Erosion–corrosion of carbon steel in simulated tailing slurries

Corrosion Science 53 (2011) 1000–1008

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Erosion–corrosion of carbon steel in simulated tailing slurries B.T. Lu 1, J.F. Lu, J.L. Luo ⇑ Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alta., Canada T6G 2G6

a r t i c l e

i n f o

Article history: Received 28 June 2010 Accepted 28 November 2010 Available online 4 December 2010 Keywords: A. Steel B. Erosion Anodic dissolution Weight loss

a b s t r a c t This paper investigates the synergism of mechanical and electrochemical factors in erosion–corrosion. The fact that active corrosion in the tailing slurry donates a small portion of total material loss indicates that the synergism results mainly from corrosion-enhanced erosion. As theoretically predicted, the erosion rates in corroding slurry under same hydrodynamic condition is a linear function of logarithmic corrosion rate, suggesting that the corrosion-induced surface plasticity is the dominate mechanism of corrosion-enhanced erosion. The reduced resistance to plastic deformation in surface layer while exposed to corroding media is demonstrated by the in situ micro-hardness measurements. The erosion-enhanced corrosion in flowing slurry of steel is a result of dynamic plastic deformation caused by erodent impingement. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Erosion–corrosion is a serious problem for the oil sands industry of Northern Alberta, Canada, where handling and processing of essentially silica-based solids results in material loss with an unacceptably high rate [1]. Comprehensive understanding of the erosion–corrosion mechanisms is practically important to establish the mitigation strategy. Mechanical erosion and electrochemical corrosion are in nature two different mechanisms of material loss in erosion–corrosion. The former is a result of various mechanical forces produced by fluid and the later is produced by electrochemical dissolution. They are normally controlled very different parameters. The resistance to mechanical erosion in an inert environment depends mainly on the mechanical properties of targets [2] while the corrosion resistance is governed by the chemical characteristics of electrodes [3]. The rate of total material loss W is a sum of erosion component E and corrosion component C.

W ¼EþC

ð1Þ

However, the synergism of erosion and corrosion in slurrytransport system often gives rise to a material loss higher than the sum of the erosion rate in the inert environment ðE0 Þ and the corrosion rate under the erosion free condition ðC 0 Þ [4–7]. The additional material loss produced by the synergistic effects of mechanical erosion and electrochemical corrosion can be separated ⇑ Corresponding author. Tel.: +1 780 492 2232; fax: +1 780 492 2881. E-mail addresses: [email protected] (B.T. Lu), [email protected] (J.L. Luo). Present address: Environmental Performance of Materials, Materials Engineering Department, Mechanical Engineering Division, Southwest Research Institute, San Antonio, TX 78238, USA. 1

0010-938X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.corsci.2010.11.034

into, in line with the mechanisms, the components of erosionenhanced corrosion C E and corrosion-enhanced erosion EC . As such, we have

E ¼ E0 þ EC

ð2Þ

C ¼ C0 þ CE

ð3Þ

The erosion-enhanced corrosion is still in nature a result of electrochemical dissolution while the corrosion-enhanced erosion is caused by the mechanical damage due to the material property degradation induced by corrosion. Although efforts have been made to quantitatively assess the corrosion and erosion in flowing slurry [3,8–12], standard test procedures for slurry erosion to simulate the operational conditions of real slurry systems are yet unavailable. To evaluate the corrosion-enhanced erosion and erosionenhanced corrosion, the two non-dimensional parameters were recommended by ASTM G119 [13]

C CE ¼1þ C0 C0 E EC ¼1þ Erosion augmentation ¼ E0 E0

Corrosion augmentation ¼

ð4Þ ð5Þ

The corrosion augmentation is related to the mechanical factors controlling the erosion process, while the erosion augmentation is a function of the parameters relating to electrochemical reactions [14–16]. Theoretically, failure of materials caused either by mechanical forces or by electrochemical reactions can be related to occurrence of certain irreversible thermodynamic processes. During erosion– corrosion, at least two irreversible processes take place simultaneously, namely, electrochemical reactions resulting in corrosion and surface plastic deformation produced by erodent impingements.

