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Technical Letter Report

[TLR-RES/DE/REB10]2024

Assessing Uncertainty in Modeling Chloride-Induced Stress Corrosion Cracking

Date:

June 28, 2024

Prepared in response to Task 3 in User Need Request NMSS2021004, by:

Hector Mendoza Lindsay Gilkey Sandia National Laboratories Sandia National Laboratories Dusty Brooks Sandia National Laboratories

NRC Point of

Contact:

Christopher Nellis Reactor Engineer Reactor Engineering Branch Division of Engineering Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the U.S.

Government. Neither the U.S. Government nor any agency thereof, nor any employee, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for any third party's use, or the results of such use, of any information, apparatus, product, or process disclosed in this publication, or represents that its use by such third party complies with applicable law.

This report does not contain or imply legally binding requirements. Nor does this report establish or modify any regulatory guidance or positions of the U.S. Nuclear Regulatory Commission and is not binding on the Commission.

SANDIA REPORT SAND202401093 Printed January 2024

Assessing Uncertainty in Modeling Stress Corrosion Cracking

Hector Mendoza, Lindsay Gilkey, and Dusty Brooks

Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Issued by Sandia National Laboratories, operated for the United States Department of Energy by National Technology & Engineering Solutions of Sandia, LLC.

NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors.

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v vi EXECUTIVE

SUMMARY

Over 90 % of Dry Cask Storage Systems (DCSSs) in the United States utilize welded, austenitic, stainless-steel (SS) canister-based designs deployed in either a vertical or horizontal configuration. The material and design choice are to safely provide confinement of the spent nuclear fuel (SNF). Under certain conditions, tensile stresses at weld locations on the SS material may lead to chloride-induced stress corrosion cracking (CISCC) when canisters are exposed to corrosive environments.

Due to the variance in age for DCSSs across the U.S., it is important to understand the mechanisms and evolution of CISCC for aging management.

This report summarizes the collaboration between Sandia National Laboratories (SNL) and the U.S. Nuclear Regulatory Commission (NRC) staff to improve the state of knowledge on CISCC for SS SNF canisters. This report provides information on technical issues related to risk-informing CISCC including a comparison of crack growth rate models and an evaluation of the effects of key parameter uncertainties on CISCC model behavior. However, this report does not suggest or endorse one model over another, and the probabilistic model results are intended only to show trends in model behavior.

The foundation of this work relied on using SNLs probabilistic CISCC computer code to assess the current state of knowledge for modeling CISCC on stainless-steel canisters [5]. SNLs CISCC computer code was designed to simulate a canister environment and probabilistically model canister penetration by stress corrosion cracking (SCC) at prescribed weld locations. The code has been continuously updated since 2014 as informed by research advances and experimental studies.

The code captures the mechanisms of SCC through various sub-models, from chloride deposition up to corrosion initiation and crack growth that can lead to through-wall penetration.

The study presented in this report was addressed in three tasks. Task 1 independently compared three different crack growth rate (CGR) models used by the CISCC research community: (1) a CGR model previously used by the Electric Power Research Institute, (2) a model based on the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code Case N860, and (3) the current

vii model used in SNLs CISCC code. Task 2 employed SNLs CISCC computer code infrastructure in a sensitivity study to assess how three critical input parameters with large uncertainty affected the evolution of CISCC on a horizontal canister: (1)

Limiting relative humidity for corrosion initiation (RHL), (2) salt deposition rate (DD),

and (3) threshold crack tip stress intensity factor (Kth). Three values were considered for each critical input parameter, resulting in 27 critical parameter realizations when all combinations of these parameters were considered for the study. For each critical parameter realization, 400 realizations with variations in secondary model parameters were considered to capture aleatory uncertainty. The sensitivity study was completed using two different CGR models based on results from Task 1 for four sites with distinct weather. The sensitivity study for Task 2 thus resulted in a total of 10,800 realizations executed per site per CGR model, allowing results to be presented in the form of cumulative distribution function (CDF) plots.

Task 3 consisted of summarizing realistic input parameter ranges identified from Tasks 1 and 2. Identification of input parameter ranges was performed considering potential future canister integrity analyses with using probabilistic fracture mechanics

When looking at CDF plots for through-wall crack (TWC) status, the analysis from Task 1 revealed conservatism from the ASME and SNL CGR models. These two models were subsequently used for the sensitivity analysis in Task 2. The quantities of interest (QoI) for the sensitivity analysis were: (1) time to pit initiation, (2) time to crack initiation, and (3) time to reach a TWC. Figure E-1 through Figure E-3 summarize model outputs for one of the sites (anonymous Site A). Each figure captures a sensitivity to one critical input parameter for each of the two CGR models, showing CDF plots for each of the three QoIs. Each CDF plot resembles the percentage of welds that attain the QoI (pit initiation, crack initiation, or TWC) from all realizations. The modeled time period was 292 years, but the simulations presented here are not intended to be predictive. The CDF plots are therefore presented as a function of a normalized time to focus on trends.

The sensitivity study on RHL showed effects on all three QoIs, and impacts were observed on TWC status before reaching the fully modeled time (Figure E-1).

viii Larger RHL values generally resulted in formed cracks reaching TWC status faster than smaller RHL values. For varying DD, there were no effects on pit initiation times since pit initiation is only a function of RH (Figure E-2). However, the effects of varying DD on crack formation and TWC times were more significant than the effect from the RHL values considered. For varying Kth, effects on pit initiation times were also not observed (Figure E-3). Variations were observed when looking at crack formation and TWC times. Overall, the most prominent differences were observed when considering the uncertainty from varying DD.

When comparing the two CGR models in each figure, differences were only observed in the TWC times. This result was expected since TWC time was the only QoI dependent on the CGR. In general, the ASME model resulted in the full suite of simulations reaching TWC status faster than the SNL model, but the gradual transition of the SNL CDF plots showed that aleatory uncertainty might be better captured by the SNL model.

For the conditions modeled, the impacts of varying RHL, and Kth on TWC status were significant at intermediate times. When considering the entire time period being modeled, the impacts of the uncertainty in these two parameters is less obvious since most realizations reached TWC status for the modeled period. These variations at intermediate time periods, however, should not be ignored as the probabilities calculated for initiating a crack or reaching TWC status are not zero. On the other hand, the range of deposition rates considered in this study highlight the impact and importance of reducing uncertainty in measured deposition rates. The uncertainty considered for DD resulted in the largest variations between DD values for the QoIs in this study. This study highlighted how it is one of the parameters with the most significant influence on predictive modeling of CISCC. Salt deposition rates are site-specific and adequate values needed when modeling a specific site would have to be measured. Overall, this study provides insight into the sensitivities of probabilistically modeling SCC for parameters with measurement uncertainty.

ix Figure E-1. CDF comparisons for varying RH L (DD = 1.0 g/m 2/yr, K th = 10 MPA-m1/2) with the ASME and SNL CGR models.

Figure E-2. CDF comparisons for varying DD (RH L= f(T), RH = -7%, K th = 10 MPA-m1/2) with the ASME and SNL CGR models.

Figure E-3. CDF comparisons for varying K th (DD = 1.0 g/m 2/yr, RH L= f(T), RH = -7%) with the ASME and SNL CGR models.

x ABSTRACT This report summarizes the collaboration between Sandia National Laboratories (SNL) and the Nuclear Regulatory Commission (NRC) to improve the state of knowledge on chloride-induced stress corrosion cracking (CISCC). The foundation of this work relied on using SNLs CISCC computer code to assess the current state of knowledge for probabilistically modeling CISCC on stainless-steel canisters. This work is presented as three tasks. The first task is exploring and independently comparing crack growth rate (CGR) models typically used in CISCC modeling by the research community. The second task is implementing two of the more conservative CGR models from the first task into SNLs full CISCC code to understand the impact of the different CGR models on a full probabilistic analysis while studying uncertainty from three key input parameters. The combined work of the first two tasks showed that properly measuring salt deposition rates is impactful to reducing uncertainty when modeling CISCC. The work in Task 2 also showed how probabilistic CGR models can be more appropriate at capturing aleatory uncertainty when modeling stress corrosion cracking (SCC). Lastly, appropriate and realistic input parameters relevant for CISCC modeling were documented in the last task as a product of the simulations considered in the first two tasks.

xi ACKNOWLEDGMENTS The authors would like to thank Nathan Porter for his technical review of this report.

