Spatial Localization and Geometric Scaling of Galvanic Corrosion Between 42CrMo Steel and 410 Stainless Steel in Low-Conductivity Yangtze River Freshwater

Abstract

Galvanic corrosion between 42CrMo steel and 410 stainless steel in low-conductivity Yangtze River freshwater was investigated using electrochemical measurements and secondary current distribution modeling. Experimental polarization data were used to establish the electrode kinetics, and the numerical model was calibrated against the measured galvanic current. The effects of cathode-to-anode area ratio (A_c/A_a) and electrode separation (d) were evaluated across 20 geometric configurations. At d = 50 mm, increasing A_c/A_a from 0.5 to 4 increased the total galvanic current from 1.57 × 10⁻⁴ to 4.97 × 10⁻⁴ A and the maximum local anodic current density from 0.078 to 0.270 A m⁻². At A_c/A_a = 1, increasing electrode separation from 10 to 100 mm reduced the total galvanic current by approximately 41%, while the current-localization factor increased. These results demonstrate that electrode geometry governs both the overall galvanic corrosion intensity and the spatial distribution of anodic current. The findings provide a basis for identifying high-risk configurations and optimizing the geometric design of dissimilar-metal connections in hydropower structures.

1. Introduction

Hydraulic and hydropower structures frequently combine low-alloy steels with stainless steels to satisfy mechanical and corrosion-resistance requirements. When these dissimilar metals are electrically connected in water, the less noble metal is anodically polarized and may undergo accelerated dissolution. The resulting galvanic current depends not only on the potential difference between the metals but also on electrode kinetics, electrolyte conductivity, and geometry. Previous studies have shown that current in steel/stainless-steel couples can be strongly nonuniform, so total galvanic current alone does not fully describe local electrochemical loading [1,2,3]. Hydropower equipment experiences transient hydraulic conditions [4].

Cathode-to-anode area ratio and electrode separation are particularly important geometric variables. A larger cathode can support a greater cathodic reaction rate and increase anodic demand, whereas a larger separation lengthens the ionic transport path and increases ohmic loss [3,5]. Most quantitative studies of these effects have been performed in chloride-rich or relatively conductive electrolytes. In natural freshwater, where solution resistance is much higher, geometry can exert a stronger influence on both the magnitude and spatial redistribution of galvanic current. Exposed area ratio has also been examined for a carbon steel/13Cr stainless steel galvanic couple under supercritical CO₂ conditions [6].

Numerical electrochemical modeling provides a direct way to resolve this spatial behavior. Boundary-element and finite-element studies have successfully reproduced potential and current-density fields in dissimilar-metal systems and have shown that material combination and geometric scale can alter local electrochemical response [7,8,9,10]. These approaches complement macroscopic electrochemical measurements by resolving current distributions that are difficult to measure directly. Finite-element analysis has also been applied to trimetallic galvanic coupling under thin electrolyte films [11].

Li et al. [12] previously examined the galvanic corrosion behavior of 42CrMo steel and 410 stainless steel in Yangtze River freshwater using immersion and electrochemical measurements. Their findings established the macroscopic galvanic response of this material pair under freshwater exposure. The present work addresses a different question: how do the cathode-to-anode area ratio and electrode separation redistribute local anodic current on 42CrMo steel? This distinction is particularly relevant in a low-conductivity electrolyte, where electrode kinetics and solution resistance jointly govern the current field [13].

Stainless-steel welded joints have also been studied in simulated reservoir freshwater [14]. Water chemistry influences electrochemical reactions at metallic interfaces. Previous studies of aqueous electrocatalytic reactions and metal recovery from industrial wastewater illustrate the broader significance of metal–solution interactions [15,16]. Investigations of the Three Gorges Reservoir and river-water systems have also documented environmental variability in aquatic conditions [17,18,19].

Experimental studies of dissimilar steel couples have identified the roles of erosion, surface condition, chloride exposure, and cathode-to-anode area ratio in galvanic corrosion [20,21,22,23,24]. These studies establish important comparisons with engineered steel connections, although electrolyte composition and exposure geometry differ from those examined here.

Finite-element simulations of macrocell corrosion have further demonstrated the value of resolving spatial current distributions and electrolyte-resistance effects [25]. Combining established secondary-current-distribution modeling with the 42CrMo/410 freshwater measurements therefore permits comparison of both integrated current and localized anodic loading across systematically varied geometries.

In this study, a finite-element model based on experimentally determined electrode kinetics is used to assess the galvanic interaction between 42CrMo steel and 410 stainless steel in Yangtze River freshwater. Galvanic-current measurements provide baseline calibration, while systematic variations in cathode-to-anode area ratio (A_c/A_a) and electrode separation (d) resolve geometric effects. Total galvanic current (I_gal), maximum local anodic current density (i_max), and a normalized current-localization factor (L_i; defined in Section 2.8) are evaluated as complementary measures of corrosion loading.

The central contribution is to separate overall galvanic loading from spatial current concentration and to show how these two responses evolve differently with geometry. A full A_c/A_a–d parameter matrix is used to map the coupled effects of cathode size and ionic transport distance, while three-dimensional calculations assess finite-size current spreading. This framework extends the previous macroscopic description of the 42CrMo/stainless-steel couple to a spatially resolved evaluation of geometry-controlled galvanic corrosion in low-conductivity freshwater.

2. Experimental and Numerical Methods

2.1. Materials and Yangtze River Freshwater

Commercial 42CrMo low-alloy steel and 410 stainless steel were selected as the anodic and cathodic materials, respectively, to represent the dissimilar-metal combination used in hydropower gate-slot assemblies. The metallic specimens were machined into 50 × 50 × 5 mm plates. Prior to electrochemical and galvanic-corrosion measurements, the exposed surfaces were mechanically ground to remove surface oxides and obtain a reproducible surface condition. The specimens were subsequently cleaned with distilled water and organic solvent and dried before testing. For galvanic measurements, a copper lead was connected to the back surface of each specimen, while all nonworking surfaces were sealed with epoxy resin so that only the designated working surface was exposed to the electrolyte. The nominal exposed working face was 50 × 50 mm for both materials in the baseline galvanic experiment. The chemical compositions of the two steels are summarized in Table 1.

