 
DTN: LL000319805924.143 
NOTE: (a) Finite element model 
(b) Sections for stress profile 
Figure 18. Finite Element Model Used for Study of Corrosion

 64 
DTN: LL000319905924.144 
Figure 19. Effect of Corrosion on Radial Stress in Outer Lid 
DTN: LL000319905924.144 
Figure 20. Effect of Corrosion on Hoop Stress in Outer Lid

 65 
DTN: LL000319905924.144 
NOTE: (a) X-axis is crack depth in inches. 
(b) X-axis is shown as the ratio of crack depth (a) vs. thickness (t). 
Figure 21. Stress Intensity Factor for Full-Circumference Flaw in Outer Lid

 66 
DTN: LL000319905924.144 
NOTE: (a) X-axis is crack depth in inches. 
(b) X-axis is shown as the ratio of crack depth (a) vs. thickness (t). 
Figure 22. Stress Intensity Factor for Radial Elliptical Crack in Outer Lid

 67 
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. SCC can be reduced to a manageable state if the weld residual 
stress in the WP can be effectively mitigated. 
Weld residual stress can be mitigated by optimizing the geometrical configuration of the WP 
design. 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 WP, in accordance with Arthur 2003, Attachment 1, p. 6, nonthermal 
mitigation (laser peening or low-plasticity burnishing) can be applied without heating the 
spent fuel elements within the WP but, for the purpose of license application (LA), Arthor 2003 
indicated that laser peening is the non-thermal mitigation method. The laser peening treatment, 
which will be used for the 25-mm outer lid of the outer barrier, 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 a much-improved technology. 
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 in Hornbach (1999), 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 Alloy 22 plate. The depth of stress reduction may be increased by 
repeated application of laser peening (Hornbach 1999). A typical example is shown in Figure 23 
for stress profiles at the weld center line 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. 
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 CRM-21 PWR design was reduced from tensile 
stress to 40 ksi compressive stress for a depth of 0.06 in at the outside surface (see Figure 24). 
The residual stress then varies linearly from 0.06 in. to 0.12 in. From this point on, the stress 
remains undisturbed. 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 25. 
For radial and hoop stresses in ksi in the laser peened 25-mm outer lid of the WP design, the 
stress coefficients with stress in ksi and distance x in inches are obtained from DTN: 
LL000316205924.142, file name: Skvrbr1, sheet "Peening,Sx", cells C9 - C12 for radial stress 
and sheet "Peening,Sz", cells C9-C12 for hoop stress. The coefficients are listed in the seventh 
and eighth rows of Table 4.1-2. Table 6-8 shows the converted stress coefficients, A0, A1, A2, 
and A3, in the metric unit system. Table 6-9 shows the calculated stress and stress intensity 
profiles for the outer WP lid subjected laser peening.

 68 
Table 6-8. Stress coefficients for the Laser Peened WP 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 
DTN: LL000320005924.145 
Figure 23. Mitigation of Weld Stress in Alloy 22 with Laser Peening

 69 
Table 6-9. Stresses and Stress Intensity Factors for Laser Peened WP Outer Lid 
(Output DTN: LL030607012251.065) 
Depth, 
mm 
Radial stress (Sx), 
MPa 
SIF due to Sx, 
MPa-m0.5 
Hoop stress (Sz), 
MPa 
SIF due to Sz, 
MPa-m0.5 
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 
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 

 70 
DTN: LL000319905924.144 
NOTE: (a) Radial Stress, Sx 
(b) Hoop Stress, Sz 
Figure 24. Stress in Outer Lid with and without Laser Peening

 71 
DTN: LL000319905924.144 
NOTE: (a) Stress Intensity Factor Plots due to Radial Stress 
(b) Stress Intensity Factor Plots due to Hoop Stress 
Figure 25. Stress Intensity Factors with and without Laser Peening 
(a/t=0.5) 
(a/t=0.5)

