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The role of surface film on the critical flow velocity for erosion-corrosion of pure titanium
Accepted Manuscript The role of surface film on the critical flow velocity for erosion-corrosion of pure titanium Z.B. Wang, Y.G. Zheng, J.Z. Yi PII:
S0301-679X(19)30012-X
DOI:
https://doi.org/10.1016/j.triboint.2019.01.006
Reference:
JTRI 5547
To appear in:
Tribology International
Received Date: 31 August 2018 Revised Date:
4 January 2019
Accepted Date: 4 January 2019
Please cite this article as: Wang ZB, Zheng YG, Yi JZ, The role of surface film on the critical flow velocity for erosion-corrosion of pure titanium, Tribology International (2019), doi: https://doi.org/10.1016/ j.triboint.2019.01.006. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
The role of surface film on the critical flow velocity for erosion-corrosion of pure titanium
a
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Z.B. Wanga, Y.G. Zhenga,∗∗, J.Z. Yia,b
CAS Key Laboratory of Nuclear Materials and Safety Assessment, Institute of Metal
Research, Chinese Academy of Sciences, 62 Wencui Road, Shenyang 110016, PR
School of Materials Science and Engineering, University of Science and Technology
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b
SC
China
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EP
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of China, Shenyang 110016, PR China
∗
Corresponding author.
Tel.: +86 24 23928381, fax: +86 24 23894149 E-mail: [email protected] (Y.G. Zheng).
ACCEPTED MANUSCRIPT
Abstract One of the key issues in clarifying the mechanism of critical flow velocity (CFV) for erosion-corrosion is whether the surface film is ruptured mechanically below the
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CFV. This paper aims to address such an issue for titanium by using ion-labelling and colour-labelling methods. The results show that the pre-labelled ion and colour cannot be detected on the titanium surface after impingement in liquid-solid two-phase fluid
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below the CFV, suggesting the surface film has been ruptured mechanically.
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Accordingly, the phenomenon of CFV is attributed to the competition between the depassivation process induced by solid particle impacting and the subsequent repassivation process. Furthermore, a critical criterion is proposed and the expressions
Keywords:
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of depassivation time and repassivation time are derived and discussed.
Erosion-corrosion;
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Depassivation-repassivation
Critical
flow
velocity;
Surface
film;
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1. Introduction Erosion-corrosion is the main damage mode for the flow-handling components, such as impellers, turbines, pumps and pipelines, which is typically caused by the
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mechanical damage from solid particle impacting, electrochemical corrosion and their synergistic effects [1]. It has been widely reported that there is a flow velocity related critical phenomenon for erosion-corrosion damage of some metallic materials [2–15].
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When the flow velocity is low, the erosion-corrosion damage is quite slight, while
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once the flow velocity exceeds a critical value, the material loss increases sharply. This critical value is usually called as the critical flow velocity for erosion-corrosion [3, 7, 12–15]. The higher critical flow velocity means that the material can resist the erosion-corrosion damage at a higher flow velocity. Obviously, such a critical flow
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velocity can be regarded as one of the evaluation criteria for erosion-corrosion resistance and is of practical significance.
Many efforts have been made to find out the mechanism of the critical
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phenomenon mentioned above and it has been documented that the surface film plays
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a key role in it [3, 7, 11, 16–20]. However, the root cause of the critical phenomenon, which is related to the surface film, is still controversial. One view holds that the bearing ability of surface film dominates the critical phenomenon [3, 7, 11], which suggests that the surface film will not be ruptured mechanically until the flow velocity exceeds the critical value. Burstein et al. [16] found that there was a threshold impact energy of a solid particle required to rupture the passive film on 304L stainless steel mechanically by using the acoustic emission technique. Neville et al. [19] also
ACCEPTED MANUSCRIPT reported the similar phenomenon of threshold energy. It is worthy to note that the threshold energy found by Burstein et al. corresponds to the flow velocity of 0.02– 0.09 m/s at the impact angle of 90o [16, 17], which is far lower than the critical flow
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velocity of 9–12 m/s determined by Zheng et al. for 304 stainless steel suffering from impingement under similar conditions [15]. It indicates that it seems to be not so reasonable to take the bearing ability of surface film as the key controlling factor of
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critical flow velocity. In contrast, the other view tends to believe that the critical
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phenomenon lies on the competition between the depassivation process caused by solid particle impacting and electrochemical repassivation process [12, 14, 15]. This mechanism prevails only on the basis that surface film has been ruptured mechanically before it reaches the critical condition. However, although the
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repassivation of metals in liquid-solid media has been widely investigated and discussed [21–28], almost all related research focused on the effects of solid particle impacting on the electrochemical repassivation response, i.e., the erosion enhanced
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corrosion, to the best knowledge of the authors. No direct trials have been made to
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correlate the repassivation and the critical flow velocity, while only some studies speculated
that
the
critical
phenomenon
should
be
related
to
the
depassivation-repassivation process [12, 14, 15]. Based on the analyses above, the root cause of the critical flow velocity
phenomenon is still unclarified. But it seems to be sure that the surface film should be ruptured mechanically by the solid particle impacting during the erosion-corrosion process. Now, the key point of the controversy above is that under what conditions,
ACCEPTED MANUSCRIPT below or exactly at the critical flow velocity, the surface film will be ruptured mechanically. In other words, confirming whether the surface film is ruptured mechanically below the critical flow velocity should be an essential issue for
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clarifying the mechanism of critical phenomenon. Once the surface film can be confirmed to be ruptured mechanically below the critical flow velocity, the mechanism of critical phenomenon should be the competition between mechanical
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depassivation and electrochemical repassivation, otherwise the mechanism should be
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related to the bearing ability of surface film. The former and latter mechanisms will lead to the different focuses on further research, i.e., depassivation-repassivation behaviour and bearing ability of the surface film respectively. Therefore, it is of significance to find out whether the surface film is ruptured mechanically below the
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critical flow velocity, and this paper aims to address such an issue by investigating the behaviour of surface film under the erosion-corrosion condition, which is fulfilled by using ion-labelling and colour-labelling methods inspired by some features of the
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surface film of pure titanium [29, 30]. It is well known that the surface of titanium
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will colour when titanium is anodized electrochemically or heat oxidized due to the thin layer interference [29]. Meanwhile, our previous work has found that the fluoride ion can penetrate into the passive film of pure titanium [30]. Accordingly, surface colour and fluoride ion can act as the marker to clarify the behaviour of surface film in the erosion-corrosion process. It can be predicted that the surface film should have already been ruptured if the surface colour changes or the fluoride ion cannot be detected anymore after erosion-corrosion tests. In the last, the mechanism of critical
ACCEPTED MANUSCRIPT flow velocity for erosion-corrosion is proposed and discussed.
2. Experimental 2.1 Materials and surface preparation
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This study chose pure titanium, the typical passive metal, as the research material. The specimen was cut from an as-received commercial Grade 2 pure titanium sheet with the thickness of 1.5 mm. After being ground and cleaned, the working electrode
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was embedded in epoxy resin to ensure an exposed area of 0.5 cm2. Then the surface
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of working electrode was wet ground mechanically to 800# with a series of silicon carbide abrasive papers for the experiments of colour labelling, ion labelling and determining the critical flow velocity.