The authors would also like to thank Ryan Katona, Rebecca Schaller, and Charles Bryan for their consultations and expertise that made this work possible. Many other Sandians have contributed to advance the state of SNLs CISCC code over time, either through direct modifications to the code or through experimental work that has supported these modifications. The authors would like to thank all of these past contributors.

xii CONTENTS Abstract.....................................................................................................................................ix

Acknowledgments....................................................................................................................x

Acronyms and Terms.............................................................................................................xv

1. Introduction.........................................................................................................................1

2. Overview of CISCC mechanism and SNLs CISCC Model...........................................3

3. Task 1: Crack Growth Rate Model Comparisons..........................................................7 3.1. SNL Crack Growth Rate Model Summary.............................................................7 3.2. EPRI Crack Growth Rate Model Summary............................................................9 3.3. ASME Code Case N860 Crack Growth Rate Model Summary........................11 3.4. Crack Growth Rate Model Comparisons.............................................................11

4. Task 2: Sensitivity Studies..............................................................................................19 4.1. Parameter Values....................................................................................................19 4.1.1. Chloride Deposition Rate, DD....................................................................21 4.1.2. Limiting Relative Humidity, RHL................................................................23 4.1.3. Threshold Stress Intensity Factor, Kth......................................................25 4.2. Sensitivity Study Results........................................................................................25 4.2.1. Sensitivity Results with SNL CGR Model................................................27 4.2.2. Sensitivity Results with ASME Code Case N-860 Model......................31

5. Task 3: Inputs Development and Documentation......................................................33 5.1. Note on Canister Surface Temperatures.............................................................35 5.2. Note on Canister Weld Residual Stresses..........................................................37

6. Summary............................................................................................................................41

7. References........................................................................................................................43

Appendix A. Sensitivity Study Results for Site B using SNL and ASME CGR Models 46

Appendix B. Sensitivity Study Results for Site C using SNL and ASME CGR Models 47

xiii Appendix C. Sensitivity Study Results for Site D using SNL and ASME CGR Models 48

LIST OF FIGURES

Figure 1-1. Typical dry cask storage system: Left is a vertical system, right is a horizontal system [2].......................................................................................................13 Figure 2-1. Evolution of corrosion with relevant sub-models in SNLs CISCC code..15 Figure 3-1. Average yearly temperatures at the ISFSI sites as a function of site latitude [9].........................................................................................................................24 Figure 3-2. Weld nomenclature used for SNLSCC model. Left if for vertical canister, right is for horizontal canister........................................................................25 Figure 3-3. Horizontal canister showing the location of example weld [1.0, 0.3].......26 Figure 3-4. SNL CGR model TWC CDFs comparing different sites..............................27 Figure 3-5. EPRI CGR model TWC CDFs comparing different sites.............................27 Figure 3-6. Comparison of SNL and ASME CGR model TWC CDFs comparing different sites....................................................................................................................28 Figure 3-7. Comparison of SNL and ASME CGR model crack depth evolution for a single set of crack growth parameters, varying Kth....................................................28 Figure 3-8. Activation energy, Q, calculated from parameter values in Table 3-1 and Equation 3-2. Distribution for 400 realizations...................................................29

xiv Figure 4-1. SNL SCC horizontal canister deposition scaling factor with respect to normalized circumferential location and dust samples at Sites A and B...............34 Figure 4-2. Predicted deliquescence behavior of salts that precipitate when seawater is evaporated for temperatures between 20°C and 80°C.........................35 Figure 4-3. Site-A CDF comparisons for varying RHL (DD = 1.0 g/m2/yr, Kth = 10 MPA-m1/2)..........................................................................................................................40 Figure 4-4. Site-A CDF comparisons for varying DD (RHL= f(T), RH = -7%, Kth =

10 MPA-m1/2)....................................................................................................................41 Figure 4-5. Site-A CDF comparisons for varying Kth (DD = 1.0 g/m2/yr, RHL= f(T),

RH = -7%)........................................................................................................................42 Figure 4-6. CDF comparisons for varying RHL (DD = 1.0 g/m2/yr, Kth = 10 MPA-m1/2) with the ASME and SNL CGR models.................................................................44 Figure 4-7. CDF comparisons for varying DD (RHL= f(T), RH = -7%, Kth = 10 MPA-m1/2) with the ASME and SNL CGR models......................................................44 Figure 4-8. CDF comparisons for varying Kth (DD = 1.0 g/m2/yr, RHL= f(T), RH

-7%) with the ASME and SNL CGR models.............................................................44 Figure 5-1. Node configuration for PNNL thermal model [11, 12]................................47 Figure 5-2. Canister surface temperatures over time as calculated by the PNNL thermal model [11, 12]....................................................................................................47 Figure 5-3. ICHD, DHD, and SCC model-fit residual stress data for weld centerline and HAZ locations at normalized depths..................................................50 Figure 5-4. ICHD, DHD, and SCC model-fit residual stress data for weld centerline and HAZ locations at shallow normalized depths...................................51 Figure 7-1. Site-B CDF comparisons for varying RHL (DD = 1.0 g/m2/yr, Kth = 10 MPA-m1/2)..........................................................................................................................58 Figure 7-2. Site-B CDF comparisons for varying DD (RHL= f(T), RH = -7%, Kth

10 MPA-m1/2)....................................................................................................................58 Figure 7-3. Site-B CDF comparisons for varying Kth (DD = 1.0 g/m2/yr, RHL= f(T),

RH = -7%)........................................................................................................................58 Figure 7-4. Site-C CDF comparisons for varying RHL (DD = 1.0 g/m2/yr, Kth = 10 MPA-m1/2)..........................................................................................................................59

xv Figure 7-5. Site-C CDF comparisons for varying DD (RHL= f(T), RH = -7%, Kth =

10 MPA-m1/2)....................................................................................................................59 Figure 7-6. Site-C CDF comparisons for varying Kth (DD = 1.0 g/m2/yr, RHL= f(T),

RH = -7%)........................................................................................................................59 Figure 7-7. Site-D CDF comparisons for varying RHL (DD = 1.0 g/m2/yr, Kth = 10 MPA-m1/2)..........................................................................................................................60 Figure 7-8. Site-D CDF comparisons for varying DD (RHL= f(T), RH = -7%, Kth =

10 MPA-m1/2)....................................................................................................................60 Figure 7-9. Site-D CDF comparisons for varying Kth (DD = 1.0 g/m2/yr, RHL= f(T),

RH = -7%)........................................................................................................................60

LIST OF TABLES Table 3-1. SNL CGR parameterization from 2023 model [7].........................................20 Table 3-2. EPRI CGR parameterization..............................................................................22 Table 5-1. Relevant Geometric and Flaw Parameters for xLPR....................................45

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xvii ACRONYMS AND TERMS

Acronym/Term Definition ASME American Society of Mechanical Engineers ADAMS Agencywide Documents Access and Management System CDF cumulative distribution function CGR crack growth rate CISCC chloride-induced stress corrosion cracking CoC certificate of compliance DCSS dry cask storage system DHD deep-hole drilling DRH deliquescence relative humidity EPRI Electric Power Research Institute HAZ heat affected zone ICHD incremental center-hole drilling ISFSI independent spent fuel storage installation LHS Latin hypercube sampling NRC Nuclear Regulatory Commission PNNL Pacific Northwest National Laboratory RH relative humidity SCC stress corrosion cracking SNF spent nuclear fuel SNL Sandia National Laboratories SS stainless-steel TWC through-wall crack xLPR Extremely Low Probability of Rupture (probabilistic fracture mechanics code)

xviii

1. INTRODUCTION Over 90 % of Dry Cask Storage Systems (DCSSs) in the United States utilize welded, austenitic, stainless-steel (SS), canister-based designs deployed in either a vertical or horizontal configuration (see Figure 1-1) [1, 2]. In vertical systems, the welded canister sits upright within a steel-lined concrete overpack. The canister is passively cooled through convection by air entering through inlets at the bottom of the overpack while exiting through vents near the top. In horizontal systems, the welded canister rests on its side upon rails within a reinforced concrete vault. Air enters the overpack through a vent in the base, flows up and around the canister, and exits through vents on the roof.

Bundle of used fuel assemblies Canister Storage cask

Figure 1-1. Typical dry cask storage system: Left is a vertical system, right is a horizontal system

[2].

Most welded canisters are fabricated from formed austenitic stainless-steel (SS),

primarily 304 and 316 SS grades. These SS grades provide confinement of the spent nuclear fuel (SNF), and the canister serves as the primary barrier to ensure that radioactive material is not released to the exterior.

During operation of DCSSs, the cooling convective airflow entrains dust particulates with minerals and salts (and other deposits such as pollen, concrete dust, insects, etc) from the exterior, which can deposit and accumulate on the canister external surface over time. Particularly at near-marine environments, deposited salts may be chloride-bearing and can establish corrosive environments. These corrosive

1 environments, in the presence of sufficient tensile stresses on the SS canister material (particularly at weld locations), may lead to chloride-induced stress corrosion cracking (CISCC). Welded austenitic stainless steels (SS) are known to be susceptible to localized corrosion and CISCC in chloride environments [3].

Therefore, the potential occurance of localized corrosion and CISCC during extended periods of dry storage has led to investigative efforts to ensure that adequate measures are taken so that its progression is limited and does not compromise the safety of DCSSs [4].

This report summarizes the collaboration between Sandia National Laboratories (SNL) and the U.S. Nuclear Regulatory Commission (NRC) staff to improve the state of knowledge on CISCC. This report provides information on technical issues related to risk-informing CISCC including a comparison of crack growth rate models and an evaluation of the effects of key parameter uncertainties on CISCC model behavior.

However, this report does not suggest or endorse one model over another, and the probabilistic model results are intended only to show trends in model behavior.

The foundation of this work relied on using SNLs CISCC computer code to assess the current state of knowledge for modeling CISCC on stainless-steel canisters.

SNLs CISCC computer code was designed to probabilistically model canister penetration by stress corrosion cracking (SCC), and it has been continuously updated since 2014 [5]. The code captures all phases of SCC, from chloride deposition up to corrosion initiation and crack growth that can lead to through-wall penetration. Existing physics-based sub-models and experimental studies have both influenced improvements to the modeling approach. To this day, the codes primary objective has been to guide CISCC research by: (1) exploring and identifying important modeling assumptions, (2) identifying experimental data needs for improved modeling, and (3) identifying needed improvements to model developments [4, 6, 7, 8, 9]. An overview of SNLs CISCC code is presented in Section 2 as a preface to the main tasks for the work presented in this report.

