Propagation of Localised Corrosion: FEM Approach M. Stroe *,1, R. Oltra 1, B. Vuillemin 1, G. Girardin 2 1. Institut Carnot de Bourgogne (ICB), 2. AREVA NP *ICB, UMR 5209 CNRS-Université de Bourgogne,9 Av. A. Savary, BP 47870 F-21078 DIJON Cedex, France, Mioara.Stroe@u-bourgogne.fr Abstract: Crevice corrosion of stainless steel in chloride media was investigated based on a 11 species model. The role of parameters like ph inside the crevice, external potential, chloride concentration of the bulk solution and crevice geometry was studied. A thermodynamic criterion for arrest / propagation of the crevice corrosion was used in order to identify the conditions for which the localised corrosion can propagate. This study shows that there is a combination of crevice geometry and potential for which the crevice is not blocked by precipitates and thus the corrosion can proceed. The time dependent resolution showed the evolution of the conditions inside the crevice from the initiation of the corrosion until the steady state was reached. Keywords: crevice corrosion, stainless steel, chloride. 1. Introduction Crevice corrosion is a phenomenon of localised corrosion that develops in confined regions of a metallic material in contact with a corrosive medium, with the majority of the surface being in contact with the same medium and in a state of relative immunity. The most frequent cases relate to the passive materials (stainless steels, aluminium and sometimes titanium alloys) and occur mainly in aerated media containing halides (generally chlorides). The mechanism of the crevice corrosion involves three stages: incubation, initation and propagation. During incubation the occluded solution is depleted in oxygen due to limited diffusion from the external environment. The absence of oxygen leads to the separation between the anodic site (inside the crevice) and the cathodic site (the external surface). The anodic process, that continues inside the crevice, increases the concentration of metal cations. Due to hydrolysis of metal cations, the acidity inside the cavity increases. The excess of positif charges inside the crevice determines a diffusion flux of anions (chloride) from bulk solution toward the crevice. Thus, during incubation period the occluded solution becomes exempted of oxygen, more acidic and more concentrated in chloride, whithout any apparent damage of the metallic surface. This period is characterised by the time of incubation which can vary from a few hours to years. The inititation stage is intermediate between the incubation and the active propagation of the corrosion. Two theories were proposed for the initiation mechanism: critical crevice solution (CCS) theory and ohmic drop (IR- drop) theory. According to the first mechanism [1], the metallic surface inside the crevice is activated due to increase of the agressivness of the solution (increased acidity and chloride content). The process is autocatalytic: the acidification and chloride enrichement induce an enhancement of the corrosion rate. This theory allows an accurate estimation of incubation time and can explain the dependency on the composition of the sensitivity to localised corrosion. The CCS theory neglects the effects of potential. The second theory proposed, IR drop theory [2], considers only the effect of the potential, neglecting the role of changes of solution chemistry inside the crevice. According to this theory, the separation of the cathodic and the anodic sites occurs due to depletion of the oxydant within the crevice. A potential drop between the external surface and the interior of the cavity is developed. For the metals with Tafel behaviour, the potential drop will reduce the corrosion, and thus it has beneficial consequences. For metals that exhibit active/ passive transition, the ohmic drop can bring the potential inside the crevice in the active zone. In this case, the potential drop will have a negative effect, enhancing the corrosion. This theory explains the location of the attack but its main weakeness is that it can be applied only for the materials that exhibit active passive transition. The next stage is the propagation of the crevice corrosion. During this stage, the anodic current can increase, and thus enhances the rate of localised corrosion. Other processes like new
