Introduction

Stress corrosion cracking (SCC) of steel in near-neutral pH environment has been a vital threat to the safe operation of buried oil/gas pipelines (Ref 1, 2). Although SCC behavior of pipelines has been extensively studied, quantifying the crack growth rate (CGR) during SCC is still difficult. The growth rate of stress corrosion cracks is related to the synergetic effect of hydrogen and stress on the anodic dissolution rate of fresh metal surface at the crack tip (Ref 3, 4). However, the direct in situ measurement of the rates of the important electrode processes, namely metal dissolution and reduction of water and hydrogen ions, is impractical. The kinetics can be quantified to a degree by conducting separate electrochemical experiments in conditions simulating that of the crack tip states, including the solution environment, mechanical levels, hydrogen content and fresh metal surface.

The mechanical and electrochemical states of the crack tip can be characterized using the following four aspects: solution environment, high strain and strain rate, high hydrogen concentration, and fresh metal surface (Ref 5-8). First, the solution near the crack tip is acidic because of the hydrolysis of Fe2+ and the occlusion effect. The generation of H+ attracts Cl− to migrate to the crack tip area, resulting in a solution with low pH and high Cl− concentration, which has been verified in our previous study, in which the solution pH and Cl− concentration were identified as pH 4.0 and 3.8 mol/L (Ref 5), respectively. Secondly, during the crack propagation, a plastic deformation zone will form around the crack front, resulting in a high degree of strain and strain rate at the crack tip. Parkins et al. (Ref 6) noted that the strain rate of the crack tip could reach or even exceed 10−4 s−1. Thirdly, an enrichment of hydrogen will occur around the crack tip because the stress level at the crack tip is high and the tensile stress can accelerate hydrogen invasion as well as increase hydrogen concentration. Qiao et al. (Ref 7) reported that the hydrogen concentration around the crack tip of pipeline steel in the acidified solution is approximately 7.0 ppm in weight. Finally, during crack propagation, fresh metal surface is produced at the crack tip. In this case, the electrochemical reaction around the crack tip is the polarization process of the fresh metal surface in the crack tip solution (Ref 9, 10).

The importance of the transient electrochemical reactions that proceed on freshly exposed metal surface at the crack tip has been emphasized because they are believed to control the crack growth in some material-environment systems (Ref 11-16). Beck et al. (Ref 11) and Alavi et al. (Ref 12) reviewed the techniques used to create fresh metal surfaces and separated them into five major groups as follows: forming liquid metal droplets, scraping or scratching a surface, straining a wire, shearing a wire, and rapid fracturing of a tensile specimen. A number of modifications have also been made based on these techniques in recent studies (Ref 13-16). Among them, the rapid fracturing of a tensile specimen has received attention particularly in the area of SCC. Zhao et al. (Ref 16) conducted simulation experiments using the rapid tensile test and obtained the contribution of anodic dissolution at the crack tip to the corrosion fatigue crack propagation rate for X80 steel in NaCl solution; however, the fresh metal surface and the enrichment of hydrogen at the crack tip in the simulation test were not considered. Therefore, a difference of at least three orders of magnitude between the measured CGR and the anodic dissolution-induced CGR was observed.

To advance understanding of the SCC mechanism of pipeline steel in near-neutral pH environment, it is necessary to evaluate the electrochemical processes that occur at the crack tip more realistically. For this purpose, a galvanic corrosion simulation technique that facilitates the measurement of the electrochemical reactions at crack tip is proposed in this work. The corrosion current variation of the X70 specimen during straining is analyzed. The CGR induced by anodic dissolution of fresh metal surface at crack tip is calculated.

Experimental

Materials

The testing specimens were cut form a hot-rolling plate of API X70 pipeline steel with chemical composition (wt.%): 0.065 C, 1.57 Mn, 0.23 Si, 0.2 Ni, 0.18 Cr, 0.22 Cu, 0.056 Nb, 0.002 S, 0.0019 P, and Fe balance. The microstructure shown in Fig. 1 contained a ferrite matrix with a few small, dark martensite-austenitic particles at the grain boundaries. The yield strength of the material was 490 MPa, and its ultimate tensile strength was 610 MPa (determined under a strain rate of 1 × 10−6 s−1).

