ML16165A171

Risk-Informed Approach for Model Abstraction in Canister Damage from Localized Corrosion and Stress Corrosion Cracking in the Disposal of Spent Nuclear Fuel and High-Level Waste

ML16165A171
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Issue date:	03/23/2017
From:	Tae Ahn Division of Spent Fuel Management
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U.S. Nuclear Regulatory Commission (NRC), Agencywide Document Access and Management System (ADAMS), Report Number: ML16165A171, March 23, 2017 Risk-Informed Approach for Model Abstraction in Canister Damage from Localized Corrosion and Stress Corrosion Cracking in the Disposal of Spent Nuclear Fuel and High-Level Waste Tae M. Ahn Office of Nuclear Material Safety and Safeguards U.S. Nuclear Regulatory Commission (NRC), Washington, DC 20555-0001 Abstract This paper presents risk-informed model abstraction (representation) for long-term perspectives and quantification of the informed important degradation processes of canister for the long-term geological disposal of high-level nuclear waste (HLW). The work independently analyzes appropriate but shorter-term data/understanding available in literature. The results intend to offer part of framework for probabilistic system performance (or risk) assessment in the HLW disposal. Model abstraction to be used in probabilistic system performance (or risk) assessment may be simple and representative, often conservative, considering long-term perspectives. The abstraction includes selection and assessment (rationalization) of existing data, theories and models. The metals considered are stainless steels/carbon steels and nickel-based alloys in chloride bearing solution. General corrosion is assessed regarding the persistence of passive film. Localized corrosion is assessed for latent repassivation and cathode capacity. The assessment of stress corrosion cracking (SCC) considers precursory steps and uncertainties associated with single crack propagation, and potential maximum opening areas of multiple cracks.

Disclaimer: The NRC staff views expressed herein are preliminary and do not constitute a final judgment or determination of the matters addressed or of the acceptability of any licensing action that may be under consideration at the NRC.

1. Introduction This paper presents risk-informed model abstraction (representation) for long-term perspectives and/or quantification of the informed important degradation processes involved in canister for the long-term geological disposal of high-level nuclear waste (HLW). The work independently analyzes appropriate but shorter-term data/understanding available in literature. The results intend to offer part of framework for establishing system probabilistic performance (or risk) assessment in the HLW disposal. Model abstraction to be used in probabilistic system 1

performance assessment may be simple and representative, and is often conservative, considering long-term perspectives. Metal canisters (or containers) serve to confine radionuclides. Corrosion of the metal can potentially compromise the radionuclide confinement.

If a canister were to fail, a limited amount of radionuclides may be released through the corrosion-induced damage (i.e., an opening area on the metal canister). The abstraction includes relevant selection and assessment (or rationalization) in existing data and detailed process-models (or theories). Recently the author presented (i) a summary of radionuclide confinement process (Ahn, 2016) and (ii) the assessment of risk-informed controlled release of radionuclides (Ahn, 2017).

This paper presents some details of how the canister maintains its integrity and keeps limited opening area if failed, along with model abstraction for the system performance assessment.

The paper primarily proposes two damage models, and discusses radionuclide confinement, for localized corrosion and SCC. Persistence of passive film with no damage is also summarized.

A conservative analysis assumes the conditions for localized corrosion and SCC, with no inspection and remediation adopted.

Figure 1 shows a schematic of confinement without an opening area and limited radionuclide release through an opening area.

Radionuclide Source Term: Transport Path: Area Boundary:

degradation of SNF, air, groundwater dose cladding and HLW Figure 1. Canister confinement is without damage (opening area)

With opening area, limited radionuclides are released through the opening area.

The release of the radionuclides leads to dose. Radionuclide sources are inside the canister.

The materials considered are stainless steels/carbon steels and nickel-based alloys under consideration or used selectively in the world. The environment considered in this paper includes chloride bearing solution, as a representative conservative example in performance 2

assessment. The radionuclide confinement is discussed with the persistence of passive film.