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Nomenclature A ðm2 Þ target surface area A_ e ðs1 Þ fresh surface area generation rate produced by slurry impingement Acrater ðm2 Þ surface area of craters produced by erodent impingement AP ðJ=molÞ affinity of plastic deformation e ðJ=molÞ affinity of anodic dissolution reaction A C ðmm=y; m=sÞ material loss rate due to corrosion in presence of erosion C 0 ðmm=y; m=sÞ material loss rate due to corrosion in absence of erosion C E ðmm=y; m=sÞ material loss rate due to erosion-enhanced corrosion ð¼ C  C 0 Þ C s ðkg=m3 Þ concentration of solid particles in slurry E ðmm=y; m=sÞ material loss rate due to erosion in presence of corrosion E0 ðmm=y; m=sÞ material loss rate due to erosion in absence of corrosion EC ðmm=y; m=sÞ material loss rate due to corrosion-enhanced erosion ð¼ E  E0 Þ ED ðN  m=mol  KÞ potential barrier to be overcome to activate dislocation sources f ðs1 Þ impingement frequency F ðC=molÞ Faraday’s constant F c ðN  m=mol  KÞ generalized driving force for corrosion reaction F p ðN  m=mol  KÞ generalized driving force for plastic deformation HV ; Hcv ðMPa; N=m2 Þ in situ hardness in inert and corrosive environments DHV ðMPa; N=m2 Þ ¼ HVC  HV iA ðA=m2 Þ average anodic current density over sample surface iA ðA=m2 Þ applied anodic current density under galvanostatic control icorr ðA=m2 Þ self-corrosion current density icorr;0 ðA=m2 Þ self-corrosion current density under conditions free of erosion Dicorr ðA=m2 Þ ¼ icorr  icorr;0 ith ðA=m2 Þ threshold anodic current density to cause the chemomechanical effect L iA ðA=m2 Þ local anodic current density over wear scars during sand impingement iLA;peak ðA=m2 Þ peak value of iLA caused erodent impingement

The flux of corrosion can be characterized by anodic current density, iA , and the dynamically plastic deformation can be evaluated by the plastic strain rate c_ P . In accordance with non-equilibrium thermodynamics, the enhanced fluxes of these two irreversible processes due to the synergisms can be formulated with Onsager’s relations [17,18].

c_ P ¼ LP F P þ LCP F C

ð6Þ

iA ¼ LPC F P þ LC F C

ð7Þ

LP ; LC ; LCP and LPC are Onsager’s coefficients, F P and F C are the generalized driving forces for the plastic deformation and anodic dissolution, respectively. In light of the theories of dislocation dynamics [19], the plastic strain rate c_ P under a given applied shear stress is proportional to the probability to activate (Frank–Read) dislocation sources, which is proportional to m  exp ½ðED  sPN V D =RD T . The affinity of plastic deformation AP ¼ sPN V D ; m is the vibrational frequency of dislocation source; ED is the potential barrier for activating the dislocation source; sPN is the Peierls–Nabarro stress, i.e., the flowing shear stress component for overcoming short range

LP ; LCP ðmol  K=N  m  sÞ Onsager’s coefficients LC ; LPC ðmol  K=N  m  AÞ Onsager’s coefficients m exponent of power function to correlate average plastic strain rate and erosion rate M ðkg=molÞ atomic weight of metallic anode m ðkgÞ mass of erodent n; nH ; nV exponents in the expressions correlating E0 to ðV=HV Þ; HV and V, respectively 1 Nmax ðmol Þ the maximum number of dislocations in metal with molar mass r (m) radius of cylinder sample RðN  m=mol  KÞ the gas constant RD ðN  m=mol  KÞ kNmax T (K) absolute temperature maximum time the current on new cater surface startt 0 ðsÞ ing decay V (m/s) apparent flow velocity at the surface of RCE ð¼ xrÞ V crater ðm3 Þ average velocity of dislocation’s movement V D ðm3 =molÞ activation volume of F–R source W (mm/y, m/s) material loss rate due to erosion–corrosion y ðm1 Þ the average surface/volume ratio of wear scar z number of valence electrons in corrosion reaction Z a coefficient in the expression correlating EC =E0 and logðia =ith Þ a charge transfer coefficient of the anodic dissolution reaction Me $ Mezþ þ ze b current decay exponent ba ; bc ðV=decadeÞ Tafel slope c_ P ðs1 Þ plastic strain rate c_ p ðs1 Þ average plastic strain rate in surface layer produced by erosion e j ðN  m=mol  KÞ electrochemical potential l impingement angle h ð Þ q ðkg=m3 Þ density of target material j; jH ; jV coefficients in the expressions correlating E0 to ðV=HVÞ; HV and V, respectively m ðs1 Þ vibrational frequency of a dislocation source mj stoichiometric coefficient sPN ðMPaÞ Peierls–Nabarro stress DsA ðMPaÞ degradation of shear strength due to the presence of anodic dissolution x ðs1 Þ rotating angle speed of cylinder sample

obstacles in microstructure of metals; V D is the activation volume of dislocation source; RD ¼ kNmax where k is the Boltzmann constant and N max is the maximum dislocation density in a material; T is the absolute temperature. Accordingly, the driving force of the irreversible slip of dislocations F P is formulated by [17,18]

  AP F P ¼ RD exp 1 RD T

ð8Þ

It is known from electrochemistry that the driving force for the electrochemical dissolution F C is given by [17,18]

