Journal of The Electrochemical Society, 155 共12兲 C583-C587 共2008兲

C583

0013-4651/2008/155共12兲/C583/5/$23.00 © The Electrochemical Society

Influence of the Alloying Elements on Pitting Corrosion of Stainless Steels: A Modeling Approach B. Malki,z T. Souier, and B. Baroux* Science et Ingénierie des Matériaux et Procédés, Centre National de la Recherche Scientifique UMR 5266-INP–UJF, 38402 Saint-Martin d’Hères, France Modeling of corrosion pit chemistry in applied polarization mode is carried out using finite element method calculations. The results lead to the formulation of critical conditions for pit stabilization in terms of the pit geometry and the applied potential. More detailed computing is performed to compare the behavior of both ferritic and austenitic stainless steels. The results fairly predict the beneficial effects of nickel on pitting resistance of 304 stainless steels, attributed to nickel-induced changes in dissolution laws. © 2008 The Electrochemical Society. 关DOI: 10.1149/1.2996565兴 All rights reserved. Manuscript submitted May 14, 2008; revised manuscript received September 12, 2008. Published October 17, 2008.

Extensive works have been devoted to pit stability in conventional stainless steels.1-13 Most of these studies portray various phenomenological aspects of the pit active/passive transition. Many investigations have suggested that during pit growth a thick film, mainly composed of salts, may cover the pit mouth.4,5 It is proposed that it plays the role of an extra barrier to diffusion, keeping the local medium rather corrosive.6,7 The pit in this case is regarded as stable when the cover remains intact for a period long enough to allow for salt film precipitation. Thus, pit growth is largely controlled by the ohmic resistance of the porous cover, and only its breakdown leads to a dilution of the pit medium, followed by stepwise current decreases, and then repassivation.9 Regarding pit chemistry, Pistorius and Burstein affirm that a critical concentration of metal chlorides is required to form the salt films.5,7 Laycock and Newman8 have shown elsewhere that salt precipitation is not a necessary condition for stabilization provided that the pit environment is sufficiently concentrated to avoid repassivation. Williams et al.9 state that active/passive transition is the result of a local decrease in the concentration of an anolyte inside the pit, while Sato3 argues in favor of the existence of a critical ion concentration for the pit electrolyte 共⌬c*兲 above which the pit will stabilize. From another point of view, Pistorius and Burstein5,7,14 quantified the critical condition for pit stability in terms of the product of pit radius 共r兲 and dissolution current density 共 j兲: 共r·j兲 as stipulated in the Williams, Wescott, and Fleischman models.9 The latter works are worth studying, because they put the emphasis on the possible formulation of a meaningful link between pit chemistry and pit geometry. However, troublesome points remain. Pit chemistry and in particular the local acidity is likely to control the passive film stability and in turn the current density. Moreover, regarding the pit morphology and the chemically heterogeneous stainless steel substrate, little information is known about the critical repassivation conditions as a function of the stainless steel chemical composition. All these effects are encapsulated in the current density parameter 共 j兲, and it is then hardly practical to sort out the pros and cons of the multiple physicochemical parameters. An appropriate mechanistic description of pit repassivation conditions still awaits new developments. The question of how far a possible combination of both pit geometry and chemistry can control the stability transition needs to be examined more closely. In this regard, the present paper aims to investigate the critical conditions of active/passive transition, focusing on the influence of pit geometry and the stainless steel chemical composition. Particular attention is paid to the ferritic and austenitic stainless steel alloys. In a previous work,15 a simplified analytical description of pit chemistry has shown, without referring to any salt formation, that stable pits can survive when the critical acidity level at the active/

* Electrochemical Society Active Member. z

E-mail: [email protected]

