Assessment of Critical Conditions for Corrosion Fatigue Crack Initiation Life of Stainless Steel

1 Assessment of Critical Conditions for Corrosion Fatigue Crack Initiation Life of Stainless Steel Won Beom Kim1,* and Hiroshi Yajima2 1 Department of Naval Architecture and Ocean Engineering, Ulsan College, Ulsan, Korea 2Department of Mechanical Engineering, Nagasaki Institute of Applied Science, Nagasaki, Japan Abstract. In this study, corrosion fatigue crack initiation tests were conducted using 13Cr stainless steel in a 3% NaCl aqueous solution to investigate the corrosion fatigue crack initiation life (Nc). For this purpose, the initiation of a crack from a corrosion pit was directly observed. In particular, crevice corrosion conditions were introduced to one specimen to induce the formation of a corrosion pit within a designated observation area. In addition, a model describing corrosion fatigue crack initiation and propagation was proposed. To date, the concept of corrosion fatigue crack initiation life has been ambiguously defined. The key aspect of the proposed model is identifying the point in the corrosion fatigue crack initiation life when the corrosion pit reaches its critical size and transitions into a crack. Since a crack initiating from a pit is generally small, it was regarded as a small crack and evaluated using the intrinsic crack model. When the corrosion pit was considered a small crack, the critical conditions for corrosion fatigue crack initiation were evaluated by comparing the stress intensity factor (ΔK) with the crack length–dependent threshold stress intensity factor, (ΔKth)s. The results of this study indicate that the critical condition for corrosion fatigue crack initiation can be estimated by determining (ΔKth)s through the intrinsic crack model. Based on these findings, the following conclusion was drawn: when no distinct stress concentration point is associated with the corrosion fatigue crack initiation life, the moment when the fatigue crack propagation rate surpasses the corrosion pit growth rate—thereby causing the fatigue crack to initiate from the pit and propagate significantly—can be defined as a reasonable and universal criterion for corrosion fatigue crack initiation life (Nc). Keywords: Corrosion fatigue crack initiation life, Corrosion pit, Crevice corrosion, Pit-to-crack, 13Cr stainless steel 1. Introduction In structural components operating in corrosive environments, corrosion fatigue crack initiation life (Nc) has traditionally been treated ambiguously in cases where no apparent stress concentrators—such as geometric discontinuities or welded joints—are present. Particularly, when fatigue cracks are initiated by stress concentration effects induced by corrosion pits alone, there remain issues to be resolved before a clear and consistent framework for evaluating Nc can be established. Fatigue cracks in corrosive environments tend to initiate earlier than those in atmospheric conditions due to the synergistic effects of corrosion and cyclic loading. Therefore, in order to ensure the structural reliability of steel components and to facilitate more rational fatigue design, it is essential to clearly define a generalized criterion for corrosion fatigue crack initiation life (Nc) . In this regard, many researchers have conducted studies related to crack initiation induced by corrosion pits. To date, the following insights have been established. For martensitic 12–13%Cr stainless steels used in chloride-bearing and CO₂–brine environments, corrosionfatigue (CF) durability is frequently initiation-controlled. Repeated observations identify corrosion pits as dominant crack starters, with passive-film rupture under cyclic strain preceding pit-controlled initiation. Under free-corrosion CO₂/Cl⁻ conditions, localized attack at surface features (e.g., machining marks) promotes the sequence surface state → pit formation → crack nucleation. In high-cycle fatigue, initiation at corrosion defects in solution leads to a marked drop in strength versus air, consistent with in-situ electrochemical evidence of passive-film breakdown during cycling [1–4]. In addition, to isolate pit severity, numerous studies have pre-conditioned pits by controlled exposure or electrochemistry. In austenitic grades (e.g., 304/316), electrochemically induced pits in chloride media reduce the endurance limit, and simple √area approaches can overestimate fatigue limits in the presence of pits. * Correspondence to: [email protected] 16th International Symposium on Practical Design of Ships and Other Floating Structures PRADS 2025 Ann Arbor, MI, USA, October 19th – 23rd 