COMSOL 6.4 - Accelerated Corrosion Test of a Scratched Galvanized Steel Sample

Accelerated Corrosion Test of a Scratched Galvanized Steel Sample

An established method for benchmarking the atmospheric corrosion resistance of materials is the use of accelerated corrosion tests (ACT) performed in climate chambers. The main purpose of ACTs is to make reliable and fast predictions of the long-time behavior. The tests expose samples to cyclic conditions during a few weeks. Elevated temperature, repeated drying and wetting together with salt addition are conditions that typically speed up corrosion and characterize ACTs. The samples can be of all shapes and sizes, in setups targeting crevice or galvanic corrosion, or have artificial damage.

This example studies a galvanized steel sample with crossing scratches that fully penetrate the zinc coating and expose the underlying steel. The corrosion is simulated for a dummy ACT running for 7 days. The model solves for a thin liquid film that covers the sample surface. Local variations in pH, corrosion products, and coating damage are shown.

Model Definition

GEOMETRY

The 2D sample and model geometries with scratches are shown in Figure 1.

Figure 1: The galvanized steel sample geometry with 0.1 mm wide scratches exposing the steel. The model geometry is marked with dashed lines.

As indicated in the figure, due to symmetry, only one quarter of the sample is needed to investigate the full sample surface. The 2D geometry neglects the thickness of the liquid film. Since the atmospheric corrosion is limited to thin films, in the range of up to tens of micrometers, negligible gradients across the film thickness are expected and makes the thickness dimension redundant.

More information on atmospheric corrosion can be found in the Atmospheric Corrosion example.

ACCELERATED CORROSION test Model

The ACT is displayed in Figure 2. The temperature interval is between 278.15 K and 323.15 K, and the relative humidity ranges between 70% and 95%. The low RH periods are oscillating around the deliquescence of the NaCl salt (~RH 75%). 1 wt% NaCl solution is sprayed onto the sample at the beginning of day 1, 3, and 6.

Figure 2: ACT. Solid black line indicates periods of spraying 1 wt% NaCl solution onto the sample.

During spray periods, the liquid film thickness is assumed to be constant at 100 μm and the film volume is fully replenished ten times. When not sprayed, the thickness depends on both the salt load density and the relative humidity. Low RH dries up the film while higher RH leads to condensation of gaseous water which thickens the film. Below the deliquescence RH, the film is assumed to be discontinuous.

The dependence of RH on film thickness and (other properties) is described in the Atmospheric Corrosion example. A general approximation from that example and throughout this model is that parameters that possibly could depend on the total aqueous species concentration in the film (or ionic strength) are dependent on the NaCl concentration only. The weak temperature dependence that is characteristic for the NaCl salt solubility and deliquescence is also practiced.

Mass transport of several relevant species, reactions (electrochemical, homogeneous, and heterogeneous) and interactions with atmosphere (gas dissolution and drying/condensation) are all phenomena considered during the ACT. For simplicity a horizontal sample orientation is considered.

Aqueous Electrolyte Transport Interface

The interface is used to define material balances accounting for the mass transport of species, i, and various sources in a liquid film covering the galvanized steel sample:

(1)

In the equation, Ji is the diffusion and migration flux, and S any type of source (mol/(m3·s)).

With the use of and nodes, reactions at the metal surface and at the atmosphere-liquid boundary are accounted for on the 2D geometry. The approach assumes that the liquid film is thin with no gradients along the film. The setting is by default activated (on the physics top node) and is left untouched. In this manner if the film grows and shrinks due to evaporation and condensation, respectively, concentrations will change.

Electrochemical Reactions

The electrochemical reactions on zinc and steel are defined using polarization data available in the folder in the . Metal dissolution is set at zinc and oxygen reduction on steel. Thus these two reactions are accounted for:

The metal dissolution data are adjusted for changes in salt concentration using a simplified linear dependence and the oxygen reduction reaction uses a simple linear dependence approximation of the dissolved oxygen concentration. Both reactions include an Arrhenius equation factor to incorporate the temperature fluctuations. The volumetric current formulations, iv,Ox and iv,Red, are defined as:

(2)

(3)

where iloc,Zn and iloc,Fe are the polarization data (current density versus potential) for the two reactions, θ the corrosion product surface coverage degree, Ea the activation energy, L the film thickness, and subscript “ref” indicate parameter values at experimental data conditions. The film discontinuity below RH deliquescence is accounted for in the reaction expressions, by turning the volumetric currents off using a function factor.

