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C306 Journal of The Electrochemical Society,163 (6) C306-C315 (2016)
Numerical Investigation of the Role of Mill Scale Crevices on the
Corrosion Initiation of Carbon Steel Reinforcement in Concrete
Kosta Karadakis,aVahid Jafari Azad,bPouria Ghods,cand O. Burkan Isgorb,∗,z
aMcIntosh Perry Consulting Engineers, Ottawa, Ontario, Canada
bSchool of Civil and Construction Engineering, Oregon State University, Corvallis, Oregon 97331, USA
cDepartment of Civil and Environmental Engineering, Giatec Scientific Inc. and Carleton University, Ottawa,
Ontario, Canada
A numerical investigation was conducted to test the hypothesis that the composition of the pore solution in mill scale crevices on
carbon steel rebar surfaces in concrete might be different from that of the bulk concrete pore solution, and this difference may
create the necessary conditions for the premature breakdown of the passive film. The modeling was performed using a non-linear
transient finite element algorithm, which involved the solution of coupled extended Nernst-Planck and Poisson’s equations in a
domain that represented typical mill scale crevices on carbon steel rebar. The numerical simulations showed that the chemistry of
the pore solution, in particular pH and Cl−/OH−, within mill scale crevices provided more favorable conditions for depassivation
than the bulk concrete pore solution. Local acidification and increase in Cl−/OH−within crevices were observed in all simulations,
albeit to different degrees. Crevice geometry has been found to be the most important parameter affecting local acidification and the
increase in Cl−/OH−. Simulations supported the hypothesis that the chemical composition of the pore solution within the crevices
differs from that of the bulk solution through a process similar to the suggested mechanism of typical crevice corrosion.
© The Author(s) 2016. Published by ECS. This is an open access article distributed under the terms of the Creative Commons
Attribution Non-Commercial No Derivatives 4.0 License (CC BY-NC-ND, http://creativecommons.org/licenses/by-nc-nd/4.0/),
which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is not changed in any
way and is properly cited. For permission for commercial reuse, please email: oa@electrochem.org. [DOI: 10.1149/2.0731606jes]
All rights reserved.
Manuscript submitted January 25, 2016; revised manuscript received March 1, 2016. Published March 11, 2016.
Within the alkaline environment of concrete, carbon steel rein-
forcement is protected against corrosion by a passive film, but chlo-
rides from deicing chemicals or marine salts might cause the loss
of this film when their concentrations exceed threshold values.1–7
Whether they are represented in terms of total or free chloride con-
centrations, or chloride-to-hydroxide concentration ratio, Cl−/OH−,
reported values of chloride thresholds for carbon steel reinforcement in
concrete cover a wide range and have a large degree of variability.9,10
The surface conditions of rebar, in particular, the presence of mill
scale on the steel surface, is one of the potential causes of the reported
uncertainty and variability in chloride thresholds.8,11–15
It has been widely reported that higher chloride thresholds were
observed for rebars with modified surfaces (i.e., without mill scale)
through sandblasting, polishing or pickling than those in as-received
conditions with mill scale.12,13,15,16 In some cases, it was observed
that corrosion did not initiate in highly-polished rebar even after the
specimens were exposed to chloride concentrations in excess of that
is typically found in sea water.11 In addition, modifying the rebar
surface leads to reduced variability and fluctuations in electrochemi-
cal measurements, which can be explained by the fact that modified
surfaces are nearly uniform, whereas as-received surfaces are locally
much more diverse and complex due to the presence of mill scale.17
These results suggest that the variability associated with the reported
chloride thresholds may be partially attributed to the variability in mill
scale properties resulting from the variability in manufacturing.
In a recent microscopic study, Ghods et al.18 investigated the effect
of mill scale on chloride-induced depassivation of carbon steel to ex-
plain why as-received rebar is more susceptible to corrosion initiation
than rebar without mill scale. Cross-sectional SEM images of rebar
specimens showed that voids and crevices exist along the interface
between steel and mill scale. An example interface between carbon
steel and mill scale is provided in Figure 1. As it can be observed in
this figure, some of these voids and crevices were connected to the
pore solution by cracks, which serve as pathways for concrete pore
solution to reach the steel surface, hence allowing ion movement be-
tween the pore solution and the crevices through electrical migration
and diffusion. It was hypothesized that over time, the chemical com-
position of the pore solution within the crevices begins to differ from
∗Electrochemical Society Member.
zE-mail: Burkan.isgor@oregonstate.edu
that of the bulk solution through a process similar to the suggested
mechanisms of typical crevice corrosion.18
Ghods et al.18 proposed a mechanism of crevice corrosion initiation
within mill scale crevices, which is briefly described here: While the
steel is in the passive state, initially, pore solution composition (i.e.,
concentrations of anions and cations) in the crevice are the same as
those in the bulk concrete pore solution. In particular, Cl−/OH-,which
is a measure of chloride threshold, is the same for the bulk solution
and for the solution inside the crevice. During the passive stage, iron
oxidizes and moves into the concrete pore solution in the crevice as a
result of the anodic reaction on the steel surface:
Fe →Fe+2+2e [1]
The rate of metal loss is proportional to the passive current density
because initially the steel is in the passive state. At the same time,
in the presence of oxygen, the following cathodic reaction also takes
Figure 1. A sample SEM micrograph showing crevices between mill scale
and steel on a typical carbon steel rebar surface.18
Journal of The Electrochemical Society,163 (6) C306-C315 (2016) C307
place on the steel surface:
1/2O2+H2O+2e →2OH−[2]
As the anodic and cathodic reactions proceed, depending on the
geometry of the crevice, and the size of the cracks, oxygen consumed
in the cathodic reaction inside the crevice cannot be replenished by the
diffusion-driven transport of oxygen from the bulk solution; therefore,
after some time, oxygen is depleted in some crevices. In these crevices,
the cathodic reaction and the local production of hydroxide slows.