2.2 Colour-labelling and ion-labelling methods
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Prior to the erosion-corrosion tests, the surface film of pure titanium was labelled by colour and fluoride ion (F-). The colour labelling was performed by anodizing the working electrode electrochemically at the potential of 22 V for 15 s, which resulted
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in the surface colour of blue-purple [29]. The anodizing process was carried out in 1
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M H2SO4 solution by using a DC power supply with pure titanium as the anode and a Pt foil as the cathode. The ion labelling was conducted by immersing the titanium sample in the solution of 0.05 M H2SO4 + 0.0005 M F- for 24 h, which led to a double layer passive film with a compact inner layer and a porous outer layer containing the fluoride ion [30]. After being colour-labelled and ion-labelled, the samples were washed by deionized water and placed in the impingement chamber immediately for the following erosion-corrosion tests.
ACCEPTED MANUSCRIPT 2.3 Erosion-corrosion tests The erosion-corrosion tests were conducted using a jet impingement apparatus, which has been described in our previous work [14]. The jet nozzle diameter was 3
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mm, through which the liquid-solid two-phase fluid impacted on the sample surface. It should be noted that the flow velocity at the nozzle exit was regarded as the flow velocity of medium in this paper [12, 15]. The stand-off distance from the jet nozzle
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exit to the sample surface was 5 mm and the impact angle was set to be 90o. The
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medium used in this study was a slurry composed of 3.5 wt.% NaCl solution and 2 wt.% silica sand particles with the sizes of 75-150 mesh.
In this work, there were two types of erosion-corrosion tests: one for determining the critical flow velocity and the other for the pre-labelled samples. In order to clarify
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whether the surface film is ruptured below the critical flow velocity for erosion-corrosion, the critical flow velocity of pure titanium must be determined first. The potentiostatic polarization test was used for this type of erosion-corrosion test,
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which was also employed in our previous work and in the other research [12, 14, 15,
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20]. A three-electrode cell placing in the impingement chamber was used. It consisted of a titanium sample without pre-labelling as the working electrode, a Pt foil with a larger area as the counter electrode and a saturated calomel electrode (SCE) connecting to the cell via a salt bridge with a Luggin capillary as the reference electrode. A Potentiostat/Galvanostat (PARSTAT 2273) was used to control the potentiostatic polarization test. The potential was set at 0 V vs. SCE, which located in the potential range of stable passivation of titanium in 3.5 wt.% NaCl solution. The
ACCEPTED MANUSCRIPT flow velocity in this type of erosion-corrosion test was controlled to vary with time in the manner as shown in Fig. 1. During the whole period of this test, the passive current was recorded.
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After confirming the critical flow velocity, the other erosion-corrosion test was carried out for the pre-labelled samples at the open circuit potential, so that the behaviour of surface film would not be probably affected by the applied potential. In
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order to assess the evolution of surface colour with impingement time at different
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flow velocities, the colour-labelled samples were impinged for 1 min, 5 min, 10 min and 60 min at 5 m/s and 7 m/s, which was far below the determined critical flow velocity of titanium as shown in the next section. In contrast, the ion-labelled sample was only impinged for 5 min at 5 m/s because the surface film was too thin and the
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content of labelled fluoride ion in the film was too low to assess the content evolution with impingement time. Besides, the test time of 5 min was properly short to detect the changes of fluoride ion content in the film based on the pre-experiments. At least
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two tests under identical conditions were performed to ensure the reproducibility.
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2.4 Surface characterization
The changes in surface colour were recorded by the stereo microscope (ZEISS
Stemi 508) before and after the erosion-corrosion tests. The fluoride ion in the surface film was detected by X-ray photoelectron spectroscopy (XPS). XPS analyses were performed to the ion-labelled samples after the erosion-corrosion tests, using an ESCALAB250 X-ray photoelectron spectrometer with a monochromatic AlK (1486.6 eV) radiation source. The X-ray gun was operated at 150 W (15 kV, 10 mA) with the
ACCEPTED MANUSCRIPT photoelectron take-off angle of 90∘. The base pressure was maintained at approximately 10−8 Pa during the experiments. High resolution spectra with an analysed area of 500 µm2 were recorded at a pass energy of 50.0 eV with an energy
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step of 0.1 eV and energy resolution of 0.5 eV. High resolution spectra of F 1s, and C 1s were registered and the values of binding energies were aligned to carbon peak C 1s at 284.6 eV.
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3. Results
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3.1 Determination of the critical flow velocity for erosion-corrosion of titanium Fig. 2 shows the changes of current density of pure titanium at 0 V vs. SCE with the flow velocity under impingement. The current densities remain at low values when the flow velocities are lower than 14 m/s, indicating the passive feature. As
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increasing the flow velocity to 15 m/s, the current density steps up remarkably. According to our previous work, the flow velocity, above which the current density starts to increase noticeably during the potentiostatic polarization test, can be regarded
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as the critical flow velocity for erosion-corrosion [14, 15, 20]. Hereby, the critical
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flow velocity can be determined as 14 m/s for pure titanium. Besides, it is worthy of noting that there are some small current peaks at lower flow velocities, such as 7–11 m/s, as shown in the enlarged view in Fig. 2. These current peaks seem to be more likely to result from the film rupture caused by the solid particle impacting [17] rather than the breakdown of passivity involved in the metastable pitting [31], since titanium does not suffer from pitting corrosion at 0 V vs. SCE in neutral chloride-containing solutions [32].
ACCEPTED MANUSCRIPT 3.2 Colour-labelling and ion-labelling tests According to the determined critical flow velocity (14 m/s as shown in Fig. 2), 5 m/s and 7 m/s were selected to investigate the behaviour of pre-labelled surface film
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below the critical flow velocity. Fig. 3 displays the changes in surface colour of colour-labelled titanium samples after impingement below the critical flow velocity for different time. At either 5 m/s or 7 m/s, pale annular regions, in which the original
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colour disappears, can be always distinguished after impingement for any test time.
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The pale regions look like whiter and their areas get larger with increasing the flow velocity and impingement time. In contrast, no other colour, except the original blue-purple colour, can be identified in the other surface regions. The results of spectrophotometer test also manifest that only the pale area increases but no other
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characteristic peaks appear in the wavelength-reflection percentage curve (not shown). Since these annular regions just locate in the region where the solid particles impact most severely [15], it suggests that the colour-labelled surface film has been removed
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after impingement below the critical flow velocity. The removing of colour-labelled
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film should result from either the mechanical rupture or chemical/electrochemical dissolution during the impingement process. A control test was conducted under the impingement condition without solid particles, as also shown in Fig. 3. No pale region can be identified on the surface, indicating that the chemical/electrochemical dissolution mechanism can be excluded. Accordingly, it can be preliminarily confirmed that the surface film is ruptured mechanically even at the flow velocities lower than the critical value.
ACCEPTED MANUSCRIPT In order to further confirm the mechanical rupture of surface film found above, the fluoride ion-labelled titanium sample was used. Fig. 4 shows the detailed F 1s XPS spectra of fluoride ion-labelled titanium sample after impingement at 5 m/s for 5
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min, in which the two curves represent the signals detected from the unimpinged region and impinged region respectively. In the unimpinged region where the surface film will be thinned or be removed only by chemical/electrochemical dissolution, the
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F 1s XPS peak can be still recognized and shows the same feature with that of the
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original fluoride ion-labelled film, demonstrating the existence of fluoride ion in the surface film. It manifests that the chemical/electrochemical dissolution process has little effects on the detection of fluoride ion in the surface film. In contrast, no F 1s XPS peak can be identified in the impinged region, indicating that the surface film
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containing fluoride ion has been removed during the impingement. Since the chemical/electrochemical dissolution mechanism for film removing has been excluded based on the result of unimpinged region, it can be concluded that the
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disappearance of F 1s XPS peak in impinged region must be attributed to the film
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mechanical rupture caused by solid particle impacting. It agrees well with the conclusion made from the colour-labelling test.