The electrochemical reactions are defined using the electrode kinetics option in the available at the nodes. By setting the to the inverse of the liquid film thickness, the settings are equal to that of a thin liquid film with no gradients along the film thickness (i.e. homogenized properties across the thickness).

Homogeneous Reactions in Liquid Film

Carbonates originating from the atmosphere are accounted for. Three dissociation steps are defined using the node, in which the following equilibrium reactions are accounted for:

The node defines the mass balance accounting for all carbonate species: CO2(aq), H2CO3, HCO3-, and CO32-.

Zinc ions from the dissolution of the zinc coating hydrolyze in four steps (Ref. 2):

The hydrolysis is defined with an node. Similar to the node, it sets up the mass balance accounting for the total of all reacting species, in this case: Zn2+, Zn(OH)+, Zn(OH)2(aq), Zn(OH)3-, and Zn(OH)42-.

NaCl Salt Species

The film conductivity together with the salt dependent parameters requires the presence of sodium and chloride ions. Both ions are added to the model using the node.

Corrosion Products and Passivation

Corrosion products are formed and are considered to passivate the metallic surface. This example accounts for the formation of ZnO according to the following reaction:

The reaction is defined as fully reversible (ZnO both precipitates and dissolves). It is defined as a reaction rate, RZnO (mol/(m3·s)), in a node that is added at the nodes. The rate formulation is based on the corrosion product solubility, as follows:

(4)

(5)

In the above, kZnO is the rate constant for the corrosion product conversion (mol/(m2·s)) and KS,ZnO the equilibrium constant of the reaction.

The precipitated ZnO is set to cover the sample surface and assumed to inhibit (passivate) both electrochemical reactions. The ZnO coverage degree, θ, is assumed to change according to the following expression (Ref. 3):

(6)

where mZnO is the precipitated molar amount of ZnO per surface area (mol/m2) and mtot,surf is the molar metal surface availability per surface area and monolayer for ZnO precipitation. Note that with the use of the expression above more than mtot,surf needs to precipitate for the surface to become fully passivated.

The precipitated ZnO concentration in the film is defined using the at top nodes.

Dissolved Atmospheric Gases

Two atmospheric gases are accounted for.

Carbon dioxide dissolves into the film and affects the carbonate concentration and pH. The aqueous carbon dioxide saturation concentration, cCO2,sat, depends on the partial pressure, pCO2, together with temperature and the salt concentration (Ref. 1). A reaction source, Scarbonate (mol/(m3·s)), is defined in a node for the carbonate species. The source minimizes the difference between the carbonate concentration in the film and the saturation concentration, as follows:

(7)

In the expression, kCO2,sat is the rate constant for the carbon dioxide (1/s).

Oxygen dissolves into the film as well which affects the oxygen reduction reaction. The dissolved oxygen concentration is set equal to the saturation concentration that is dependent on the oxygen content in the atmosphere, temperature and salt concentration (compare with Atmospheric Corrosion example).

Spraying

During spraying, aqueous species concentrations are replaced with the compositions of the 1 wt% NaCl spray solution, ci,spray. This is defined using nodes for the species. The generalized source expression used is as follows:

(8)

The rate constant, kspray (1/s), controls how well the solution is replenished.

Results and Discussion

Several variables are monitored during the run giving indications of the aggressiveness of the ACT (Figure 3, Figure 4, and Figure 5). In Figure 6 and Figure 7, the corrosion damage is shown in terms of loss of zinc coating mass and maximum decrease in coating thickness. At low RH the corrosion progresses very slowly. The precipitated amount of ZnO increases with time(Figure 6) and, as seen in both Figure 4 and Figure 7, acts to decrease the corrosion rate.

Figure 3: Salt concentration and liquid film thickness during ACT.

Figure 4: Total current of electrochemical reactions during ACT.

Figure 5: Maximum and minimum pH at sample during ACT.

Figure 6: Mass changes over sample during ACT.

Figure 7: Maximum thickness decrease of coating during ACT.

The coating thickness after 7 days is shown in Figure 9. The coating is mainly consumed near the scratches and especially near the crossing of the scratches.

Figure 8: Local coating thickness decrease after 7 days.

The localized pH is displayed in Figure 9 for different times. The oxygen reduction reaction in the scratch keeps the pH basic there at all times, favoring passivation.

Figure 9: Local pH at the sample surface at different times during the ACT.