However, the cathodic reaction can still take place on other parts of
the steel surface that are not covered with mill scale, or even on the mill
scale surface if the mill scale is sufficiently conductive; this continues
to drive iron corrosion inside the crevice. Chlorides and hydroxides
move into the crevice to maintain electro-neutrality, but incoming
hydroxides are consumed through the precipitation of iron hydroxides.
The result is that Cl−/OH−increases within the crevice relative to
the bulk value. Hence, depending on the shapes and sizes of cracks,
voids and crevices in the mill scale, which depends on manufacturing
particularities, different rebar steel surfaces could see much different
ratios of Cl−/OH−for the same operational/experimental conditions
and, hence, we should expect large variability in reported chloride
depassivation thresholds (Cl−/OH−ratios), as is observed.
Although Ghods et al.18 provided SEM micrographs clearly
demonstrating corrosion pits mostly initiate within mill scale crevices,
the testing of the proposed crevice corrosion mechanism experimen-
tally is not practically possible. This paper presents a computational
approach to test the proposed mechanism and to conduct a parametric
investigation to develop fundamental understanding on the effects of
steel surface conditions on chloride-induced depassivation of carbon
steel in concrete.
Theory
The numerical investigation is based on the solution of coupled
Nernst-Planck and Poisson’s equations under constraints imposed by
the chemical reactions and equilibrium requirements in domains that
represent typical mill scale cracks and crevices of carbon steel re-
inforcement in concrete. The description of the numerical modeling
theory involves the definitions of the governing equations, pore so-
lution chemistry, the geometry of the domain, initial and boundary
conditions, and the transport properties of the modelled species. The
concrete pore solutions that are investigated in this study were as-
sumed to contain only the major ionic, gaseous and solid species that
are typically found in concrete pore solutions. Specifically, six ionic
(i.e., OH−,Fe
2+,Ca
2+,Cl
−,Na
+,K
+), one gaseous (i.e., dissolved
O2(g)) and two solid species (i.e., Fe(OH)2(s) and Ca(OH)2) were con-
sidered in the numerical simulations.
Governing equations.—The transport of ionic, solid and gaseous
species within the concrete pore solution is modelled using the ex-
tended Nernst-Planck equation20:
∂ci
∂t+∂cis
∂t+∇·Ni=0[3]
where subscript iis the index representing each ionic (i.e., OH−,
Fe2+,Ca
2+,Cl
−,Na
+,K
+), and gaseous (i.e., dissolved O2(g)) species
modelled; ci(mol/m3) is the concentration of species in the ionic or
in the gaseous state; cis (mol/m3) is the concentration of the stationary
species in solid state (e.g. the components Fe(s) and OH(s) as they exist
in solid Fe(OH)2); t(s) is time; and Niis the total flux of species.
The ∂cis/∂ tterminEq.3is the sink/source term that accounts for
the exchange between the solid and ionic species in the concrete
pore solution (i.e., the exchange between Fe(s) and Fe+2, and the
exchange between OH(s) and OH−). For species that do not experience
precipitation/dissolution processes this term is set to zero. The total
flux of species, Ni, in the concrete pore solution can be written as:20
Ni=−Di∇ci−Dici∇ln γi−DiziF
RT ci∇ϕ[4]
where Di(m2/s) is the effective diffusion coefficient for the species in
water, ziis the valence of the ionic species, Ris the ideal gas constant
(8.3143 J/mol/K), T(K) is the temperature, Fis the Faraday’s constant
(96,488 C/mol), γiis the chemical activity coefficient for the various
ionic species in water, and ϕ(V) is the electric potential.
Equation 4includes three mechanisms that are used to describe the
flux of species in concrete pore solution: diffusion, electrical migration
and chemical activity. Advection flux is not considered as part of the
total flux of species because the analysis domain is assumed to be
fully saturated with the concrete pore solution that is stationary. The
diffusion term in the total flux expression (the first term in Eq. 4)
represents the movement of species based on a concentration gradient.
The chemical activity term in Eq. 4(the second term) represents
the ion-ion and ion-solvent interactions that take place in an ionic
solution. Ion-ion interactions may reduce the mobility of certain ions
in solutions due to the fact that opposite charges attract; hence, an
ion of a given charge moving in the solution will have oppositely
charged ions attaching themselves around it. Ion-solvent interactions
may also reduce the mobility of ions in a solution, but this interaction
is caused by ions dragging solvent (water) molecules with them as
they move in the solution. When dealing with solutions with low
ionic strength, the chemical activity coefficients can be approximated
as one; however, as the overall ionic concentration increases in the
solution, more ionic interactions are likely to occur. This, in turn,
causes the chemical activity coefficient to gradually deviate from
unity. The modified Davies equation, as described by Davies21 and
modified by Samson et al.,20 can accurately predict single ion activity
coefficient of concrete pore solutions made of monovalent and divalent
ions up to an ionic strength of 1200 mol/m3:20
ln γi=−Az2
i√I
1+aiB√I+0.2−4.17 ×10−5IAz2
iI
√1000 [5]
where I(mol/m3) is the ionic strength of the solution, ai(m) is the radii
of the ions in the solution, and coefficients Aand Bare temperature
dependent parameters defined as:
A=√2F2e0
8π(εRT)1.5[6]
B=2F2
εRT [7]
where e0is the charge of one electron (1.602 ×10−19 C) and εis the
permittivity of the medium, which is assumed in this study to be the
same as water (7.092 ×10−10 C2/N/m2). The ionic strength of the
solution can be calculated from:20
I=0.5
ns
i=1
ciz2
i[8]
Although there is no external current applied to the system, the
diffusion of ions within the pore solution creates electric potential
gradients since different ions move at different velocities, and this,
in turn, leads to an imbalance in the electro-neutrality of the system.