Table 1. Chemical compositions of 42CrMo steel and 410 stainless steel used in this study (wt%).

Element	42CrMo	410 SS
C	0.405	0.031
Si	0.248	0.422
Mn	0.781	0.101
P	0.0152	0.0261
S	0.0030	0.0019
Cr	0.965	12.109
Ni	0.021	0.057
Mo	0.184	<0.01
Cu	0.045	<0.01
Al	0.030	<0.01
Fe	Balance	Balance

Note: Fe is the balance element in both steels. Values listed as <0.01 wt% are below the reporting limit. The C content of 42CrMo (0.405 wt%) is within the 0.38–0.45 wt% range specified in GB/T 3077-2015; the C content of 410 stainless steel (0.031 wt%) is below the 0.15 wt% maximum specified in ASTM A240.

The electrolyte was authentic Yangtze River freshwater collected from the gate environment of the Three Gorges hydropower station. Its measured ionic composition and water-quality properties are reported in Table 2.

Table 2. Major composition and model-relevant properties of the authentic Yangtze River freshwater.

Parameter	Value
Ca2+	48.6 mg L−1
Mg2+	11.8 mg L−1
Cl−	26.9 mg L−1
SO42−	50.1 mg L−1
HCO3−	133 mg L−1
Sulfide	<0.002 mg L−1
Total dissolved solids	243 mg L−1
Total hardness	170 mg L−1
Suspended solids	1.50 mg L−1
Electrical conductivity σ0 (nominal, 25 °C)	0.043 S m−1

For the numerical model, the electrolyte was treated as a homogeneous ohmic conductor. A nominal conductivity of

σ₀ = 0.043 S m⁻¹

was used for the baseline calculation. Conductivity sensitivity was evaluated over 0.5 to 1.5 times σ₀.

2.2. Electrochemical Characterization and Galvanic-Coupling Experiment

Electrochemical measurements were conducted using a conventional three-electrode configuration, with the metallic specimen as the working electrode, a saturated calomel electrode (SCE) as the reference electrode, and a Pt electrode as the counter electrode. A Gamry electrochemical workstation was used for polarization and impedance measurements. In the previous electrochemical experiments, the corrosion potential was monitored before polarization, and potentiodynamic scans were subsequently performed to characterize the anodic and cathodic reaction kinetics.

Galvanic-coupling experiments were performed in a custom electrically insulating rectangular acrylic cell (internal dimensions: 200 × 150 × 150 mm; length × width × height) at 25 ± 1 °C. After the epoxy-encapsulated specimens and insulating fixtures had been placed in the cell, approximately 2.8 L of authentic Three Gorges Yangtze River freshwater was added to establish a liquid height of approximately 100 mm. The nominal electrolyte-domain dimensions at this liquid level were 200 × 150 × 100 mm (length × width × liquid height), consistent with the geometric envelope used in the three-dimensional finite-element model. The nominal baseline electrolyte conductivity was 0.043 S m⁻¹. Commercial 42CrMo steel and 410 stainless steel specimens (50 × 50 × 5 mm) served as the anode and cathode, respectively. Each specimen had a 50 × 50 mm working face; all remaining surfaces and the rear copper-lead connection were sealed with epoxy resin.

The two specimens were held vertically by insulating fixtures near the center of the cell, with their working faces parallel and directly facing one another. Their baseline separation, d = 50 mm, was the normal distance between the exposed working faces; thus, A_c/A_a = 1. A saturated calomel electrode was positioned symmetrically between the specimens for potential measurements. The specimen leads were connected through the zero-resistance ammeter (ZRA) mode of a Gamry electrochemical workstation, permitting continuous monitoring of the galvanic current over 50 days. Three replicate measurements (n = 3) were conducted under the baseline condition.

The measured galvanic current increased during approximately the first 48 h and subsequently decreased as interfacial corrosion products and passive films developed. A representative galvanic current of 0.250 mA (2.50 × 10⁻⁴ A) at 48 h was used for baseline model calibration (A_c/A_a = 1; d = 50 mm). The calibrated kinetic parameter was then held constant in subsequent geometry, conductivity, and three-dimensional calculations.

2.3. Electrochemical Kinetic Parameters

The polarization data of 42CrMo steel obtained from previous experiments were used to determine the electrochemical kinetic parameters. The data obtained at 0 d were selected to represent the initial surface condition of the electrodes.

The anodic and cathodic Tafel branches were independently fitted in terms of

E = a + blog₁₀|I|.

(1)

To minimize the influence of the immediate corrosion-potential region and the highly polarized nonlinear regions, the anodic fitting interval was defined as

E_corr + 0.05 ≤ E ≤ E_corr + 0.30 V,

whereas the cathodic interval was

E_corr − 0.30 ≤ E ≤ E_corr − 0.05 V.

For 42CrMo steel, the resulting anodic and cathodic Tafel slopes were 0.2513 and 0.3476 V dec⁻¹, respectively, with coefficients of determination of R² = 0.961 and 0.947, respectively. The experimentally determined corrosion potential and corrosion current density were used directly in the numerical model:

E_corr,42 = −0.746 V vs. SCE

i_corr,42 = 0.243 A m⁻².

For 410 stainless steel, previous experiments gave

E_corr,410 ≈ −0.480 V vs. SCE

i_corr,410 ≈ 5.0 × 10⁻⁶ A cm⁻² = 0.050 A m⁻²,

and showed a characteristic passive response. The anodic and cathodic Tafel slopes used in the numerical model were

β_a,410 = 0.120 V dec⁻¹

β_c,410 = 0.300 V dec⁻¹.

The influence of the cathodic Tafel slope was evaluated using β_c,410 = 0.24, 0.30, and 0.36 V dec⁻¹. The kinetic parameters used in the baseline calculations are summarized in Table 3.

Table 3. Electrochemical kinetic parameters used in the baseline model.