 72 
6.4.5 Uncertainty and Variability of Residual Stress and Stress Intensity Factor in WP 
It was stated in Section 6.4.2.2 that, although the determination of weld residual stress for the 
WP 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 of this 
assumption is that the stress distribution is axisymmetrical about the WP axial centerline, i.e., 
constant along the circumference. An investigation of cause of cracking in austenitic stainless 
steel piping (Klepfer 1975, Figure 9-95, pp. 9-119) indicated that the residual stress for a 26 inch 
pipe inside surface 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 ) can be represented by the following equation: 
S.(x)= S0(x)  .S(1  cos(.)) (Eq. 25a) 
where, 
. is the angle measured from a reference location (. = 0o) on the circumference, 
S.(x) is the weld residual stress profiles at an angle ., 
S0(x) is calculated weld residual stress profile at . = 0o, 
.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, i.e., 
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, 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 associated with Mohr's data was empirically developed by bounding the 
measured residual stress scatter developed for 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 WP 
design, the various parameters contributing to residual stress variation will be closely controlled. 
This includes close, automated control on the welding process parameters, the allowable material 
and weld wire yield strength range, the weld joint configuration and spacing, etc.

 73 
In contrast to the high degree of scatter noted in Mohr (1996), data available on shot peened 
(analogous to laser peened) nickel alloy Incoloy 908 (Pasupathi 2000) indicate a narrow residual 
stress scatter range for as-welded and as-welded plus shot peened nickel alloy material with one 
sigma values of 3% of the measured stress value for shot peened surfaces (Pasupathi 2000, 
Table II and Table 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, 
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 4-1-4. For conservative purpose, the higher YS value at the room temperature may be 
used. 
The data listed in Pasupathi (2000) are for both welded and non-welded samples (peened and 
unpeened), many of which also contain some cold work due to tube reduction drawing. Thus, 
they represent a good sampling of the entire range of material conditions the YMP WP may 
encounter. 
Further, in the case of the final closure welds of the dual-lid WP design, very tight process 
control plus periodic quality control measurements of weld surface residual stresses will be 
made in the hot-cell on the final post-processed Alloy 22 material in the near-surface region of 
the weld and heat affected zone. The quality control meaurement process(es) to be used will 
depend on the finally selected stress mitigation process. For the laser peening process, the socalled 
Almen Strips, which are commonly used to control shot peening processing and laser 
peening processing, may be used. 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 WP lid. The stress intensity factor calculated from the mean stress as 
described in Section 6.4.2.2 is assumed to be 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.

 74 
( ) ( ) ( )
( ) . .. 
. 
. .. 
. . - 
= 
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 4.1-4).

 75 
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 by PA 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 SCC 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 SCC for cracks in the radial direction. Based 
on stress distributions shown in Figure 14, rapid weld residual stress decay is observed with 
increasing distance normal to the weld/metal 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 will be approximately 
two times the plate thickness. 
With respect to the expected minimum spacing between parallel through-wall radial cracks, 
detailed analysis Structural Integrity Associates Support of Waste Package Design for 2001 
(Structural Integrity Associates 2002, Section I), 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) 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 comprehensive finite element 
analysis may be attempted in order to estimate the crack opening. A simplified approach, 
however, 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 WP. 
2. A circumferential crack is assumed to have a semi-elliptical shape with depth a and 
length 2c. The aspect ratio c/a for a radial crack is assumed to be 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. Under this assumption, most 
cracks will grow in both directions of the minor (depth a) and major (length 2c) axes 
and assume the semi-circular shape (i.e., a = c) when they become through-wall cracks. 
According to fracture mechanics (Ewalds and Wanhill 1984, 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. So

 76 
eventually a semi-elliptical crack will become a semi-circular 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 semi-circular 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. (1973, p. B.5), 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 
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).