phases (precipitate or gas) formation, can take place. The present work is focused on the propagation of the localised corrosion of a stainless steel crevice in chloride environment. Steady state composition of the occluded solution was studied in order to identify the combination of ph, potential, chloride concentration and geometry conditions that lead to localised corrosion. 2. Background of modelling The model is based on solving Nernst- Planck equation at steady state. Nernst Planck application from the Chemical Engineering Module of COMSOL software was used. A rectangular crevice of length L and opening w was considered (Figure 1). The dimension in the third direction is much higher compared to the other two dimensions, and it can be considered as infinitely high. For a crevice thin enough, an uniform distribution of chemical species across the width is assumed and the transport through w can be neglected. Therefore, the crevice can be reduced to a 1D geometry. For 1D crevice with active walls, the opening w of crevice is involved indirectly by the averaging the electrochemical fluxes across the crevice width [3 5]. Bulk mouth mouth wall occluded wall L wall + occluded solution Figure 1. Crevice geometry A critical point in modeling is the choice of species taken into account, in order to have a representative model. In the present work the most thermodynamically stable species were considered. The chemical reactions involved were: tip tip w 2D 1D Fe 2+ + H 2 O FeOH + +H + H 2 O H + +OH - Fe 2+ + Cl - FeCl + Cr 3+ + H 2 O CrOH 2+ + H + Cr 3+ +Cl - CrCl 2+ The chemical reactions are fast and considered to be at the equilibrium. A model with 11 species seems to be representative for the crevice corrosion of a stainless steel. The electrochemical reactions that take place inside the crevice are: Fe Fe 2+ + 2e Cr Cr 3+ + 3 e H + + 1e ½ H 2 A non selective dissolution [6] of iron and chromium was considered: both metals are oxidised in quantities proportionals to their amount in the alloy. The dissolution obeys a Tafel like law. No ph dependency was considered for the metal oxidation. The reduction of protons can occurs inside the crevice and follows a Tafel like law which is ph dependent [7]. The permeation of atomic hydrogen into the metal is neglected. All the parameters used in the modelling are presented in the Appendix. In addition, a time dependent resolution for the same model was attempted in order to investigate the evolution of the occluded environment during corrosion processse, from the initiation until the steady state is reached. 3. Simulation results The case of the crevice corrosion of a stainless steel (18%Cr) in chloride media was investigated. Based on the model described above the conditions inside the crevice at the steady state were calculated (Figure 2). It is worth noting that the ph profile (Figure 3) has a minimum located near the crevice mouth. A rise of ph can be observed toward the crevice tip.
Cl - CrCl2+ H2 FeCl+ Fe2+ ph 8 6 Cr3+ 4 FeOH+ 2 H+ 0 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 L²/w Figure 2. Concentration profiles for a 18%Cr stainless steel crevice of 2 mm depth and w = 1µm in 0.1M NaCl and polarised at -0.1V/SCE Figure 4. Geometry dependency of ph min (red) and ph at the tip (black) for a 18%Cr stainless steel crevice of 2 mm depth in 1M NaCl at -0.1 V/SCE Increasing potential -0.5 V/SCE -0.1 V/SCE 10-3 M Cl - 1M Cl - Increasing bulk Cl - Figure 3. ph profile for a 18%Cr stainless steel crevice of 2 mm depth and w = 1µm in 0.1M NaCl for different external potentials The crevice geometry strongly influences the ph rise, whereas the minimum of ph is nearly independent of the geometry (Figure 4). Very low ph values (as low as 2.9 ph units) were calculated with this model. Lower ph values are quoted in the litterature [8]. Chloride content in the bulk solution plays an important role in the localised corrosion. An increases of external chloride concentration leads to more agressive conditions in the occluded environment (Figure 5). Figure 5. ph dependency on the chloride concentration of the bulk solution for a 18%Cr stainless steel crevice of 2 mm depth and w = 1µm at - 0.1 V/SCE An arrest / propagation criterion was searched. A purely thermodynamic approach was used to identify the conditions of geometry and external potential for which precipitates are formed inside the crevice. The precipitates are blocking the crevice surface and they stop the corrosion. New phases formation and stability was studied (Figure 6): the limits of precipitation or dissolution of new phases at crevice tip depend strongly on the geometry of the crevice (w ), the applied potential (Vm) and on the chloride