2025 2 In PH-martensitic 17-4PH blade steels, single depth-controlled pits (≈100–250 µm) reduce the endurance limit by ≈45–65%. Once an empirical geometry factor is calibrated, El-Haddad/Kitagawa–Takahashi small-crack frameworks capture the pit effect; near-threshold growth in chloride solutions shows closure-affected behavior with R-ratio sensitivity [5–8]. Furthermore, a central modeling challenge is the pit-to-crack transition and the behavior of short (small) cracks, which may propagate even below the long-crack threshold ΔKth due to size effects, crack-closure, or environmental assistance. Recent short-crack microstructural models explicitly treat pits as micro-notches to quantify S–N knock-downs and transition criteria. Across dilute-to-concentrated chloride conditions in precipitation-hardened (PH) martensitic steels, total life increases mainly through longer initiation life as chloride decreases, whereas longand short-crack propagation shows comparatively weaker chloride dependence. Classic NASA analyses and subsequent reviews frame CF crack-tip kinetics as a superposition of cyclic fatigue and timedependent (chemical/SCC) processes, providing a mechanistic basis for threshold-based assessments when pits are treated as effective small cracks [9–13]. From the above, for 13Cr stainless steels in chloride-bearing media, the foregoing evidence shows CF life is governed primarily by initiation from corrosion defects, with pit geometry (size/acuity), mean stress (R-ratio), and environment ([Cl⁻], potential, temperature, oxygenation) controlling the knock-down relative to air. This motivates a study that (i) treats observed pits as small cracks within an intrinsic-length/threshold framework, (ii) quantifies initiation life against measured pit geometry and environment, and (iii) consistently couples this with nearthreshold crack-growth data (including R-dependence/closure) to deliver service-relevant life prediction for 13Cr. Consistent with this approach, prior work on 13Cr demonstrated an operational definition of Nc by directly linking pit growth to small-crack mechanics: initiation occurs at the instant when the fatigue crack growth rate first overtakes the pit growth rate, marking the onset of genuine crack propagation from a pit. In that work (synthetic seawater, 60 °C, R=0.1, 1.7 Hz), pits were treated as small cracks; the intrinsic crack model (ICM)[14] provided the assessment basis. The measured critical ΔK at initiation lay below the long-crack threshold yet conformed to the ICM trend, and inverse fractography with the Newman–Raju solution reproduced observed crack-length histories—validating both the Nc definition and the ICM-based threshold assessment for 13Cr [15]. The present study adopts this generalized definition of Nc for cracks initiated from small corrosion pits, and examines its validity through experiments in 3% NaCl using 13Cr stainless steel (SUS410J1) coupled with a fracture-mechanics-based analysis incorporating the ICM . In particular, whereas many prior investigations relied on artificial pits for practicality, experiments that generate and follow naturally formed pits under simulated service conditions are rare. To capture the co-evolving corrosion phenomena that accompany pit formation—often missed with artificial pits—this study tracks the entire sequence from pit formation and growth through crack nucleation and early propagation to identify a rational initiation criterion (Nc). To ensure the structural reliability of steel components and to enable more rational fatigue design, it is essential to establish a generalized criterion for corrosion fatigue crack initiation life (Nc). In this study, a generalized definition of Nc is proposed for cracks initiated from small corrosion pits, representing the pit-to-crack transition. The validity and rationality of this definition are examined through both experimental investigation and theoretical analysis. Specifically, corrosion fatigue crack initiation tests were conducted in a 3% NaCl aqueous solution using a 13Cr stainless steel (SUS410J1), and the results were evaluated using a fracture mechanics-based analysis incorporating an intrinsic crack model[14]. 