For the work described in this report, the SNL CISCC model framework was leveraged to address the three main tasks. These tasks focused on:

2

1. Independently comparing different crack growth rate (CGR) models used by the CISCC research community.

2. With the results from (1), implementing the most conservative CGR models into SNLs CISCC computer code and performing a sensitivity study of three key input parameters with the largest uncertainty (based on values from literature reviews):

a. Limiting relative humidity for corrosion initiation (RHL)

b. Chloride deposition rate (DD)

c. Threshold crack tip stress intensity factor (Kth)

where the quantities of interest used to characterize uncertainty in the sensitivity study were:

a. Time to pit formation

b. Time to crack initiation

c. Time for a through-wall crack to form

3. Leveraging (1) and (2) for the identification of realistic parameter ranges for key variables that can be helpful to perform probabilistic fracture mechanics of canister integrity. These variables included:

a. Canister geometries

b. Canister operating conditions

c. Canister weld residual stresses

d. Canister materials

A detailed discussion of each of the tasks is presented in Sections 3 through 5, respectively. Results for each of the three tasks are presented and discussed in their respective sections.

3

2. OVERVIEW OF CISCC MECHANISM AND SNLS CISCC MODEL As mentioned in Section 0, welded canisters for SNF experience a continuously evolving environment over their licensed storage period. CISCC is a potential failure mechanism over the life of a canisters storage period. The heat-driven convective air flowing through the overpacks can bring in atmospheric aerosols (salt, dust, pollen, etc., depending on storage location for overpack) that are deposited on the canister surface. When welded canisters are initially stored, heat production from the SNF is dependent on the SNFs initial heat load and cooling time lapsed while submerged in a pool. This initial heat load and cooling time affects the heat load when the SNF canisters are placed in their overpack, which in turn influences the resulting relative humidity (RH) on the local surface environment.

Canisters with higher heat loads have a lower starting RH. Over time, heat production decays and the canisters cool. These conditions can allow the local RH to increase, allowing deposited salts to absorb moisture from the atmosphere and form a corrosive brine, a process known as deliquescence. For stainless-steel welded canisters used to store spent nuclear fuel, deliquescence can lead to the formation and growth of small pits. Pits forming via deliquescence on canister welded regions can be of particular concern due to interaction with residual stresses in the welded canister material. With sufficient weld residual stresses present while pits form and grow, cracks can initiate from these evolving pits. The cracks can grow and propagate through the canister wall, potentially compromising the confinement boundary if they fully penetrate the container. These conditions can eventually lead to release of radioactive material if the cracks become through-wall.

To better evaluate the potential occurrence and timing of canister stress corrosion cracking, SNL has developed a probabilistic model for CISCC. The different phases of CISCC and corresponding sub-models from SNLs CISCC code are captured by the schematic shown in Figure 2-1.

4 Figure 2-1. Evolution of corrosion with relevant sub-models in SNLs CISCC code.

The SNL CISCC code aims to comprehensively capture all the relevant mechanisms experienced by a canister as cracks develop and grow. The arrows in Figure 2-1 highlight major phases or transitions of CISCC. The boxes below each major phase highlight the various sub-models in SNLs CISCC code that contribute to capturing the physical mechanisms in each phase. These sub-models have been described with detail in prior work [4, 10], but the function of each is summarized here for context as follows:

• Canister thermal model o The canister thermal model calculates the canister temperature maps based on thermal models developed at Pacific Northwest National Laboratory (PNNL) [11, 12]. The thermal model calculates the canister surface temperature by determining the nominal canister surface temperature given an assumed initial heat load and reference ambient temperature. Different ambient temperatures are considered and implemented as a delta to the nominal canister temperature.

• Weather model 5

o The weather model generates site-specific ambient weather conditions for a given site, informed by site-specific data. The model is designed to capture seasonal and diurnal variations in ambient temperature and dew point and is calibrated to real weather data at a given independent spent fuel storage installation (ISFSI) site. The weather model data includes temperature and dewpoint for 64 relevant ISFSI sites that store welded canisters [13].

• Salt deposition model o Based on experimentally collected field data from SNL and the Electric Power Research Institute (EPRI) [14], the salt deposition model determines the distribution of salt load on a canister surface. As a result of this prior work, salt deposition is modeled with a dependence on circumferential location, but it is currently maintained with no variations in the longitudinal direction for the horizontal canisters considered in this work.

• Maximum pit size model o Pit sizes are critical in determining crack initiation when using a model based on the Kondo criterion [15]. A maximum pit size model is implemented based on the work of Chen et al [16, 17, 18]. Under given environmental and electrochemical conditions (relative humidity, temperature, salt load, brine properties, etc.), this model determines the maximum pit size that can form on a weld location. When a pit is large enough, the maximum pit size model influences when a crack initiates.

• Weld residual stress model o Stresses resulting from weld and heat affected zones (HAZs) near the weld region can influence how fast a crack initiates and grows.

Through experimental field tests, SNL developed a model that captures stress variations as a function of wall depth at a weld location [19].

These stresses are then used to determine a crack tip stress intensity factor. This crack tip stress intensity factor can influence crack

6 initiation as well as crack growth, depending on the type of crack growth model used.

• Crack growth model o Once a crack initiates, the crack growth models function is to determine how fast a crack grows over time, depending on the environmental factors that influence the chosen crack growth model.

Direct and indirect relationships exist between the various sub-models that compose SNLs CISCC code. How the aforementioned sub-models directly influence the different phases of CISCC can be summarized as follows:

• Incubation o Incubation is the interval of time occurring between two key points:

(Point 1) when emplacement of the canister occurs and (Point 2) when a given canister surface location cools to the point where local relative humidity is sufficiently high for salts to deliquesce and consequently form a corrosive brine. Put simply, incubation is the phase between canister placement and deliquescence. During this time, the canister thermal sub-model and weather sub-model are used to calculate local RH. A salt deposition model is also utilized during this period (and throughout a simulation) to calculate salt loads on the canister.

• Pit Initiation o Pit initiation is dependent on an RH criterion. If the RH at a weld location exceeds a specified threshold value, pits form and nucleate instantaneously. The RH at a weld location depends on the ambient temperature, ambient absolute humidity, and the canister temperature.

Therefore, pit initiation depends on the thermal and weather models.

• Pit Growth o Once pits form, they are assumed to be hemispherical. Pits can grow, changing the local stress field and potentially serving as nucleation sites for stress-driven cracks. The maximum pit size model based on the work of Chen et al [16, 17, 18] is used in this work to determine how pits grow. The Chen formulation for the pit size is dependent on 7

the local electrochemical kinetics, which are a function of brine properties. The brine properties are a function of the salt load and absorbed moisture, thereby making pit growth dependent on the brine composition, salt deposition models, and weather models.

• Crack Initiation o Stress concentrations intensify because of pit growth. Once stress concentrations reach a prescribed level, cracks can nucleate. In the SNL code, a modified Kondo criterion is used to define when a pit transitions to a crack [15]. A crack tip stress intensity factor, K, is calculated using the weld residual stresses (measured and discussed in prior work [10, 20]) along with characteristics from an assumed crack nucleating from a pit, where the analyzed pit depth used as a characteristic length. The calculated K is then compared to a threshold crack tip stress intensity factor, Kth, to determine whether the calculated K has exceeded the threshold. When the threshold is exceeded, the analyzed pit transitions to a crack. Crack initiation is thus directly dependent on the maximum pit size model, weld residual stresses, and chosen Kth. Indirectly, crack initiation depends on all sub-models that influence pit size.

• Crack Growth o Multiple CGR models exist to estimate crack growth in SNF canisters.

The SNL SCC code utilizes an Arrhenius-based CGR model that is a function of the local temperature and crack tip stress intensity factor

[10, 3, 21, 22, 6, 23]. Crack growth is therefore dependent on the implemented CGR model, which is dependent on factors that are influenced by the canister thermal model and the weld residual stress model.

• Crack Penetration o Once a crack initiates, cracks continue to grow according to the calculated CGR. During the modeled timeframe, if a crack reaches the length of the canister wall thickness, the crack is considered a through-wall crack.

8 The tasks for the work discussed in this report tested parts of the CISCC code. The focus of Task 1 was on the CGR model, and Task 2 focused on analyzing the sensitivity of outputs from the SNL CISCC code to various input parameters with large uncertainties using the CGRs identified as conservative in Task 1. Subsequent sections of this report present a deeper discussion on the CGR models considered along with the associated relevant parameters.

9

3. TASK 1: CRACK GROWTH RATE MODEL COMPARISONS SNLs probabilistic SCC code models crack growth rates based on an Arrhenius relationship with temperature. The current implementation of SNLs crack growth model is compared in this section to other models found in the literature for comparable conditions; a crack growth rate model based on a prior implementation from EPRI [24], and a crack growth rate model based on the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code Case N860 [25].

3.1. SNL Crack Growth Rate Model Summary The SNL crack growth model is described in detail in report [9]. The core of the relevant content from the report is presented here to make model comparisons.

The SNL SCC code initiates cracks from pits that have reached a sufficient size. A sufficiently sized pit is one such that the apparent crack tip stress intensity factor of a crack (with the same equivalent depth as the weld pit size it can nucleate from) exceeds a user specified value of the threshold stress intensity factor, Kth.

K is calculated by the following equation:

= (3-1)

where is the tensile weld residual stress, Y is a shape factor (commonly set equal to 1.0 for surfaces where radius of curvature is much larger than a crack), and is the depth of a crack, which is assumed to be equal to the pit radius during the pit growth phase of a modeled weld location, as calculated using the maximum pit size model [26]. A crack nucleates from a pit when K > Kth.

Once a crack initiates at a specific weld location, the maximum pit size model calculations cease as the CGR model is invoked for the crack. The current SNL CGR model is defined by Equations (3-2) and (3-3), where (3-2) is an activation energy obtained form for a base case at 80°C.

= ln 80°C 1 1 (50) (3-2) 353.15 1 1

= = exp ( ) (3-3)

10 where:

is the CGR (m/s), also denoted as 80°C is the reference CGR (m/s) at 80°C,

is the correlated crack growth amplitude,

is the correlated crack growth exponent,

is the activation energy term (J/mol) for crack growth,

is the universal gas constant (8.314 J mol-1 K-1),

is the reference temperature (K) at which = 288.75 K is used in SNL CGR model),

is the canister surface temperature (K),

is the crack tip stress intensity factor (MPa-m1/2), and

is the threshold crack tip stress intensity factor (MPa-m1/2).