F C ¼ R exp

a Ae RT

! 1

ð9Þ

e ¼ P mj l is the affinity of electrochemical dissolution, where A j j respectively, mj are the stoichiometric coefficients in corrosion reace j are the electrochemical potentials. R is the gas constant tions, l and a is the charge transfer coefficient for the anodic reaction. The second term in Eq. (6) and the first term in Eq. (7) represent the synergistic effects between the two irreversible processes

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B.T. Lu et al. / Corrosion Science 53 (2011) 1000–1008

controlled tests ðiA Þ were in a range from 0.01 to 0:5 mA=cm2 . A caution was taken to keep the potential during the erosion–corrosion within a range from 0.15 V above the OCP to 1 VSCE . As such, the anodic dissolution rate of specimen was governed by the applied current density that is independent of hydrodynamics of slurry. The corrosion rates C and C 0 were measured electrochemically in the flowing slurry and flowing electrolyte free of solid particles, respectively. The contribution of erosion-enhanced corrosion was calculated with the equation: C E ¼ C  C 0 . The uniform electrochemical corrosion rates in the tests of group 2 were approximately determined from the applied currents iA . The corrosion rate under the galvanostatic control was calculated using Faraday’s second law.

above mentioned. The positive Onsager’s coefficients indicate that the synergistic effects will lead to the enhanced plastic deformation and accelerated anodic dissolution. Based on these concepts, Lu and Luo [18] developed physical models for the synergism in the erosion–corrosion process. In this article, the synergistic effects of carbon steel in simulated tailing slurries are studied and the theoretical predictions will be validated by the experimental results. 2. Experimental methods 2.1. Specimen, slurry and erosion–corrosion facility The test material was A1045 carbon steel. To investigate the effect of hardness of steel on erosion resistance, a part of specimens were annealed at 500, 850 and 1050 °C in flowing nitrogen for 1 h to obtain different hardness without altering microstructure of steel substantially. The Vicker’s hardness listed in Table 1 was measured using indent load of 2 kg. The microstructure of steel both as-received and annealed was typically a mixture of ferrite and pearlite with different grain sizes. The thickness of specimen was 8 mm and the outer diameter of cylinder 25 mm. A rotating cylinder electrode (RCE) system illustrated in Fig. 1 was used in erosion–corrosion tests. A saturated calomel electrode (SCE) was used as the reference electrode connected to the electrochemical cell through a salt bridge. The counter electrode was a platinum wire ring placed near the bottom of the electrochemical cell to minimize perturbation. To simulate the tailing slurry, the tap water of Edmonton city was used to prepare the slurries. Its quality parameters are listed in Table 2. The erodent concentrations in the slurries were 250 and 428 kg=m3 (20 and 30 in weight percent), respectively. The erodent was commercial available underground silica sand (US Silica Company, Ottawa) with size of 50–70 mesh (0.2–0.3 mm). The rotating speeds used in the erosion tests were 3000, 3750, 4500, 5250 and 6000 rpm, corresponding to the apparent flowing velocities V ¼ xr ¼ 4; 5; 6; 7; 8 m=s, respectively, where x is the rotating angle speed and r is the radius of the specimen.

C¼

The erosion–corrosion tests were divided into two groups, group 1 was carried out at the open circuit potential (OCP) and group 2 was conducted under galvanostatic control. Group 1 was designed to determine the contributions of each component to the erosion–corrosion wastage under natural corrosion conditions. At the OCP, the corrosion current density would change with hydrodynamics of slurries. Group 2 was employed to investigate the effect of anodic current density on corrosion-enhanced erosion. The applied anodic current densities in the galvanostatically

Table 1 Hardness of A1045 steel. Asreceived

500 °C/ annealed

850 °C/ annealed

1050 °C/ annealed

Hv (MPa)