4. Discussion
Based on the results above, it can be concluded that mechanical rupture of the
surface film on titanium occurs at the flow velocity lower than the critical value. The reason for film mechanical rupture should be related to the impact energy or impact-induced stress resulting from the solid particles. Burstein and Sasaki [16, 17]
ACCEPTED MANUSCRIPT found the threshold energy of solid particle impacting, below which the surface film of stainless steel would not be ruptured by erosion. However, they did not explain the reason for the threshold energy phenomenon primarily. It is well accepted that the
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mechanical failure will occur for a certain material if the applied stress exceeds its tensile or compressive strength. Accordingly, we try to explain why the film is ruptured mechanically at low flow velocities by calculating the impact-induced mean
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stress theoretically rather than considering the impact energy.
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Based on the Herzian contact theory [33, 34], the mean stress (σm) generated by single solid particle impacting is as follows by assuming that the external mean pressure (Pm) transfers to the internal stress completely: 1 5πρ s 4 k σ m = Pm = π 3 3 E1 0.2
−0.8
V 0.4
(1)
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where ρs is the density of solid particle (2.65 × 106 g/m3 for silica sand particle), E1 is the elastic modulus of impacted target sample and V is the flow velocity. Here, TiO2 is
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regarded as the impacted sample because the solid particle impacts directly on the surface film that mainly consists of TiO2 [30]. Thus, E1 is 230 GPa for TiO2 [35]. The
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parameter k in Eq. (1) is a constant whose value can be calculated using the following equation:
k=
9 2 2 E1 (1 − ν 1 ) + (1 −ν 2 ) 16 E2
(2)
where ν1 and ν2 are the Poisson’s ratios of TiO2 (0.27 [35]) and solid particle (0.23) respectively, E1 has the same meaning with that in Eq. (1), and E2 is the elastic modulus of a solid particle (59 GPa). Substituting all parameter values in Eq. (1) and
ACCEPTED MANUSCRIPT Eq. (2), the mean stress induced under the condition of 5 m/s impingement can be calculated as 11.7 GPa. Even at a flow velocity as low as 0.5 m/s, the mean stress is still as high as 5.4 GPa. Moreover, further stress concentration may be also generated
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when the angular particle impacts on the surface. It means that the stress induced by solid particle impacting is undoubtedly so high that almost no materials can bear. As a result, the surface film must be ruptured mechanically. Replacing the TiO2 impacted
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target with the titanium substrate, the corresponding mean stress can be calculated as
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10.2 GPa at 5 m/s by using E1= 115 GPa and ν1= 0.33 for titanium. This high stress can lead to severe plastic deformation of titanium substrate. As a result, the surface film will be also ruptured because it is too brittle to deform together with the substrate.
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Accordingly, it can be concluded that the mechanical rupture of surface film must occur at low flow velocities via the mechanism of either being ruptured directly by solid particle impacting or being ruptured indirectly due to the deformation of
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substrate. It means that the higher the flow velocity is and the longer the test time is,
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the more solid particles will impact on the surface and the more surface film will be removed consequently. This agrees well with the experimental results shown in Fig. 3. This conclusion can be seemingly extended to other passive metals because the impact induced stress is high enough to rupture the common surface films mechanically. It demonstrates that the mechanism of critical flow velocity for erosion-corrosion should be exactly related to the competition between the depassivation process caused by solid particle impacting and the electrochemical
ACCEPTED MANUSCRIPT repassivation process. It can be proposed as follows: when the flow velocities are lower than the critical value, the repassivation rate is faster than the depassivation rate, and the surface film can form quickly and timely to repair the mechanically ruptured
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film. In this situation, some transient current spikes will probably occur at lower flow velocities, just as those shown in Fig. 2. As a result, the surface film is still intact and protective, leading to inconspicuous damage, i.e., the feature of almost unchanged low
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current density in Fig. 2. In contrast, the depassivation rate will exceed the
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repassivation rate when the flow velocities are higher than the critical value. Consequently, the mechanically ruptured film cannot be repaired in time anymore and the surface film will lose its protectiveness, resulting in severe damage, i.e., the feature of abrupt increase of current density in Fig. 2. Accordingly, the critical
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condition must be the depassivation rate equalling to the repassivation rate. It is known that the repassivation rate corresponds to the repassivation time [36, 37]. Therefore, the critical condition can be considered as depassivation time (τde)
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equalling to repassivation time (τre), i.e., τde=τre. Here, we define the depassivation
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time as the time interval between two successive solid particle impacting at one single point on the surface and define the repassivation time as the time duration for completing the repassivation after being impacted. Apparently, the critical flow velocity for erosion-corrosion can be predicted if the critical equation can be resolved. The depassivation time, τde, should be the reciprocal of impact number per second at a single point, nimpact, since the depassivation process is caused by the solid particle impacting [22]. The nimpact can be obtained via multiplying the total impact
ACCEPTED MANUSCRIPT number per second on the whole surface, Nimpact, by the probability of repeated impact (Asingle/Atotal), which is expressed as follows: nimpact = N impact
(3)
Atotal
π d s 2 sin θ
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Asingle =
Asingle
(4)
4
where Asingle is the projected area of one solid particle on the impact surface, Atotal is
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the total impact area, ds is mean diameter of solid particle and θ is the impact angle.
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The exact expression of Atotal seems to be unclear now, but it should be related to the diameter of nozzle, impact angle and the stand-off distance from the jet nozzle exit to the sample surface [38]. If these influencing parameters are fixed, the value of Atotal should be obtained roughly by measuring the total damage area experimentally. In our
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previous work that applied the same experimental parameters with present paper, a circular damage area was observed with a diameter of approximately 6 × 10–3 m [15]. So Atotal can be calculated as 2.826 × 10–5 m2.
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In general, Nimpact can be obtained via multiplying the number of solid particles
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containing in unit volume of the flow medium (Nvolume = 6c/πρsds3) by the volume of medium that flows through the nozzle in unit time (Vimpact = 0.25πVdn2), which is given as follows:
N impact = N volumeVimpact
3cVd n2 = 2 ρs d s3
(5)
where c, ρs and ds are the concentration, density and mean diameter of the solid particle respectively, V is the flow velocity and dn is the diameter of nozzle. Substituting Eq. (4) and Eq. (5) in Eq. (3) and taking the reciprocal, the depassivation
ACCEPTED MANUSCRIPT time, τde, can be obtained:
τ de =
1 nimpact
=
8 Atotal ρs ds 3π cVd n2 sin θ
(5)
As to the repassivation time, τre, it depends on the repassivation kinetics.