Fig. 1
figure 1

Microstructure of X70 steel used in this work

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Electrochemical Measurement

Simulation experiments were carried out on a slow strain rate tensile test machine (WDML-30kN Materials Test System, Xi’an Lichuang, China) to determine the anodic dissolution of the crack tip. An electrochemical cell (Fig. 2a) was set up to simulate the mechanical and electrochemical states of the crack tip analyzed in the Introduction section. Traditional near-neutral pH solution (NS4) with a composition of 0.181 g/L CaCl2·2H2O, 0.122 g/L KCl, 0.131 g/L MgSO4·7H2O and 0.483 g/L NaHCO3 was acidified with acetic acid to obtain a pH of 4.0, and NaCl was added to obtain a Cl− concentration of 0.4 mol/L. The solution chemistry was determined based on our previous work in which the pH and Cl− concentration of the crack tip environment were identified as pH 4.0 and 3.8 mol/L by in situ measurements (Ref 5). Through the polarization curve testing, corrosion current density in solution with 0.4 mol/L of Cl− is similar with that in a concentrated solution containing 4 mol/L of Cl−. Therefore, the 0.4 mol/L was chosen in this work. The solution was purged with N2 gas for 4 h to achieve an anaerobic environment and the gas flow was maintained throughout the test. This solution was used to simulate the crack tip environment. The tensile specimen (work electrode, WE), which was fabricated according to GB/T 15970 (Ref 17), was used to simulate the crack tip area. The dimensions of the specimen are shown in Fig. 2(b), in which the samples were ground gradually to 2500 grit paper, rinsed with acetone and then covered with silicone rubber to leave an exposed area of 1.0 cm2. Before the electrochemical test, the specimen was charged in 0.2 mol/L NaOH + 0.25 g/L thiourea (H2NCSNH2) with a current density of 100 mA/cm2 for 24 h. The hydrogen concentration was 7.1 ppm in weight measured using the hydrogen oxidization current method (Ref 18). For simplification, the crack tip and the crack walls are considered as the anode and cathode, respectively. As the crack tip area is much smaller than that of the crack walls, X70 steel with a dimension of 50 mm × 50 mm was used as the counter electrode (CE) to simulate the crack walls. The galvanic corrosion module in Gamry Reference 3000 was used to measure the current between WE and CE. When the tensile specimen is stretched with a high strain rate, the mechanical state around the crack tip was simulated, and the strain-induced reduction of the electrode potential caused difference in potential between the WE and CE. Galvanic corrosion occurred afterward, and the tensile specimen served as anode and experienced dissolution. Meanwhile, the unloaded X70 specimen with a large area served as cathode to facilitate anodic dissolution. All the experiments were repeated three times to maintain the reproducibility, and all the tests were performed at ambient temperature (about 22 °C).

Fig. 2
figure 2

Schematic diagram of the galvanic corrosion test to simulate the anodic dissolution of the crack tip (a) and geometry of the tensile specimen used in the electrochemical test

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Crack Growth Test

Compact tension (CT) specimens were used for the crack growth test of X70 pipeline steel which has been described in our previous work (Ref 19). The specimens were made in accordance with ASTM E647 (Ref 20), with the machined notch perpendicular to the rolling direction of the steel. The detailed sizes are shown in Fig. 3(a). The machined CT specimen was pre-cracked by fatigue in air to initiate a sharp crack tip from the machined notch. The crack lengths on both sides were controlled at 2.5 mm, and the total crack length from the loading line (including the notch) was typically 30.5 mm at the surface in this case. After pre-cracking, the specimen was cyclically loaded in the near-neutral pH solution. A triangle waveform was used with a loading frequency of 0.002 Hz and a stress ratio of 0.625. The maximum stress was controlled to achieve a maximum stress intensity factor (I max) of 72.87 MPa m0.5, and the stress intensity factor range (ΔK) was 27.3 MPa m0.5. These values were calculated according to the following equation in ASTM E647 (Ref 20):

$$K = \frac{P}{{BW^{{{1/2}}} }} \cdot \frac{{(2 + \alpha )\alpha^{{{1/2}}} }}{{(1 - \alpha )^{{{3/2}}} }} \cdot [0.886 + 4.64\alpha - 13.32\alpha^{2} + 14.72\alpha^{3} - 5.6\alpha^{4} ]$$
(1)

where K is the stress intensity factor, P is the applied load, B is the thickness of the specimen, and W is the width of the specimen and the coefficient α = a/W (a is the crack length).

Fig. 3
figure 3

Geometry of the compact tensile specimen (a) and the schematic diagram of crack length in situ measurement system (b)

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The crack length of the X70 pipeline steel in near-neutral pH environment was monitored through an in situ observation system (Fig. 3b), which has been used to investigate the crack growth behavior in our previous studies (Ref 19, 21). The surface of the CT specimen during the crack growth test could be observed using a high-performance charge-coupled device (CCD) camera system. The head part of the CCD camera was mounted on an X-Z stage to monitor the crack tip. The system was operated using a computer, and reasonably clear images of the crack growth behavior could be obtained in the test.