These potential gradients, through the electrical migration term (the
third term in Eq. 4), slow down the faster ions while accelerating the
slower ions so that electro-neutrality of the system is maintained.19 The
potential gradients change over time, and they need to be calculated
for each time step during the numerical solution of equation Eq. 3;
therefore, in this study, Eq. 3is coupled with the Poisson’s equation
that directly relates the electric potential distribution with the electric
charge distribution in the concrete pore solution:22
∇2ϕ=F
ε
ns
i=1
cizi[9]
where nsis the number of ionic species.
C308 Journal of The Electrochemical Society,163 (6) C306-C315 (2016)
Figure 2. The analysis domain representing the crevice between mill scale and
the steel surface. (1: crack opening, 2: symmetry axis, 3: steel surface,
4-6: mill scale surfaces, te: half of mill scale crack thickness, l: mill scale
crack length, c: crevice length, tc: crevice thickness.).
Analysis domain and boundary conditions.—The numerical in-
vestigation is carried out on a simplified and generic mill scale crevice
on carbon steel rebar as illustrated in Fig. 2. The crevice is connected
to the pore solution by a crack, which serves as pathway for concrete
pore solution to reach the steel surface, hence allowing ion movement
between the pore solution and the crevice through electrical migration
and diffusion. It is assumed that mill scale is non-conductive, and
only the steel surface is the source of electrochemical reactions that
take place within the crevice. This assumption is conservative in the
sense that not defining any electrochemical reactions on the surfaces
of mill scale will reduce the rate of oxygen and hydroxide ion deple-
tion within the crevice and will slow down the transport of species in
the pore solution.
Figure 2shows the axisymmetric domain and boundaries for a
typical crevice simulation including a crack in the mill scale and the
crevice between mill scale and steel surface. In this figure, boundary
1is the opening of the crevice to the bulk concrete pore solution;
boundary 2is the axis of symmetry; boundary 3is the steel surface;
and boundaries 4-6represent the mil scale surfaces.
Boundary conditions for the extended Nernst-Planck equations.—
Since boundary 1represents the opening of the crack to the bulk
concrete pore solution, where concentrations of species are assumed
to remain constant, Dirichlet boundary conditions are defined at this
boundary based on the assumed concentration levels in the bulk con-
crete pore solution. These concentrations are obtained from chemical
equilibrium as discussed in the Chemical reaction constraints and ini-
tial conditions section. The steel surface, 3, is assumed to be covered
with a passive film where corrosion rate is equal to the passive current
density, ip. The existing literature on the passive current density of
carbon steel in concrete or simulated concrete pore solutions show
that ipdepends on pore solute composition and steel surface finish,
and varies between 1 ×10−2to 1 ×10−4A/m2.16,23–25 The bound-
ary conditions along the steel surface (3) should represent, as per
Eq. 1and Eq. 2,OH
−production, Fe2+dissolution and O2depletion
in the passive state; therefore, the following Neumann conditions were
defined along boundary 3:
n·NOH−=ip
F[10]
n·NFe2+=ip
2F [11]
n·NO2=−ip
4F [12]
where nis the unit vector in the direction normal to the boundary.
Since no other activity other than anodic and cathodic reactions given
by Eq. 1and Eq. 2are assumed to exist on boundary 3,thefluxes
for all other species are set to zero on this boundary via:
n·Ni=0 [13]
Similarly, the no flux boundary conditions as per Eq. 8are defined
for the symmetry axis, 2, and boundaries 4-6, which represent
the mill scale surfaces that are assumed to be non-conductive.
Boundary conditions for the Poisson’s equation.—The solution
of the Poisson’s equation (Eq. 9) provides a potential gradient in
the electrical migration term of the extended Nernst-Plank equation
(Eq. 3). Since it is assumed that no external current was applied,
for the solution of the Poisson’s equation, all boundaries, except for
boundary 1, are represented by no flux condition. Boundary 1
was defined as a Dirichlet condition. Since the ultimate goal of the
solution of the Poisson’s equation is to solve for the potential gradient,
the actual value of the Dirichlet condition defined on boundary 1is
not important as long as all other boundaries are defined as no-flux
conditions. For convenience, the Dirichlet condition on boundary 1
was defined as:
ϕ=0 [14]
Chemical reaction constraints and initial conditions.—In this
study, the simulations were conducted in two simulated concrete pore
solutions named CH and CP. The CH is a saturated calcium hydrox-
ide solution with a pH of about 12.5. The CP solution (pH ∼13.3)
is composed of calcium hydroxide (at saturation), sodium hydroxide
(NaOH) and potassium hydroxide (KOH), with typical concentrations
that can be found in concrete pore solutions with ordinary Portland
cement, as given in Table I. At the beginning of the simulations it
is assumed that the pore solution composition within the crevice is
equal to the composition of the bulk concrete pore solution. The ini-
tial chemical activities presented in Table Ihave been calculated using
the modified Davies equation. Furthermore, the electro-neutrality re-
quirement is satisfied. Dissolved oxygen concentration in both CH
and CP pore solutions is assumed to be equal to 0.15 mol/m3(0.0043
mol/ft3),26 and the concentrations of Fe(s) and OH(s) from Fe(OH)2(s)
were assumed to be zero.
