Investigation of corrosion behavior of 16Mn steel gusset plates in marine alternating dry-wet environments using response surface methodology

Abstract

The harsh marine environment causes the corrosion of gusset plates on offshore platforms, which seriously threatens their safety and lifespan. This study investigates the corrosion behavior of 16Mn steel gusset plates in a marine environment, focusing on the effects of chloride ion concentration, dry-wet ratio, and applied stress. The mathematical model, developed using Response Surface Methodology (RSM) and COMSOL Multiphysics simulations, reveals that chloride ion concentration exerts the greatest influence on the corrosion rate, followed by the dry-wet ratio and applied stress. A significant interaction between chloride ion concentration and dry-wet ratio was observed. The model’s R² value is 0.9961, confirming its accuracy. Corrosion mainly occurs at the right-angled edges and curved edges of the gusset plates. These research findings provide a scientific basis for the anti-corrosion design of marine materials, contributing to ensuring the safety of offshore platforms and extending their service life.

Introduction

The corrosion of metals in marine environments has garnered significant attention from engineers and materials scientists^1,2,3. In particular, in complex structures such as marine exploration platforms, metal components like gusset plates are often positioned at critical connection points (e.g., between columns and decks, buoys, and cross braces)^4,5,6. These components exhibit complex and unpredictable corrosion behaviors in the alternating dry and wet marine environment, which not only compromise the structural integrity and shorten the service life of the platforms but also present significant challenges to the safety and economics of offshore projects^7,8,9,10. Therefore, conducting in-depth research on the corrosion behavior of gusset plates under alternating dry and wet conditions, particularly regarding the influence of multi-factor interactions, is essential for improving the durability and reliability of marine exploration platforms.

Although experimental studies provide a crucial foundation for understanding corrosion behavior, existing research typically lacks systematic mathematical models, which limits the predictability and generalizability of the experimental results. Response Surface Methodology (RSM), a tool that integrates mathematics and statistics, can efficiently analyze and predict the impact of multiple factors on corrosion behavior, thus addressing the shortcomings of traditional experimental approaches^11,12. For instance, Liu et al. employed RSM to examine the effects of chloride concentration, pH, and pressure on pipeline corrosion¹³, while Wang et al. investigated the effects of temperature, pH, and NaCl concentration on alloy corrosion¹⁴. However, comprehensive studies on gusset plate corrosion remain scarce, particularly regarding the quantitative analysis of multi-factor interactions.

Additionally, with advancements in numerical simulation technology, particularly the use of tools such as COMSOL Multiphysics, researchers are now able to simulate the corrosion behavior of metal materials in complex environments through multi-physics coupling¹⁵. These simulations not only accurately predict the corrosion process but also offer theoretical support for corrosion protection design^16,17. Existing studies have shown that COMSOL simulations can reveal the relationship between the corrosion current distribution and the experimental results^18,19.

However, current studies predominantly focus on single-variable or dual-variable analyses, lacking a thorough exploration of the combined effects of multiple factors (such as dry-wet ratio, chloride ion concentration, and stress). This study seeks to address this gap by employing a combined approach of Response Surface Methodology (RSM) and numerical simulation tools (COMSOL) to systematically investigate the influence of these factors on the corrosion behavior of 16Mn steel gusset plates. By developing a mathematical model to predict the corrosion rate (CR) and revealing the interactions among multiple factors, this research provides a theoretical foundation for the corrosion protection design of marine platforms, aiming to enhance their safety, reliability, and to mitigate economic losses due to corrosion.

Results

Results of electrochemical testing experiments

The corrosion current density (i_corr) was calculated using the Tafel extrapolation method, while the CR was determined through the use of Faraday’s law and the dynamic polarisation curves obtained through RSM. The experimental results under varying conditions—specifically, dry-wet ratio, chloride ion concentration, and applied stress—were incorporated into the RSM for modeling and prediction of CR outcomes. Table 1 presents the experimental parameter design matrix used to generate the RSM model interface, along with the corresponding response data. Experiment 3 demonstrated the most significant CR, with a dry-wet ratio of 1:1, a chloride ion concentration of 3 mol/L and an applied stress of 324 MPa. These results are presented in Table 1. In contrast, Experiment 11 demonstrated the lowest CR, with a dry-wet ratio of 2:1, a chloride ion concentration of 1 mol/L, and an applied stress of 421 MPa.

Table 1 Box–Behnken design matrix for the three variables and the response data obtained

Statistical analysis and model construction

The Design Expert software and Response Surface Methodology (RSM) were used to study the influence and interactions of multiple independent variables on the response variable. In this study, a second-order polynomial regression equation was adopted to establish the relationship between the CR and multiple factors, such as chloride ion concentration, dry-wet ratio, and stress. This equation includes linear terms, quadratic terms, and interaction terms, which capture the complex nonlinear relationships among the independent variables. Specifically, the linear terms reflect the direct influence of individual factors on the CR, the quadratic terms account for the nonlinear effects, and the interaction terms reveal the combined effects of multiple factors. Through experimental design and least squares fitting, the influence of different factors on the CR was systematically analyzed, and the experimental conditions were optimized, providing theoretical support for corrosion protection design.

$$\begin{array}{ll}\text{CR}=1.00314-1.48351{\text{X}}_{1}-1.32163{\text{X}}_{2}\text{+}0.0155909{\text{X}}_{3}\text{+}0.1475{\text{X}}_{1}{\text{X}}_{2}\\ \qquad-0.000360825{\text{X}}_{1}{\text{X}}_{3}\text{+}0.00056710{\text{X}}_{2}{\text{X}}_{3}\text{+}0.262917{\text{X}}_{1}^{2}\text{+}0.307917{\text{X}}_{2}^{2}-0.000027{\text{X}}_{3}^{2}\end{array}$$

(1)

The model equation is used to determine the response variable once the model coefficients are calculated. The discrepancies between the model and the experimental data are primarily attributed to residuals caused by random fluctuations in the experimental measurements, rather than issues with model fitting. These residuals serve as an important indicator of model accuracy. The model’s accuracy is validated by the experimental data’s normal distribution with low variance, as shown in the normal probability plot of the residuals in Fig. 1a. Figure 1b illustrates the fluctuation of residuals with the experimental run sequence. The model’s stability and dependability are confirmed by the residuals’ slight oscillations, which imply that the impact of latent variables on the CR may be ignored.