2540

2470

2043

1982

ð10Þ

where F is Faraday’s constant, z, M and q are the number of valence electrons, atomic weight and density of the metallic electrode, respectively. For the tests of group 1, iA would be replaced by icorr , the corrosion current density at the OCP that was determined from the polarization resistance ðRp Þ. Considering low electric conductivity of the tap water, the IR drop compensation was employed in the polarization resistance measurements. The corrosion current density at the OCP was given by ba bc =Rp ðba þ bc Þ, where ba ð¼ 0:112 V=decadeÞ and bc ð¼ 0:08 V=decadeÞ were Tafel slopes. The total material loss rate W and the pure mechanical erosion rate E0 were determined with the weight loss measurements. Before measuring the initial mass of a specimen, the test surface was abraded with sand papers up to 600 grit, then rinsed with de-ionized water and acetone, and dried in hot flowing air, successively. Same procedures were used to prepare the specimen to obtain the initial surface condition with roughness as close as possible. After the initial mass measurement, a lacquer coating was used to protect the top and bottom surfaces of cylindrical specimens from crevice corrosion. After the erosion–corrosion test was completed, the corrosion product on the specimen surface was cleaned in line with ASTM Standard G1-90. An aqueous solution of hydrochloric acid and hexamethylene tetramine was used to remove any corrosion product on the test surface. Then the lacquer coating on the specimens was dissolved in acetone. Before measuring the final mass, the specimens were rinsed again in de-ionized water and acetone, and dried in flowing air, successively. The mass of specimen was measured using a balance with accuracy of ±0.1 mg. To obtain a weight loss larger than 10 mg, 100 times of the resolution of the balance, 30 min was chosen as the minimum duration of erosion tests. A calibration test indicated that the sand degradation within this test duration was negligible. All the components of erosion–corrosion in figures would be presented in mm/y. The pure mechanical erosion rate E0 was measured under the cathodic protection that was achieved by applying potential of 0:9 VSCE . The erosion rate in corroding slurry could not be measured directly from experiments. After the total material loss W was determined in corroding slurry, the erosion rate in the corroding slurry would be calculated by subtracting the corrosion component:

Erosion–corrosion tests

Condition

iA M zF q

Table 2 Quality parameters of tap water (Source: EPCOR, Edmonton). 

Fe2þ <0.003

Mg2þ <0.0005

Naþ 9

Kþ 0.9

Cl

mg/L Parameters:

Total dissolved solids (mg/L)

pH

Value

193

Alkalinity ðCaCO3 Þ ðmg=LÞ 110

Hardness ðCaCO3 Þ ðmg=LÞ 165

Conductivity ðlS=cmÞ 350

Ions:

7.8

2.52

SO4 2 56.1 Caustic soda dose (NaOH) (mg/L) <20

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B.T. Lu et al. / Corrosion Science 53 (2011) 1000–1008

C0 E0 W

25 20

PTFE washer

Material loss rate (mm/y)

Rotator

Agar tip CE

RE

WE

Potentiostat

15 10 5

0.2 0.1 0.0

Specimen

CE EC

SCE

4

5

6

7

8

Apparent flowing velocity (m/s)

Computer

(a) C S = 250 kg/m3

Fig. 1. Schematic illustration of the erosion–corrosion test set-up.

60

Material loss rate (mm/y)

E ¼ W  C. Then, the material loss rate due to the corrosionenhanced erosion would be given by EC ¼ E  E0 ¼ W  C  E0 . 2.2. In situ micro-hardness measurement The in situ micro-hardness of test material was used to demonstrate the effect of anodic current density on the surface hardness. The measurements were conducted in a three electrode cell. A platinum wire was utilized as counter electrode and a saturated calomel reference electrode was connected to cell via a Luggin capillary. The cell was fixed on the movable stage of hardness tester. The applied anodic current density was controlled by EG&G potentiostat. Prior to the hardness measurement, the epoxy molded specimen was polished mechanically, rinsed with de-ionized water and acetone, and dried in air. Then it was fixed into the cell with the test surface upward. The de-ionized water was added into cell as the electrolyte. The Vick’s hardness was measured using Shimazhu micro-hardness tester while anodic current was applied until the test surface of specimen was immersed. The indentation load was 200 g and the time for applying the maximum load was 15 s. The other details about the test set-up and experimental procedures have been described elsewhere [18]. 3. Results and discussion Contribution of each component to total material loss Fig. 2 indicates the effects of flowing velocity and erodent concentration on the total material loss rates, as well as each component, measured at the OCP. It can be seen that the erosion rates are much higher than corrosion rates. The percentage donated by each wastage component to the total material loss relies on the hydrodynamic conditions. As shown in Fig. 3, except the pure mechanical erosion E0 , the relative contributions of the other three components (C E ; C 0 and EC ) decrease with increasing erodent concentration and flowing velocity. This result agrees with the experimental observations reported by Wood [16,20]. Under the present test conditions, the total contribution of electrochemical corrosion to the total material loss is less than 6%. This fact indicates that, under the natural corrosion conditions, the erosion is the main mechanism of material loss and the additional wastage due to the synergistic effects results mainly from corrosion-enhanced erosion.

C0 E0 W

40

CE EC

20

0.8

0.4

0.0

4

5

6

7

8

Apparent flowing velocity (m/s) (b) C S = 428 kg/m3 Fig. 2. Dependences of various components of erosion and corrosion on the apparent flowing velocity and erodent concentrations of slurries at the OCP.

3.1. Erosion-enhanced corrosion A typical crater created by the particle impingement is shown in Fig. 4, where plastic deformation caused by the particle impingement is clearly demonstrated. If the anodic dissolution during the solid particle impingement is controlled by the interface charge transfer mechanism, as predicted by Eq. (7), the increase of local anodic current density immediately after the crater is created L ðiA;peak Þ will be a linear function of local plastic strain rate over the crater surface during the solid particle impingement. L

iA;peak ¼ Lc_ P

ð11Þ

where L ¼ LP C=LP . The linear relation between the active dissolution current density and plastic strain rate has been experimentally observed [17,21,22]. After the particle impingement, the local current density over the crater surface will decay with time. Although a universal model is yet unavailable for the current decay, the power law is often a good approximation [23].