The persistency is determined by the extent of (a) steady-state thickness of film, (b) steady-state chemistry of film, and (c) impurity effects. If pitting or crevice corrosion initiates, the latent (or delayed) repassivation may still provide the confinement. The latent repassivation of stable pits has distinction from transient repassivation of metastable pits. If pitting or crevice corrosion continues and penetrates through the canister wall, some radionuclides may be released through the opening area as depicted in Figure 1 (e.g., Ahn, et al., 2011; Jung, et al., 2011).

The extent of the opening area would be determined by the initiation rate, the latent repassivation rate, and cathode capacity for continuous anodic dissolution of the canister material. In the crevice, pitting corrosion or active dissolution would occur depending on the electrochemical conditions inside the crevice.

This paper also discusses the impact of stress corrosion cracking (SCC) on the radionuclide confinement boundary and models for SCC damage (i.e., opening area) of a canister. The approach considered for the SCC-induced opening area includes the following five stages. The first stage is the precursory step for SCC, such as pitting or fabrication flaws. The second and third stages include single crack propagation and analysis of a recently developed model for estimating potential canister opening area, respectively. To bound the uncertainties associated with single crack propagation, the model is based on a possible maximum number of multiple through-wall cracks for a predominant range of crack aspect ratios (i.e., potential maximum opening area). The model was previously developed under seismic conditions in a geologic disposal system by the Sandia National Laboratory (SNL, 2007a, hereinafter referred to as the SNL model). The fourth and fifth stages include example reactor inspection data for the number and size of cracks and application of the SNL model in weld regions of the various canister materials.

This paper is organized to discuss the persistence of passive films, localized corrosion, and stress corrosion cracking of the canister materials. A summary is presented in the end.

2. Persistence of Passive Film A thin chromium barrier oxide less than 5 nm is considered to be responsible for the passivity in nickel-based alloys (a primary review and evaluation by the author, Ahn, et al., 2008). In stainless steels, a few-nanometer compact layer of iron-chromium spinel is responsible for the passivity (Beverskog, et al., 2002). A dense and comparatively thicker oxide layer is considered responsible for the passivity of carbon steel (Bataillon, et al., 2012). Generalized non-steady state approaches in various metal components are also presented by Seyeux et al. (2013) and Leistner et al. (2013). The steady-state thickness of the layer responsible for the passivity is considered finite with time for these models. The point defect model (PDM) (Macdonald since 1981) suggests the presence of a finite thickness of oxide layer in nickel-based alloys, and similar models for carbon steel in the alkaline environment also suggest the finite thickness with some exceptions with concrete (Bataillon, et al., 2012). The non-steady state generalized model also postulates the steady state in a longer term. The steady-state chemistry of the passive layer with time was suggested in nickel-based alloys (Pensado, et al., 2002). However, 3

the chemistry of the passive layer in carbon steel varies with time, although the corrosion rates either remain steady or decrease with time, depending on pH (4).

Based on the thermodynamic modeling results and literature short-term experimental results, a chromium-rich barrier oxide passive film is expected to be stable at elevated temperatures. An example is given below assuming a single activation process for nickel-based alloy. The estimated activation energy is reported to be 50 kJ/mol (Kim, et al., 2010) in the temperature range of 350 C and neutral water for 10 days. Given the same barrier oxide thickness based on a single activation process, the time elapsed is approximated by an inverse Arrhenius

relation, Time ~ EXP [(Activation Energy)/(R T)]

Where R is gas constant and T is temperature.

The time ratio at 100 C to 350 C is ~ 630. Nickel-based alloys are used in nuclear reactor (e.g., steam generator). They have been stable over 10 years at ~ 315 C. The time scaling of 350 to 315 C will be ~ a factor of 1.8. Therefore, ~ 350 time ratio is expected at 100 C scaling from 315 C. For 10 year stability, this is equivalent to ~3500 year stability at 100 C. Similar passive film formations have been reported for nickel-based alloys and stainless steels (Montemor, et al., 2003).