It is assumed in this study that the anodic and cathodic micro-cell
reactions on the passive steel surface are, respectively, iron dissolution
from the steel surface to the concrete pore solution (Eq. 1) and the
reduction of dissolved oxygen in the pore solution (Eq. 2). These
reactions are assumed to take place simultaneously on all locations on
the steel surface.27 For simplicity, iron and calcium ions are assumed
to only react with hydroxide, i.e.:
Fe2++2OH−Ksp,Fe2+
←→ Fe(OH)2[15]
Ca2++2OH−Ksp,Ca2+
←→ Ca(OH)2[16]
where Ksp,Ca2+and Ksp,Fe 2+are the solubility product constants as
5500 and 4.87 ×10−8mol3/m9, respectively.28 It should be noted
that, in addition to these reactions, the metal ions that are released in
the pore solution within crevices might also lead to hydrolysis, which
Table I. Initial concentrations and activity coefficients of species
in the CH and CP solutions before chloride addition.
Concentration (Activity coefficient)
Solution Cl−OH−Fe2+(×10−12)Ca
2+Na+K+
CH 0 31.313 138.6 15.657 0 -
(0.829) (0.521) (0.521) (0.824)
CP 0 300.597 2.64 0.298 100 200
(0.726) (0.386) (0.386) (0.740) (0.710)
Journal of The Electrochemical Society,163 (6) C306-C315 (2016) C309
will further acidify the crevice pore solution, reinforcing the hypoth-
esis that mill scale crevices might be zones of local acidification. In
this version of the model, these hydrolysis reactions are ignored in
order to differentiate the crevice geometry effects from the confound-
ing chemical reactions (such as hydrolysis) on the local acidification
process. Furthermore, the formation of a critical crevice solution can
lead to a potential IR drop that, when combined with the increasing
activity of H+ions, may promote hydrogen evolution in later stages of
crevice corrosion, causing further changes in pH. Since the modeling
process in this paper is limited to early stages of depassivation, the
confounding effects of possible hydrogen evolution processes are also
ignored.
The stoichiometric balance among the solid species of Eq. 15 and
Eq. 16 require that in the bulk concrete pore solution the following
constraint exists:
cFe(s)+cCa(s)=0.5c
OH(s)[17]
Because of the fact that Ksp,Ca2+is almost 11 orders of magni-
tude larger than Ksp,Fe2+,the concentrations of Ca(s) and OH(s) from
Ca(OH)2(s) are significantly smaller than the concentrations of Fe(s)
and OH(s) from Fe(OH)2(s). Consequently, Ca(OH)2(s) isassumedtobe
consumed within the mill scale crack and crevice such that the follow-
ing constraints are applied in the numerical solution of the extended
Nernst-Plank equation:
γCa2+cCa2+×(γOH−cOH−)2=Ksp,Ca2+[18]
γFe2+cFe2+×(γOH−cOH−)2=Ksp,Fe2+[19]
cFe(s)=0.5c
OH(s)[20]
These solubility relations must be satisfied at every node in the
pore solution when their respective solid compound is present in
the concrete pore solution. In addition, electro-neutrality of all ionic
species in the domain of analysis is strictly enforced at every step of
the analysis. When externally added NaCl is present in the bulk CH
solution, the electro-neutrality condition requires that the following
condition must be satisfied:
zOH−cOH−+zFe2+cFe2++zCa2+cCa2++zCl−cCl−+zNa+cNa+=0
[21]
where z refers to the valence numbers of the corresponding ionic
species. Note that since Cl−and Na+ions come only from NaCl salt
in the CH solution, the electro-neutrality of these two ions are satisfied
such that:
zCl−cCl−+zNa+cNa+=0 [22]
The initial concentrations of Cl−and Na+were explicitly defined
based on the amount of NaCl salt that was present in each simulation.
Using Eqs. 18,19,and21, the following non-linear expression can be
obtained for the calculation of initial concentrations of the hydroxide
ion:
cOH−=Ksp,Ca2+
γCa2+γOH−2+Ksp,Fe2+
γFe2+γOH−21/3
[23]
The equation requires an iterative solution using the modified
Davies equation, given in Eq. 3, since the activity coefficients and
concentrations of species are related to each other. A similar itera-
tive procedure was used for the CP solution. The main difference
in the iteration schemes for the two solutions originates from the
electro-neutrality condition. Na+ions in the CP solution come from
both NaCl and NaOH compounds; therefore, the following electro-
neutrality condition should be used:
zOH−cOH−+zFe2+cFe2++zCa2+cCa2++zCl−cCl−
+zNa+cNa++zK+cK+=0 [24]
Table II. Concentrations and activity coefficients of species in the
bulk CP and CH solutions with chlorides.
