Procedure for Determination of Electrochemical Metal Dissolution in a Corrosion Crack
I.M.Dmytrakh and O.A.Yezerska
Karpenko Physico-Mechanical Institute
National Academy of Sciences of Ukraine
5 Naukova Str., 290601, Lviv, Ukraine
email: dmytrakh@Vision.IPM.Lviv.UA
Prediction of a corrosion crack growth in materials under operating conditions require more precision data about electrochemical processes which are occurred in prefracture zone at the crack tip [1-3]. These data in contain with a parameters of fracture mechanics can give the new understanding of the initiation and corrosion crack growth behavior when an electrochemical process between deformed material and electrolyte play a dominant role.
An electrochemical processes on deformed metal surfaces may be studied both through the reactions of a hydrogen reduction and the reactions of metal oxidation under environmental influence. As well known these reactions of metal dissolution in corrosive crack take place in its tip and lead to intensification of crack growth [1]. They have stage character and are localized in very small volume at the crack tip ( so called process zone).
A metal dissolution processes may be characterized by the anodic polarization curves, which obtained under corresponding testing conditions. The main electrochemical parameters of local anodic dissolution that are determine from polarization curves can be used in some electrochemical formulas for identification the reaction rate, number of electrons which take part in a reaction process, etc. [4].
The proposed below procedure for determining of a local metal dissolution in corrosion cracks under static loading are based on such approaches.
For experimental studies the model scheme of a corrosion crack was assumed (Fig.1a). According to this scheme a corrosion crack is determined by length a and crack opening dI, and also that metal dissolution process is occurred only in crack tip region (process zone). It is acceptable for aqueous environments, when an electrochemical process between deformed material and electrolyte play a dominant role.
Fig.2. Principal scheme of testing system: 1 - testing specimen;
2 - corrosion cell; 3 - heating element; 4 - temperature gauge;
5 - unit for temperature control; 6 - specimen loading mechanism;
7 - device for load measurement; 9 - mechanism for mini-electrodes
movement; 10 - step motor; 11 - operating unit; 12 - block for
registration of investigated parameters; 13 - personal computer;
14 - keyboard; 15 - monitor; 16 - printer.
A local electrochemical investigations in the corrosion crack
tip were carried out a standard potentiostat and a special mini
electrodes (Fig.1b). The special automatic testing system which
allows to carry out the simultaneously electrochemical and mechanical
investigations in various corrosion defects was used [5,6]. The
principal scheme of its system is shown on Fig.2. The system is
characterized by high sensitivity and enables to register and
to process data arrays during one experiment. It enables to fix
practically and continuously the change of electrochemical situation
on the local metal surface in all stages of materials fracture
process and to observe all kinetic possibilities of this process.
The low strength carbon steel, that containing 0.2%C and having
yield stress 270MPa for tension was investigated object. The 3%NaCl
solution under ambient temperature was used as a corrosion environment.
The modified beam specimens by height 20mm and thickness of 10mm
were used for all tests. Local electrochemical parameters of metal
in the crack tip area were received by linear polarization procedures
under potential scan rate 20MV/s. This scan rate provides, as
shown in preparatory result, the highest rate of the anodic process
of metal dissolution for a given material - environment system.
The first part of studies was dedicated of determining a potentiodynamic
polarization curves for metal in the corrosion crack tip. These
tests were conducted under stabilized electrochemical conditions,
i.e. when the pH of a solution and an electrode potential of metal
achieve the some characteristic stable values [2,3]. This situation
is inherent for a long-term environmental action on metal under
operating conditions. In this case a diffusion processes becomes
more slowly and oxygen is exhausted in the electrolyte of the
crack cavity.
The potentiodynamic polarization curves for metal in the corrosion
crack tip were received under different crack length a
and diverse crack opening displacement dI
The obtained data showed the significant increasing of intensity
and rate of metal dissolution in the crack tip with comparison
a smooth deformed surface [7]. For example, the characteristic
parameter of process - Tafel constant b have the value
range b~10…20mV, then for a smooth
open surface b~30…40mV [4,7]. These numerical data confirm
the distinction between a mechanisms of metal dissolution in corrosion
cracks and on the metallic surface and the open surfaces.
Consequently, a traditional mechanisms [4,7] of electrochemical
metal dissolution are not realize in the crack tip for given conditions.