Fig. 1: Residual analysis.

a Residual vs. Probability plot and b Residual vs. Run plot.

Two crucial methods for assessing the accuracy of corrosion prediction models are the coefficient of determination (R²) and ANOVA²⁰. The degree of fit between the predictions and the experimental data is represented by the R² value. A value approaching 1 indicates a higher degree of congruence between the model and the experimental data, confirming the model’s accuracy. Consequently, a polynomial equation can be used to predict the CR under certain conditions. With an R² value of 0.9961, this model accounts for 99.61% of the variation in the expected outcomes. The actual values closely match the predicted ones, further validating the model’s reliability and suggesting that it can accurately forecast experimental results. Figure 2 illustrates the relationship between the experimental data and the predicted outcomes. Equation (1) can be used for additional CR predictions, with prediction errors remaining within an acceptable range.

Fig. 2: The relationship between experimental data and prediction results.

Plot of corrosion rate prediction versus actual value.

F-values and p-values are commonly used in ANOVA to assess the significance of the model²¹. The F-value is calculated by taking the ratio of the model mean square to the error mean square, indicating the extent to which the variability explained by the model is relative to the unexplained variability. A larger F-value suggests that the model is better at explaining the variability of the response variable. The p-value represents the probability of obtaining the observed result under the assumption that the null hypothesis is true. Generally, a smaller p-value indicates a more significant model. In a regression model, a lower p-value and a larger F-value typically indicate a stronger predictive ability, meaning the model is more effective in capturing variations in the data. The analysis of variance also aids in evaluating the goodness of fit of the regression model. For instance, the R² value quantifies the proportion of total variability explained by the model, reflecting its fit. The mean square (MS) measures the contribution of a specific factor to the variation in the response variable. The F-value reveals the significance of the model by comparing the model mean square with the error mean square. Furthermore, the residual row represents the portion of variability in the response that remains unexplained by the model, and the lack of fit test evaluates the consistency between the model’s predictions and the observed values. If the probability of lack of fit exceeds the F-value, it indicates that the model is unreliable and unsuitable for accurate predictions. In the analysis of variance in this study (Table 2), the F-value of the quadratic regression model is 143.40, indicating a minimal error margin (less than 0.01%). The p-value is less than 0.0001, confirming the high significance of this model. Among the three factors affecting the CR, namely the dry-wet ratio ${X}_{1}$, chloride ion concentration ${X}_{2}$, and stress ${X}_{3}$, statistical data show that the chloride ion concentration ${X}_{2}$ has the smallest p-value and the largest F-value, far exceeding the corresponding values of the dry-wet ratio ${X}_{1}$ and stress ${X}_{3}$. This clearly indicates that among these three factors, the chloride ion concentration has the most prominent impact on the CR and is the key factor dominating the change of CR. The impact of the dry-wet ratio ranks second, and the impact of stress on the CR is relatively weak.

Table 2 Examining the fitted quadratic polynomial model using ANOVA

Upon further analysis of the interaction between various factors, the p-value of the interaction ${X}_{1}{X}_{2}$ between the dry-wet ratio and chloride ion concentration is less than 0.05. According to statistical principles, this fully confirms that there is a significant interaction between the dry-wet ratio and chloride ion concentration. This means that in the process of affecting the CR, the dry-wet ratio and chloride ion concentration do not act independently but are related and interact with each other, jointly influencing the change of CR.

Table 3 summarizes the fitting statistics for the CR prediction model. The standard deviation represents the difference between the actual measured response values and the predicted values. The mean is the arithmetic average of the response data points. The Coefficient of Variation (C.V.) is defined as the ratio of the standard deviation to the mean. The R² value indicates the extent to which the variability in the response can be accounted for by the model. The adjusted R² score reflects the degree of variability in the model’s response, taking into account the number of predictor variables and experimental observations, with a range from 0 to 100%. Finally, Leave-One-Out Cross-Validation (LOOCV) was employed to re-evaluate the model performance. The specific settings are as follows: Extract features (dry-wet ratio, sodium chloride concentration (NaCl), stress) and the response variable (CR) from the experimental data, and generate quadratic polynomial features. After initializing LOOCV, each sample was successively used as the test set (with the remaining 14 samples as the training set) for linear regression modeling. Record the predicted values, actual values, and errors (Mean Squared Error (MSE), Mean Absolute Error (MAE)). Ultimately, calculate the average error metrics and the standard deviation of the prediction error, and output the prediction results for each sample to evaluate the generalization performance of the model on small-sample data.

Table 3 Fitting statistics for the corrosion rate model

The empirical model only explains 0.39% of the overall variability, demonstrating a remarkable correlation (R² = 99.61%) between the actual and anticipated response values (Table 3). The corrected R² value of 98.92% indicates that 1.08% of the overall variability in the CR can be attributed to the independent factors. The close alignment between R² and adjusted R² reflects the model’s high reliability^22,23. Furthermore, the signal-to-noise ratio measurement accuracy value of 41.1003 is higher than 4. A high accuracy value indicates that the model possesses a sufficient signal to evaluate the design space. The CR model also exhibits a low standard deviation of 0.0467, demonstrating a strong correlation between the predicted and actual CR responses. MSE = 0.0396: The relatively small mean squared error indicates that the average of the squared differences between the predicted and actual values is low. MAE = 0.1532: The small mean absolute error shows that the absolute values of the prediction errors are within a reasonable range. Standard Deviation = 0.1946: The concentrated error distribution implies a high stability in the model’s predictions.

The influence of dry-wet ratio on CR

The potentiodynamic polarization curves are presented in Fig. 3 for various dry-wet ratios. Additionally, the results in Table 4 indicate that as the dry-wet ratio increases, the i_corr decreases.