Material	Ecorr (V vs. SCE)	icorr (A m−2)	βa (V dec−1)	βc (V dec−1)	Origin
42CrMo	−0.746	0.243	0.2513	0.3476	Experimental Ecorr/icorr + Tafel fitting
410 SS	−0.480	0.050	0.120	0.300	Experimental Ecorr/icorr + adopted Tafel slopes

2.4. Numerical Formulation

Galvanic-current distributions were computed using the established Secondary Current Distribution interface in FEniCSx (DOLFINx version 0.8), rather than a newly developed numerical algorithm. The electrolyte was modeled as an electroneutral, homogeneous, isotropic ohmic conductor, without explicitly resolving species-concentration gradients. Under these assumptions, the governing charge-conservation and current-transport relationships follow the conventional secondary-current-distribution formulation [26].

∇⋅i_l = 0,

(2)

with

i_l = −σ∇ϕ_l,

(3)

where i_l is the electrolyte current-density vector, σ is the electrolyte conductivity, and ϕ_l is the electrolyte potential.

The local electrode overpotential was defined as

η = ϕ_s − ϕ_l − E_corr,

(4)

where ϕ_s denotes the metal potential. Because the two electrodes were electrically short-circuited in the galvanic couple, they shared the same metallic potential. A common value of ϕ_s = 0 was therefore used as the electrical reference without affecting the calculated galvanic-current distribution.

For each electrode, anodic and cathodic partial currents were represented using Tafel expressions with positive Tafel-slope magnitudes [27].

$$i=i_{\mathrm{corr}}\left[{10}^{\eta /{\beta }_a}-{10}^{-\eta /{\beta }_c}\right].$$

(5)

For 410 stainless steel, the cathodic branch was multiplied by a kinetic correction factor k_cat,

$$i_{410}=i_{\mathrm{corr},410}\left[{10}^{{\eta }_{410}/{\beta }_{a,410}}-k_{\mathrm{cat}}{10}^{-{\eta }_{410}/{\beta }_{c,410}}\right].$$

(6)

The correction factor k_cat was calibrated using the baseline experimental condition and then held constant in all geometric parameter studies.

2.5. Two-Dimensional Geometric Model and Boundary Conditions

The main calculations were performed using an idealized two-dimensional electrolyte domain to isolate the effects of cathode-to-anode area ratio and electrode separation from other geometric complexities. The 42CrMo anodic boundary had a fixed active length

L_a = 50 mm,

while the active length of the 410 cathode was defined as

$$L_c=\left({\displaystyle \frac{A_c}{A_a}}\right)L_a.$$

(7)

An out-of-plane width of t = 50 mm was assigned so that the baseline L_a = 50 mm configuration represented a 50 × 50 mm anodic surface. The baseline electrode spacing was d = 50 mm. The electrolyte-domain height was initially set to H_dom = 250 mm, with both active boundaries centered within the computational domain. The remaining external boundaries were electrically insulating.

The two-dimensional geometry was used to quantify geometric scaling, while finite electrode-size effects were evaluated separately using three-dimensional calculations.

A free triangular mesh was used in the 2D domain. The electrode boundaries were locally refined using a maximum element size of 1 mm and a minimum element size equal to one-tenth of the maximum size. A maximum growth rate of 1.2 was applied near the active surfaces.

2.6. Baseline Model Calibration

The kinetic correction factor k_cat was calibrated using the baseline condition A_c/A_a = 1 and d = 50 mm. For each trial value, the calculated total galvanic current was compared with the reference experimental value using

εI = |I_gal,sim − I_gal,exp|/I_gal,exp × 100%.

(8)

A parameter sweep over k_cat was conducted between approximately 0.40 and 1.50, with finer sampling around the minimum-error region. The minimum deviation was obtained at

k_cat = 0.625.

The optimized correction factor (k_cat = 0.625) was then fixed in all subsequent studies of cathode-to-anode area ratio, electrode separation, electrolyte conductivity, and three-dimensional geometry. The calibrated baseline current was 0.25155 mA versus the experimental reference of 0.25000 mA (0.62% deviation). This agreement characterizes baseline calibration; mesh convergence and parameter sensitivities were examined separately in Section 2.9.

2.7. Geometric Parameter Studies

Two geometric parameters were systematically investigated. First, the cathode-to-anode area ratio was varied as

A_c/A_a = 0.5, 1, 2, 4,

while maintaining d = 50 mm. Second, the electrode separation was varied as

d = 10, 25, 50, 75, 100 mm,

with A_c/A_a = 1. To resolve the coupled influence of both variables, a full factorial combination of the four area ratios and five separations was subsequently calculated, producing 20 independent geometric configurations (Table 4). These data were used to construct two-dimensional response maps of total galvanic current, maximum local anodic current density, and current-localization factor. All geometric sweeps were performed with the same calibrated kinetic parameters and electrolyte properties so that changes in the predicted electrochemical response resulted exclusively from geometry.

Table 4. Geometric parameters used in the finite-element study.

Parameter	Values
Cathode-to-anode area ratio Ac/Aa	0.5, 1, 2, 4
Electrode separation, d (mm)	10, 25, 50, 75, 100
Baseline experimental condition	Ac/Aa = 1, d = 50 mm
Full factorial design	4 area ratios × 5 separations = 20 configurations

2.8. Quantification of Galvanic Current and Current Localization

The total anodic current was obtained by integrating the normal current density over the 42CrMo surface,

$$I_a={\int }_{A_a}{i}_n\hspace{0.17em}\mathrm{d}A.$$

(9)

The total galvanic current was defined as

I_gal = |I_a|.

(10)

For the 2D model, the boundary integral was multiplied by the out-of-plane width t. The average anodic current density was then calculated from

$$i_{\mathrm{avg}}={\displaystyle \frac{I_{\mathrm{gal}}}{A_a}}.$$

(11)

Because numerical current densities can exhibit endpoint enhancement near electrode/insulator junctions, the maximum local current density was evaluated after excluding a small edge region from both ends of the 42CrMo surface. The baseline cutoff distance was δ_edge = 1 mm. The localization factor was defined as

$$L_i={\displaystyle \frac{i_{\max }}{i_{\mathrm{avg}}}}.$$

(12)

Thus, L_i = 1 corresponds to a spatially uniform anodic current distribution, whereas increasing L_i indicates progressively stronger current localization.