content of the bulk solution. In the case under study (18%Cr stainless steel in chloride solution) it was found that there is a combination of potential and geometry (grey area in the Figure 6.) for which the crevice is not blocked by the precipitation of a new phase. In this domain the localised corrosion can propagate. Nevertheless, in this area gazeous hydrogen is formed. The corrosion domain is reduced when chloride concentration of bulk solution increases. There is a shift of the chlorides formation toward the cathodic domain (dashed lines in the Figure 6.) corresponding to the fact that the precipitation limits are reached at lower potentials when chloride concentration increases. According to this representation it can be seen that for the same crevice length, the lower the opening w (thin crevice) the easier is the precipitation of the new phase. Thus thin crevice will be less severe. w 1E-04 1 E-05 1 E-06 1E-07 Fe(OH)2,s H3,gaz Figure 6. Stability domain for solid and gaseous phases calculated for 2 mm long 18% Cr crevice in neutral 10-3 M NaCl solution (solid lines) and in 0.1 M NaCl (dashed lines) Fast chemical equilibria were considered for the transient resolution of this model (kif = 1000). The steady state was reached after about 10 4 s (Figure 7). The final conditions are identical with the one obtained by the resolution at the steady state. 4. Conclusions H3,gaz Cr(OH) The model considered in this work indicates that 11 aqueous species are representative for a stainless steel crevice in chloride media. 3,s FeCl2,s CrCi3,s -1.3-1.1-0.9-0.7-0.5-0.3-0.1 Vm (V/ECS) Cl- Fe2+ Figure 7. Evolution of the conditions inside a 18Cr stainless steel crevice of 2mm length and 10-5 m opening in 1M NaCl at -0.1 V/SCE Chromium hydrolysis leads to very low ph values, as low as 2.9 units. The map of stability domain for different phases indicates that there is a combination of geometry and potential for which the crevice can propagate. Another important output of this model is that the more occluded the crevice (small w), the higher the saturation inside the crevice. This result is somehow contradictory to the trend of real crevices. More studies will be conducted in order to elucidate the mechanism of Fe-Cr alloys dissolution and to find an appropriate passivation criterion. 5. Aknowledgements The authors are kindly aknowledge the Conseil Régional de Bourgogne for supporting this work. 6. References FeCl+ Cr3+ FeOH+ 1. J.W. Oldfield and W.H. Sutton, Crevice corrosion of stainless steels 1-A mathematical model, Br. Corros. J., 13, 14 23 (1978) 2. H.W. Pickering, Important Early Developments and Current Understanding of the IR Mechanism of Localized Corrosion, J. Electrochem. Soc., 150, K1 K13 (2003) 3. S.M. Sharland, P.W. Tasker, A Mathematical model of crevice and pitting corrosion - I. The physical model, Corros. Sci., 28, 603 620 (1988) H2 H+
4. G.Engelghardt, D.D.Macdonald and P.Millet, Transport processes in steam generator crevices - I.General corrosion model, Corros. Sci., 41, 2165-2190 (1999) 5. A. Turnbull and D.H. Ferriss, Mathematical modelling of the electrochemistry in corrosion fatigue cracks in structural steel cathodically protected in sea water, Corros. Sci., 26, 601 628 (1986) 6. A. Turnbull, Implication of internal cathodic reactions for crevice attack of stainless steels in chloride environments, Br. Corros. J., 32, 283-290 (1997) 7. B. Vuillemin, R. Oltra, R. Cottis, D. Crusset, Consideration on the formation of solids and gases in steady state modelling of crevice propagation, Electrochim. Acta, 52, 7570 7576 (2007) 8. A. Alavi, R.A. Cottis, The determination of ph, potential and chloride concentration in corroding crevices on 304 stainless steel and 7475 aluminium alloy, Corros. Sci., 27, 443-451(1987) Electrochemical reactions Fe Fe 2+ + 2e Cr Cr 3+ + 3 e H + + 1e ½ H 2 flux (1-p)*i0cr*exp[acr*F*(Vm- V)/(R*T)]/(2*F) p*i0cr*exp[acr*f*(vm- V)/(R*T)]/(3*F) i02*ch*exp[a2*f*(vm- V)/(R*T)]/F where p is the atomic ratio of Cr in the alloys, i0cr the exchange current for pure chromium dissolution, acr the transfert coefficient for chromium, i02 the exchange current for proton reduction, a2 transfert coefficient for proton reduction. 7. Appendix Table 1: Parameters used in modelling Chemical reactions Log K Fe 2+ + H 2 O FeOH + +H + -6.5 H 2 O H + +OH - -8 Fe 2+ + Cl - FeCl + -3.16 Cr 3+ + H 2 O CrOH 2+ + H + -0.8 Cr 3+ +Cl - CrCl 2+ -3.16