passive transition point reaches the depassivation pHd of the stainless steel. A linear relationship is found between a geometrical factor 共log L2 /r, L and r are, respectively, pit depth and pit mouth兲 and a critical applied potential Vc above which pits will stabilize. In this paper we propose an extension of the model to include realistic pit chemistry for a better application to stainless steels systems. Numerical simulations using the finite elements method 共FEM兲 seem the appropriate method to employ. We use it to examine the applied potential mode under which pit initiation is supposed to occur. We focus particularly on the evolution of acidity at the transition point 共pHt兲 as a function of the pit geometry and the applied potential. More detailed calculations are made to compare pit stabilization of both ferritic and austenitic stainless steels. The consequences of the established critical repassivation conditions are explored to throw light particularly on the role of alloying elements, a key question as far as the durability of stainless steels is concerned. Model Pit reactive system.— We study two typical stainless steel grades in dilute chloride solution: the ferritic grade 共AISI 430兲 and the austenitic ones 共AISI 304 and 316兲 共see Table I兲. Most of the reported calculations are performed on AISI 430 considered as a prototype system. We investigate in particular the relevance of the two following parameters: the repassivation variable noted p/L 共see Fig. 1兲 and the applied potential Vapp. The advantage of using the FEM technique is that it avoids numerous assumptions inherent to any analytical approach.15-21 This requires taking into account all the chemical species involved in a real material as well as their corresponding chemical and electrochemical reactions. Nevertheless, we still need to make two assumptions particularly about the anodic dissolution and the hydrolysis reactions: 1. Due to a lack of information on the anodic dissolution law for the boundary conditions, we use empirical current densities 共see Table II兲, which are drawn from measurements in deaerated bulk electrolyte NaCl 共2 M兲 pH 1 at room temperature, and are believed to reflect the anodic dissolution in slightly growing stabilized pits. Indeed, the important point is not to obtain absolute quantitative predictions but to compare the behavior of the three stainless steel grades under investigation

Table I. Chemical composition of the investigated materials in wt %. AISI

C

Mn

Cr

Ni

Mo

Cu

S 共ppm兲

N

430 304 316

0.042 0.016 0.02

0.38 1.2 1.7

16.39 18.5 17.6

0.16 8.1 11.2

0.032 0.15 2.1

0.038 0.18 0.08

15 5 2

0.028 0.04 0.03

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Journal of The Electrochemical Society, 155 共12兲 C583-C587 共2008兲

C584

ci = ci ,0 ci = ci ,0

Table III. Diffusion coefficients and initial concentrations used in the simulation. These kinetics values are quite reasonable in relatively dilute aqueous solutions.

ci = ci ,0 z N i .n = 0

N i .n = 0

r p

ϕ(z)

L

⎛ αi J⎞ × ⎟ N i .n = ⎜ ⎝ 2 + αi F ⎠

Figure 1. 2D axis-symmetric pit geometry used for finite element calculations. The repassivation variable is defined by ratio p/L corresponding to nonactive walls. Given the chemical composition ␣i, of the stainless steel, the dissolution flux of species is calculated using an empirical current density J 共see Table II兲, n being the outward normal vector from the pit wall and ␸ the electrostatic potential. Far from the pit reactive system, the species concentration is assumed to be constant, ci = ci,0.

2. In the second, only one hydrolysis reaction is considered for each dissolved cation. No significant changes in the acidity are expected from more complicated hydrolysis reactions. The pit reactive systems include the following ionic species: Fe2+, Cr3+, CrOH2+, FeOH+, H+, Na+, and Cl− for the AISI 430 steel; and, Ni++ and NiOH+ for the AISI 304 grade. The corresponding chemical and electrochemical reactions are the following Fe → Fe2+ + 2e−

关1兴

k1,f

Fe2+ + H2O
FeOH+ + H+

关2兴

Cr → Cr3+ + 3e−

关3兴

k1,b

k2,f

Cr3+ + H2O
CrOH2+ + H+

关4兴

k2,b

kw,f

H2O
H+ + OH−

关5兴

kw,b

for the AISI 430 grade, supplemented by the following two reactions for the AISI 304 grade Ni → Ni

2+

+ 2e

关6兴

−

Table II. Empirical parameters used in the calculations. The Tafel’s law coefficients are obtained in 2 M NaCl at pH 1 and at room temperature and the depassivation pHd are taken from Ref. 24.

a

AISI

Vcorr 共V/SCEa兲

J0共␮A cm−2兲

b 共V/dec兲

pHd

430 304 316

−0.56 −0.45 −0.39

130 35 29

0.06 0.06 0.11

3 2.4 1.8

Saturated calomel electrode.