Current conservation was evaluated using

$$R_{\mathrm{bal}}={\displaystyle \frac{\left|I_a+I_c\right|}{0.5\left(\left|I_a\right|+\left|I_c\right|\right)}}\times 100\%.$$

(13)

In addition, the mean electrolyte potentials adjacent to the anodic and cathodic surfaces, ${\bar{\varphi }}_A$ and ${\bar{\varphi }}_C$, were evaluated to determine the effective ohmic potential drop,

$$\mathit{\Delta }{\varphi }_{\Omega }=\left|{\bar{\varphi }}_A-{\bar{\varphi }}_C\right|,$$

(14)

and the corresponding effective electrolyte resistance,

$$R_{\mathrm{eff}}={\displaystyle \frac{\mathit{\Delta }{\varphi }_{\Omega }}{I_{\mathrm{gal}}}}.$$

(15)

These quantities were used to interpret the influence of electrode separation in terms of electrolyte ohmic resistance rather than geometry alone.

2.9. Numerical Sensitivity and Convergence Analysis

Numerical and electrochemical sensitivity analyses were performed. Mesh convergence was examined by varying the maximum element size at the electrode surfaces between 2, 1, 0.5, and 0.25 mm. The influence of the endpoint exclusion distance was examined using δ_edge = 0.5, 1, 2, and 3 mm. The computational-domain height was varied between 250 and 400 mm to assess boundary-size effects.

Electrolyte conductivity was varied using

σ = (0.5, 0.75, 1, 1.25, 1.5)σ₀.

A common Tafel-slope scaling factor of 0.8, 1.0, and 1.2 was applied to evaluate sensitivity to the polarization parameters. The cathodic Tafel slope of 410 stainless steel was independently varied over β_c,410 = 0.24, 0.30, and 0.36 V dec⁻¹. Numerical convergence was evaluated from the stability of I_gal and i_avg, whereas i_max and L_i were tracked separately because local extrema are more sensitive to spatial discretization and electrode-edge treatment.

Detailed mesh-refinement, computational-domain-height, endpoint-exclusion, and nonlinear-solver checks are provided in the Supporting Information (Figures S1–S4 and Tables S1–S7). The total galvanic current varied by only 0.01100% between electrode-boundary mesh sizes of 0.5 and 0.25 mm and by 0.01341% between domain heights of 250 and 400 mm in the tested area-ratio-4 configuration. In contrast, the core peak anodic current density and the current-localization factor were more sensitive to numerical settings: the peak differed by 4.4531% between the 1 and 0.25 mm meshes, and by 12.0186% between domain heights of 350 and 400 mm when referenced to the 400 mm result. These checks support stability of the integrated current within the tested conditions, but do not establish full domain independence of the local peak or localization factor.

2.10. Three-Dimensional Finite-Size Assessment

Supplementary three-dimensional simulations were performed to evaluate finite electrode dimensions. The 3D electrolyte domain had dimensions 200 × 150 × 100 mm. For the baseline case, both the 42CrMo and 410 electrode surfaces were 50 × 50 mm with a normal separation of 50 mm between facing working surfaces. A second model was constructed for A_c/A_a = 4 using a 50 × 50 mm 42CrMo anode and a 100 × 100 mm 410 cathode, again with a nominal 50 mm separation.

The same electrochemical parameters k_cat = 0.625, and σ = 0.043 S m⁻¹ were retained without additional fitting. Free tetrahedral elements were used, with local refinement to 0.5–2 mm near the active electrode surfaces.

The three-dimensional calculations were used to quantify finite-width current spreading and edge effects. Total galvanic currents were compared with the corresponding two-dimensional results, and changes at large A_c/A_a were analyzed in terms of three-dimensional current spreading.

3. Results and Discussion

3.1. Electrochemical Parameters and Baseline Model Calibration

The electrochemical boundary conditions were obtained from previous polarization experiments. For 42CrMo steel, the 0 d data were used to represent the initial electrode condition. The measured corrosion potential and corrosion current density were used directly, while the anodic and cathodic branches were fitted over +50 to +300 mV and −300 to −50 mV relative to E_corr. The resulting Tafel slopes were 0.2513 and 0.3476 V dec⁻¹, with R² values of 0.961 and 0.947, respectively (Figure 1a).

Figure 1. Electrochemical boundary conditions and baseline calibration of the galvanic-corrosion model. (a) Tafel fitting of the anodic and cathodic polarization branches of 42CrMo steel at the initial exposure condition (0 d). (b) Experimental evolution of galvanic current for the 42CrMo/410 stainless-steel couple; the dotted line indicates the current used for baseline model calibration. (c) Dependence of the simulated galvanic current on the cathodic kinetic correction factor k_cat for 410 stainless steel. (d) Comparison of the experimental reference current with the simulated baseline current before and after calibration.

For 410 stainless steel, the experimentally obtained corrosion potential and corrosion current density were combined with baseline anodic and cathodic Tafel slopes of 0.120 and 0.300 V dec⁻¹, respectively. These parameters, together with the 42CrMo kinetics, defined the electrode boundary conditions used in the galvanic model.

Figure 1b shows the galvanic-current history for the baseline couple (A_c/A_a = 1, d = 50 mm). The current increased during approximately the first 48 h and then decreased as the electrode surfaces evolved. A representative current of 0.250 mA was selected for steady-state baseline calibration.

With k_cat = 1, the calculated current was 0.3190 mA. A cathodic kinetic correction factor k_cat was therefore introduced for 410 stainless steel and calibrated to the baseline experiment.

As illustrated in Figure 1c, the simulated galvanic current decreased systematically with decreasing cathodic kinetic activity. A parameter sweep identified

k_cat = 0.625

as the value that best reproduced the selected baseline reference. At this value, the calculated galvanic current was

I_gal,cal = 2.5155 × 10⁻⁴ A

compared with

I_gal,ref = 2.5000 × 10⁻⁴ A.

The calibrated model reproduced the reference current with a deviation of 0.62% (Figure 1d). The resulting k_cat was then held constant in all subsequent simulations, so the effects reported below arise from changes in geometry, electrolyte conductivity, or model dimensionality rather than repeated fitting.

The calibrated baseline was used as the reference state for the geometric analyses. The influence of the 410 stainless-steel cathodic Tafel slope (0.24–0.36 V dec⁻¹) is examined separately in Section 3.6.