Parameters 80°C are normally distributed parameters that are sampled.

After sampling, a correlation is imposed between andGRparameters sdin ndlog normaldistributionswiththeirparamesrQ TheactationenergyQiscafromthecorrelated and 80°C (Equation (3-2)).

Table 3-1. SNL CGR parameterization from 2023 model [7].

Parameter 2023 Model

e

NormQQ%Qe

Q%

80°C Log-Norm.(-20.50, 1.23)

11 3.2. EPRI Crack Growth Rate Model Summary The EPRI CGR model is described in [24] and summarized here for context. It is also based on an Arrhenius relationship with temperature, but fundamental differences exist when compared to the current SNL implementation. The EPRI model assumes that the CGR decreases after the initial ~2 to 3 mm of crack growth to a much smaller growth rate. The model also assumes that crack growth is also only active when the RH is greater than a prescribed critical relative humidity, RHc. The values for the shallow CGR, the transition depth of the two-stage CGR, and the ratio of the shallow CGR to deep CGR are sampled from distributions. The EPRI CGR model can be characterized by the relationship and conditions in Equation (3-4).

Q 1 1 for RHRHc and K>0 (3-4

= = exp 0 for RH<RH or K0 )

c

where:

is the CGR (m/s), also denoted as,

is the depth-dependent crack growth amplitude,

is the activation energy term (40.0E+3 J/mol) for crack growth, is the universal gas constant (8.314 J mol-1 K-1),

is the reference temperature (K) (= 353.15 K is used in EPRI CGR model),

is the canister surface temperature (K),

is the crack tip stress intensity factor (MPa-m1/2),

RH is the relative humidity, and

RHc is the critical relative humidity of the deposited chloride salts.

Depth-dependent CGR is implemented by setting parameter as dependent on the crack depth. The shallow CGR, the ratio of the shallow-todeep CGR, and the transition depth for the CGR model parameters are used to determine the ultimate value of. The corresponding EPRI CGR parameters are listed in Table 3-2. Note

12 that is not a growth rate but rather the depth at which the growth rate transitions from to.

The formulation to determine is shown by Equation (3-5) with = 7%.

()= 1 33.677.974x 103( 273.15)1.090x 103( 273.15)2 (3-5) 100

Table 3-2. EPRI CGR parameterization.

Parameter 2023 Model

[mm/yr] Log-Norm.(2.39,1.66),

truncated to [ln(0.01), ln(500)]

Log-Norm.(-3.54,1.66),

/ truncated to [ln(0.0003),

ln(1.0)]

[mm] Norm.(2.235,0.561), truncated to [0.1,12.0]

13 3.3. ASME Code Case N860 Crack Growth Rate Model Summary The CISCC CGR model in ASME Code Case N860 [25] (referred to as the ASME model hereafter) has a simpler implementation when compared to the SNL and EPRI implementations. The ASME CGR model is independent of stress intensity factor and crack depth, and it is defined by Equation (3-6).

= = exp 1 1 (3-6)

where:

is the CGR (mm/yr), also denoted as,

is the crack growth amplitude (= 1.25 mm/yr),

is the activation energy term (J/mol) for crack growth (80.0E+3 J/mol),

is the universal gas constant (8.314 J mol-1 K-1),

is the reference temperature (K) at which was derived (=313.15 K) and

is the canister surface temperature (K).

3.4. Crack Growth Rate Model Comparisons

A standalone python script was developed to compare the SNL, EPRI, and ASME CGR models. In the standalone python script, the weather and canister thermal models from the SNL SCC code were used to generate local temperature and RH for a set of weld locations on a horizontal canister for different sites. To maintain anonymity, these sites are referred to as Sites A, B, C, and D. These comparisons from the standalone scripts are meant to only highlight differences in the three different CGR models; they are not meant to comment on the accuracy of a given model or how a given CGR model would perform in a model that also predicts pit growth. Assumptions were made for these standalone CGR model comparisons to ensure that cracks initiate at the same time across all sites.

Sites A, C, and D were chosen because they are good representations of the minimum, average, and maximum, respectively, of the average yearly temperature and dewpoint across the 64 ISFSI sites used to inform the weather model. Site B 14 was included as an outlier; it is a site in a desert location with low humidity. Figure 3-1 shows the average yearly temperature and dewpoint at the different ISFSI sites as a function of the site latitude, with sites A, B, C, and D labeled. The dewpoint is a relevant threshold to keep in mind as it is the temperature to which the local air needs to be cooled to achieve saturated conditions (RH=100%). Furthermore, a sites ambient weather will affect the canister surface temperatures, which is an input parameter to the SNL, EPRI, and ASME CGR models.

35 Site B Site D Avg. Yearly Dewpoint 30 Avg Yearly Temperature

25

20 Site C 15 10 Site B Site A

5

0 25 30 35 40 45 50 Latitude, degrees

Figure 3-1. Average yearly temperatures at the ISFSI sites as a function of site latitude [9].

To compare the CGR models, an example weld location was chosen. In the SNL

CISCC code, there are 24 weld locations considered per simulation. Welds on the

horizontal canister are predefined along two normalized axial locations (axial=0.0

and 1.0 represent ends of canister) and by the parameters weld_1_location and weld_2_location, which define the weld 1 and weld 2 normalized circumferential coordinates (see Figure 3-2). Weld location [1.0, 0.3] ([axial, circumferential]

coordinates) was chosen as an example weld location at which to run the standalone python CGR models since it was the first weld to initiate a crack in a previously analyzed example SCC CISCC model evaluation. The weld configuration just described for a horizontal canister is shown in Figure 3-2 and Figure 3-3. The

15 analyzed weld location [1.0, 0.3] in this work was for a horizontal canister and is highlighted in red in Figure 3-3 for visualization purposes.

Circum. Circum.

weld Weld 1 weld

Weld 2

Basal weld

Figure 3-2. Weld nomenclature used for SNL SCC model. Left if for vertical canister, right is for horizontal canister.

As the three compared CGR models have different model parameters, direct

comparisons are not trivial to execute. However, differences between the general

model behavior can be discussed. For all three model comparisons, a crack initiation time and size were assumed. The initial crack size was set such that >

= 10 MPa m1/2.

Based on statistical convergence, 400 samples of the model parameters were run for each site using the SNL and the EPRI CGR models. The same seed for randomization was used to ensure that samples of the CGR parameters for the SNL and EPRI models were the same between sites. Additionally, the same weather seed (per site) was used, i.e., all models were evaluated using the same sampled weather conditions at Site A, which vary day-today and year-toyear according to daily and

16 seasonal fluctuations in conditions. Consequently, the differences observed between Sites A, B, C, and D for a given model would be specifically a result of different ambient conditions at the sites.

Figure 3-3. Horizontal canister showing the location of example weld [1.0, 0.3].

As implemented, the EPRI CGR model has some major differences in behavior that

differ from the SNL CGR model. In the EPRI model, cracks can only grow when RHRHc whereas in the SNL CGR model, a minimum relative humidity is not a requirement for crack growth (though it is a requirement for pit formation and growth prior to crack initiation). This difference leads to some discrepancies between model results, where the through-wall crack (TWC) time was the metric used for model comparisons. For comparisons presented here, TWC times are normalized by the maximum modeled time (292 years, but results are stated as normalized times to avoid predictive implications from model) so that results are treated as trends rather than absolute predictions. Results are presented in the form of empirical cumulative distribution functions (CDFs) that are generated from the 400 realizations executed per CGR model.

Figure 3-4 shows results for the example standalone SNL CGR model evaluations.

For the period being observed in the simulation, the chosen weld location, and the set of parameter results, the CDF results for TWCs demonstrate the most through-

17 wall cracks at Sites B and D followed by Sites C and D. This matches what is expected of the standalone SNL CGR model based on the description of the sites above; CGRs increase as local temperature increases, (see Figure 3-1 above to contextualize the relevant site average temperatures). That is, assuming identical crack initiation times across the sites and the same set of sampled parameters, the SNL CGR model will predict the highest CGRs for the two hottest sites (Sites B and D). This result leads to the highest percentage of model evaluations displaying a TWC for these two sites. Site A, which is the coldest site, is therefore expected to have the smallest percentage of instances with TWCs. Figure 3-5 shows the EPRI standalone CGR results. In contrast to the SNL CGR model, the figure shows that Site B has the lowest percentage of TWCs. This result matches the expected behavior for the EPRI CGR model; Site B is a hot, dry site, and the EPRI CGR model will only predict crack growth when RH RHc, which results in a suppression of crack growth in Site B as compared to Site D (a hot and humid site).

The EPRI model also shows a smaller percentage of instances of TWCs compared to the SNL CGR model, resulting in the SNL CGR model being more conservative than the EPRI model under the assumed conditions and prerequisites (that a crack has already initiated). This is due to the EPRI model generally having a lower CGR than that predicted by the SNL model, resulting in fewer TWCs by the end of the simulated run time.

18 Figure 3-4. SNL CGR model TWC CDFs Figure 3-5. EPRI CGR model TWC CDFs comparing different sites. comparing different sites.

As shown in Equation 3-6, the ASME CGR model only varies with temperature.

Unlike the SNL and EPRI CGR models, there are no sampled parameters that affect the ASME CGR model (thereby making it deterministic instead of probabilistic). This implementation means that, for the standalone ASME CGR model, only one model evaluation can be run per site. The resulting TWC CDF is compared to the SNL CGR model in Figure 3-6. The abrupt vertical lines associated with the ASME CGR curves are because the ASME CDFs only have one sample associated with them. The CDFs thus show binary behavior for the realization results; either 0 (for no TWC) or 1 (for TWC).