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B.T. Lu et al. / Corrosion Science 53 (2011) 1000–1008

Contribution to total material loss (%)

60

L

L iA

50

¼ iA0 þ

L iA;peak

 b t t0

t > t0

ð12aÞ

t 6 t0

ð12bÞ

where iA0 is the anodic current density free of particle impingement, aA and bð0 6 b < 1Þ are experimental constants, t is time after the L crater is created and aA ¼ iA;peak t b0 . As a result of solid particle impingement and local current decay, the anodic current density during erosion–corrosion will be non-uniform on micro-scale. The average current density over the whole electrode surface iA can be expressed as,

40

4

2

iA ¼

C0

CE

E

E

1 A

Z 0

A

L

iA dA

ð13Þ

60

where A is the electrode surface area. Since the maximum transient current over the fresh crater surface is the upper limit of average current density and normally much higher than iA [24,25], the anodic dissolution rate increases with increasing impingement frequency, as shown in Fig. 5. The impingement frequency is approximately proportional to the erodent concentration when the flowing velocity is constant. In line with the kinetic analysis of slurry impingement [26,27],

50

1 dA ¼ A_ e expðA_ e tÞdt A

0

C

0 4

5

6

7

8

Nominal flowing velocity (m/s)

(a) C S = 250 kg/m 3 Contribution to total material loss (%)

L

iA ¼ iA0 þ aA t b ¼ iA0 þ iA;peak

where A_ e is the generation rate of the fresh surface area due to particle impingement on an electrode with unit area [26,27].

40

  C S V sin h Acrater A_ e ¼ m

4

C0

C

E

E

0

E

C

2

0

ð14Þ

4

5

6

7

8

Apparent flowing velocity (m/s)

(b) C S = 428 kg/m3 Fig. 3. Relative contributions of various components of erosion and corrosion to the total material loss as functions of flowing velocities and erodent concentrations of slurries at the OCP.

ð15Þ

C S ; V and h are the erodent concentration, impact velocity and impingement angle of slurry, respectively, m the average mass of sand particles and Acrater the average surface area of the crater. Under the test conditions of this study, C S 6 500 kg=m3 ; V < 10 m=s; h < 15 ; m ¼ 2  108 kg; Acrater < 7:5  1011 m2 , thus A_ e < 5 s1 . t0 is quite small (6 0:01 s [23,27]). As a result, A_ e t 0 6 0:05. Substituting Eqs. (13) and (15) into Eq. (14) and considering that the A_ e t0 value is quite small, we have [27]:

iA  iA0  aA

Z

t0

1

t b expðA_ e tÞdt ¼ iA0 þ aA A_ b1 Cð1  bÞ e

ð16Þ

R1

C ¼ 0 ub expðuÞdu. In the range of b-value of interest, Cð1  bÞ  ð1  bÞ1 [27]. If the particle impingement frequency is

0.12

A1045CS Tap water + silica sand V = 8 m/s @ 0 V SCE

428 kg/m

3

3

0.08

2

iA (mA/cm )

0.10

667 kg/m

250 kg/m

3

0.06 111 kg/m

3

0.04 C S= 0 kg/m 3

0.02 0.00

0

200

400

600

800

t (s) Fig. 4. Typical morphology of craters created by the impingement of sand particles under cathodic protection (the test duration = 30 s and V ¼ 8 m=s).

Fig. 5. Effect of erodent concentration on anodic current density in flowing slurries under the potentiostatic control.

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B.T. Lu et al. / Corrosion Science 53 (2011) 1000–1008

f ; E ¼ f V crater =A ðm=sÞ and A_ e ¼ f Acrater =A ðs1 Þ. V crater and Acrater are the average volume and surface area of crater produced by the solid particle impingement. Therefore, A_ e can be correlated to E as follows [26],

Acrater E A_ e ¼ yE ¼ V crater

ð17Þ

In Eq. (17), y ¼ Acrater =V crater . Owing to technical difficulties, it is still difficult to estimate the exact value of plastic deformation rate produced by solid particle impact. As a first approximation, it is reasonable to assume that the average plastic deformation during slurry impingement is a power function of erosion rate [18],

c_ P ¼ lEm

ð18Þ

Assuming that the electrode surface in uniform and each erodent has same mass, shape and velocity and impact angle, we will have

c_ P  A_ e c_ P

ð19Þ

According Eqs. (11), and (17)–(19), we have L

iA;peak ¼ Lc_ P ¼

Ll m1 E y

ð20Þ

Substitute Eqs. (17) and (20) into Eq. (16),

iA  iA0 ð1 þ kEmþb2 Þ

ð21Þ

where k ¼ Llyb2 tbo =iAo ð1  bÞ. At the OCP, iA ¼ icorr and iA0 ¼ icorr;0 . In line with Eq. (21), the erosion-enhance corrosion can be characterized by