The anodic segregation of sulfur impurity was analytically assessed in the nickel-based alloys in the previous paper (Ahn, et al., 2008). Later experiments show that sulfur does not increase corrosion rates in Ni-22Cr-13Mo-3W-4Fe alloy (Jung and Ahn, 2013, 2015). Repassivation behavior was investigated in chloride-containing solutions with and without sulfur at temperatures of 22 °C (room temperature) and 60 °C using a scratch technique. The effect of silica impurity was also considered in nickel-based alloys.

Unless pitting or crevice corrosion conditions exist at high chloride concentrations, the passivity appears to persist on the canister materials such as nickel-based alloys and carbon steel. The steady-state thickness and chemistry of passive film, and the absence of impurity effects support this hypothesis.

3. Localized Corrosion 3.1 Latent Repassivation A background review of localized corrosion conditions was also conducted recently for long-term behavior (Ahn, et al., 2013) of canister materials; therefore, discussion on conditions causing the localized corrosion is not presented here. In a long period of time involved in the high-level waste (HLW) management, the corrosion potential may vary, leading to the passivity breakdown and initiating pitting/crevice corrosion. The extent of the fast propagation of pitting/crevice corrosion would depend on the latent repassivation behavior. The latent repassivation of pitting/crevice corrosion would result in the confinement or limiting opening area.

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While crevice corrosion occurs in an occluded area, pitting corrosion occurs on the free metal surface or inside crevice. Literature information (Macdonald and Urquidi-Macdonald, 1992; Shibata, 1983) suggests that the extent of pitting corrosion can be quantified by (1)

=

where pit repassivation probability pit death constant (reciprocal time) time pit induction time Once all parameter values in Equation (1) are known under given material and environmental conditions, time-dependent statistical distributions of size and density of pits can be quantitatively determined for system performance assessment. This also includes information on pit initiation conditions of environments and materials with/without inspections. Recently, such an exercise was conducted using pit growth kinetics and periodic inspection for nuclear power plant aging (Shukla and Pensado, 2013). Three cases of latent repassivation are presented below in conservative severe environments. In addition, one case of active dissolution in crevice is also presented. The data provide parameter values for Equation (1),

where the repassivation times are short for all cases except the active dissolution case.

3.1.1 Crevice Repassivation He and Dunn (2005) measured current density and potential using a single crevice assembly in Ni-22Cr-13Mo-3W-4Fe alloy cylindrical specimen. The specimen was galvanically coupled to a large plate of the same alloy in 5 M NaCl solution with the addition of 2 x 10-4 M CuCl2 at 95 ºC.

A large number of pits initially formed in the crevice were repassivated under open-circuit conditions. The repassivation rate was rapid, considering the typical long time period of waste management. No pits penetrated through the thickness while the repassivation was complete.

Figure 2 shows the current density and potential with time, showing the repassivation in a later time with lower current density and higher potential.

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Figure 2. Measured current density and potential using the single crevice assembly for Ni-22Cr-13Mo-3W-4Fe alloy cylindrical specimen galvanically coupled to a large plate of the same alloy in 5 M NaCl solution with the addition of 2 x 10-4 M CuCl2 at 95 ºC, (after He and Dunn, 2005). A large number of pits initially formed in the crevice were repassivated under open-circuit conditions.

3.1.2 Repassivation of Open Surface Rodriguez et al. (2007) measured corrosion potential as a function of immersion days for Ni-22Cr-13Mo-3W-4Fe specimens in 18 M CaCl2 + 0.9 M Ca(NO3)2. The specimens were creviced, but the pitting occurred outside the crevice. Rapid general corrosion was likely to occur without concentration cell formation. The corrosion potential oscillated in large potential changes (~ 500 mV) for ~days intervals. The corrosion potential increased with time and the passivity broke down. As the bare metal surface was exposed, the corrosion potential dropped rapidly. At the lower potential, the bare metal repassivated. This oscillation was repeated over one-and-a-half years. In some samples, pitting and presumably repassivation were observed outside the crevice. The net thickness of passivity oxide layer was preserved during this potential oscillation.