Fig. 3: Polarization curves of 16Mn steel.

Dynamic potential polarization curves under different dry-wet ratio conditions.

Table 4 Corrosion current density at different dry-wet ratios

The Design Expert software generates both two-dimensional (2D) and three-dimensional (3D) surface plots, which provide a visual representation of the prediction model equations²⁴. In order to gain insight into the relationships between stress, chloride ion concentration and the dry-wet ratio, it is essential to examine the surface and curve plots of the response functions. Although this study examines the combined effects of three factors, the response plots are unable to demonstrate the impact of one additional variable on the CR of 16Mn steel. In accordance with the specified conditions (a constant stress of 324 MPa), the impact of the dry-wet ratio and chloride ion concentration on the CR is illustrated in the 3D surface and 2D curve plots in Fig. 4 The 2D plot demonstrates that as the dry-wet ratio increases, the CR declines; conversely, an increase in chloride ion concentration results in a gradual increase in the CR. Additionally, the contour lines are elliptical, indicating a strong relationship between chloride ion concentration and dry-wet ratio. The slope showing variations in the dry-wet ratio is less steep, according to further examination of the 3D plot, indicating that the dry-wet ratio has less of an impact on the material’s CR than the concentration of chloride ions.

Fig. 4: Visual analysis of the response surface methodology.

Three-dimensional surface and two-dimensional plot of dry-wet ratio versus chloride ion concentration at constant stress value (324 MPa).

Figure 5 shows the SEM micrographs of the sample surfaces after the removal of corrosion products, with a stress value of 324 MPa, a chloride ion concentration of 1 mol/L, and different dry-wet ratios of (a) 1:1 and (b) 3:1. These images indicate that the degree of corrosion decreases as the dry-wet ratio increases. At a dry-wet ratio of 1:1, Fig. 5a specifically shows large corrosion pits on the sample surface, indicating severe corrosion under these conditions. These findings align with the results observed in the potentiodynamic polarization curve (Fig. 3). In contrast, as shown in Fig. 5b, increasing the dry-wet ratio to 3:1 significantly reduces the extent and area of corrosion. This suggests that increasing the dry-to-wet ratio inhibits corrosion. Additionally, residual NaCl crystals remaining on the sample surface during the drying process may continue to contribute to corrosion by absorbing moisture from the surrounding environment, thereby sustaining the corrosion reaction. Therefore, it is likely that the sample surface did not completely dry during the drying cycle and retained some moisture.

Fig. 5: Scanning electron microscope images of 16Mn steel.

Surface morphology of 16Mn steel at different dry-wet ratios of a 1:1, b 3:1, stress value (324 MPa), and chloride ion concentration of (1 mol/L).

The influence of chloride ion concentration on CR

Figure 6 shows the potentiodynamic polarization curves for different chloride ion concentrations. The results in Table 5 and Fig. 6 demonstrate that the i_corr increases in parallel with the chloride ion concentration from 1 to 3 mol/L. This trend indicates that the corrosion process intensifies as the chloride ion concentration increases. The increased concentration of Cl⁻ ions adsorbed on the surface film layer accelerates anodic polarization, thereby speeding up the corrosion of 16Mn steel²⁵.

Fig. 6: Polarization curves of 16Mn steel.

Dynamic potential polarization curves under different chloride ion concentration conditions.

Table 5 Corrosion current density under different chloride ion concentration conditions

Figure 7 illustrates the influence of stress and chloride ion concentration on the CR of 16Mn steel at a constant dry-wet ratio of 2:1. This is demonstrated using both two-dimensional curve plots and three-dimensional surface plots. As the concentration of chloride ions increases, the two-dimensional plot reveals a corresponding increase in contour density, indicating a gradual climb in CR before a more rapid ascent. Stress, on the other hand, has a pattern of initially rising and then lowering CR. Further analysis of the 3D plot reveals that the changes along the chloride ion concentration axis are more pronounced, with a steeper slope, suggesting that chloride ion concentration has a greater impact on CR than stress.

Fig. 7: Visual analysis of the response surface methodology.

Three-dimensional surface and two-dimensional plot of chloride ion concentration versus stress for a constant dry-wet ratio of (2:1).

Figure 8 shows SEM images of the samples after the corrosion products have been removed. These pictures were acquired using a dry-wet ratio of 2:1, a stress value of 227 MPa, and two distinct chloride ion concentrations (a) 1 mol/L and (b) 3 mol/L. Under the identical test conditions, a comparison clearly reveals that raising the chloride ion concentration speeds up the corrosion process. At a chloride ion concentration of 1 mol/L, the surface exhibits only a few discrete corrosion pits. However, when the concentration of chloride ions is increased to 3 mol/L, the number and size of corrosion pits increase. This behavior is consistent with the polarization curve illustrated in Fig. 6.

Fig. 8: Scanning electron microscope images of 16Mn steel.

Surface morphology of 16Mn steel at different chloride ion concentrations a 1 mol/L, b 3 mol/L, stress value (227 MPa), and dry-wet ratio (2:1).

The effect of stress on CR

Figure 9 presents potentiodynamic polarization curves under varying stress conditions. An analysis of the data from Table 6 and Fig. 9 reveals a decrease in i_corr as the stress increases from the elastic stress of 227 MPa to the plastic strain value of 421 MPa.

Fig. 9: Polarization curves of 16Mn steel.

Dynamic potential polarisation curves for different stress conditions.

Table 6 Corrosion current density under different stress conditions

Under specific conditions (a chloride ion concentration of 2 mol/L), Fig. 10 presents a 2D curve and a 3D surface plot that illustrate how stress and the dry-wet ratio affect the CR. The 2D plot shows that the CR of 16Mn steel varies as it transitions from elastic stress to plastic strain. Specifically, when the elastic stress reaches 227 MPa, the CR begins to rise, peaks near the yield strength of 324 MPa, and then steadily decreases once entering the plastic strain phase. Additionally, as the dry-wet ratio decreases, the CR gradually increases, and the 3D plot shows that the influence of stress on CR is much less significant than that of the dry-wet ratio.