CE ¼

M M Dicorr ¼ iA0 kEmþb2 zF q zF q

ð22Þ

where Dicorr ¼ icorr  icorr;0 . Inserting Eq. (22) into Eq. (4), we will have

C Corrosion augmentation ¼ ¼ 1 þ kEmþb2 C0

ð23Þ

The results shown in Fig. 6 indicated that Eq. (23) provided a good fit for the correlation between the corrosion augmentation and the erosion rate. According to the slope of straight line in log–log plot given by Fig. 6, m þ b  2:8. Hence the corrosion augmentation is a function of erosion rate and hence it can be related to various factors that affect erosion.

3.2. Effects of hardness and hydrodynamic parameters on erosion resistance The erosion rate is mainly controlled by mechanical factors and an increase in pure mechanical erosion rate will be caused by increasing momentum and impingement frequency of erodent in slurry. Experimental results have indicated that the dependence of erosion rate on the apparent flowing rate, V, can be approximately formulated by [18]

E0 ¼ jV V nV

jV and nV are experimental constants. In agreement with the experimental observations reported by Hutchings [2], Madsen [28], and Heitz [29], the material loss rate due to mechanical erosion increases with decreasing hardness, as shown in Fig. 7. This is not surprising because hardness is regarded as the resistance against locally plastic deformation. The straight lines in Fig. 7 in log–log scale indicate that the erosion rate, under the test conditions, can be correlated to hardness by the follow expression [18]:

E0 ¼ jH Hv nH

 n V E0 ¼ j Hv

ð26Þ

j and n are also experimental constants. As shown in Fig. 8, the value of E0 increased monotonically with the ratio V/Hv. Same phenomenon was observed in A1018 carbon steel [18]. 3.3. Corrosion-enhanced erosion Substituting Eqs. (8) and (9) into Eq. (6)

" ! #     e s VD a A 1 c_ p ¼ Lp RD exp  1 þ LCP R exp RT RD T

0.1

A1045CS 4 V = 4 - 8 m/s OCP 3

2

0.05

0.02 C S =250 kg/m

5

10

20

E (mm/y) Fig. 6. Dependence of corrosion augmentation on erosion rate.

3

V (m/s) 4 8

3

C S (kg/m ) 250 428 2

ð27Þ

Imagining two tensile experiments under the constant strain rate control: test 1 is conducted in an inert environment and test 2 is performed in a corroding medium. In line with Eq. (7), the anodic      e current density during the testing is iA ¼ LC R exp aRTA  1 .

E 0 (mm/y)

Corrosion augmentation

ð25Þ

jH and nH ð> 0Þ are the constants experimentally determined. In line with the experimental results of this study, nV  nH . As such, Eqs. (24) and (25) can be combined into Eq. (26).

5

1

ð24Þ

0.01 1800 50

2000

2200

2400

2600

Hv (MPa) Fig. 7. Dependence of mechanical erosion rate on hardness of steel (in log–log scale).

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B.T. Lu et al. / Corrosion Science 53 (2011) 1000–1008

0.00 2 -0.05

Δ Hv / Hv

E0 (mm/y)

1

0.5

CS (kg/m3 ) 250 428

0.2

-0.15

A1045CS Deionized water

0.1 2

1

3 -1

4

-1

V/Hv (kN ms )

Lp RD

ð28Þ

According to Eq. (28), the change of flow stress in surface layer induced by corrosion DsA is given by [18]:

Ds A ¼   0 i ith ¼ RAD

  RD T iA ln VD ith

LC LP LCP



ð29Þ

is the threshold current density to cause the surface

strength degradation, where is the anodic current density at the equilibrium state. Eq. (29) indicates that the anodic dissolution present at surface will reduce the surface strength [17,18]. Because the effect of corrosion-induced surface strength will decay with increasing depth to surface [18], it is difficult to measure DsA directly. If the yield behavior of target material is assumed to obey von-Mises flowing rule and that Tabor’s factor is equal to 3 [30], we will have

  RD T iA DHv ¼ Hv c  Hv ¼  pffiffiffi ln i th 3V D

10-3

10-2

10-1

100

Fig. 9. Dependence of the in situ surface hardness-degradation on anodic current density.