Concentrations (mol/m3) (Activity coefficients)
Solution Cl−OH−Fe2+(×10−12)Ca
2+Na+K+
CH 100 35.773 158.4 17.886 100 -
(0.770) (0.760) (0.416) (0.416) (0.749)
60 34.584 153.1 17.292 60 -
(0.786) (0.778) (0.439) (0.439) (0.769)
40 33.773 149.5 16.887 40 -
(0.797) (0.790) (0.457) (0.457) (0.782)
20 32.732 144.9 16.366 20 -
(0.812) (0.807) (0.482) (0.482) (0.800)
CP 300 300.618 2.376 0.3090 400 200
(0.710) (0.726) (0.387) (0.387) (0. 741) (0. 710)
150 300.623 2.757 0.3113 250 200
(0.710) (0.726) (0.387) (0.387) (0. 741) (0. 710)
125 300.621 2.750 0.3106 225 200
(0.710) (0.725) (0.387) (0.387) (0.741) (0.710)
100 300.619 2.740 0.3094 200 200
(0.710) (0.725) (0.387) (0.387) (0.741) (0.710)
which yields the following non-linear expression to be satisfied at
initial conditions:
cOH−3+cOH−2(−cCl−+cNa++cK+)
+Ksp,Ca2+
γCa2+γOH−2+Ksp,Fe2+
γFe2+γOH−2=0 [25]
Since the simulations in this study have been carried out for various
chloride concentrations, the initial concentrations and chemical activ-
ity coefficients of the species at different chloride concentrations in
the CH and CP bulk solutions are calculated using the aforementioned
approach and are provided in Table II.
Transport properties.—The effective diffusion coefficients of
ionic species in the concrete pore solution, which is a water-based
solvent, are calculated using Einstein’s relation:28
Di=RTu i
ziF[26]
where uiis the mobility of species. These coefficients are assumed to
be variable based on solid iron hydroxide formation within the crevice.
As iron hydroxide precipitates, it progressively occupies more space
within the mill scale crack and the crevice; this buildup could cause a
decrease in the rate of transport of species. To account for this effect,
the diffusion coefficients were assumed to decrease in time relative to
the Fe(OH)2(s) concentration at any given point in the analysis domain.
In this model, Fe(OH)2(s) was assumed to build up in the space within
the mill scale crack and crevice until there was no more space left. The
maximum amount of Fe(OH)2(s) that can be found in a unit volume
is 37,840 mol/m3.28 When the Fe(OH)2(s) reaches 37,840 mol/m3,
the diffusion coefficients of all species in that element were assumed
to be very small. The diffusion coefficients of species at all other
precipitation levels of Fe(OH)2(s) are linearly interpolated between
the maximum and minimum diffusion coefficients as per Table III.
Finite element analysis.—The initial-value problem defined in
this study was implemented and solved using a commercial finite el-
ement analysis software.29 The verification and benchmarking of the
model in predicting problems that are governed by coupled extended
Nearst-Plank and Poisson’s equations are performed separately and
are not presented in this paper for brevity; however, further details can
be found in.30 Since the modeled problem in this paper cannot be prac-
tically validated experimentally, additional experimental support for
the presented results is provided in the Results and discussion section.
For the CH solution, the modelling of the problem requires the
coupled solution of six extended Nernst-Plank equations (Eq. 3)for
C310 Journal of The Electrochemical Society,163 (6) C306-C315 (2016)
Table III. Transport properties of all species in the concrete pore
solutions at 298 K.
Species
Mobility,
ui(10−8
m2·s−1·V−1)
Diffusion
coefficient,
Dmaxi(m2/s) @
cFe(s)=0
Diffusion coefficient,
Dmini(m2/s) @
cFe(s)=37,840 mol/m3
OH−20.56 5.28 ×10−95.28 ×10−13
Fe2+5.60 0.72 ×10−90.72 ×10−13
Ca2+6.17 0.79 ×10−90.79 ×10−13
Cl−7.92 2.03 ×10−92.03 ×10−13
Na+5.19 1.33 ×10−91.33 ×10−13
K+7.62 1.96 ×10−91.96 ×10−13
O2-2.20×10−92.20 ×10−13
each of the species that are present in the solution (i.e., OH−,Fe
2+,
Ca2+,Cl
−,O
2(g), Fe(OH)2(s) and Ca(OH)2) and Poisson’s equation
(Eq. 9) with two chemical reaction constraints (Eqs. 18 and 19). For
the CP solution, the implementation requires the coupled solution of
the transport problem for K+ions as well. All equations are solved
at room temperature using coupled transient and non-linear solution
algorithms.
Finite element discretization of the cases that are modeled in this
work have been performed using the automatic mesh generation and
optimization algorithms of the finite element software to achieve the
optimum computational efficiency, convergence, accuracy and sta-
bility (with non-oscillating predictions). The analysis domain is dis-
cretized using quadratic triangular Lagrangian elements. Additionally,
the parallel processing abilities of the software and server are used for
increasing computational efficiency when required.
A detailed investigation on the meshing for different crevice
models were performed to obtain the optimum finite element
discretization.30 The criteria for the best meshing were efficiency
(CPU time) and accuracy (minimum element quality and rate of con-
vergence with mesh results comparisons). Finally, the optimum mesh
was decided as a three layer Lagrangian triangular elements across
the mill scale crack and crevice lengths, for all simulations. The con-
centrations were found to be accurate, even for large changes from
the bulk pore solution to the tip of the crevice, and the computational
times were faster than those of all other mesh cases considered. Based
on the analyzed cases in this study and using a 32-core server, (2.7
GHz) and 128 GB RAM, the analysis time ranged from 4–8 hours for
approximately 0.5-2 million elements for the domain.