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3.1.3 Pit Repassivation Ernst and Newman (2002) measured current-time response for a pencil electrode of 304 stainless steel in 1 M NaCl at 15 ºC. The potential was stepped to 700 mV (SCE) for 10 minutes, then stepped to 450 mV (SCE) for 1 minute, and then back-scanned (at 1 mV/second, see Figure 4) until repassivation. Figure 3 shows the current responses to the varied potentials (times). Pit depth at 600 mV at 15 ºC for 440 seconds was ~ 0.10 to 0.15 mm. Only minor penetration is expected before repassivation as shown in many field data (Engelhardt and Macdonald, 2013).

Figure 3. Current-time response for a pencil electrode of 304 stainless steel in 1 M NaCl at 15 °C. The potential was stepped to 700 mV (SCE) for 10 minutes, stepped to 450 mV (SCE) for 1 minute, and then back-scanned until repassivation (Ernst and Newman, 2002). Pit depth at 600 mV (SCE) and 15 °C after 440 seconds was about 0.10 to 0.15 mm. Here D: diffusivity of dissolved metal cations, h: diffusion length, CS: saturated concentration, C*: critical concentration, iS: saturated current density, and i*: critical current density 7

3.2 Active Dissolution of Crevice DeForce (DeForce, 2010) observed active dissolution in the crevice corrosion of 304 stainless under salt fog or spray tests at ambient temperature. Figure 4 shows the active dissolution. A separate corrosion map was made for potential versus chloride concentration. At pH 1 active regions were shown, but passivity and pitting were observed at pH 2 without active region.

Enos and Bryan (2013) reported similar test results independently.

Figure 4. Potential versus chloride concentration corrosion map for 304 stainless steel in pH 1, showing regions of active, passive, and pitting corrosion. No active peak at pH 2. (after DeForce, 2010) (permission by The Pennsylvania State University) 3.3 Cathode Capacity The opening area can be further limited by cathode capacity. In the initiation and propagation of crevice or pitting corrosion, excess cathode current, which is generated outside the crevice or pit, must be available. The cathode capacity is the amount of excess cathode current that balances the metal dissolution current inside the crevice or pit. This limits propagation rate of crevice or pitting corrosion in the area adjacent to crevice or pit under active dissolution.

Numerical exercises on the cathode capacity were presented in the literature (Shukla, et al.,

2008; Cui, et al., 2005). These led to maximum opening area.

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4. Stress-Corrosion Cracking (SCC) 4.1 Precursory Steps for SCC Precursory steps considered for SCC are pitting by initial corrosion and fabrication flaws formed during welding and other fabrications. In case of pitting by initial corrosion, limited density and size of pits are discussed above with respect to existing pitting theories and data. In case of fabrication flaws, there is a relatively high density of potential incipient surface cracks associated with microscopic discontinuities.

4.2 Pit-Induced SCC: Example Calculation Corrosion data are available for austenitic stainless steels exposed to the coastal environment at test facilities in Kure Beach, North Carolina for 15 years (review summary by the Electric Power Research Institute, EPRI, 2005). During this exposure, pitting corrosion occurred on the coupons or U-bend specimens with salt deposits. EPRI (2005) also summarized SCC observations for (a) sensitized 304 stainless steel in Kure Beach and (b) thermally annealed or sensitized 304 and 304L stainless steels in the coastal environment of Okinawa, Japan, both under stress. Using the reported data from the exposure tests at room temperature, pit sizes are estimated to range 10 - 100 µm, with a uniform distribution. Residual stress can be due to welding or other fabrication (such as rolling), which was not relieved by thermal annealing or other mitigation processes (such as applying compressive stress). Available measured data in Japan for austenitic stainless steel suggest that weld residual stress can be 0 - 600 MPa (Shirai, et al., 2011). The stress distribution is assumed to be normal, based on the trend of the measured data. Using the distributions of the pit size and stress, the cumulative probability of stress intensification factor, K (MPa m1/2), is calculated, using GoldSim Version 10.11 for a probabilistic simulation (GoldSim Technology Group, 2010). The stress intensification factor was calculated using the formula in Table 1.