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Summarily, there are three types of decay law for the current density response after the surface film is ruptured mechanically by solid particle impacting or by scratching
(i) Single-exponential decay law [23, 39]:
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t I = I s + I peak exp − τ
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in various metal/electrolyte systems:
(6)
where Is is the stable current density without solid particle impacting, Ipeak is the maximum current density caused by solid particle impacting and τ is a constant
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related to the film formation on the bared impacted surface. (ii) Double-exponential decay law [24, 25, 27]:
(7)
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t t I = I s + I1 exp − + I 2 exp − τ1 τ2
where Is has the same meaning with that in Eq. (6), and I1, I2, τ1 and τ2 are the
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constants related to the film formation on the bared impacted surface (I1 + I2 = Ipeak). (iii) Power decay law (t>τ) [24, 28, 37, 40]:
t I = I s + I peak τ
−α
(8)
where Is, Ipeak and τ have the same meanings with those in Eq. (6) and α is a constant (0<α<1). The key point is how to determine τre from Eq. (6), Eq. (7) and Eq. (8). In
ACCEPTED MANUSCRIPT principle, only when the current density decays to the original value, i.e., I = Is, should the repassivation process be totally completed. Hassel et al. [21, 41] took this criterion to determine the repassivation time from the current-time curve directly. However,
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from the point of mathematics, I = Is can be achieved precisely only under the condition of t = +∞ for any of Eq. (6), Eq. (7) and Eq. (8), which is obviously not possible. Hussain and Robinson [22] also believed that the film cannot grow to the
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original state by repassivation process alone in limited time interval after solid particle
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impacting. Therefore, it does not seem feasible to determine τre by means of the criterion of I = Is. As an alternative, Kwon et al. [37] regarded the time when the current density decayed to a certain value close to Is as the repassivation time, while Sawada et al. [42] specialized this value to 1/e (e is a constant whose value is
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approximately 2.7) of Ipeak. This method is quite useful to compare the repassivation ability of various materials. But it is still not suitable to get the absolute value of τre since there is no fundamental or explanations for choosing such a current density
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value. In addition, Rajahram et al. [27] also reported the τre value for UNS S31603
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stainless steel under erosion-corrosion condition, but without providing the specific method.
The discussion above demonstrates that there is lack of the criterion for
evaluating the totally complete repassivation, which restricts the derivation of τre expression based on the repassivation kinetics as shown in Eq. (6), Eq. (7) and Eq. (8). Furthermore, the impact angle (θ) [25], impact area (Atotal) [25] and flow velocity (V) [27] were found to have some effects on the repassivation kinetics. However, the
ACCEPTED MANUSCRIPT quantitative relation between τre and these parameters cannot be derived theoretically but can be only established by experimental determination. Unfortunately, there are no relevant investigations to our best knowledge. It should be interesting but
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complicated to clarify when the repassivation process is totally completed and how the environmental factors, such as V and θ, affect the repassivation process, which will be of significance for the study of not only erosion-corrosion but also the other
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aspects involved in the repassivation process, such as pitting corrosion. In this paper,
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the main objective is to find out whether the surface film is ruptured mechanically below the critical flow velocity, so that we can try to further clarify the mechanism of the critical flow velocity for erosion-corrosion. Fig. 3 and Fig. 4 have already confirmed the film mechanical rupture at the flow velocity lower than the critical
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value, and the critical phenomenon has also been attributed to the competition between the depassivation process induced by solid particle impacting and the electrochemical repassivation process. Here, we just try to highlight the issue about
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the repassivation by the preliminary discussion. More detail work has been designed
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and is being conducted now.
By considering the uncertainty of τre in the current situation, the critical condition
for erosion-corrosion is given as follows:
τ re = τ de =
8 Atotal ρs ds 3π cVc d n2 sin θ
(9)
where Vc represents the critical flow velocity for erosion-corrosion. This critical equation can be used to predict the effects of some factors on the critical flow velocity, although the specific Vc value cannot be calculated directly yet. In Eq. (9), τre should
ACCEPTED MANUSCRIPT be independent on c and ds because the solid particle should have no effects on the passive process at low concentrations, such as 2 wt.% used in this work. Accordingly, it can be predicted that Vc of pure titanium will increase with decreasing c or
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increasing ds, which agrees with the experimental results of Fe-based amorphous metallic coating and stainless steel in our previous wok (c = 0 wt.% ~ 5 wt.% and ds = 54 µm ~ 330 µm) [15, 43]. But there are no specific experimental results for pure
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titanium, so further relevant experimental verification is still needed. In contrast, the
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dependence of θ on Vc cannot be predicted since the effect of θ on τre is unclear, although the effect of θ on Vc has been clarified experimentally in the range of 30o ~ 90o [43]. Moreover, the variation of Vc with the other parameters can be only predicted with assuming that they have no effects on τre. But this assumption cannot
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be verified because no relevant experimental results are available now. Therefore, further investigations are needed for clarifying the dependence of τre on the environmental factors, such as the flow velocity, c, ρs, ds, dn and θ, and for
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determining the Vc values of pure titanium under various conditions experimentally,
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such as at different values of c, ρs, ds, dn and θ.
4. Conclusions
This paper find out that the surface film of titanium is ruptured mechanically at
the flow velocities lower than the critical flow velocity by using the colour-labelling and ion-labelling methods. The mechanical rupture of surface film can be attributed to the extremely high stress induced by the solid particle impacting. Accordingly, we try to attribute the mechanism of critical flow velocity phenomenon for erosion-corrosion
ACCEPTED MANUSCRIPT to the competition between the depassivation process caused by solid particle impacting and the repassivation process. Then, the equation of depassivation time (τde) equalling to repassivation time (τre), i.e., τde=τre, is proposed to be the critical condition
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for erosion-corrosion. Some efforts have been made to derive the specific expressions of τde and τre theoretically. Based on the derivation results, the dependence of concentration and diameter of solid particle on the critical flow velocity is predicted
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for pure titanium and the crucial issues involved in the repassivation process, such as
Acknowledgements
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the definition of complete repassivation, are highlighted.
The authors would like to acknowledge the financial supports from the National Natural Science Foundation of China (grant numbers 51801218, 51571200) and the
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Strategic Priority Research Program of the Chinese Academy of Sciences (grand number XDA13040500).
References
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[1] Wood RJK. Erosion-corrosion interactions and their effect on marine and offshore
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ACCEPTED MANUSCRIPT [5] Zhou S, Stack MM, Newman RC. Characterization of synergistic effects between erosion and corrosion in an aqueous environment using electrochemical techniques. Corrosion 1996;52:934–46.
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2004;256:565–76.
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[11] Tan KS, Wharton JA, Wood RJK. Solid particle erosion-corrosion behaviour of a novel HVOF nickel aluminium bronze coating for marine applications - correlation between mass loss and electrochemical measurements. Wear 2005;258:629–40. [12] Hu X, Neville A. The electrochemical response of stainless steels in liquid-solid impingement. Wear 2005;258:641–8. [13] Zheng YG, Yu H, Jiang SL, Yao ZM. Effect of the sea mud on erosion-corrosion
ACCEPTED MANUSCRIPT behaviors of carbon steel and low alloy steel in 2.4% NaCl solution. Wear 2008;264:1051–8. [14] Zheng ZB, Zheng YG, Sun WH, Wang JQ. Erosion-corrosion of HVOF-sprayed
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erosion-corrosion using a slurry pot erosion tester. Tribol Int 2011;44:232–40. [28] Lu BT, Luo JL, Guo HX, Mao LC. Erosion-enhanced corrosion of carbon steel at passive state. Corros Sci 2011;53:432–40. [29] Gaul E. Coloring titanium and related metals by electrochemical oxidation. J Chem Educ 1993;70:176–8. [30] Wang ZB, Hu HX, Liu CB, Zheng YG. The effect of fluoride ions on the corrosion behavior of pure titanium in 0.05 M sulfuric acid. Electrochim Acta
ACCEPTED MANUSCRIPT 2014;135:526–35. [31] Burstein GT, Liu C. Nucleation of corrosion pits in Ringer's solution containing bovine serum. Corros Sci 2007;49:4296–306.