Results

As described in section 2.2, the galvanic current density between the tensile specimen and the unloaded specimen are measured during the tensile test. Figure 4 illustrates the reproducibility of the galvanic current densities under a strain rate of 1 × 10−4 s−1. The variation tendencies of the three curves are very close and the mean values are used in the following calculation. Three distinct regions are observed in the stress-t and i-t curves. In the elastic deformation region, the galvanic current fluctuates around a low value, indicating that galvanic corrosion is negligible. In the plastic deformation region, the galvanic current increases linearly with the tensile time (or strain) although some fluctuations also exist. After necking, the area of the specimen is visibly changed, and the galvanic current is not considered.

Fig. 4
figure 4

Time dependence of the stress and current density flowing between deformed and non-deformed specimens of X70 steel

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The galvanic current densities between the tensile specimen and the unloaded specimen under various strain rates are shown in Fig. 5. The corresponding stress-t curves are also shown in this figure. All of the i-t curves show similar shapes, with three distinct zones. The change in current density at the elastic deformation stage is negligible, but significantly increases at the plastic deformation stage. Moreover, under all strain rates, the current densities are proportional to the amount of the strain. Both the increment and the increase rate (i.e., the increase slope) of the galvanic current density during the plastic deformation exhibit changes with the strain rates. Therefore, the two parameters are calculated based on these curves.

Fig. 5
figure 5

Variations of the current densities during plastic deformation under different strain rates: (a) 1 × 10−5 s−1, (b) 2.5 × 10−4 s−1, (c) 5 × 10−4 s−1, (d) 5 × 10−3 s−1

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Figure 6 shows the increment and increase rate of the galvanic current during the plastic deformation. The increment in the current density induced by plastic deformation is calculated as the current density difference between the two dotted lines. Given that the galvanic current density increases linearly with the strain in the plastic deformation stage, the increase rate is calculated as the slope of the i-strain curve. Using this method, the calculated results are listed in Table 1 and shown in Fig. 7 and 8. It is shown that the increment in current density induced by the plastic deformation increases with the strain rate (Fig. 7). In addition, the slope of the i-strain curve increases linearly with the logarithm of strain rate (Fig. 8). These results are in accordance with Hoar et al. (Ref 14) who reported that the rate of current increase was higher for higher strain rates.

Fig. 6
figure 6

Schematic diagram of the calculation method of the increments and increase rate (slope) of the current density during plastic deformation

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Table 1 Increment and increase rate of the current density during plastic deformation under various strain rates
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Fig. 7
figure 7

Increment of the current density of X70 steel during plastic deformation under different strain rates

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Fig. 8
figure 8

Increase rate of the current density of X70 steel during plastic deformation under different strain rates

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Figure 9 shows the CGR in terms of da/dt as a function of ΔK. The CGR increases with the ΔK, with some fluctuations. The mean CGR during the crack propagation test is 8.56 × 10−5 mm/s.

Fig. 9
figure 9

Crack growth rate of X70 steel in near-neutral pH environment in terms of da/dt as a function of ΔK

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Discussion

In general, galvanic corrosion will occur because of the potential difference between two metals in the presence of corrosive medium. According to the mechanochemical model proposed by Gutman (Ref 22), the potential of metal will shift negatively when tensile stress is applied. Cheng et al. (Ref 23) pointed out that the potential drop of X70 steel in near-neutral pH environment is negligible in the elastic region, and this decrease becomes significant under plastic strain. Therefore, a potential difference exists between the loaded and unloaded specimen when the tensile test is started. The higher potential difference in the plastic deformation region results in higher galvanic current density as shown in Fig. 4, 5 and 6.