Table 1. Cumulative probability of stress intensification factor, K(MPa m1/2) = 1/2 x stress x (crack size)1/2 Probability 0.001 0.05 0.25 0.75 0.95 K(MPa m1/2) 0.43 1.57 2.59 4.57 6.94 (Conversion factor: 1 MPa m1/2 = 0.91 ksi in1/2)

The stress intensity factor values (K) were measured using the fracture mechanics SCC tests with salt deposits (EPRI, 2005; Kosaki, 2008; Shirai, et al., 2011). The measured K values for SCC ranged between 0.5 - 7.0 MPa m1/2. The calculated data are consistent with the values observed in the coastal area tests (EPRI, 2005) discussed above.

It is also noted that additional applied stress may be present. Any adjacent component may exert force on a canister; seismic-induced stress may occur in a longer term. The annual 9

probability of annual seismic events may be of a fixed value. However, the likelihood of seismic events inducing significant stress have occurred increases with time.

4.3 Single SCC Crack Propagation (Perspectives)

After SCC initiates, the induced cracks are generally understood to propagate continuously.

However, this understanding is based on conservatisms such as sustained applied stress or sharp crack geometry. In the disposal of spent nuclear fuel (SNF) and high-level waste (HLW),

materials characteristics and the stress state at the crack tip will change during crack propagation. The residual or applied stress may decrease, or the crack tip shape may be modified to decrease the stress intensification factor, thereby slowing the crack propagation rate. The following summarizes such modifications, as discussed in various industry literatures (e.g., discussion in SNL, 2007a).

Residual stress along the thickness of a canister varies near the weld and affects the crack propagation rates. Stress will be redistributed around the crack tip during crack propagation. If crack branching or a tortuous crack path decreases the local stress, the crack propagation rate would decrease, whether it is inter- or trans-granular cracking. Plasticity in terms of Jmaterial (energy per unit fracture surface area) may increase more than Japplied with crack propagation, which may affect the slip or twin process for film rupture at the crack tip for SCC propagation.

Cracks cannot propagate without appropriate stress. Residual stress decreases rapidly as one moves away from the weld area. There will be no significant stress from internal gas pressure inside a canister. Under seismic impact conditions in a longer term, stress decreases from the outside surface along the thickness. It is expected that the seismic stress is applied to the outer surface during the collision of a canister with neighboring canisters or rocks (SNL, 2007b).

Environmental variations such as chloride concentration in the air may decrease the crack propagation rate. For example, the SCC under unsaturated conditions could occur with the deliquescence of deposited salts on the canister surface (Shirai, et al., 2011). The deliquescence in turn depends on the temperature and relative humidity (RH) on the canister surface. This temperature and RH are determined primarily by the canister heat loading, and ambient atmospheric temperature and RH. At higher temperatures without salt deliquescence, SCC will not propagate. In addition SCC propagation rates themselves depend on the temperature. In light-water reactor (LWR) experiences, SNL determines that material degradation due to through-wall growth of neighboring cracks has not been observed (SNL, 2007a). According to SNL (2007a), depending on the stress distribution SCC may initiate and propagate through-wall. If several cracks were to initiate in the same area, coalesce, propagate through-wall while remaining straight (i.e., perpendicular to the surface), and maintain smooth crack faces, material could fall out. The simultaneous occurrence of all of these events is improbable. For through-wall cracks, tighter and relatively separate cracks are more likely.

However, it is noted that some events such as coalescence of multiple cracks are important for the structural integrity assessment of nuclear power plants. For example, Figure 5 shows an example of an analytical simulated single SCC natural crack through the wall of reactor component (Rudland, et al., 2008). This simulation predicts a leaking reactor component (Rudland, et al., 2008).

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Figure 5. Example of arbitrary crack front developed by PipeFracCAE (after Rudland et al., 2008). A crack initiates inner side, propagates circumferentially, and penetrates through the wall.

Mitigation processes will decrease the probability of crack propagation. For example, thermal annealing, if appropriate, or applying compressive stress may mitigate crack initiation.