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https://www.azom.com/properties.aspx?ArticleID=1179; 2002 [accessed 30 August 2018].
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[38] Gnanavelu A, Kapur N, Neville A, Flores JF. An integrated methodology for predicting material wear rates due to erosion. Wear 2009;267:1935–44. [39] Hanawa T, Kohayama Y, Hiromoto S, Yamamoto A. Effects of biological factors on the repassivation current of titanium. Mater Trans 2004;45:1635–9.
ACCEPTED MANUSCRIPT [40] Wu PQ, Celis JP. Ion conduction model applied to repassivation kinetics of tribo-activated surfaces. J Electrochem Soc 2004;151:B551–7. [41] Abelev E, Smith AJ, Hassel AW, Ein-Eli Y. Copper repassivation characteristics
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in carbonate-based solutions. J Electrochem Soc 2006;153:B337–43. [42] Sawada T, Schille C, Almadani A, Geis-Gerstorfer J. Fretting corrosion behavior of experimental Ti-20Cr compared to titanium. Materials. 2017;10:1–12.
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[43] He SY. Effect of environmental factors on the critical flow velocities for
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erosion-corrosion of 304 stainless steel in liquid-solid two-phase flow. Master of
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Engineering Thesis, University of Chinese Academy of Sciences; May 2016.
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S0301-679X(19)30012-X
DOI:
https://doi.org/10.1016/j.triboint.2019.01.006
Reference:
JTRI 5547
To appear in:
Tribology International
Received Date: 31 August 2018 Revised Date:
4 January 2019
Accepted Date: 4 January 2019
Please cite this article as: Wang ZB, Zheng YG, Yi JZ, The role of surface film on the critical flow velocity for erosion-corrosion of pure titanium, Tribology International (2019), doi: https://doi.org/10.1016/ j.triboint.2019.01.006. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
The role of surface film on the critical flow velocity for erosion-corrosion of pure titanium
a
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Z.B. Wanga, Y.G. Zhenga,∗∗, J.Z. Yia,b
CAS Key Laboratory of Nuclear Materials and Safety Assessment, Institute of Metal
Research, Chinese Academy of Sciences, 62 Wencui Road, Shenyang 110016, PR
School of Materials Science and Engineering, University of Science and Technology
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b
SC
China
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of China, Shenyang 110016, PR China
∗
Corresponding author.
Tel.: +86 24 23928381, fax: +86 24 23894149 E-mail: [email protected] (Y.G. Zheng).
ACCEPTED MANUSCRIPT
Abstract One of the key issues in clarifying the mechanism of critical flow velocity (CFV) for erosion-corrosion is whether the surface film is ruptured mechanically below the
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CFV. This paper aims to address such an issue for titanium by using ion-labelling and colour-labelling methods. The results show that the pre-labelled ion and colour cannot be detected on the titanium surface after impingement in liquid-solid two-phase fluid
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below the CFV, suggesting the surface film has been ruptured mechanically.
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Accordingly, the phenomenon of CFV is attributed to the competition between the depassivation process induced by solid particle impacting and the subsequent repassivation process. Furthermore, a critical criterion is proposed and the expressions
Keywords:
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of depassivation time and repassivation time are derived and discussed.
Erosion-corrosion;
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Depassivation-repassivation
Critical
flow
velocity;
Surface
film;
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1. Introduction Erosion-corrosion is the main damage mode for the flow-handling components, such as impellers, turbines, pumps and pipelines, which is typically caused by the
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mechanical damage from solid particle impacting, electrochemical corrosion and their synergistic effects [1]. It has been widely reported that there is a flow velocity related critical phenomenon for erosion-corrosion damage of some metallic materials [2–15].
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When the flow velocity is low, the erosion-corrosion damage is quite slight, while
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once the flow velocity exceeds a critical value, the material loss increases sharply. This critical value is usually called as the critical flow velocity for erosion-corrosion [3, 7, 12–15]. The higher critical flow velocity means that the material can resist the erosion-corrosion damage at a higher flow velocity. Obviously, such a critical flow
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velocity can be regarded as one of the evaluation criteria for erosion-corrosion resistance and is of practical significance.
Many efforts have been made to find out the mechanism of the critical
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phenomenon mentioned above and it has been documented that the surface film plays
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a key role in it [3, 7, 11, 16–20]. However, the root cause of the critical phenomenon, which is related to the surface film, is still controversial. One view holds that the bearing ability of surface film dominates the critical phenomenon [3, 7, 11], which suggests that the surface film will not be ruptured mechanically until the flow velocity exceeds the critical value. Burstein et al. [16] found that there was a threshold impact energy of a solid particle required to rupture the passive film on 304L stainless steel mechanically by using the acoustic emission technique. Neville et al. [19] also
ACCEPTED MANUSCRIPT reported the similar phenomenon of threshold energy. It is worthy to note that the threshold energy found by Burstein et al. corresponds to the flow velocity of 0.02– 0.09 m/s at the impact angle of 90o [16, 17], which is far lower than the critical flow
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velocity of 9–12 m/s determined by Zheng et al. for 304 stainless steel suffering from impingement under similar conditions [15]. It indicates that it seems to be not so reasonable to take the bearing ability of surface film as the key controlling factor of
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critical flow velocity. In contrast, the other view tends to believe that the critical
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phenomenon lies on the competition between the depassivation process caused by solid particle impacting and electrochemical repassivation process [12, 14, 15]. This mechanism prevails only on the basis that surface film has been ruptured mechanically before it reaches the critical condition. However, although the
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repassivation of metals in liquid-solid media has been widely investigated and discussed [21–28], almost all related research focused on the effects of solid particle impacting on the electrochemical repassivation response, i.e., the erosion enhanced
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corrosion, to the best knowledge of the authors. No direct trials have been made to
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correlate the repassivation and the critical flow velocity, while only some studies speculated
that
the
critical
phenomenon
should
be
related
to
the
depassivation-repassivation process [12, 14, 15]. Based on the analyses above, the root cause of the critical flow velocity
phenomenon is still unclarified. But it seems to be sure that the surface film should be ruptured mechanically by the solid particle impacting during the erosion-corrosion process. Now, the key point of the controversy above is that under what conditions,
ACCEPTED MANUSCRIPT below or exactly at the critical flow velocity, the surface film will be ruptured mechanically. In other words, confirming whether the surface film is ruptured mechanically below the critical flow velocity should be an essential issue for
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clarifying the mechanism of critical phenomenon. Once the surface film can be confirmed to be ruptured mechanically below the critical flow velocity, the mechanism of critical phenomenon should be the competition between mechanical
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depassivation and electrochemical repassivation, otherwise the mechanism should be
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related to the bearing ability of surface film. The former and latter mechanisms will lead to the different focuses on further research, i.e., depassivation-repassivation behaviour and bearing ability of the surface film respectively. Therefore, it is of significance to find out whether the surface film is ruptured mechanically below the
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critical flow velocity, and this paper aims to address such an issue by investigating the behaviour of surface film under the erosion-corrosion condition, which is fulfilled by using ion-labelling and colour-labelling methods inspired by some features of the
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surface film of pure titanium [29, 30]. It is well known that the surface of titanium
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will colour when titanium is anodized electrochemically or heat oxidized due to the thin layer interference [29]. Meanwhile, our previous work has found that the fluoride ion can penetrate into the passive film of pure titanium [30]. Accordingly, surface colour and fluoride ion can act as the marker to clarify the behaviour of surface film in the erosion-corrosion process. It can be predicted that the surface film should have already been ruptured if the surface colour changes or the fluoride ion cannot be detected anymore after erosion-corrosion tests. In the last, the mechanism of critical
ACCEPTED MANUSCRIPT flow velocity for erosion-corrosion is proposed and discussed.