The corrosion product coverage after 7 days is substantial, as shown in Figure 10.

Figure 10: Local degree of coverage after 7 days.

References

1. M. Nordsveen, S. Nesic, R. Nyborg, and A. Stangeland, “A Mechanistic Model for Carbon Dioxide Corrosion of Mild Steel in the Presence of Protective Iron Carbonate Films-Part 1: Theory and Verification,” Corrosion, vol. 59, no. 5, pp. 443–455, 2023

2. V. Topa, A.S. Demeter, L. Hotoiu, D. Deconinck, and J. Deconinck, “A transient multi-ion transport model for galvanized steel corrosion protection,” Electrochimica Acta, vol. 77, pp. 339–347, 2012.

3. T.G. Zavalis, M. Ström, D. Persson, E. Wendel, J. Ahlström, K.B. Törne, C. Taxén, B. Rendahl, J. Voltaire, K. Eriksson, D. Thierry, and J. Tidblad, “Mechanistic Model with Empirical Pitting Onset Approach for Detailed and Efficient Virtual Analysis of Atmospheric Bimetallic Corrosion,” Materials, vol. 16, pp. 923–946, 2023.

Corrosion_Module/Atmospheric_Corrosion/act_scratched_galvanized_steel

Modeling Instructions

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New

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Global Definitions

Load the model parameters from a text file.

Parameters 1

In the window, under click .

In the window for , locate the section.

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Browse to the model’s Application Libraries folder and double-click the file act_scratched_galvanized_steel_parameters.txt.

Geometry 1

Draw the geometry.

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type w_sample.

In the text field, type h_sample.

Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type w_sample.

In the text field, type h_scratch.

Locate the section. From the list, choose .

In the text field, type w_sample/2.

In the text field, type h_sample/2.

Locate the section. In the text field, type 45.

Rectangle 3 (r3)

Right-click and choose .

In the window for , locate the section.

In the text field, type 315.

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Your geometry should now look like this:

Due to symmetry, only one quarter of the drawn geometry is modeled. The upper right corner is selected as model geometry.

Rectangle 4 (r4)

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In the window for , locate the section.

In the text field, type w_sample/2.

In the text field, type h_sample.

Rectangle 5 (r5)

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In the window for , locate the section.

In the text field, type w_sample/2.

In the text field, type h_sample/2.

Locate the section. In the text field, type w_sample/2.

Difference 1 (dif1)

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Select the objects , , and only.

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Click to select the

toggle button for .

Select the objects and only.

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button in the toolbar.

Your model geometry should now look like this:

Make selections to help with the model setup.

Definitions

Zinc

In the toolbar, click

In the window for , type Zinc in the text field.

Select Domain 2 only.

Steel

In the toolbar, click

In the window for , type Steel in the text field.

Select Domains 1 and 3 only.

Wetted Surface

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In the window for , type Wetted Surface in the text field.

Locate the section. Select the checkbox.

Add some integration operators for probes and postprocessing.

Integration - Zinc

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and choose .

In the window for , type Integration - Zinc in the text field.

In the text field, type intop_zinc.

Locate the section. From the list, choose .

Integration - Steel

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and choose .

In the window for , type Integration - Steel in the text field.

In the text field, type intop_steel.

Locate the section. From the list, choose .

Integration - Wetted Surface

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In the window for , type Integration - Wetted Surface in the text field.

In the text field, type intop_wet.

Locate the section. From the list, choose .

The ACT cycle is added as three separate interpolation files. The first describes the variation in RH, the second temperature, and the third spraying periods over time. Use the piecewise cubic interpolation alternative for smoother transitions.

Interpolation - Relative Humidity

In the toolbar, click

In the window for , type Interpolation - Relative Humidity in the text field.

Locate the section. In the text field, type RH_ACT.

Click

Browse to the model’s Application Libraries folder and double-click the file act_scratched_galvanized_steel_rh.txt.

Locate the section. From the list, choose .

Locate the section. In the table, enter the following settings:


Function	Unit
RH_ACT	1

In the table, enter the following settings:


Argument	Unit
t	s

Interpolation - Temperature

In the toolbar, click

In the window for , type Interpolation - Temperature in the text field.

Locate the section. In the text field, type T_ACT.

Click

Browse to the model’s Application Libraries folder and double-click the file act_scratched_galvanized_steel_temperature.txt.

Locate the section. From the list, choose .