 77 
7. MODEL VALIDATION 
7.1. INTENDED PURPOSE OF THE MODEL 
Stress corrosion cracking (SCC) is a potential corrosion mode that can result in penetration of the 
drip shield, waste package outer barrier and the stainless steel structural materials. Since no 
lifetime credit is taken for the stainless steel structural material it is not currently modeled. 
Therefore, in accordance with the Technical Work Plan for Waste Package Materials Data 
Analyses and Modeling (BSC 2002 [161132]), the intended purpose of the SCC model is to 
evaluate the potential for SCC of the drip shield (titanium grade 7) and the waste package outer 
barrier (Alloy 22) and to develop models for inclusion in abstracted form into the Integrated 
Waste Package Degradation (IWPD) model. This latter model provides the Performance 
Assessment Science and Analysis Project realistic waste package and drip shield SCC estimates 
as a function of time under the exposure conditions anticipated in the proposed repository. 
This SCC model, based on BSC 2002 [161132], directly supports the following principal factors: 
 Performance of the drip shield/drift invert system 
 Performance of the waste package 
 Probability of criticality event 
 Radionuclide delay through the unsaturated zone 
and the following TSPA components: 
 Drip Shield Stress Corrosion Cracking and Other Corrosion Modes 
 Waste Package Stress Corrosion Cracking and Other Corrosion Modes 
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 SCC initiation and growth on both smooth surfaces and at defects such as those that 
might exist in the region of the closure welds. Thus, although SCC is unlikely to initiate and/or 
grow under waste package highly static loading conditions where the only significant stresses are 
tensile residual fabrication and welding related stresses, the Project has conservatively chosen to 
mitigate the SCC potential by residual stress reversal processes that result in a compressive layer 
over the outer waste package surfaces. Under compression, SCC cannot initiate or grow. 
However, once the surface compressive layers are removed by general corrosion, SCC 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 10,000 year regulatory period. 
Further, finite element model calculations of the expected residual tensile stress patterns present 
at the Alloy 22 final closure welds (as well as for the residual stresses generated in the deformed 
region of a drip shield that was impacted by a rock drop) indicate that if SCC were to initiate and 
grow through-wall, the cracks would be extremely tight and very limited in length and any water 
transport through the drip shield or waste package or radionuclide egress through these tight

 78 
waste package outer barrier cracks would be extremely limited and would not significantly 
contribute to the dose rate at the regulatory site boundary (BSC 2001 [156807], Table 5.14). 
In establishing the required level of confidence for the SCC 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 SCC Model, these uncertainties are 
not large. 
Will the model be used to demonstrate compliance or licensing positions? 
Yes. The SCC Model is used as an input to IWPD which provides the Performance Assessment 
Science and Analysis Project realistic waste package and drip shield SCC degradation estimates 
as a function of time under the exposure conditions anticipated in the potential repository. The 
SCC Model inputs to IWPD support several primary factors and TSPA components. 
Will the output of the model have impacts (positive or negative) on TSPA dose calculation 
results? 
Yes. Although the effect of SCC penetrations in the drip shield and waste package outer barrier 
are estimated to have relatively small impacts on TSPA dose calculations, the SCC Model is 
used as an input to WAPDEG which is used to provide the Performance Assessment Science and 
Analysis Project realistic waste package and drip shield degradation estimates as a function of 
time under the exposure conditions anticipated in the proposed repository. The Integrated Waste 
Package Degradation Model supports several primary factors and TSPA components. 
Based on the current Project conservative SCC mitigation approach, it is reasonable to limit the 
SCC Model level of confidence to moderate. 
7.3. CRITERIA USED TO DETERMINE THAT THE REQUIRED LEVEL OF 
CONFIDENCE HAS BEEN OBTAINED 
The SCC Model involves the slip dissolution/film rupture crack growth model and the threshold 
stress intensity factor (KISCC) parameter; both are described in peer reviewed scientific journals. 
Validation of the stress corrosion cracking model(s) is done through quantitative comparisons of 
input parameters and model predictions to calculated data available in the peer-reviewed 
published literature as well as "Q" data generated by the Project. The criteria to be used to 
determine that the required level of confidence has been obtained are discussed in this section. 
Criterion One: This criterion deals with the validity of the model predictions of crack growth 
rate versus stress intensity. This criterion includes two parts: 
Criterion 1A: Are crack growth rates for stainless steel predicted by the slip 
dissolution/film rupture crack growth model for several applied stress intensity factors in