Analysis Cases
Testing of the hypothesis.—It was hypothesized that over time,
the chemical composition of the pore solution within the crevices
begins to differ from that of the bulk solution through a process
similar to the suggested mechanisms of typical crevice corrosion.
The proposed mechanism of crevice corrosion was described earlier
in the paper; therefore, it is not repeated here. This hypothesis is
tested for a simulated mill scale crevice with domain and boundary
conditions that are described in Fig. 2with the following dimensions
which represent a typical mill scale crevice geometry: mill scale crack
length (l)=1×10−5m; half of mill scale crack thickness (te)=1×
10−7m; crevice length (c/2)=1.3 ×10−3m; crevice thickness (tc)=
1×10−6m. The simulations were carried out in the CP solution; the
chloride concentration in the bulk CP solution was 125 mol/m3,which
is typically lower than chloride thresholds that are observed for carbon
steel in the CP solution.18 Initial activities in the CP solution with
chlorides are given in Table II. A constant passive current density, ip,of
1×10−2A/m2was applied on steel surface following the investigation
by Ghods et al.25 that provided electrochemical measurements of the
passive current density of carbon steel in the CP solution. Diffusion
coefficients of species were assumed to linearly decrease from Dmax
to Dmin due to the progressive precipitation of iron hydroxide in the
crevice domain, as per Table III.
Parametric study.—The parametric study cases include crevice
dimensions, pore solution composition (CH and CP), and chloride
content of the bulk concrete pore solution. The dimensions of the
crack that provides an opening from the mill scale crevice and the
bulk concrete pore solution, as shown in Fig. 2, are assumed to be
constant in all analysis cases. The initial values of all species in the
concrete and crevice pore solutions are obtained from Eq. 18 through
Eq. 23 and shown in Table II for all chloride, sodium and potassium
concentrations in the concrete bulk pore solution. The transient anal-
yses are continued until the species reach their steady state. Different
passive current densities were used for passive steel in the CH and CP
solution following the investigation by Ghods et al.25 that provided
electrochemical measurements of the passive current density of car-
bon steel in the CP solution. Therefore, a time of 1 ×109(sec) is
considered for all analyses. Table IV provides the analysis grid for
CH and CP solutions with different values for crevice length, crevice
thickness, chloride content and pore solution type.
Results and Discussion
Testing of the hypothesis.—The analysis results of the ionic
species are reported in terms of activities, rather than concentrations,
due to the high ionic strength of the CP solution. The activities of the
ionic species (i.e., OH−,Ca
+2,Fe
+2,Na
+and K+) and the concentra-
tion of O2are presented in Fig. 3along the steel surface (boundary 3)
after steady-state conditions are reached (around t =109s). The activ-
ities of the cations are presented in Figs. 3a and 3b; these figures show
that while Fe+2is increasing toward the crevice tip, the activities of
K+,Na
+,andCa
+2are decreasing in the same direction. It is also clear
from Fig. 3c that at steady-state conditions the activity of hydroxide
ions is decreasing while the activity of chloride is increasing toward
the tip of the crevice. It is important to note that oxygen concentration
within the crevice is mostly depleted after steady-state conditions are
reached, as suggested by the proposed crevice corrosion hypothesis
(Fig. 3d).
In order to explain these trends, changes in the activities of hy-
droxide and chloride, and the change in oxygen concentration, are
plotted at the tip of the crevice (i.e., the farthest point from the bulk
Table IV. Parameter definitions for the parametric study.
Solution Current Density, Crack Crack Crevice Crevice Chloride
Type ip(A/m2) Length (m) thickness (m) Length (m) thickness (m) concentration mol/m3
CH 0.001 1 ×10−61×10−70.5 ×10−31.0 ×10−520
1.0 ×10−31.0 ×10−640
1.5 ×10−31.0 ×10−760
100
CP 0.01 1 ×10−61×10−70.5 ×10−31.0 ×10−5100
1.0 ×10−31.0 ×10−6125
1.5 ×10−31.0 ×10−7150
300
Journal of The Electrochemical Society,163 (6) C306-C315 (2016) C311
Figure 3. Species activities and oxygen concentration at steady state in CP solution along the crevice length: (a) iron and calcium ions; (b) sodium and potassium
ions; (c) chloride and hydroxide and (d) oxygen concentration. (crevice length =1.3 ×10−3m; crevice thickness =1×10−6m; chloride content in bulk pore
solution =125 mol/m3).