Fig. 10: Visual analysis of the response surface methodology.

Three-dimensional surface and two-dimensional plot of stress versus dry-wet ratio at constant chloride ion concentration (2 mol/L).

Following the elimination of corrosion products, SEM images of corroded surfaces with stress levels of 227 MPa (Fig. 11a) and 421 MPa (Fig. 11b) are displayed in Fig. 11. The images reveal that, under the same experimental conditions, the CR decreases as stress increases. At a stress of 227 MPa (Fig. 11a), the corrosion pits are more extensive and interconnected, whereas at 421 MPa (Fig. 11b), the number of corrosion pits decreases, though they remain distinctly visible. This observation aligns with the trends shown in the polarization curves in Fig. 9.

Fig. 11: Scanning electron microscope images of 16Mn steel.

Surface morphology of 16Mn steel at different stress values a 227 MPa, b 421 MPa, chloride ion concentration (2 mol/L), and dry-wet ratio (3:1).

COMSOL finite element simulation results analysis

Based on the maximum CR conditions identified from the trials (i.e., a dry-wet ratio of 1:1, a chloride ion concentration of 3 mol/L, and a stress of 324 MPa), finite element models were created to further examine the corrosion behavior of gusset plates under complicated maritime environments. The exchange current densities for the anodic and cathodic processes were calculated using the Tafel extrapolation method, employing the polarization curves from Experiment 3, as illustrated in Fig. 12¹⁸. The parameters for electrochemical corrosion that were utilized as starting inputs for the finite element simulations are shown in Table 7.

Fig. 12: Obtaining electrochemical corrosion parameters by Tafel extrapolation method.

Tafel curves of 16Mn steel in simulated solutions and fitting methods.

Table 7 Initial electrochemical parameters of finite element modeling

The simulation results in Fig. 13 offer a detailed description of the stress distribution characteristics of the gusset plate under specific environmental conditions. When external forces are applied to one side of the gusset plate’s right-angle edge, stress concentration occurs at both the right-angle edge and the curved edge. As the stress propagates along the right-angle edge from left to right, the stress level gradually decreases before dropping sharply. In contrast, the stress distribution along the curved edge peaks primarily at the bend and then gradually decreases, illustrating the structural response characteristics of the gusset plate under loading conditions.

Fig. 13: Stress distribution of 16Mn steel gusset plates.

Stress distribution curves at right-angled and curved edges under the condition of maximum corrosion rate. (dry-wet ratio 1:1, chloride ion concentration 3 mol/L, stress value 324 MPa).

Figure 14 presents the simulation results for the corrosion potential distribution of the gusset plate under conditions of a dry-wet ratio of 1:1, chloride ion concentration of 3 mol/L, and stress of 324 MPa. According to the results, the corrosion potential is more negative on the left side of the gusset plate’s right-angle section, initially increasing before stabilizing. In contrast, the corrosion potential at the bend of the gusset plate reaches its lowest value, where it first stabilizes, then decreases, increases, and stabilizes again. In general, the corrosion potential of the gusset plate varies within the range of −0.65 V (SCE), which is consistent with the corrosion potential in the polarization curves measured in the laboratory. This suggests that, although there are variations in corrosion behavior across different regions of the gusset plate, the potential remains within a relatively stable range.

Fig. 14: Corrosion potential distribution of 16Mn steel gusset plates.

Corrosion potential distribution curves at right-angled and curved edges under the condition of maximum corrosion rate (dry-wet ratio 1:1, chloride ion concentration 3 mol/L, stress value 324 MPa).

Figure 15 presents the simulation results for the anodic current density of the gusset plate under conditions of a dry-wet ratio of 1:1, chloride ion concentration of 3 mol/L, and stress of 324 MPa. The i_corr is primarily concentrated on the left side of the right-angle edge, initially decreasing, then slightly increasing, and ultimately stabilizing. The sudden fluctuations in i_corr are strongly correlated with the location of the stress, suggesting that the magnitude of the stress has a significant impact on the variability of i_corr. At the curved edge, the i_corr is mainly concentrated at the bend, where it first stabilizes, then increases, decreases, and stabilizes again. The trends observed in the corrosion potential and stress curves are consistent with those of the i_corr. The i_corr of the gusset plate is generally maintained at 1.45 A/m², and the experimental and numerical simulation findings concur.

Fig. 15: Distribution of corrosion current density of 16Mn steel gusset plates.

Anodic current density distribution curves at the right-angle edge and curve edge under the condition of maximum corrosion rate (dry-wet ratio 1:1, chloride ion concentration 3 mol/L, stress value 324 MPa).

Discussion

Through the Response Surface Methodology (RSM) and COMSOL multi-physics coupling simulations, the corrosion failure mechanism of 16Mn steel gusset plates in marine alternating dry-wet environments was systematically revealed. The combination of experimental results and numerical simulation analysis can further clarify the regulatory mechanism of multi-factor interactions on corrosion behavior and its engineering significance.