Species

D cm2 s−1

Electrolyte concentration mol L−1

H+ OH− Na+ Cl− Fe2+ Cr3+ Ni2+ CrOH2+ FeOH+ NiOH+

9.3 5.3 1.3 2.0 7.1 7.5 5.9 7.3 5.9 7.3

⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻

10−7 10−7 Estimated 0.1 0 0 0 0 0 0

10−5 10−5 10−5 10−5 10−6 10−6 10−6 10−6 10−6 10−6

k3,f

Ni2+ + H2O →
NiOH+ + H+ k3,b

关7兴

ki represents the kinetic constant rates. Tables III and IV summarize all kinetic and thermodynamic data used in the calculations. Master equations.— The governing equations are deduced first from the mass balance principle, neglecting the advection term and in the case of dilute aqueous solutions, the so-called Nernst–Planck equation

⳵ci + ⵜ 共− Di ⵜ ci − zi␻iFci ⵜ ␸兲 = Ri ⳵t

关8兴

where the parameters ci, Di, zi, ␻i, and ␸ are, respectively, concentration, diffusion coefficient, valence number, and ionic mobility of species “i” in SI units. Ri is the corresponding net creation rate 共mol L−1 s−1兲. Extended Nernst–Planck equation analysis in the case of deviations from dilute aqueous solutions hypothesis22 show slight shifts in the potential profiles that can be treated in a second step of this work to give a more complete picture. Second, from the electroneutrality condition

兺zc

i i

=0

关9兴

i

this condition is made possible by assuming that the diffusion relaxation time 共␶d ⬃ 1 ms兲 is much greater than the charge relaxation one 共␶c ⬃ 1 ns兲. Given these master equations, the mathematical description of the transport phenomena inside the pit reactive system is well-posed. FEM can now be used to solve the stationary problem. Boundary conditions.— We chose to work on axis-symmetric two-dimensional 共2D兲 pit geometries as illustrated in Fig. 1. The pit size ranges from 1 to 200 ␮m, a length scale well above the lower limit required for the validity of the continuum approximation. The boundary conditions are fixed as follows: 1. On the pit walls, dissolution of Fe, Cr, and Ni species obeys an empirical Tafel’s law under charge-transfer-controlled conditions18 J = J0 exp关− b共Vapp兲 − Vcor − ␸兴

关10兴

where the corrosion current J0, the corrosion potential Vcorr, and the Tafel slope b are fitted from experimental data. The applied potential Vapp is considered as a control parameter. Depending on the stainless steel chemical composition 共␣i兲, the net flux of each species is given by

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Journal of The Electrochemical Society, 155 共12兲 C583-C587 共2008兲

C585

Table IV. Equilibrium constants „Keq… of the used hydrolysis reactions Eq. 2, 4, and 7 and the corresponding kinetics rate constants.16 The latter are estimated from equilibrium constants „ki,b = Keq Õki,f… assuming fast forward reaction rates. Keq

ki,f

5 ⫻ 10−9 共mol L−1兲 10−4 共mol L−1兲 1.38 ⫻ 10−10 共mol L−1兲 10−14 共mol L−1兲2

Fe2+ Cr3+ Ni2+ H 2O

Ni·n =

冉

J ␣i ⫻ 2 + ␣i F

冊

10−3

关11兴

ki,b 2 ⫻ 1011 共mol L−1兲−1 s−1 1011 共mol L−1兲−1 s−1 7.2 ⫻ 1012 共mol L−1兲−1 s−1 1011 共mol L−1兲−1 s−1

103 s−1 107 s−1 103 s−1 共mol L−1兲s−1

pit repassivation mechanism is not yet elucidated. Such diagrams are expected to illustrate more clearly the different behavior between different stainless steels.

where n is the normal direction to the boundary and F the Faraday constant. 2. Passivation is expected to occur when dissolution fluxes is null 关12兴

Ni·n = 0

3. Finally, within the electrolyte and at an infinite distance from the pit, the concentration of all species as well as the electrostatic potential are assumed to be constants of the so-called Dirichlet conditions: ci = ci,0 and ␸ = 0. The numerical implementation of the resulting partial differential equations is performed using the software Comsol Multiphysics that is practical for this kind of nonlinear problem.23 For a given pit depth 共L兲 the stationary state for each repassivation state p/L is calculated. In so doing, we obtain a variation of the transition pHt as a function of p/L that can be considered as an average estimation of the acidity level for a given pit geometry. By comparing this curve to a given depassivation pHd, one should be able to verify if the growth of a given pit is stable or not. Furthermore, a parametric study of the influence of the pit geometry 共in terms of L and r兲 for every applied potential Vapp is required to demarcate between passive and active zones in the 共L2 /r, Vapp兲 plane. Last, one alternative to the use of pHt as a criterion for transition is simply to use the minimum pHmin inside the pit to reach the same conclusions. The gap in between can be considered as a transition zone given that the