pore solution) over time in Figs. 4a and 4b, respectively. Anodic re-
actions (see Eq. 1) produce Fe+2ions on the steel surface (hence the
increase in the activity of Fe+2observedinFig.3a), and cathodic
reactions (see Eq. 2) consumes oxygen from the pore solution and
produces hydroxide near the steel surface. When anodic and cathodic
reactions are in balance, the expected outcome is an increase in the
activity of hydroxide; however, as shown in Fig. 3c and Fig. 4a,an
opposite pattern is observed. It can be seen in Fig. 4b that, after a short
period during which anodic and cathodic reactions at crevice end are
in balance, the oxygen concentration at this location starts decreasing
sharply from its initial condition of 0.15 mol/m3to zero in less than
one second. The decrease is mainly due to the oxygen consumption by
the cathodic reactions on the steel surface, but is accelerated due to the
slow diffusion of oxygen from the bulk solution toward the tip of the
crevice; the consumed oxygen is not replenished by the oxygen diffus-
ing from the bulk solution. When the oxygen is completely consumed
at the crevice end, the cathodic reaction cannot continue there, but the
anodic reaction still takes place since electrons produced in the anodic
reaction can still be consumed in cathodic reactions on other parts of
the steel where the pore solution still contains oxygen. The termina-
tion of the cathodic reaction at crevice end results in the termination
of hydroxide production there; therefore, the hydroxide activity starts
to decrease because the Fe+2ions produced in the anodic reaction
reacts with hydroxides to produce Fe(OH)2(s). Eventually, continued
production of Fe+2ions and decreased amounts of hydroxide causes
an imbalance in the electro-neutrality in the pore solution near the
crevice end such that total positive charge becomes larger than total
negative charge. This imbalance in electro-neutrality creates a strong
electrochemical gradient between the pore solution near crevice tip
and the bulk pore solution, which contains large amounts of negatively
charged ions such as hydroxides and chlorides; therefore, hydroxides
and chlorides start moving toward the tip of the crevice where they are
needed to establish electro-neutrality. As it can be seen in Table III,
the mobility of chlorides is smaller than that of hydroxides by a factor
of ∼3; however, the chloride activity near crevice tip starts increasing
sharply, while hydroxide activity decreases, as shown in Fig. 3c and
Fig. 4a, because hydroxides are continuously being consumed to pro-
duce Fe(OH)2(s) in the crevice. The tip of the crevice was selected for
the description above since it is the farthest point within the crevice
from the bulk pore solution. However, the same mechanism occurs at
C312 Journal of The Electrochemical Society,163 (6) C306-C315 (2016)
Figure 4. Variations over time at crevice tip in CP solution: (a) Cl−and OH−
activities, (b) oxygen concentration. (crevice length =1.3 ×10−3m; crevice
thickness =1×10−6m; chloride content in bulk pore solution =125 mol/m3).
Figure 5. pH and chloride to hydroxide ratio at steady state in CP solution
along the crevice length. (crevice length =1.3 ×10−3m; crevice thickness =
1×10−6m; chloride content in bulk pore solution =125 mol/m3).
other parts of the crevice; therefore, when steady-state conditions are
reached, the profiles given in Fig. 4can be plotted along the mill scale
crack and crevice boundaries. The result is an increase in the chlo-
rides and a decrease in the hydroxides within the mill scale crack and
crevice. Figure 5shows the pH profile and the increase in Cl−/OH−
ratio along the steel surface after steady-state conditions are reached.
These observations are supported by experimental studies8,12,13,31
that report that the Cl−/OH−threshold (at which the depassivation
process starts) is higher for the polished rebars (without mill scale)
than that of as-received rebars (with mill scale) when all other possible
confounding factors that might affect chloride thresholds are kept the
same. The increase in Cl−/OH−threshold in experimental studies due
to removal of mill scale is clearly shown in Fig. 6. On the same plot
theincreaseinCl
−/OH−of pore solution within mill scale crevices
obtained from the numerical model are presented for both CH and
CP solutions. This increase is reported for two crevice lengths: 0.5
mm and 1.2 mm, which cover typical mill scale crevice lengths that
are observed for as-received carbon steel rebar.18 It is seen that the
Figure 6. The Cl−/OH−increase in crevice area of mill-scale reported by the experimental studies compared to those obtained numerically in the current study.
(∗CL =crevice length).
Journal of The Electrochemical Society,163 (6) C306-C315 (2016) C313
Figure 7. The effects of crevice length change on Cl−/OH−and pH ratios
in CH and CP solutions: (a) for CH over crevice length and (b) for CP over
crevice length. (crevice thickness =1×10−6m; chloride content in bulk pore
solution =125 mol/m3).
experimental data are located between those calculated for the upper
value and lower value of the crevice length (i.e., 0.5 mm and 1.2 mm).
The amount of increase in Cl−/OH−ratio in crevice area is comparable
with those experimentally obtained from the polished and as-received
surfaces. This indicates that the results of the developed numerical
model are in agreement with the experimental evidences reported in
the literature.
Parametric study.—The main objective of the simulations in this
section is to investigate the pore solution chemistry within mill scale
cracks and crevices when the passive current density is assumed to
remain constant until depassivation. Especially, the Cl−/OH−ratio
is checked to monitor if it exceeds the typically-observed chloride
thresholds. Furthermore, the pH values for high Cl−/OH−are investi-
gated to check if the pore solution in the crevice domain shows signs
of acidification that might lead to depassivation and subsequent pitting
of steel. Ionic concentration of species, pH and Cl−/OH−profiles are
reported along the crevice domain.
In the microscopic studies conducted by Ghods et al.18 the dimen-
sions of the mill scale cracks and crevices on carbon rebar surface
show a large degree of variability. To cover a relatively wide range of
results, the responses in three sets of crevice thicknesses and lengths
from Table IV are compared, and the results for Cl−/OH−and pH
profiles and change over time plots (at crevice end) are shown in
Fig. 7through Fig. 10.
The effect of crevice length on pH and Cl−/OH−along the crevice
crack and steel surface for CH and CP solutions are shown in Fig. 7.
For the analysis of the 5 ×10−4m crevice length, Cl−/OH−increases
slightly (about 1.2% for both CH and CP solutions) at the tip of
the crevice (point B), and the pH remains relatively constant after
steady state conditions are reached. For the largest analyzed crevice
length (1.5 ×10−3m), Cl−/OH−at the tip of the crevice increases
by about 397% and 257% for the CH and CP solutions, respectively.