3 2. Proposal for the Assessment of Corrosion Fatigue Crack Initiation Life (Nc) 2.1. Corrosion Fatigue Crack Initiation and Propagation Model The corrosion fatigue crack initiation and propagation model proposed in this study is shown in Figure 1 [15]. In this model, corrosion pits are regarded as precursors to structural failure. The corrosion fatigue crack initiation life (Nc) is defined as the point where a fatigue crack initiates and begins to propagate from the base of a growing corrosion pit, at a rate exceeding the growth rate of the pit. As illustrated in Figure 1, the corrosion fatigue crack initiation and propagation process can be classified into the following distinct stages. ① Corrosion pit initiation/growth. ② Corrosion fatigue crack initiates by the stress concentration of the corrosion pit. ③ Corrosion pit growth speed is faster than the corrosion fatigue crack. ④ Corrosion fatigue crack propagation speed is equal to the corrosion pit growth speed. Fatigue crack propagates in earnest. ⑤ Corrosion fatigue crack propagates. Corrosion fatigue crack propagation speed surpasses corrosion pit growth speed. ⑥ Fracture. Figure 1. Proposed corrosion fatigue crack initiation and propagation model, illustrating six sequential stages from pit formation to final fracture (①–⑥). Detailed descriptions of each stage are provided in Section 2. The point at which fatigue cracks initiate and propagate from the base of growing corrosion pits is defined as the corrosion fatigue crack initiation life (Nc) [15]. In the present study, Nc is specifically defined as the point corresponding to stage ④, as described above. The objective of this study is to verify the validity of the proposed Nc through both experimental investigation and theoretical analysis. A flowchart for predicting corrosion fatigue life based on the proposed model illustrated in Figure 1 is presented in Figure 2. This flowchart outlines the procedure for identifying and evaluating the initiation and growth behavior of corrosion pits, which are influenced by material properties, corrosive environment, and loading conditions. In parallel, the corrosion pit is modeled as a small crack to calculate its stress intensity factor range (ΔK), allowing for the assessment of the critical condition for corrosion fatigue crack initiation. If the calculated ΔK of the corrosion pit is lower than the threshold stress intensity factor range (ΔKth), crack initiation does not occur. Conversely, when ΔK exceeds ΔKth, a corrosion fatigue crack is considered to have initiated and to propagate visibly. The propagation rate of the corrosion fatigue crack originating from the pit is then determined and compared with the pit growth rate. If the pit growth rate exceeds the crack propagation rate, the corrosion fatigue crack is regarded as not yet initiated. Once the definition of Nc, as stated above, is satisfied, the corrosion fatigue crack propagation behavior is evaluated for the interval from Nc to the final fracture life (Nf). The total fatigue life (Nf) is thus determined by combining the evaluation of corrosion pit initiation and growth with that of corrosion fatigue crack initiation and propagation. Furthermore, to determine Nc, the critical pit dimensions must be assessed by applying linear elastic fracture mechanics to small-scale cracks. In this study, an analysis was conducted on these aspects, and the results are presented sequentially in the following sections. 4 Figure 2. Flow chart of corrosion fatigue initiation life prediction. 2.2. Concept of Intrinsic Crack Model Cracks near the corrosion pits or corrosion fatigue crack initiation life (Nc) are very small in size and therefore need to be treated as small cracks. It is well known that conventional fracture mechanics cannot be directly applied to small cracks [16]. In this study, to evaluate the corrosion fatigue crack initiation life (Nc) in a reasonable manner, a simple and practical intrinsic crack model [14] considering the presence of latent crack was introduced. Using this model, the corrosion fatigue crack initiation life (Nc) was evaluated using a fracture mechanics method considering the influence of small cracks. Morita et al. applied this model to (1) round-shaped macro flaws, (2) small flaws, (3) clustered small flaws, and (4) macro cracks. In this study, the intrinsic crack model (ICM) was applied to estimate the corrosion-fatigue crack initiation life. This choice was motivated by the expectation that the ICM would enable a quantitative and unified evaluation of corrosion fatigue over the entire life cycle, from initiation to propagation, across the small and long crack regimes. The concept of the intrinsic crack model is as follows. In conventional linear fracture mechanics, when considering a crack penetrating the outer surface of a semi-infinite plate, the fatigue limit of a cracked plate △σth is determined as follows. ∆ = 1.12∆√ = ∆ from which ∆ = ∆/(1.12√) (1) As shown in Figure 3, the relationship between the fatigue limit △σth of a cracked material, as given in equation (1) and the crack