In the dry-wet alternating environment, the metal corrosion behavior is dominated by the dynamic electrochemical processes in the wet and dry stages. During the wet stage, a thin liquid film formed on the metal surface dissolves Cl⁻, which destroys the passive film through adsorption and diffusion, triggering local anodic dissolution (Eq. (8)). In the dry stage, the evaporation of the liquid film leads to a non-linear increase in the Cl⁻ concentration. According to the Nernst equation, an increase in the Cl⁻ concentration significantly reduces the equilibrium potential of the anodic reaction (E_e,a), accelerating metal dissolution (Eq. (10)). In addition, high-concentration Cl⁻ reacts with Fe³⁺ in the passive film to form soluble FeOCl (Eq.(2))²⁶, further damaging the protective layer and forming an autocatalytic cycle:

$$\text{F}{\text{e}}^{3+}+\text{C}{\text{l}}^{-}+{\text{OH}}^{-}\to \text{FeOCl}+{\text{H}}^{+}$$

(2)

FeOCl hydrolyzes to form FeOOH and releases C⁻ (Eq. (3)), continuously exacerbating corrosion (Fig. 8b)²⁷.

$$\text{FeOCl}+{\text{OH}}^{-}\to \text{FeOOH}+\text{C}{\text{l}}^{-}$$

(3)

The dry-wet ratio directly affects the cathodic oxygen reduction reaction (Eqs. (9) and (11)) by regulating the liquid-film coverage time and the diffusion rate of oxygen^28,29. Experimental data indicate that a low dry-wet ratio (such as 1:1) prolongs the wetting time, promotes the continuous enrichment of Cl⁻ and the diffusion of oxygen, and forms “corrosion hotspots” (Fig. 6 and Fig. 8b). At this time, the sufficient supply of O₂ enhances the cathodic reaction, and synergistically increases the corrosion current density with the high Cl⁻ concentration. Conversely, a high dry-wet ratio (such as 3:1) reduces the liquid-film coverage due to the longer drying time, hinders oxygen diffusion, decreases the cathodic reaction rate, and thus slows down the CR.

The interaction between Cl⁻ concentration and the dry-wet ratio (p = 0.0015) is manifested as follows: In a high-Cl⁻ environment (3 mol/L), a low dry-wet ratio exacerbates the autocatalytic cycle of corrosion products. During the wet stage, Cl⁻ accumulates in the pores of the corrosion product layer, and in the dry stage, it concentrates to form local high-concentration regions, resulting in a non-linear increase in the CR (Fig. 8)³⁰. The Tafel equation quantifies this mechanism: Cl⁻ reduces the stability of the passive film (increasing the exchange current density i_₀), while the dry-wet ratio changes the over-potential (η) by regulating oxygen diffusion, jointly driving an increase in i_corr.

Dry-wet alternation promotes the periodic rupture and regeneration of the corrosion product layer. Under the condition of a low dry-wet ratio, frequent wetting causes Cl⁻ to accumulate in the pores of the product layer, generating FeOCl which then hydrolyzes to release Cl⁻ (Eqs. (2) and (3)), forming local acidified micro-zones. This process is particularly notable at high Cl⁻ concentrations, leading to the loss of the protective property of the corrosion product layer and accelerating the propagation of pitting corrosion (Fig. 8b).

Stress corrosion is an important failure mechanism in the alternating dry-wet environment. Especially under the influence of chloride ions (Cl⁻), it can significantly accelerate the CR of steel²⁶. Research shows that although stress has a weak direct impact on CR, it can significantly change the local corrosion morphology through the mechano-electrochemical coupling effect. Finite-element simulations indicate that the anodic current density in stress-concentrated areas such as the right-angled corners and curved edges of the gusset plate (Fig. 13) increases significantly (Fig. 15), which is closely related to the internal stress concentration caused by dislocation accumulation during the plastic deformation process. In the elastic stress stage (227 MPa), the “local melting zone” formed due to the hindrance of dislocation movement exacerbates anodic dissolution, which is in line with the Gutman mechanochemical effect model (Eq. (15))³¹. When the stress approaches the yield strength (324 MPa), the synergistic effect of stress concentration and Cl⁻ enrichment makes the CR reach a peak (Fig. 15). After entering the plastic strain stage (421 MPa), dynamic recrystallization can release part of the strain energy. Meanwhile, dislocation rearrangement and the formation of slip systems can slow down the aggravation of corrosion³². The mechanisms include: ① weakening the electrochemical driving force of the Gutman effect through dynamic recrystallization; ② plastic deformation promotes the densification of the corrosion product film to inhibit the penetration of Cl⁻³³. In addition, Ciuplys³⁴ pointed out that changes in dislocation density and arrangement after exceeding the yield strength can alter the corrosion behavior. Different stress states (such as elastic/plastic tension) can also lead to differential corrosion responses by affecting the shape of the anodic polarization curve and the dislocation suppression mechanism (such as the stress-concentration effect described by the elastic continuum model^31,35). Therefore, in engineering practice, it is necessary to focus on optimizing the stress distribution at structural connections to reduce the risk of stress corrosion.

COMSOL simulations further reveal the spatial heterogeneity of gusset-plate corrosion. The stress-concentrated areas at the left end of the right-angled edge and the curved part (Fig. 13) correspond to a more negative corrosion potential (−0.65 V vs. SCE, Fig. 14) and a higher anodic current density (1.45 A/m², Fig. 15). The accumulation of this local corrosion may trigger stress-corrosion cracking, ultimately leading to structural failure. The research findings are in accordance with the multi-physical-field coupling model proposed by Xu et al.¹⁸, validating the significance of the mechano-electrochemical interaction in corrosion prediction under complex environments.

The CR prediction model established in this study (R² = 0.9961) provides a theoretical basis for the anti-corrosion design of materials used in offshore platforms. For extreme working conditions with a high Cl⁻ concentration (>2 mol/L) and a low dry-wet ratio (1:1), it is recommended to apply surface coating or cathodic protection technologies to inhibit Cl⁻ adsorption. Meanwhile, reducing the stress concentration at the edges of the gusset plates through structural optimization (such as arc-transition design) can effectively extend the service life.

Methods

Sample and solution preparation

Large marine platforms commonly utilize 16Mn steel, which is also one of the most widely used steels for gusset plates in offshore exploration platforms^36,37. The 16Mn steel used in this study has the following chemical composition (mass fractions %): C 0.017, Si 1.5, Mo 0.1, P 0.03, Mn 1.55, Cr 0.3, Ni 0.4, Al 0.015, S 0.025, Cu 0.22, V 0.11, and Fe (balance). The tensile test specimens required for the experiments were prepared with a working surface area of 1 cm², and the remaining surfaces were sealed with silicone. Figure 16 shows a schematic of the tensile test specimen. Sandpapers with grit sizes of 80#, 150#, 400#, 800#, 1000#, 1500#, and 2000# were used to polish the electrochemical specimen’s working surface until it was smooth and free of scratches. A polishing paste was then applied to further refine the specimens. After polishing, the specimen surface underwent a series of cleaning steps, starting with deionized water and followed by acetone and anhydrous ethanol. Deionized water was used to remove any residual grease, while acetone and anhydrous ethanol were employed to eliminate surface moisture. Finally, the specimens were air-dried and stored in a drying cabinet for future use.