Due to the different implementations between the SNL and ASME CGR models, the crack tip stress intensity factor was used in the model comparisons. All models depend on the crack tip stress intensity factor for initial crack depth. However, the SNL CGR model also has a dependence on the crack tip stress intensity factor during crack growth in addition to its dependence on crack growth amplitude (which is a sampled parameter). The ASME CGR model does not have these direct dependencies. Figure 3-7 shows the effect of varying the Kth values on crack growth in each model. In the SNL CGR model, Kth determines the minimum pit size needed

19 to initiate crack growth, and it is also a parameter In Equation 3-3. In the ASME CGR model, Kth only influences the minimum pit size needed to nucleate a crack as implemented in the standalone python model. In Figure 3-7, using a different Kth value in the ASME model results in the same CGR (same slope), despite the cracks starting at different sizes due to different Kth values. In the SNL CGR model, the Kth value affects the CGR, resulting in different crack evolutions (different slopes) when comparing example simulations that employ either = 5 MPa m1/2 or = 15 MPa m1/2 (where lower Kth values produce faster CGRs). The activation energy of

the SNL implementation is also calculated from sampled parameters (see Figure 3-8), as compared to the ASME version which has a fixed value of 80 kJ/mol. These described variations, including the sampled activation energy, ultimately lead to an ASME implementation that is generally more conservative than the SNL CGR implementation when looking at longer time frames as captured by Figure 3-6.

Figure 3-6. Comparison of SNL and ASME CGR model TWC CDFs comparing different sites.

20 Figure 3-7. Comparison of SNL and ASME CGR model crack depth evolution for a single set of crack growth parameters, varying K th.

Figure 3-8. Activation energy, Q, calculated from parameter values in Table 3-1 and Equation 3-2.

Distribution for 400 realizations.

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22

4. TASK 2: SENSITIVITY STUDIES After performing comparisons on the different CGR models, the SNL and ASME models were chosen as base CGR models due to their potential conservatism. As base models, the SNL and ASME CGR models were both considered in a series of sensitivity studies as part of the full SNL CISCC code ecosystem (described in Section 2). The sensitivity studies were executed to identify how uncertainty in critical input parameters contributes to variation in the model results. The quantities of interest of the sensitivity study are: probability of pitting, probability of cracking, and probability of through-wall crack occurrence.

4.1. Parameter Values

Three critical input parameters in SNLs SCC code were selected for the sensitivity analysis to understand their effect on the overall code outputs: DD, RHL, and Kth.

These parameters were selected by technical analysis (and subject matter expert advice) due to their prominent impact on overall results and variance observed from literature reviews: DD, the chloride deposition rate, affects the brine chemistry, which in turn influences the evolution of pits that can nucleate a crack; RHL affects the point at which pits can initiate on a canister surface; and Kth influences the acceleration and deceleration of CGRs. For the sensitivity study, each of these parameters was assigned three possible values that capture uncertainty in values obtained from literature reviews.

Some of the sub-models in the SNL SCC code also have other input parameters with uncertain values due to natural variations in nature. The uncertainty in these parameters is captured by a separate sampling loop that is nested within each of the critical variable realizations. This secondary set of parameters results in simulations being executed in a dual loop structure: an outer epistemic loop that accounts for uncertainties due to limited data, and an inner aleatoric loop that accounts for uncertainties due to natural variations. Specifically, the outer loop handles the critical parameters, while the inner loop handles the secondary parameters.

23 With the three critical parameters (DD, RHL, and Kth), the outer loop consists of three defined levels,, {1,2,3}. Each critical parameter realization is defined by a triplet (DD(i), RHL(j), and Kth(k)) for,, {1,2,3}. This is also known as a full factorial experiment. Because there are three levels for each of the three critical parameters, there are 27 such realizations.

A total of seven secondary parameters are considered in this analysis. Latin hypercube sampling (LHS) with SNLs Dakota software [9] was used to sample values for the secondary parameters from their defined uncertainty distributions.

Each iteration of the inner loop handled a set of these sampled secondary parameters, where each set created for the inner loop consisted of a seven element tuple ( 1(), 2(), 3(), 4(), 5(), 6(), 7()). Each element in the tuple was a sampled secondary parameter. A total of 400 sets were generated for the inner loop, and the same 400 sets were used in each critical parameter realization. This means that any variations in results between critical parameter realizations can be attributed to the effects of the critical parameter levels (and interactions between the critical parameters and the secondary parameters) and not to sampling error.

The secondary parameters are input parameters to some of the sub-models in the SNL SCC code. Discussing details on these secondary parameters is beyond the scope of this report as their uncertainty is not expected to have significant impact on the model outputs. The reader is referred to prior documentation on the SNL model for further details [7]. For the scope of this report, details on the critical parameters and their value selections are provided in Subsections 4.1.1 through 4.1.3 below.

24 4.1.1. Chloride Deposition Rate, DD Experimental sampling has observed chloride deposition to be non-uniform around SNF canisters [27, 28, 29, 30, 14]. To estimate chloride deposition rates for the model presented here, the range of values used in this analysis is informed by prior work. Data was compiled for deposition rates collected from canister sampling campaigns that occurred at ~10 years after initial loading from eight independent spent fuel storage installations [27, 28, 29, 30, 14]. However, variability exists in the collected dataset for multiple reasons: Sampling methods, canister locations, canister orientations, and canister ages (and therefore heat load) all varied from one study to another. Weather conditions and proximity to a source of seawater were also variable for data collected from different sites. Due to these variations, the scope of sources was narrowed to manage the relevant data. Data from three sites were used to inform the range of values chosen for DD as these datasets provided the most comprehensive information (canister surface sampling locations) to estimate deposition rates as a function of canister surface location. As in Section 3.4, these ISFSI locations are kept anonymous and are referred to as Sites A, B, and C, where Sites A and B are inland sites and Site C is a near-marine site (note, the nomenclature of Sites A/B/C used in the experiments to estimate deposition rate was used in in prior documentation and kept here for consistency. However, these sites are not the same as Sites A/B/C/D used in the rest of this report).

The nominal surface area sampled was the same for each site, but sampling was done robotically, leading to uncertainty associated with the measurement [28, 29, 30]. Salt/chloride deposition rates (g/m2/yr) were estimated by summing up the measured mass of cation and anion species, then dividing that mass by the nominal area sampled (19.35 cm2), which was further divided by the age of the canister at the time it was sampled (in years). The uncertainty in the measured amount of salt (or chloride) present is tied to both the analytical uncertainty of the ion chromatography measurement (generally <5%, depending on how light the load was), and to the collection efficiency of the robotic sampling methodology, which is poorly known. Changes made to the collection robot between sampling Site A and Site B may have also increased the sampling efficiency. This improvement led to

25 uncertainty in whether differences between Sites A and B are actually due to geographic location. For Site C, the sampled areas and sampling efficiency is less precisely known. Relevant dates for canisters at these sites are well-known; the date fuel was added to canisters, emplacement dates, and sampling dates.

However, it is unknown if deposition was uniform during the period between emplacement and dust sampling, and therefore the best that can be done with this information is to calculate deposition rates only as averages. Lastly, deposition is expected to vary around a canister. Sample radial position is known for the canisters studied at all three sites considered, but axial location is not well documented. Due to this latter point, variations of DD in the axial direction are not considered for the studies of this report.

The deposition model used in the study presented here is introduced based on the above considerations. Figure 4-1 presents how the model-form captures deposition (normalized using deposition at the top, DDtop) as a function of canister radial location. Here, a normalized radial value of 0.0 represents the bottom circumferential location of a horizontal canister, and 0.5 represents the top (with symmetry being assumed across the axial midplane). Corresponding values for measured samples at Sites A and B show how the type of deposition model used is representative of the measured data; the chosen model (labeled SCC model) is such that the modeled radial variations capture the variations observed in the measured samples. Sites A and B observed peak DDtop values of 0.25 mg/m2/yr and

~1.3 mg/m2/yr, respectively. However, a summary of measured chloride deposition rates documented by EPRI [14] shows sheltered canisters at Fukushima with higher chloride deposition rates, up to 0.5 g/m2/yr. Given this range of documented values, the DDtop examined here were selected to be 0.01, 0.1, and 1.0 g/m2/yr.

26 Figure 4-1. SNL SCC horizontal canister deposition scaling factor with respect to normalized circumferential location and dust samples at Sites A and B.

27 4.1.2. Limiting Relative Humidity, RHL Deliquescence is defined as the process in which a salt absorbs moisture from humid air and forms a solution. The RH at which this occurs is called the deliquescence RH (DRH). DRH corresponds to the point at which the activity of water in the air (the RH in unit form) is equal to the activity of water in a solution that is saturated with the salt or salt mixture. From a thermodynamic perspective, DRH is a property of the bulk salt that describes thermodynamic equilibrium between a salt-saturated solution and the air. For salt mixtures, DRH for the mixture is generally lower than that of any of the constituent salts, and it generally decreases with increasing temperature (see Figure 4-2 for predicted deliquescence behavior of seawater salts from prior work [9]). However, water can adsorb onto salts as surface films at RH levels below the deliquescence RH. These films can encourage corrosion that can lead to stress corrosion cracking. This gives rise to the concept of a limiting RHL for corrosion control, which is the point at which corrosion can occur - this point is commonly below the DRH level.

28 Figure 4-2. Predicted deliquescence behavior of salts that precipitate when seawater is evaporated for temperatures between 20°C and 80°C.