Bockris et al. (Ref 24) suggested that the major factors affecting the anodic current of the specimens during straining were as follows: charging of the electric double layer on the fresh metal surface, increase in the surface roughness, emergence of the dislocation slip steps, and high index planes. They calculated the current increase induced by these factors and deduced the following equations:

$$\Delta i = k_{1} yi_{e} + k_{2} \Delta E\dot{\varepsilon } + (k_{3} fi_{ns} + k_{4} i_{\text{hip}} )\varepsilon \dot{\varepsilon } - k_{5} i_{\text{hip}} \varepsilon^{2} \dot{\varepsilon }$$
(2)

where y is the length of the dislocation slip steps, ΔE is the potential variation, f is the roughness coefficient, ε and\(\dot{\varepsilon }\)are the strain and strain rate, respectively. The k 1~k 5 are constants, and i e, i ns, and i hip are the current densities caused by slip steps, surface roughness and high index planes, respectively. This equation provides the probability to calculate the anodic current density cause by plastic strain, but the parameters in this equation are difficult to determine. Therefore, a simplified formula considering the anodic dissolution current of the crack tip is proposed according to the results that the current density increases linearly with the plastic strain:

$$i = i_{0} + k_{{\dot{\varepsilon }}} \Delta \varepsilon$$
(3)

where i is the instantaneous galvanic current density, i 0 is the galvanic current density at the yield point, Δε is the variation of plastic strain, and k is the increase slope that related to the strain rate. Gutman pointed out (Ref 22) that the mechanochemical effects in every dynamic plastic deformation were linearly dependent on deformation rate. Li et al. (Ref 25) also reported that a higher strain rate would significantly decrease the electron work function and thus enhance the electrochemical activity. In the present study, the increase slope of the galvanic current increases linearly with the logarithm of the strain rates (Fig. 8) and it can be fitted as follows:

$$k_{{\dot{\varepsilon }}} = 5.13 + \log \dot{\varepsilon }$$
(4)

Therefore, the instantaneous galvanic current density could be determined as follows:

$$i = i_{0} + (5.13 + \log \dot{\varepsilon })\Delta \varepsilon$$
(5)

This equation can be used as the anodic current density of the crack tip during crack propagation.

Anodic dissolution (AD) and hydrogen embrittlement (HE) have been shown to be involved in the crack growth mechanism of pipeline steels in near-neutral pH environment (Ref 10, 26). Both of them contribute to the crack growth during the SCC process under cyclic load (Ref 27). In general, the crack growth rate of pipeline steels under cyclic load can be drawn as follows (Ref 28):

$$\left( {\frac{{{\text{d}}a}}{{{\text{d}}t}}} \right)_{\text{total}} = \left( {\frac{{{\text{d}}a}}{{{\text{d}}t}}} \right)_{\text{fatigue}} + \left( {\frac{{{\text{d}}a}}{{{\text{d}}t}}} \right)_{\text{SCC}} = C(\Delta K)^{m} + \left( {\frac{{{\text{d}}a}}{{{\text{d}}t}}} \right)_{\text{AD}} + \left( {\frac{{{\text{d}}a}}{{{\text{d}}t}}} \right)_{\text{HE}}$$
(6)

According to Faraday’s law, CGR induced by AD can be obtained by (Ref 29)

$$\left( {\frac{{{\text{d}}a}}{{{\text{d}}t}}} \right)_{\text{AD}} = i\frac{M}{zF\rho } = [i_{0} + (5.13 + \log \dot{\varepsilon })\Delta \varepsilon ]\frac{M}{zF\rho }$$
(7)

where M is the atomic weight of the metal (g/mol), i is corrosion current density (A/cm2), F is Faraday’s constant (96,500 C/mol), z is the number of electrons exchanged during corrosion, and ρ is the density of the metal (g/cm3). In the present study, i 0 is negligible because the potential variation during the elastic deformation is small. Δε is identified as 10% which is a high uniform plastic strain around the crack tip. In this case, the crack propagation induced by anodic dissolution can be determined when the strain rate at the crack tip during the cyclic load is obtained.

The crack tip strain rate during crack propagation under cyclic load has been reported by many researchers (Ref 16, 30-33). According to Shoji et al. (Ref 30, 31) and Lu et al. (Ref 32, 33), the strain rate at the tip of the propagating crack under cyclic loading can be calculated from the following formula:

$$\dot{\varepsilon } = \dot{\varepsilon }_{K} + \dot{\varepsilon }_{{\dot{a}}} = fd_{n} \frac{{\Delta K^{2} }}{{E\sigma_{y} }} + \frac{{N^{*} }}{{N^{*} - 1}}\frac{{\dot{a}}}{{r_{0} }}\frac{{\beta \sigma_{y} }}{E}\left\{ {\ln \left[ {\frac{{\left( {1 + R} \right)^{2} \Delta K^{2} }}{{4 \cdot (1 - R)^{2} 3\pi r_{0} \sigma_{y}^{2} }}} \right]} \right\}^{{\frac{1}{{N^{*} - 1}}}}$$
(8)

The physical meanings and the corresponding values of the parameters used in this equation are listed in Table 2. The strain rates at the crack tip can be calculated using the instant crack growth velocity (\(\dot{a}\)) and ΔK values from the test results in Fig. 9. Then, the CGR induced by AD is calculated and shown in Fig. 10 as compared with the measured crack propagation rate. It is seen that the CGR caused by AD is much smaller than the total CGR. Therefore, other aspects should be considered to provide more reliable results. In the above calculations, the current density increments are supposedly equivalent to the anodic dissolution current induced by uniform plastic deformation (Ref 16). However, the AD current of the fresh metal surface, which really controls the AD-induced crack propagation, is disregarded. The anodic current of the fresh metal surface during straining should be calculated.