Fig. 16: Tensile specimens of 16Mn steel.

Tensile specimen dimensions (unit: mm).

In a dry-wet alternating environment, metal surfaces tend to form liquid layers, and as these layers evaporate, the concentration of chloride ions (Cl⁻) may exceed that of seawater. The experiments used NaCl solutions (1, 2, and 3 mol/L) to replicate this environment. Since natural seawater typically has a pH range of 7.8–8.2, 4 wt% acetic acid and 10 wt% sodium hydroxide were added to adjust the pH of the solutions to approximately 8.0 ± 1. All experiments were conducted at ambient temperature (27 °C)³⁸.

Slow strain rate tensile (SSRT) experiment

A slow strain rate test was conducted on 16Mn steel utilizing the LETRY WDML-30 stress corrosion slow tensile testing apparatus. Figure 16 illustrates the methodology employed for the utilisation of bone-shaped tensile specimens with an effective length of 32 mm. The tensile specimens were subjected to a preload of 300 N and maintained at a constant strain rate of 1 × 10⁻⁶ s⁻¹; until failure occurred. The actual stress-strain curve data for 16Mn steel were obtained.

Dry-wet alternating experiment

An experimental setup for tensile testing of 16Mn steel specimens was designed and constructed in this study, as shown in Fig. 17. The experiment utilized a specially designed solution box, through which the specimens were passed via a tensile rod, fixed to the loading frame, and sealed with silicone to ensure a tight connection between the specimen and the solution box. Stress was applied to the specimens through the gear wheel system of a reducer, inducing mechanical responses at different strain stages (80% σs, 100% σs, and 5% PS plastic strain zone), with corresponding stress values of 227 MPa, 324 MPa, and 421 MPa, respectively. The number of rotations required to achieve 5% plastic deformation was calculated based on the device’s reduction rate and pitch, while a force sensor monitored tension fluctuations in real time³⁹. To account for creep effects, the specimens were adjusted every 24 h to maintain the preset stress. To ensure sufficient electrical insulation for electrochemical testing, the tensile specimens were connected to the electrochemical workstation using a three-electrode setup, with reference and auxiliary electrodes placed at the top of the solution box .

Fig. 17: Experimental setup for simulating the marine dry-wet alternating environment.

Experimental setup for dry/wet alternating tests. Note: 1. Peristaltic pump 1; 2. Simulated solution; 3. Peristaltic pump 2; 4. Solution device box; 5. Tensile sample; 6. Reference electrode; 7. Tensile rod; 8. Force sensor; 9. Load frame; 10. Worm gear reducer; 11. Reducer; 12. Electrochemical workstation; 13. Auxiliary electrode.

The dry-wet cycle ratios of 1:1, 2:1, and 3:1 were determined through a process of careful adjustment, whereby the start and stop durations of the peristaltic pump were modified with the intention of imitating the natural dry-wet alternating process observed in marine environments⁴⁰. This process was conducted with consideration of the tropical marine environment of the South China Sea^41,42. Three experimental groups were designed based on drying and wetting times: Group 1 (dry-wet = 1:1) used peristaltic pump number 1 to introduce the simulated solution into the device box, allowing the 16Mn steel sample to soak for 30 min to simulate wet corrosion conditions, followed by draining with peristaltic pump number 2, and allowing the sample to air-dry for 30 min, completing one cycle. In Group 2 (dry-wet = 2:1), the soaking time was reduced to 20 min, while the drying time was extended to 40 min. Group 3 (dry-wet = 3:1) further reduced the soaking time to 15 min, while extending the drying time to 45 min. For the experiment to be stable and continuous, each group went through 72 iterations of the dry-wet alternating procedure. The simulated solution was replaced after 24 cycles to minimize the impact of ambient factors on the trial results⁴³.

Electrochemical testing experiment

The experiment was conducted using a high-precision PARSTAT 2273 electrochemical workstation (AMETEK, USA). In accordance with the conventional three-electrode setup, the platinum electrode served as the auxiliary electrode, the Ag/AgCl electrode as the reference electrode, and the tensile specimen as the working electrode. The experimental procedure involved two main parts: open-circuit potential testing and dynamic potential polarization testing. To stabilize the open-circuit voltage, the test was first run for 3600 s. Subsequently, the dynamic potential polarization test was conducted, whereby dynamic polarization curves were recorded within the potential range of −1.2 V to −0.2 V at a scan rate of 0.6667 mV/s. To minimize errors and dampen fluctuations caused by random factors, three parallel tests were conducted for each trial set. This approach was employed to guarantee the validity, reliability, and reproducibility of the experimental data.

RSM experiment

The effects of combinatorial factors on the response are commonly examined using Box–Behnken Design (BBD). Using Design Expert (version 13), the experimental design was produced.

The response is represented by the following equation⁴⁴:

$$Y=f\left({X}_{1},{X}_{2},\ldots ,{X}_{n}\right)\pm E$$

(4)

Where Y is the response, f is the response function, ${X}_{1},{X}_{2},\ldots ,{X}_{n}$ are the influencing variable factors, n is the number of variables, and where, E is the experimental error. X₁, X₂ and X₃ represent the three experimental variables under investigation: the dry/wet ratio, chloride ion concentration, and stress. In order to establish a correlation between the response and the selected variables, a second-order polynomial regression model was employed¹³:

$$Y={b}_{0}+\mathop{\sum }\limits_{i=1}^{n}{b}_{i}{x}_{i}+\mathop{\sum }\limits_{i=1}^{n}{b}_{{ii}}{x}_{i}^{2}+\mathop{\sum }\limits_{i=1}^{n-1}\mathop{\sum }\limits_{j > i}^{n}{b}_{{ij}}{x}_{i}{x}_{j}+E$$

(5)

Where Y is the experimental result; x_i and x_j are the coded experimental variables; b₀ is a constant; where the linear, quadratic, and interaction parameters are denoted by the letters b_i, b_ii, and b_ij, respectively; where the experimental error is denoted by E.