 79 
reasonable agreement with observed rates published in the peer reviewed literature for 
stainless steel using the slip dissolution/film rupture model documented in this AMR? 
Criterion 1B: Are crack growth rates predicted for Alloy 22 by the slip dissolution/film 
rupture crack growth model in reasonable agreement with (or representing conservative 
upper bounds of) growth rates to be determined under a Project sponsored and OQA 
accepted Q test program at General Electric Corporate Research and Development 
Laboratory? 
Criterion Two: Does the establishment of the threshold stress intensity KISCC satisfy an 
acceptable approach for Alloy 22 under environmental conditions relevant to the waste package? 
The acceptable approach is that the KISCC will be determined by using crack growth rate versus 
applied stress intensity measurements obtained under Q conditions. The measured values will be 
extrapolated to a conservative threshold value using the K dependence of crack growth rate 
described in the validated slip dissolution/film rupture model described in Criterion One. 
Criterion Three: Does the establishment of threshold stress satisfy an acceptable approach for 
Alloy 22 under environmental conditions relevant to the waste package? The approach taken is 
to experimentally establish the material specific threshold stress value based on ongoing 
qualified experimental testing at General Electric Corporate Research and Development 
Laboratory and utilizing an accepted precedent in establishing a conservative threshold value. 
7.4. ACTIVITIES PERFORMED TO GENERATE CONFIDENCE IN THE MODEL 
DURING MODEL DEVELOPMENT 
For Criterion 1A, input parameter (exponent n) obtained for stainless steel is 0.54 as 
documented in section 6.3.3 of this AMR. Figure 5 indicated that crack growth rates predicted by 
the slip dissolution/film rupture crack growth model are in reasonable agreement with observed 
rates published in the peer reviewed literature for stainless steel using the slip dissolution/film 
rupture model (Ford and Andresen. 1988). This has assured that the model details and 
calculational methods yield results fully consistent with the peer reviewed journal published 
values. 
For Criterion 1B, validity and predictive capacity of the model being used for Alloy 22 is 
established because crack growth rates predicted for Alloy 22 by the slip dissolution/film rupture 
crack growth model are in reasonable agreement with growth rates determined by direct 
measurements under a Project sponsored and OQA accepted Q test program at General Electric 
Global Research Center (GEGRC). Essentially, recent SCC crack growth rate measurements 
from GEGRC (DTN: LL021105312251.023) were made available for the assessment of model 
uncertainties as well as validation of the assumptions and parameter values developed for the 
base-case SCC model to be used for Alloy 22 (see Figure 6 in section 6.3.4). It was determined 
in section 6.3.4 that the mean value of n is 1.304 and the standard deviation is 0.16 with a 
truncated normal distribution with upper and lower bounds of 1.624 and 0.984, respectively. (see 
Table 6-2 in Section 6.3.4). 
Criterion Two is related to the threshold stress intensity factor. Stress corrosion crack growth can

 80 
occur at a rate, such as that predicted by the slip dissolution/film rupture model, only if the 
calculated stress intensity at any flaw of given dimensions of length and depth exceeds a 
threshold value known as KISCC. This criterion specifies an acceptable approach for the 
establishment of KISCC for Alloy 22 under environmental conditions relevant to the waste 
package. Since there is no accepted theoretical basis for a priori or deterministic calculation of 
KISCC this parameter is determined by using crack growth rate versus applied stress intensity 
measurements obtained under Q conditions. The measured values are then extrapolated to a 
conservative threshold value using the K dependence of crack growth rate described in the 
validated slip dissolution/film rupture model described in the first criterion. A defensible, 
conservative KISCC value was obtained by extrapolating crack growth rate versus K to a crack 
growth rate equal to the mean general corrosion rate at the alloy surface. 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 
SCC will effectively arrest. 
Based on the crack blunting theory, it follows that an SCC crack will not grow if the general 
corrosion rate exceeds the mean crack growth rate. If Vgc is the mean general corrosion rate, the 
threshold stress intensity factor KISCC can be calculated from Equation 20 of Section 6.3.5: 
KISCC = (Vgc / A ) n / 1 (Eq. 20) 
The mean general corrosion rate, Vgc, based on Section 6.3.5, is 7.23 nm/y. The threshold stress 
intensity factor for Alloy 22, accordingly, can be expressed in Table 6-3 of Section 6.3.5, based 
on the "n" values shown in Table 6-2. 
Criterion Three specifies an acceptable approach for the establishment of a defensible threshold 
stress model. The threshold stress is that value below which stress corrosion cracking will not 
initiate on a smooth metal surface. The threshold stress conceptual model is published in peer 
reviewed journal papers and is described in Section 6.2.1. However, there is no firm accepted 
basis for calculating a threshold stress value for a given material/environment combination. 
Therefore, it is necessary to experimentally establish the threshold stress value. 
Recently obtained SCC crack initiation stress measurements reported in DTN: 
LL021105312251.023 are summarized in Figure 1 in section 6.2.1, where the measurements of 
crack initiation stress is presented as failure stress vs. time-to-failure for specimens subjected to 
9,600 hours of exposure in hot concentrated salt solution (pH=10.3 at 105oC) designed to 
simulate the chemistry of concentrated Yucca Mountain ground water. The report indicated that 
Alloy 22 exhibits excellent SCC resistance since failure was not observed for any of the 120 
Alloy 22 specimens under applied stress up to about 2.0 times the yield strength (YS) of the 
material. Titanium grade 7, although still faily resistant to SCC, did see some failures at applied 
stress levels of about 1.1 times the yield strength. An extrapolation scheme is needed in order to 
derive the threshold stress associated with the lifetime of waste packages from the available 
experimental results. The ASME Boiler Pressure Vessel code (ASME 1969, p. 80) typically uses 
a safety factor of 2 on stress when discussing fatigue lifetime cycles. Following this practice, the 
threshold stress may be derived from the stress levels from the test (i.e., 2.0(YS) for Alloy 22 
and 1.1(YS) for titanium grade 7) by applying an appropriate safety factor. It is recommended a