Table 2 Physical meanings and the corresponding values of the parameters used in the formula of the crack tip strain rate
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Fig. 10
figure 10

Comparison of the crack growth rate of X70 steel between the measured results on CT specimen and the calculated results from the anodic dissolution

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Assuming that the newly generated fresh surface area is ΔS at a certain plastic strain, the relationship among the ΔS, the original surface area (S 0), and the gauge length (L 0) follows the equation below proposed by Bubar et al. (Ref 34):

$$\frac{\Delta S}{{S_{0} }} = 1 - \left( {\frac{{L_{0} }}{L}} \right)^{{\frac{1}{2}}}$$
(9)

where L is the gauge length after plastic strain. Assuming that the corrosion current densities of the specimen before and after plastic strain are i 0 and i p, respectively, and the corrosion current density of the fresh metal surface is i f, then the following equation is satisfied approximately:

$$S_{0} i_{0} + \Delta Si_{f} = S_{0} i_{p}$$
(10)

Then, the corrosion current of the fresh metal surface can be calculated:

$$i_{f} = \frac{{S_{0} (i_{p} - i_{0} )}}{\Delta S} = \frac{{i_{p} - i_{0} }}{{1 - \left( {\frac{{L_{0} }}{L}} \right)^{{\frac{1}{2}}} }}$$
(11)

During plastic deformation, the relationship between the strain value and the gauge length follows the formula:

$$\varepsilon = \frac{{L - L_{0} }}{{L_{0} }},\quad {\text{and}}\quad \frac{{L_{0} }}{L} = \frac{1}{1 + \varepsilon }$$
(12)

Equation 12 is then factored into Eq 11 and the corrosion current of the fresh metal surface during plastic strain is obtained as follows:

$$i_{f} = \frac{\Delta i}{{1 - \left( {\frac{1}{1 + \varepsilon }} \right)^{{\frac{1}{2}}} }}$$
(13)

where Δi is the corrosion current variation due to the plastic strain. By combining Eq 7, 8, and 13, the CGR induced by AD of the fresh metal surface at the crack tip can be calculated, and the results are also shown in Fig. 10. The CGR induced by the AD of the fresh metal surface is about 2.5 × 10−7 mm/s, which is one order greater than that calculated using the corrosion current of the whole surface. However, a difference of at least one order of magnitude between the measured CGR and the AD-induced CGR is observed, which is mainly attributed to several reasons. Firstly, the loading frequency used in this work is 0.002 Hz, which is a very low frequency for the mechanical fatigue. Therefore, the CGR caused by the pure mechanical fatigue could be ignored. The second aspect that affects the stress corrosion cracking is the HE effect. During the SCC process of pipeline steel in near-neutral pH environment, the hydrogen will migrate to the crack tip area and produce enrichment around the crack tip. The accumulated hydrogen atoms not only facilitate the AD but also accelerate the HE, resulting in a high crack growth rate. Therefore, in this work, the higher measured CGR on the CT specimen is mainly attributed to the hydrogen-induced cracking.

Conclusions

The anodic dissolution at the crack tip of X70 steel during SCC was investigated using a simulation technique. The main conclusions can be drawn as follows:

  1. (1)

    The mechanical and electrochemical states at the crack tip can be simulated using the well-controlled galvanic corrosion method.

  2. (2)

    Corrosion current of the specimen during fast stretching increases linearly with the plastic strain.

  3. (3)

    The increment of the corrosion current and the increase rate during the plastic deformation stage is related to the strain rate. An empirical formula between the corrosion current and the plastic strain and strain rate is obtained.

  4. (4)

    CGR induced by AD of the fresh metal surface at the crack tip is calculated based on Faraday’s law and crack tip strain rate. The value is roughly one order smaller than the measured CGR during cyclic load.

  5. (5)

    Hydrogen embrittlement may play a dominate role in stress corrosion crack propagation of pipeline steels in near-neutral pH environment.