The flowing stress of surface layer produced by the strain hardening in the inert environment is denoted as s1 and that measured in the corroding medium is s2 . Owing to the chemo-mechanical effect, s2 < s1 . Let DsA ¼ s2  s1 . Adjust the anodic current density to eliminate strain-hardening effect so that the plastic strain rate induced by the anodic dissolution in the corroding environment is equal to the one produced by the mechanical force in test 1. In this case, s2 ¼ 0; DsA ¼ s1 and Eq. (27) will become

       Ds A V D aA LCP 1 ¼ exp iA  1 ¼ LCP R exp RT RD T LC

-0.20

iA (mA/cm2)

Fig. 8. Correlation between mechanical erosion rate and V/Hv.



-0.10

ð30Þ

where Hv and Hv c is the surface hardness value measured in air and corroding environment, respectively. Eq. (9) has been validated by the in situ micro-hardness measurements shown in Fig. 9. More experimental evidence has been given in Ref. [18]. Since the erosion resistance of test material increases with hardness of material, the corrosion-induced surface hardness-degradation, as predicted by Eq. (30), will lead to an increase in erosion rate. It is denoted as DE0 . If the corrosion-induced surface hardness-degradation is the sole mechanism of corrosion-enhanced erosion, the increment of erosion rate due to the corrosion-induced surface hardness-degradation will equal to the wastage of corrosion-enhanced erosion, i.e., DE0 ¼ EC ¼ E  E0 . When the test parameters except the corrosion rate are held unchanged, the erosion rate will be a function of surface hardness of steel and the increment of erosion rate caused by corrosion is given by

 n EC ¼ E  E0 ¼ jV n Hv n ¼ E0 c  Hv   DHv  nE0 Hv

n   Hv c 1 Hv ð31Þ

The right side of Eq. (31) was derived using the first term of Taylor’s series. Inserting Eq. (30) into Eq. (31), and reorganizing, we have:

  EC nRD T iA ¼ pffiffiffi ln E0 ith 3V D Hv

ð32Þ

As predicted by Eq. (32), the normalized corrosion-enhanced erosion rate EC =E0 will increase linearly with the logarithm of anodic current density. This relationship is shown in Fig. 10. It is also consistent with experimental results reported elsewhere [18,31]. The data in Fig. 10 indicated that the correlation of EC =E0 vs. logarithm of average anodic current density relied on the hydrodynamics of slurry. The effect of corrosion-enhanced erosion was governed by the local anodic current densities over the crater surL face during particle impingement ðiA;peak Þ, which was much higher than the average anodic current density ðiA Þ. The changes of flowing velocity and erodent concentration will alter the impingement frequency of solid particles. Obviously, the difference between iA and L iA;peak will be reduced as the impingement frequency is increased. After taking the effect of transient current distribution over the crater surface into account, Eq. (32) can be modified into [18],

  EC C þB ¼ Z ln E0 E0

ð33Þ

where Z ¼ pffiffi3nRVD THv and B ¼ Z ln g; g is a non-dimensional constant D L relating to the ratio of iA;peak =iA [18]. As illustrated in Fig. 11, Eq. (33) can be used to approximately normalize the effects of erodent concentration and flow velocity on the corrosion-enhanced erosion rate, suggesting that Z and B are both experimental constants. Equivalently, the erosion augmentation is given as

Erosion augmentation ¼ Z ln

  C þ B E0

ð34Þ

where B ¼ B þ 1. Eq. (34) correlates the erosion augmentation to the corrosion rate and pure mechanical erosion rate of material. The data in Figs. 10 and 11 were measured under the galvanostatic conditions while slurry components are normally operated under the free corrosion condition. Therefore, it is of practical importance to validate the applicability under service conditions,

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2.8

EC / E0

8

6

4

C S = 250 kg/m V (m/s) 4 6 8

2

0

0.01

0.02

0.05

0.1

0.2

3

0.5

Erosion augmentation

10

V C S (kg/m 3 ) (m/s) 250 428 2.6 4 5 2.4 6 7 2.2 8 Eq.(34)

2.0 1.8

A1045CS OCP

1.6 1.4 0.1

0.15

iA (mA/cm2) (a)

CS = 428 kg/m V (m/s) 4 6 8

10

EC / E0

8

Fig. 12. Comparison of erosion augmentation at OCP and the predicted line given by Eq. (34) that is determined from the results of galvanostatically controlled tests (C=E0 is presented in logarithm scale).

3

6

4

2

0 0.01

0.02

0.05

0.1

0.2

0.5

2

iA (mA/cm ) (b) Fig. 10. Dependence of corrosion-enhanced erosion on anodic current density.