 81 
threshold stress of 0.5(YS) for titanium grade 7 (with a safety factor of about 2.2). The same 
safety factor will result in a threshold stress of 0.9(YS) for Alloy 22. 
Additionally, 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. It was concluded in Section 6.3.6 that both the slip dissolution/film rupture 
model and the CEF model are capable of predicting the crack growth rate for stress corrosion 
cracking. However, it was discovered that the CEF model appears to have the tendency of 
underestimating the crack growth rate as compared to the slip dissolution/film rupture model 
when both models were applied to predict the crack growth rate for Type 304 stainless steel in 
the light boiling water reactor (BWR) environment. This is evidenced by Figure 7. Comparison 
with experimental data summarized by Ford and Andresen (1988) for crack propagation rate 
versus stress intensity factor for sensitized Type 304 stainless steel in fully aerated, high purity 
water at elevated temperature indicated that the crack growth rate predicted by the CEF model 
(i.e., 3.2x10-9 cm/s at 20 MPa-m0.5) tends to be at the lower end of the range cited by Ford and 
Andresen (1988) (Macdonald and Urquidi-Macdonald 1991). For this reason, the CEF model 
was not included for further evaluation but only used to validate the base case slip 
dissolution/film rupture model. 
In summary, the slip dissolution/film rupture SCC Model was validated by comparing Type 304 
Stainless Steel measured crack growth rates reported in peer reviewed literature with SDFR 
Model predictions as well as with a less conservative alternate conceptual model and by 
comparing Alloy 22 SDFR Model predicted rates with subsequently developed experimentally 
measured Alloy 22 rates and demonstrating good agreement. For the empirical threshold stress 
intensity factor described in peer reviewed literature, a conservative approach was used to 
establish a threshold KISCC value by extrapolating qualified Alloy 22 crack growth rate results 
experimentally obtained at higher KI values down to rates representative of the mean general 
corrosion rate where crack blunting occurs. 
Finally with respect to the threshold stress used to describe crack initiation on smooth surfaces, 
establishment of an acceptable conservative threshold SCC initiation stress was based on the 
ASME Boiler Pressure Vessel Code fatigue lifetime precedent of utilizing a factor of 2.2 
reduction in stress below the fatigue runout failure stress. As a result of the above model 
validation approaches and the selection of conservative threshold values, the required level of 
confidence has been obtained. 
7.5. POST-DEVELOPMENT VALIDATION ACTIVITIES. 
Post-development validation activities per Section 5.4.1(C) of AP-SIII.10Q [162696] to be 
considered were identified in Technical Work Plan for Waste Package Materials Data Analyses 
and Modeling (BSC 2002 [161132]). Judged from the satisfactory results of the model 
validation, extended activities specifically for the purpose of validating the current SCC model 
do not appear to be necessary.