Although traditional statistical analysis methods are effective, a large number of test combinations are required to determine their effects when analyzing the impacts of multiple variables on the response. The BBD approach of the RSM was employed to develop a quantitative model of the corrosion behavior of 16Mn steel under alternating dry and wet circumstances, with the objective of enhancing efficiency. The main environmental conditions were as follows: X₁ represents the dry/wet ratio (1:1, 2:1, 3:1), X₂ represents the chloride ion concentration (1, 2, and 3 mol/L), and X₃ represents the stress (80% and 100% σ_s stress states and 5% PS plastic strain, with corresponding stress values of 227, 324, and 421 MPa, respectively). The system’s output response determines the CR of 16Mn steel. Table 8 presents the independent variables, experimental ranges, levels, and corresponding coded values of the design model.

Table 8 Experimental levels and variable

To make the computation easier, the variables’ real values were changed to coded values^45,46:

$${x}_{i}=\frac{\left({X}_{i}-{X}_{i}^{* }\right)}{\Delta {X}_{i}}$$

(6)

Variable’s coded value is represented by x_i, its real value is indicated by X_i, its actual value at the center of the experimental field is indicated by ${X}_{i}^{* }$, and its range of variation is denoted by $\Delta {X}_{i}$. In order to define the lowest, middle, and maximum levels for each variable as −1, 0, and 1, respectively, the variables were subjected to a process of coding for the purpose of facilitating statistical computations. In this model, N represents the number of trials, k is the number of factors, and Cp denotes the number of experiments conducted at the center point. The model requires N = 2k(k−1)+C_P experiments. This method exhibits approximate rotational symmetry, as illustrated in Fig. 18 by multiple orthogonal cubes, and incorporates a center point. Compared to first-order models, this design is preferred as it estimates complex response functions with fewer variable combinations and minimizes the occurrence of extreme points. Twelve factorial points and three center points—aimed at preventing singularities and accounting for experimental errors—were utilized in designing the 15 experimental points, with three factors at three levels in this study⁴⁶.

Fig. 18: Cube diagram designed by the response surface method.

Cube diagram of corrosion rate experiments based on dry-wet ratio, chloride ion concentration, and stress factors using Box–Behnken design.

Observation of corrosion morphology

To further examine the corroded samples, the tensile force was gradually released after the experiment, and the samples were then removed. To more comprehensively analyze the corrosion morphology, the central portion of the samples was cut into rectangular pieces measuring one square centimeter. These rectangular pieces were immersed in a rust removal solution and then ultrasonically cleaned for one minute. The samples were subsequently submerged for five minutes in alcohol solutions with varying concentrations (50%, 60%, 70%, 80%, 90%, and 100%). Finally, scanning electron microscopy (SEM; Hitachi SU8010) was used to perform a detailed analysis of the corrosion morphology on the sample surfaces.

COMSOL finite element simulation

Finite-element analysis of 16Mn steel gusset plates was carried out using COMSOL Multiphysics 6.1 software. During the simulation process, the secondary current distribution type (current distribution, shell) was selected to simulate the electrolyte charge transfer phenomenon at the boundary of the thin electrolyte layer under alternating dry-wet conditions. The thickness of the electrolyte layer was set to 0.001 m, and the conductivity of seawater was determined to be 3 S/m. In the established finite-element model, a fixed constraint was applied to the left-hand end of the gusset plate, and an external force load per unit area was applied to its upper end. All regions of the gusset plate were defined as linear elastic-plastic materials. For mesh generation, a physical-field-controlled strategy was adopted, with the element size set to an extremely refined level, applicable to both the current-distribution shell and the solid-mechanics physical field. Statistical data of element types in the model are as follows: 115,587 tetrahedral elements, 8714 triangular elements, 387 edge elements, and 10 vertex elements. Calculation shows that the model has a minimum element quality of 0.1956, an average element quality of 0.665, an element volume ratio of 0.04183, a total mesh volume of 0.05719 m³, and a maximum element growth rate set to 1.3. Ultimately, the model was solved using a steady-state solver to obtain the analysis results. The mesh division and geometric model of the gusset plate are shown in Fig. 19.

Fig. 19: Establishment of the geometric model and mesh generation.

Geometric model and meshing of gusset plate.

The stress-strain curve of 16Mn steel was determined through the utilisation of tensile testing, as illustrated in Fig. 20. Furthermore, the hardening impact upon yielding was approximated using an isotropic hardening model, as shown below⁴⁷:

$${{\rm{\sigma }}}_{{yhard}}={{\rm{\sigma }}}_{\exp }({\varepsilon }_{{eff}})-{{\rm{\sigma }}}_{{ys}}={{\rm{\sigma }}}_{\exp }\left({\varepsilon }_{{p}}+\frac{{{\rm{\sigma }}}_{{e}}}{{E}}\right)-{{\rm{\sigma }}}_{{ys}}$$

(7)

Fig. 20: Obtaining the stress-strain curve from the slow tensile test for stress corrosion of 16Mn steel.

Stress simulation of stress-strain curve of 16Mn steel.

In the equation, $\sigma$_exp represents the mechanical performance curve of the stress-strain of 16Mn steel obtained from tensile testing, $\varepsilon$_eff is the total effective strain, $\sigma$_ys is the yield strength, which is 324 MPa, $\varepsilon$_p is the plastic strain, $\sigma$_e is the von Mises stress, E is the Young’s modulus, which is 210 GPa, and $\sigma$_e/E is the elastic strain. The elastoplastic simulation used the Von Mises yield criterion.