10

EC / E 0

3

V C S (kg/m ) (m/s) 250 428

8

6

4 6 8

4

2

0 0.1

1

0.2

C / E0

10

conditions. In Fig. 12, the test result Fig. 12 are compared with the predicted line given by Eq. (34) that is determined by fitting the test results of group 2. The good agreement indicates that Eq. (33) or Eq. (34) determined from the test results obtained under galvanostatic control can be utilized to predict the corrosionenhanced erosion at the OCP. The corrosion rates in erosive slurries can be determined with various standard procedures of electrochemical measurements (such as ASTM G59 and ASTM G5). Following the pioneer work of Finnie [32] and Bitter [33], many theoretical models have been proposed for mechanical erosion based on different hypotheses, as indicated by an exhaustive overview provided by Meng et al, where they summarized the work in this area up to 1995 and collected 182 equations [34]. Although a universal erosion model is yet unavailable, the existing models provide some useful concepts that will be employed in building an integrated model for erosionenhanced corrosion that can reflect the impacts of mechanical properties of target materials, the kinetics of particle impingement and the erosion mechanisms. Since the corrosion-induced surface hardness-degradation is the mechanism of corrosion-enhanced erosion, it is reasonable to expect that the average crater sizes created under the anodic polarization conditions are larger than those under the cathodic protection, because the anodic current cannot alter the hydrodynamics of slurry. An attempt was made to compare the average crater sizes under the cathodic protection and anodic polarization conditions that were measured from the SEM images and the test data are summarized in Table 3. It can be found both the average length and width or craters produced in erosion–corrosion test under the anodic polarization ðiA ¼ 0:2 mA=cm2 Þ are marginally larger than those under the cathodic protection. Such a difference is much smaller than that predicted from the data of erosion– corrosion tests. The reason behind may be related to the intensive dissolution over the crater surface immediately after the solid particle impingement. The anodic current density at the crater edge is higher than that at the crater bottom because of the geometric

C / E0 Fig. 11. Correlation between normalized mechanical erosion rate and wastage ratio C=E0 under galvanostatic control.

for the conclusion drawn from the galvanostatically controlled experiments. For this purpose, the erosion augmentation obtained from the test data group 1 is plotted against C=E0 under same test

Table 3 Comparison of the crater sizes produced under the cathodic protection and anodic polarization ðiA ¼ 0:25 mA=cm2 Þ conditions. Test condition

Crater length ðlmÞ

Crater width ðlmÞ

Cathodic protection Anodic polarization

8.9 ± 2.6 9.5 ± 1.7

2.5 ± 0.6 2.8 ± 0.5

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B.T. Lu et al. / Corrosion Science 53 (2011) 1000–1008

effect, leading to quick dissolution of crater edge. As a result, the real crater sizes produced in the erosion–corrosion tests are likely larger than those measured from the ex situ SEM images [27]. It should be noted that the values of EC estimated directly from the hardness-degradation data were smaller than the experimental data shown in Figs. 11 and 12. The discrepancy can be attributed in part to the relatively high indent load used in the hardness measurements. The indent depth in the micro-hardness test was a few micrometers while the crater depth created by slurry erosion was around 30—40 nm. The anodic current can only affect the mechanical properties of a very thin layer subsurface with thickness no more than the mean free path of dislocations. The chemo-mechanical effect decays quickly with increasing distance away from surface. Therefore, the in situ micro-hardness measurements would underestimate the real surface strength degradation caused by the anodic dissolution [18]. To verify the above deduction, the in situ nano-indentation technique has been employed to examine the response of dislocation mobility in the surface layer to the anodic dissolution [35]. The measurements indicated that the indent depth produced by the nano-indentation was about 50–250 nm, slightly larger but still comparable with the crater depth created by the particle impingement during slurry erosion. The experimental values of corrosion-induced surface hardness reduction measured with the nano-indentation technique were 2–3 times higher than those determined with the in situ microhardness measurements [35]. The impingement of solid particles with larger momentum will create deeper and larger craters, as well as a higher erosion rate. Since the chemo-mechanic effect decreases with increasing indent depth, the impact of corrosionenhanced erosion will decline with increasing flowing velocity. This statement is in agreement with the test data in Figs. 2 and 10. In addition, the impingement of slurry with high sand concentration will lead to a high impingement frequency. This will promote the strain-hardening effect in surface layer and reduce the contribution of corrosion-enhanced erosion to the total material loss of erosion–corrosion. 4. Conclusions (1) The corrosion augmentation of A1045 steel in the simulated tailing slurries is a power function of erosion rate. (2) The rate of material loss produced by corrosion-enhanced erosion increases with the anodic current density, while the pure erosion rate increases with decreasing hardness. Therefore, the hardness-degradation caused by the anodic dissolution is an important mechanism of corrosionenhanced erosion. (3) The erosion augmentation of carbon steel exposed to the simulated tailing slurries can be expressed as a linear function of the logarithm of anodic current density.

(4) The effects of sand concentration and flow velocity on the erosion augmentation under the test conditions can be normalized with the parameter C=E0 , i.e., the ratio of the weight loss rate produced by electrochemical corrosion to pure erosion rate.

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