 82 
8. CONCLUSIONS 
8.1 CONCLUSION 
This AMR is a complete document which provides a detailed description of the process-level 
models and the associated input that have been developed for 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 welds. All the welds with the exception of the final closure welds will 
be subjected to heat treatment to relieve the residual stress when the entire WP is heat treated 
before the loading of spent fuel elements. 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. Failure 
criteria governing seismic initiated residual stress have been developed for the WP material, i.e., 
Alloy 22. The failure criteria are based on a stress threshold which is discussed in Section 6.2.1 
of this AMR. If the seismic induced residual stress exceeds the threshold, then the affected areas 
of the waste package or drip shield are assumed to have failed as a barrier to flow and transport. 
The drip shield is excluded from the SCC evaluation because the drip shield will be annealed to 
relieve the weld residual stress and SCC resulting from rock fall will result in very tight crack 
openings and will not degrade the water diversion or function of the DS (see section 6.3.7). The 
only remaining issue of concern for SCC associated with the DS is the potential for crack 
initiation due to plastic residual stress caused by seismic events. Failure criteria governing 
seismic initiated residual stress for the DS material, i.e., Titanium Grade 7, are based on a stress 
threshold which is discussed in Section 6.2.1 of this AMR. The Type 316 stainless steel inner 
barrier of the WP is excluded from the SCC evaluation because the performance assessment will 
not take credit from the inner barrier. 
The base-case slip dissolution/film rupture model relates crack initiation and the subsequent 
advance to the metal oxidation that occurs when the protective film at the crack tip is ruptured. 
The slip dissolution/ film rupture model can be applied to assess the failure (or the lack of it) of 
the waste package due to the SCC crack propagation for given manufacturing cracks and/or 
cracks initiated by the combined effects of stress and environment. 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 pre-existing crack or flaw having a stress 
intensity factor less than the threshold value. The threshold SIF provides a criterion for 
determining if an SCC crack will reach an arrest state or enter a propagation phase. 
The model validation was accomplished by comparing experimental measurements of key model 
parameters to data measurements directly sponsored by the project and corroborative data 
available from the open scientific literature and by comparing with another alternative 
conceptual model. Uncertainty and variability associated with model parameters have been 
assessed. 
The application of the SCC models to the WP and DS 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

 83 
10-mm middle lid. This AMR also provides other needed input for a complete TSPA for the 
degradation of the waste package due to SCC 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 (TPO) of the calculation Analysis of Mechanisms for Early Failure [161238]]) is given 
in Section 6.2.2, but is not part of the TPO of this AMR. 
8.2 ACCEPTANCE CRITERIA 
As indicated in Section 4.2, the Waste Package Technical Work Plan identifies the following 
acceptance criteria for this AMR: 
1. System Description and Demonstration of Multiple Barriers 
2. Scenario Analysis and Event Probability 
3. Degradation of Engineered Barriers 
A closer examination indicates that only Criteria 3 (Degradation of Engineered Barriers) is 
applicable to this AMR. Criteria 3 (including AC1, AC2, AC3, AC4, and AC5) are addressed as 
follows: 
AC1 (System Description and Model Integration are Adequate) is addressed in Sections 1.1, 
6.3.4, 6.3.7, 6.4.2 and 6.4.3. 
AC2 (Data are Sufficient for Model Justification) is addressed in Section 7 
AC3 (Data Uncertainty is Characterized and Propagated Through the Model Abstraction) is 
addressed in Section 6.4.5 and Tables 8-1, 8-2 and 8-3. 
AC4 (Model Uncertainty is Characterized and Propagated Through the Model Abstraction) is 
addressed in Tables 8-1, 8-2, and 8-3. 
AC5 (Model Abstraction Output is Supported by Objective Comparisons) is addressed in Tables 
8-1, 8-2, and 8-3. 
AC3, AC4 and AC5 will also be addressed by the Integrated Waste Package Degradation Model 
(IWPDM) AMR which describes the abstracted SCC models and the propagation of uncertainties 
in those models. 
8.3 SUMMARY OF OUTPUT 
The output of this AMR (DTN: LL030607012251.065) is summarized in Tables 8-1, 8-2, and 8- 
3 and can be used as input for the IWPDM AMR with no restrictions if the WP design, material, 
and environment are consistent with those considered in the modeling activities of this AMR. 
The model uses 25 mm and 10 mm (see Figure 8 in Section 6.4.2.1 and Table 8-1) for the outer 
and middle lids of the waste packages. The model is also applicable to thicker lids as the use of

 84 
smaller thicknesses makes the model more conservative. Weld induced residual stress in the 
waste package cylinder will be eliminated by an annealing process. 
Stress profiles for both radial stress and hoop stress vs. depth are presented in look-up Tables 8.2 
and 8.3. For the laser peened WP outer lid, it is clear from Table 8-3 that the hoop stress is the 
predominant stress component. Based on the hoop stress profile and yield stress of 286 MPa for 
Alloy 22, according to the first row of Table 8-1, 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 
4.57 mm.