3.2. Spatial Distribution of Galvanic Potential and Current Density Under the Baseline Geometry

The baseline geometry (A_c/A_a = 1, d = 50 mm) was first used to establish the spatial reference state. The calibrated model predicted a total galvanic current of

I_gal = 2.516 × 10⁻⁴A

corresponding to an average anodic current density on the 42CrMo surface of

i_avg = 0.1006 Am⁻²

Because the two electrodes had equal exposed dimensions, this configuration isolates the intrinsic spatial redistribution of galvanic current before area asymmetry or spacing changes are introduced.

Figure 2a shows the electrolyte-potential distribution between the coupled 42CrMo steel and 410 stainless steel. The mean electrolyte potentials adjacent to the anodic and cathodic surfaces were approximately 0.721 and 0.636 V, respectively. Their difference corresponds to an effective ohmic drop of about 0.0853 V and, with the calculated galvanic current, an effective electrolyte resistance of approximately 339 Ω. The strongest potential variation occurred between the facing electrode surfaces, indicating the importance of solution resistance in low-conductivity freshwater.

Figure 2. Spatial distribution of galvanic potential and current density for the baseline 42CrMo/410 stainless-steel couple (A_c/A_a = 1, d = 50 mm). (a) Electrolyte-potential distribution. (b) Magnitude of the electrolyte current-density field. (c) Current streamlines illustrating the principal ionic-current transport pathways between the coupled electrodes. (d) Local anodic current-density profile along the 42CrMo surface, showing edge-enhanced current localization.

The current-density contours and streamlines (Figure 2b,c) show that current is concentrated in the region directly connecting the active surfaces and is further enhanced near the electrode ends. The pattern reflects the combined effects of short ionic transport paths and current-line convergence, demonstrating that galvanic current is redistributed spatially even when the anodic and cathodic areas are equal. Similar geometry-controlled current focusing has been reported for dissimilar-metal couples, where area ratio, separation distance, and edge geometry altered local current-density distributions [28,29].

The local anodic-current-density profile along 42CrMo (Figure 2d) was approximately symmetric and U-shaped, with current increasing toward both electrode ends. After excluding a 1 mm region at each electrode/insulator junction to avoid numerical endpoint singularities, the maximum core anodic current density was 0.1272 A m⁻², approximately 26% higher than the area-averaged value. The corresponding localization factor was L_i = 1.264.

The profile demonstrates why integrated galvanic current and localized anodic loading should be distinguished: even an equal-area couple develops significant edge-enhanced current concentration. This spatial interpretation is consistent with local-probe and numerical studies of galvanic-current distributions [30,31].

3.3. Effect of Cathode-to-Anode Area Ratio on Galvanic Current and Localization

The cathode-to-anode area ratio is one of the most important geometric factors governing galvanic corrosion because it directly controls the amount of cathodic reaction area available to sustain anodic dissolution. To isolate this effect, the electrode separation was fixed at d = 50 mm while the cathode-to-anode area ratio was varied as

$${\displaystyle \frac{A_{\mathrm{c}}}{A_{\mathrm{a}}}}=0.5,1,2,4$$

The anodic area of 42CrMo was kept constant, whereas the exposed 410 stainless-steel cathode area was systematically increased. All electrochemical parameters, electrolyte properties, and the calibrated cathodic kinetic correction factor were maintained unchanged.

As shown in Figure 3a, the total galvanic current increased monotonically with increasing cathode-to-anode area ratio. When the area ratio increased from 0.5 to 4, the calculated galvanic current rose from

I_gal = 1.568 × 10⁻⁴ A

to

I_gal = 4.971 × 10⁻⁴ A

corresponding to an increase of approximately 217%. The response was nonlinear: increasing A_c/A_a from 1 to 2 raised I_gal from 2.516 × 10⁻⁴ to 3.813 × 10⁻⁴ A, whereas the relative increase became smaller when A_c/A_a was further raised to 4. The added cathodic area therefore increased the galvanic current but with diminishing gain as electrolyte resistance and electrode polarization became increasingly important. The nonlinear increase with cathodic area is consistent with experimental and numerical studies showing that area ratio amplifies anodic demand, while polarization and transport resistances can cause departures from simple proportional scaling [32,33,34,35].

Figure 3. Effect of cathode-to-anode area ratio on the galvanic response of the 42CrMo/410 stainless-steel couple at a fixed electrode separation of d = 50 mm. (a) Total galvanic current as a function of A_c/A_a. (b) Average anodic current density and maximum core anodic current density on the 42CrMo surface. (c) Current-localization factor L_i. (d) Effective ohmic potential drop and effective electrolyte resistance as functions of cathode-to-anode area ratio.

Because the 42CrMo anodic area remained constant throughout the area-ratio sweep, the change in total galvanic current was directly reflected in the average anodic current density. As shown in Figure 3b, i_avg increased from 0.0627 A m⁻² at A_c/A_a = 0.5 to 0.1988 A m⁻² at A_c/A_a = 4, representing the same approximately 3.17-fold increase as the total current. The maximum core anodic current density increased even more strongly, from

i_max = 0.0780 Am⁻²

to

i_max = 0.2698 Am⁻²

equivalent to an increase of approximately 246%. Thus, i_max increased more strongly than the total or average anodic current as the cathode became larger.

The stronger increase in i_max relative to i_avg resulted in a systematic increase in the current-localization factor, as shown in Figure 3c. Specifically,

L_i = 1.243, 1.264, 1.310, 1.357

For A_c/A_a = 0.5, 1, 2, and 4, L_i increased from 1.243 to 1.357. The area-ratio effect therefore had two simultaneous components: a strong increase in overall anodic loading and a smaller but systematic increase in spatial concentration. This distinction is central to the present analysis because a larger cathode changes not only how much current flows, but also where that current is concentrated on the 42CrMo surface.