In conjunction with this discussion, Rudland et al. (2009) postulates that the probability of a single crack penetrating through the canister wall can be low. An example from the literature is shown in Figure 6 below. Figure 7 shows a schematic of crack development process.

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Figure 6. Crack tip near the outside diameter surface of a type 304 stainless steel piping system contaminated with chlorides. Trans-granular crack is arrested. Crack depth in the picture is about 1.2 mm (Stein, et al., 1986) (reprint permission by ASM International)

Figure 7. Proposed sequence of crack initiation, coalescence, and growth for steel undergoing subcritical cracking in aqueous environments (Ford and Andresen, 2002).

Crack depth for initiation is aint and crack depth for failure is afail 12

There are other literature data that show gradual increase in crack growth rate with increase of stress intensification factor or time (Shirai, et al., 2011; Newman, 2002; Sridhar, et al., 1992).

This implies that crack growth rate can decrease as the local stress intensification factor decreases for various reasons. Unlike the reactor studies, however, the probability of the through-wall cracking has not been quantitatively studied in SNF and HLW disposal by implementing mitigation strategies to ensure safety.

Also, initiation of SCC involves a relatively narrow range of environmental and materials conditions. The environmental conditions include electrochemical potential, pH, temperature, aqueous chemistry (e.g., carbonate, or chloride), and applied stress (typically only in the weld/HAZ or deformed area). In humid corrosions, appropriate relative humidity is also a factor.

The thermal treatment of materials may lead to microstructure alteration in many cases. More comprehensive discussion is referred to in literature (Staehle, 2001) and in the authors ongoing work (Ahn, et al., 2012). This range of conditions initially limits the SCC susceptibility on the canister surface. However, large uncertainties associated with SCC initiation make it difficult to determine quantitative values of damage parameter to be used in the system performance assessment.

4.4 Potential Maximum Opening Area of Multiple Cracks in SCC The above sections discussed that the opening area of multiple cracks will be limited by: (a) density and size of pits and flaws; (b) unlikelihood of cracks extending through the wall; and (c) environmental and materials conditions for SCC. The SCC issue has been considered for some specific disposal environments. If the canister were to fail, a potential maximum opening area can be used as a conservative and bounding approach in disposal for the assessment of radionuclide release, considering uncertainties associated with single SCC propagation. This opening area is for a possible maximum number of multiple through-wall cracks for a predominant range of crack aspect ratios. Ideally, the analytic model representing the potential maximum opening area should be simple for incorporating in a system performance model.

4.4.1 Sandia National Laboratory (SNL) Model: Basis Models for potential maximum opening area of multiple cracks under seismic impact scenarios have been developed for disposal canisters in an open drift repository design (Sandia, 2007a).

The SNL seismic model allows all possible surface cracks to penetrate through the wall thickness. The following summarizes the SNL model and its applicability for performance assessment.

The SNL model is stress based, and conservatively assumes that the environment for SCC exists. The centers of two parallel SCC-induced cracks are separated by a parameter (approximately the canister thickness, related to crack geometry) considering the stress attenuation with thickness. In particular, the distance between two neighboring through-wall cracks is to be greater than the wall thickness for the stress (and resultant stress intensity) to be 13

sufficient to drive a flaw through-wall. This conclusion is based on stress field interactions between closely spaced parallel cracks.

The crack aspect ratio (ratio of length to depth) has distribution for various possible crack geometries in a probabilistic system approach, and each value was sampled in the performance assessment. The ratio is in a short range of values. Literature data in experiments partly support the SNL approach. For example, Parkins (1994) shows a good correlation of maximum lengths and depths of SCC in ferritic steels exposed to CO32-/HCO3- solution. More recently, Lee et al. (2013) modeled the elliptic crack shapes based on the electrochemical principles for nuclear power reactor piping. Larger aspect ratio is modeled as multiple parallel cracks (Figure 8, Chu, 2014).