2. Experimental 2.1 Materials and surface preparation
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This study chose pure titanium, the typical passive metal, as the research material. The specimen was cut from an as-received commercial Grade 2 pure titanium sheet with the thickness of 1.5 mm. After being ground and cleaned, the working electrode
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was embedded in epoxy resin to ensure an exposed area of 0.5 cm2. Then the surface
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of working electrode was wet ground mechanically to 800# with a series of silicon carbide abrasive papers for the experiments of colour labelling, ion labelling and determining the critical flow velocity.
2.2 Colour-labelling and ion-labelling methods
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Prior to the erosion-corrosion tests, the surface film of pure titanium was labelled by colour and fluoride ion (F-). The colour labelling was performed by anodizing the working electrode electrochemically at the potential of 22 V for 15 s, which resulted
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in the surface colour of blue-purple [29]. The anodizing process was carried out in 1
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M H2SO4 solution by using a DC power supply with pure titanium as the anode and a Pt foil as the cathode. The ion labelling was conducted by immersing the titanium sample in the solution of 0.05 M H2SO4 + 0.0005 M F- for 24 h, which led to a double layer passive film with a compact inner layer and a porous outer layer containing the fluoride ion [30]. After being colour-labelled and ion-labelled, the samples were washed by deionized water and placed in the impingement chamber immediately for the following erosion-corrosion tests.
ACCEPTED MANUSCRIPT 2.3 Erosion-corrosion tests The erosion-corrosion tests were conducted using a jet impingement apparatus, which has been described in our previous work [14]. The jet nozzle diameter was 3
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mm, through which the liquid-solid two-phase fluid impacted on the sample surface. It should be noted that the flow velocity at the nozzle exit was regarded as the flow velocity of medium in this paper [12, 15]. The stand-off distance from the jet nozzle
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exit to the sample surface was 5 mm and the impact angle was set to be 90o. The
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medium used in this study was a slurry composed of 3.5 wt.% NaCl solution and 2 wt.% silica sand particles with the sizes of 75-150 mesh.
In this work, there were two types of erosion-corrosion tests: one for determining the critical flow velocity and the other for the pre-labelled samples. In order to clarify
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whether the surface film is ruptured below the critical flow velocity for erosion-corrosion, the critical flow velocity of pure titanium must be determined first. The potentiostatic polarization test was used for this type of erosion-corrosion test,
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which was also employed in our previous work and in the other research [12, 14, 15,
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20]. A three-electrode cell placing in the impingement chamber was used. It consisted of a titanium sample without pre-labelling as the working electrode, a Pt foil with a larger area as the counter electrode and a saturated calomel electrode (SCE) connecting to the cell via a salt bridge with a Luggin capillary as the reference electrode. A Potentiostat/Galvanostat (PARSTAT 2273) was used to control the potentiostatic polarization test. The potential was set at 0 V vs. SCE, which located in the potential range of stable passivation of titanium in 3.5 wt.% NaCl solution. The
ACCEPTED MANUSCRIPT flow velocity in this type of erosion-corrosion test was controlled to vary with time in the manner as shown in Fig. 1. During the whole period of this test, the passive current was recorded.
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After confirming the critical flow velocity, the other erosion-corrosion test was carried out for the pre-labelled samples at the open circuit potential, so that the behaviour of surface film would not be probably affected by the applied potential. In
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order to assess the evolution of surface colour with impingement time at different
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flow velocities, the colour-labelled samples were impinged for 1 min, 5 min, 10 min and 60 min at 5 m/s and 7 m/s, which was far below the determined critical flow velocity of titanium as shown in the next section. In contrast, the ion-labelled sample was only impinged for 5 min at 5 m/s because the surface film was too thin and the
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content of labelled fluoride ion in the film was too low to assess the content evolution with impingement time. Besides, the test time of 5 min was properly short to detect the changes of fluoride ion content in the film based on the pre-experiments. At least
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two tests under identical conditions were performed to ensure the reproducibility.
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2.4 Surface characterization
The changes in surface colour were recorded by the stereo microscope (ZEISS
Stemi 508) before and after the erosion-corrosion tests. The fluoride ion in the surface film was detected by X-ray photoelectron spectroscopy (XPS). XPS analyses were performed to the ion-labelled samples after the erosion-corrosion tests, using an ESCALAB250 X-ray photoelectron spectrometer with a monochromatic AlK (1486.6 eV) radiation source. The X-ray gun was operated at 150 W (15 kV, 10 mA) with the
ACCEPTED MANUSCRIPT photoelectron take-off angle of 90∘. The base pressure was maintained at approximately 10−8 Pa during the experiments. High resolution spectra with an analysed area of 500 µm2 were recorded at a pass energy of 50.0 eV with an energy
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step of 0.1 eV and energy resolution of 0.5 eV. High resolution spectra of F 1s, and C 1s were registered and the values of binding energies were aligned to carbon peak C 1s at 284.6 eV.
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3. Results
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3.1 Determination of the critical flow velocity for erosion-corrosion of titanium Fig. 2 shows the changes of current density of pure titanium at 0 V vs. SCE with the flow velocity under impingement. The current densities remain at low values when the flow velocities are lower than 14 m/s, indicating the passive feature. As
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increasing the flow velocity to 15 m/s, the current density steps up remarkably. According to our previous work, the flow velocity, above which the current density starts to increase noticeably during the potentiostatic polarization test, can be regarded
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as the critical flow velocity for erosion-corrosion [14, 15, 20]. Hereby, the critical
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flow velocity can be determined as 14 m/s for pure titanium. Besides, it is worthy of noting that there are some small current peaks at lower flow velocities, such as 7–11 m/s, as shown in the enlarged view in Fig. 2. These current peaks seem to be more likely to result from the film rupture caused by the solid particle impacting [17] rather than the breakdown of passivity involved in the metastable pitting [31], since titanium does not suffer from pitting corrosion at 0 V vs. SCE in neutral chloride-containing solutions [32].
ACCEPTED MANUSCRIPT 3.2 Colour-labelling and ion-labelling tests According to the determined critical flow velocity (14 m/s as shown in Fig. 2), 5 m/s and 7 m/s were selected to investigate the behaviour of pre-labelled surface film
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below the critical flow velocity. Fig. 3 displays the changes in surface colour of colour-labelled titanium samples after impingement below the critical flow velocity for different time. At either 5 m/s or 7 m/s, pale annular regions, in which the original
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colour disappears, can be always distinguished after impingement for any test time.