Experimental studies have indeed observed adsorbed water films on sea salts that have led to corrosion reactions occurring at RH values below corresponding DRH levels [31]. For example, while DRH for NaCl is ~76%. Dai et al. [31] showed films forming for NaCl at ~35% RH, while Schindelholz et al. showed corrosion as low as 33% RH for a 21°C study on metal coupons. In separate studies, Schindelholz et al.

observed that corrosion can persist at even lower RH values once it initiates, and RHL can also decrease as a salt load increases [32, 33]. Subsequent studies by Schindelholz et al. on MgCl2 also showed similar behavior [34]. This work implied that at low RH, smaller salt loads can lead to an insufficient amount of brines to support corrosion, but larger salt loads at the same RH can induce corrosion.

Similarly, as RH increases, a larger fraction of surface salt loads can deliquesce, thereby allowing small salt loads to form corrosive brines. Studies on SCC in 304 SS have shown similar behavior. He et al. observed SCC formation between 12%-25%

RH for sea salts at 60°C, where lighter sea-salt loads were only corrosive at higher RH values, and heavier salt loads were corrosive at lower RH [35]. While the coating methods differed, resulting in variation in coating uniformity, Fairweather et al. and Shirai et al. also saw SCC near 15% RH, where Fairweather et al. used salt loads of

29 20 mg/m2 and 100 mg/m2 at 60°C and 45°C [36]. Fairweather et al. noted that the frequency of cracking was independent of salt load at lower RH, but a dependence exists at higher RH values where higher frequencies were correlated and observed for increasing salt loads.

There are a couple of takeaways from these aforementioned studies. First, the RHL for corrosion is likely below DRH for sea salts. Second, the data suggest that RHL for SCC may depend on salt load. This dependency for crack initiation on RHL is captured by the SNL model through the implementation of the maximum pit size model and the Kondo criterion [7].

The sensitivity analysis performed in this study varied RHL in three forms to capture the uncertainty obtained from the literature, as discussed above. Based on these studies, the three implementations for RHL are, from lowest to highest:

1. RHL = 15%

2. RHL = DRHseasalt - 7%

3. RHL = DRHseasalt

The first implementation is conservatively set at a fixed 15%. In the second

approach, DRH for seawater is calculated as a function of temperature and is then

offset by 7%. The DRH calculation uses data from Greenspan [37], where DRH is

about 34% at room temperature and drops ~1% for every 10°C temperature increase.

This approach to offset RHL by 7% (byEPRIi 4]QTheths L to the seawater DRH (

rarithereviewedexalworkQ

30 4.1.3. Threshold Stress Intensity Factor, Kth The SNL code currently considers the possibility of pit-tocrack transitions at weld locations, which are the regions of highest tensile residual stress on a canister. Pit-tocrack transitions are handled by a model based on the Kondo criterion [15]. This model depends on determining the crack tip stress intensity factor, K, that is calculated as was shown in Section 3.1 by Equation (3-1). This relationship showed how K can be correlated to the tensile weld residual stress theshapeparameter Y (commonly set equal to 1.0), and the radius, ofapitbeirk tensileweldresitatablesf weldresidualstressthsQThesdatatablweructed datawhereweldidualstresseswermeuredasa functstmkbasedon TransNuclearNUHOMS7Pdesignforhorizontaricatedwith srwdproceduresandgeeiQStrongitudinal weldsaredrmfentialwelandtheap r %QThestressintensity rrresents udeofthestresityattheanatomical rbasedonthe givenweldlocationisresholdcracktipstress intensityfactor calculated acrackis offtheanal valuesrepresentleresholto rkand

Currently, there are no standardized methods to measure and determine QThis lackofarangeofmethodologiesthatgiveu theexae aspartof analysesthisworkiityinthemethodsusedbyprior capturethevariabilityraeofvalues usedintudyencompassedtherangeobservcompiled ratureQmlowerboundwasselectedbasedonthromSpeidel[is tionsof7Mgl 2 were utilized to investigate the for7

°C. These conditions are intended to capture an aggressive environment that is

31 thought to be conservative relative to what a canister experiences in real-world conditions. These investigations identified a %MPam 1/2 as a lower bound.

While lower thedifficultyoftestingfrnga foruseintheSNLiwi experimentalmeFornowestedhereuses%MPa 1/2 as a lower bound and spans a range that consists of 5, 10, and 15 MPa-m1/2 as the chosen set for exploration. The lower bound captures a low barrier for initiating cracks based on the Kondo criterion, while the upper bound represents a more difficult but realistic threshold to nucleate a crack.

4.2. Sensitivity Study Results

The sensitivity study focused on three quantities of interest to measure output uncertainty propagated from uncertainty in DD, RHL, and Kth. The three chosen quantities of interest are meant to capture meaningful and characteristic metrics for SCC, and they are: (1) time to pit initiation, (2) time to crack initiation, and (3) time to reach a TWC. The sensitivity study was performed using the two more conservative CGR models presented and analyzed in Section 3: the SNL version, and the ASME Code Case N860 version. The discussion begins with a thorough analysis of the sensitivity study with the SNL CGR model, and then a discussion follows where sensitivity outputs are compared between the two CGR models.

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33 4.2.1. Sensitivity Results with SNL CGR Model The four site locations discussed in Section 3.4 were again considered in this sensitivity study. However, results from the sensitivity study are presented only for Site A to present a concise discussion. Results for Sites B, C, and D show similar behavior and these results are documented in Appendixes A-C of this report.

Results are presented in terms of CDFs to make probabilistic comparisons, where the CDFs were compiled from the realizations simulated per explored critical parameter. The simulated times are normalized with the maximum time to focus on trends rather than absolute times, where the maximum time used for all sites is the same to facilitate comparisons between sites. The analyzed site location, distinguished by its weather model, is again kept anonymous due to data privacy, but it refers to the same nomenclature and weather characteristics discussed in Section 3.4. The location of Site A is conservative in that the weather considered is cold and humid. The location thus observes conditions that generally allow the canister to cool faster and expose the surface to higher relative humidities. Given the number of realizations that were simulated for this study, results are presented for a select few (but significant) conditions to maintain a focused discussion.

Figure 4-3 shows results for varying RHL with fixed chloride deposition rate and Kth.

For conciseness, the figure legends use RH in simulations where the model for RHL was based on the DRH (e.g., RHL = DRHseasalt - 7% is equivalent to saying RH = -

7%). The impact of varying RHL is observed in all quantities of interest, some more noticeable than others. In all quantities of interest, RHL = 15% RH resulted in the most conservative outcome. All realizations in Figure 4-3 (left) saw pit formations, but the realizations with RHL = 15% RH tended to form pits sooner than realizations with the other two RHL models. The realizations with RHL set to the deliquescence RH were the slowest to form pits. Given that the pit-formation models depend on a weld RH approaching RHL, these results are logical; an RHL set to DRH would represent the largest barrier for a pit to form.

A similar pattern of RHL dependence is observed for crack initiation times (Figure 4-3, center). All realizations experienced crack initiation, but the RHL = 15%

RHmodel showed the fastest crack initiation times. Variations are observed early on

34 between the two DRH-dependent RHL models, but ultimately these differences become insignificant at later times as all realizations experienced a crack.

Interpretation of these differences in crack initiation times for the different RHL models is not as direct as for the pit formation times. Local electrochemical kinetics, which are a function of brine properties, influence the evolution of a pit (once they are formed) via the maximum pit size model. Pit growth, and therefore crack initiation, are dependent on the various parameters and models that influence brine composition, which includes RH. The results generally show that canisters that experienced earlier pit formations also experienced earlier crack formations.

Variations in through-wall crack times were also observed when varying RHmodels (Figure 4-3, right), and the variation patterns were like the variations seen in pit initiation and crack initiation times. Again, the more conservative scenario occurred for the RHL = 15% RHmodel, where these realizations experienced through-wall cracks faster than the DRH-dependent RHmodels. The CDFs for the DRH-dependent models overlap similarly to the overlaps seen in the crack initiation times. It is noted that through-wall crack times are measured from the onset of a realization. Once cracks initiate from a pit, through-wall crack times are dependent on the crack growth model and all the factors that influence it. The conditions from Figure 4-3 reveal that the SCC model can be responsive to a low threshold for RHL,

resulting in higher likelihoods of developing through-wall cracks faster.

Figure 4-3. Site A CDF comparisons for varying RH L (DD = 1.0 g/m 2/yr, K th = 10 MPA-m1/2).

35 Figure 4-4 shows results for varying chloride deposition rate with RHL = DRH - 7%

and fixed Kth. Unlike with the cases for varying RHL, the impact of varying DD is only observed in two out of three quantities of interest. Pit initiation times (Figure 4-4, left) did not vary as a function of deposition rate, but all realizations saw pit formations at each of the analyzed weld locations. Given the model implementation, this result is expected. As previously mentioned, pit initiation is dependent on RHL and should therefore not be affected by the deposition rate, as shown by the leftmost plot in Figure 4-4. The lack of variation in the pit initiation times serves as a form of verification on proper code implementation.

Crack initiation times (Figure 4-4, center) experienced a large variation between the different deposition rates. The lowest value for DD, 0.01 g/m2/year, did not lead to any crack formation during the modeled time period. Realizations for DDs of 0.1 g/m2/year and 1.0 g/m2/year observed significant differences between each other, but all realizations with these parameters still experienced a crack. These differences can be understood through the model dependencies. Crack formation is dependent on a form of the Kondo criterion, where pit depth is the characteristic length that is used to calculate a crack tip stress intensity factor used for the Kondo criterion. As pit growth is dependent on the local electrochemical kinetics that are a function of brine properties, it is apparent why the chloride deposition rate that affects pit growth would also affect crack initiation times. The lowest DD does not produce conditions that foster crack initiation, and between the two deposition rates for which cracks from, realizations with the larger rate are more likely to experience fast crack formations. Eventually, all weld locations experience a crack formation for realizations corresponding to the two larger deposition rates.

