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Modeling of Cathode Efficiency of Stainless Steel Under Fully Immersed Conditions

^{1}resulting in failure of high-value metallic components in cyclic stress environments. In order to prevent such failure, design engineers use structural integrity analyses that can predict the maximum damage that will be suffered by a component in a given environment. From a localized corrosion standpoint, such analyses would benefit from knowing the pit sizes that can be attained on a metallic surface in a particular environment

^{2,3}. Several studies in this regard have looked at how this damage can be characterized

^{4–9}

^{ }and modeled. These studies consider the metal surface under a thin film of electrolyte, as would be expected under atmospheric conditions. Power laws are used to extrapolate long-term estimates from short-term measurements made from atmospheric exposures

^{8}. In all these studies, a limiting pit size is seen, which implies that there is an upper bound on the pit size for a particular alloy and environment.

More recent work in this respect has rationalized this observation of a maximum pit size using electrochemical fundamentals based on the understanding that the galvanic couple that arises in localized corrosion can be analyzed separately for stability^{10,11}. Following the development of expressions for anodic and cathodic current separately in terms of a length dimension, the conservation of charge was used to combine the system to obtain an estimate of the maximum pit size. Under thin film conditions, the ohmic drop along the cathode that defines the potential gradient across which the current will be supplied to the pit can be simplified to a one-dimensional distribution since the water layer thickness is small compared to the length of the cathode. This concept has been experimentally validated for stainless steel coupons under thin films of ferric chloride^{12} (Fig. 1). For assets that are constantly exposed to bulk corrosive solutions, such as offshore installations as well as naval vessels, modeling that considers conditions in which the metal is fully immersed in the electrolyte is more representative than thin film conditions. As a result, extending maximum pit size estimation methods to full immersion conditions would enhance predictive design of such components. Simplifications of electrolyte geometry cannot be considered in such cases, presenting new challenges which need to be addressed by numerical modeling. This study describes the computation of the maximum current that can be provided by a cathode surrounding a hemispherical pit on a metallic surface under full immersion conditions. Finite element modeling employing kinetics information from cathodic polarization was performed to calculate the potential distribution along the length of the cathode (Fig. 2).

These results were used to generate the maximum cathode current delivery capacity for the system and consequently, an estimate of the maximum pit size attainable on the surface. In addition, exposure studies were conducted using stainless steel samples submerged in ferric chloride solution over different periods of time to evaluate the actual maximum pit size attainable. The results from experimental and modeling runs were compared to determine the upper bound on the pit size under full immersion conditions. The results from these tests can be compared with earlier results from thin film electrolyte experiments and modeling to evaluate the transition between bulk and thin film conditions and its effects on cathode efficiency. Furthermore, the utility of these upper pit size estimates as input data into generalized extreme value (GEV) models^{13–15} for very long-term pitting can also be assessed, experimentally validating such statistical models as well.

**References**

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2. R. H. Jones, *JOM*, **55**, 42–46 (2003).

3. H. Kamoutsi et al., *Corros. Sci.*, **48**, 1209–1224 (2006).

4. T. Yoshii et al., *Nisshin Seiko Giho Nisshin Steel Tech. Rep.*, **59**, 54–67 (1988).

5. I. Muto et al., *Zair.--Kankyo*, **42**, 714–720 (1993).

6. T. Shibata et al., *Zair.--Kankyo*, **44**, 281–286 (1995).

7. M. Nakata et al., *Zair.--Kankyo*, **46**, 559–564 (1997).

8. I. Muto et al., in *Proceedings of the International Symposium on Plant Aging and Life Prediction of Corrodible Structures*, p. 153, NACE, Houston, TX (1997).

9. M. Tochihara et al., *Zair.--Kankyo*, **46**, 572–579 (1997).

10. Z. Y. Chen et al., *J. Electrochem. Soc.*, **155**, C360–C368 (2008).

11. Z. Y. Chen and R. G. Kelly, *J. Electrochem. Soc.*, **157**, C69–C78 (2010).

12. M. T. Woldemedhin et al., *J. Electrochem. Soc.*, **161**, E3216–E3224 (2014).

13. P. J. Laycock et al., *J. Electrochem. Soc.*, **137**, 64–69 (1990).

14. P. A. Scarf et al., *J. Electrochem. Soc.*, **139**, 2621–2627 (1992).

15. P. J. Laycock and P. A. Scarf, *Corros. Sci.*, **35**, 135–145 (1993).