Results and Discussion Figure 2 illustrates the simulated species concentration distribution along the pit depth for a given pit geometry: r = 1 ␮m, L = 10 ␮m, and p/L = 0.5, which follows a nonuniform profile near the pit mouth. This is because of the high concentration gradients between the pit and the electrolyte outside the pit. As expected, this distribution is strongly dependent on the pit geometry and the passive area, making the working point of the pit reactive system highly sensitive to any change in these two major parameters. Note that the relatively high concentration of chloride anions in this case suggests a possible salt precipitation which may cause an additional shift of the working point. This is not taken into account in our model as mentioned above. Figure 3 reports the various calculated transition pHt as a function of p/L and Vapp for a pit size of r = 1 ␮m and L = 10 ␮m. Two observations emerge from these results. First, a parabolic shape of the transition function pHt共p/L兲 is found by this method as predicted by the analytical model.15 Given a critical pH 共pHd兲 and depending on the repassivation variable p/L, this function presents two saddle points, typically the hallmark of multiple steady states. This is primarily related to a competition between dissolution and repassivation kinetics. Accordingly, during the propagation step pits may experience transient regimes, leading to unpredictable dynamical effects encountered in some corrosion situations. Second, the average acidity level reached in the pit is lowered with increasing the applied potential Vapp. Any increase in Vapp 共indirectly the dissolu-

6 2

-0,56 V

-

10

++

Fe

+++

Cr

-2

10

H

+

CrOH

-4

10

5

-0,46 V

+

T

Cl 0

pH

specie concentration /mol.L

-1

10

-0,36 V 4

-6

10

+

FeOH

-8

10

-0,26 V

+

Na

3 -0,16 V

pH

-10

10

0

Pit buttom

2

4 6 Distance (µm) Active wall

8

d

10

2

Passive wall (p)

0

0,2

0,4

0,6

0,8

1

p/L z

Figure 2. Simulation of concentration distributions along the pit depth obtained for r = 1 ␮m, L = 10 ␮m, p/L = 0.3, and for AISI 430 in 0.05 M NaCl at Vapp = 0.16 V/ECS.

Figure 3. 共Color online兲 Evolution of the pH at the active/passive transition 共pHt兲 for a pit size of r = 1 ␮m and L = 10 ␮m as a function of the repassivation variable p/L and the applied potential Vapp for AISI 430 in 0.05 M NaCl.

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Journal of The Electrochemical Society, 155 共12兲 C583-C587 共2008兲

C586

0,25

-0,1 (Active zone)

0,2 (V/ECS)

(V/ECS)

-0,15

0,15 0,1

Critical

(Transition zone)

V

-0,25

V

Critical

-0,2

1E-4 M

0,02 M

0,05

-0,3

0

(Passive zone) -0,35

0

0,5

1

1,5

2

2,5

3

-0,05

3,5

0

0,5

1

2

2

2,5

3

3,5

2

log(L /r)

log(L /r)

Figure 4. 共Color online兲 Plot of the critical applied potential for pit stabilization as a function of the pit geometry. Given a depassivation pHd 共case of AISI 430 in 0.05 M NaCl兲, there is a threshold of the pit acidity above which the pit repassivates, i.e., when pHt ⬍ pHd the pit is entirely active, when pHtmin ⬎ pHd the pit is entirely passive, and in between a transition zone can be defined.

tion current兲 will necessarily lead to more stable pits. Thus, given a pit geometry 共L2 /r兲 and depassivation pHd, it is always possible to define a critical applied potential above which pits can stabilize. In this way, one can build a stability diagram as mentioned above for each stainless steel 共see Fig. 4兲. This figure clearly illustrates that small pits are more difficult to stabilize than the large ones, as they require higher potentials to cross the active zone. Moreover, it is tempting to link the critical potential Vc to the pitting potential 共Vpit兲 obtained experimentally. Although they are undoubtedly correlated, this correlation depends on the pit’s geometry distribution,23 and only the knowledge of this distribution should allow for a formal connection between Vc and Vpit. Notice that the active/passive transitions follow various “path transitions” with regard to pit geometry and polarization conditions. That is, the shape and the position of the parabolic curves depend on the environmental variables. Figures 5 and 6 illustrate examples of such effects. For example, as one enlarges the pit opening 共breakdown of the pit cover兲, the increase of the outward proton fluxes leads to a reduction of the local acidity and hence to a possible pit repassivation 共Fig. 5a兲. Moreover, the pit shape 共in the case of a spherical morphology; see Fig. 5b兲, as well as the initial chloride concentration 共Fig. 6兲, together lead to a significant shift in the working point. Therefore, for realistic materials one can logically expect deviations from the proposed linear relationship between Vc and log共L2 /r兲. This is due to the above nonlinear contributions besides those not taken into account in the model 共dissolution aniso-