For this crevice length the pH drops below 10 for the CH solution and
below 11.5 for the CP solution, indicating local acidification within
the crevice. These conditions are likely to cause depassivation of steel
within the crevice. The changes in Cl−/OH−andpHatthetipofthe
crevice over time for the crevices exposed to the CH and CP solutions
are illustrated in Fig. 8. It is clear from this figure that the changes start
relatively quickly, shortly after the consumption of oxygen at the tip of
the crevice. The changes are larger for longer crevices, for which the
oxygen and OH−take longer time to replenish the consumed species.
In addition, the larger steel surface area within the crevice also causes
Figure 8. The effects of crevice length change on Cl−/OH−and pH ratios in
CH and CP solutions: (a) for CH over time at crevice end and (b) for CP over
time at crevice end. (crevice thickness =1×10−6m; chloride content in bulk
pore solution =125 mol/m3).
C314 Journal of The Electrochemical Society,163 (6) C306-C315 (2016)
Figure 9. The effects of crevice thickness change on Cl−/OH−and pH ratios
in CH and CP solutions: (a) for CH over crevice length and (b) for CP over
crevice length. (crevice length =1.3 ×10−3m; chloride content in bulk pore
solution =125 mol/m3).
larger amounts of iron to dissolve into the pore solution within the
crevice, which react with hydroxides to form the Fe(OH)2(s), thus
further decreasing the hydroxide concentration inside the crevice.
The effects of crevice thickness on pH and Cl−/OH−along the
crevice crack and steel surface for CH and CP solutions are shown
in Fig. 9. The change of these parameters at the tip of the crevice
over time are shown in Fig. 10. For these simulations, crevice length
was 1.3 ×10−3m and the chloride content in bulk pore solution was
125 mol/m3. In general, it can be observed that the effect of crevice
thickness on pH and Cl−/OH−is smaller than the effects observed by
changing crevice lengths. It can be seen in Fig. 9that the pH changes
with decreasing crevice thickness are rather small for both solution
types. For the CH solution, pH decreases to about 12.1 (from 12.4),
while the pH decreases to about 13 (from 13.5) in the CP solutions,
when the crevice thickness is decreased from 10−5mto10
−7m. On
the other hand, the same decrease in crevice thickness results in about
2.5-fold increase in Cl−/OH−for both solutions. This is a significant
increase when compared to chloride thresholds in the sense that steel
surfaces that are exposed to pore solutions in crevices that are rather
thin will depassivate faster than those that are exposed to thicker
crevices, while all other conditions remain the same.
Figures 11 and 12 illustrate the effect of chloride content in bulk
concrete pore solution on pH and Cl−/OH−. Four sets of different
chloride content are investigated for CH and CP solutions, separately.
The results of Cl−/OH−and pH over crevice base length (i.e., 1 ×10−3
m) are illustrated in Fig. 11, which show a relatively small decrease
Figure 10. The effects of crevice thickness change on Cl−/OH−and pH ratios
in CH and CP solutions: (a) for CH over time at crevice end, (b) for CP over
time at crevice end. (crevice length =1.3 ×10−3m; chloride content in bulk
pore solution =125 mol/m3).
Figure 11. The effects of bulk concrete pore solution chloride content change
on Cl−/OH−and pH ratios in CH and CP solutions: (a) for CH over crevice
length and (b) for CP over crevice length. (crevice length =1.3 ×10−3m;
crevice thickness =1×10−6m).
Journal of The Electrochemical Society,163 (6) C306-C315 (2016) C315
Figure 12. The effects of bulk concrete pore solution chloride content change
on Cl−/OH−and pH ratios in CH and CP solutions: (a) for CH over time at
crevice end and (b) for CP over time at crevice end. (crevice length =1.3 ×
10−3m; crevice thickness =1×10−6m).
in pH along the crevice length (maximum of about 0.2 for CH and
CP), while Cl−/OH−is relatively large (maximum of about 6 for CH
and 2.5 for CP). While the pH profiles are almost on top of each other
when different chloride levels exist in the bulk concrete pore solutions,
Cl−/OH−is very sensitive to the concrete bulk pore solution chloride
content (differences are about 5.5 units for CH and 2.0 units for CP).
For all cases, the largest drop for pH and increment in Cl−/OH−occurs
at crevice end, where the oxygen pathway is the longest. The decrease
in pH is mainly the result of the cessation of cathodic reaction as
earlier. A slight increase of pH at crevice end, between 103and 104
(sec), can be attributed to the change in chemical composition due to
the increase in chloride activity in the bulk solution.
Conclusions
The numerical simulations showed that the pore solution compo-
sition in the mill scale crevices that exist on rebar surface is different
from that of the bulk pore solution: local acidification (i.e., a drop in
pH) and increase in Cl−/OH−were observed in all simulations. The
largest drop in pH and the largest increase in Cl−/OH−occurred at
the tip of the crevice, which was the farthest point of the crevice from
the bulk solution. The changes in pH and Cl−/OH−increased with
increasing length of the crevice, indicating a relationship between
crevice geometry and the composition of the pore solution within the
crevice. It was also shown that the amount of chloride in the bulk con-
crete pore solution affects the local composition of the pore solution
(i.e., pH and Cl−/OH−) in the crevice. Simulations supported the hy-
pothesis proposed that the chemical composition of the pore solution
within the crevices differs from that of the bulk solution through
a process similar to the suggested mechanism of typical crevice
corrosion.
Acknowledgments
This research was supported by a grant from the Natural Sciences
and Engineering Research Council (NSERC) of Canada, and funds
from Oregon State University, which are gratefully acknowledged.
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