For such case the autocatalytic mechanism of metal dissolution
in the crack tip [6] is proposed, which is realized through following
reactions:
Fe --> Fe+ + e; (1)
Fe+ --> Fe2+
+ e;
Fe2+ + e --> 2Fe+ (2)
Fe2+ + Fe+ + 2OH- + Cl- --> [FeII {FeII(OH}2Cl]+ + e; (3)
[FeII {FeII(OH}2Cl]+
+ OH- ® [FeIII
{FeIII(OH}3Cl]2+ + 2e
(4)
The given mechanism describes formation ions Fe2+
by electrochemical reactions (1). One part of these ions autocatalitically
interacts with a surface of metal that provides the realization
of the reaction (2). Other part reacts with the ion OH
and Cl through consecutive reactions (3) and
(4). In result, the iron compounds of a maximum oxidation degree
will be formed in the crack tip. In this case the stage (1) is
a source of formation of ions Fe2+ and the stage (3)
is "decelerating", as result of limitation of a diffusion
processes that lead to accumulation of ions Fe2+ in
the process zone.
The reaction (1) is electrochemical and the equilibrium concentration
CFe2 may be found from the Nernst equation:
where j is equilibrium potential; j0
is standard potential; z* is number of electrons, which
participate in a stage (1). From the equation (5) we receive:
Taking into account the limitation of a stage (3) a current density
of iron dissolution i will be in this case described by
the expression:
where k* and k** is constants; CFe2+
is a concentration of Fe2+, C is a coefficient which
represents a concentrations product of Fe2+, Cl-,
OH-, which takes part in the reactions (3); z**
is a number of electrons in the reactions (3).
By substitution dependence (6) in the equation (7), we receive
the next final expression for determining of the metal dissolution
rate according to the proposed autocatalytic mechanism:
where k is a some constant.
From the formula (8) the magnitude of Tafel coefficient can be
determined from following relation:
The formula (9) at z+=2, z++=3, a=0.5 gives
the next analytical value b=11mV. Comparison this calculated
value and the average experimental value (b=15mV) which was determined
by polarization method in corrosion crack of different length
and different crack opening displacements shows their satisfactory
coincidence. This fact validates the realization of autocatalytic
mechanism of metal dissolution in the corrosion crack tip according
to stages which are described by reactions (1-4).
During the exposition time the crack tip (process zone) is characterized
by increasing of quantity of Fe2+ ions. Accounting
this fact, the determination of influence Fe2+ ions
concentration on metal dissolution process in the crack tip is
important. This test were carry out under Fe2+ ions
concentration range equal 1·10-5…2·10-1
mol/l, which achieved by addition of salt FeSO4 7H2O
in bulk corrosion environment.
The dependencies of Tafel constant b on Fe2+
ions concentration for cracks of different length 
and under constant value of crack opening displacement dI
~13.0mm are shown in Fig. 3. The main
observation which is illustrated from these plots is decreasing
of a parameter b under increasing of Fe2+ ions
concentration. The same tendencies are observed for another values
of dI.
Fig.3 Dependencies of Tafel constant b on Fe2+
ions concentration for cracks of different length a
and under constant value of crack opening displacement (dI
~ 13.0 mm).
Obtained results reflect the significant acceleration of metal dissolution process in the crack tip with increasing if quantity of Fe2+ ions, i.e. a corrosion current Icorr in the crack tip is increasing, when a iron concentration is increased. Corrosion current Icorr as function Fe2+ ions concentration under different crack opening dI and constant crack length is shown in Fig. 4.
In addition, it may be noted, that received above data also highlight
the dependence of metal dissolution process on parameters of crack
geometry a and . Based on previous
research has been supposed, that these effects are connected with
a volume Vcr of electrolyte in the crack cavity. Results
showed that for all considered cases dependence Icorr
on Vcr is linear in logarithmic coordinates under Vcr
> 0.2mm3. Therefore these data is described
by the following relationship:
where kFe2 is parameter depends on Fe2+
ions concentration; m is constant of material - environment
system. It has been shown, that for given material - environment
system kFe2 may be determined as
where CFe2+ is a concentration of Fe2+ ions;
k0 and q are some constants of experiments.
Fig.4. Corrosion current Icorr in the crack tip as
function of crack opening displacement and Fe2+ ions
concentration for cracks of a constant length (a~5mm).
Substitution of the relation (11) into equation (10) and expressing
Vcr through a and dI
[1,8] we have:
where t and h are thickness and height of specimen,
respectively.
Formula (12) allows a prediction of corrosion current value Icorr
in the crack tip as function of the crack geometry parameters
and environmental concentration of Fe2+ ions.
The results obtained in this study, highlights the characteristic
features of a metal dissolution in the corrosion cracks, under
conditions when oxygen is exhausted in the environment of a crack
cavity. For such case the autocatalytic mechanism of metal dissolution
in the crack tip was proposed and corresponding stages of this
process were identified. Based on obtained results and experimental
data, an expression has been derived, which predicts the value
of corrosion current as function of crack length and crack opening,
and also Fe2+ ions concentration in environment of
the crack cavity.
Acknowledgment - The research described in this publication was
made possible in part by Grant ¹ K2V100 from the Joint Fund
of the Government of Ukraine and International Science Foundation.