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The pale regions look like whiter and their areas get larger with increasing the flow velocity and impingement time. In contrast, no other colour, except the original blue-purple colour, can be identified in the other surface regions. The results of spectrophotometer test also manifest that only the pale area increases but no other
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characteristic peaks appear in the wavelength-reflection percentage curve (not shown). Since these annular regions just locate in the region where the solid particles impact most severely [15], it suggests that the colour-labelled surface film has been removed
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after impingement below the critical flow velocity. The removing of colour-labelled
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film should result from either the mechanical rupture or chemical/electrochemical dissolution during the impingement process. A control test was conducted under the impingement condition without solid particles, as also shown in Fig. 3. No pale region can be identified on the surface, indicating that the chemical/electrochemical dissolution mechanism can be excluded. Accordingly, it can be preliminarily confirmed that the surface film is ruptured mechanically even at the flow velocities lower than the critical value.
ACCEPTED MANUSCRIPT In order to further confirm the mechanical rupture of surface film found above, the fluoride ion-labelled titanium sample was used. Fig. 4 shows the detailed F 1s XPS spectra of fluoride ion-labelled titanium sample after impingement at 5 m/s for 5
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min, in which the two curves represent the signals detected from the unimpinged region and impinged region respectively. In the unimpinged region where the surface film will be thinned or be removed only by chemical/electrochemical dissolution, the
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F 1s XPS peak can be still recognized and shows the same feature with that of the
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original fluoride ion-labelled film, demonstrating the existence of fluoride ion in the surface film. It manifests that the chemical/electrochemical dissolution process has little effects on the detection of fluoride ion in the surface film. In contrast, no F 1s XPS peak can be identified in the impinged region, indicating that the surface film
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containing fluoride ion has been removed during the impingement. Since the chemical/electrochemical dissolution mechanism for film removing has been excluded based on the result of unimpinged region, it can be concluded that the
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disappearance of F 1s XPS peak in impinged region must be attributed to the film
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mechanical rupture caused by solid particle impacting. It agrees well with the conclusion made from the colour-labelling test.
4. Discussion
Based on the results above, it can be concluded that mechanical rupture of the
surface film on titanium occurs at the flow velocity lower than the critical value. The reason for film mechanical rupture should be related to the impact energy or impact-induced stress resulting from the solid particles. Burstein and Sasaki [16, 17]
ACCEPTED MANUSCRIPT found the threshold energy of solid particle impacting, below which the surface film of stainless steel would not be ruptured by erosion. However, they did not explain the reason for the threshold energy phenomenon primarily. It is well accepted that the
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mechanical failure will occur for a certain material if the applied stress exceeds its tensile or compressive strength. Accordingly, we try to explain why the film is ruptured mechanically at low flow velocities by calculating the impact-induced mean
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stress theoretically rather than considering the impact energy.
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Based on the Herzian contact theory [33, 34], the mean stress (σm) generated by single solid particle impacting is as follows by assuming that the external mean pressure (Pm) transfers to the internal stress completely: 1 5πρ s 4 k σ m = Pm = π 3 3 E1 0.2
−0.8
V 0.4
(1)
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where ρs is the density of solid particle (2.65 × 106 g/m3 for silica sand particle), E1 is the elastic modulus of impacted target sample and V is the flow velocity. Here, TiO2 is
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regarded as the impacted sample because the solid particle impacts directly on the surface film that mainly consists of TiO2 [30]. Thus, E1 is 230 GPa for TiO2 [35]. The
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parameter k in Eq. (1) is a constant whose value can be calculated using the following equation:
k=
9 2 2 E1 (1 − ν 1 ) + (1 −ν 2 ) 16 E2
(2)
where ν1 and ν2 are the Poisson’s ratios of TiO2 (0.27 [35]) and solid particle (0.23) respectively, E1 has the same meaning with that in Eq. (1), and E2 is the elastic modulus of a solid particle (59 GPa). Substituting all parameter values in Eq. (1) and
ACCEPTED MANUSCRIPT Eq. (2), the mean stress induced under the condition of 5 m/s impingement can be calculated as 11.7 GPa. Even at a flow velocity as low as 0.5 m/s, the mean stress is still as high as 5.4 GPa. Moreover, further stress concentration may be also generated
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when the angular particle impacts on the surface. It means that the stress induced by solid particle impacting is undoubtedly so high that almost no materials can bear. As a result, the surface film must be ruptured mechanically. Replacing the TiO2 impacted
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target with the titanium substrate, the corresponding mean stress can be calculated as
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10.2 GPa at 5 m/s by using E1= 115 GPa and ν1= 0.33 for titanium. This high stress can lead to severe plastic deformation of titanium substrate. As a result, the surface film will be also ruptured because it is too brittle to deform together with the substrate.
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Accordingly, it can be concluded that the mechanical rupture of surface film must occur at low flow velocities via the mechanism of either being ruptured directly by solid particle impacting or being ruptured indirectly due to the deformation of
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substrate. It means that the higher the flow velocity is and the longer the test time is,
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the more solid particles will impact on the surface and the more surface film will be removed consequently. This agrees well with the experimental results shown in Fig. 3. This conclusion can be seemingly extended to other passive metals because the impact induced stress is high enough to rupture the common surface films mechanically. It demonstrates that the mechanism of critical flow velocity for erosion-corrosion should be exactly related to the competition between the depassivation process caused by solid particle impacting and the electrochemical
ACCEPTED MANUSCRIPT repassivation process. It can be proposed as follows: when the flow velocities are lower than the critical value, the repassivation rate is faster than the depassivation rate, and the surface film can form quickly and timely to repair the mechanically ruptured
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film. In this situation, some transient current spikes will probably occur at lower flow velocities, just as those shown in Fig. 2. As a result, the surface film is still intact and protective, leading to inconspicuous damage, i.e., the feature of almost unchanged low
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current density in Fig. 2. In contrast, the depassivation rate will exceed the
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repassivation rate when the flow velocities are higher than the critical value. Consequently, the mechanically ruptured film cannot be repaired in time anymore and the surface film will lose its protectiveness, resulting in severe damage, i.e., the feature of abrupt increase of current density in Fig. 2. Accordingly, the critical
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condition must be the depassivation rate equalling to the repassivation rate. It is known that the repassivation rate corresponds to the repassivation time [36, 37]. Therefore, the critical condition can be considered as depassivation time (τde)
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equalling to repassivation time (τre), i.e., τde=τre. Here, we define the depassivation
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time as the time interval between two successive solid particle impacting at one single point on the surface and define the repassivation time as the time duration for completing the repassivation after being impacted. Apparently, the critical flow velocity for erosion-corrosion can be predicted if the critical equation can be resolved. The depassivation time, τde, should be the reciprocal of impact number per second at a single point, nimpact, since the depassivation process is caused by the solid particle impacting [22]. The nimpact can be obtained via multiplying the total impact
ACCEPTED MANUSCRIPT number per second on the whole surface, Nimpact, by the probability of repeated impact (Asingle/Atotal), which is expressed as follows: nimpact = N impact
(3)
Atotal
π d s 2 sin θ
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Asingle =
Asingle
(4)
4
where Asingle is the projected area of one solid particle on the impact surface, Atotal is
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the total impact area, ds is mean diameter of solid particle and θ is the impact angle.