The nonlinear current increase is consistent with the solution response in Figure 3d. As A_c/A_a increased from 0.5 to 4, the effective resistance decreased from about 430 to 270 Ω because the larger cathode broadened the current-transfer region, while the ohmic potential drop increased from about 0.0674 to 0.1343 V as the total ionic current rose. The combined behavior explains why cathode enlargement produces a progressively weaker increment in I_gal at high A_c/A_a. Comparable area-ratio effects and geometry-dependent current redistribution have been reported across several galvanic systems [28,32,33,34,35].

Overall, increasing A_c/A_a intensified both global galvanic loading and local current concentration. This dual effect is particularly relevant when a relatively small exposed low-alloy-steel region is electrically connected to a much larger stainless-steel component.

3.4. Effect of Electrode Separation on Galvanic Current and Ohmic Transport

Electrode separation provides a second geometric control parameter for the galvanic interaction between 42CrMo steel and 410 stainless steel. In contrast to the cathode-to-anode area ratio, which primarily modifies the available cathodic reaction area, changing the electrode separation directly alters the ionic transport distance through the low-conductivity freshwater electrolyte. To isolate this effect, A_c/A_a was fixed at 1, while the separation distance was varied as

d = 10, 25, 50, 75, 100 mm

All electrochemical kinetic parameters, electrolyte properties, and the calibrated value of k_cat = 0.625 were kept unchanged.

As shown in Figure 4a, increasing the electrode separation produced a pronounced decrease in the total galvanic current. At d = 10 mm,

I_gal = 3.582 × 10⁻⁴ A

whereas at d = 100 mm it decreased to

I_gal = 2.113 × 10⁻⁴ A

Figure 4. Effect of electrode separation on the galvanic response of the 42CrMo/410 stainless-steel couple at a fixed cathode-to-anode area ratio of A_c/A_a = 1. (a) Total galvanic current as a function of electrode separation. (b) Average and maximum core anodic current densities on the 42CrMo surface. (c) Current-localization factor L_i. (d) Effective electrolyte ohmic potential drop and effective electrolyte resistance as functions of electrode separation.

This corresponds to an overall reduction of approximately 41.0%. Because the exposed area of the 42CrMo anode remained constant, the average anodic current density showed the same trend, decreasing from 0.1433 to 0.0845 A m⁻². Thus, increasing the physical separation between the coupled metals effectively reduces the overall anodic electrochemical load imposed on 42CrMo.

The decrease in I_gal is controlled by the solution-phase resistance. R_eff increased from approximately 87.5 Ω at d = 10 mm to 518.2 Ω at d = 100 mm, while the ohmic potential drop rose from 0.0314 to 0.1095 V (Figure 4d). Increasing separation therefore lengthened the ionic current path and dissipated a larger fraction of the electrochemical driving force within the electrolyte. Related spacer, separation-distance, and thin-electrolyte studies similarly show that increasing the ionic transport path suppresses galvanic current through greater solution-phase resistance [36,37,38].

This spacing effect can be summarized as

d↑ ⇒R_eff↑ ⇒ Δφ_Ω↑ ⇒I_gal↓

Electrode separation therefore acts as an ionic-transport variable in low-conductivity freshwater, with the effective resistance and current magnitude changing together.

The maximum core anodic current density also decreased, from 0.1518 A m⁻² at d = 10 mm to 0.1108 A m⁻² at d = 100 mm. Thus, both the average and maximum absolute anodic current densities were reduced as the electrodes were separated.

However, the relative spatial nonuniformity of the anodic current showed the opposite tendency. As presented in Figure 4c, the current-localization factor increased systematically from

L_i = 1.060

at d = 10 mm to

L_i = 1.311

At the same time, L_i increased from 1.060 to 1.311, an increase of approximately 23.7%. The spacing effect therefore differs fundamentally from the area-ratio effect: increasing d decreases both I_gal and i_max, but increases the relative nonuniformity of the remaining current distribution.

This contrast is a second key result of the study. A lower absolute galvanic load does not necessarily correspond to a more uniform anodic current distribution. At larger separation, the current field spreads through a greater electrolyte volume, so some regions of the 42CrMo surface retain a larger fraction of the reduced total current. Accordingly, both absolute local current and normalized localization are needed to describe the geometric effect.

d↑ ⇒I_gal↓,i_max↓, but L_i↑

3.5. Coupled Geometric Control of Galvanic Current and Current Localization

The opposite one-dimensional trends in Section 3.3 and Section 3.4 indicate that area ratio and separation must be considered together. A full factorial matrix combining

A_c/A_a = 0.5, 1, 2, 4

with

d = 10, 25, 50, 75, 100 mm

was evaluated, giving 20 geometric configurations. The resulting response maps (Figure 5) directly compare how cathode size and ionic transport distance jointly control I_gal, i_max, and L_i.

Figure 5. Coupled effects of cathode-to-anode area ratio and electrode separation on the galvanic response of the 42CrMo/410 stainless-steel couple. (a) Response map of total galvanic current I_gal. (b) Response map of maximum core anodic current density i_max on the 42CrMo surface. (c) Response map of the current-localization factor L_i. The maps were constructed from 20 numerical configurations combining A_c/A_a = 0.5, 1, 2, and 4 with d = 10, 25, 50, 75, and 100 mm.

Figure 5a reveals a clear coupled dependence of the total galvanic current on both geometric variables. The largest galvanic current occurred at the combination of the largest cathode-to-anode area ratio and the shortest electrode separation,

A_c/A_a = 4,d = 10 mm

for which

I_gal = 5.476 × 10⁻⁴ A

In contrast, the smallest current was obtained for

A_c/A_a = 0.5,d = 100 mm

with

I_gal = 1.380 × 10⁻⁴ A

Across the matrix, I_gal varied by nearly a factor of four, showing that geometry alone can strongly alter the electrochemical load on 42CrMo even when material and electrolyte properties are unchanged.

More importantly, the two geometric variables interacted rather than contributing independently. At A_c/A_a = 1, increasing d from 10 to 100 mm reduced I_gal from 3.582 × 10⁻⁴ to 2.113 × 10⁻⁴ A (about 41%), whereas at A_c/A_a = 4 the same spacing change reduced the current from 5.476 × 10⁻⁴ to 4.139 × 10⁻⁴ A (about 24%). A larger cathode therefore weakened the suppressive effect of increasing separation, so the galvanic response is better represented as

I_gal = F(A_c/A_a,d)

rather than as the simple sum of two independent one-dimensional contributions.