Examples of such a crack network are illustrated in Figure 9 in the SNL report. The crack network is generated only in the limited area of the canister surface deformed from seismic impact (SNL, 2007b). Cracks that are in close proximity can reduce the overall driving force for crack growth because the stress intensification factor for parallel is less than that for a single crack. Depth and size of surface crack are correlated (Lee, et al., 2013; Parkins, 1994). It is improbable that several cracks were to initiate in the same general area, coalesce, propagate through wall, resulting in material fall out (1). Once the crack penetrates through the wall, the distance between two neighboring through-wall cracks is to be greater than the wall thickness for the stress to be sufficient to drive a crack penetrating through the wall thickness (SNL, 2007a). SNL (2007a) furthered statistical sampling of the aspect ratio, including multiple parallel cracks. Therefore, the pattern of surface cracks is likely to be similar to that of through-wall cracks.

To support this hypothesis of the crack separation by stress attenuation, a stress analysis was conducted with a crack network (Structural Integrity Associates, 2002). Figure 9 shows the analysis results. The upper figure shows a number of cracks separated horizontally and vertically. The lower figure shows longitudinal stress distribution along the center. The stress is attenuated near the crack. This implies that a new crack cannot form between two cracks spaced by the parameter.

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Figure 8. Crack network from SCC with the depicted densities of cracks (Sandia, 2007a). The symbol "t" denotes distance between two cracks, and is also the wall thickness.

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Figure 9. Stress analysis with through-wall crack network in top surface view (Structural Integrity Associates, 2002). Dimensions of the plate and setup for the analysis (upper) and longitudinal stress distribution along center with 5.1 cm spacing between cracks (lower), 1 ksi = 6.9 MPa 4.4.2 SNL Model: Mathematical Description Although the model in SNL (2007a) primarily dealt with the seismic case, supporting data for crack behavior were from LWR experiences without seismic impacts. The SCC induced by weld residual stress was also assessed. The contribution from weld residual stress was insignificant in this case because the weld residual stress was mitigated by applying 16

compressive stress as part of the fabrication process. Also, unlike the LWR case, the disposal environment does not have pressure-induced primary stress or severe neutron effects.

At a crack length, a(t), the crack width, w(t), is estimated by the following equation w(t) = C a(t)/E (2) where applied stress (MPa)

E Youngs modulus (MPa)

C geometric constant, which can be statistically sampled value t Time Each crack area is a product of crack length and crack width. The number of cracks is proportional to the sample area divided by a(t)2. The potential maximum opening area of multiple cracks is the product of each crack area and the number of cracks. The density per unit deformed or weld/HAZ area (cm2/cm2) is

= C /E (3)

Equations (2) and (3) apply in the conditions of plane stress and infinite size (conservative assumption). Equation (3) can be used in the system performance assessment with elaboration of the constant term.

4.4.3 Reactor Operational Experience of Crack Pattern In an example of an LWR case, the number and size of surface cracks were reported from welds at the Nine Mile Point Unit 1 main recirculation lines (Xu, et al., 2006). Figure 11 shows cracks at various welds on circumferential locations. Other example crack patterns are in CEA (CEA, 2010), Holston (2010), and Van Dalen et al. (2008), which include parallel cracks and network- type cracks. Figure 12 is a re-plot of the crack area versus crack length. The crack area has an arbitrary unit by multiplying crack width by crack length with arbitrary proportionality value in Equation (3).

The total number from Nine Mile Point surface cracks in welds is comparable with that from Figure 8. Although the number of through-wall cracks may increase with time, the maximum number could be limited due to the stress attenuation between neighboring cracks. However, the dominant area of surface cracks appears to fall in a range of crack size as shown in Figure 10.

The SNL model appears to be partly consistent with the LWR example exercises of surface cracks above with respect to the number of cracks, the most probable dominant crack size in 17

the opening area, and potential crack aspect ratio present for dominant crack sizes. However, only a small fraction of surface cracks penetrated through the wall thickness, with a low probability by observation and prediction (Rudland, et al., 2009). The crack aspect ratio is considered to increase with large surface cracks up to 10 to 150 (Xu, et al., 2006), which is considered also low-probability event.

Figure 10. Area is based on the width formula of Equations (2) and (3) (Ahn, 2016).