length a is such that △σth becomes infinite as the crack length a approaches zero. However, △σth cannot be greater than the fatigue limit △σw0 of a smooth material. Therefore, to determine the fatigue limit of a defect-free smooth material from a fracture mechanics perspective, it is assumed that material-intrinsic potential cracks exist in both the smooth material and the cracked material, and these are referred to as intrinsic cracks as illustrated in Figure 4. In a cracked material, the crack length is represented as the sum of the actual crack length and the intrinsic crack length. The length of the intrinsic crack, a0, can be expressed using the following equation (2) based on the fatigue limit of the smooth plate and the threshold stress intensity factor range (△Kth). = (1/)[∆/(1.12∆)] (2) where △σw0 is fatigue limit of smooth plate 5 Figure 3. Concept of intrinsic crack length a0 (a) at plane body (b) at cracked body Figure 4. Concept of intrinsic crack length a0 at plane body and at cracked body 3. Corrosion Fatigue Crack Initiation Test To validate the corrosion fatigue crack initiation and propagation model illustrated in Figure 1, fatigue tests were performed in a corrosive environment using a 3% NaCl aqueous solution. The aim of these experiments was to observe and characterize the initiation and growth of corrosion pits, as well as the initiation and propagation of corrosion fatigue cracks. For direct observation of these process, in-situ visual monitoring with a portable microscope was conducted during testing. Additionally, each specimen was examined multiple times using both a stereomicroscope and a metallurgical microscope for more detailed analysis. After final fracture, the fracture surfaces were also observed under a microscope to obtain valuable information relevant to the study objectives. 3.1. Materials, Specimens, and Experimental Methods Although rolled steels, such as those used in large-scale marine structures, are desirable as test materials for corrosion fatigue crack initiation studies, they are expected to undergo general corrosion in a seawater environment [17,18], making the observation and evaluation of corrosion pit and corrosion fatigue crack behavior extremely difficult. In the present study, the aim was to investigate the initiation and growth of corrosion pits, together with the initiation and propagation of corrosion fatigue cracks. For this purpose, a 13Cr-based stainless steel (SUS410J1) was selected, as it can be used in seawater environments without undergoing general corrosion, thereby facilitating the observation of localized pitting. This material has been used for turbine blades, and more recently it has also been considered for applications in marine structures such as risers [3]. The chemical composition and mechanical properties of the material are given in Table 1 and Table 2, respectively. Table 1. Chemical composition of material used C Si Mn P S Ni Cr Mo 0.13 0.32 0.51 0.024 0.002 0.55 11.99 0.36 (wt%) Table 2. Mechanical properties of material used Y.P.(kgf/mm2) T.S.(kgf/mm2) El.(%) R.A.(%) Hv 61.6 75.4 23.8 68.7 223 0.01 0.1 1 10 100 Crack Length a (mm) 0 20 40 60 80 Threshold Stress Range a0 △σW0 LEFM △σth (mm) , , 6 Two specimens were fabricated from the selected material and used for testing. These were designated as Specimen No. 1 and Specimen No. 2, respectively, and their geometries are illustrated in Figure 5. Both specimens were prepared without notch machining and used as smooth specimens. The surfaces of the specimens were finished using #1600 emery paper. Additionally, to facilitate the observation of corrosion pits, the gauge section of each specimen was defined by applying a masking treatment. To prevent fatigue crack initiation from the edges of the specimen and to ensure adequate adhesion of the masking film, the four corners of the parallel section of the specimens were chamfered. The masking was applied in two layers using K.T. Clean AC818T and K.T. Clean AC832T, with each coating applied three times in total along both the longitudinal and transverse directions of the specimens. The masking conditions of Specimen No. 1 and Specimen No. 2 are shown in Figure 6. In addition, for Specimen No. 2, a transparent plastic plate was attached to the observation area to promote crevice corrosion intentionally. Figure 7 illustrates the masking configuration and a schematic representation of the crevice corrosion condition for Specimen No. 2. Figure 5. Shape of corrosion fatigue initiation test specimen. Front view of Specimen No. 1 Figure 6. View of masked Specimens No. 1 and No. 2. Front view of Specimen No. 1 