Figure 6. 共Color online兲 Confirmation of the enhancing chlorides effect on pit stabilization.

tropy, salts precipitation, etc.兲. Nevertheless, it is still possible to provide valuable insights into the role of alloying elements using the above linear approximation. Indeed, if one compares the transition curves of ferritic AISI 430 and austenitic AISI 304 stainless steels, given their depassivation pHd 共see Table II兲, AISI 430 exhibits a low transition curve 共see Fig. 7兲. Low applied potentials are sufficient to bring the working point of a given pit 共L2 /r兲 to stable regimes. To answer the question whether this can be attributed to nickel-induced change in the dissolution behavior or to nickel hydrolysis reactions, we have checked the response of both ferritic and austenitic stainless steels when inverting their empirical dissolution laws. Surprisingly, the transition curves also have been inverted. This confirms the predominant role of nickel-induced change in the dissolution embodied by the large difference in the empirical dissolution laws 共see Table II兲. The case of AISI 316 grade appears to behave in the same way: the passivity zone is wider than the previous grades. The only dissolution law 共implicitly the effect of alloying elements兲 is enough to determine the stability behavior of the grade, although no assumption has been made on molybdenum chemistry. Conclusions We have presented a corrosion pit reactive system from FEM calculations. Our findings capture correctly the major asymptotic behaviors and yield thresholds of the critical parameters in qualitative agreement with experimental knowledge. Both pit chemistry and topology are linked together to build a stability diagram portraying the critical pit stabilization conditions. A linear relationship between a “critical propagation potential” Vc and log共L2 /r兲 共L and r are, respectively, pit depth and pit mouth兲 has been established. This

3,8

4,5

(b)

(a) Vapp = - 0,16 V/ECS

V

3,6

app

= - 0,16 V/ECS

Figure 5. 共Color online兲 Transition pHt dependence: 共a兲 on the pit opening where the reduction of the local acidity may lead to pit repassivation, 共b兲 on the pit morphology: in this case a spherical pit is used instead of a cylinder and the principle of calculations is exactly the same. The simulation was performed for AISI 430 in 0.05 M NaCl at Vapp = 0.16 V/SCE and for a pit size of r = 1 ␮m and L = 10 ␮m.

pHT

pHT

4

cylindrical

3,4

3,5

pit mouth 3µm

3,2

3

3

spherical

pit mouth 1µm 2,5 0

1,5

2,8 0,2

0,4

0,6

p/L

0,8

1

0

0,2

0,4

0,6

0,8

1

p/L

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Journal of The Electrochemical Society, 155 共12兲 C583-C587 共2008兲 0,8

Centre National de la Recherche Scientifique assisted in meeting the publication costs of this article.

AISI 316

C

V (V/ECS)

0,6

References

0,4

1. 2. 3. 4.

AISI 304

0,2

5. 6. 7.

0 AISI 430

-0,2 -0,4

C587

8. 9.

0

0,5

1

1,5

2

2,5

3

3,5

10.

2

log(L /r) Figure 7. 共Color online兲 Comparison between AISI 430, AISI 304, and AISI 316 grades in terms of critical potentials Vc for pit stabilization.

diagram allows one to clearly distinguish passive and active zones for given experimental conditions. The extension of the calculations to compare ferritic and austenitic stainless steels reveals that the chemical alloy composition governs the delimitation of the transition zones. As should now be evident, the dissolution law of stainless steels is the key factor behind pitting corrosion resistance of the austenitic stainless steels compared to ferritic ones. As we look to the future, this approach if improved should become a powerful tool for a truly gestalt understanding of the pitting corrosion of stainless steels.

11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

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