Plot is made by a curve-fitting of the data in Xu, et al. (2006).

4.4.4 Application of SNL Model Results of the numerical analysis of crack spacing are not sensitive to Youngs modulus and Poissons ratio, for tested stress on the order of 207 MPa (Structural Integrity Associates, 2002).

An exercise was conducted (Gwo, et al., 2011) for various metals with example parameter values for the various metals. Yield stress is used as an example applied stress. In the probabilistic confinement assessment, the yield stress is one of the sampled values.

Table 2. Materials properties for various metals (Gwo, et al., 2011)

Materials Yield Stress (MPa) E(MPa) x 103 YS/E (mean) x 103 Stainless Steel 170-310 193-207 1.2 18

Carbon Steel 207 207 1.0 Copper 70-310 108-117 1.7 Zircaloy 241 99 2.4 Conversion factor: E denotes Youngs Modulus and YS denotes yield stress Using these values, the potential maximum opening area of multiple cracks was calculated for each metal. For stainless steel, the mean value of potential maximum opening area of multiple cracks per unit weld/HAZ or deformed area is approximately 1.2x10-3 (fraction, cm2/cm2) for 170-310 MPa of applied stress and (193-207)x103 MPa of Youngs modulus. The weld/HAZ area fraction is about 10 10-1 (Ahn, et al., 2013). The fraction of the open area is small.

If the calculation from this method shows fast radionuclide releases without substantial dilution by dispersion, then a more-rigorous approach as used in reactors (e.g., Rudland, et al., 2009; Rudland, et al., 2008; Xu, et al., 2006; Shim, et al., 2011) should be pursued.

5. Summary

• Persistence of passive film is summarized considering finite thickness, chemistry, and impurity effects in the steady state. Unless pitting or crevice corrosion conditions react with high chloride concentrations, passivity conditions should remain, thereby limiting the potential for pitting and crevice corrosion.

• Latent repassivation of crevice corrosion and pitting corrosion is highlighted for performance (or risk) assessment. It considered repassivation in exposed surfaces, crevices and pits.

This latent repassivation contributes to limited initiation and propagation of stable pitting or crevice corrosion. This limitation can be furthered by cathode capacity with limited electrolytes present (e.g., thin film of water).

• An exception of active dissolution without latent repassivation is likely when an anodic region and low pH solution reaches in the crevice of stainless steel. However, such conditions appear in a very narrow range of pH and chloride concentration.

• An approach is presented on abstracting analytic models for stress-corrosion cracking (SCC) damage of canisters to assess the release of radionuclides in performance (or risk) assessment. In addition to fabrication flaws, localized corrosion mainly in pitting form can initiate SCC. An example calculation with field data shows this possibility. However, pits are limited in density and size due to latent repassivation and limited cathodic capacity.

• The propagation rate of single SCC may decrease during propagation, if the local stress intensification factor decreases. The values of environmental and material parameters for SCC could be in narrow ranges. Uncertainties associated with SCC initiation make it difficult to determine quantitative values of damage parameter.

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• For disposal under seismic conditions, the possible potential maximum opening area of multiple cracks is estimated based on the SNL model. From the weld behavior at operating reactor component and the SNL stress analysis, the model appears to be conservative. The SNL model can be used for welds and various metals. The SNL model is considered conservative in regard to maximizing the potential of dispersal of radionuclides if a canister was to fail.

• Based on the above assessment, two formulas to estimate damage by localized corrosion and SCC are presented for system performance assessment on a conservative basis.

Acknowledgments Additional abstracted versions of this paper were presented at the Risk Management Conference of National Association of Corrosion Engineers (NACE) (Ahn, 2013a) and the American Society of Mechanical Engineers (ASME) (Ahn, 2013b) with proceedings to elicit initial expert views. The author also acknowledges the staff of the NRC and the Center for Nuclear Waste Regulatory Analyses of Southwest Research Institute, including Xihua He, Aladar Csontos, Darrell Dunn, Tianqing Cao, and Pavan Shukla for their critical reviews.

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