Locate the section. In the table, enter the following settings:


Function	Unit
T_ACT	K

In the table, enter the following settings:


Argument	Unit
t	s

Interpolation - Spray

In the toolbar, click

In the window for , type Interpolation - Spray in the text field.

Locate the section. In the text field, type spray_ACT.

Click

Browse to the model’s Application Libraries folder and double-click the file act_scratched_galvanized_steel_spray.txt.

Locate the section. From the list, choose .

Locate the section. In the table, enter the following settings:


Function	Unit
spray_ACT	1

In the table, enter the following settings:


Argument	Unit
t	s

Add zinc and iron from the branch in the .

Add Material

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to close the window.

Materials

Fe in 3% NaCl (mat1)

In the window for , locate the section.

From the list, choose .

Zn in aerated 3.5 wt% NaCl (mat2)

In the window, click .

In the window for , locate the section.

From the list, choose .

Add variables describing the system. Unknown variables warnings will be resolved as soon as the physics have been set up.

Definitions

Variables - Global

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In the window for , type Variables - Global in the text field.

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file act_scratched_galvanized_steel_global_variables.txt.

Variables - Rates

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In the window for , type Variables - Rates in the text field.

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From the list, choose .

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Browse to the model’s Application Libraries folder and double-click the file act_scratched_galvanized_steel_rate_variables.txt.

Variables - Film

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In the window for , type Variables - Film in the text field.

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From the list, choose .

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file act_scratched_galvanized_steel_film_variables.txt.

Variables - Zinc

In the toolbar, click

In the window for , type Variables - Zinc in the text field.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file act_scratched_galvanized_steel_zn_variables.txt.

Variables - Steel

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In the window for , type Variables - Steel in the text field.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file act_scratched_galvanized_steel_fe_variables.txt.

Start defining the transport and reactions in the interface. The is set to the film thickness. Leave the default active setting on the interface top node untouched. In this manner, species concentrations will change with the film thickness. The approach assumes that the film is so thin that no gradients exist along the thickness of the film.

Aqueous Electrolyte Transport (aqt)

In the window, under click .

In the window for , locate the section.

In the dz text field, type d_film.

Electrolyte 1

In the window, under > click .

In the window for , locate the section.

From the T list, choose . In the associated text field, type T_ACT(t).

Locate the section. In the DH+ text field, type DH.

In the DOH− text field, type DOH.

Use an node to model the hydrolysis equilibrium reactions of the aqueous zinc species.

Ampholyte - Zinc

In the toolbar, click

and choose .

In the window for , type Ampholyte - Zinc in the text field.

Locate the section. In the text field, type Zn.

In the k text field, type 4.

In the table, enter the following settings:


Dissociation step (1)	pKa (1)
1	-log10(K_Znstep1)
2	-log10(K_Znstep2)
3	-log10(K_Znstep3)
4	-log10(K_Znstep4)

In the z0 text field, type -2.

Locate the section. In the D text field, type DZn.

Use a node to model the carbonic acid dissociation.

Electrolyte 1

In the toolbar, click

and choose .

Carbonic Acid 1

In the window for , locate the section.

In the DCO2(aq) text field, type DCO2aq.

In the DH2CO3 text field, type DH2CO3.

In the DHCO3− text field, type DHCO3.

In the DCO32- text field, type DCO3.

Add the NaCl as two fully dissociated species, sodium and chloride ions, with the node.

Electrolyte 1

In the toolbar, click

and choose .

Fully Dissociated Species - Na

In the window for , type Fully Dissociated Species - Na in the text field.

Locate the section. In the text field, type Na.

In the z text field, type 1.

Locate the section. In the D text field, type DNa.

Electrolyte 1

In the toolbar, click

and choose .

Fully Dissociated Species - Cl

In the window for , type Fully Dissociated Species - Cl in the text field.

Locate the section. In the text field, type Cl.

In the z text field, type -1.

Locate the section. In the D text field, type DCl.

Initial Values 1

In the window, under > click .

In the window for , locate the section.

In the ϕl,0 text field, type V0.

Locate the section. In the cH2CO3,0 text field, type cCO2aq0.

In the cNa,0 text field, type cNaCl0.

In the cCl,0 text field, type cNaCl0.

Local electrochemical reactions are incorporated using the nodes. These reactions are user-defined, with the material properties for zinc and steel being imported accordingly. Additionally, the Dissolving–Depositing Species feature is used to account for the effects of corrosion product formation as well as metal dissolution and deposition.

Highly Conductive Porous Electrode - Steel

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