Through-wall crack times (Figure 4-4, right) behave similarly to the crack initiation times. Realizations with the lowest deposition rate did not experience any through-wall cracks because there were never any crack formations under this DD. For realizations with the two larger deposition rates, not all experienced through-wall cracks for the considered time frame. Cracks with realizations employing a DD of 1.0 g/m2/year show an almost guaranteed likelihood of becoming through-wall cracks. Cracks with realizations employing a DD of 0.1 g/m2/year, however, only

36 show an ~80% likelihood of becoming through-wall cracks during the considered time frame. Overall results showed a more significant sensitivity to varying deposition rate when compared to varying RHL.

Figure 4-4. Site A CDF comparisons for varying DD (RH L= f(T) = -7%,, RHK th = 10 MPA-m1/2).

Figure 4-5 shows results for varying Kth with fixed chloride deposition rate and RHL =

DRH - 7%. Similar to the case for varying DD, the impact of varying Kth is not observed in all quantities of interest. Again, pit initiation times (Figure 4-5, left) did not vary as a function of deposition rate, while all realizations saw pit formations at each of the analyzed weld locations. This behavior is again expected due to pit initiation being dependent on RHL, which is not directly or indirectly influenced by variations in Kth. The lack of variation in the pit initiation times for varying Kth again serves as a form of verification on the code implementation.

The effect of varying Kth on crack times (Figure 4-5, center) was existent but less pronounced than the realizations with varying DD (Figure 4-4, center), yet the effect was more pronounced than the realizations simulated with varying RHL. Kth directly affects the point at which a crack can initiate through the current implementation of the Kondo criterion. As Kth is lowered, this directly reduces the threshold at which a crack can form using the calculated crack tip stress intensity factor for a particular pit (Equation (3-1)). Therefore, realizations with the larger Kth experienced the highest barrier for pit-tocrack transitions. Regardless of the differences tested in this sensitivity study, all realizations with varying Kth experienced a crack formation for the conditions modeled.

37 Variations in through-wall crack times (Figure 4-5, right) were also observed in similar ways to the variations seen in crack initiation times. Again, the realizations with a Kth of 5 MPa-m1/2 experienced the more conservative scenario, where these realizations experienced through-wall cracks faster than realizations with the two larger Kth values. The variation between the different Kth values was not as drastic as was observed with varying deposition rate (Figure 4-5, right). Recalling from Sections 3.1 and 3.4, CGRs have a direct dependence on Kth in the SNL model, as expected. Through-wall crack times are therefore affected by Kth in multiple ways; by affecting the point at which cracks initiate, and by directly influencing the crack growth rate. While all realizations experienced through-wall cracks for the two lower values of Kth, there was a small percentage of the realizations with a Kth of 15 MPa-m1/2 for which cracks did not progress through-wall for the simulated conditions and time frame. Overall, the sensitivity of the model to Kth varies depending on the time frame being considered.

Figure 4-5. Site A CDF comparisons for varying K th (DD = 1.0 g/m 2/yr, RH L= f(T), RH = -7%).

38 4.2.2. Sensitivity Results with ASME Code Case N-860 Model Results for the sensitivity study using the ASME Code Case N860 CGR model are presented in relation to the results of the SNL SCC code with the implemented SNL CGR model.

Figure 4-6 through Figure 4-8 respectively show results for: (1) varying RHL with fixed chloride deposition rate and Kth; (2) varying chloride deposition rate with fixed Kth and RHL = DRH - 7%; and (3) varying Kth with fixed chloride deposition rate and RHL = DRH - 7%. Solid lines refer to the ASME CGR model implementation, and dashed lines refer to the SNL CGR model implementation.

In all cases, there was no difference in impact to the pit initiation (Figure 4-6 to Figure 4-8, left) or crack initiation times (Figure 4-6 to Figure 4-8, center) when implementing either the ASME or SNL CGR model. This result is intuitive as the CGR model only comes into play after a crack has initiated, and all other mechanisms in the SNL code are otherwise handled the same prior to crack initiation. Again, these comparisons showing lack of variation between the two implementations serve as a form of verification on the code implementation. The comparisons further show how the implementation of the ASME CGR model into the SNL code did not perturb any of the other sub-models in the SNL code, as expected.

Figure 4-6 through Figure 4-8 (right) show differences in the through-wall crack times for the two different crack growth model implementations. For varying RHL and in general, the CDFs show that the ASME and SNL CGR implementations are similar for earlier normalized times, but the ASME model realizations reach through-wall status faster than the SNL CGR model implementations. Figure 4-6 (right) shows that there were little differences in through-wall crack status between the two RH models when looking at the ASME or SNL CGR implementations. Figure 4-6 and Figure 4-7 (right) both show that, when sweeping through the range of deposition rates, the ASME CGR implementation always resulted in through-wall crack status when the deposition rates promoted crack initiation. This phenomenon occurred even for cases where a lower deposition rate prevented the SNL CGR model implementation from always resulting in TWC status. Figure 4-8 (right) shows a similar pattern as the previous two figures, where the ASME CGR model

39 implementation again generates faster through-wall crack times for the full set of realizations.

The SNL and ASME CGR model implementations are similar in that they both have an Arrhenius formulation. The SNL version, however, has a dependence on the crack tip stress intensity factor, and the crack growth amplitude is sampled as opposed to fixed (previously discussed in Sections 3.1 through 3.4). The activation energy for the SNL implementation is also sampled from a normal distribution (see Figure 3-8),

compared to the ASME version which has a fixed value of 80 kJ/mol. The combined effect of these variations ultimately leads to an ASME CGR model implementation that can be more conservative than the SNL implementations.

Figure 4-6. CDF comparisons for varying RH L (DD = 1.0 g/m2/yr, K th = 10 MPA-m1/2) with the ASME and SNL CGR models.

Figure 4-7. CDF comparisons for varying DD (RH L= f(T), RH = -7%, K th = 10 MPA-m1/2) with the ASME and SNL CGR models.

40 Figure 4-8. CDF comparisons for varying K th (DD = 1.0 g/m2/yr, RH L= f(T), RH = -7%) with the ASME and SNL CGR models.

41

5. TASK 3: INPUTS DEVELOPMENT AND DOCUMENTATION Probabilistic analysis of CISCC ultimately requires proper handling of uncertainty for input parameters that cover a broad range of expected input values. The third task of the work discussed in this report focused on the identification of realistic parameter ranges for key variables that can be leveraged and used in the Extremely Low Probability of Rupture (xLPR) probabilistic fracture mechanics code. The identification of ranges for a key set of input variables included: canister geometries, canister operating conditions, and flaw conditions. Relevant parameters as handled by the SNL SCC code are tabulated below. References are documented where applicable. User discretion is advised to consider either uniform or normal distribution for parameters where ranges are provided.

Table 5-1. Relevant Geometric and Flaw Parameters for xLPR.

Parameter Notes on range or distribution Reference

Canister outside 67-71 [inches] Storage and Transport diameter Cask Data for Used Commercial Nuclear Fuel [40]

Canister wall 0.5-0.625 [inches] Storage and Transport thickness Cask Data for Used Commercial Nuclear Fuel [40]

Initial Flaw A maximum pit size model (See Various sources that length/depth Sections 2 and 3) is used to discuss the maximum determine initial crack pit size model in depth lengths/depths in the SNL SCC [20, 8]

code. Flaw depth and length are assumed to be the same in the current implementation. The pits

42 Parameter Notes on range or distribution Reference

from which cracks nucleate are assumed hemispherical, so relationships are derived from these assumptions. Initial crack dimensions are the same as the pit that allowed the flaw to nucleate.

Canister surface Surface temperatures are PNNL models. See temperatures extracted from a thermal model Section 5.1 below [11, formulated and analyzed by 12].

PNNL. For the horizontal canisters considered in this study, the model calculates temperatures in the range between ~50°C to ~250°C for an initial heat load of 24 kW if exposed to a 15.6°C (60°F). After 292 years, the heat load decays so that temperatures vary between ~20°C to ~50°C.

Canister internal Variable. Some canisters are SNL subject matter operating pressures filled to eight bars initially, but experts and the cooling promotes pressure Agencywide drops. Other canisters can be Documents Access and filled to one bar initially but can Management System experience negative internal (ADAMS) pressures as they cool. [41]

43 Parameter Notes on range or distribution Reference

Normal operating Operating loads are not SNL subject matter loads or stresses independently handled by the experts and the SNL SCC code. Loads Agencywide experienced by canisters are Documents Access and variable and canister-specific. Management System SNL recommends investigating (ADAMS) canister-specific Certificates of [41]

Compliance (CoCs) for this parameter. The SNL SCC code currently only requires weld residual stresses to be known, which were acquired through experimental methods for a single configuration.

Canister weld Canister weld residual stresses See Section This page residual stress are accounted for through data left blank below [21, tables. These data tables were 19]

constructed from experimental field data for a mockup based on the TransNuclear NUHOMS 24P design for horizontal storage canisters. Detailed discussion below.

Canister material Various types of stainless-steel Storage and Transport are common (304, 304/304L, Cask Data for Used 316/316L). Most trans-nuclear Commercial Nuclear canisters are 304L, but ISFSIs at Fuel [40]

high risk for corrosion are

44 Parameter Notes on range or distribution Reference

commonly 316L. Some systems use combined materials.

Canister weld Weld material is either a Characterization of material material stronger than the base Canister Mockup Weld material (e.g., 304/304L base Residual Stresses [19]

material with 308L weld filler),

or the weld material can match the base material. Weld material should never be weaker than the base material.