 85 
Table 8-1 (part 1 of 3). Summary of Output 
(Output DTN: LL030607012251.065) 
Output name Output value or equation Unit Note 
Yield strength (YS) for 
Alloy 22 from Table 
4.1-4 
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 4.1-4 
275-450 at room temperature 
138-152 at 477K 
MPa Same as above & 
use average at 
temperature 
Threshold stress 
(Alloy 22) 
0.9 (YS) 
(Section 6.2.1) 
MPa YS at 200oC 
(473K) for WP 
Threshold stress 
(Titanium Grade 7) 
0.5 (YS) 
(Section 6.2.1) 
MPa YS at 140oC 
(413K) for DS 
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 
(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 
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 K n x n x t V 4 14 10 1 . 4 6 . 3 2 10 8 . 7 .. .
.. .
- - = 
(Section 6.3.4, Eq. 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, Eq. 20), where 
( )n 14 6 . 3 2 10 x 1 . 4 n 10 x 8 . 7 A - - =
(Section 6.3.4, Eq. 18) and 
n 4 n = (Section 6.3.3, Eq. 16) 
MPa m0.5 n is the 
repassivation 
slope 
Vgc in mm/s

 86 
Table 8-1 (part 2 of 3). Summary of Output 
(Output DTN: LL030607012251.065) 
Output name Output value or equation Unit Note 
Radial stress coeff. A0, 
WPML, as-welded 
181.636 
(Section 6.4.2.4, Table 6-5) 
MPa 
Radial stress coeff. A1, 
WPML, as-welded 
-177.592 
(Section 6.4.2.4, Table 6-5) 
MPa/mm 
Radial stress coeff. A2, 
WPML, as-welded 
23.385 
(Section 6.4.2.4, Table 6-5) 
MPa/mm2 
Radial stress coeff. A3, 
WPML, as-welded 
-0.900 
(Section 6.4.2.4, Table 6-5) 
MPa/mm3 
Hoop stress coeff. A0, 
WPML, as-welded 
219.908 
(Section 6.4.2.4, Table 6-5) 
MPa 
Hoop stress coeff. A1, 
WPML, as-welded 
56.494 
(Section 6.4.2.4, Table 6-5) 
MPa/mm 
Hoop stress coeff. A2, 
WPML, as-welded 
-20.848 
(Section 6.4.2.4, Table 6-5) 
MPa/mm2 
Hoop stress coeff. A3, 
WPML, as-welded 
1.083 
(Section 6.4.2.4, Table 6-5) 
MPa/mm3 
Radial stress coeff. A0, 
WPOL, laser-peened 
-265.920 
(Section 6.4.4, Table 6-8) 
MPa 
Radial stress coeff. A1, 
WPOL, laser-peened 
103.987 
(Section 6.4.4, Table 6-8) 
MPa/mm 
Radial stress coeff. A2, 
WPOL, laser-peened 
-9.857 
(Section 6.4.4, Table 6-8) 
MPa/m2 
Radial stress coeff. A3, 
WPOL, laser-peened 
0.254 
(Section 6.4.4, Table 6-8) 
MPa/mm3 
Hoop stress coeff. A0, 
WPOL, laser-peened 
-292.607 
(Section 6.4.4, Table 6-8) 
MPa 
Hoop stress coeff. A1, 
WPOL, laser-peened 
178.277 
(Section 6.4.4, Table 6-8) 
MPa/mm 
Hoop stress coeff. A2, 
WPOL, laser-peened 
-14.135 
(Section 6.4.4, Table 6-8) 
MPa/mm2 
Hoop stress coeff. A3, 
WPOL, laser-peened 
0.320 
(Section 6.4.4, Table 6-8) 
MPa/mm3 
Mean stress profile at 
.=0, S0(x) 
S0(x) = A0 + A1x + A2x2 + A3x3 
(Section 6.4.2.3, Eq. 23) 
MPa x (in mm) is 
crack depth 
S0(x), radial stress, 
WPML, as-welded 
Table 8-2, 2nd column MPa Calculated from 
Eq. 23 
S0(x), hoop stress, 
WPML, as-welded 
Table 8-2, 4th column MPa Calculated from 
Eq. 23 
SIF, K0(x), radial stress, 
WPML, as-welded 
Table 8-2, 3rd column MPa m0.5 
SIF, K0(x), hoop stress, 
WPML, as-welded 
Table 8-2, 5th column MPa m0.5