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The exact expression of Atotal seems to be unclear now, but it should be related to the diameter of nozzle, impact angle and the stand-off distance from the jet nozzle exit to the sample surface [38]. If these influencing parameters are fixed, the value of Atotal should be obtained roughly by measuring the total damage area experimentally. In our
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previous work that applied the same experimental parameters with present paper, a circular damage area was observed with a diameter of approximately 6 × 10–3 m [15]. So Atotal can be calculated as 2.826 × 10–5 m2.
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In general, Nimpact can be obtained via multiplying the number of solid particles
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containing in unit volume of the flow medium (Nvolume = 6c/πρsds3) by the volume of medium that flows through the nozzle in unit time (Vimpact = 0.25πVdn2), which is given as follows:
N impact = N volumeVimpact
3cVd n2 = 2 ρs d s3
(5)
where c, ρs and ds are the concentration, density and mean diameter of the solid particle respectively, V is the flow velocity and dn is the diameter of nozzle. Substituting Eq. (4) and Eq. (5) in Eq. (3) and taking the reciprocal, the depassivation
ACCEPTED MANUSCRIPT time, τde, can be obtained:
τ de =
1 nimpact
=
8 Atotal ρs ds 3π cVd n2 sin θ
(5)
As to the repassivation time, τre, it depends on the repassivation kinetics.
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Summarily, there are three types of decay law for the current density response after the surface film is ruptured mechanically by solid particle impacting or by scratching
(i) Single-exponential decay law [23, 39]:
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t I = I s + I peak exp − τ
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in various metal/electrolyte systems:
(6)
where Is is the stable current density without solid particle impacting, Ipeak is the maximum current density caused by solid particle impacting and τ is a constant
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related to the film formation on the bared impacted surface. (ii) Double-exponential decay law [24, 25, 27]:
(7)
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t t I = I s + I1 exp − + I 2 exp − τ1 τ2
where Is has the same meaning with that in Eq. (6), and I1, I2, τ1 and τ2 are the
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constants related to the film formation on the bared impacted surface (I1 + I2 = Ipeak). (iii) Power decay law (t>τ) [24, 28, 37, 40]:
t I = I s + I peak τ
−α
(8)
where Is, Ipeak and τ have the same meanings with those in Eq. (6) and α is a constant (0<α<1). The key point is how to determine τre from Eq. (6), Eq. (7) and Eq. (8). In
ACCEPTED MANUSCRIPT principle, only when the current density decays to the original value, i.e., I = Is, should the repassivation process be totally completed. Hassel et al. [21, 41] took this criterion to determine the repassivation time from the current-time curve directly. However,
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from the point of mathematics, I = Is can be achieved precisely only under the condition of t = +∞ for any of Eq. (6), Eq. (7) and Eq. (8), which is obviously not possible. Hussain and Robinson [22] also believed that the film cannot grow to the
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original state by repassivation process alone in limited time interval after solid particle
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impacting. Therefore, it does not seem feasible to determine τre by means of the criterion of I = Is. As an alternative, Kwon et al. [37] regarded the time when the current density decayed to a certain value close to Is as the repassivation time, while Sawada et al. [42] specialized this value to 1/e (e is a constant whose value is
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approximately 2.7) of Ipeak. This method is quite useful to compare the repassivation ability of various materials. But it is still not suitable to get the absolute value of τre since there is no fundamental or explanations for choosing such a current density
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value. In addition, Rajahram et al. [27] also reported the τre value for UNS S31603
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stainless steel under erosion-corrosion condition, but without providing the specific method.
The discussion above demonstrates that there is lack of the criterion for
evaluating the totally complete repassivation, which restricts the derivation of τre expression based on the repassivation kinetics as shown in Eq. (6), Eq. (7) and Eq. (8). Furthermore, the impact angle (θ) [25], impact area (Atotal) [25] and flow velocity (V) [27] were found to have some effects on the repassivation kinetics. However, the
ACCEPTED MANUSCRIPT quantitative relation between τre and these parameters cannot be derived theoretically but can be only established by experimental determination. Unfortunately, there are no relevant investigations to our best knowledge. It should be interesting but
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complicated to clarify when the repassivation process is totally completed and how the environmental factors, such as V and θ, affect the repassivation process, which will be of significance for the study of not only erosion-corrosion but also the other
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aspects involved in the repassivation process, such as pitting corrosion. In this paper,
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the main objective is to find out whether the surface film is ruptured mechanically below the critical flow velocity, so that we can try to further clarify the mechanism of the critical flow velocity for erosion-corrosion. Fig. 3 and Fig. 4 have already confirmed the film mechanical rupture at the flow velocity lower than the critical
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value, and the critical phenomenon has also been attributed to the competition between the depassivation process induced by solid particle impacting and the electrochemical repassivation process. Here, we just try to highlight the issue about
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the repassivation by the preliminary discussion. More detail work has been designed
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and is being conducted now.
By considering the uncertainty of τre in the current situation, the critical condition
for erosion-corrosion is given as follows:
τ re = τ de =
8 Atotal ρs ds 3π cVc d n2 sin θ
(9)
where Vc represents the critical flow velocity for erosion-corrosion. This critical equation can be used to predict the effects of some factors on the critical flow velocity, although the specific Vc value cannot be calculated directly yet. In Eq. (9), τre should
ACCEPTED MANUSCRIPT be independent on c and ds because the solid particle should have no effects on the passive process at low concentrations, such as 2 wt.% used in this work. Accordingly, it can be predicted that Vc of pure titanium will increase with decreasing c or
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increasing ds, which agrees with the experimental results of Fe-based amorphous metallic coating and stainless steel in our previous wok (c = 0 wt.% ~ 5 wt.% and ds = 54 µm ~ 330 µm) [15, 43]. But there are no specific experimental results for pure
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titanium, so further relevant experimental verification is still needed. In contrast, the
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dependence of θ on Vc cannot be predicted since the effect of θ on τre is unclear, although the effect of θ on Vc has been clarified experimentally in the range of 30o ~ 90o [43]. Moreover, the variation of Vc with the other parameters can be only predicted with assuming that they have no effects on τre. But this assumption cannot
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be verified because no relevant experimental results are available now. Therefore, further investigations are needed for clarifying the dependence of τre on the environmental factors, such as the flow velocity, c, ρs, ds, dn and θ, and for
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determining the Vc values of pure titanium under various conditions experimentally,
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such as at different values of c, ρs, ds, dn and θ.
4. Conclusions
This paper find out that the surface film of titanium is ruptured mechanically at
the flow velocities lower than the critical flow velocity by using the colour-labelling and ion-labelling methods. The mechanical rupture of surface film can be attributed to the extremely high stress induced by the solid particle impacting. Accordingly, we try to attribute the mechanism of critical flow velocity phenomenon for erosion-corrosion
ACCEPTED MANUSCRIPT to the competition between the depassivation process caused by solid particle impacting and the repassivation process. Then, the equation of depassivation time (τde) equalling to repassivation time (τre), i.e., τde=τre, is proposed to be the critical condition
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for erosion-corrosion. Some efforts have been made to derive the specific expressions of τde and τre theoretically. Based on the derivation results, the dependence of concentration and diameter of solid particle on the critical flow velocity is predicted
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for pure titanium and the crucial issues involved in the repassivation process, such as
Acknowledgements
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the definition of complete repassivation, are highlighted.
The authors would like to acknowledge the financial supports from the National Natural Science Foundation of China (grant numbers 51801218, 51571200) and the
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Strategic Priority Research Program of the Chinese Academy of Sciences (grand number XDA13040500).
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