5.1. Note on Canister Surface Temperatures For the horizontal canister considered by the SCC code in this study, canister surface temperature maps are based on thermal models developed at PNNL [11, 12]. The PNNL thermal model calculates thermal distributions by determining the nominal canister surface temperature given an assumed initial heat load and reference ambient temperature. PNNL analyzed temperatures at 35 node locations as shown in Figure 5-1.

Figure 5-1. Node configuration for PNNL thermal model [11, 12].

45 Ambient temperatures that differ from the reference temperatures used in the PNNL modeling are reflected in the SCC model as a linear delta. For example, if ambient temperatures considered in a simulation from the SCC model were 5 degrees warmer than those considered in the PNNL model, then all surface temperatures from the PNNL model are increased by 5 degrees for use in the SCC simulations.

Canister surface temperatures over time are shown in as calculated by the PNNL model for a horizontal canister emplaced at 24 kW. The figure shows how surface temperatures cool over 292 years (line for 0 yrs is point of emplacement).

Figure 5-2. Canister surface temperatures over time as calculated by the PNNL thermal model [11, 12].

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47 5.2. Note on Canister Weld Residual Stresses The SNL SCC code depends on knowledge of the tensile weld residual stresses (as a function of through-wall depth) to calculate a crack tip stress intensity factor, which is then used as part of the Kondo criterion to determine whether a crack nucleates from a pit or not. As noted in Equation (3-1), calculation of this factor depends on knowledge of the weld residual stresses. The SCC code employs tables generated from experimental testing to determine the needed through-wall stress profiles for longitudinal and circumferential welds. The experimental data collected for the longitudinal and circumferential weld stresses was sourced from a full-diameter canister mockup (based on the TransNuclear NUHOMS 24P design for horizontal storage canisters) that was fabricated with typical canister weld procedures and geometries [19]. Due to accuracy concerns, two different methods were used: shallow stresses (0-0.5 mm deep, measured from the outer surface of the shell) were measured using the incremental center-hole drilling (ICHD) method; deeper stresses were measured using incremental deep-hole drilling (DHD). DHD can provide accurate measurements through the thickness of a weld but is not as accurate near the surface, and ICHD is more accurate for near-surface measurements but becomes progressively less accurate with depth. The SCC model employs a combination of this data by (1) fitting a trend to the DHD data at deeper locations and (2) fitting to the ICHD data at shallow (surface) locations. Figure 5-3 below shows these fits for the heat affected zone as well as for the weld centerline locations, where stresses are shown as a function of depth (normalized by wall thickness). Matching the ICHD and DHD data at the shallow location was not trivial, and the DHD data was set to fit to a mean of the ICHD data near the surface. This fitting and matching of data near the surface can be more closely observed in Figure 5-4, which shows a reduced scale for the normalized depth to better appreciate the ICHD data.

48 Figure 5-3. ICHD, DHD, and SCC model-fit residual stress data for weld centerline and HAZ locations at normalized depths.

49 Figure 5-4. ICHD, DHD, and SCC model-fit residual stress data for weld centerline and HAZ locations at shallow normalized depths.

50 This page left blank

51

6.

SUMMARY

This report discussed the collaboration between SNL and the U.S. NRC staff to understand the state of knowledge on CISCC. The foundation of this work relied on SNLs CISCC code to assess the current state of knowledge on modeling CISCC on stainless-steel canisters. The work presented was divided into three main tasks.

In the first task, the SNL CGR model was isolated as a standalone module and compared to two other CGR models from the literature: a model documented by EPRI and a model documented in ASMEs Boiler and Pressure Vessel Code Section XI Code Case N860. Model comparisons were characterized by generating CDFs of through-wall crack. All models are dependent upon temperature and activation energy through an Arrhenius relationship. The three models are parameterized differently. The ASME model is the simplest in that it is deterministic with conservative secondary input parameters, while the other models sample the secondary input parameters from assumed distributions. The EPRI CGR model is unique in that it has a two-stage implementation, where crack growth amplitude is incorporated as a depth-dependent sampled variable. It is also unique in that activation of the CGR model is conditional. Crack growth with the EPRI CGR model only occurs if a weld is exposed to a minimum critical RH (RHc), while the SNL and ASME CGR models remain active as soon as a crack nucleates. The models were compared using sampled weather conditions at four relevant ISFSI locations. While the models are uncertain, the SNL and ASME models produced more conservative results in these standalone comparisons. These two models produced TWC instances at least 50% more frequently than the EPRI model for the conditions and timeframe considered.

In the second task, a sensitivity study was performed using the SNL CISCC infrastructure. The sensitivity study was based on the input parameters with the largest uncertainty, referred to as critical input parameters. Both the SNL and the ASME CGR models were incorporated into the study. The effects of the different CGR models on the quantities of interest from the sensitivity study were also compared in the latter part of the second task. The critical input parameters of interest were DD, RHL, and Kth due to the range of uncertainty obtained in literature

52 reviews from experimental measurements. The quantities/metrics of interest used in the sensitivity study were: time for pit initiation, time for crack initiation, and time to reach a through-wall crack.

When considering the quantities of interest in the second task, pit initiation times were sensitive to RHL, but not to the chloride deposition rate or Kth. Crack initiation times were responsive to all critical input parameters, but they were most sensitive to variations in the chloride deposition rate. Through-wall crack times were similarly responsive to all critical parameters but were most sensitive to variations in the chloride deposition rate.

When considering the two CGR models in the second task, differences were only observed in the through-wall crack times, as expected. Both CGR implementations showed similar results with some differences. For the conditions analyzed and for all pits that led to cracks, the ASME CGR model resulted in all cracks reaching through-wall crack status. This outcome was not the case for the SNL CGR model, where crack initiation did not guarantee through-wall crack within the simulated time period, especially for the cases with varying chloride deposition. This latter comparison of the CGR models as part of the full SNL CISCC infrastructure thus showed that the ASME CGR model can be more conservative in predicting through-wall crack times despite having fixed input parameters.

Results from the modeling presented here are not meant to be predictive, and further work is needed to bring SNLs CISCC code to a predictive state. Instead, the work presented in this report identified model uncertainties and conservatisms that can be considered when modeling stress corrosion cracking with the approach of the SNL CISCC infrastructure. This work highlights the impact and importance of reducing uncertainty in measuring deposition rates as it is one of the parameters with the most significant influence on predictive modeling of CISCC. For the conditions modeled, the impact of varying RHL, and Kth was still significant at intermediate times but less so when considering the entire time period being

53 modeled. These intermediate time periods should not be ignored as the probabilities predicted for initiating a crack or reaching TWC status are not zero.

There are still opportunities for improvement in the realm of modeling for CISCC when considering the work presented here. The uncertainty propagated to quantities of interest from uncertainties with Kth can possibly be reduced by considering a different approach for calculating the crack tip stress intensity as presented in Section 3. The current approach as used is based on simplifications that ignore the stress gradients within a pit. It conservatively assumes a uniform stress distribution across a pit by using the maximum stress in a pit to calculate a threshold for crack initiation. Furthermore, SNLs CISCC code also conservatively uses the Kondo criterion for handling cracks. With the current implementation of the CGR model, a crack initiates as soon as the calculated crack tip stress intensity factor is equal to or greater than Kth, and growth continues until the simulation ends or until the crack becomes through-wall. This is a conservative approach that can benefit from making K a function of an integrated stress profile to calculate crack tip stress intensity factors. Other approaches have been adopted in probabilistic fracture analyses calculations. Such alternative approaches can likely be beneficial in reducing uncertainties associated with Kth and crack initiation. For improvements that can affect RHL, the weather model incorporated into SNLs CISCC code can benefit from further calibration. Improving the correlations between temperature and dewpoints can eliminate occasional predictions of unlikely high RH values.

Furthermore, the maximum pit size model has not been calibrated at conditions for extreme values of RH, so testing its sensitivity to high and low values of RH and comparing to experiments can also help better understand its adequacy.

54 55

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60 APPENDIX A. SENSITIVITY STUDY RESULTS FOR SITE B USING SNL AND ASME CGR MODELS

Figure 7-1. Site B CDF comparisons for varying RH L (DD = 1.0 g/m 2/yr, K th = 10 MPA-m1/2).

Figure 7-2. Site B CDF comparisons for varying DD (RH L= f(T), RH = -7%, K th = 10 MPA-m1/2).

Figure 7-3. Site B CDF comparisons for varying K th (DD = 1.0 g/m 2/yr, RH L= f(T), RH = -7%).

61 APPENDIX B. SENSITIVITY STUDY RESULTS FOR SITE C USING SNL AND ASME CGR MODELS

Figure 7-4. Site C CDF comparisons for varying RH L (DD = 1.0 g/m 2/yr, K th = 10 MPA-m1/2).

Figure 7-5. Site C CDF comparisons for varying DD (RH L= f(T), RH = -7%, K th = 10 MPA-m1/2).

Figure 7-6. Site C CDF comparisons for varying K th (DD = 1.0 g/m 2/yr, RH L= f(T), RH = -7%).

62 APPENDIX C. SENSITIVITY STUDY RESULTS FOR SITE D USING SNL AND ASME CGR MODELS

Figure 7-7. Site D CDF comparisons for varying RH L (DD = 1.0 g/m 2/yr, K th = 10 MPA-m1/2).

Figure 7-8. Site D CDF comparisons for varying DD (RH L= f(T), RH = -7%, K th = 10 MPA-m1/2).

Figure 7-9. Site D CDF comparisons for varying K th (DD = 1.0 g/m 2/yr, RH L= f(T), RH = -7%).

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ML24183A003; ML24183A005 OFFICE RES/DE/REB RES/DE/CIB RES/DE NAME CNellis CN RIyengar RI MSampson JMcKirgan for JM DATE Jul 1, 2024 Jul 5, 2024 Jul 12, 2024