A similar coupled pattern is evident in the maximum core anodic current density shown in Figure 5b. The highest value,

i_max = 0.322 Am⁻²

again occurred at A_c/A_a = 4 and d = 10 mm, whereas the minimum value,

i_max = 0.0719 Am⁻²

was obtained at A_c/A_a = 0.5 and d = 100 mm. The high-I_gal and high-i_max regions largely coincided, indicating that the geometry producing the greatest global galvanic load also produced the greatest absolute local anodic loading.

However, the response of the current-localization factor is more complex. As shown in Figure 5c, L_i does not vary monotonically with either geometric parameter over the entire design space. The maximum localization factor

L_i = 1.470

was obtained at A_c/A_a = 4 and d = 10 mm, whereas the minimum value,

L_i = 1.060

occurred at A_c/A_a = 1 and d = 10 mm. Unlike I_gal and i_max, L_i showed a nonmonotonic response across the design space: at A_c/A_a = 1 it increased from 1.060 to 1.311 as d increased from 10 to 100 mm, whereas at A_c/A_a = 4 it decreased from 1.470 to 1.344. Relative localization is therefore controlled by the interaction among current spreading, electrode size, and solution resistance rather than by either geometric parameter alone. Configuration-dependent interactions in multimetal systems have likewise been shown to redistribute potential and current density in ways that cannot be inferred from a single geometric parameter [39].

The coupled matrix shows that I_gal, i_max, and L_i are complementary rather than interchangeable descriptors: total galvanic current quantifies global anodic demand, maximum local current density indicates the highest absolute local loading, and the localization factor defined in Section 2.8 quantifies relative spatial nonuniformity. Their different responses explain why a geometry with lower total current can still exhibit relatively strong localization, and why total current alone cannot capture the spatial character of galvanic attack.

The response maps further show that the combination

A_c/A_a↑,d↓

defines the region of highest absolute galvanic risk. In this regime, a large cathodic surface supplies substantial cathodic reaction capacity while the short electrolyte path minimizes ohmic losses, leading simultaneously to high I_gal and high i_max. Conversely,

A_c/A_a↓,d↑

produces the lowest absolute galvanic loading because the smaller cathode limits cathodic reaction capacity and the larger separation increases ionic transport resistance.

From an engineering perspective, lower A_c/A_a and larger d both reduce the absolute electrochemical load, but their effectiveness depends on the coupled configuration; at high A_c/A_a, increasing separation provides a smaller reduction in current because the larger cathodic area sustains galvanic reaction despite the longer transport path. Recent secondary-current-distribution simulations of dissimilar-metal joints also demonstrate that insulation distance and geometric configuration can serve as practical variables for controlling galvanic current [40].

3.6. Parameter Sensitivity and Three-Dimensional Finite-Size Effects

Parameter sensitivity and three-dimensional calculations were used to determine which conclusions are controlled by electrochemical inputs and which are controlled by geometry.

The conductivity of the freshwater electrolyte had a pronounced influence on the magnitude of the galvanic current. As shown in Figure 6a, the conductivity was varied from 0.5 to 1.5 times the baseline value,

σ₀ = 0.043 S m⁻¹

and the total galvanic current increased from 1.864 × 10⁻⁴ to 2.881 × 10⁻⁴ A. This increase was accompanied by a decrease in the effective electrolyte resistance from approximately 674 to 227 Ω. The conductivity dependence can therefore be summarized as

σ ↑ ⇒ R_eff ↓ ⇒ I_gal ↑

Figure 6. Parameter sensitivity and three-dimensional finite-size effects for the 42CrMo/410 stainless-steel galvanic model. (a) Effect of normalized electrolyte conductivity σ/σ₀ on the total galvanic current I_gal. (b) Effect of normalized electrolyte conductivity on the current-localization factor L_i and effective electrolyte resistance R_eff. (c) Sensitivity of total galvanic current I_gal and maximum core anodic current density i_max to the cathodic Tafel slope of 410 stainless steel. (d) Comparison of total galvanic current predicted by the 2D and 3D models for A_c/A_a = 1 and 4 at d = 50 mm; the corresponding localization factors are indicated for comparison.

Thus, conductivity primarily controls the absolute current scale through electrolyte resistance. Similar sensitivity of galvanic response to electrolyte transport properties has been reported in validated finite-element studies [35,38].

L_i changed in the opposite direction, decreasing from 1.388 to 1.201 as conductivity increased from 0.5σ₀ to 1.5σ₀. Higher conductivity therefore increased total current but promoted broader current spreading, again separating current magnitude from normalized localization.

The influence of the 410 stainless-steel cathodic Tafel slope was examined by varying its magnitude over:

|β_c,410| = 0.24, 0.30, and 0.36 V dec⁻¹

The corresponding total galvanic currents were 2.891 × 10⁻⁴, 2.516 × 10⁻⁴, and 2.234 × 10⁻⁴ A, respectively. In contrast, the localization factor remained nearly unchanged:

L_i = 1.267, 1.264, 1.262

for the three cathodic Tafel slopes, respectively. The cathodic kinetic parameter therefore changed the absolute current magnitude much more strongly than the normalized spatial distribution.

Mesh refinement from 2 to 0.25 mm changed I_gal by less than 0.1%, whereas L_i changed from approximately 1.25 to 1.32. Endpoint-cutoff variation showed the same pattern: integrated current was stable, while maximum-based localization metrics were more sensitive.

The influence of dimensional representation was finally examined by comparing the simplified 2D model with finite-size 3D calculations. For the baseline geometry,

A_c/A_a = 1, d = 50 mm

the 2D model predicted

I_gal,2D = 2.516 × 10⁻⁴ A

whereas the corresponding 3D model gave

I_gal,3D = 2.332 × 10⁻⁴ A

The relative difference was approximately 7.86% (Figure 6d), indicating similar global current levels for the baseline geometry.