 87 
Table 8-1 (part 3 of 3). Summary of Output 
(Output DTN: LL030607012251.065) 
Output name Output value or equation Unit Note 
S0(x), radial stress, 
WPOL, laser-peened 
Table 8-3, 2nd column MPa Calculated from 
Eq. 23 
S0(x), hoop stress, 
WPOL, laser-peened 
Table 8-3, 4th column MPa Calculated from 
Eq. 23 
SIF, K0(x), radial 
stress, WPOL, laserpeened 
Table 8-3, 3rd column MPa m0.5 
SIF, K0(x), hoop 
stress, WPOL, laserpeened 
Table 8-3, 5th column MPa m0.5 
WPOL thickness (h) 25 
(Section 6.4.2.1, Fig. 8) 
mm 
WPML thickness (h) 10 
(Section 6.4.2.1, Fig. 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, Eq. 25a) 
MPa 
SIF profile, K.(x), at 
angle . from K0(x) 
K.(x)= K0(x) (S.(h) / S0(h)) 
(Section 6.4.5, Eq. 25b) 
MPa m0.5 
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, Eq. 26a) 
MPa 
Upper bound of stress 
variation ( ) ( ) ( )
( ) . .. 
. 
. .. 
. . + 
= 
h S 
S h S x S x S 
. 
. 
. . max 
(Section 6.4.5, Eq. 26b) 
MPa 
Lower bound of SIF 
variation ( ) ( ) ( )
( ) . .. 
. 
. .. 
. . - 
= 
h S 
S h S x K x K 
. 
. 
. . min 
(Section 6.4.5, Eq. 26c) 
MPa m0.5 
Upper bound of SIF 
variation ( ) ( ) ( )
( ) . .. 
. 
. .. 
. . + 
= 
h S 
S h S x K x K 
. 
. 
. . max 
(Section 6.4.5, Eq. 26d) 
MPa m0.5

 88 
Table 8-2. Stresses and Stress Intensity Factors for the As-Welded WP Middle Lid 
(Output DTN: LL030607012251.065, also Section 6.4.2.4, Table 6-7) 
Depth, 
mm 
Radial stress (Sx), 
MPa 
SIF due to Sx, 
MPa-m0.5 
Hoop stress (Sz), 
MPa 
SIF due to Sz, 
MPa-m0.5 
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 
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 

 89 
Table 8-3. Stresses and Stress Intensity Factors for Laser Peened WP Outer Lid 
(Output DTN: LL030607012251.065, also Section 6.4.4, Table 6-9) 
Depth, 
mm 
Radial stress (Sx), 
MPa 
SIF due to Sx, 
MPa-m0.5 
Hoop stress (Sz), 
MPa 
SIF due to Sz, 
MPa-m0.5 
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 
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

 90 
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and the Stainless Steel Structural Material. Submittal date: 03/22/2000.

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9.1 PROCEDURES 
AP-2.27Q, Rev. 0, ICN 0. Planning for Science Activities. Washington, D.C.: U.S. Department 
of Energy, Office of Civilian Radioactive Waste Management. ACC: MOL.20020701.0184. 
AP-SI.1Q, Rev. 4, ICN 0. Software Management. Washington, D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste Management. ACC: MOL.20030113.0149. 
AP-SIII.10Q, Rev. 1, ICN 0. Models. Washington, D.C.: U.S. Department of Energy, Office of 
Civilian Radioactive Waste Management. ACC: DOC.20030312.0039. 
AP-SV.1Q, Rev. 0, ICN 2. Control of the Electronic Management of Information. Washington,

 95 
D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste Management. ACC: 
MOL.20000831.0065. 
10. ATTACHMENTS 
No attachments.