The electrochemical anodic and cathodic process of 16Mn steel in a simulated solution with a pH of 8.0 ± 1 is represented by iron oxidation and oxygen depolarisation.

$$\text{Anodic}\!\!:\text{Fe}\to {\text{Fe}}^{2+}+2{\text{e}}^{-}$$

(8)

$$\text{Cathodic}\!\!:{\text{O}}_{2}+2{\text{H}}_{2}\text{O}+4{\text{e}}^{-}\to 4{\text{OH}}^{-}$$

(9)

This study investigates and simulates the cathodic reduction process of oxygen depolarization, while the anodic reaction is primarily characterized by iron dissolution. The Tafel equation was used to derive the electrochemical kinetic equation for both the cathode and the anode.

The corrosion of the steel was controlled via activation. The following is an explanation of the Nernst equation, which describes the electrode kinetics for both the anodic and cathodic processes¹⁸:

$${{i}}_{{a}}={{i}}_{0,{a}}\exp \left(\frac{{{\rm{\eta }}}_{{a}}}{{{b}}_{{a}}}\right)$$

(10)

$${{i}}_{{c}}={{i}}_{0,{c}}\exp \left(\frac{{{\rm{\eta }}}_{{c}}}{{{b}}_{{c}}}\right)$$

(11)

$${\rm{\eta }}={E}-{{E}}_{{e}}$$

(12)

In the equation, the subscripts a and c refer to the anodic and cathodic reactions, respectively. $E$ represents the electrode potential, ${E}_{e}$ denotes the equilibrium electrode potential, i is the charge transfer current density, i₀ is the exchange current density for the electrochemical reaction, $\eta$ is the overpotential, and b is the Tafel slope.

The equilibrium potentials for oxygen depolarization by the cathodic reaction and steel surface oxidation by the anodic reaction were determined using the Nernst equation⁴⁸:

$${E}_{c,a}={E}_{e,a}^{0}+\frac{2.303{RT}}{{zF}}\log \left[{\text{Fe}}^{2+}\right]={E}_{e,a}^{0}+\frac{0.059\text{V}}{2}\log \left[{\text{Fe}}^{2+}\right]$$

(13)

$${E}_{e,c}={E}_{e,c}^{0}+\frac{2.303{RT}}{{zF}}\log \frac{\frac{P\left({O}_{2}\right)}{{P}^{\theta }}}{{\left[{\text{OH}}^{-}\right]}^{4}}={E}_{e,c}^{0}+\frac{0.059\text{V}}{4}\log \frac{\frac{P\left({O}_{2}\right)}{{P}^{\theta }}}{{\left[{\text{OH}}^{-}\right]}^{4}}$$

(14)

In the equations, ${E}_{e}^{0}$ represents the standard equilibrium potential. The standard equilibrium potentials of the anodic reaction and the cathodic reaction are −0.441 V and 0.401 V, respectively. R is the ideal gas constant (8.314 J/mol K), z is the number of transferred charges, F is Faraday’s constant (F = 96485 C/mol), T is the absolute temperature (T = 298.15 K), and P(O₂) is 21 kPa, while ${P}^{\theta }$ is 100 kPa. The equilibrium potentials for processes (13) and (14) were determined to be −0.861 V and 0.745 V, respectively, assuming a ferrous ion concentration of 10⁻⁶ M and a solution pH of 8⁴⁹.

The influence of elastic-plastic deformation on the equilibrium potential of the anodic reaction was quantified by Gutman^50,51:

$$\varDelta {{E}}_{{e},{a}}^{{s}}=-\frac{\varDelta {P}{{V}}_{{m}}}{{zF}}-\frac{{TR}}{{zF}}{\mathrm{ln}}\left(\frac{\nu \alpha }{{{N}}_{0}}{\varepsilon }_{{p}}+1\right)$$

(15)

In the equation, $\Delta {E}_{{\rm{e}},{\rm{a}}}^{{\rm{s}}}$ represents the change in the equilibrium potential of the anodic reaction, Vm is the molar volume of steel (7.13 × 10⁻⁶ m³/ mol), T is the absolute temperature, $\Delta P$ is the overpressure from elastic deformation, which is one-third of the yield strength of the steel, R is the ideal gas constant, v is the orientation factor (v = 0.45), z is the charge number, $\alpha$ is the coefficient 1.67 × 10¹¹cm⁻², N₀ is the initial dislocation density (1 × 10⁸cm⁻²), and $\varepsilon$_p is the plastic strain calculated through stress simulation in this study. The equilibrium potential after applying force is expressed as follows:

$${{{E}}}_{{e},{{a}}}^{{{s}}}={{E}}_{{{e}},{{a}}}+\varDelta {{{E}}}_{{{e}},{{a}}}^{{{s}}}$$

(16)

Whereas ${E}_{e,a}$ denotes the anodic equilibrium potential at the electrode surface in the absence of any applied force, ${E}_{e,a}^{s}$ in the equation indicates the anodic equilibrium potential following the application of force.

Mechanical deformation lowers the cathodic reaction’s activation energy by increasing the cathodic reaction’s effective area. Consequently, the exchange current density reflects the impact of stress on the cathodic reaction⁵²:

$${i}_{c}={i}_{0,c}\times 1{0}^{\frac{{{\rm{\sigma }}}_{\text{Mises}}{\text{V}}_{\text{m}}}{6\text{F}(-\text{bc})}}$$

(17)

In the equation, i_c stands for the exchange current density of the cathodic reaction of 16Mn steel when stress is applied, i_0,c for the cathodic reaction of 16Mn steel when stress is not applied, b_c is the Tafel slope of the cathodic reaction, and ${\sigma }_{{\rm{Mises}}}$ is the stress value determined by von Mises at the electrode surface as calculated by finite element simulations.

The computational process of multiphysical field coupling simulation can be divided into two stages: the calculation of stress in the gusset plate and the calculation of the electrochemical physical field. These two processes are coupled by the mechanical-electrochemical effects on the surface of the gusset plate⁵³.