At A_c/A_a = 4, the 2D and 3D currents were 4.971 × 10⁻⁴ and 4.165 × 10⁻⁴ A, respectively, a difference of approximately 19.36%. The larger deviation reflects finite-width current spreading and three-dimensional edge effects as the cathode size increases. Validated finite-element studies have similarly shown that finite-dimensional geometry and evolving local interfaces can change spatial corrosion patterns even when the global electrochemical response is reproduced [41,42].

The difference between 2D and 3D descriptions was even more evident for the current-localization factor. For the baseline configuration,

L_i,2D = 1.264, L_i,3D = 1.725

whereas at A_c/A_a = 4 the corresponding values were

L_i,2D = 1.357, L_i,3D = 1.950

The dimensional comparison therefore reinforces the same global-local distinction observed in the geometric sweeps: the 2D model captures the overall current scale and relative geometry trends efficiently, whereas the 3D model resolves stronger finite-size local concentration. Related validated models likewise show that spatially resolved corrosion fields can be more geometry-sensitive than integrated current metrics [41,42].

Overall, conductivity and cathodic kinetics mainly shifted the absolute current magnitude, while model dimensionality had a stronger effect on local peak localization. The principal geometry-dependent separation among I_gal, i_max, and L_i remained evident across these sensitivity analyses.

3.7. Engineering Implications and Corrosion Mitigation

The 20 geometric configurations provide a basis for identifying galvanic-coupling arrangements that impose greater anodic loading on 42CrMo steel. At d = 50 mm, increasing A_c/A_a from 0.5 to 4 increased the total galvanic current from 1.57 × 10⁻⁴ to 4.97 × 10⁻⁴ A and the maximum core anodic current density from 0.0780 to 0.2698 A m⁻². A large stainless-steel cathode connected to a relatively small 42CrMo surface therefore increases both the integrated galvanic current and localized anodic demand.

Electrode separation controls the electrolyte transport path. At A_c/A_a = 1, increasing d from 10 to 100 mm reduced the total galvanic current by approximately 41% and the maximum anodic current density from 0.1518 to 0.1108 A m⁻². However, the current-localization factor increased from 1.060 to 1.311, showing that a reduction in absolute current does not necessarily imply a more uniform anodic distribution. The largest total galvanic current in the computed matrix occurred at A_c/A_a = 4 and d = 10 mm; the smallest occurred at A_c/A_a = 0.5 and d = 100 mm.

For corrosion mitigation, reducing the exposed cathode-to-anode area ratio and increasing separation, where structurally feasible, can lower galvanic loading. Electrical isolation through insulating gaskets, sleeves, or bushings can interrupt the metallic conduction path between dissimilar components; protective coatings can additionally reduce the electrochemically exposed area. Such measures should be evaluated with regard to mechanical requirements, coating integrity, and service conditions. The present simulations quantify the effects of electrode geometry, whereas the protective effects of electrical isolation and coatings were not independently simulated in this work [22,23,24].

These results support the combined use of total galvanic current, maximum local anodic current density, and normalized localization when screening connection geometries. The computed distributions offer comparative guidance for configurations in low-conductivity freshwater rather than direct predictions of long-term material-loss depth. Related studies have examined high-temperature oxidation [43] and aqueous ferrihydrite transformation [44].

4. Conclusions

The galvanic corrosion of 42CrMo steel coupled with 410 stainless steel in low-conductivity Yangtze River freshwater was investigated by integrating electrochemical characterization with numerical current-distribution analysis. The principal conclusions are as follows:

1. Galvanic coupling produced a strongly nonuniform anodic current distribution on 42CrMo steel. Under the baseline geometry (A_c/A_a = 1, d = 50 mm), the calibrated model yielded a total galvanic current of 2.52 × 10⁻⁴ A, an average anodic current density of 0.101 A m⁻², and a maximum core current density of 0.127 A m⁻², corresponding to a localization factor of approximately 1.26. The spatial current profile showed enhanced anodic loading near the electrode boundaries, indicating that the total galvanic current alone cannot fully represent local corrosion severity.

2. The cathode-to-anode area ratio strongly controlled both global and local galvanic loading. At a fixed separation of 50 mm, increasing A_c/A_a from 0.5 to 4 increased the total galvanic current from 1.57 × 10⁻⁴ to 4.97 × 10⁻⁴ A and increased the maximum anodic current density from 0.078 to 0.270 A m⁻². The localization factor also increased from approximately 1.24 to 1.36, demonstrating that enlargement of the cathodic area increases not only the overall anodic demand but also the relative degree of current concentration.

3. Increasing electrode separation suppressed the absolute galvanic current through increased electrolyte resistance, but did not necessarily improve current uniformity. At A_c/A_a = 1, increasing d from 10 to 100 mm reduced the total galvanic current by approximately 41% and increased the effective electrolyte resistance from about 88 to 518 Ω. However, the localization factor increased from 1.06 to 1.31. Thus, greater separation reduces the absolute electrochemical load but can simultaneously increase the relative nonuniformity of the remaining anodic current.

4. Area ratio and electrode separation exhibited a coupled rather than purely additive effect. Across the 20 simulated geometries, the total galvanic current ranged from 1.38 × 10⁻⁴ A for A_c/A_a = 0.5 and d = 100 mm to 5.48 × 10⁻⁴ A for A_c/A_a = 4 and d = 10 mm. The regions of high total current and high maximum local current largely coincided, whereas the localization factor showed a more complex response. Therefore, I_gal, i_max, and L_i should be considered complementary descriptors of global loading, absolute local loading, and relative spatial localization, respectively.

5. Sensitivity analysis showed that electrolyte conductivity and the 410 stainless-steel cathodic Tafel slope mainly affected the absolute galvanic-current magnitude. The 2D and 3D total currents differed by 7.9% for the baseline geometry and by 19.4% at A_c/A_a = 4, while the 3D calculations produced stronger edge-current concentration. These results highlight the different sensitivities of global current and local peak current to electrochemical and dimensional parameters.

Overall, the galvanic corrosion behavior of the 42CrMo/410 stainless-steel couple in low-conductivity freshwater is controlled by the interaction among cathodic area, ionic transport distance, and current redistribution. Reducing the cathode-to-anode area ratio and increasing the separation between dissimilar metals reduce the absolute galvanic load on 42CrMo steel, while the spatial distribution of anodic current provides additional information on local electrochemical loading.