Observing area of Specimen No. 1 Condition of crevice corrosion for Specimen No. 1 7 Figure 7. Crevice corrosion and masking configuration of Specimen No. 2. Table 3. Chemical composition of material used Maximum load No.1 4.7 tonf No.2 3.6 tonf Stress ratio 0.1 Test frequency 1.7 Hz Temperature 60 ℃ Environment 3% NaCl solution A uniaxial, five-link electro-hydraulic fatigue testing machine with a load capacity of 10 tonf was employed for the corrosion fatigue crack initiation tests. The test conditions are summarized in Table 3. The maximum load was set to 4.7 tonf, corresponding to a maximum stress of 59.4 kgf/mm², for Specimen No. 1, and 3.6 tonf (57.0 kgf/mm²) for Specimen No. 2. All tests were conducted under axial tension-compression loading with a stress ratio of 0.1 and a loading frequency of 1.7 Hz. A 3% NaCl aqueous solution was used as the corrosive environment, maintained at a temperature of 60 ℃ and saturated with air through continuous aeration. The solution was replaced with fresh electrolyte once per week. The solution was circulated using the system schematically illustrated in Figure 8. The size of the corrosion solution tank was determined based on the specimen's dimensions and fabricated from acrylic resin plates, allowing easy visual observation with a portable microscope. Additionally, to facilitate rapid observation when direct visual monitoring was impractical, the tank was designed to be detachable at its interface with the specimen. The specimen was also electrically insulated to prevent unintended current flow. To achieve this, the jig was coated with an insulating layer and equipped with a Teflon seat. An insulating gasket was inserted between the jig and the testing machine, and insulating washers were used in the bolted connections. Furthermore, the pin was wrapped in a glass fiber tube, which was coated with grease to enhance insulation. Figure 9 presents the experimental view. Furthermore, for Specimens No. 1 and No. 2, in order to trace the corrosion fatigue crack propagation process, beachmarks were introduced on the fracture surface by applying cyclic loading corresponding to a stress ratio of approximately 0.9. Beachmarks were created through cyclic loading of about 3 × 10³ to 2 × 10⁴ cycles for Specimens No. 1 and No. 2. Figure 8. Corrosion fatigue crack initiation test apparatus. 8 Figure 9. Experimental setup for corrosion fatigue crack initiation test. 3.2. Materials, Specimens, and Experimental Methods The fatigue life (Nf) of Specimen No. 1 and No. 2 was 1.48 × 10⁵ cycles and 1.35 × 10⁶ cycles, respectively. The observation results for Specimen No. 1 and No. 2 are presented as follows. 3.2.1. Observation Results for Specimen No. 1 (without crevice corrosion condition) The observation results of Specimen No. 1 are presented in Table 4 and Figure 10. The detailed observations are described below in the order of the numbering in Table 4. <1> A newly formed corrosion pit was discovered near the site where crevice corrosion had occurred. <2> The corrosion pit continued to grow. <3> It was observed that cracks were propagating from both ends of the corrosion pit. At this stage, beachmarking was performed for the first time by applying cyclic loading of 4.2–4.7 tonf at 10,000 cycles. <4> - <5> The second beachmark was introduced by applying cyclic loading of 4.2–4.7 tonf at 5,000 cycles. <6> - <7> - <8> The specimen fractured. The fracture condition of Specimen No. 1 is shown in Figure 11. On the fracture surface, a corrosion pit with a diameter (surface length 2c) of 0.27 mm and a depth of 0.19 mm was present at the crack initiation site. It was confirmed that the corrosion fatigue crack initiated from this corrosion pit and progressed to final fracture. Table 4. Observation results of Specimen No.1 Observation No. Number of cycles, N(cycles) △N(cycles) c(mm) Remark <1> 105,620 - 0.11 * Corrosion pit <2> 112,640 7,020 0.12 * Corrosion pit <3> 121,820 9,180 0.24 ** Crack begin to propagate, 1st beachmark <4> 127,450 5,630 0.60 ** - <5> 130,200 2,750 1.53 * 2nd beachmark <6> 131,090 890 2.42 * - <7> 131,900 810 2.91 * - <8> 132,990 1,090 3.73 ** Fractured N does not include beachmark period 2c: diameter of corrosion pit/ length of corrosion fatigue crack * : measured by travelling microscope **: measured by measuring microscope 9 <3> Crack after the first beachmark, N=121,820 cycles (Specimen No. 1) <5> Crack after the second beachmark, N=130,200 cycles (Specimen No. 1) Figure 10. Observation results of Specimen No.1. Figure 11. Condition of fracture and fracture surface of Specimen No.1. 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